Table of contents

Clinching is a mechanical joining technique which involves severe local plastic deformation of two or more metal sheet parts resulting in a permanent mechanical interlock. Today, it is a reliable joining technique used in automotive, HVAC and general steel constructions whilst still gaining interest. As it is not computationally feasible to include detailed sub models of these type of joints in FE simulations of real-life clinched assemblies, this paper proposes a methodology to represent these connections with simplified elements. In order to calibrate the parameters governing the equivalent model, a simple shear lap and pullout test is used. This methodology is applied to clinched configurations and validated using a modified Arcan test in which both shear and pull-out loads are considered.

A novel forming method aimed at large size aluminum sheet is introduced. In this method, aluminum sheet is clamped between a common flat spiral electromagnetic actuator and a punch matrix. Driven by pulsed electromagnetic force and restrained by punch matrix, the blank sheet will form local shallow dome accordingly. Moving actuator along sheet surface and triggering the pulsed power generator in sequence results in dome matrix that is uniformly distributed. Superposition of those spherical domes leads to macroscopically curved figuration of aluminum sheet. This paper demonstrates the newly proposed method experimentally, which verifies its feasibility. The mechanism analysis of this method is also presented using a simplified analytical model. The results show that this novel method is feasible and can be explained by the proposed mechanism well.

In the numerical simulation of elastomer forming process, Henckys isotropic hyperelastic material model can guarantee relatively accurate prediction of strain range in terms of large deformations. It is shown, that this material model prolongate Hooke's law from the area of infinitesimal strains to the area of moderate ones. New representation of the fourth-order elasticity tensor for Hencky's hyperelastic isotropic material is obtained, it possesses both minor symmetries, and the major symmetry. Constitutive relations of considered model is implemented into MSC.Marc code. By calculating and fitting curves, the polyurethane elastomer material constants are selected. Simulation of equipment for elastomer sheet forming are considered.

Surface deflections occur during springback, which follows deep drawing. They highly affect the visual appearance of outer skin components and are, therefore, undesirable. In this work, the influence of the part geometry on the shaping of surface deflections is investigated. The geometrical parameters of an exemplary component are varied and existing surface deflections are detected. For this, a component consisting of a multiple curved surface with an inserted door handle hollow is used, and AA6016, with a sheet thickness of 1.0 mm, as well as DC06, with a sheet thickness of 0.7 mm, are chosen. After the simulations are performed in AutoForm plus R6^TM, a virtual stone, Three-Point Gauging and the analysis of curvatures of the part before and after springback are used to detect surface deflections.

The simulation of the stretch forming of A5182-O aluminum alloy sheet with a spherical punch is performed using the crystal plasticity (CP) finite element method based on the mathematical homogenization theory. In the simulation, the CP constitutive equations and their parameters calibrated by the numerical and experimental biaxial tensile tests with a cruciform specimen are used. The results demonstrate that the variation of the sheet thickness distribution simulated show a relatively good agreement with the experimental results.

Phase-field modeling of brittle and ductile fracture is a modern promising approach that enables a unified description of complicated failure processes (including crack initiation, propagation, branching, merging), as well as its efficient numerical treatment [1-4]. In the present work, we apply this approach to model fracture in shell structures, considering both thin and thick shells. For thin shells, we use an isogeometric Kirchhoff-Love shell formulation [5-6], which exploits the high continuity of the isogeometric shape functions in order to avoid rotational degrees of freedom, i.e., the shell geometry is modeled as a surface and its deformation is fully described by the displacements of this surface. For thick shells, we use an isogeometric assumed natural strain (ANS) solid shell formulation [7], i.e., a 3D solid formulation enhanced with the ANS method in order to alleviate geometrical locking effects. According to the discretization of the structural formulations, an isogeometric basis is also used for the phase-field. While the phase-field fracture formulation for solid shells is basically the same as for standard solids, some reformulation is necessary for thin shells, accounting for the interaction of stresses devoted to membrane and bending deformation. We test both formulations on several numerical examples and perform comparisons of the results obtained by the two methods to each other as well as to reference solutions, which confirm the validity and applicability of the presented methods.

An adaptive line bead model that continually updates according to the changing conditions during the forming process has been developed. In these calculations, the adaptive line bead's geometry is treated as a 3D object where relevant phenomena like hardening curve, yield surface, through thickness stress effects and contact description are incorporated. The effectiveness of the adaptive drawbead model will be illustrated by an industrial example.

We consider the shape optimization for mechanical connectors. To avoid the gap between the representation in CAD systems and the finite element simulation used by mathematical optimization, we choose an isogeometric approach for the solution of the contact problem within the optimization method. This leads to a shape optimization problem governed by an elastic contact problem. We handle the contact conditions using the mortar method and solve the resulting contact problem with a semismooth Newton method. The optimization problem is nonconvex and nonsmooth due to the contact conditions. To reduce the number of simulations, we use a derivative based optimization method. With the adjoint approach the design derivatives can be calculated efficiently. The resulting optimization problem is solved with a modified Bundle Trust Region algorithm.

To this day, conventional sheet metal spinning processes are designed with a very low degree of automation. They are usually executed by experienced personnel, who actively adjust the tool paths during production. The practically unlimited freedom in designing the tool paths enables the efficient manufacturing of complex geometries on one hand, but is challenging to translate into a standardized procedure on the other. The present study aims to propose a systematic methodology, based on a 3D FEM model combined with a numerical optimization strategy, in order to design tool paths.

The accurate numerical modelling of the spinning process is firstly discussed, followed by an analysis of appropriate objective functions and constraints required to obtain a failure free tool path design.

Tube hydroforming has been used as a lightweight design approach to reduce CO₂ emission for the automotive industry. For the high strength steel tube, the strength and quality of the welding line is very important for a successful tube hydroforming process. This paper aims to investigate the effect of the welding line's strength and the width of the heat-affected zone on the tube thinning during the hydroforming process. The simulation results show that both factors play an important role on the thickness distribution during the tube expansion.

Under process conditions such as bending of flat wire made from high strength spring steel, the occurring strains are many times higher than the maximum strains determined from uniaxial tensile tests. To determine the elasto-plastic material behaviour of high strength spring steel (X10CrNi18-8), an inverse modelling approach using a simple testing method is presented. A 3-point bending test with the resulting force-displacement measurements is used for the inverse analysis. The inverse approach is used for determining the Young's modulus and hardening parameters of the Ludwik-Hollomon's law for bending of high strength spring steel. FE simulations with the optimised material data meet the experimentally measured punch forces during bending. The optimised material data considerably enhances the springback prediction.

A fracture criterion for sheet metals subjected to draw-bending is investigated using the concept of the forming limit stress criterion. The test material used is a 1.0-mm-thick high- strength steel sheet with a tensile strength of 590MPa. The specimen undergoes bendingunbending under tension when passing over the die profile. The drawing speed was set to 5-100 mm • s^-1. The magnitude of true stress σ_DB when a specimen fractured has been precisely determined. Moreover, multiaxial tube expansion tests of the test material are performed to measure the forming limit stress σ_PT of the test material under plane-strain tension. It is found that σ_DB is larger than σ_PT by 2.8-6.3%. Therefore, it is concluded that the forming limit stress criterion is effective as a fracture criterion in draw-bending.

Digital image correlation (DIC) data are being extensively used for many forming applications and for comparisons with finite element analysis (FEA) simulated results. The most challenging comparisons are often in the area of strain localizations just prior to material failure. While qualitative comparisons can be misleading, quantitative comparisons are difficult because of insufficient information about the type of strain output. In this work, strains computed from DIC displacements from a forming limit test are compared to those from three commercial FEA software. Quantitative differences in calculated strains are assessed to determine if the scale of variations seen between FEA and DIC calculated strains constitute real behavior or just calculation differences.

Achieving robust production of deep drawn sheet metal parts is challenging. The fluctuations of process and material properties often lead to robustness problems. Numerical simulations are used to validate the feasibility and to detect critical regions of a part. To enhance the consistency with the real process conditions, the measured material data and the force distribution are taken into account. The simulation metamodel contains the virtual knowledge of a particular forming process, which is determined based on a series of finite element simulations with variable input parameters. Based on the metamodels, process windows can be evaluated for different parameter configurations. This helps improving the operating point search, to adjust process settings if the process becomes unstable and to visualize the influence of arbitrary parameters on the process window.

The forming limit curve (FLC) is a valid instrument for the evaluation of failure in sheet metal processes. However, its experimental evaluation is challenging, in particular for modern lightweight sheet metals, in which the failure occurs without an evident necking transition. Therefore, the numerical analysis can represent a valid alternative for the investigation of the onset of necking phenomena. Prerequisite for realistic failure prediction are an accurate material characterization for high strain levels and a stable and coherent numerical model. Within this paper, an approach for the determination of forming limits by using the time dependent evaluation method is investigated and an analysis of the material sensitivity on the simulation results is performed. The results are discussed for mild steel DX56 and first suggestions for the improvement of the simulation input data are derived.

Micro-channel tube is the most important component of flat tube heat exchangers. The folded microchannel tube is made of clad aluminum sheet through roll forming process, and has great advantage in the aspect of corrosion resistance over extruded tube. The folded tube's sub-millimeter channel size as well as tight dimensional precision requirement brings great challenge to roll forming process design. In this paper, the finite element model of the whole roll forming process of a ten-channel tube is established by using ABAQUS/Explicit. The deformation at different forming stands are investigated and compared with experiment. The hydraulic pressure test is carried out on the developed tube and its pressure bearing capacity is evaluated.

The Quenching and Partitioning (QP) steel sheet is new generation material to induce phase transformation for plasticity in forming vehicle parts. The phase transformation is strongly stress state dependent behavior in experiments, which should affect the failure timing and limit strain in forming processes. In this paper, Nakajima test with QP980 and DP1000 steel sheets under equal-biaxial loading condition is performed for failure behavior. X-ray diffraction (XRD) is adopted to obtain the volume fraction of retained austenite (f_A). Digital Image Correlation (DIC) is used to record the surface strain field and its evolution during equal-biaxial tension deformation. The same level Dual Phase (DP) steel is also employed for the purpose of comparison. The results show that phase transformation in QP steel gives small impact on failure strain under equal biaxial tension condition which is contradicted with our understanding. It suggests that failure behavior under uniaxial tension of QP980 is strongly phase transformation dependent. But it shows almost independent under equal biaxial tension condition.

Hot blank - cold die (HB-CD) stamping, non-isothermal hot stamping, of aluminium alloy sheets offers great opportunities for high production rates at low cost, while overcoming limited material formability issues. Yet developing an accurate model that can describe the complex material behavior over the wide ranging conditions of HB-CD stamping (temperatures ranging between 25 and 350 °C) is challenging. Moreover, validation of the developed models under transient conditions is problematic. This work presents he results of a comprehensive characterization, material modeling, FE simulation and experimental validation effort to capture the behavior of an aluminium alloy sheet during HB-CD stamping. In particular, we highlight the integration between temperature measurements (thermography) and strain measurements (digital image correlation) for the accurate validation of model predictions of non-isothermal material deformation.

Transformation-induced plasticity (TRIP) assisted steels possess improved strain hardening behavior and resistance to necking that are favorable for automotive body applications. However, the TRIP effect causes complex springback behavior of these steels that can hardly be predicted by existing constitutive models for other steels. In this work, the functions in the original Yoshida-Uemori model describing isotropic and kinematic hardening were modified by adding new parameters that can represent the TRIP effect. Cyclic tension/compression experiments were performed on a selected TRIP-steel grade, and the results were used to calibrate the modified model. The modified model was coded via user subroutine into a commercial FE solver. The springback predictions were compared with actual try-out stamping experimental results for highlighting the improvement of predictions with the modified model.

Accurate prediction of failure and forming limits is essential when modelling sheet metal forming processes. Since traditional Forming Limit Curves (FLCs) are not valid for materials subjected to triaxial loading, a new failure criterion is proposed in this paper based on the stress triaxility and the effective plastic strain accumulated during the history of material loading. Formability zones are identified inside the proposed Triaxial Failure Diagram (TFD). FLCs may be mapped into the TFD defining a new Triaxial Failure Curve, or it can be defined by triaxial failure experiments. Several TFD examples are validated and constrasted showing acceptable accuracy in the numerical prediction of forming failure/limit of 3D thick sheet parts.

Fracture prediction is one of the challenging problems in sheet metals. Forming limit curves at fracture (FLCF), as a tool to determine fracture in sheet metal processes, are obtained through the use of numerical analyses. As one of the approaches, the ductile fracture criteria (DFCs) represent the fracture initiation of the sheets formed by different loading histories. In this study, the effects of three different hardening models on different DFCs to predict the fracture for stainless steel 304L have been investigated. The results show that most of DFCs work better in the region ɛ₂ <0 especially with the kinematic hardening model. However, for the region ɛ₂>0 where the stretching conditions are dominant, none of them could precisely estimate the fracture initiation.

In-plane biaxial tension and combined tension-compression tests are carried out for AA3104 aluminum alloy sheets. Linear stress paths are applied to cruciform specimens to measure the contours of plastic work in the stress space and the directions of plastic strain rates at each stress path. Coefficients α₁- α₈ and exponent M of the Yld2000-2d yield function are determined to minimize the mean square error of the analytical yield locus from a measured work contour. The values of the weighting coefficients in the evaluation of the error are varied to check the effect of a specific stress state on the earing behavior. The effects of the combinations of the weighting coefficients on the accuracy of earing prediction in the cup drawing process are discussed.

Cyclic tension-compression tests were carried out for austenitic stainless steel (SUS304) at elevated temperatures. The significant Bauschinger effect was found in the obtained stress-strain curve. In addition, stagnation of deformation induced martensitic transformation was observed just after stress reversal until the equivalent stress reached the maximum value in the course of experiment. The constitutive model for SUS304 at room temperature was developed, in which homogenized stress of SUS304 was expressed by the weighed summation of stresses of austenite and martensite phases. The calculated stress-strain curves and predicted martensite volume fraction were well correlated with those experimental results.

The hot-press forming of a U-channel was conducted on a boron-steel blank. The die consisted of two separate parts in order to perform the partial quenching process. The cold die was initially at 25 °C while the heated die was set to five different temperatures, namely, 25, 120, 220, 320 and 400 °C. The cooling temperature history, Vickers hardness and springback of the channel were measured. A thermo-mechanical-metallurgical model, which accounts for the prior austenite deformation effect, was successfully implemented in the LS-DYNA explicit solver to simulate the hot-press forming process under partial quenching conditions. The predicted and experimental results were compared and found in reasonable agreement.

This paper introduces a new hole expansion (HE) testing method that could be more relevant to the edge cracking problem observed in stamping advanced high strength steel (AHSS). The new testing method adopted a large hole diameter of 75 mm compared to the standard hole diameter of 10 mm. An inline monitoring system was developed to visually monitor the hole edge cracking during the test and synchronize the load-displacement data with the recorded video for capturing the initial crack. A new hole expansion testing method was found to be effective in evaluating the edge cracking by considering the effects of material properties and trimming methods. It showed a much larger difference, up to 11%, of the HE ratio between DP980 and TRIP780 compared to the standard HE testing method giving less than a 2% difference.

Hot compression test data taken from Zhang [1] of metastable austenitic stainless steel AISI 316LN over a range of strain rates and temperatures shows typical dynamic recovery and recrystallization behavior. It is proposed to model this behavior by incorporating not only the hardening and recovery into the Bergstrom dislocation evolution equation, but also the recrystallization. It is shown that the initial mechanical response before recrystallization can be accurately represented by assuming that the mean free path evolves as the microstructure evolves from homogeneously spaced dislocations to cell-pattern. Results show that this novel continuum mechanical model can predict the observed behavior, showing a good match to the experimental data and capturing the transition from recrystallization to (almost) no recrystallization.

A neutron diffraction measurement was performed to reveal microstructural aspects of the ductile fracture in ferritic steel. The diffraction patterns were continuously measured at the center of the reduced area while a tensile specimen was loaded under tension until the end of the fracture process. The measurement results showed that the volume fraction of (110)-oriented grains increased when the texture evolved as a result of plastic deformation. But the mechanism of texture evolution may be changed during necking, decreasing an increase rate of the volume fraction.

Numerous types of yield functions have been proposed to describe the shape of a realistic yield surface. Major commercial finite element codes include few anisotropic functions. Alternatively, the codes allow users to implement material models through user- subroutines. We develop the Unified Material Model Driver for Plasticity (UMMDp) subroutine library, which enables users to implement an arbitrary yield function easily. In this paper, the framework of the UMMDp is presented and its availabilities is shown through examples of sheet metal forming analyses.

The reduction of springback for a U-shaped channel using a double drawing process was investigated. In this test, the punch strokes of the 1^st and 2^nd stamping steps were controlled and each followed by unloading. The simulations were conducted using kinematic and distortional hardening models, which were implemented into a finite element (FE) code to describe the Bauschinger effect and its associated anisotropic hardening effects during strain path change. In addition to the usual mechanical characterization tests, in-plane compression- tension experiments were conducted on DP980 and TWIP980 to determine the constitutive parameters pertaining to load reversal. Experimental and FE simulated results of the channel shape were compared for both materials in order to understand the effect of anisotropic hardening under non-proportional loading on springback.

A new computational scheme is presented to addresses cold recyclability of sheet- metal products. Cold recycling or re-manufacturing is an emerging area studied mostly empirically; in its current form, it lacks theoretical foundation especially in the area of sheet metals. In this study, a re-formability index was introduced based on post-manufacture residual formability in sheet metal products. This index accounts for possible levels of deformation along different strain paths based on Polar Effective Plastic Strain (PEPS) technique. PEPS is strain-path independent, hence provides a foundation for residual formability analysis. A user- friendly code was developed to implement this assessment in conjunction with advanced finite- element (FE) analysis. The significance of this approach is the advancement towards recycling of sheet metal products without melting them.

World-wide there is a trend to develop higher permeability grades, thin thickness and coarse grain of non-oriented electrical steels, a core function material of motors. Blanking is the most popular technique for producing the motor laminations. However, the deformation of material is significantly influenced by grain size. In this paper, Voronoi polygon is used for generate the random microstructures of the studied non-oriented electrical steel. Finite Element (FE) model considering grain size is thus established to analysis the blanking process. The material behaviour of grains is derived from the widely accepted surface layer model. Compared to the conventional model without considering the grain size, the novel model shows good matching with the experimental results.

The result of a preliminary numerical investigation on local deformation characteristics of a multi-layered spacer-grid structure with five guide tubes is reported based on implicit finite element analysis. For the numerical analysis, displacements of top and bottom cross sections of each guide tube in a single-layer model were constrained while a lateral displacement was imposed on the single layer. Unlike the impact hammer test that is generally employed to characterize the deformation characteristics of the space-grid structure, the buckling phenomenon occurs locally in this study; it takes place at the inner grids around each tube and the degree of bucking is more apparent for tubes near the lateral surface where the lateral displacement was imposed.

The thermomechanical finite element analysis of warm forming processes enables an improved comprehension of the process parameters affecting the material formability. However, the thermal and mechanical coupling problem is still a challenge from the computational standpoint. A staggered strategy for the thermomechanical coupling problem is presented in this study, which is based on an isothermal split approach and allows the treatment of the two problems separately. The exchange of information between the mechanical and the thermal problem is performed to achieve a compromise between computational cost and accuracy. The proposed algorithm was implemented in DD3IMP in-house finite element code. Its performance is analysed and compared with a classical strategy commonly employed for solving thermomechanical problems.

Roll levelling is a primary manufacturing process used to remove residual stresses and imperfections of metal strips in order to make them suitable for subsequent forming operations. In the last years the importance of this process has been evidenced with the apparition of Ultra High Strength Steels with strength > 900 MPa. The optimal setting of the machine as well as a robust machine design has become critical for the correct processing of these materials. Finite Element Method (FEM) analysis is the widely used technique for both aspects. However, in this case, the FEM simulation times are above the admissible ones in both machine development and process optimization. In the present work, a semi-analytical model based on a discrete bending theory is presented. This model is able to calculate the critical levelling parameters i.e. force, plastification rate, residual stresses in a few seconds. First the semi-analytical model is presented. Next, some experimental industrial cases are analyzed by both the semi-analytical model and the conventional FEM model. Finally, results and computation times of both methods are compared.

New materials are been introduced on the car body in order to reduce weight and fulfil the international CO2 emission regulations. Among them, the application of aluminum alloys is increasing for skin panels. Even if these alloys are beneficial for the car design, the manufacturing of these components become more complex. In this regard, numerical simulations have become a necessary tool for die designers. There are multiple factors affecting the accuracy of these simulations e.g. hardening, anisotropy, lubrication, elastic behavior. Numerous studies have been conducted in the last years on high strength steels component stamping and on developing new anisotropic models for aluminum cup drawings. However, the impact of the correct modelling on the latest aluminums for the manufacturing of skin panels has been not yet analyzed. In this work, first, the new AC600 aluminum alloy of JLR-Novelis is characterized for anisotropy, kinematic hardening, friction coefficient, elastic behavior. Next, a sensitivity analysis is conducted on the simulation of a U channel (with drawbeads). Then, the numerical an experimental results are correlated in terms of springback and failure. Finally, some conclusions are drawn.

Structural analysis, in Abaqus, of a stamping die and subsequent morphing of the tool surfaces in AutoForm were performed to improve a sheet metal forming simulation. First, the tool surfaces of the XC90 rear door inner were scanned. They were not matching when the die was unloaded and could therefore not give any satisfying results in sheet metal forming simulations. Scanned surface geometries were then added to a structural FE-model of the complete stamping die and some influential parts of the production press. The structural FE- model was analysed with Abaqus to obtain the structural deformations of the die. The calculated surface shapes were then transferred to AutoForm where a forming simulation was performed. Results from the different sheet metal forming simulations were compared to measured draw in curves and showed a substantial increase in accuracy and ability to analyse dies in running production when the morphed surfaces were used.

In conventional machining and sheet metal forming processes, in general, lubrication assists to increase the quality of the final product. Similarly it is observed that there is a positive effect of the use of lubrication in Single point incremental forming, namely in the surface roughness. This study is focused on the investigation of the most appropriate lubricant for incremental forming of copper sheet. The study involves the selection of the best lubricant from a range of several lubricants that provides the best surface finishing. The influence of the lubrication on other parameters such as the maximum forming angle, the fracture strains and the deformed profile are also studied for Copper.

Wrinkling during draw is typically a local instability problem. When the structural instability is localized, there will be a local transfer of strain energy from one part of the structure to neighboring parts, and global solution methods, which is typically represented by the arc length method, may not work. So, this type of problems has to be solved either dynamically or with the artificial damping. On the other hand, the essential nature of the buckling behavior can be regarded as a static problem, even though it may be possible to raise some side issues due to the inertia effect. In this study, we traced the local buckling behavior of anisotropic elasto-plastic thin shells in Numisheet2014 BM4 using the artificial damping method.

To shorten the development stage of automobiles, FEM simulation has been applied. It was important to increase the accuracy of the sheet metal simulation results. The friction coefficient between the sheet metal and dies the greatly affected the simulation results. Therefore, apparatus for measuring the friction coefficient with a specific press forming speed (300 mm/s) has been developed. The materials of the sheet metals and dies were aluminum alloys and die steel respectively. It was found that the friction was affected by the difference between the velocity of the sheet metal and that of the dies.

Hot forming has grown significantly in the manufacturing of structural components within the vehicle Body-In-White construction. The superior strength of press hardened steels not only guarantee high resistance to deformation, it also brings a significant weight saving compared to conventional cold formed products. However, the benefit of achieving ultrahigh strength with hot stamping, comes with a reduction in ductility of the press hardened part. This will require advanced material modeling to capture the predicted performances accurately. A technique to optically measure and map the thinning distribution after hot stamping has shown to improve numerical analysis for fracture prediction. The proposed method to determine the forming effects and mapping to CAE models can be integrated into the Vehicle Development Process to shorten the time to production.

The Knowledge Based Cloud FEA (KBC-FEA) simulation technique allows multiobjective FE simulations to be conducted on a cloud-computing environment, which effectively reduces computation time and expands the capability of FE simulation software. In this paper, a novel functional module was developed for the data mining of experimentally verified FE simulation results for metal forming processes obtained from KBC-FE. Through this functional module, the thermo-mechanical characteristics of a metal forming process were deduced, enabling a systematic and data-driven guideline for mechanical property characterization to be developed, which will directly guide the material tests for a metal forming process towards the most efficient and effective scheme. Successful application of this data-driven guideline would reduce the efforts for material characterization, leading to the development of more accurate material models, which in turn enhance the accuracy of FE simulations.

The aim of the present paper is to evaluate existing constitutive models and to fitting hardening laws of SS304 tubes for the accurate prediction of the deformation behaviors of the tubes in hydroforming. Uniaxial tensile test (UTT) and free hydro-bugling (FHB) experiments were conducted on SS304 tubes, and a hi-speed three-dimensional (3D) digital image correlation (DIC) system was applied to obtain the deformation data of the samples. Eight constitutive relationships of the tubes were then established by fitting the equivalent stress and strain data with the four existing constitutive models of Hollomon, Ghosh, Voce and Ghosh/Voce, and the fitting accuracy of the obtained constitutive relationships were analyzed and compared. The results show that Ghosh/Voce model holds the highest accuracy in describing the deformation behaviors of the tubes in UTT and FHB, followed by the Ghosh model and then the Hollomon model. The Voce model holds the lowest accuracy. A distinct discrepancy between the constitutive relationships obtained using UTT and FHB experiments are observed in present research conditions.

This paper is about an advanced stamping simulation methodology used in automotive industry to shorten total die manufacturing times in a new vehicle project by means of benefiting leading edge virtual try-out technology.

This paper is dealing with the material modelling of steel sheets and is focused on the input parameters for a correct earing prediction. The cause of earing is the anisotropy of the rolled sheet which is usually modelled by a yield criterion. In a first study earing predictions with the Hill'48 yield criterion and with the Barlat'2000 yield criterion are conducted for different steel grades between 200 and 800 MPa yield strength. A comparison of the results shows that the Barlat'2000 yield criterion leads in almost all cases to a better earing prediction. In a second study the measurements for the Barlat'2000 law were analysed, to find the main parameter influencing the accuracy in earing prediction. The results of this study show that it is not affected by the biaxial measurements, but by the yield strength in 45° regarding to rolling direction.

Most of sheet metal forming processes comprise intermediate trimming operations to remove superfluous material. These operations are required for subsequent forming operations. On the other hand, the springback is strongly influenced by the trimming operations that change the part stiffness and the stress field. From the numerical point of view, this involves the geometrical trimming of the finite element mesh and subsequent remapping of the state variables. This study presents a remapping method based on Dual Kriging interpolation, specifically developed for hexahedral finite elements, which has been implemented in DD3TRIM in-house code. Its performance is compared with the one of the Incremental Volumetric Remapping method, using the split-ring test to highlight their advantages and limitations. The numerical simulation of the forming processes is performed with DD3IMP finite element solver.

Neutron diffraction is well known to be a useful technique for measuring a bulk texture of metallic materials taking advantage of a large penetration depth of the neutron beam. However, this technique has not been widely utilized for the texture measurement because large facilities like a reactor or a large accelerator are required in general. In contrast, RANS (Riken Accelerator-driven Compact Neutron Source) has been developed as a neutron source which can be used easily in laboratories. In this study, texture evolution in steel sheets with plastic deformation was successfully measured using RANS. The results show the capability of the compact neutron source for the analysis of the crystal structure of metallic materials, which leads us to a better understanding of plastic deformation behavior.

Results of an experimental study on the quasi-static and high-rate plastic deformation due to impact of a high-purity, polycrystalline, a-titanium material are presented. To quantify the plastic anisotropy and tension-compression asymmetry of the material, first monotonic uniaxial compression and tension tests were carried out at room temperature under quasi-static conditions. It was found that the material is transversely isotropic and displays strong strength differential effects. To characterize the material's strain rate sensitivity, Split Hopkinson Pressure Bar tests in tension and compression were also conducted. Taylor impact tests were performed for impact velocity of 196 m/s. Plastic deformation extended to 64% of the length of the deformed specimen, with little radial spreading. To model simultaneously the observed anisotropy, strain-rate sensitivity, and tension-compression asymmetry of the material, a three-dimensional constitutive model was developed. Key in the formulation is a macroscopic yield function [1] that incorporates the specificities of the plastic flow, namely the combined effects of anisotropy and tension-compression asymmetry. Comparison between model predictions and data show the capabilities of the model to describe with accuracy the plastic behavior of the a-Ti material for both quasi-static and dynamic loadings, in particular, a very good agreement was obtained between the simulated and experimental post-test Taylor specimen geometries.

To investigate the local strain and stress at the crack initiation position in shear fracture test pieces of ultra-high strength steels, a butterfly shear fracture specimen was employed. The crack initiation position and propagation direction were observed during shear fracture tests by high speed cameras and investigated through analysing the fracture surface by scanning electron microscope. Further, the finite element method was employed and the stress-triaxiality at the crack initiation position was investigated. It can be obtained that the crack initiated at the position where the stress state is close to uniaxial tensile state or plane strain state more than pure shear stress state.

For the purpose of accuracy improvement of sheet metal forging FE analysis, we have developed a new measurement method of work hardening behavior in large plastic strain by repeatedly performing simple shear test using pre-strained steel sheet. In this method, it is possible to measure work hardening behavior more than equivalent plastic strain 2.0. In addition, it was carried out a comparison between developed method and compression test in order to verify the validity of the results by the developed method. As a result, both results were in good agreement. The validity of developed method has been verified.

Modelling the response of titanium alloys under plastic deformation is challenging. In addition to strong anisotropy, these materials exhibit tension-compression asymmetry as well as anisotropic hardening even under monotonous loading conditions. The present contribution aims to propose a new modelling approach for titanium materials, by a homogeneous introduction of asymmetry into existing symmetric yield functions. Furthermore, anisotropic hardening effects are tracked describing the strain dependant yield surface evolution. The results are validated using the earing profile of deep drawn cups.

A study on plastic deformation and damage in titanium was conducted. The X-ray tomography data reveal that damage distribution and evolution in titanium is markedly different than for a FCC material. Theoretically, it is shown that only by modelling both the anisotropy and the tension-compression asymmetry in plastic behaviour it is possible to realistically predict titanium behaviour. For a smooth specimen under uniaxial tension, the model predicts that damage initiates at the centre of the specimen, and is diffuse; the level of damage close to failure being very low. In contrast, for a notched specimen under the same loading it is predicted that damage initiates at the outer surface of the specimen, and grows towards the centre of the specimen, which corroborates with XCMT data.

This work presents the main strategies and algorithms adopted in the DD3MAT inhouse code, specifically developed for identifying the anisotropy parameters. The algorithm adopted is based on the minimization of an error function, using a downhill simplex method. The set of experimental values can consider yield stresses and r -values obtained from in-plane tension, for different angles with the rolling direction (RD), yield stress and r -value obtained for biaxial stress state, and yield stresses from shear tests performed also for different angles to RD. All these values can be defined for a specific value of plastic work. Moreover, it can also include the yield stresses obtained from in-plane compression tests. The anisotropy parameters are identified for an AA2090-T3 aluminium alloy, highlighting the importance of the user intervention to improve the numerical fit.

Industrial components are far too complex in shape and far too large in size compared to the laboratory scale test samples used to establish failure criteria like the forming limit diagram (FLD). These have been traditionally used to predict failure, but are found to often make wrong predictions due to their sensitivity to strain path, and forming conditions like temperature. The Strain Nonuniformity Index (SNI), a single parameter determined from the spatial strain distribution, may be used to predict failure and identify locations of failure or even imminent failure. This is possible regardless of temperature or even the method of forming (cold forming, hot forming, superplastic forming etc.). The paper presents a few results demonstrating successful applications of this novel SNI based technique.

The Finite Block Method has been employed in this paper to evaluate the stress intensity factor of a bi-material plate. The complex stress intensity factor components K₁ and K₂ determined by the Finite Block Method is compared with an equivalent Finite Element Method (ABAQUS) analysis. The paper demonstrates the accuracy of the Meshfree approach by the Finite Block Method without the arduous demand of meshing around the crack surface as seen on standard FEM crack analysis. This paper also describes the application of the polygonal singular core and the collocations points around the interface crack. A computational example for various E₁/E₂ material combinations is presented.

Plastic instabilities like Portevin-Le Châtelier were quite thoroughly investigated experimentally in tension, under a large range of strain rates and temperatures. Such instabilities are characterized both by a jerky flow and a localization of the strain in bands. Similar phenomena were also recorded for example in simple shear [1]. Modelling of this phenomenon is mainly performed at room temperature, taking into account the strain rate sensitivity, though an extension of the classical Estrin-Kubin-McCormick was proposed in the literature, by making some of the material parameters dependent on temperature.

A similar approach is considered in this study, furthermore extended for anisotropic plasticity with Hill's 1948 yield criterion. Material parameters are identified at 4 different temperatures, ranging from room temperature up to 250°C. The identification procedure is split in 3 steps, related to the elasticity, the average stress level and the magnitude of the stress drops. The anisotropy is considered constant in this temperature range, as evidenced by experimental results [2]. The model is then used to investigate the temperature dependence of the critical strain, as well as its capability to represent the propagation of the bands. Numerical predictions of the instabilities in tension and simple shear at room temperature and up to 250°C are compared with experimental results [3]. In the case of simple shear, a monotonic loading followed by unloading and reloading in the reverse direction ("Bauschinger-type" test) is also considered, showing that (i) kinematic hardening should be taken into account to fully describe the transition at re-yielding (ii) the modelling of the critical strain has to be improved.

In this paper, mechanical tests aimed at characterizing the plastic anisotropy of a commercially pure α-titanium sheet are presented. Hemispheric and elliptic bulge tests conducted to investigate the forming properties of the material are also reported. To model the particularities of the plastic response of the material the classical Hill [1] yield criterion, and Cazacu et al. [2] yield criterion are used. Identification of the material parameters involved in both criteria is based only on uniaxial test data, while their predictive capabilities are assessed through comparison with the bulge tests data. Both models reproduce qualitatively the experimental plastic strain distribution and the final thickness of the sheet. However, only Cazacu et al. [2] yield criterion, which accounts for both the anisotropy and tension-compression asymmetry of the material captures correctly plastic strain localization, in particular its directionality. Furthermore, it is shown that accounting for the strong tension-compression asymmetry in the model formulation improves numerical predictions regarding the mechanical behavior close to fracture of a commercially pure titanium alloy under sheet metal forming processes.

Affected by texture, Bauschinger effect and different deformation mechanisms, plastic deformation behavior of the sheet metals are complicated, especially for HCP metals, such as magnesium and titanium. With more and more enhanced demand to describe the materials' yield behavior precisely and efficiently in numerical simulation, application of traditional continuous type yield functions encounters great challenge. So an interpolation type anisotropic yield function for plane stress is proposed. This yield function is represented by a yield surface in the polar coordinate system. The radius vector to the yield surface represents the yield stress at yielding, while the outer normal is related with the R values. The physical meaning of the parameters is directly defined. Accuracy, efficiency and flexibility can be achieved by application of such yield functions.

A ductile damage model for sheet bulk metal forming processes and its efficient and accurate treatment in the context of the Finite Element Method is presented. The damage is introduced as a non-local field to overcome pathological mesh dependency. Since standard elements tend to show volumetric locking in the bulk forming process a mixed formulation is implemented in the commercial software simufact.forming to obtain better results.

The information hidden in the diffuse neck of a tensile test on a thin metal sheet can be extracted using a special case of the non-linear virtual fields method yielding the so-called post-necking strain hardening behaviour. The method, however, requires a number of assumptions which are scrutinized in this paper. To eliminate experimental errors which could potentially hamper the assessment, virtual test data (i.e. strain fields at different load steps) is generated using a FE model of the tensile test. The identification strategy is then used to retrieve the reference strain hardening behaviour used in the FE simulation. This approach is used to study the necessity of incorporating rate-dependent plasticity in the identification procedure. Additionally, the necessary plane stress condition in the diffuse neck is studied.

The damage and failure process of ductile metals is characterized by different mechanisms acting on the micro-scale as well as on the macro-level. These deterioration processes essentially depend on the material type and on the loading conditions. To describe these phenomena in an appropriate way a phenomenological continuum damage and fracture model has been proposed.

To detect the effects of stress-state-dependent damage mechanisms, numerical simulations of tests with new biaxial specimen geometries for sheet metals have been performed. The experimental results including digital image correlation (DIC) show good agreement with the corresponding numerical analysis. The presented approach based on both experiments and numerical simulation provides several new aspects in the simulation of sheet metal forming processes.

Today the methods of numerical simulation of sheet metal forming offer a great diversity of possibilities for optimization in product development and in process design. However, the results from simulation are only available as virtual models. Because there are any forming tools available during the early stages of product development, physical models that could serve to represent the virtual results are therefore lacking. Physical 3D-models can be created using 3D-printing and serve as an illustration and present a better understanding of the simulation results. In this way, the results from the simulation can be made more "comprehensible" within a development team. This paper presents the possibilities of 3D-colour printing with particular consideration of the requirements regarding the implementation of sheet metal forming simulation. Using concrete examples of sheet metal forming, the manufacturing of 3D colour models will be expounded upon on the basis of simulation results.

The present approach deals with the dynamical analysis of thin structures using an isogeometric Reissner-Mindlin shell formulation. Here, a consistent and a lumped mass matrix are employed for the implicit time integration method. The formulation allows for large displacements and finite rotations. The Rodrigues formula, which incorporates the axial vector is used for the rotational description. It necessitates an interpolation of the director vector in the current configuration. Two concept for the interpolation of the director vector are presented. They are denoted as continuous interpolation method and discrete interpolation method. The shell formulation is based on the assumption of zero stress in thickness direction. In the present formulation an interface to 3D nonlinear material laws is used. It leads to an iterative procedure at each integration point. Here, a J2 plasticity material law is implemented. The suitability of the developed shell formulation for natural frequency analysis is demonstrated in numerical examples. Transient problems undergoing large deformations in combination with nonlinear material behavior are analyzed. The effectiveness, robustness and superior accuracy of the two interpolation methods of the shell director vector are investigated and are compared to numerical reference solutions.

The formability of aluminium alloy sheet can be greatly improved by warm forming. However predicting constitutive behaviour under warm forming conditions is a challenge for aluminium alloys due to strong, coupled temperature- and rate-sensitivity. In this work, uniaxial tensile characterization of 0.5 mm thick fully annealed aluminium alloy brazing sheet, widely used in the fabrication of automotive heat exchanger components, is performed at various temperatures (25 to 250 °C) and strain rates (0.002 and 0.02 s^-1). In order to capture the observed rate- and temperature-dependent work hardening behaviour, a phenomenological extended-Nadai model and the physically based (i) Bergstrom and (ii) Nes models are considered and compared. It is demonstrated that the Nes model is able to accurately describe the flow stress of AA3003 sheet at different temperatures, strain rates and instantaneous strain rate jumps.

Incremental forming (ISF) is an innovative flexible sheet metal forming process which can be used to manufacture complex shapes from various materials. Due to its flexibility, it has attracted more and more attention over recent decades. Localized deformation and shear through the thickness are essential characteristics of ISF. These lead to specific failure modes and formability of ISF that are different from the conventional stamping process. In this contribution, three continuum damage models (Lemaitre, Gurson, extended GTN models) are formulated and fully coupled with the finite element simulation in a commercial software ABAQUS to predict failure in incremental forming. A comparative investigation of these three damage models has been carried out to analyze both the deformation behavior and failure mechanisms.

Conventional forming limit curves (FLCs) are inappropriate for describing formability for advanced high strength (AHS) steel sheets, since such steel grades experience fracture without localized necking occurrence. The aim of this work was to develop a fracture curve (FC) for the AHS steel grade DP980. The FC was determined by means of the Nakajima stretch forming test and tensile tests of various sample geometries, by which shear fracture governed. An optical strain measurement system was used to capture strain histories of deformed samples up to failure. From these results, fracture strains were gathered and plotted in a strain space. Subsequently, the strain based curve was transformed to space between stress triaxiality and plastic strain. Hereby, effects of anisotropic yield function, namely, the Hill'48 model on obtained stress fracture loci were investigated. In order to verify applicability of the determined limit curves, a Mini-tunnel part was pressed and simulated. It was found that the stress based FC do predict failure of the DP980 steel sheet more accurately than the strain based F C.

In this study, a plane stress yield function which is described by 3rd-degree spline curve is proposed. This yield function can predict a material anisotropy with flexibility and consider evolution of anisotropy in terms of both r values and stresses. As an application, hole expanding simulation results are shown to discuss accuracy of the proposed yield function.

In actual manufacturing, some empirical methods such as the bottoming technique are generally used in order to adjust the bend angles of products. However, the problem with this is that it relies on the technique of the engineer. In this study, quantitative springback control by lump-punch penetration after V-bending is investigated with FEM analysis and experimentation. The lump at the punch tip is pushed into a bent section at the final stage of V-bending and stretches the inside surface at the bent section. The method of springback control is suggested based on the deformation state. Then, the suitability of springback control using this mechanism is investigated. It is confirmed that the springback amount is reduced by lump-punch penetration. Accordingly, it is recommended to control springback by sheet forging with a lump punch.

Micro-forming of ultra-thin sheet metals raises numerous challenges. In this investigation, the predictions of state-of-the-art crystal plasticity (CP) and phenomenological models are compared in the framework of industrial bending-dominated forming processes. Sheet copper alloys 0.1mm-thick are considered, with more than 20 grains through the thickness. Consequently, both model approaches are valid on theoretical ground. The phenomenological models' performance was conditioned by the experimental database used for parameter identification. The CP approach was more robust with respect to parameter identification, while allowing for a less flexible description of kinematic hardening, at the cost of finer mesh and specific grain-meshing strategies. The conditions for accurate springback predictions with CP-based models are investigated, in an attempt to bring these models at the robustness level required for industrial application.

The effect of the r-value change on the accuracy of the forming limits predicted using the Marciniak-Kuczynski-type (M-K) forming limit analysis for a cold rolled interstitial- free (IF) steel sheet is investigated. Uniaxial tensile tests with a digital image correlation system are used to measure the r-value change. A tube subjected to tension-expansion loading under linear paths in the first quadrant of the stress space are performed to measure the multiaxial plastic deformation behavior and the forming limits of the test material. The observed differential hardening (DH) behavior is approximated by changing the material parameters of the Yld2000-2d yield function (Barlat et al, 2003) as functions of the reference plastic strain. The M-K analyses are performed using the r-value change and r-value constant DH model. It is concluded that the DH model considering the r-value change leads to the more accurate predicted forming limits.

A crystal-plasticity finite-element method was used to examine the deformation mechanism in a commercially pure titanium sheet. The following tension-compression asymmetry was exhibited in the stress-strain curves: the yield stress was larger under tension than under compression, whereas the work-hardening was smaller under tension than under compression. The strain hardening behaviour was predicted qualitatively well using the crystal-plasticity analysis. The simulation results suggested that the tension-compression asymmetry could be explained in terms of the difference in the activity of the twinning systems.

The prediction of formability of titunium is more difficult than steels since its strong anisotropy. If computer simulation can estimate the formability of titanium, we can select the optimal forming conditions. The purpose of this study was to acquire knowledge for the formability prediction by the computer simulation of the square cup deep-drawing of pure titanium. In this paper, the results of FEM analsis of pure titanium were compared with the experimental results to examine the analysis validity. We analyzed the formability of deepdrawing square cup of titanium by the FEM using solid elements. Compared the analysis results with the experimental results such as the forming shape, the punch load, and the thickness, the validity was confirmed. Further, through analyzing the change of the thickness around the forming corner, it was confirmed that the thickness increased to its maximum value during forming process at the stroke of 35mm more than the maximum stroke.

This paper accounts for nonlinear strain path, sheet curvature, and sheet-tool contact pressure to explain the differences in measured forming limit curves (FLCs) obtained by Marciniak and Nakajima Tests. While many engineers working in the sheet metal forming industry use the raw data from one or the other of these tests without consideration that they reflect the convolution of material properties with the complex processing conditions involved in these two tests, the method described in this paper has the objective to obtain a single FLC for onset of necking for perfectly linear strain paths in the absence of through-thickness pressure and restricted to purely in-plane stretching conditions, which is proposed to reflect a true material property. The validity of the result is checked using a more severe test in which the magnitude of the nonlinearity, curvature, and pressure are doubled those involved in the Nakajima Test.

Modelling and analysis of underwater explosive forming process by using FEM and SPH formulation is presented in this work. The explosive forming of a steel cone is studied. The model setup includes a low carbon steel plate, plate holder, forming die as well as water and C4 explosive.

The effect of multiple explosives on rate of targets deformation has been studied. Four different multi-explosives models have been developed and compared to the single explosive model. The formability of the steel plate based on forming limit failure criteria has been investigated. Aspects such as shape of plates deformation and thickness of the plate during the forming process have been examined.

The model results indicate that a multi-explosives model does not always guarantee a faster rate of target deformation without central explosive. On the other hand the model results indicate that the multi-explosives setup is capable of preventing crack failure of the steel plate during the forming process which would occur if a single explosive model was used.

This paper presents different extensions of the classical GTN damage model implemented in a finite element code. The goal of this study is to assess these extensions for the numerical prediction of failure of a DC01 steel sheet during a single point incremental forming process, after a proper identification of the material parameters. It is shown that the prediction of failure appears too early compared to experimental results. Though, the use of the Thomason criterion permitted to delay the onset of coalescence and consequently the final failure.

Usage of high-strength steels in conventional air bending is restricted due to limited bendability of these metals. Large-radius punches provide a typical approach for decreasing deformations during the bending process. However, as deflection progresses the loading scheme changes gradually. Therefore, modelling of the contact interaction is essential for an accurate description of the loading scheme. In the current contribution, the authors implemented a plane frictional contact element based on the penalty method. The geometrically exact contact algorithm is used for the penetration determination. The implementation is done using the OOFEM - open source finite element solver. In order to verify the simulation results, experiments have been conducted on a bending press brake for 4 mm Weldox 1300 with a punch radius of 30 mm and a die opening of 80 mm. The maximum error for the springback calculation is 0.87° for the bending angle of 144°. The contact interaction is a crucial part of large radius bending simulation and the implementation leads to a reliable solution for the springback angle.

Beads are used in deep drawn sheet metal parts for increasing the part stiffness. Thus, reductions of sheet metal thickness and consequently weight reduction can be reached. Style guides for types and positions of beads exist, which are often applied. However, higher stiffness effects can be realized using numeric optimization. The optimization algorithm considers the two-stepped manufacturing process consisting of deep drawing and bead stamping. The formability in both manufacturing steps represents a limiting factor. Considering nonlinear strain paths using generalized forming limit concept (GFLC), acceptable geometries will be determined in simulation. Among them, the efficient geometry which has higher stiffness effects will be selected in numerical and experimental tests. These will be integrated in the optimization algorithm.

Two point incremental forming receives widespread study with its advantages of economy and flexibility in small batch products, such as aircraft parts. Aircraft parts, however, are rigorous in their shape errors. In this paper, one real airplane part is selected and formed with different process parameters to investigate the shape error level of part. Comparing the geometric errors caused by different process parameters, such as tool diameter, step size, feed rate and tool path, it is found that the geometric errors reduce as tool diameter increases. Meanwhile, the effect of step size is not linear. Influence law of feed rate is various with different other parameters. The bidirectional tool path, having opposite processing direction at adjacent layer, reduces the errors.

In hot stamping processes, the interfacial heat transfer coefficient (IHTC) between the forming tools and hot blank is an essential parameter which determines the quenching rate of the process and hence the resulting material microstructure. The present work focuses on the characterization of the IHTC between an aluminium alloy 7075-T6 blank and two different die materials, cast iron (G3500) and H13 die steel, at various contact pressures. It was found that the IHTC between AA7075 and cast iron had values 78.6% higher than that obtained between AA7075 and H13 die steel. Die materials and contact pressures had pronounced effects on the IHTC, suggesting that the IHTC can be used to guide the selection of stamping tool materials and the precise control of processing parameters.

For foil blanking process, the usage of flexible tool can effectively reduce the requirement of the manufacturing and assembling precision, compared with using conventional tool. However, the blanking mechanism using rubber tool is not clear. To investigate this question, the Finite Element (FE) model of rubber and process is established using ABAQUS package. The result of FE simulation affirm that the fracture emerges as a result of shear, not tensile. Then, for titanium foil with 0.08mm thickness, the cutting experiment is executed to verify the validity of blanking mechanism and FE simulation.

This paper discusses the evolution of friction coefficient for the multi-layered Molybdenum Disulphide (MoS₂) and WC coated substrate during sliding against Aluminium AA 6082 material. A soft MoS₂ coating was prepared over a hard WC coated G3500 cast iron tool substrate and underwent friction test using a pin-on-disc tribometer. The lifetime of the coating was reduced with increasing load while the Aluminium debris accumulated on the WC hard coating surfaces, accelerated the breakdown of the coatings. The lifetime of the coating was represented by the friction coefficient and the sliding distance before MoS₂ coating breakdown and was found to be affected by the load applied and the wear mechanism.

The drawbeads in stamping tools are usually designed based on experience from the forming of steel. However, aluminium alloys display different forming behaviour to steels, which is not reflected in the drawbead design for tools used for stamping aluminium. This paper presents experimental results from different semi-circular drawbead geometries commonly encountered in automotive dies and compares them to those obtained from Stoughton's analytical drawbead model and the 2D plane strain drawbead model set up using LS-DYNA. The study was conducted on lubricated NG5754 strips. The results presented are in terms of drawbead restraining force versus strip displacement, as a function of drawbead depth. The FE drawbead model agrees well with the experiments whereas the analytical model overpredicted the drawbead forces.

In the hole-expansion of anisotropic AA6022-T4 sheets, the strain around the hole is non-uniformly distributed due to the anisotropy of the material. This was examined by performing experiments with a flat-headed punch and using Digital Image Correlation (DIC). In the experiments, failure always initiated at a unique location, oriented at 45° to the Rolling Direction of the sheet. The use of DIC allowed the probing of the full-strain-field in real-time. Subsequently, the experiments were simulated in DYNAFORM using shell elements and the Yld2000-2D anisotropic non-quadratic yield function, properly calibrated for this material. In addition, the hardening curve of the material was inversely identified at large strains from the tail of the tensile test. The strain evolution is compared between the experiments and the model.

Low qualified rate and inferior quality frequently occurring in the general deep drawing process of a certain box-shaped part, now use hydroforming to optimize forming process, in order to study the effect of hydroforming for improving the quality and formability, purposed five process schemes: general deep drawing, active hydroforming, passive hydroforming, general deep drawing combined with active hydroforming, passive combined with active hydroforming. Each process was simulated by finite element simulation and results were analysed. The results indicate the passive combined with active hydroforming is the best scheme which can obtain smallest thickness thinning and satisfactory formability, then optimized hydroforming pressure, blank holder force subsequently by adjust the simulation parameters. Research result proves that active/passive hydroforming is a new method for complex parts forming.

The purpose of this study is to investigate the influences of numerical parameters on the electromagnetic forming (EMF) simulation. The 3-dimensional coupled electromagnetic- mechanical simulations were conducted to predict the deformation behavior of the advanced high strength steel (AHSS) sheet receiving support in EMF with aluminum driver sheet. Dual phase (DP) 780 steel workpiece was formed into a hemi elliptical protrusion shape with aluminum alloy AA1050 driver sheet using a flat spiral coil actuator and open cavity die. The deformed shape of the DP780 workpiece and the computation time with respect to element size, N cycle number and time step of electromagnetic (EM) solver were analysed.

A multi-scale modeling of multiphase advanced high strength steels was developed based on crystal plasticity and evolutionary yield function. An analytical model to directly predict the mechanical behavior of each phase was developed from crystal plasticity model and EBSD data. Considering the grain size and orientation distribution, evolution of the yield surface could be directly predicted by the analytical prediction model. The yield surface prediction results were applied to the evolutionary yield function model. Macroscopic mechanical behavior of the multiphase material could be predicted by considering the volume fraction of each phase, which enables to optimize the desired material properties during the development of the multiphase material.

The present work deals with the advantages in the Hydromechanical Deep Drawing (HDD) when AA5754 Tailored Heat Treated Blanks (THTBs) are adopted. It is well known that the creation of a suitable distribution of material properties increases the process performance. When non heat-treatable alloys are considered, the THTB approach can be successfully applied to increase the Limit Drawing Ratio (LDR) by changing the peripheral zone into the annealed state starting from a cold-worked blank. If this approach is combined with the advantages of a counterpressure, even more remarkable improvements can be achieved. Due to the large number of involved parameters, the optimized design of both the local treatment and the pressure profile were investigated coupling an axial symmetric Finite Element model with the integration platform modeFRONTIER. Results confirmed the possibility of increasing the LDR from 2.0 (Deep Drawing using a blank in the annealed state) up to about 3.0 if combining the adoption of a THTB with the optimal pressure profile.

This study is about typical sheet metal forming processes applied in aerospace industry including flexform, stretch form and stretch draw. Each process is modelled by using finite element method for optimization. Tensile, bulge, forming limit and friction tests of commonly used materials are conducted for defining the hardening curves, yield loci, anisotropic constants, forming limit curves and friction coefficients between die and sheet. Process specific loadings and boundary conditions are applied to each model. The models are then validated by smartly designed experiments that characterize the related forming processes. Lastly, several examples are given in which those models are used to predict the forming defects before physical forming and necessary die design and process parameter changes are applied accordingly for successful forming operations.

This paper presents research on modelling the impact of a 150g projectile on a 35mm thick aluminium sandwich panel. The objective of the work is a predictive modelling capability for the ballistic limit of the panel. A predictive modelling capability supports the design of capture and deorbit missions for large items of space debris such as satellites and rocket upper stages. A detailed explicit finite element model was built using the LSDYNA software and results were compared with experimental data for the projectile exit velocity to establish key parameters. The primary parameters influencing the model behaviour were the strength and failure of the aluminium face sheets and the friction between projectile and panel. The model results showed good agreement with experimental results for ogive nose projectiles, but overestimated the exit velocity for flat nose projectiles.

The quality of sheet metal formed parts is strongly dependent on the friction and lubrication conditions that are acting in the actual production process. Although friction is of key importance, it is currently not considered in detail in stamping simulations. This paper presents project results considering friction and lubrication modelling in stamping simulations of the Volvo XC90 inner door. For this purpose, the TriboForm software is used in combination with the AutoForm software. Validation of the simulation results is performed based on door-inner parts taken from the press line in a full-scale production run. The project results demonstrate the improved prediction accuracy of stamping simulations.

In the stamping of automotive parts, friction and lubrication play a key role in achieving high quality products. In the development process of new automotive parts, it is therefore crucial to accurately account for these effects in sheet metal forming simulations. Only then, one can obtain reliable and realistic simulation results that correspond to the actual try-out and mass production conditions. In this work, the TriboForm software is used to accurately account for tribology-, friction-, and lubrication conditions in stamping simulations. The enhanced stamping simulations are applied and validated for the door-outer of the Mercedes- Benz C-Class Coupe. The project results demonstrate the improved prediction accuracy of stamping simulations with respect to both part quality and actual stamping process conditions.

For the characterization of friction conditions under sheet metal forming process conditions, different friction test set-ups are being used in industry. However, different friction tests and test set-ups are known to result in scattering friction results. In this work, the TriboForm software is utilized to numerically model the frictional behavior. The simulated coefficients of friction are experimentally validated using friction results from a standardized strip drawing friction test set-up. The experimental and simulation results of the friction behavior show a good overall agreement. This demonstrates that the TriboForm software enables simulating friction conditions for varying tribology conditions, i.e. resulting in a generally applicable approach for friction characterization under industrial sheet metal forming process conditions.

The manufacturing process and the behaviour of a spring manufactured from an aluminium sheet is described and investigated in this work considering the specifications for the in-service conditions. The spring is intended to be applied in car multimedia industry to replace bolted connections. Among others, are investigated the roles of the constitutive parameters and the hypothesis of evolutive elastic properties with the plastic work in the multistep forming process and in working conditions.

The effects of forming on the crash simulation of a vehicle have been investigated by considering the load paths produced by sheet metal forming process. The frontal crash analysis has been performed by the finite element method, firstly without considering the forming history, to find out the load paths that absorb the highest energy. The sheet metal forming simulations have been realized for each structural component of the load paths and the frontal crash analysis has been repeated by including forming history. The results of the simulations with and without forming effects have been compared with the physical crash test results available in literature.

For a sufficiently wide range of stresses the titanic and aluminummagnesium alloys, as a rule, strained differently in the process of creep under tension and compression along a fixed direction. There are suggested constitutive relations for the description of the steady-state creep of transversely isotropic materials with different tension and compression characteristics. Experimental justification is given to the proposed constitutive equations. Modeling of forming of wing panels of the aircraft are considered.

Stamping simulations usually make the plane stress simplifying assumption. However, this becomes less valid when material draws around features with radius to sheet thickness ratios less than 20. Pereira, Yan & Rolfe (Wear, Vol.265, p.1687 (2008)) predicted that out-of-plane stress equivalent to material yield can occur because a line contact forms briefly at the start of the draw process. The high transient stress can cause high rates of tool wear and may cause the 'die impact line' cosmetic defect. In this work, we present residual strain results of a channel section that was drawn over a small radius. Using the neutron source at the Institut Laue-Langevin, in-plane and out-of-plane strains were measured in the channel part to show some support for the conclusions of Pereira et. al.

Automotive manufacturers have been reducing the weight of their vehicles to meet increasingly stringent environmental legislation that reflects public demand. A strategy is to use higher strength materials for parts with reduced cross-sections. However, such materials are less formable than traditional grades. The frequent result is increased processing and piece costs. 3D roll forming is a novel and flexible process: it is estimated that a quarter of the structure of a vehicle can be made with a single set of tooling. Unlike stamping, this process requires material with low work hardening rates. In this paper, we present results of ultra high strength steels that have low elongation in a tension but display high formability in bending through the suppression of the necking response.

This paper explores the effect of the part geometry on the variation of the Strain NonUniformity Index (SNI) at failure in shapes drawn from a single material. Forming of different shapes, namely, a square cup, an equibiaxially stretched sample was performed experimentally as well as simulated using AUTOFORM 5.2 Plus software. Failure predictions were made using the SNI based methodology and the FLD, and compared with experimental outcomes. Forming of the cross draw (FTF benchmark), was simulated and corresponding critical SNI was established based on the failure predicted with reference to the FLD. The SNI values so obtained are discussed in light of different component shapes and draw depths during forming of various geometries.

Gas detonation forming is an unconventional technique, which has the potential to form complex geometries, including sharp angles and undercuts in a very short process time. To date, most of the numerical studies on detonation forming neglect the highly dynamic pressure profile of the detonation obtained from experiments. In the present work, it is emphasised that the consideration of the actual detonation pressure as measured in the experiment is crucial. The thickness distribution and radial strain are studied using a strain-rate dependent Johnson-Cook material model. The obtained results vary significantly with change in loading rate. Moreover, the model is capable of predicting extremely sharp edges.

It has been widely observed that below the yield stress the loading/unloading stress-strain curves of plastically deformed metals are in fact not linear but slightly curved, showing a hysteresis behaviour during unloading/reloading cycles. In addition to the purely elastic strain, extra dislocation based micro-mechanisms are contributing to the reversible strain of the material which results in the nonlinear unloading/reloading behaviour. This extra reversible strain is the so called anelastic strain. As a result, the springback will be larger than that predicted by FEM considering only the recovery of the elastic strain. In this work the physics behind the anelastic behaviour is discussed and experimental results for a dual phase steel are demonstrated. Based on the physics of the phenomenon a model for anelastic behaviour is presented that can fit the experimental results with a good accuracy.

For many applications, such as in structural components, it is required to join two tubes - sometimes with dissimilar material properties. Only few research studies have investigated the joining of tubular metallic components by means of high-velocity forming processes. In this paper, we present the novel process of joining of two tubes by a gas detonation pressure wave. In particular, the joining of a copper and a steel tube is discussed by means of a finite element study and a conducted experiment.

A validated numerical model for in-plane stress/strain prediction is essential in understanding the deformation behaviour of sheet metal forming process, in particular, asymmetric deep drawing of advanced high strength steel sheet. In this work, the Yld2000-2d anisotropic yield criterion integrated with the initial homogeneous anisotropic hardening model was employed to describe the complex material behaviours of DP780 steel as well as the adoption of Yoshida chord model for elastic modulus degradation. Digital image correlation technique was utilized to measure the in-plane strain and shape deviation of the developed P- channel. The validity of the numerical model was assessed by comparing the predicted strain distribution and twist springback with the measured results. It indicates that the developed numerical model based on the selected constitutive models is acceptable for the deformation analysis, although the predicted discrepancies still exist.

The flex-forming process is used extensively in aerospace industry for net shape forming of sheet metal structural components. Common metals used in the manufacture of these components include 7075 and 2024 aluminium alloys; usually in an as quenched condition following solution heat treatment. While the process is commonplace, the level of manual rework remains high, driven by inherent process and material variability and the lack of upfront analysis before the manufacture of tooling. A suitable process modelling method using AutoForm is presented along with an industrial validation study for the manufacture of an aerospace frame component in 7075-W aluminium alloy. The results illustrate the importance of material model accuracy and the inclusion of through thickness compressive stresses in predicting the flange springback of the component.

Forming limit diagram (FLD) is an important tool to measure the material's formability for metal forming processes. In order to successfully manufacture a component through tube hydroforming process it is very important to know the effect of material properties, process and geometrical parameters on the outcome of finished product. This can be obtained by running a finite element code which not only saves time and money but also gives a result with considerable accuracy. Therefore, in this paper the mutual effect of diameter as well as thickness has been studied. Firstly the finite element based prediction is carried out to assess the formability of seamless and welded tubes with varying thickness. Later on, effect of varying diameter and thickness on strain path is predicted using statistical based regression analysis. Finally, the mutual effect of varying material property alongwith varying thickness and diameter on constraint factor is studied.

Forming limit diagram (FLD) is a tool which is widely used to measure the material formability of hydroforming process. It is well known that strain based FLD is dependent on strain path which the material undergoes during the course of deformation. This work is based on understanding the deformation and fracture behaviour of as-received (AR) tube and annealed tube during hydroforming process. The strain path is being measured at different locations of the AR tube as well as annealed tube and is co-related with the microhardness value to understand the localization and fracture behaviour. The annealed tube tends to fracture suddenly from the weld line and fracture surface study reveals sudden dominant brittle mode of fracture indicating the impact of weld notch on the fracture process and thus giving lower limiting strains and hardness value.

Numerical analysis of hot stamping process is very complex mainly due to thermomechanical processes involved. Many variables such as heat transfer coefficient, density, young modulus and other thermal parameters are temperature and pressure dependent. The paper presents results of CFD analysis on the near optimized cooling system of hot stamping die for automotive structural part. By using actual parameters obtained from the industry production line, this research is aimed at comparing the performance of actual cooling system with the results obtained by CFD simulation using commercial software. The die and blank were modelled as 3D volume mesh in a closed position thus ignoring blank history data prior to stamping operation. Temperature distribution representing hardness of the simulated final part is an agreement with the QA data of the actual part thus showing viability of this method to be used in cooling system design

A crystal plasticity based full-field microstructure simulation approach is used to virtually determine mechanical properties of sheet metals. Microstructural features like the specific grain morphology and the crystallographic texture are taken into account to predict the plastic anisotropy. A special focus is on the determination of the Lankford coefficients and on the yield surface under plane stress conditions. Compared to experimental procedures, virtual material testing allows to generate significantly more data points on the yield surface. This data is used to calibrate anisotropic elasto-plastic material models which are commonly used for sheet metal forming simulations. A numerical study is carried out to analyze the influence of the chosen points on the yield surface on the calibration procedure.

Formability of the sheet metal depends upon the uniformity of strain distribution, which depends on material properties, tooling and process parameters. Nakazima Test was conducted to study the strain distribution and establish the forming limits of AA 6016. The experimental conditions were simulated using AUTOFORM 5.2 Plus software and the failure predicted using the SNI based methodology. The failure predictions were correlated with the state of the experimentally deformed Nakazima samples, and also with the FLD based forming limits. The failure prediction from the SNI based methodology was found to correlate well with the state of the experimental Nakazima sample.

This paper represents the temperature-dependent study which is performed on AA7075. This was performed through the application of deep drawing experiments at high temperature of 250, 300, 350, 400, 450 and 500°C and different forming speeds. FEM study is applied at room and 300 and 400 0C temperature with different strain rates. Softening model is used to model the thermo-mechanical constitutive equation. Forming limit curve models (based on M-K model) were used in the analysis of simulation results in order to predict the onset of necking. Simulation results were compared with experimental data to evaluate the accuracy of onset of necking simulation and failure location prediction

In this paper is presented a systematic experimental investigation of the mechanical response of polycrystalline commercially pure molybdenum (Mo). It was established that the material has ductility in tension at 10^-5/s and that the failure strain is strongly dependent on the orientation. A specimen taken along the rolling direction sustains large axial strains (20%), while a specimen cut at an angle of 45^o to the rolling direction could only sustain 5% strain. Irrespective of the loading orientation the yield stress in uniaxial compression is larger than in uniaxial tension. While in tension the material has a strong anisotropy in Lankford coefficients, in uniaxial compression it displays weak strain-anisotropy. An elastic- plastic orthotropic model that accounts for all the specificities of the plastic deformation of the material was developed. Validation of the model was done through comparison with data on notched specimens. Quantitative agreement with both global and local strain fields was obtained.

Twinning induced plasticity steels (TWIP) are very good candidate for automotive industry applications because they potentially offer large energy absorption before failure due to their exceptional strain hardening capability and high strength. However, their behaviour is drastically influenced by the loading conditions. In this work, the mechanical behaviour of a TWIP steel sheet sample was investigated at room temperature under monotonic and reverse simple shear loading. It was shown that all the expected features of load reversal such as Bauschinger effect, transient strain hardening with high rate and permanent softening, depend on the prestrain level. This is in agreement with the fact that these effects, which occur during reloading, are related to the rearrangement of the dislocation structure induced during the predeformation. The homogeneous anisotropic hardening (HAH) approach proposed by Barlat et al. (2011) [1] was successfully employed to predict the experimental results.

Experimental and numerical investigations on the characterisation and prediction of cold formability of a ferritic steel sheet are performed in this study. Tensile tests and Nakajima tests were performed for the plasticity characterisation and the forming limit diagram determination. In the numerical prediction, the modified maximum force criterion is selected as the localisation criterion. For the plasticity model, a non-associated formulation of the Hill48 model is employed. With the non-associated flow rule, the model can result in a similar predictive capability of stress and r-value directionality to the advanced non-quadratic associated models. To accurately characterise the anisotropy evolution during hardening, the anisotropic hardening is also calibrated and implemented into the model for the prediction of the formability.

High strength titanium bent tubes present promising usages in advanced aircraft and spacecraft to achieve lightweight and improve overall performance. However, the high ratio of yield strength to Young's modulus results in significant springback in bending, which limits their forming accuracy. In this work, the Bauschinger effect and nonlinear unloading behavior of high strength Ti-3Al-2.5V tube are experimentally investigated. Then, to describe such behaviors, the Yoshida-Uemori (Y-U) two-surface hardening model and Chord unloading model are introduced into the elastoplastic constitutive framework and numerically implemented. Taking rotary draw (RDB) bending as a case, the springback angles are predicted and analyzed by comparison with the experimental results.

The effect of reduction of material geometry in metal forming process is important and is more effective when material size less than 100 micron. Thin brass sheet of 30. 50. 90 micron thickness were tested by in-plane uniaxial and out-of-plane limit dome height (LDH) test to investigate the size effect. The test was carried for both as-received and annealed specimen. The microstructure of all tests was determined in details by electron back scattered diffraction (EBSD) microscopy technique. There was a clear dependency of mechanical behaviour observed on part miniaturized of both tensile and LDH test. The limiting strain is obtained maximum at plane strain path in LDH test having more misorientation. The 50 micron sheet in biaxial strain path required more load and have larger major strain, more texture and Taylor factor value.

The tube joining by plastic deformation proves to be a more efficient and environmentally friendly way to achieve the tube-tube joining compared with other traditional types, such as metallurgical joining and mechanical joining. In this study, to reveal the effects of the processing parameters on the filling quality and residual contact stress, an axisymmetric finite element (FE) model of the whole joining process, including extrusion-bulging forming and unloading, was established and validated. The aluminum alloy (AA) 6061-T4 tubes, the stainless steel (ST) 15-5PH sleeve and polyurethane (PU) elastomer medium were characterized and modeled. And the implicit algorithm was adopted by comparing the prediction results between explicit and implicit FE models. The characteristics of stress distribution and plastic strain for the tube, PU elastomer and sleeve were discussed.

Experiment results from uniaxial tensile tests, bi-axial bulge tests, and disk compression tests for a beverage can AA3104-H19 material are presented. The results from the experimental tests are used to determine material coefficients for both Yld2000 and Yld2004 models. Finite element simulations are developed to study the influence of materials model on the predicted earing profile. It is shown that only the YLD2004 model is capable of accurately predicting the earing profile as the YLD2000 model only predicts 4 ears. Excellent agreement with the experimental data for earing is achieved using the AA3104-H19 material data and the Yld2004 constitutive model. Mechanical tests are also conducted on the AA3104-H19 to generate fracture data under different stress triaxiality conditions. Tensile tests are performed on specimens with a central hole and notched specimens. Torsion of a double bridge specimen is conducted to generate points near pure shear conditions. The Nakajima test is utilized to produce points in bi-axial tension. The data from the experiments is used to develop the fracture locus in the principal strain space. Mapping from principal strain space to stress triaxiality space, principal stress space, and polar effective plastic strain space is accomplished using a generalized mapping technique. Finite element modeling is used to validate the Modified Mohr-Coulomb (MMC) fracture model in the polar space. Models of a hole expansion during cup drawing and a cup draw/reverse redraw/expand forming sequence demonstrate the robustness of the modified PEPS fracture theory for the condition with nonlinear forming paths and accurately predicts the onset of failure. The proposed methods can be widely used for predicting failure for the examples which undergo nonlinear strain path including rigid-packaging and automotive forming.

Tube hydroforming process is an advanced manufacturing process in which tube is placed in between the dies and deformed with the help of hydraulic pressure. A sound tube hydroformed part depends upon die conditions, material properties and process conditions. In this work, a finite element study, along with response surface methodology (RSM) for designing the simulation, has been used to construct models with loading path, friction, anisotropic index, strain hardening exponent and tube thickness. The responses studied are the die corner radius filling and strain non-uniformity index (SNI) chosen in each step of the tube with maximum 30% thinning as stopping criteria. The factors effect and their interactions on each response were determined and analysed.

The Yoshida nonlinear isotropic/kinematic hardening material model is often selected in forming simulations where an accurate springback prediction is required. Many successful application cases in the industrial scale automotive components using advanced high strength steels (AHSS) have been reported to give better springback predictions. Several issues have been raised recently in the use of the model for higher strength AHSS including the use of two C vs. one C material parameters in the Armstrong and Frederick model (AF model), the original Yoshida model vs. Original Yoshida model with modified hardening law, and constant Young's Modulus vs. decayed Young's Modulus as a function of plastic strain. In this paper, an industrial scale automotive component using 980 MPa strength materials is selected to study the effect of two C and one C material parameters in the AF model on both forming and springback prediction using the Yoshida model with and without the modified hardening law. The effect of decayed Young's Modulus on the springback prediction for AHSS is also evaluated. In addition, the limitations of the material parameters determined from tension and compression tests without multiple cycle tests are also discussed for components undergoing several bending and unbending deformations.

Earing tendency in a deep drawn cup of circular blanks is one the most prominent characteristics observed due to anisotropy in a metal sheet. Such formation of uneven rim is mainly due to dissimilarity in yield stress as well as Lankford parameter (r- value) in different orientations. In this paper, an analytical function coupled with different yield functions viz., Hill 1948, Barlat 1989 and Barlat Yld 2000-2d has been used to provide an approximation of earing profile. In order to validate the results, material parameters for yield functions and hardening rule have been calibrated for ASS 304 at 250°C and deep drawing experiment is conducted to measure the earing profile. The predicted earing profiles based on analytical results have been validated using experimental earing profile. Based on this analysis, Barlat Yld 2000-2d has been observed to be a well suited yield model for deep drawing of ASS 304, which also confirms the reliability of analytical function for earing profile estimation.

In the present work, the edge stretchability of advanced high strength steel (AHSS) was investigated experimentally and numerically using both a hole expansion test and a tensile specimen with a central hole. The experimental fracture strains obtained using the hole expansion and hole tension test in both reamed and sheared edge conditions were in very good agreement, suggesting the tests are equivalent for fracture characterization. Isotropic finite-element simulations of both tests were performed to compare the stress-state near the hole edge.

In this work, experimental tests were carried out, under different loading conditions, in order to assess different ductile failure criteria, namely based on GTN, Johnson-Cook or Lemaitre models and to establish new proposals for improvement. Corresponding characterization for damage parameters is performed by an inverse analysis procedure, using reference experimental tests. Numerical simulations of a cross-shaped component are considered for the damage models, and results show a similar trend related with the experimental fracture evidence.

Isogeometric Analysis (IGA) has been growing in popularity in the past few years essentially due to the extra flexibility it introduces with the use of higher degrees in the basis functions leading to higher convergence rates. IGA also offers the capability of easily reproducing discontinuous displacement and/or strain fields by just manipulating the multiplicity of the knot parametric coordinates. Another advantage of IGA is that it uses the Non-Uniform Rational B-Splines (NURBS) basis functions, that are very common in CAD solid modelling, and consequently it makes easier the transition from CAD models to numerical analysis. In this work it is explored the contact analysis in IGA for both implicit and explicit time integration schemes. Special focus will be given on contact search and contact detection techniques under NURBS patches for both the rigid tools and the deformed sheet blank.

Die Starter, a new system developed by ESI Group, allows the user to drastically reduce the number of iterations during the early tool process feasibility. This innovative system automatically designs the first quick die face, generating binder and addendum surfaces (NURBS surfaces) by taking account the full die process. Die Starter also improves the initial die face based on feasibility criteria (avoiding splits, wrinkles) by automatically generating the geometrical modifications of the binder and addendum and the bead restraining forces with minimal material usage.

This paper presents a description of the new system and the methodology of Die Starter. Some industrial examples are presented from the part geometry to final die face including automatic developed flanges, part on binder and inner binder.

In the last decade numerous research has been done in the area of Isogeometric Analysis (IGA). The intention of this rather new technology is the wish to have a stronger integration of Computer Aided Design (CAD) and Finite Element Analysis (FEA). Its basic idea is to use the same mathematical description for the geometry as well in the design process (CAD) as in the later analysis (FEA). One of the wide spread geometry description methodology in CAD-systems is the usage of Non-Uniform Rational B-Splines (NURBS) as basis functions. NURBS-based finite elements have been proven to be very well suited for computational analysis leading to qualitatively more accurate results in comparison with standard finite elements based on Lagrange polynomials. Therefore continuous development of Isogeometric Analysis has been added to LS-DYNA in the last years. The present contribution will give an overview about the current possibilities in LS-DYNA to use NURBS-based CAD-geometry description for numerical simulation and outline future plans for their enhancements.

An important part in robustness evaluation of production processes is the identification of shape deviations. A systematic approach is typically based on the numerical evaluation of a DoE and the application of metamodels. They provide knowledge on solver noise and sensitivities of individual model parameters. This article presents the sensitivity analysis workflow of a linked deep drawing and joining process chain. LS-DYNA^®, optiSLang and SoS is used. The challenge is to separate simulative from process and material parameters of AA 6014. Spatial quantities like variations in geometry, thinning and strain have to be considered in the next process steps. At the same time the number of required virtual CAE model evaluations must be limited. The solution is based on nonlinear metamodels and random fields.

A constitutive law was developed based on a rate-independent crystal plasticity to account for the mechanical behavior of multiphase advanced high strength steels. Martensitic phase transformation induced by the plastic deformation of the retained austenite was represented by considering the lattice invariant shear deformation and the orientation relationship between parent austenite and transformed martensite. The stress dependent transformation kinetics were represented by adopting the stress state dependent volume fraction evolution law. The plastic deformation of the austenite was determined to have the minimum- energy associated with the work during the phase transformation. In addition to the martensitic phase transformation, yield point elongation and subsequent hardening along with inhomogeneous plastic deformation were also represented by developing a hardening stagnation model induced by the delayed dislocation density evolution.

The solid-shells are an attractive kind of element for the simulation of forming processes, due to the fact that any kind of generic 3D constitutive law can be employed without any additional hypothesis.

The present work consists in the improvement of a triangular prism solid-shell originally developed by Flores[2, 3]. The solid-shell can be used in the analysis of thin/thick shell, undergoing large deformations. The element is formulated in total Lagrangian formulation, and employs the neighbour (adjacent) elements to perform a local patch to enrich the displacement field. In the original formulation a modified right Cauchy-Green deformation tensor (C) is obtained; in the present work a modified deformation gradient (F) is obtained, which allows to generalise the methodology and allows to employ the Pull-Back and Push-Forwards operations.

The element is based in three modifications: (a) a classical assumed strain approach for transverse shear strains (b) an assumed strain approach for the in-plane components using information from neighbour elements and (c) an averaging of the volumetric strain over the element. The objective is to use this type of elements for the simulation of shells avoiding transverse shear locking, improving the membrane behaviour of the in-plane triangle and to handle quasi-incompressible materials or materials with isochoric plastic flow.

A fully modularized framework was established to combine isotropic, kinematic, and cross hardening behaviors under non-monotonic loading conditions. Three sets of state variables were defined and applied to consider the effects of, a) loading history, b) twinning and de-twinning and c) different pre-strain. Experiments under two types of non-proportional loading conditions were conducted along different orientations, 1) uniaxial compression-tension reversal loading with different amounts of compressive strains, and 2) two-step uniaxial tension, known as cross-loading conditions, with different pre-strains. No apparent cross-hardening effect was observed for this material. The calibrated new hardening model, with an anisotropic CPB06ex2 yield criterion and an eMMC anisotropic fracture model, has been implemented into Abaqus/ Explicit as a user material subroutine (VUMAT). Good correlation was observed between experimental and simulation results.

Nowadays, manufactured pieces can be divided into two groups: mass production and production of low volume number of parts. Within the second group (prototyping or small batch production), an emerging solution relies on Incremental Sheet Forming or ISF.

ISF refers to processes where the plastic deformation occurs by repeated contact with a relatively small tool. More specifically, many publications over the past decade investigate Single Point Incremental Forming (SPIF) where the final shape is determined only by the tool movement. This manufacturing process is characterized by the forming of sheets by means of a CNC controlled generic tool stylus, with the sheets clamped by means of a non-workpiece-specific clamping system and in absence of a partial or a full die. The advantage is no tooling requirements and often enhanced formability, however it poses a challenge in term of process control and accuracy assurance. Note that the most commonly used materials in incremental forming are aluminum and steel alloys however other alloys are also used especially for medical industry applications, such as cobalt and chromium alloys, stainless steel and titanium alloys. Some scientists have applied incremental forming on PVC plates and other on sandwich panels composed of propylene with mild steel and aluminum metallic foams with aluminum sheet metal. Micro incremental forming of thin foils has also been developed.

Starting from the scattering of the results of Finite Element (FE) simulations, when one tries to predict the tool force (see SPIF benchmark of 2014 Numisheet conference), we will see how SPIF and even micro SPIF (process applied on thin metallic sheet with a few grains within the thickness) allow investigating the material behavior. This lecture will focus on the identification of constitutive laws, on the SPIF forming mechanisms and formability as well as the failure mechanism. Different hypotheses have been proposed to explain SPIF formability, they will be listed however the lecture will be more focused on the use of SPIF to identify material parameters of well-chosen constitutive law. Results of FE simulations with damage models will be investigated to better understand the relation between the particular stress and strain states in the material during SPIF and the material degradation leading to localization or fracture.

Last but not least, as industrial world does not wait that academic scientists provide a deep and total understanding on how it works, to use interesting processes, the lecture will review some applications. Examples in fields as different as automotive guard, engine heat shield, gas turbine, electronic sensor, shower basin, medical component (patient-fitted organic shapes) and architecture demonstrate that the integration of SPIF within the industry is more and more a reality.

Note that this plenary lecture is the result of the research performed by the author in the University of Liege (Belgium) and in Aveiro (Portugal) with the team of R. de Souza during PhD theses of C. Henrard, J. Sena and C. Guzman and different research projects. It is also a synthesis of the knowledge gathered during her interactions with many research teams such as the ones of J.R. Duflou from KU Leuven in Belgium, J. Cao from Northwestern University in USA, M. Bambach in BTU Cottbus-Senftenberg in Germany, J. Jeswiet from Queen's University, Kingston, Canada who are currently working together on a state-of-the-art paper. The micro SPIF knowledge relies on contacts with S. Thibaud from the University of Franche Comte.

This paper presents the meshless local integral equation method (LIEM) for nonlocal analyses of two-dimensional dynamic problems based on the Eringen's model. A unit test function is used in the local weak-form of the governing equation and by applying the divergence theorem to the weak-form, local boundary-domain integral equations are derived. Radial Basis Function (RBF) approximations are utilized for implementation of displacements. The Newmark method is employed to carry out the time marching approximation. Two numerical examples are presented to demonstrate the application of time domain technique to deal with nonlocal elastodynamic mechanical problems.

It is widely recognized that macroscopic material properties depend on the features of the microstructure. The understanding of the links between microscopic and macroscopic material properties, main topic of Micromechanics, is of relevant technological interest, as it may enable deep understanding of the mechanisms governing materials degradation and failure. Polycrystalline materials are used in many engineering applications. Their microstructure is determined by distribution, size, morphology, anisotropy and orientation of the crystals [1]. At temperature below 0.3-0.5 Tmelting there are no ductile or creep mechanisms and two are the main failure patterns: intergranular, where the damage follows the grain boundaries and transgranular where instead the damage goes through the grain by splitting it into two parts.

In this talk a two-scale approach to degradation and failure in polycrystalline materials will be presented. The formulation involves the engineering component level (macro-scale) and the material grain level (micro-scale). The macro-continuum is modelled using two- and three-dimensional boundary element formulation in which the presence of damage is formulated through an initial stress approach to account for the local softening in the neighborhood of points experiencing degradation at the micro-scale. The microscopic degradation is explicitly modelled by associating Representative Volume Elements (RVEs) to relevant points of the macro continuum, for representing the polycrystalline microstructure in the neighbourhood of the selected points. A grainboundary formulation is used to simulate intergranular/transgranular degradation and failure in the microstructure, whose morphology is generated using the Voronoi tessellations. Intergranular/transgranular degradation and failure are modeled through cohesive and frictional contact laws. To couple the two scales, macro-strains are transferred to the RVEs as periodic boundary conditions, while overall macro-stresses are obtained as volume averages of the micro-stress field. The comparison between effective macro-stresses for the damaged and undamaged RVE allows to define a macroscopic measure of material degradation. To avoid pathological damage localization at the macroscale, integral non-local counterparts of the strains are employed. A multiscale processing algorithm is described. Two multiscale simulations are performed to demonstrate the capability of the method.

Finally numerical simulations have been performed in order to demonstrate the validity of the model in comparison with experimental observations and literature results.

Ductile damage can be dealt with continuous descriptions of material, resorting, for example, to continuous damage mechanic descriptions or micromechanical constitutive models. When it comes to describe material behaviour near and beyond fracture these approaches are no longer sufficient or valid and continuous/discontinuous approaches can be adopted to track fracture initiation and propagation. Apart from more pragmatic solutions like element erosion or remeshing techniques more advanced approaches based on the X-FEM concept, in particular associated with non-local formulations, may be adopted to numerically model these problems. Nevertheless, very often, for practical reasons, some important aspects are somewhat left behind, specially energetic requirements to promote the necessary transition of energy release associated with material damage and fracture energy associated to a crack creation and evolution. Phase-field methods may combine advantages of regularised continuous models by providing a similar description to non-local thermodynamical continuous damage mechanics, as well as, a "continuous" approach to numerically follow crack evolution and branching

Multi-scale simulations are computationally expensive if a two-way coupling is employed. In the context of sheet metal forming simulations, a fine-scale representative volume element (RVE) crystal plasticity (CP) model would supply the Finite Element analysis with plastic properties, taking into account the evolution of crystallographic texture and other microstructural features. The main bottleneck is that the fine-scale model must be evaluated at virtually every integration point in the macroscopic FE mesh. We propose to address this issue by exploiting a verifiable assumption that fine-scale state variables of similar RVEs, as well as the derived properties, subjected to similar macroscopic boundary conditions evolve along nearly identical trajectories. Furthermore, the macroscopic field variables primarily responsible for the evolution of fine-scale state variables often feature local quasi-homogeneities. Adjacent integration points in the FE mesh can be then clustered together in the regions where the field responsible for the evolution shows low variance. This way the fine-scale evolution is tracked only at a limited number of material points and the derived plastic properties are propagated to the surrounding integration points subjected to similar deformation. Optimal configurations of the clusters vary in time as the local deformation conditions may change during the forming process, so the clusters must be periodically adapted. We consider two operations on the clusters of integration points: splitting (refinement) and merging (unrefinement). The concept is tested in the Hierarchical Multi-Scale (HMS) framework [1] that computes macroscopic deformations by means of the FEM, whereas the micro-structural evolution at the individual FE integration points is predicted by a CP model. The HMS locally and adaptively approximates homogenized stress responses of the CP model by means of analytical plastic potential or yield criterion function. Our earlier work investigated simple test cases [2]. In this contribution we present a deep drawing process simulated using the HMS framework improved to exploit local quasi-homogeneities. We conclude that large performance gains (e.g. a speedup of 25) are obtained at the expense of introducing only a minor (e.g. below 1%) modelling error compared to the HMS simulation with no clustering of integration points.

In this study, a continuum-based approach for the description of the plastic hardening behavior of magnesium alloy sheets subjected to non-proportional strain path changes is discussed. The constitutive model is based on an anisotropic distortional yield function combining a stable component and a fluctuating component. The stable component initiates the yield criterion that characterizes the typical strength differential between tension and compression in magnesium alloys at room temperature. The evolution of the fluctuating component is reformulated based on its cubic metal counterpart to represent the deformation nature of magnesium alloys that consist of slip and twin dominant modes. The model is not formulated with a kinematic hardening rule, but it reasonably reproduces complex features of the stress-strain responses under the load reversal in magnesium alloy sheet: i.e., asymmetric hardening behavior under tension and compression, sigmoidal nature of hardening curve during monotonic compression and compression followed by tension, strong anisotropy etc.

A new thermo-elasto-viscoplastic (TEV) crystal plasticity constitutive formulation is developed and implemented in the well-known Marciniak-Kuczynski analysis to predict the formability of aluminum alloys (AA) 5754 and 3003 at elevated temperatures. The model takes into account the temperature dependence of the single crystal elastic coefficients, single slip hardening parameters, thermal softening and slip rate sensitivity. Temperature dependent single slip hardening parameters are determined from uniaxial tension simulations at room and elevated temperatures. The new model is able to accurately predict the experimental forming limit diagrams (FLDs) without the need for further curve fitting. The effects of elastic constants and thermal softening on FLD predictions are discussed, and a new expression to represent the temperature dependence of the initial imperfection (for the M-K analysis) is developed to enable the model to successfully predict the FLDs for any temperature in the warm forming regime prior to recrystallization.

In this paper, an uncoupled shear ductile fracture criterion is developed for prediction of ductile fracture in sheet metal forming from shear to balanced biaxial tension. The ductile fracture criterion is calibrated by four tests of sheet metal: shear tests, uniaxial tension, plane strain tension and the Nakajima test. Specimens are designed for AA6082 T6 (t1.0) for the calibration of the proposed ductile fracture criterion. The calibrated ductile fracture criterion is then implemented into numerical simulation for the prediction of ductile fracture of the aluminum alloy. For the purpose of comparison, onset of ductile fracture is also estimated by MMC3, DF2012 and DF2014 criteria. The comparison indicates that the developed criterion can accurately predict onset of ductile fracture for all four loading conditions, but the other three criteria can only provide reasonable prediction for three tests. Accordingly, the newly developed ductile fracture criterion is suggested to be used in prediction of ductile fracture for sheet metal forming in wide loading condition from shear to the balanced biaxial tension. Discussion on calibration of this ductile fracture criterion also indicates that the ductile fracture criterion can be employed in estimation of ductile fracture for bulk metal forming processes with better predictability.

Metallic materials often exhibit anisotropic behaviour under complex load paths because of changes in microstructure, e.g., dislocations and crystallographic texture. In this study, we present the development of constitutive model based on dislocations, point defects and texture in order to predict anisotropic response under complex load paths. In detail, dislocation/solute atom interactions were considered to account for strain aging and static recovery. A hardening matrix based on the interaction of dislocations was built to represent the cross-hardening of different slip systems. Clear differentiation between forward and backward slip directions of dislocations was made to describe back stresses during path changes. In addition, we included dynamic recovery in order to better account for large plastic deformation. The model is validated against experimental data for AA5754-O with path changes, e.g., Figure 1 [1]

Another effort is to include microstructure in forming predictions with a minimal increase in computational time. This effort enables comprehensive investigations of the influence of texture-induced anisotropy on formability [2]. Application of these improvements to predict forming limits of various BCC textures, such as γ, ρ, α, η and fibers and a random (R) texture. These simulations demonstrate that the crystallographic texture has significant (both positive and negative) effects on the forming limit diagrams (Figure 2). For example, the y fiber texture, that is often sought through thermo-mechanical processing due to high r-value, had the highest forming limit in the balanced biaxial strain path but the lowest forming limit under the plane strain path among textures under consideration.

The basic idea of isogeometric analysis (IGA) is to use splines, which are the functions commonly used in computer-aided design (CAD) to describe the geometry, as the basis function for the analysis as well. A main advantage is that a sometimes elaborate meshing process is by-passed. Another benefit is that spline basis-functions possess a higher-order degree of continuity, which enables a more accurate representation of the stress. Further, the order of continuity of the basis-functions can be reduced locally by knot insertion. This feature can be used to model interfaces and cracks as discontinuities in the displacement field.

In order to study failure-mechanisms in thin-walled composite materials, an accurate representation of the full three-dimensional stress field is mandatory. A continuum shell formulation is an obvious choice. Continuum shell elements can be developed based on the isogeometric concept. They exploit NURBS basis functions to construct the mid-surface of the shell. In combination with a higher-order B-spline basis function in the thickness direction a complete three-dimensional representation of the shell is obtained. This isogeometric shell formulation can be implemented in a standard finite element code using Bézier extraction.

Weak and strong discontinuities can be introduced in the B-spline function using knot-insertion to model material interfaces and delaminations rigorously as discontinuities in the displacement field. The exact representation of material interfaces vastly improves the accuracy of the through-the- thickness stress field. The ability to provide a double knot insertion enables a straightforward analysis of delamination growth in layered composite shells. Illustrative examples will be given.

In manufacturing processes anisotropic metals are often exposed to the loading with high strain rates in the range from 10² s^-1 to 10⁶ s^-1 (e.g. stamping, cold spraying and explosive forming). These types of loading often involve generation and propagation of shock waves within the material. The material behaviour under such a complex loading needs to be accurately modelled, in order to optimise the manufacturing process and achieve appropriate properties of the manufactured component.

The presented research is related to development and validation of a thermodynamically consistent physically based constitutive model for metals under high rate loading. The model is capable of modelling damage, failure and formation and propagation of shock waves in anisotropic metals. The model has two main parts: the strength part which defines the material response to shear deformation and an equation of state (EOS) which defines the material response to isotropic volumetric deformation [1]. The constitutive model was implemented into the transient nonlinear finite element code DYNA3D [2] and our in house SPH code. Limited model validation was performed by simulating a number of high velocity material characterisation and validation impact tests.

The new damage model was developed in the framework of configurational continuum mechanics and irreversible thermodynamics with internal state variables. The use of the multiplicative decomposition of deformation gradient makes the model applicable to arbitrary plastic and damage deformations.

To account for the physical mechanisms of failure, the concept of thermally activated damage initially proposed by Tuller and Bucher [3], Klepaczko [4] was adopted as the basis for the new damage evolution model. This makes the proposed damage/failure model compatible with the Mechanical Threshold Strength (MTS) model Follansbee and Kocks [5], 1988; Chen and Gray [6] which was used to control evolution of flow stress during plastic deformation. In addition the constitutive model is coupled with a vector shock equation of state which allows for modelling of shock wave propagation in orthotropic the material.

Parameters for the new constitutive model are typically derived on the basis of the tensile tests (performed over a range of temperatures and strain rates), plate impact tests and Taylor anvil tests.

The model was applied to simulate explosively driven fragmentation, blast loading and cold spraying impacts.

Deformation and failure behaviors of magnesium (Mg) alloys (AZ31 and E-form) were investigated using V-bending test. Formability of these Mg alloys was discussed in terms of minimum bending radius. Microtexture evolution in the deformed Mg alloys was examined via electron back-scattered diffraction (EBSD) technique. Two level simulation technique which combined continuum finite element method (FEM) and crystal plasticity FEM successfully simulated the microtexture evolution in Mg alloys during V-bending test. The effect of deformation twinning on the failure in Mg alloys was also examined.

We introduce the isogeometric shape optimisation of thin shell structures using subdivision surfaces. Both triangular Loop and quadrilateral Catmull-Clark subdivision schemes are considered for geometry modelling and finite element analysis. A gradient-based shape optimisation technique is implemented to minimise compliance, i.e. to maximise stiffness. Different control meshes describing the same surface are used for geometry representation, optimisation and finite element analysis. The finite element analysis is performed with subdivision basis functions corresponding to a sufficiently fine control mesh. During iterative shape optimisation the geometry is updated starting from the coarsest control mesh and proceeding to increasingly finer control meshes. The proposed approach is applied to three optimisation examples, namely a catenary, a roof over a rectangular domain, and free-form architectural shell roof. The influence of the geometry description and the used subdivision scheme on the obtained optimised curved geometries are investigated in detail.

The growth and coalescence of voids in sheet metals are not only the main active mechanisms in the final stages of fracture in a necking band, but they also contribute to the forming limits via changes in the normal directions to the yield surface. A widely accepted method to include void effects is the development of a Gurson-type model for the appropriate yield criterion, based on an approximate limit analysis of a unit cell containing a single spherical, spheroidal or ellipsoidal void. We have recently [2] obtained dissipation functions and Gurson-type models for porous sheet metals with ellipsoidal voids and anisotropic non-quadratic plasticity, including yield criteria based on linear transformations (Yld91 and Yld2004-18p) and a pure plane stress yield criteria (BBC2005). These Gurson-type models contain several parameters that depend on the void and cell geometries and on the selected yield criterion. Best results are obtained when these key parameters are calibrated via numerical simulations using the same unit cell and a few representative loading conditions. The single most important such loading condition corresponds to a pure hydrostatic macroscopic stress (pure pressure) and the corresponding velocity field found during the solution of the limit analysis problem describes the expansion of the cavity.

However, for the case of sheet metals, the condition of plane stress precludes macroscopic stresses with large triaxiality or ratio of mean stress to equivalent stress, including the pure hydrostatic case. Also, pure plane stress yield criteria like BBC2005 must first be extended to 3D stresses before attempting to develop a Gurson-type model and such extensions are purely phenomenological with no due account for the out- of-plane anisotropic properties of the sheet. Therefore, we propose a new calibration method for Gurson- type models that uses only boundary conditions compatible with the plane stress requirement. For each such boundary condition we use a spectral method to solve the limit analysis problem, using as spectral basis a newly developed Mie decomposition of incompressible velocity fields for ellipsoidal cells with confocal ellipsoidal voids, extending the well-known Lee and Mear family corresponding to the spheroidal axisymmetric case [1]. We thus obtain a series of points located on the Gurson-type yield surface and their corresponding normal directions. These points are used as input to some enhanced parameter identification method developed for anisotropic yield criteria [1] to determine the calibration of the Gurson-type models. We finally use these newly calibrated Gurson-type models to evaluate forming limits for porous sheet metals.

Some metal sheets forming processes need trimming in a final stage for achieving the net- shape specification and for removing micro-cracks and irregularities. In numerical simulation, since the exact final edge location is a priori unknown in the original metal blanket, the trimming needs to be done once the forming is finished. During the forming internal stresses are generated inside the sheet. When trimming those stresses configuration is changed to achieve equilibrium as a consequence of the material removal. In this paper a novel method for simulating the trimming is presented. The part to trim is modelled using isogeometric analysis (IGA). The new surface generated is modelled with non-uniform rational B-splines (NURBS). Due to the IGA characteristics a total geometrical accuracy and an efficient residual stresses recalculation are accomplished.

Non-Associated Flow Rule (Non-AFR) can be used as a convenient way to account for anisotropic material response in metal deformation processes, making it possible for example, to eliminate the problem of the anomalous yielding in equibiaxial tension that is mistakenly attributed to limitations of the quadratic yield function, but may instead be attributed to the Associated Flow Rule (AFR). Seeing as in Non-AFR based models two separate functions can be adopted for yield and plastic potential, there is no constraint to which models are used to describe each of them. In this work, the flexible combination of two different yield criteria as yield function and plastic potential under Non-AFR is proposed and evaluated. FE simulations were carried so as to verify the accuracy of the material directionalities predicted using these constitutive material models. The stability conditions for non-associated flow connected with the prediction of yield point elongation are also reviewed. Anisotropic distortion hardening is further incorporated under non-associated flow. It has been found that anisotropic hardening makes the noticeable improvements for both earing and spring-back predictions. This presentation is followed by a discussion of the topic of the forming limit & necking, the evidence in favor of stress analysis, and the motivation for the development of a new type of forming limit diagram based on the polar effective plastic strain (PEPS) diagram. In order to connect necking to fracture in metals, the stress-based necking limit is combined with a stress- based fracture criterion in the principal stress, which provides an efficient method for the analysis of necking and fracture limits. The concept for the PEPS diagram is further developed to cover the path-independent PEPS fracture which is compatible with the stress-based fracture approach. Thus this fracture criterion can be utilized to describe the post-necking behavior and to cover nonlinear strain-path. Fracture modeling in the stress space including mean stress contribution is also conducted and compared with M-C criterion. Strain-path effect on fracture criteria and the role of a damage parameter have been also discussed.

The modelling of material degradation due to nucleation, growth and coalescence of micro-voids is vital in sheet metal forming process due to the large deformation typically experienced by the part. Nonlocal damage modelling or nonlocal continuum is gaining a lot of interest because it is an effective approach to modelling the strain-softening, whilst avoiding the spurious localization that gives rise to strong mesh sensitivity in numerical computations. However to accurately resolve the evolving narrow bands of highly localised strain, it is necessary to use sufficient computational grids. In this paper an ALE formulation is used for modelling the localization pattern. An approach for relocating the node points is presented and explored.