Table of contents

Micro-voids of varying sizes exist in most metals and alloys. Both experiments and numerical studies have demonstrated the critical influence of initial void sizes on void growth. The classical Gurson–Tvergaard–Needleman model summarizes the influence of voids with a single parameter, namely the void-volume fraction, excluding any possible effects of the void-size distribution. We extend our newly proposed model including the multi-sized void (MSV) effect and the void-interaction effect for the capability of working for both moderate and high loading rate cases, where either rate dependence or microinertia becomes considerable or even dominant. Parametric studies show that the MSV-related competitive mechanism among void growth leads to the dependence of the void growth rate on void size, which directly influences the void's contribution to the total energy composition. We finally show that the stress–strain constitutive behavior is also affected by this MSV-related competitive mechanism. The stabilizing effect due to rate sensitivity and microinertia is emphasized.

This work presents an integrated experimental and modeling approach for examining the deformation of a pure nickel polycrystal utilizing micro-mechanical testing and a crystal-based elasto-viscoplastic finite-element model (CPFEM). The objective is to study the influence of microstructure on the heterogeneous deformation in polycrystalline materials, and to utilize a modeling framework to explore aspects of the deformation that are difficult or impossible to measure experimentally. To accomplish this, a micro-tension specimen containing 259 grains was created from a pure nickel foil material and deformed in uniaxial tension. After the deformation, the specimen was destructively serial sectioned in concert with electron back scattering diffraction, and these data were used to instantiate a CPFEM simulation. The material parameters in the CPFEM model were calibrated by matching the experimental macroscopic stress-strain response of the micro-tension specimen, and then the simulation results were compared with experimental surface deformations measured with digital image correlation. After validating the simulation results by comparing measured and predicted surface strain distributions, a parametric study of the influence of both crystallographic texture and grain morphology is presented to better understand the influence of microstructure on the development of heterogeneous deformation in the pure nickel polycrystalline material.

While several laboratories can produce 3D models of microstructure from serial sectioning or tomography, the more widespread practice is to attempt to infer 3D shapes from 2D sections of different orientations. We have developed a forward modeling approach that, given a 3D particle shape, produces statistically representative 2D sections whose projections are characterized by 2D moment invariants (MI). Since the sectioning plane is random, each particle will produce a statistical distribution of 2D moments and an ensemble of particles in a microstructure will produce its own characteristic distribution of 2D moments and can be used as a representation of the microstructure. This distribution can be represented as a point in a metric space. We use the Hellinger distance as the measure for this space, which allows us to quantify the similarity of two microstructures. Example applications include: determination of a 3D shape by computing the Hellinger distance between MI density maps derived from random 2D section micrographs and the density map database; automated detection and quantification of rafting in cuboidal microstructures; and quantitative comparison of pairs of microstructures.

The competition between free surfaces and internal grain boundaries as preferential sites for dislocation nucleation during plastic deformation in aluminum bicrystalline nanowires is investigated using molecular dynamics simulations at room temperature. A number of nanowires containing various minimum energy interfaces are studied under uniaxial compression at a constant applied strain rate to provide a broad, inclusive look at the competition between the two types of sources. In addition, we conduct a detailed study on the role of the grain boundaries to act as a source, sink, or obstacle for lattice dislocations, as a function of grain boundary structure. This work compares the behavior of bicrystalline nanowires containing both random high-angle boundaries and a series of symmetric tilt grain boundaries to further elucidate the effect of interface structure on its behavior. The results show that grain boundaries in nanowires can be preferred nucleation sites for dislocations and twin boundaries, in addition to efficient sinks and pinning points for migrating dislocations. Plastic deformation behavior at high imposed strains is linked to the underlying deformation processes, such as twinning, dislocation pinning, or dislocation exhaustion/starvation. We also detail some important reactions between lattice dislocations and grain boundaries observed in the simulations, along with the activation of a single-arm source. This work suggests that the cooperation of numerous mechanisms and the structure of internal grain boundaries are crucial in understanding the deformation of bicrystalline nanowires.

The determination of the volume fraction of interfacial layers is very significant for assessing the quantitative relationship between the microstructure and macroscopic physical properties of complex multiphase materials. In this work, based on a three-phase composite structure, an approximate analytical model for the volume fraction of interfacial layers around ellipsoidal aggregate particles is presented in detail. To verify the accuracy and reliability of the derived analytical model, a numerical model is introduced by means of random packing of polydispersed ellipsoidal aggregate particles, in which the relative spatial position between an arbitrary point and an ellipsoidal particle is precisely and conveniently determined. With the analytical and numerical models applied, the dependence of the volume fraction of interfacial layers on various factors, such as the particle shape, the volume fraction and the maximum particle size of aggregates, and the thickness of the interfacial layers, is evaluated. Furthermore, the results from the analytical model and the numerical model with these factors are compared. It is found that the theoretical results are favorably consistent with the simulated results.

Wide-ranging inter-atomic potentials are necessary for modeling many problems in material physics that involve multiple atomic environments and phases. The domains of thermodynamic and mechanical stability of embedded-atom-type potentials are examined for the cubic phases. It is shown that the choice of the pair potential is critical in determining the domain of stability of embedded-atom-type potentials. In particular, the Lennard-Jones embedded-atom potential is shown not to stabilize the bcc phase. A simple four-parameter universal equation of state-based embedded-atom potential is shown to have a domain of stability for all the cubic phases and to reproduce the high-pressure equation of state. A model phase diagram for the three cubic phases is presented. This potential is fitted to 17 elemental systems and found to be able to reproduce both the elastic constants and the ground state crystalline structure. For elements with a low degree of elastic anisotropy, this potential can also reproduce the high-pressure behavior.

Based on experiments and first-principles calculations, a Ni–Al–Re system embedded atom method (EAM) potential is constructed for the γ(Ni)/γ'(Ni₃Al) superalloy. The contribution of the inner elastic constants is considered in the fitting of Re with a hexagonal close-packed structure. Using this potential, point defects, planar defects and lattice misfit of γ(Ni) and γ'(Ni₃Al) are investigated. The interaction between Re and the misfit dislocation of the γ(Ni)/γ'(Ni₃Al) system is also calculated. We conclude that the embedding energy has an important effect on the properties of the alloys, such as the planar fault energies of Ni₃Al, by considering the relationship between the charge transfer calculated from first-principles, the elastic constants of Ni₃Al and the host electron density of the EAM potential. The multi-element potential predicts that Re does not form clusters in γ(Ni), which is consistent with recent experiments and first-principles calculations.

This paper investigates a recently developed elasto-plastic constitutive model. For this purpose, the model was implemented in a commercial finite element code and was used to simulate the cross-die deep drawing test. Deep drawing experiments and numerical simulations were conducted for five interstitial-free steels and seven dual-phase (DP) steels, each of them having a different thickness and strength. The main interest of the adopted model is a very efficient parameter identification procedure, due to the physical background of the model and the physical significance of some of its parameters and state variables. Indeed, the dislocation density, grain size and martensite volume fraction explicitly enter the model's formulation, although the overall approach is macroscopic. For the DP steels, only the chemical composition and the average grain sizes were measured for the martensite and ferrite grains, as well as the martensite volume fraction. The mild steels required three additional tensile tests along three directions, in order to describe the plastic anisotropy. Information concerning the transient mechanical behavior after strain-path changes (reverse and orthogonal) was not collected for each material, but for only one material of each family of steels (IF, DP), based on previous works available in the literature. This minimalistic experimental base was used to feed the numerical simulations for the twelve materials that were confronted to deep drawing experiments in terms of thickness distributions. The results suggested that the accuracy of the numerical simulations is very satisfactory in spite of the scarce experimental input data. Additional investigations indicated that the modeling of the transient behavior due to strain-path changes may have a significant impact on the simulation results, and that the adopted approach provides a simple and efficient alternative in this regard.

Bulk properties of hcp-Ti, relevant for the description of dislocations, such as elastic constants, stacking faults and γ-surface, are computed using density functional theory (DFT) and two central force embedded atom interaction models (Zope and Mishin 2003 Phys. Rev. B 68 024102, Hammerschmidt et al 2005 Phys. Rev. B 71 205409). The results are compared with previously published calculations, except pair potential calculations, which are not appropriate for the description of the metallic bond. The comparison includes N-body central force (NB-CF) and N-body angular (NB-A) empirical potentials, tight-binding approximation to the electronic structure (TB), DFT pseudopotential (DFT-P) and all electron (DFT-A) calculations. None of the considered interaction models are fully satisfactory for the description of these properties. In particular, NB-CF, NB-A and TB interaction models are unable to describe the softening of the easy prismatic γ-surface leading to the appearance of a metastable stacking fault, as evidenced in all the DFT calculations. Most often, when the basal stacking fault excess energy is underevaluated, this leads to an inversion of the energetic stability between the I₂ basal and the prismatic easy stacking faults. Even the DFT-pseudopotential calculations need to be improved regarding the description of the shear elastic constants. The implications of these results on the core structure and gliding properties of the $a/3\,\langle1 1\, \bar{2}\, 0\rangle$ screw dislocation are analyzed. The calculated dissociation lengths into Shockley partials in both the basal and prismatic planes for the different models compare well with the measured ones in the corresponding simulations of the dislocation core structure when available. Finally, the Peierls stress is also evaluated using the Peierls–Nabarro model and compared with the experimentally measured one.

The estimation of stress at a continuum point from the atomistic scale requires volume averaging over a region that contains this point. A hypothesis is put forth to obtain a lower bound for the size of this region based on an analogy to the Ising model. This hypothesis is tested on copper using two classical elasticity problems.

Grain boundaries (GBs) can play an important role in governing the mechanical behavior and damage evolution of a material during both quasistatic and dynamic loading. However, the general consensus of the shock physics community has been that minute details about the GB structure should not affect the response of a material to dynamic loading. In this paper, we present results of molecular-dynamics simulations investigating whether or not small changes in boundary structure are 'recognized' by the shock wave and can in turn affect the spall strength of a material. As a test case, we study a Σ11 asymmetric tilt GB in copper with an ordered and a disordered structure. The results are also compared with face-centered-cubic single crystals which correspond to the crystal orientations of the two grains in the bi-crystal. These results show that ordered and disordered boundaries undergo dissimilar amounts of plastic deformation during shock loading, which leads to spall strengths that vary by 12%, likely due to differences in the GB structures.