A structural-thermal coupled modeling approach on the formation of adiabatic shear bands in steel sheet blanking process

Adiabatic shear banding reflects an unstable and dynamic plastic deformation mechanism occurring at high strain and strain rates which is strongly conjugated to fracture. Current work carries out a numerical study on the initiation and development of adiabatic shear bands (ASBs) in blanking process of AISI 4340 steel sheet. A structural-thermal coupled finite element analysis is developed in LS-DYNA software by implementing a thermo-viscoplastic flow rule for material plasticity and a damage criterion considering dynamic failure. The numerical simulations are focused on capturing ASB genesis through intense shear localization by evincing strain instability. Also, the evolution of ASB mechanism is investigated, aiming to contribute a stage-by-stage propagation and highlight its connection to dynamic failure. Further, the effect of ASB temperature and strain field on fracture is analysed, while the influence of strain/strain rate hardening and thermal softening on strain instability, peak force and the blanked surface is studied. The results revealed an S-shaped ASB due to severe shear localization and significant temperature increase, leading to dynamic recrystallization around punch-die corners and reacting to strain instability and dynamic. Finally, high magnitude thermal softening during ASB development resulted in earlier ASB generation and reduction of the peak blanking force, while further it decreased shear zone expansion and increased fractured length in the blanked surface.


Introduction
Plastic deformation under low and intermediate strain/strain rate levels is characterized by stable and homogenous evolution, where slipping and twinning are the dominant mechanisms.In contrast, unstable and catastrophic mechanisms dominate at higher strain/strain rates, such as adiabatic shear banding (ASB), causing strain instability, leading to uncontrollable and dynamic failure.ASB is initially manifested via intense shear strain localization along narrow bands, while microstructural and thermal softening occur due to temperature rise as shear bands propagate, facilitating fracture initiation and evolution.Due to high strain and strain rate, the deformation energy is converted into internal adiabatic heat, which reacts to significant temperature rise, causing thermal softening and phase transformation phenomena such as dynamic recrystallization (DRX), dynamic recovery and rotational dynamic recrystallization.Thus, ASBs initially form as deformed bands, while at next evolve to transformed bands, reflecting in that way a thermomechanical instability whose initiation is attributed to the superiority of thermal softening against strain/strain rate hardening.
Due to its strong connection to dynamic failure, the ASB mechanism has been studied regarding its influence on peak force and fracture characteristics in case of adiabatic sheet blanking process.Winter et al. [1] carried out a parametric analysis of clearance, punch velocity and impact energy on ASB formation in blanking of 22MnB5 hardened steel sheet, revealing an S-shaped shear band formulation, while also higher velocity and lower clearance increased material sensitivity against ASB occurance.Further, Schmitz et al. [2] revealed that shear bands expand along S-shaped traces in case of adiabatic blanking of high-strength steels, also obtaining that material strain rate hardening behavior strongly affects the width and hardness of ASB.Also, ASB formation in blanked AA6082-T6 sheets has been studied experimentally and numerically to capture the shear strain field, showing an intense shear localization around punch-die corners [3].In addition, burr formation on sheared surface has been analyzed numerically in ABAQUS in case of AA6082-T6 blanked sheets, revealing a severe strain concentration around punch corner, while higher punch radius and clearance increased burr height [4].Fazily et al. [5] studied the damage on sheared edge of blanked AZ31B magnesium alloy sheets aiming to capture the influence of clearance and temperature.Microstructural observations and microhardness tests on fractured surface showed that higher temperature results in less sheared edge defects and microcracks.Further, Chen et al. [6] indicated a white-etching trace along ASB path of blanked surface, showing phase transformation as highly elongated fine subgrains occurred inside ASB.Finally, Sidhu et al. [7] studied numerically the cut-edge profile of blanked surface highlighting the importance of implementing an adaptive remeshing technique during finite element (FE) modeling due to severe mesh distortion along ASB, while Song and Jun [8] developed a ductile fracture initiation criterion model examining shearing fracture along blanked surface.
This study investigates numerically the evolution of ASB mechanism during AISI 4340 steel sheet blanking process.In order to evaluate the macroscopic characteristics of ASB and capture their influence on the induced strain instability and failure propagation, a structural-thermal coupled FE modeling is developed in LS-DYNA by implementing a thermo-viscoplastic material model which allows to capture properly the thermomechanical behavior of the phenomenon, while further a damage criterion is utilized aiming to capture the relation between ASB stages and failure initiation.Finally, a numerical analysis on the effect of strain hardening (SH), strain rate hardening (SRH) and thermal softening (TS) magnitudes is conducted by assessing their influence on both material behavior and related damage, aiming to highlight their impact on peak blanking force and critical strain instability.

Test configuration
Current work studies numerically the macroscopic characteristics of ASB mechanism evolution during adiabatic blanking of AISI 4340 steel sheet.The case study of this work consists of 4 mm thick steel sheet of 120 mm diameter, blanked by a punch of 50 mm diameter with 0.25 mm punch-die clearance.In addition, a blankholder of the same clearance completes the test configuration, while the half domain is studied due to its cylindrical axisymmetric geometry as shown in Figure 1 which depicts the derived FE model developed in LS-DYNA software.Finally, a constant punch velocity of 3 m/s is applied securing adiabatic blanking conditions [1,2].

Finite element modeling
For the purpose of numerical investigation, a structural-thermal coupled FE model is developed in LS-DYNA where the geometry is initially generated regarding the half computational domain due to cylindrical axisymmetric configuration.At next, a Lagrangian variable density FE mesh is implemented until 10 μm sizing, while 2D solid elements are adjusted considering the physical half-plane around yaxis of symmetry.Also, Flanagan -Belytschko stiffness form formula is implemented under an 0.1 hourglass coefficient in order to prevent from hourglass deformation due to severe mesh distortion inside ASB region, which would result in zero deformation energy modes and volumetric blocking causing computational instabilities.Regarding material modeling, a thermo-viscoplastic Johnson-Cook (JC) constitutive equation is implemented for plastic flow stress computation for the needs of the thermomechanical coupled analysis.JC formula considers the effect of both strain hardening (SH) and strain rate hardening (SRH) representing the first and second terms in Equation 1 respectively, while also thermal softening (TS) is further considered regarding the third term in JC formula which utilizes homologous temperature in order to assess its effect on plastic flow stress.In specific, SH material behavior is described via A-B-n coefficients, SRH with C-parameter and TS with m-parameter.In addition, a JC thermo-viscoplastic damage criterion is implemented in order to assess dynamic failure initiation and progress by predicting strain failure considering the effect of SH, SRH and TS via D1-D2-D3-D4-D5 damage coefficients as shown in Equation 2.Moreover, SH effect on strain failure requires the computation of effective stress and pressure which is assessed through a linear polynomial equation of state utilizing material bulk modulus.Further, the JC criterion predicts failure occurance when damage parameter D which is defined in Equation 3, becomes equal to 1 eroding that way the respective element from calculations.Therefore, micro-voiding can be predicted and following cracking initiation and propagation allowing to capture the connection between ASB evolution and dynamic and catastrophic failure.
In addition, a thermal isotropic material behavior is considered for AISI 4340 steel material by assuming its density, specific heat and thermal conductivity.In that way, the thermal diffusivity is assessed during the calculations of FE thermal solver which computes the temperature field from heat conduction equation.The respective mechanical and thermal material properties are listed in Table 1 according to open literature data.Finally, the necessary boundary conditions are implemented by adjusting static and dynamic friction coefficients of 0.2 and utilizing 2D surface-to-surface and singlesurface contact algorithms preventing from any penetration between undeformable bodies and sheet, and between crack edges respectively.

Structural-thermal coupling
For modeling the thermomechanical behavior of ASB mechanism, a structural-thermal coupled FE analysis is developed.For this purpose, the mechanical behavior of material is approached via a thermoviscoplastic JC plastic flow rule, while an isotropic thermal behavior is considered while solving heat conduction equation.In addition, a thermo-viscoplastic JC damage criterion is implemented in order to capture the connection between ASB and dynamic failure.Thus, structural-thermal coupling is achieved by assuming a 0.9 Taylor-Quinney coefficient representing the fraction of plastic strain energy converted to internal heat as high strain rate provides a heat production rate via produced internal work, which is greater than the respective heat diffusion rate representing so adiabatic conditions.Therefore, numerical computations of structural and thermal FE solver are coupled between each other during numerical solving due to both thermomechanical material modeling and strain energy -internal heat conversion in real computation time as Figure 2 illustrates.

ASB macroscopic characteristics
The numerical results of FE simulations revealed a S-shaped ASB forming along sheet thickness and between punch-die clearance.Figure 3 depicts the shear strain and temperature fields at different punch displacement states, highlighting the severe shear localization along ASB and reflecting that ASB initially forms as deformed band, generated at first around punch-die corners and expanding along maximum shear direction.Following, the increase in punch displacement results in greater deformation energy and in consequence greater internal heat which causes significant temperature increase inside ASB due to adiabatic conditions, reacting to thermal softening.In fact, specific areas inside ASB subject to DRX at final stage of blanking, as temperature overcomes DRX temperature point which is about 723 K.Then, micro-voiding and following cracking are captured, leading to dynamic failure until final fracture at about 2 mm punch displacement.The surrounding matrix outside of ASB seems less affected revealing lower strain and temperature levels compared to the ones captured inside ASB. Figure 4 ensures the above illustrating transverse distributions of shear strain and temperature from ASB centreline at final stage, showing that temperature decreases far away from ASB as shear deformation is localized along ASB, and therefore plastic work magnitude is significantly higher there.Further, the transverse shear strain distribution reveals a ASB width of about 160 μm considering critical shear strain of 1.45 which reflects strain instability point and in consequence ASB initiation for AISI 4340 steel.On the other hand, Figure 5 depicts the longitudinal temperature fluctuation along ASB as punch displacement progresses, revealing that points near punch-die corners (A and F) initially show a higher temperature increase rate due to severe shear strain and produced internal heat, without however reaching maximum temperature as fail earlier than others.In contrast, intermediate points inside ASB (B-E) reveal a greater temperature concentrating higher plastic work and internal heat.Therefore, ASB interior microstructure subjects to significant thermal softening which facilitates cracking propagation leading to dynamic failure.Finally, Figure 6 depicts the variance in blanking force with punch displacement showing a peak force of about 70 kN at punch stroke of 0.7 mm, after which force seems to slightly decrease as microstructure inside ASB softens due to increased temperature, facilitating so micro-voiding.Then, dynamic failure occurs via cracking propagation revealing a sharper drop in blanking force at about 1.5 mm punch displacement.

Effect of plasticity model
In this last part, the influence of plasticity model on peak force, ASB formation and fracture surface is evaluated examining the effect of SH, SRH and TS terms on JC constitutive relation for plastic flow stress and JC damage criterion.The three examined cases consist of a single plasticity model (SH), a viscoplastic one (SH+SRH) and a thermo-viscoplastic one (SH+SRH+TS) which implements the full form of JC model.Figure 7a shows that TS reveals slightly lower peak force facilitating failure initiation and propagation, while Figure 7b ensures that the consideration of TS effect during ASB modeling reacts to lower critical strain for deformation instability, as full model (SH+SRH+TS) reveals a critical strain of 1.5 compared to other cases which show one of 1.7.Therefore, TS effect highlights an earlier ASB formation which reflects strain instability due to the superiority of TS against SH and SRH.Finally, Figure 8a depicts the blanked surface profiles for the three cases, while Figure 8b shows TS effect reacted to lower sheared zone length and greater fractured zone one.

Conclusions
In current work, a structural-thermal coupled FE analysis was developed in order to investigate ASB formation and its macroscopic characteristics during adiabatic blanking of AISI 4340 steel sheet.The aim of the study was focused on analyzing the macroscopic behavior of ASBs regarding their stage-bystage evolution, strain and temperature fields, blanking force and strain instability leading to dynamic failure.Also, the effect of plasticity flow rule was investigated in order to assess the influence of TS on ASB initiation, peak force and blanked surface profile.The results revealed a 160 μm wide S-shaped ASB forming along sheet thickness and through punch-die clearance, by being initially manifested via intense shear localization around punch-die corners and propagating along maximum shear direction.The highly localized shear along ASB led to significant temperature rise reacting to high magnitude TS and facilitating dynamic failure.Further, DRX occurred at specific areas inside ASB and at the center of its length due to the highly increased temperature, as ASB edges did reveal high enough initial temperature but failed earlier without reaching DRX temperature.Also, a critical strain of 1.45 was revealed due to the superiority of TS against SH and SRH, resulting in strain instability and sharp drop in blanking force.Finally, the consideration of TS during ASB modeling revealed an earlier ASB genesis and in consequence lower peak blanking force, while it reduced sheared zone length and increased the expansion of fractured surface.

Figure 3 .
Figure 3. Shear strain and temperature fields inside ASB at different punch displacement states.

Table 1 .
AISI 4340 steel material mechanical and thermal properties.