Yield Locus Research Articles

Mechanism of microstructure and texture evolution during hot rolling of pure Mg and Mg-0.2%Ce alloy

ABSTRACT The extruded samples of pure Mg and Mg-0.2%Ce alloy were subjected to a 90% reduction in thickness at 250°C during hot rolling. The microstructure, texture, and mechanical properties of the hot-rolled samples were evaluated. The microstructural evolution shows the presence of shear bands in Mg-0.2%Ce alloy at an angle of 30-35° concerning the normal direction and no such bands are observed in pure Mg. Upon annealing the samples at 400°C for one hour, it is observed that the grain size of Mg-0.2%Ce is smaller than pure Mg indicating that the precipitates of Ce arrest grain boundary mobility. The ex-situ EBSD microstructure analysis results show a higher change in the value of α33 components after annealing for pure Mg compared to Mg-0.2%Ce alloy suggesting the precipitates of Mg12Ce stabilises the pyr. <c + a > dislocations. The basal texture is observed in both samples after hot rolling. The experimental texture was simulated using the visco-plastic self-consistent (VPSC) modelling where it is observed that the initial extruded texture is favourable for the higher activity of pyr. <c + a > dislocation and extension twinning in Mg-0.2% e alloy. Further, the yield locus shows that Mg-0.2%Ce alloy shows relatively lower anisotropy compared to pure Mg. The yield strength and UTS of the pure Mg are higher than the Mg-0.2%Ce alloy which is attributed to the relatively more dislocation-dislocation interaction in pure Mg compared to Mg-0.2%Ce alloy resulting in the lower mean free path of the dislocations in pure Mg.

Numerical springback prediction for high-strength aluminum alloys based on the sheet metal upsetting test

Springback prediction continues to play a special role in the process design of sheet metal forming processes. During the forming process, elastic energy is stored in the sheet metal, which is released after the tool is opened. The dimensional accuracy and the function of the component in particular can be negatively affected by this. For this reason, the springback is predicted by means of numerical modeling in order to improve the process design. The simulation accuracy depends primarily on the used material model to map the stress-dependent material behavior and the quality of the experimental input data. High-strength aluminum alloys, which have a distinctive springback behavior, have a slightly pronounced tensile-compressive asymmetry. Since tensile and compressive stresses often occur in sheet metal forming processes, the consideration of this effect can lead to an improvement in springback prediction. Besides modeling the yield locus curve for describing the yield strength in the plane stress area, the yield curve data is also relevant for determining the strain hardening behavior. The work hardening is usually characterized by the tensile test or the hydraulic bulge test, which is used to describe the material behavior in the tensile stress state. A promising experimental method for the analysis of the material in the uniaxial compressive stress state is the sheet metal upsetting test. In addition to a local characterization of sheet metal materials, this test also enables the investigation of the material behavior at significantly higher plastic strains than in the tensile test. Thus, in this contribution it is examined to what extent the sheet metal upsetting test is suitable for improving the springback prediction quality of material models in sheet metal forming processes.

Exploring mechanical behavior at interfaces of laser powder bed fusion (LPBF) deposits on wrought Inconel 718: an indentation-based approach

PurposeThis study used an indentation-based mechanical testing framework for the mechanical characterization of laser powder bed fusion (LPBF) processed Inconel 718 on a wrought Inconel 718 substrate. The purpose of the paper is to investigate the effectiveness of the indentation-based approach for localized mechanical evaluation.Design/methodology/approachThe LPBF-processed wrought substrate was sectioned into three sections for microstructural and mechanical characterization. A 3D heat source model was used for the thermal analysis of the interface region. The developed interface region is probed using the Knoop hardness indenter in different orientations to determine the textural anisotropy and mechanical behavior of the region.FindingsLPBF process develops a melted interface zone (MIZ) at the deposition-substrate interface. The MIZ exhibited a coarse grain structure region along with a larger primary dendritic arm spacing (PDAS), signifying a slower cooling rate. FE modeling of the LPBF process reveals heat accumulation in the substrate along with intrinsic heat treatment (IHT) induced due to layer-wise processing. The obtained yield locus shows strong anisotropy in the deposition region, whereas reduced anisotropy with a nearly uniform ellipse locus for the MIZ regions. This reduced anisotropy is attributable to IHT and heat accumulation in the substrate.Originality/valueAn alternative localized mechanical characterization tool has been investigated in this work. The approach proved sensitive to thermal variations during LPBF processing in an isolated region which extends its suitability to variable geometry parts. Moreover, the approach could serve as a screening tool for parts made from dissimilar metals.

Straightforward identification of flow curve and yield locus parameters from three-point bending experiments

Material testing and modeling is one of the cornerstones of virtual analysis of sheet metal forming processes. However, it is also becoming more and more relevant for incoming goods inspection, especially in view of the increasing amount of recycled material or frequent changes of suppliers, e.g. to provide workers, processes and/or process models with relevant information about a new batch of material. Efficient material testing and straight-forward test evaluation is essential for this. The flow curve and yield locus are central to describe the forming behavior of sheet metal materials. However, the parameters of the associated models are currently determined in various tests on different systems and with special sample geometries. The present work presents a methodology that allows the determination of a set of flow curve and yield locus parameters from three three-point bending tests only. The evaluation routine does not require finite element simulation and processes only the force-displacement information of the bending tests, which also places low demands on the measurement technology. The results were compared with a conventionally determined parameter set using a validation test, and the results are of reasonable quality, especially considering the minimal effort involved.

A flexible yield criterion for strength modeling from biaxial compression to biaxial tension

Accurate strength modeling from equi-biaxial tension (EBT) to equi-biaxial compression (EBC) is critical for the plastic behavior prediction covering the wide-range of stress triaxiality encountered in sheet metal forming. To date, however, few yield criteria are available that can precisely model the initial yield and hardening behavior under six typical stress states between EBC and EBT, simultaneously. Furthermore, there is still a lack of a unified yield criterion for accurate strength modeling across various stress state ranges. To address the issues, a theoretical framework for constructing yield criteria dependent on stress states is provided and a new analytically described isotropic yield criterion is presented in this study. The flexibility in terms of the yield locus and application range is thoroughly explored to make the new yield criterion general. Subsequently, the isotropic yield criterion is extended into an analytically described anisotropic-asymmetric yield criterion. Furthermore, the extended yield criterion is applied to capture the initial yield behavior of DP980, AA5754-O, and AZ31 sheets, and the strain hardening behavior of QP1180 sheets at various stress states ranging from EBC to EBT along different loading directions. The predicted results from the extended criterion agree well with the corresponding experimental findings. The applications demonstrate that the proposed anisotropic-asymmetric yield criterion can effectively model the initial yield and hardening behavior of HCP, BCC, and FCC metal sheets under EBT, EBC, uniaxial tension (UT), plane strain tension (PST), shear (SH), and uniaxial compression (UC) in an analytical way.

A homogenized anisotropic constitutive model of perforated sheets for numerical simulation of stamping

Perforated sheets exhibit strong anisotropy related to the arrangement of holes during plastic deformation, which poses significant challenges for accurate prediction of the macroscopic plastic behavior in stamping. Addressing this, unit cell simulations were conducted to determine the homogenized yielding and hardening behaviors of perforated sheets with hexagonal or square arrays of circular holes under in-plane loading conditions. The local deformation mode, which determines the macroscopic anistropy, is unveiled. A mechanism-motivated homogenized yield criterion was proposed based on the local deformation modes, which provides a concise yet unified approach to modeling complex material anisotropic behavior with high accuracy. Additionally, a mixed hardening strategy was developed to capture the evolution of yield loci in term of size and shape. The proposed constitutive model demonstrates precise predictions of flow stress variations and the apparent r-value with loading angles during uniaxial tension. Furthermore, it successfully forecasts two distinct types of earing profiles in the deep drawing of perforated sheets with square arrays of circular holes at different hole fractions. This modeling approach provides a feasible way for predicting the deformation behavior of perforated sheets during stamping with high computational efficiency.

Towards improved description of plastic anisotropy in sheet metals under biaxial loading: A novel generalization of Hill48 yield criterion

Lightweight design and development of automobiles are strongly dependent on lightweight high-strength sheet metals. An accurate prediction of anisotropy and yield surface evolution of these materials under different sampling directions of biaxial tension (BT) is a necessary condition for the numerical analyses of stamping forming. In this work, the Hill48 model considering the principal stress direction is generalized to describe the anisotropic evolution and the yield loci on the normal and diagonal planes. The material parameters of the generalized M-Hill48 model (GM-Hill48) have analytical form and can be calibrated by the yield stresses and r-values expressed by the continuous equivalent plastic strain (EPS). A quadratic function interpolation method based on the near-plane strain (NPS) stress is established to control the yield locus under different plane stress states. In addition, a method for predicting the yield loci in arbitrary sampling directions under BT is proposed by tensor coordinate transformation. Different from the traditional model which can only determine material parameters by using equi-biaxial tension (EBT) or NPS stress along the rolling direction (RD) and transverse direction (TD), the yield stresses of BT in different sampling directions can be incorporated into the generalized model. The predictive capability of the GM-Hill48 model is verified by capturing the continuous evolution of yield stresses and strain for DP590 and AA6016-T4 materials. The convexity condition of the established modified model is given and discussed. Finally, the advantages of new model are further expounded in terms of the prediction accuracy and identified parameters compared with the advanced yield models.

Characterization and modeling of biaxial plastic anisotropy in metallic sheets

The anisotropic behavior of cold-rolled sheet metals has been extensively studied, typically characterized by uniaxial loading tests in different directions to determine yield strengths and plastic flow (Lankford r-values). However, biaxial principal stress states often focus solely on yield loci in the RD/TD (rolling/transverse) directions, with limited studies on other loading directions. This study analyzes the relationship between the principal stress yield loci and the material principal anisotropic stress directions based on the Hill48 yield function. Biaxial tensile tests are conducted on DP590 high-strength steel using cruciform specimens cut in various directions different from the sheet RD/TD directions. The evolution of the anisotropic yield locus and plastic flow of DP590 under biaxial tensile directions beyond the traditional RD/TD anisotropic directions is revealed. Furthermore, a modified Hill48 model that considers any principal stress direction of loading is proposed, accurately describing the continuous evolution of equi-biaxial tension stress, near-plane strain stress, and plastic flow direction for different principal stress directions of loading. The issues of failing to predict plastic flow under biaxial loadings in the original Hill48 model, and the degraded representation of existing constitutive models when accounting for out-of-plane anisotropy are addressed by decoupling the relationship between anisotropic parameters and stress state. In addition, the proposed calibration strategy of anisotropic parameters, using experimental data from various principal stress directions of loading, effectively captures the anisotropic evolution caused by changes in principal stress directions. Comprehensive evaluation and verification of the plasticity model should consider yield locus for any principal stress directions of loading, and also the normal and shear planes.

Study on the Yield Surface of a Fibre-Reinforced Stabilised Soil – Effect of the Number of Loading Cycles

Cyclic loading may induce changes in the geomechanical behaviour of materials that should be characterised. This work studies the impact of the number of loading cycles on the mechanical behaviour of a fibre-reinforced stabilised soil focusing on its behaviour before failure (yield surface). To this end, an experimental testing program based on triaxial tests was performed on samples not subjected to a cycling loading stage, as well as on samples previously subjected to a cycling loading stage varying the number of loading cycles from 1,000 to 100,000. The results were studied in terms of the accumulated permanent axial strain and the yield surface of the composite material. It was observed that increasing the number of loading cycles led to a rise in the accumulated permanent axial strain and in the undrained resilient modulus. The results also showed an expansion of the yield surface during the first 1,000 loading cycles (the yield occurs later due to the partial mobilization of the tensile strength of the fibres during the cyclic stage) but its shape is maintained. The results also showed a progressive reduction in the yield loci with the increase in the number of loading cycles, reflecting the greater degradation of the solid matrix induced by the accumulated permanent axial strains.

Investigation on the biaxial tensile testing method for metal foil using cruciform specimen

The assessment of mechanical properties of metal foil under complicated stress states poses a considerable challenge, requiring the development of new testing methods and the optimization of new specimen geometry. In this research, the biaxial tensile method and specimen shape were designed and optimized by using simulation and experiment. It is determined that the strain measurement area can be suggested as the central area of 0.6 to 0.8 times the arm width. The influence of different parameters on the tensile results of cruciform specimens was comprehensively evaluated by finite element method and multi-factor analysis. The results indicate that the number of slits markedly impacts the stress–strain uniformity and shear stress in the central region, followed by the slit length. The effect of the arm width and the slit width is comparable, more influential than the corner radius. According to the analyzed results and application requirements, a four-axis independently driven biaxial tensile test machine for small scale samples was fabricated. During the biaxial tension, the center point offset of the specimen remains within ±0.01 mm. The displacement and load synchronization errors do not exceed 0.01 mm and 50 N, respectively, facilitating the precise control of four-axis synchronization. Conclusively, cruciform specimens featuring diverse geometric characteristics were designed for industrial pure titanium, 304 stainless steel, and Inconel 718 superalloy with thickness of less than 0.3 mm. The biaxial tensile tests were performed to delineate the yield loci, revealing notable anisotropy and size effect. The validation confirms the suitability of the testing method and optimized cruciform specimens for conducting biaxial tensile mechanical properties testing on metal foils characterized by diverse types and thicknesses.

Objective texture evaluation of cosmetic sericite powders mixed with oil using constant-volume shear cell tester

Although sensory evaluation is often used to evaluate cosmetic powder textures, such evaluations are problematic because they are subjective and depend on human senses. Consequently, an objective evaluation is highly desired. We therefore report herein the use of a constant-volume shear tester to objectively evaluate the physical properties of a cosmetic powder. The goal of the study is to detect the differences in the physical properties of powders, which is done by applying a constant-volume shear test to oil-wet powders of differing textures mixed with dimethicone or squalane. Differences between dimethicone and squalane mixtures appear in the stress relaxation ratio (softness), the shear cohesion (moist feeling), the internal friction coefficient for friction (for normal stress of <10 kPa) between powder beds (smoothness), and the dynamic friction coefficient for friction between powder beds. Although the oils presented a similar degree of the powder yield locus, the shape of the powder yield locus indicates the state of the powder beds. The results of the study show that constant-volume shear testing can be used to objectively evaluate oil-wet powder textures.

Modeling the anisotropy evolution in sheet metals with heterogeneous properties

The adoption of local heat treatments to effectively modify the material behavior is an interesting solution for improving the formability limits of sheet metals during complex forming processes. Being the Finite Element approach the most effective way to design the material modification, in this study we develop a comprehensive constitutive framework to describe the spectrum of plastic responses associated with different levels of annealing, while considering the effect of the anisotropy.Both changes of the flow stress and the anisotropy with the level of annealing are modeled using sigmoidal functions and introduced in a metal plasticity anisotropic model (Hill48). This approach provides a constitutive framework that, relying on a limited number of experimental characterization tests, allows to predict the evolution of the yield locus according to the level of annealing experienced by the material during the heat treatment. The proposed approach revealed to be an effective tool for modeling the spectrum of heterogeneous mechanical responses, particularly valuable, for instance, in the context of local heat treatments, such as laser-based methods or welding processes. It allows to capture the material behavior in terms of R-values distribution, not only in the region irradiated by the laser spot but also in the transitional region. The detailed hybrid numerical/experimental methodology allows to plug-in any anisotropic plasticity model, making the constitutive framework extremely versatile and needing a very limited number of tests. The calibration of the model from experiments and the accuracy of the predictions are thoroughly discussed.

Yield locus and texture evolution of AA7475-T761 aluminum alloy under planar biaxial loading: An experimental and analytical study

AA7475 aluminum alloy is used as a structural material in aerospace and automobile applications where complex loading conditions are applicable. The material properties under multi-axial loading are recommended for efficient component design. Hence, the mechanical behaviour of AA7475-T761 aluminium alloy was investigated through planar biaxial tensile tests. The yield locus evolution and plastic strain direction were measured at higher plastic strain values (up to 7 %) at various load ratios. The yield loci were constructed and compared with existing yield criteria. Yld2000–2d yield criterion demonstrated accurate predictions with a deviation of approximately 1 %, highlighting its effectiveness in capturing the yield behavior of AA7475. Microstructure analysis using Electron Backscatter Diffraction (EBSD) was conducted to understand the misorientation evolution under the multi-axial loading. Bulk-texture analysis was performed using X-ray diffraction method. Texture analysis revealed that uniaxial deformation favoured the development of Cube and Inverse-Copper textures, while biaxial deformation yielded split Inverse-Goss texture formation. Fractography study shows very different fracture surfaces of biaxial samples compared to uniaxial samples. Overall, this study contributes to a comprehensive understanding of the yield behavior, microstructure, and texture evolution of AA7475-T761 aluminium alloy under different loading conditions at very large strains.

Investigation of the influence of plane strain constrained anisotropic plastic flow on the localized necking prediction

PurposeThe purpose of this manuscript is to investigate the influence of the satisfying of plane strain conditions on the prediction of the localized necking and to evaluate this effect by the different hardening models.Design/methodology/approachHigh-order anisotropic Drucker yield function, two types of hardening models, namely Hollomon power and Voce saturated, and the modified maximum force criterion (MMFC) are employed to predict the forming limit strains of AA3104-H19 alloy. Two identification methods, namely conventional and plane strain constrained, are applied and forming limit diagrams of the material are predicted by the incorporation of the anisotropic Drucker criterion and the hardening models into the MMFC for both calibration methods.FindingsThe enhancement in the prediction accuracy of the forming limits provided by the implementation of the plane strain constrained method is strongly dependent upon the selected hardening model type in the MMFC. About 18% improvement in the prediction of the biaxial limit strains is provided via Hollomon power law hardening, whereas the opposite result is occurred in case that the Voce saturated hardening law is used, and the predictions match with the experimental data only in the plane strain point and its surroundings.Originality/valueThe plane strain constrained identification method precisely predicts the location of the plane strain point on the yield locus and also any yield stress or anisotropy coefficient in the plane strain state is not required during the calibration, therefore the method can reduce the number of the required experiments for the constitutive characterization, and it will be attractive for both academy and industry. Additionally, the improvement in the prediction of the biaxial forming limits can be provided by applying of this method along with the appropriate hardening law.

Biaxial tensile behavior of CoCrFeNi high-entropy alloy under dynamic and proportional loadings

The dynamic failure behavior of CoCrFeNi High-Entropy Alloy (HEA) under plane biaxial stress was investigated in detail. The dynamic biaxial tensile tests were conducted using an Electromagnetic Biaxial Split Hopkinson Tensile Bar (EBSHTB) system. For comparison, the quasi-static uniaxial and biaxial tensile tests, as well as dynamic uniaxial tensile tests, were performed respectively. A cruciform specimen suitable for large plastic deformation was designed and employed in the experiments. The Finite Element Method (FEM) verified that the improved cruciform specimen could satisfy the basic requirements. The feasibility of the proposed specimen was further confirmed through loading tests. Finally, the quasi-static and dynamic yield loci of the HEA in the first quadrant of the principal stress space were plotted. The results indicate that the alloy exhibits obvious strain hardening effect and strain rate strengthening effect, the yield locus and plastic work contours can be accurately described by Hill’48 criterion.

Anisotropic-asymmetric mechanical behaviour for an Mg-Gd-Y alloy under various temperatures: Experiment and modelling

The study focuses on the anisotropic-asymmetric behaviour of an Mg-Gd-Y alloy at the temperature range of 25∼300 °C. The mechanical experiments were carried out, including the uniaxial tension and compression specimens along rolling direction (RD), diagonal direction (DD), and transverse direction (TD). The deformation behaviour of all specimens was recorded through adopting the digital image correlation technology, obtaining the corresponding force-stroke curves. It is obviously seen that the variation of true stress-plastic strain curve is related with the coupling effect of temperature and strain. The Mg-Gd-Y alloy possesses the remarkable tension-compression asymmetry and anisotropy under various temperatures. A SVT model is proposed to characterize the temperature-related plastic flow behaviour under various loading condition. The evolution of yield loci at different equivalent plastic strain levels and temperatures of the Mg-Gd-Y alloy is accurately characterized by the A-Yoon2014.

How to characterise the anisotropy of laser powder bed fusion-processed parts? Towards a surrogate, non-destructive indentation-based approach

This work proposes a non-destructive indentation (NDI)-based surrogate mechanical testing framework for anisotropy and mechanical property evaluation of LPBF processed Inconel 718 superalloy. A Knoop-hardness tester was employed to develop the surrogate framework. Further post-heat treatments (PHTs) were performed at various cooling rates. The as-printed and PHT (SA, SB, SC, and SD) samples were characterized using X-ray diffraction (XRD) optical microscopy (OM), scanning electron microscopy (SEM), and electron back-scattered diffraction (EBSD) techniques. The yield locus plots show strong anisotropy for the as-printed sample. The IPF maps and pole figures for the as-printed samples showed elongated columnar grains with strong fiber texture along the (001) plane parallel to the build direction. They corroborated sufficiently with XRD, grain boundary map (GBM), and Kernel average misorientation (KAM) analysis. The yield locus shape of samples subjected to homogenization treatment becomes a nearly uniform ellipse with a reduction in the difference between σx and σy values, which can be attributed to the recrystallization of grains as observed by the transition from low-angle grain boundaries (LAGBs) to high angle grain boundaries (HAGBs). The PHT samples show a further increase in yield loci size due to the precipitation of γ’ and γ” strengthening phases due to aging treatment and corroborated with higher Taylor factor and dislocation density than the as-printed samples. The yield loci were sensitive to the PHT's cooling rates. Notably, among PHT ones, ‘SA’ samples exhibited a strong correlation (R2 ≈ 97.5 %) between the Taylor factor and yield locus. It was attributed to slower cooling rates (furnace cooled) with noticeably enhanced precipitation of strengthening phases, an increase in the volume fraction of recrystallized grains (from grain orientation spread (GOS) map), corroborating with higher dislocation density due to local strain as inferred from EBSD analysis. The proposed NDI surrogate approach was initially validated on an as-printed Inconel 718 stator blade. The yield locus showed a strong correlation between the stator blade and the as-printed sample, indicating the effectiveness of the proposed methodology.

Analytical study on the dynamic mechanical behaviours of foam-core sandwich plate under repeated impacts

The foam-core sandwich structures are probably subjected to repeated impact loadings in engineering applications, resulting in structural plastic deformation and accumulative damage. A valuable analytical approach is needed to predict the accumulative plastic deformation of foam-core sandwich structures under repeated impacts. In this paper, an analytical model of the dynamic responses of foam-core sandwich plates under repeated impacts is proposed using the circumscribing yield locus and the inscribing yield locus based on the rigid-perfectly plastic theory. By employing the principle of energy dissipation rate balance, the analytical expressions of structure permanent deformation and peak force are obtained from the iteration of initial conditions. In addition, polyvinyl chloride (PVC) foam has steady chemical properties and corrosion resistance, which can better adapt to the practical environment and meet the needs of structural protection. To validate the proposed analytical model, the repeated impact dynamic mechanical behaviours of PVC foam-core sandwich plates were experimentally and numerically studied. Results show that theoretical results such as the permanent deformation, peak force, and deformation modes of foam-core sandwich plates under repeated impacts are in good agreement with experimental and numerical results. With the increase in impact numbers, the global bending deformation and local indentation deformation of facesheets increase, the PVC foam core layer is constantly being compressed, and the bottom facesheet plays an increasingly important part in the repeated impact energy absorption with a maximum value of 29.20 %.

Biaxial tensile behavior of stainless steel 316L manufactured by selective laser melting

In this study, miniaturized cruciform biaxial tensile specimens were optimized by finite element simulation software Ansys to vary five geometric parameters. The optimized specimens were utilized to characterize the biaxial tensile properties of 316L stainless steel fabricated through selective laser melting (SLM), with the two loading directions being vertical (X) and parallel (Y) to the building direction. It was discovered that at load ratios of 4:2 and 2:4, the yield strengths along X and Y orientations reached their respective maxima. By comparing the experimentally obtained yield loci against predictions by theoretical criteria including Mises, Hill48 and Hosford, it was found that the Hill48 anisotropic criterion corresponded most closely with the experimental results, while the other two criteria exhibited considerably larger deviations. Therefore, Hill48 was concluded to most accurately describe the yielding behaviors of SLM 316L under complex loading conditions.

Unveiling the Strain Rate Sensitivity of G18NiCrMo3-6 CAST Steel in Tension/Compression Asymmetry

This research was devoted to unveiling the strain rate sensitivity (SRS) of G18NiCrMo3-6 cast steel in tension/compression asymmetry. For that purpose, detailed mechanical characterization tests were conducted providing a process window covering quasi-static and medium strain rate regimes (0.001, 0.1, 10 [s−1]) in tension and compression states. Through this experimental effort, the SRS of the material could be extracted by a function of strain and the strain rate which enabled us to create a mathematical expression to easily be implemented as a state variable for constitutive material modeling. Finally, a pressure- and rate-dependent constitutive material model on the basis of the Cocks’89 yield locus definition was created using a subroutine (UMAT) file and the material parameters were verified with respect to the experimental data. The UMAT file also takes into account the tension/compression asymmetry in yielding to handle the effect of the porous media plasticity concept. The predictions of the proposed material model are in line with the experimental outputs.