Anisotropic Hardening Behavior Research Articles

Neural network based rYld2004 anisotropic hardening model under non-associated flow rule for BCC and FCC metals

This paper extends the reduced Yld2004 (rYld2004) function to present the anisotropic hardening behavior for body-centered cubic and face-centered cubic metals under the proportional loading conditions based on neural network. The parameters of the rYld2004 anisotropic hardening model (AH_rYld2004) are determined by the uniaxial tensile yield stresses along 0°, 15°, 30°, 45°, 60°, 75° and 90° from the rolling direction as well as equibiaxial tension. The evolution of anisotropic parameters are described by the back propagation neural network optimized by ant colony optimization algorithm. The predicted data by AH_rYld2004 and some common anisotropic models are compared with the experimental results to verify the precision of the AH_rYld2004 in characterizing anisotropic hardening. The comparison proves that the AH_rYld2004 precisely characterize the anisotropic evolution with increasing plastic deformation for AA 3003-O and QP980. Simultaneously, the AH_rYld2004 function based on neural network is used to accurately simulate of circular cup deep drawing for AA 3003-O and uniaxial tension for QP980. The results indicate that the AH_rYld2004 model is capable to accurately represent the plastic anisotropic evolution for uniaxial tension along seven loading directions and equibiaxial tension.

Plastic Evolution Characterization for 304 Stainless Steel by CQN_Chen Model under the Proportional Loading.

In this paper, the CQN_Chen function is used to characterize the plastic anisotropic evolution of 304 stainless steel (SS304). The uniaxial tensile tests along different loading directions are conducted to experimentally investigate the anisotropic hardening behavior for SS304. The experimental data indicates that the anisotropy of SS304 is weak. The convexity analysis is carried out by the geometry-inspired numerical convex analysis method for the CQN_Chen yield locus during plastic deformation. The Hill48, SY2009 and CQN functions are used as the comparison to evaluate the accuracy of the CQN_Chen function in characterizing plastic evolution. The predicted values are compared with the experimental data. The comparison demonstrates that the CQN_Chen function can accurately characterize anisotropic hardening behavior under uniaxial tension along distinct loading directions and equibiaxial tension. Simultaneously, the CQN_Chen model has the capacity to adjust the yield surface shape between uniaxial tension and equibiaxial tension. The CQN_Chen model is recommended to characterize plastic evolving behavior under uniaxial tension along different directions and equibiaxial tension.

Quantitative representation of directional microstructures of single-crystal superalloys in cyclic crystal plasticity based on neural networks

Nickel-based single-crystal alloys undergo microstructural degradation induced by thermal exposure. The directional rafting of microstructures significantly affects the mechanical properties and makes the material anisotropic. For structural design, establishing a quantitative description of microstructural effects in a constitutive model becomes essential and is still a tough research topic in multi-scale materials modeling. In the present work, the fabric tensor was correlated with the anisotropic cyclic crystal plasticity of nickel-based single-crystal alloys with the help of neural networks. The microstructural representative volume elements with various single-crystal morphologies were generated by the phase-field method and the deformation behaviors were studied under different crystal orientations and loading configurations. The neural network analysis confirmed that the fabric tensor can present anisotropic single-crystallographic microstructural features and describe mechanical behavior under both monotonic and cyclic multi-axial loading conditions. The history-dependent anisotropic cyclic hardening or softening behavior of the material can be captured by the introduced microstructural state variable. A principal component analysis (PCA) aided gradient-based attribution method was proposed to evaluate the importance of input variables. The characterization of different material components and their contribution to the stress–strain relationships are investigated and validated. The fabric tensor was verified to be an effective microstructural indicator for the continuum plasticity of single-crystal alloys.

Characterization and modelling of evolving plasticity behaviour up to fracture for FCC and BCC metals

Yield surfaces evolve depending on loading directions (anisotropic hardening) and stress states (differential hardening) during plastic deformation of sheet metals. A new analytical yield function is proposed by coupling an enhanced pDrucker function and SY2009 anisotropic hardening functions to model both the differential and anisotropic hardening behavior. All the parameters are solved analytically for the proposed function so that the proposed function can model the differential hardening from uniaxial compression to equibiaxial tension and anisotropic hardening of uniaxial tension with three different loading directions. Its convexity during evolution is analysed from plasticity onset to ultimate fracture by a geometry-inspired numerical convex analysis approach. Several tests were conducted for an aluminium alloy 2A12-O and a high-strength steel QP1180 including uniaxial tension/compression, simple shear, notched tension and bulge tests. The proposed yield function is applied to describe the plastic behaviour of AA2A12-O and QP1180 steel under the non-associated flow rule. Parameter calibration is conducted at pre-necking and post-necking stages for modelling yield surface evolution more accurately under large deformation especially at shear and equibiaxial tension states. The applications to the two metals show that the proposed function is more suitable for pressure-sensitive face-centered cubic (FCC) and body-centered cubic (BCC) metals compared to the pressure-coupled Yld2000–2d and CQN models since both the anisotropic and differential hardening behaviours are precisely modelled by the proposed yield function. The proposed function could also be utilized as a stress-based fracture criterion to model four stress states fracture from uniaxial compression to equibiaxial tension.

A Homogeneous Anisotropic Hardening Model in Plane Stress State for Sheet Metal under Nonlinear Loading Paths.

In sheet metal forming, the material is usually subjected to a complex nonlinear loading process, and the anisotropic hardening behavior of the material must be considered in order to accurately predict the deformation of the sheet. In recent years, the homogeneous anisotropic hardening (HAH) model has been applied in the simulation of sheet metal forming. However, the existing HAH model is established in the second-order stress deviator space, which makes the calculation complicated and costly, especially for a plane stress problem such as sheet metal forming. In an attempt to reduce the computational cost, an HAH model in plane stress state is proposed, and called the HAH-2d model in this paper. In the HAH-2d model, both the stress vector and microstructure vector contain only three in-plane components, so the calculation is significantly simplified. The characteristics of the model under typical nonlinear loading paths are analyzed. Additionally, the feasibility of the model is verified by the stress-strain responses of DP780 and EDDQ steel sheets under different two-step uniaxial tension tests. The results show that the HAH-2d model can reasonably reflect the Bauschinger effect and the permanent softening effect in reverse loading, and the latent hardening effect in cross loading, while the predictive accuracy for cross-loading softening remains to be improved. In the future, the HAH-2d model can be further modified to describe more anisotropic hardening behaviors and applied to numerical simulations.

The Effect of Laser Shock Peening on Back Stress of Additively Manufactured Stainless Steel Parts

Abstract This work studies the use of laser shock peening (LSP) to improve back stress in additively manufactured (AM) 316L parts. Unusual hardening behavior in AM metal due to tortuous microstructure and strong texture poses additional design challenges. Anisotropic mechanical behavior complicates application for mechanical design because 3D printed parts will behave differently than traditionally manufactured parts under the same loading conditions. The prevalence of back-stress hardening or the Bauschinger effect causes reduced fatigue life under random loading and dissipates beneficial compressive residual stresses that prevent crack propagation. LSP is known to improve fatigue life by inducing compressive residual stress and has been applied with promising results to AM metal parts. It is here demonstrated that LSP may also be used as a tool for mitigating tensile back-stress hardening in AM parts, thereby reducing anisotropic hardening behavior and improving design use. It is also shown that the method of application of LSP to additively manufactured parts is key for achieving effective back-stress reduction. Back stress is extracted from additively manufactured dog bone samples built in both XY and XZ directions using hysteresis tensile. Both LSPed and as-built conditions are tested and compared, showing that LSPed samples exhibit a significant reduction to back stress when the laser processing is applied to the sample along the build direction. Electron backscatter diffraction (EBSD) performed under these conditions elucidates how grain morphologies and texture contribute to the observed improvement. Crystal plasticity finite element (CPFE) modeling develops insights as to the mechanisms by which this reduction is achieved in comparison with EBSD results. In particular, the difference in plastic behavior across build orientations of identified crystal planes and grain families are shown to impact the degree of LSP-induced back-stress reduction that is sustained through tensile loading.

Evolving asymmetric and anisotropic hardening of CP-Ti sheets under monotonic and reverse loading: Characterization and modeling

Commercially pure titanium (CP-Ti) sheets are promising to manufacture high-performance and lightweight components in many fields such as aerospace, marine, energy, electrics and healthcare. However, due to its low symmetric hexagonal close-packed (HCP) structure and complex thermal-mechanical processing history, CP-Ti sheets may exhibit significant asymmetry and anisotropy under monotonic and reverse loading. Therefore, the coupling effect of loading-path dependent asymmetric and anisotropic hardening behaviors of CP-Ti sheets need to be systemically characterized and accurately described under monotonic and reverse loading paths. In this study, firstly, the rheological tests were performed to systemically explore the evolving asymmetric and anisotropic hardening behavior of CP-Ti sheet under monotonic and reverse loading modes. With the help of anti-buckling support fixture and DIC system in tension and compression tests, the coupling effect of asymmetric and anisotropic hardening under monotonic and reverse loading of CP-Ti sheet was identified. Secondly, a loading-path dependent constitutive modeling framework was constructed in which the stress invariants-based model (SIM) integrated with distorted hardening (DH) under reverse loading (RL) conditions (SIM+DH+RL) were considered. Within the proposed modeling framework, a judging criterion of stress reversal for explicit solution method and an activation criterion of different reverse loading modes were introduced. Finally, the proposed SIM+DH+RL model was implemented, calibrated and further applied to simulate typical V-/U-bending of CP-Ti sheets. The results show that the proposed SIM+DH+RL model can significantly improve the prediction accuracy of V-/U-bending springback with the relative errors less than 7.8% and 2.1%, compared with 15.2% and 12% relative errors of Mises+IH, 19.5% and 7.3% relative errors of SIM+DH, 15.1% and 8.4% relative errors of Yoon2014+IH, 14.5% and 5.2% relative errors of CPB06+IH, and 17.3% and 11.5% relative errors of Hill48+IH. It is noted that for the thickness distributions after V-/U-bending springback, the above used models have similar prediction accuracies with the relative errors less than 1.8%.

Correlation of the anisotropic hardening behavior and texture features of cold rolled Zr-4 sheet under uniaxial tension

The strongly anisotropic mechanical behaviors commonly observed in Zr-4 sheets typically lead to inferior formability. In this study, the mechanical behavior and texture evolution of a cold-rolled Zr-4 sheet under uniaxial tension in various directions were systematically investigated, and the results showed both anisotropic yielding and hardening behavior in the Zr-4 sheet. The microstructure and texture features revealed by electron backscattered diffraction (EBSD) method indicate that this anisotropic mechanical behavior is closely related to the initial texture and its evolution during plastic deformation. In conjunction with experimental observations, a visco-plastic self-consistent (VPSC) model was employed to quantitatively analyze the relationship between the mechanical anisotropy and the texture features and activation of deformation modes. It was found that the yield anisotropy is affected by the distinct activity of prismatic <a> slip, while the different activities of basal <a> slip and extension twinning (ETW) result in anisotropic hardening. The distinct activation of deformation modes is mainly caused by differences in the evolution of the Schmid factor (SF) and critical resolved shear stress (CRSS) with increasing strain. Additionally, the results prove that the limited twinning activation with a fraction of less than 3% plays a non-negligible role in the hardening behavior during tension along the transverse direction. The latent hardening effect caused by the interaction between prismatic slip and tensile twinning is considered to successfully capture the anisotropic hardening behavior of the Zr-4 sheet. The implementation and insights from the predictions are presented and discussed in this work.

Measurement of Biaxial Deformation Behavior and Material Modeling for HI-PVC Using Multiaxial Tube Expansion Test

This study investigates the biaxial deformation behavior of the High Impact Polyvinyl Chloride (HI-PVC) used as a water pipe material. Multiaxial tube expansion test (MTET) was performed on the HI-PVC circular tube, and the stress-strain curves were measured for nine linear stress paths. The contours of plastic work and the directions of the plastic strain rates were also measurd. The experimental results show that the test sample has a strong anisotropy. Anisotropic hardening behavior was also confirmed from the evolution of the work contours. It was confirmed that the Yld2000-2d yield function had a better agreement with the measued work contour than Hill’s quadratic and the von Mises yield functons. Moreover, it was found that the test sample follows the normality rule with the Yld2000-2d yield function.

Experimental characterization and modeling of complex anisotropic hardening in quenching and partitioning (Q&P) steel subject to biaxial non-proportional loadings

Quenching and partitioning (Q&P) steels, as one of the third-generation advanced high strength steels, exhibit complex anisotropic hardening behavior under biaxial non-proportional loadings. In this study, a wide range of strain path changes (SPCs) defined as an angle (χ) between stress deviators before and after the SPC is experimentally applied to characterize the anisotropic hardening of a Q&P steel with a strength grade of 980 MPa (QP980). The investigated SPCs include uniaxial tension followed by compression (UT-UC; χ=180°), uniaxial compression followed by tension (UC-UT; χ=180°), uniaxial tension followed by plane strain (UT-PS; χ=30°), equi-biaxial tension followed by plane strain (EBT-PS; χ=30°), followed by uniaxial tension (EBT-UT; χ=60°) and followed by simple shear (EBT-SH; χ=90°). These SPCs are achieved by the program-controlled biaxial tensile testing equipment using novel arm-reinforced cruciforms. The experimental findings in the QP980 steel sheet are summarized as follows: (1) Strong strain-dependent Bauschinger effect, transient hardening and permanent softening are observed in both UT-UC and UC-UT loadings; (2) Bauschinger effect increases as strain increases, and it exhibits obvious tension-compression asymmetry; (3) The transient hardening behaviors are path-dependent under SPCs with various χ; (4) The Bauschinger coefficient is approximately a parabola function of cosχ; (5) The most significant strength softening occurs under EBT-SH loading. In order to describe the complex hardening behavior of the QP980 steel, a distortional hardening model is proposed on the basis of non-associated flow rule. A coupled quadratic and stress-invariant-based yield function is used to describe stress anisotropy, strength differential effect, and anisotropic hardening for proportional loadings. Then, the Bauschinger effect related hardening and path-dependent permanent softening are captured by a modified homogeneous anisotropic hardening model. The calibrated model parameters and experimental validations demonstrate that the strain- and path-dependent Bauschinger effect can be well predicted by the proposed constitutive model. Especially, the model enables to accurately describe both the asymmetric anisotropic hardening and yield surface distortions of the QP980 steel at various biaxial SPCs.

Superconducting MgB2 Wire Drawing Considering Anisotropic Hardening Behavior and Hydrostatic Effect

Superconducting MgB2 Wire Drawing Considering Anisotropic Hardening Behavior and Hydrostatic Effect

Damage modeling of oxide/oxide ceramic matrix composites under cyclic loading conditions

Ceramic matrix composites exhibit optimal high temperature property and complex nonlinear behaviors including irreversible deformations and stiffness degradation under different mechanical loading conditions. In the present work, the damage evolution of the material under multi-axial loads considering effects of loading-unloading cyclic was studied and a novel continuum damage constitutive model was proposed. The material degradation was decomposed into monotonic damages and cyclic damages. The anisotropic hardening behavior of the material was considered by taking orientation dependence into account. Compared to the experimental results, the constitutive model could accurately predict the stress-strain response and stiffness degradations of the oxide/oxide ceramic matrix composites for monotonic loading and cyclic loading.

A non-quadratic pressure-sensitive constitutive model under non-associated flow rule with anisotropic hardening: Modeling and validation

A non-associated flow rule (non-AFR) constitutive model is proposed to describe the evolving yield stress and plastic potential surfaces of sheet metal under plane stress conditions. The yield stress function is a multiplication of two yield functions, within the first part includes an asymmetric pressure-sensitivity that considers anisotropic and asymmetric yielding of sheet metals. This yield stress function can describe anisotropic hardening behavior by directly employing the hardening functions under seven different loading conditions, i.e., uniaxial tension along 0°, 45°, 90° to the rolling direction (RD) of sheet metal, uniaxial compression along the same orientations and equi-biaxial tension without any interpolation or optimization procedure at a discrete level of equivalent plastic strain. The second part is a non-quadratic isotropic function, which is the sum of two isotropic yield functions with high flexibility in shaping the yield surface. A new plastic potential function is proposed to capture the differential Lankford coefficients (r-values) between uniaxial tension and compression obtained from mechanical testing. Eight parameters in the plastic potential function were calibrated from seven r-values under the same loading conditions and one yield stress as calibrating parameters for the yield stress function. The proposed constitutive model was validated by experimental data of three engineering sheet metals, i.e., one dual-phase steel DP980, one TRIP-assisted steel QP980 and one aluminum alloy AA5754-O and compared with several classical yield criteria. The evolving yield behavior was accurately described by the proposed non-associated flow rule (non-AFR) constitutive model.

An enhanced distortional-hardening-based constitutive model for hexagonal close-packed metals: Application to AZ31B magnesium alloy sheets at elevated temperatures

In this study, a new material model for hexagonal close-packed (HCP) metals for predicting their flow responses under monotonic/cyclic loadings at various temperatures is proposed. The temperature-dependent constitutive model is re-formulated using a continuum-based distortional hardening law, which affects the shape of the yield surface depending on the loading direction, and also uses the concept of the dominant deformation modes in magnesium alloys: twin, untwin, and slip-dominate modes, considering the role of the twins in plastic deformation. In terms of the material asymmetry in yield strength, the Cazacu–Barlat–Plunkett (CPB) ’06 yield criterion is extended to include thermal effects. A numerical formulation of the material model has also been developed to allow its implementation into finite element analysis software via a user-defined material subroutine (UMAT). The predicted results of stress–strain response for monotonic and cyclic loadings are excellent agreement with the experimental data. Moreover, the simulated results show the strength differential (SD) effect and unusual flow responses of AZ31B magnesium alloy sheets at room temperature, as well as the variation in the SD effect and anisotropic hardening behavior at elevated temperatures.

Parametrically homogenized constitutive models (PHCMs) from micromechanical crystal plasticity FE simulations: Part II: Thermo-elasto-plastic model with experimental validation for titanium alloys

In this second of the two-part paper on the development of Parametrically Homogenized Constitutive Models (PHCMs), constitutive coefficients are represented in functional forms of the representative aggregate microstructural parameters (RAMPs), e.g. texture intensity parameters, misorientation parameter and grain size, identified in the first part (Kotha et al., 2019). Efficient and accurate PHCMs are developed for finite deformation, anisotropic thermo-elasto-plastic behavior of polycrystalline Ti6242S alloys. The constitutive framework in the PHCM is chosen to reflect fundamental characteristics of elasto-plastic anisotropy, tension-compression asymmetry, anisotropic hardening and rate-dependent mechanical behavior, observed in Ti alloys. The functional forms of the PHCM constitutive coefficients in terms of the RAMPs are deciphered using a machine learning code Eureqa. The machine learning data-base is generated through detailed micro-mechanical crystal plasticity FE simulations of microstructure-based statistically equivalent RVEs or M-SERVEs of the polycrystalline material. A variety of M-SERVEs with different morphology and crystallography characteristics and thermo-mechanical loadings are considered. The proposed PHCM is numerically implemented in ABAQUS as a user subroutine. The accuracy of the PHCM model is demonstrated by validating the PHCM predictions for Ti6242S with tensile test experiments at different strain-rates and temperatures.

Identification of mechanical responses of steel sheets under non-proportional loadings using dislocation-density based crystal plasticity model

A crystal-plasticity approach based on three-component dislocation density model is proposed, as a virtual experimental model, to accurately predict non-proportional anisotropic hardening behavior of ultra-thin sheet metals, a potential candidate for PEMFC (proton-exchange membrane fuel cell) bipolar plate. The model introduces three different populations of dislocations named forward, reverse and latent, which are selectively activated depending on load path changes. To validate the predictive capability as a tool for the virtual experiment, the model is validated by predicting flow behaviors of 1.2 mm thick extra-deep drawing quality steel sheet under compression–tension and two-step tension test. The model is then applied to the 0.1 mm thick ultra-thin ferritic stainless steel sheet. The model parameters are identified by the two-step tension test. The proposed model with the identified parameters can predict the tension–compression stress–strain curves, which are difficult to measure experimentally due to premature buckling for such thin sheet metals. The potential application of the crystal plasticity based virtual modeling to the springback prediction in the thin sheet metal parts is discussed in this study.

Forming Limits Under Stretch-Bending Through Distortionless and Distortional Anisotropic Hardening

The necking behavior of sheet metals under stretch-bending process is a challenge for the forming limit prediction. State-of-the-art forming limit curves (FLCs) allow the prediction under the in-plane stretching but fall short in the case under out-of-plane loading condition. To account for the bending and straightening deformation when sheet metal enters a die cavity or slide along a radius, anisotropic hardening model is essential to reflect the nonproportional loading effect on stress evolution. This paper aims to revisit the M-K analysis under the stretch-bending condition and extend it to accommodate both distortionless and distortional anisotropic hardening behavior. Furthermore, hardening models are calibrated based on the same material response. Then the detailed comparison is proposed for providing better insight into the numerical prediction and necking behavior. Finally, the evolution of the yield surface and stress transition states is examined. It is found that the forming limit prediction under stretch-bending condition through the M-K analysis strongly depends on the employed anisotropic hardening model.

A crystal plasticity model for describing the anisotropic hardening behavior of steel sheets during strain-path changes

In the present study, a viscoplastic self-consistent crystal plasticity model (VPSC-RGBV), which accounts for various microstructural features, including the accumulation and annihilation of dislocations due to slip activity and latent hardening originated from interactions between gliding dislocations on different slip planes, is described. The simulation results of the VPSC-RGBV model are compared with those of a macro-mechanical distortional plasticity model, the so-called homogeneous anisotropic hardening (HAH), and experimental data pertaining to metals undergoing complex loading histories. The differences between the simulated and experimental results under non-proportional loading, including 1) the stress-strain curve, 2) instantaneous r-value after strain-path change, and 3) yield surface evolution, are discussed. Finally, potential improvements are suggested for VPSC-RGBV model.

Kinematic hardening model considering directional hardening response

This paper proposes a kinematic hardening model to capture both asymmetric plastic behavior (early-reyielding, transient Bauschinger effect and permanent softening) and directional hardening (anisotropic hardening) response at the same time. The previously reported kinematic hardening models have brought significant improvements of ability to describe the asymmetric plastic behavior of sheet metal in cycling loading conditions at fixed one angle from the rolling direction (RD). However, their inability to cover the anisotropy in the directional hardening response has a limitation to describe the anisotropic hardening behavior because material constants of general kinematic hardening models are only fitted to one reference axis. In order to capture the anisotropic hardening with a kinematic hardening model, this work proposes a scheme to combine a kinematic hardening model with a function, which is called the condition function in this paper, to account for the change of the mechanical property with respect to the RD. The condition function should explicitly capture four independent hardening data in different directions, 0°, 45°, 90° to the RD and the equal biaxial (EB) condition in order to gain an appropriate parameter set. The new model is validated with four tests and the results are compared with other material models to clearly show that the new model can capture both the anisotropic hardening response and the asymmetric plastic behavior for monotonic and cycling loading conditions.

An Experimental and Numerical Investigation of the Anisotropic Plasticity and Fracture Properties of High Strength Steels from Laboratory to Component Scales

Experimental and numerical investigations on the plasticity, damage and fracture behavior of a pipeline steel were conducted in this study. Anisotropy effects on the plastic deformation and fracture properties of the material were taken into consideration by performing tests along different loading directions with respect to the rolling direction. Fracture behavior of the steel was characterized through conducting a comprehensive experimental program covering a wide range of stress states by using fracture specimens of various geometries along different loading angles. Besides the fracture experiments in the laboratory scale, the drop weight tear tests of full plate thickness along different loading directions were performed as well. The recently proposed evolving non-associated Hill48 model was adopted to describe the anisotropic hardening behavior of the investigated material. Finite element analysis on the fracture behavior of this material was performed by using a coupled damage mechanics model with triaxiality and Lode angle dependence. Through the hybrid experimental and numerical investigations, the influences of anisotropy on the plastic deformation and fracture behavior of the pipeline steel are analyzed.