Asymmetric Hardening Behavior Research Articles

Phenomenological modeling of thermomechanical coupling effects of highly alloyed TRIP-steels at different stress states

The considered highly alloyed TRIP-steel (TRansformation Induced Plasticity-TRIP) exhibits a phase transition from austenite to martensite during large deformation which leads to a remarkable strain hardening capability. However, the martensite evolution highly depends on temperature and stress state. Therefore, especially self heating during deformation has a great influence on the behavior of the material. A thermomechanically coupled viscoplasticity model is applied accounting for strain induced martensite formation and Lode-angle dependent strain hardening. Using fully thermomechanically coupled simulations of tensile and compression tests the model is able to capture the observed asymmetric hardening behavior of the considered CrMnNi-steel as well as the recorded crossing effect of yield curves at elevated strain rates.

Constitutive Modeling of Asymmetric Hardening Behavior of Transformation-Induced Plasticity Steels

Transformation-induced plasticity (TRIP) steels are part of advanced high strength steels capable of phase transformation, having good strength and ductility. The transformation rate is known to be dependent on the stress state, which may lead to asymmetric hardening behaviour for TRIP steels with compressive flow stresses larger than tensile ones. Sheet stamping products of TRIP steels show complex springback because of the asymmetry in addition to the large strength, which will complicate the analysis of sheet metal forming processes. In this work, the asymmetric hardening behaviour of a TRIP steel with a tensile strength of 1180 MPa was measured using the sheet tension-compression tester. An asymmetric hardening model was developed by introducing an off-centred bounding surface for the kinematic back-stress evolution, to depict the asymmetric hardening behaviour. The model parameters of the proposed constitutive equations were obtained from the stressstrain curves under tension followed by compression. The stress-strain curves were well captured by the developed constitutive model, whereas the conventional symmetric model fails to describe the asymmetric hardening behaviour of the TRIP steel. For validation, load-displacement curve and springback angles of three-point bending test were compared with the predictions by the proposed model.

Asymmetric Hardening Behavior of AZ31B Magnesium Alloy Sheet with Large Strain at Various Strain Rates

This paper investigates asymmetric hardening behavior of the magnesium alloy sheet of AZ31B at different strain rates when deformation is large. Tensile tests are carried out at the quasi-static state of 0.001 s−1 and the intermediate strain rate of 100 s−1 utilizing the Instron 5583 and the high speed material testing machine (HSMTM), respectively. Compression tests are conducted at the strain rate of 0.001 s−1 and 100 s−1 using a jig fixture mounted on the testing machines to change the loading direction into the opposite direction. A compression testing method is developed to obtain compressive properties with large strain, which includes the attachment of a fork-type clamping device and the design of specimen dimensions to achieve large strain without buckling during the test. Experimental results reveal the asymmetric behavior showing that the tensile yield stress is much larger than the compressive one at both strain rates. The difference between the flow stress level in tension and compression becomes larger when the strain rate is higher. The compressive hardening behavior is very much different from the tensile hardening behavior showing that the compressive flow stress increases remarkably as the deformation proceeds while the tensile flow stress asymptotes to a certain value.

Variable Material Properties Approach: A Review on Twenty Years of Progress

This paper provides a critical review of the advancements made in the application of the variable material properties (VMP) method over the past two decades. The VMP method was originally proposed in 1997 (Jahed and Dubey, 1997, ASME J. Pressure Vessel Technol., 119(3), pp. 264–273; Jahed et al., 1997, Int. J. Pressure Vessels Piping, 71(3), pp. 285–291) and further developed in 2001 (Parker, 2001, ASME J. Pressure Vessel Technol., 123(3), p. 271) as an elastoplastic method for the analysis of axisymmetric problems. The model was originally developed as a boundary value problem to predict the spatial distribution of stress. However, since 1997, it has been extended to include thermal effects to solve thermomechanical residual stresses; time domain to solve creep of disks and cylinders; finite deformation to solve cylinders under large strains; numerical solutions to make them more efficient; and asymmetric hardening behavior to accommodate nonslip deformation modes. These advancements, made over the past 20 years, are reviewed in this paper, and future trends and frontiers are discussed.

Distortional hardening concept for modeling anisotropic/asymmetric plastic behavior of AZ31B magnesium alloy sheets

A continuum-based approach for describing the plastic hardening behavior of magnesium alloy sheets subjected to non-proportional strain path changes at room temperature is presented. The constitutive model is based on an anisotropic distortional yield function that combines a stable component and a fluctuating component. The stable component initiates the yield criterion that characterizes the typical strength differential (SD) effect between tension and compression in magnesium alloys at room temperature. The evolution of the fluctuating component is reformulated based on its cubic metal counterpart to represent the deformation behavior of magnesium alloys, which consists of slip- and twinning-dominant deformation modes. To validate the proposed model, a predictor–corrector numerical algorithm was implemented in a finite element (FE) program by using a user material subroutine, and its numerical accuracy was evaluated by iso-error map analysis. Comparison of the experimental and simulated results obtained for various loading path changes showed that, although the model was not formulated using the kinematic hardening concept, the model could reproduce complex features of the stress–strain responses of an AZ31B magnesium alloy sheet under non-proportional loading paths, i.e., asymmetric hardening behavior under tension and compression, the sigmoidal nature of the hardening curve during monotonic compression and compression followed by tension.

Constitutive modelling of magnesium alloy sheets under strain path changes

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

Constitutive Modeling for Cyclic Behavior of AZ31B Magnesium Alloy and its Application

Fatigue testing was conducted on AZ31B-H24 magnesium alloy in strain-control condition. An unusual asymmetric shape of the hysteresis loop was the key feature of the cyclic behavior. A continuum-based cyclic plasticity model was developed to follow the asymmetric hardening behavior of wrought magnesium alloys. The proposed model was implemented in a UMAT subroutine to run with Abaqus/Standard. It was demonstrated that the UMAT was able to follow the cyclic hardening behavior of AZ31B under uniaxial loading. An energy-based damage parameter was proposed for estimating the fatigue crack initiation life. The developed UMAT along with the proposed damage parameter were used for fatigue modeling of an automotive substructure made of magnesium. It was shown that the proposed asymmetric model was more promising than a symmetric model.

A temperature-dependent elasto-plastic constitutive model for magnesium alloy AZ31 sheets

For warm forming simulations of magnesium alloy sheets, a constitutive model is proposed for describing the temperature-dependent asymmetric cyclic behavior of magnesium alloy sheets. The asymmetric hardening behavior is classified into three modes − twinning (T), untwinning (U), and slip (S) − depending on the corresponding dominant deformation mode. The yield criterion uses two separate yield functions that correspond to the twinning/untwinning and slip dominant deformation modes. Though this model is phenomenological, it adopts the concept of the deformation mechanism as magnesium alloy sheets exhibits significantly different behavior by the active deformation mechanisms for a wide range of temperatures. To obtain the model parameters, the constitutive model requires cyclic behavior at room temperature and tensile behavior at high temperatures. A numerical algorithm for efficiently integrating the constitutive equations is presented for switching deformation paths and active deformation modes. For verification, the predictions by the proposed constitutive model are compared with measurements for the simple shear behavior and the high temperature cyclic behavior.

Parametric study of multiphase TRIP steels undergoing cyclic loading

The behavior of multiphase steels assisted by transformation-induced plasticity (TRIP steels) undergoing low cycle, fully-reversed strain-controlled deformations is studied by means of numerical simulations based on micromechanical models. The ferritic phase is simulated using a single-crystal elasto-plasticity model for BCC crystals whereas the austenitic phase, which may transform into martensite, is simulated by a crystallographic phase transformation model coupled to a single-crystal elasto-plasticity model for FCC crystals. The influence of the TRIP mechanism on the overall behavior of the steel is investigated for selected variations of microstructural properties such as phase morphology, local carbon concentration in the austenite and austenitic grain size. The results of the simulations show a strong initial hardening associated to the martensitic transformation in accordance with experimental results. The simulations indicate an asymmetric hardening behavior under extension and contraction, particularly for large austenitic volume fractions and lower carbon concentrations.

OS0602 マグネシウム単結晶の非対称硬化挙動の結晶塑性解析(OS06-01 マルチスケール解析1,OS06 微視構造を有する材料の変形と破壊(1))

OS0602 マグネシウム単結晶の非対称硬化挙動の結晶塑性解析(OS06-01 マルチスケール解析1,OS06 微視構造を有する材料の変形と破壊(1))

Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets: Application to sheet springback

The constitutive model for the unusual asymmetric hardening behavior of magnesium alloy sheet presented in a companion paper (Lee, M.G., Wagoner, R.H., Lee, J.K., Chung, K., Kim, H.Y., 2008. Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheet, Int. J. Plasticity 24(4), 545–582) was applied to the springback prediction in sheet metal forming. The implicit finite element program ABAQUS was utilized to implement the developed constitutive equations via user material subroutine. For the verification purpose, the springback of AZ31B magnesium alloy sheet was measured using the unconstrained cylindrical bending test of Numisheet (Numisheet ’2002 Benchmark Problem, 2002. In: Yang, D.Y., Oh, S.I., Huh, H., Kim, Y.H. (Eds.), Proceedings of 5th International Conference and Workshop on Numerical Simulation of 3D Sheet Forming Processes, Jeju, Korea) and 2D draw bend test. With the specially designed draw bend test the direct restraining force and long drawn distance were attainable, thus the measurement of the springback could be made with improved accuracy comparable with conventional U channel draw bend test. Besides the developed constitutive models, other models based on isotropic constitutive equations and the Chaboche type kinematic hardening model were also considered. Comparisons were made between simulated results by the finite element analysis and corresponding experiments and the newly proposed model showed enhanced prediction capability, which was also supported by the simple bending analysis adopting asymmetric stress–strain response.