Transient Hardening Behaviour Research Articles

Characterisation and modelling of anisotropic hardening behaviour of cubic and hexagonal close packed polycrystalline metals

ABSTRACT In this study, anisotropic non-proportional hardening behaviour of the sheet metals with different crystalline structures is investigated. The investigated materials particularly exhibit the Bauschinger effect and complex transient hardening behaviour during loading path change. Furthermore, the finite element simulations are carried out to evaluate the performance of the distortional and multi-surface-kinematic hardening models in flow stress prediction under loading path change. Both models can well reproduce the measured anisotropic hardening, but the distortional hardening concept shows better predictive capability for flow stresses. The improved accuracy of the flow stress prediction with the distortional hardening model compared to the kinematic hardening is attributed to its flexibility in distortion of the yield surface following microstructure deviator independent on the initial yield surface. In contrast, the initial size of the yield surface in the kinematic hardening significantly affects the determination of the re-yielding stress at load reversal.

Prediction of anisotropic strengths of steel plate after prior bending-reverse bending deformation: Application of distortional hardening model

In this study, the strengths of a steel pipe in different material orientations are predicted using a distortional anisotropic hardening model, namely, the HAH model, implemented in a finite element simulation. The investigated hardening can capture the transient flow behavior under bending and reverse bending strain paths. In addition, the model reproduces the material behavior under orthogonally applied tension from the prior deformation path. To improve the predictive accuracy of the existing distortional hardening model, we additionally implement the multi-component evolution rule of the Bauschinger effect and transient hardening behavior. Two-step tension tests are used to identify the constitutive parameters related to the loading path changes in the bending and reverse bending (BRB) test, which mimics the common pipe manufacturing process in a practical manner. The predicted strengths along the circumferential and transverse directions to the major bending direction agree well with the experimentally measured strengths when the distortional hardening model is employed. By contrast, the classical isotropic hardening and kinematic hardening model over- and under-estimate the yield strength of the specimens after prior BRB loading. The improved accuracy of the strength prediction with the investigated HAH is attributed to the anisotropic identification of the flow behavior under both load reversal and cross-loading conditions, whereas the isotropic-kinematic hardening only considers the back stress evolution at load reversal. In addition to the strengths, the stagnated flow behavior after BRB loading can be well predicted with the HAH model with a properly calibrated yield point elongation using an inverse identification method.

A new material model for thermo-mechanical analysis of steels in fire

Recently developed multi-hazard frameworks for performance based engineering require material models capable of incorporating the unloading/reloading of structural materials at elevated temperatures. These include models for fire-following-earthquake events and the travelling fire methodology (which highlighted the prevalence of material’s unloading/reloading). This paper proposes a new combined isotropic-kinematic hardening material model that has been developed to assess the unloading/loading behaviour of steel materials for thermo-mechanical analysis with fire, accounting for the Bauschinger effect and transient hardening behaviour. It works within the classical rate independent plasticity framework by exploiting the latitude of the two yield-surface model. The proposed material model integrates temperature effects on the yield surfaces through the concept of a shrinking/expanding bounding surface, and on the Bauschinger effect using an exponential growth function of plastic internal variables (PIVs). Transient hardening behaviour is modelled by incorporating a second non-linear kinematic hardening variable using an exponential decay function of the PIVs, and a corresponding discrete memory parameter tracks any abrupt changes in the direction of plastic loading. Describing the Bauschinger effect and its associated transient hardening behaviour using an opposite pair of exponential functions is a novel solution that simplifies the computing effort required by classical material models developed purposefully for cyclic loading. Hence it makes the proposed material model appropriate and efficient for structural analysis with fire. The proposed material model has been implemented in Abaqus using the Umat subroutine, and verified against experimental data where good agreement was observed. Its application in analysing structures subjected to complex, realistic building fire is also demonstrated, indicating that it is suitable for incorporating within performance based engineering frameworks for structures in fire.

Pulsed Electric Current V-Bending Springback of AZ31B Magnesium Alloy Sheets

The springback of AZ31B magnesium alloy sheets subjected to pulsed electric current-assisted V-bending tests was investigated. To study the effect of pulsed electric current on the bending-dominated deformation behavior of magnesium alloy sheets, the stress–strain responses from the electric current-assisted uniaxial tension and compression tests were experimentally measured. The stress–strain curves under pulsed electric current showed an instantaneous stress drop under the application of the electric pulse. The ductility was enhanced owing to the application of electric current. The electrically assisted V-bending tests helped reduce the springback compared with conventional room-temperature V-bending tests, and the magnitude of the springback reduction increased with the increase in the electric current density. A thermo-mechanical-electrical finite element model for the electrically assisted V-bending test was developed. To consider the Joule heating effect, temperature-dependent hardening and a yield function with strength differential were implemented for simulating the AZ31B sheet. The simulations could reproduce the experimental flow stress curves of the uniaxial tension/compression tests under pulsed electric current, characterized by an instantaneous stress drop and subsequent transient hardening behavior. The simulated springback profiles were in good agreement with the measured V-bending test data, thus validating the proposed finite element modeling procedure.

Cyclic Tension Test of AZ31 Magnesium Alloy at Elevated Temperature Realized in a Miniaturized Uniaxial Tensile Test Setup

The use of new materials, e.g. aluminum and magnesium alloys, in the automotive and aviation sector is becoming increasingly important to reach the global aim of reduced emissions. Especially magnesium alloys with their low density offer great potential for lightweight design. However, magnesium alloys are almost exclusively formable at elevated temperatures. Therefore, material characterization methods need to be developed for determining the mechanical properties at elevated temperatures. In particular, cyclic tests at elevated temperatures are required to identify the isotropic-kinematic hardening behavior, which is important for numerically modeling the springback behavior. In this contribution, a characterization method for determining the cyclic behavior of the magnesium alloy AZ31B at an elevated temperature of 200 °C is presented. The setup consists of a miniaturized tensile specimen and stabilization plates to prevent buckling under compressive load. The temperature in the relevant area is introduced with the help of conductive heating. Moreover, the complex kinematic model according to Chaboche and Rousselier is identified, to map the transient hardening behavior of AZ31B after load reversal, which cannot be modeled with a single Bauschinger coefficient.

Mechanical, microstructural behaviour and modelling of dual phase steels under complex deformation paths

This paper aims to identify the mechanisms associated to the transient hardening behaviour of dual phase steels under strain path changes, and to capture the observed material behaviours with appropriate constitutive models. First, three DP steel sheets with different amounts of martensite were tested under monotonic and various strain path changes. Second, microstructural analysis of the materials before and after strain path change were performed by means of SEM, TEM, and EBSD. The contribution of texture evolution on the mechanical behaviour was also assessed using the visco-plastic self-consistent (VPSC) polycrystal plasticity model. Transient hardening behaviour and permanent softening were observed in the tension–tension tests for all the studied DP steels. These behaviours were explained by the development of strain gradients during the first load resulting from strain accommodation incompatibilities between the ferrite and martensite phases. For the purpose of describing the macroscopic material behaviours, the enhanced homogeneous anisotropic hardening (HAH) model (Barlat et al., 2014) integrated with the Yld2000-2d anisotropic yield function were adopted for constitutive modelling. The simulation results were discussed in view of the microstructure evolution.

Constitutive modelling of high strength titanium alloy Ti-6Al-4 V for sheet forming applications at room temperature

• A rigours set of experiments were performed to measure the initial yield surface of Ti-6Al-4V at room temperature under different-stress states. • A constitutive equation based anisotropic hardening model (HAH) model combined with the new determined yield function was proposed and implemented into the FEA- Abaqus implicit solver. • The proposed model showed ability to accurately predict the cyclic hardening response of Ti-6Al-4V, and therefore presents a promising approach for the prediction of deformation behaviour of Ti-6Al-4V alloy in sheet metal forming processes. To enable the design and optimisation of forming processes at room temperature the material behaviour of Ti-6Al-4 V needs to be accurately represented in numerical analysis and this requires an advanced material model. In particular, an accurate representation of the shape and size of the yield locus as well as its evolution during forming is important. In this study a rigorous set of experiments on the quasi-static deformation behaviour of a Ti-6Al-4 V alloy sheet sample at room temperature was conducted for various loading conditions and a constitutive material model developed. To quantify the anisotropy and asymmetry properties, tensile and compression tests were carried out for different specimen orientations. To examine the Bauschinger effect and the transient hardening behaviour in – plane tensile – compression and compression – tensile tests were performed. Balanced biaxial and plane strain tension tests were conducted to construct and validate the yield surface of the Ti-6Al-4 V alloy sheet sample at room temperature. A recently proposed anisotropic elastic-plastic constitutive material model, so-called HAH, was employed to describe the behaviour, in particular for load reversals. The HAH yield surface is composed of a stable component, which includes plastic anisotropy and is distorted by a fluctuating component. The key of the formulation is the use of a suitable yield function that reproduces the experimental observations well for the stable component. Meanwhile, the rapid evolution of the material structure must be captured at the macro - scale level by the fluctuating component embedded in the HAH model. Compared to conventional hardening equations, the proposed model leads to higher accuracy in predicting the Bauschinger effect and the transient hardening behaviour for the Ti-6Al-4 V sheet sample tested at room temperature.

Material Modelling and Springback Analysis for Multi-stage Rotary Draw Bending of Thin-walled Tube Using Homogeneous Anisotropic Hardening Model

The aim of this paper is to compare several hardening models and to show their relevance for the prediction of springback and deformation of an asymmetric aluminium alloy tube in multi-stage rotary draw bending process. A three-dimensional finite-element model of the process is developed using the ABAQUS code. For material modelling, the newly developed homogeneous anisotropic hardening model is adopted to capture the Bauschinger effect and transient hardening behaviour of the aluminium alloy tube subjected to non-proportional loading. The material parameters of the hardening model are obtained from uniaxial tension and forward-reverse shear test results of tube specimens. This work shows that this approach reproduces the transient Bauschinger behaviour of the material reasonably well. However, a curve-crossing phenomenon observed for this material cannot be captured by the homogeneous anisotropic hardening model. For comparison purpose, the isotropic and combined isotropic-kinematic hardening models are also adopted for the analysis of the same problem. The predictions of springback and cross-section deformation based on these models are discussed.

Work Hardening Response of Transformation‐Induced Plasticity and Dual‐Phase Steels to Prestrain

AbstractStandard uniaxial tension and repetitive uniaxial tension at different prestrain levels have been conducted for cold‐rolled TRIP780 and DP590 steels. Scan electron microscope (SEM) was performed to observe the microstructures response to prestrain. The instantaneous work hardening rate and transient hardening behavior changing with the prestrain in repetitive tension were discussed in detail. The elastic modulus degradation with prestrain was also identified for the two steels. Results indicated that TRIP780 and DP590 had different work hardening responses to prestrain although they both have preferable work hardenability. When prestrain was small, DP steel had higher work hardening rate than TRIP steel had. While when the prestrain was larger than 2.5%, TRIP780 displayed higher work hardening rate than DP590 did. After each unloading in repetitive tension, the work hardening rate of TRIP780 and DP590 steels fell off and then tended to come back to the original level. The drop of work hardening rate decreased with the prestrain only for TRIP780. It was discerned that the max elastic modulus degradation could reach 18 and 10% for TRIP780 and DP590 steels, respectively.

Strain hardening response and modeling of EDDQ and DP780 steel sheet under non-linear strain path

The anisotropic hardening behaviors of dual phase (DP780) and extra deep drawing quality (EDDQ) steel sheets under non-proportional strain paths were investigated. Two-step uniaxial tension tests, which consisted of the first loading in the rolling (RD) or transverse (TD) and the second loading in every 15° from the first loading axis, were conducted. For DP780 steel, a significant Bauschinger effect accompanied by a transient hardening behavior after reverse loading was the prominent phenomenon. In contrast, EDDQ exhibited stress overshooting followed by strain hardening stagnation with respect to the monotonic flow curve near cross-loading conditions. The extended HAH model combined with the Yld2000-2d yield function were used to reproduced the anisotropic hardening behavior of the two materials. For DP780, the extended HAH model could capture the Bauschinger effect and transient hardening behavior well for tension reloading at 0°, 15°, 75° and 90° from the RD or TD prestraining direction. However, the predictions at 30°, 45° and 60° were slightly different from the experiments. For EDDQ, this approach reproduced the strain hardening anisotropy well including flow stress overshooting followed by a stage of strain hardening stagnation.

Crystal plasticity approach for predicting the Bauschinger effect in dual-phase steels

Abstract A multi-scale micro-mechanical model was proposed to predict the cyclic behavior of dual-phase steels. The approach proposed in this study incorporates a simplified dislocation density model into the crystal plasticity finite element method (CP-FEM). The back stress resulting from dislocation pileups was used to reproduce the transient hardening behavior during load reversal. The simulations conducted using representative volume elements for the dual-phase steels lead to the following conclusions: (1) the large Bauschinger effect (BE) and permanent softening in dual-phase steels originate primarily from the inhomogeneity due to the soft and hard phases; (2) the elastic incompatibility due to the grain orientation distribution generates some BE, but is not sufficient to explain the measured stress–strain curve; and (3) the inclusion of the back stress produced by the dislocation pileup can explain the strain hardening stagnation during reverse loading.

An evaluation of a combined isotropic-kinematic hardening model for representation of complex strain-path changes in dual-phase steel

Abstract This paper aims at evaluating an elastoplastic constitutive model which accounts for combined isotropic-kinematic hardening for complex strain-path changes in a dual-phase steel, DP800. The capability of the model to reproduce the transient hardening phenomena under two-stage non-proportional loading has been assessed through numerical simulations of sequential uniaxial tension and notched tension/shear tests. Finite element simulations with shell elements were performed using the explicit non-linear FE code LS-DYNA. Numerical predictions of the stress–strain response were compared to the corresponding experimental data. The results from the experiments demonstrated that prior plastic deformation has certainly influenced the subsequent work-hardening behaviour of the material under biaxial or shear deformation modes. Furthermore, the numerical simulations from the two-stage uniaxial tension–notched tension and uniaxial tension–shear tests predicted the general trends of the experimental results such as transitory hardening and overall work hardening. However, some discrepancies were found in accurately describing the transient hardening behaviour subsequent to strain path changes between the experiments and numerical simulations.

Numerical analysis of strain path dependency in FCC metals

Strain path dependency in FCC metals is often associated with the anisotropy induced by the dislocation cell structure in deformed metals. In this paper, the mechanical behaviour of metals under various nonuniform deformation paths is studied with the use of a recently developed dislocation cell structure model. It is shown that this model correctly captures the essential features of strain path change effects for moderate strain path changes, i.e. the anisotropy and the dependency on the amount of prestrain. Next, a numerical analysis is performed to assess the micromechanical origin of the modified reloading yield stress and the transient hardening after strain path changes. The separate influence of anisotropic effects due to the cell structure morphology and residual internal stresses are thereby addressed and illustrated. The transient hardening behaviour after a strain path change is related to the adjustment of the internal stresses to the new loading. Results obtained are consistent with related experimental findings reported in literature.

Effect of stress components on fatigue crack growth rate under multiaxial stress condition: Yokobori, T.A., Isogai, T., Yokobori, T. and Koizumi, Y. J. Soc. Mater. Sci., Japan Aug 1990 39, 1106–1112 (in Japanese)

The anisotropic hardening behaviors of dual phase (DP780) and extra deep drawing quality (EDDQ) steel sheets under non-proportional strain paths were investigated. Two-step uniaxial tension tests, which consisted of the first loading in the rolling (RD) or transverse (TD) and the second loading in every 15° from the first loading axis, were conducted. For DP780 steel, a significant Bauschinger effect accompanied by a transient hardening behavior after reverse loading was the prominent phenomenon. In contrast, EDDQ exhibited stress overshooting followed by strain hardening stagnation with respect to the monotonic flow curve near cross-loading conditions. The extended HAH model combined with the Yld2000-2d yield function were used to reproduced the anisotropic hardening behavior of the two materials. For DP780, the extended HAH model could capture the Bauschinger effect and transient hardening behavior well for tension reloading at 0°, 15°, 75° and 90° from the RD or TD prestraining direction. However, the predictions at 30°, 45° and 60° were slightly different from the experiments. For EDDQ, this approach reproduced the strain hardening anisotropy well including flow stress overshooting followed by a stage of strain hardening stagnation.