Strain Path Change Research Articles

Distortional plasticity framework with application to advanced high strength steel

An improved distortional plasticity framework that describes the anisotropic hardening occurring during strain path changes, such as the Bauschinger and cross-loading effects, is developed. This approach is a modified version of the homogeneous anisotropic hardening (HAH) framework proposed almost a decade ago. In the present formulation, the yield condition includes an alternative description of the distortion suggested by crystal plasticity simulation results. In addition, it incorporates the influence of the hydrostatic pressure, which manifests itself by a higher flow stress in uniaxial compression than in tension. The state variable evolutions are modified compared with the previous HAH version to improve the material response when the strain path changes occur near a pure cross-loading condition. The model is calibrated on a DP780 dual-phase steel sheet sample using the data of a tension-compression test with three full cycles, as well as a sequence of two uniaxial tension segments in different directions. After calibration, predicted and experimental stress-strain curves obtained for independent loading sequences are compared and shown to be good agreement. Finally, theoretical predictions of two-step tension tests using the constitutive coefficients of DP780 are discussed to highlight the improvement offered by this enhanced framework.

Experimental and theoretical plasticity analyses of steel materials deformed under a nonlinear strain path

In this study, the macroscopic mechanical behavior of extra-deep drawing quality (EDDQ) and transformation-induced plasticity (TRIP1180) steels subjected to nonlinear-strain-path modes of deformation was investigated. For the nonlinear-strain-path experiments conducted on steels, an optimized experimental approach was proposed for deforming the material using two linear loading segments with a single abrupt change in the strain path. A specific medium-scale uniaxial tension specimen was designed for the pre-strain stage. The advantage of this approach over existing methods was that it enabled testing of various strain-path changes for steels with strengths greater than 1 GPa within a reasonable load range. In addition, this approach produced a more uniform strain field, which is important during the pre-strain stage. After the uniaxial pre-strain, various specimens were extracted from the uniformly deformed area for use in experiments involving changes in the strain path. To predict the material behavior under nonproportional loading, the homogeneous anisotropic hardening (HAH) distortional plasticity model was selected. The predictions of the HAH model were compared with the corresponding experimental results to assess the suitability of the constitutive model to accurately reproduce the observed effects of strain-path changes.

Mechanical anisotropy induced by strain path change for AZ31 Mg alloy sheet

Mechanical anisotropy induced by strain path change for AZ31 Mg alloy sheet

The dependence of the strain path on the microstructure, texture and mechanical properties of cryogenic rolled Al-Cu alloy

An investigation was conducted on Al-4%Cu alloy sheets to study the role of deformation path on the strength properties, evolution of microstructure and crystallographic texture during cryogenic rolling. Samples were rolled to two distinct thickness strains (50% and 75%) by unidirectional and cross rolling (bidirectional) routes. The strength and hardness properties were found to be more efficient in the cross rolled samples at 50% reduction than their counterparts rolled unidirectionally. Dynamic recovery was observed at higher rolling reductions on cross rolling. Microscopic features observed by EBSD revealed the occurrence of significant grain refinement on the samples rolled with a change of strain path. Also, the alteration of the rolling route resulted in distinct deformation textures and microstructures. TEM studies pointed out the scattered diffusion of the disintegrated dislocation cores and the redistribution of the second phase particles on higher rolling reductions with the change of strain path. Furthermore, the texture results showed a threefold increase on the Goss/Brass ratio which indicated the good fracture toughness behaviour of the cross rolled samples at lower reductions.

Revisiting anisotropy in the tensile and fracture behavior of cold-rolled 316L stainless steel with heterogeneous nano-lamellar structures

Abstract We produced a 316L stainless steel with heterogeneous nanometer-thick lamellar structures by severe cold-rolling at room temperature, and conducted micro-scale tensile tests in different orientations to evaluate both the in-plane (parallel to the nano-lamellae) and out-of-plane (normal and 45° inclined to the nano-lamellae) mechanical anisotropy. The parallel orientation demonstrates the greatest tensile strength while the inclined orientation exhibits the least strength. The tensile tests in normal and inclined directions also indicate significant transient elastic-plastic response due to the strain path change. Fractographic examination demonstrates that the specimen fails in the normal direction by premature micro-void nucleation and growth, which restricts its tensile strength; however, we identified zig-zag cracking associated with lamellar shear cracking in the inclined direction.

Characterization of kinematic hardening with a hydraulic bulge test

The increase of the mapping accuracy in numerical simulations of sheet metal forming processes is an important field of research today. In this context, the modelling of the kinematic hardening plays a major role when it comes to nonlinear strain paths during the forming process. The kinematic hardening leads, beside other effects, to a lower increase of the hardening after a change of the linear strain path. Characterization of the Bauschinger coefficient, an indicator of the portion of kinematic hardening, is normally done with cyclic tension-compression tests. The testing setup is quite challenging in the strain measurement and the specimen handling due to the small geometry and the risk of buckling during compression. Thus, a hydraulic bulge test with an optimized geometry is used for the characterization of the kinematic hardening with a strain path change for the materials DC06 and DP600. According to literature, DC06 has no significant kinematic hardening, while the high strength steel DP600 is sensitive to this hardening mechanism. The strain path change is realized by a secondary element in the die. In the beginning of the test, a conventional circular die induces an equi-biaxial strain. After this preforming step, an elliptical geometry is used to induce plane strain in the specimen. The resulting strain path changes from equi-biaxial to plane strain. The flow curves out of the experiment show the kinematic hardening effect after the strain path change for the DP600 while no change is observable for the DC06. Numerical simulation with the identified kinematic factor should lead to a better mapping accuracy regarding the springback behavior.

Unravelling Anisotropy Evolution during Spiral Pipe Forming: a Multiscale Approach

Spiral forming of bainitic steel coils into large diameter pipes involves a complex deformation history with several strain path changes. These lead to mechanical properties on pipe which are macroscopically different compared to coil. A detailed understanding of the property evolution during spiral pipe forming is crucial to tailor the coil material and to ensure safe pipe operation. However, it has proven difficult to correctly reproduce the anisotropic strength evolution during pipe forming with available phenomenological hardening models. Unravelling the factors contributing to macroscopic anisotropy is inherently a multi-scale problem due to the complex microstructures exhibited by modern bainitic linepipe steels. They promote a large Bauschinger effect, aside from cross loading-effects and more or less pronounced Lüders banding. Here, we present selected experimental and numerical results related to our efforts to predict the mechanical properties of bainitic steel pipes manufactured from hot rolled coils. Across the scales, we consider sources for anisotropy, such as residual stresses, crystallographic texture and grain substructure. A dislocation-based crystal plasticity model incorporated into a computationally efficient hierarchical multi-scale forming simulation is employed to predict texture and strength changes.

Pass number dependence of through-thickness microstructure homogeneity in tantalum sheets under the change of strain path

Microstructure and crystallographic texture are the key factors that determine the properties of sputtering target used in integrated circuit fabrication. Multi-pass clock-rolling has been used recently to produce Ta sputtering targets. However, the effect of strain per pass, or the number of passes to achieve desired thickness, in clock-rolling on the homogeneity of final microstructure has not been investigated yet. In this study, deformation and recrystallization behaviors of Ta sheets during 8-pass and 16-pass clock-rolling as well as subsequent annealing are investigated. X-ray diffraction reveal that 16-pass sample has relatively homogeneous {111} ⟨uvw⟩ {〈111〉//normal direction (ND)} and {100} ⟨uvw⟩ {〈100〉//ND} fibers along its thickness, whereas the distribution of texture in 8-pass sample is uneven. X-ray line profile analysis show that the distribution of stored energy is also more homogeneous in the 16-pass sample. Electron backscatter diffraction and transmission electron microscopy reveal numerous microshear bands and well-arranged microbands predominantly occurring in {111} deformed matrix. These prevail in the center of the 8-pass sample, whereas grain subdivision within {100} and {111} matrix in the 16-pass sample is more homogeneous through thickness. Average grain orientation spread (GOSaverage) within the {111} matrix in the center of the 8-pass sample is significantly higher than that at the surface and quarter-thickness, indicating enhanced grain subdivision. Schmid factor and Taylor model analysis demonstrate that a greater probability of activation of the primary slip system only in the 8-pass sample compared to larger number of active slip systems in the 16-pass sample. Upon annealing, uniform nucleation combined with a slower grain growth rate results in a finer and more uniform grain size in the 16-pass sample. By contrast, severe gradient in through-thickness recrystallization microstructure forms in the 8-pass sample. This is attributed to higher stored energy and preferential nucleation sites in the center leading to faster recrystallization compared to the surface. Overall, the increase of pass number improves the homogeneity of through-thickness recrystallization microstructure in Ta sheets under the change of strain path.

Effect of strain path change on the through-thickness microstructure during tantalum rolling

High purity tantalum was respectively processed by unidirectional rolling (UR) and clock rolling (CR), and the through-thickness microstructures were investigated by multiple characterization techniques including electron backscatter diffraction (EBSD), Vickers hardness (HV) and X-ray diffraction (XRD). Results show that the through-thickness stored energy distribution in CR specimens is more homogeneous than in UR specimens due to uniform texture distribution. {111} grains possess larger Schmid factors and the corresponding Schmid factor difference ratio than {100} grains, indicating the activation of uniserial slipping in {111} grains, which leads to inhomogeneous deformation and higher stored energy. Besides, X-ray line profile analysis (XLPA) suggests that the stored energy of {111} grains increases successively from the surface to center layer, regardless of strain paths, due to the influence of redundant friction on the surface layers. While the occurrence of multiple slipping in {100} grains leads to homogeneous deformation and lower stored energy.

Effect of kinematic hardening on the yield surface evolution after strain-path change

Abrupt strain path changes without elastic unloading have been used to investigate the yield surface of sheet metals, both experimentally and theoretically. These investigations emphasized an apparent non-normality phenomenon, following such a strain-path change. Subsequently, these results inspired the development of plasticity models including non-associated flow rules and non-normality theories. In this study, this type of abrupt strain-path changes is investigated using kinematic hardening models in the context of associated plasticity. The aim is to emphasize the contribution of kinematic hardening ingredient to the apparent violation of the normality condition. The results show that kinematic hardening slope and curvature of the material have a strong influence to contribute to this apparent non-normality.

Finite element modeling and durability evaluation for rubber pad forming process

Elastomer (or rubber pad) forming is a dieless forming process. The forming process has several advantages compared to general press forming process in terms of tool cost and scratch problem. However, when the elastomer is subjected to severe deformation during forming process, it can result in an expensive cost for the replacements of elastomer. Therefore, it is necessary to evaluate accurate tool life. In this study, the FE analysis was conducted for the rubber pad forming process and the fatigue life evaluation of the elastomer tool was investigated numerically using the reference experimental data. For the FE analysis, uniaxial and equibiaxial tension tests of natural rubber 50 were carried out in order to obtain the mechanical material properties of the elastomer. The hyperelastic behavior of the elastomer was characterized using Ogden model. The elastomer forming process was modeled using a commercial software LS-DYNA 3D. Two important factors of FE modeling were to calibrate the simulation conditions and to obtain the target product shape with a preformed elastomer. With the result of FE analysis, a durability of the elastomer was conducted focusing on fatigue life, because the elastomer is applied for repeated loadings during the forming process. Unlike general fatigue analysis, the fatigue life of the elastomer is predicted with respect to the strain measures due to Mullins effect. Furthermore, the Polar Effective Plastic Strain (PEPS) diagram [6] considering the strain path changes was used to check the failure of the blank during the forming process.

Twinning-induced anisotropy of mechanical response of AZ31B extruded rods

Texture and twinning-induced anisotropy of the yield stress and hardening of AZ31B extruded rods is investigated. The multidirectional compression tests involving strain path changes are performed in order to: i. assess which slip and twinning systems are active in the polycrystalline sample with a strong texture, ii. analyze the influence of the preliminary deformation upon twin formation, iii. observe the resulting change of the mechanical response. In order to fulfil these goals mechanical testing is supplemented by microstructure analysis. Experimental observations are used to validate the proposed crystal plasticity framework when it is combined with the viscoplastic self-consistent scheme. On the other hand, the results of numerical simulations are used to confirm an advocated interpretation of experimental findings. Finally, the experimental and numerical results are discussed with respect to the theoretical study of slip and twinning activity on the basis of the generalized Schmid criterion. It is concluded that twinning activity influences the mechanical response predominantly by the texture change and to lesser extent by modification of strain hardening due to slip-twin interactions.

Non-linear strain path experiment and modeling for very high strength material

The goal of this work is to develop experimental methods and modeling of very high strength steel sheets subjected to non-linear strain paths. A 1.6 mm thick TRIP steel sheet with a tensile strength of 1180 MPa was investigated. A suitable test for the uniaxial tension pre-strain was developed. A constraint was to achieve an as uniform as possible strain field over the entire gauge area. The pre-strain was conducted on a 500kN MTS tensile testing machine. The geometry of a new specimen was optimized through finite element simulations and experiments on the TRIP1180 material. Then, different types of subsequent specimens were extracted from the pre-strained material by electro-discharge machining (EDM) for the second deformation step leading to a strain path change. The subsequent plastic behavior was measured and modeled using the HAH distortional plasticity model. Comparisons between the experimental and predicted behavior are discussed.

Improvement in Accuracy of Failure Prediction in Sheet Hydroforming of Square Cups Using Stress-Based Forming Limit Diagram

Prediction of failure in sheet metal forming processes accurately is very important for successful production and optimization of parameters. A major problem of conventional strain-based forming limit diagrams (FLDs) is their inability to predict failure accurately in processes such as sheet hydroforming where there is a change in strain path and mode of deformation. In the present work, a stress-based forming limit diagram has been developed for AA 5182 alloy sheets modifying the analytical procedure, proposed by Stoughton, to determine forming limits in stress space from failure strains incorporating anisotropy using Balart’s yield criterion. The developed stress-based FLD has been used to predict failure in sheet hydroforming of square cups. Results are compared with Hill’s quadratic yield criterion. Significant difference has been found in failure prediction between strain-based and stress-based criteria when they are applied to sheet hydroforming. A change in strain path has been observed at the critical corner regions in hydroforming of square cups due to initial drawing and then biaxial stretching during calibration. The experimental validation clearly showed that accuracy in failure prediction can be improved in sheet hydroforming by using a stress-based forming limit diagram.

Effect of continuous strain path changes on forming limit strains of DP600

AbstractThe strain path may change in actual sheet metal‐forming processes, so the determination of formability of sheet metal should consider the nonlinear strain path. For identifying the forming limit (FL) strains under nonlinear strain path, a conventional two‐step procedure with unloading is classically used to produce the strain path change, which results in no continuous measure of strain. The in‐plane biaxial tensile test with a cruciform specimen is an interesting alternative to overcome the drawbacks of conventional method. The strain path change can be made without unloading during a single test. In this work, the experimental FL strains of DP600 sheets under two types of nonlinear strain path are investigated and then compared with those under linear strain paths. The Oyane ductile fracture criterion is used in the finite element simulation to predict the experimental results.

Influence of uniaxial tensile pre-strain on forming limit curve by using biaxial tensile test

This paper focused on the effect of pre-strain on forming limit curves (FLC) of 5754-O aluminum alloy sheet through utilizing biaxial tensile approach. Based on Swift model and Yld2000-2d yield criterion, the dimensions of cruciform specimen was optimized through applying finite element method for increasing the strain at specimen center. After that, with the recommended specimen size, the cruciform specimen was tested under various stroke ratios to experimentally characterize the limit strains under different pre-strain levels. Subsequently, the biaxial tensile tests were simulated by Abaqus to obtain the limit strains and validate the material models. It can be observed in both experiments and simulations that the pre-strained uniaxial tension followed by plane tension or equi-biaxial tension can improve the formability of sheet metals. Besides, the strain path change affects the trend of first derivative of strain rate difference between neighboring points with respect to time. An early increase occurred and then fell back to the stable value, the steady evolution continued until to a new increase reaching the critical value. The M–K prediction approach was simulated to verify the influence of pre-strain on FLC. It can be found that the early increase peaks of the major strain incremental ratio rose with the amplitude of pre-strain. Finally, the phenomenon of pseudolocalization caused by the strain path change was explained through evolution of stress state inside the groove.

Springback prediction for a mechanical micro connector using CPFEM based numerical simulations

The bending process of an industrial connector is considered and investigated via numerical simulation using a crystal plasticity finite element model (CPFEM). The process consists of sequentially bending a 0.1 mm thick copper-based alloy (CuBe2) with progressive tools into a miniature cylindrical connector of around 1 mm in diameter. The paper focuses on the prediction of springback through the influence of several key-parameters of the numerical simulations. The finite element characteristics, single crystal plasticity model features and the number of grains in the sheet thickness are investigated in order to highlight relevant and influential parameters in CPFEM based microforming process simulations. The influence of the elastic properties is analyzed and a modification of the Peirce-Asaro-Needleman single crystal hardening law is taken into account in order to improve the description of reverse strain path changes. Finally, the numerical results are discussed and compared to the springback measured during the industrial process of the cylindrical connector. It is demonstrated, through the very good agreement with the experimental results, that such approach can be useful to simulate industrial processes.

In-situ study of the effect of strain path change on dislocation boundary evolution in commercial purity aluminum

An in-situ study of the effect of strain-path change on deformation microstructure and slip activity has been investigated using samples of commercially pure aluminum. Changes in dislocation boundary arrangements and crystal lattice rotations were tracked using CMOS-based electron backscattered diffraction (EBSD) detector combined with in-situ tensile deformation of ε = 10%. Samples were first cold-rolled to 5% reduction and then deformed by uniaxial tensile along the transverse direction. Despite the use of a CMOS-based detector, analysis of deformation microstructure at such low plastic strains using EBSD is still challenging. Nevertheless in some grains details of the dominant deformation microstructure can be discerned. Slip line observations confirm that overall slip system activity is not influenced by the strain path change, but the EBSD observations show that in some cases dislocation boundary alignment is influenced by the presence of pre-existing boundaries, and in some grains the crystal rotations differ to those expected for tensile deformation of fully recrystallized grains of similar orientation.

Strain path dependent evolutions of microstructure and texture in AZ80 magnesium alloy during hot deformation

In the present study, the effects of strain paths (i.e., single-pass and multi-pass hot compression) on microstructural and texture evolutions of AZ80 magnesium alloy were studied at temperature of 350 °C and strain rate of 0.01 s−1. The results showed that flow stresses are remarkably dependence on strain path changes. Flow stress hardening phenomenon during interrupted holding of multi-pass hot deformation was observed, which led to higher peak stress of next pass than previous unloading stress. Strain paths presented slight influence on grain size. Significant contribution of strain paths to texture evolution was found. Due to dynamic recrystallization and meta-dynamic recrystallization, texture components gradually changed from (1¯21¯0)<0001> and (011¯0)<0001> in single-pass deformation to (0001)<011¯0> and (0001)<112¯0> in four-pass deformation. The observed flow stress hardening phenomena were interpreted by the combined functions of grain coarsening and texture evolution.

The effect of strain path changes on texture evolution and deformation behavior of Ti6Al4V subjected to accumulative angular drawing

The Ti–6Al–4V alloy wires were plastically deformed using the accumulative angular drawing (AAD) process at room temperature with a maximal logarithmic strain ε ~ 0.51. Microstructure and microtexture evolution and inhomogeneity of the Ti alloy wires were investigated quantitatively using the electron backscattered diffraction technique within the scanning electron microscope and compared to wires after conventional linear drawing. Moderate grain refinement was observed after deformation. The kernel average misorientation parameter increased significantly, pointing to evolution of subgrain structure. The yield stress and ultimate tensile strength increased after the AAD and linear drawing and decrease in hardness was observed after the first pass of the AAD and linear drawing process. However, the AAD introduced inhomogeneity in hardness values at the sample cross section. Hardness variation correlates with a local texture asymmetry parameter, while no correlation between hardness and grain size was observed. A Schmid factor analysis indicated that the AAD is inhomogeneously introducing grain orientations that are favorable for prismatic and pyramidal dislocation slip, having a positive effect on the plasticity of Ti–6Al–4V alloy wire during drawing.