Strain Path Change Research Articles

Numerical Simulation and Analysis of High-Strength Steel Autobody Panel Stamping

The high-strength steel blanks with higher yield strength had introduced many challenging formability problems for the stamping process. However, in some situations the multi-stage process is a very effective solution for the stamping of high-strength blanks with a relatively lower formability than that of commonly steel blanks. In the multi-stage process, the change of strain path will be beneficial to the reduction of strain peaks and the utilization of the potential plasticity.

Finite element modeling using homogeneous anisotropic hardening and application to spring-back prediction

A finite element (FE) implementation of the recently proposed constitutive model (Homogeneous yield function-based anisotropic hardening model or HAH; doi:10.1016/j.ij-plas.2011.03.003 in International Journal of Plasticity) that describes the plastic behavior of materials subjected to multiple strain path changes was developed. A complete formulation based on the return-mapping algorithm for the yield function was proposed. In particular, a multi-step Newton–Raphson method was introduced to calculate the gradient of the HAH model for the stress integration procedure. In addition to the numerical aspects, the theoretical proofs of the stability and convexity of the HAH model were discussed. For verification purpose, simple finite element simulations were conducted and the results were compared to those obtained from various constitutive models. Finally, mechanical characterization and U-draw bend experiments were performed on DP590 and TRIP590 steel sheet samples. The springback was quantified using the parameters defined at the NUMISHEET (1993) benchmark. Simulations of the 2D draw-bend test were performed with the FE code and the HAH constitutive description for DP590 and TRIP590 steel sheet samples. All the predicted springback values for these materials were in good agreement with experimental data.

Effect of strain path change on the evolution of texture and microstructure during rolling of copper and nickel

The effect of strain path change during rolling has been investigated for copper and nickel using X-ray diffraction and electron back scatter diffraction as well as crystal plasticity simulations. Four different strain paths namely: (i) unidirectional rolling; (ii) reverse rolling; (iii) two-step cross rolling and (iv) multi-step cross rolling were employed to decipher the effect of strain path change on the evolution of deformation texture and microstructure. The cross rolled samples showed weaker texture with a prominent Bs {1 1 0}〈1 1 2〉 and P(BND) {1 1 0}〈1 1 1〉 component in contrast to the unidirectional and reverse rolled samples where strong S {1 2 3}〈6 3 4〉 and Cu {1 1 2}〈1 1 1〉 components were formed. This was more pronounced for copper samples compared to nickel. The cross rolled samples were characterized by lower anisotropy and Taylor factor as well as less variation in Lankford parameter. Viscoplastic self-consistent simulations indicated that slip activity on higher number of octahedral slip systems can explain the weaker texture as well as reduced anisotropy in the cross rolled samples.

Study on plastic flow localization prediction using a physically-based hardening model

The present paper aims at a detailed analysis of sheet metal formability using the physically-based hardening model accounting for the evolution of the anisotropic work-hardening induced by the microstructural evolution at large strains of Teodosiu and Hu (1995) [9]. The onset of localized necking is simulated by an advanced sheet metal forming limit model which connects, through the Marciniak–Kuczinsky analysis, the respective microstructural hardening model with the phenomenological anisotropic yield criterion Yld2000-2d (Barlat et al., 2003) [17]. Linear and complex strain paths are taken into account. The selected material is a DC06 steel sheet. An exhaustive study on the evolution of internal variables of the microstructural hardening model under such loadings is presented. The origin of the increase/decrease of formability under specific strain path changes is discussed.

Modelling the plastic behaviour of metals under complex loading conditions

Aluminium alloys and low carbon steel exhibit a transient work-hardening rate when the strain path is abruptly modified. The underlying physical mechanisms are latent hardening in the case of cross-loading and massive disappearance of the dislocations pertaining to prestrain when the loading stress is reversed. The modelling approach previously proposed for strain reversal is extended to cross-loading. In the model, the work-hardening rate is controlled by the evolutionary laws of three dislocation densities related to forward, backward and cross-loading. A parameter which measures the amplitude of the strain path change is incorporated in this approach. It is believed that these three densities are sufficient to model many cases consisting of two stage strain paths.

An alternative to kinematic hardening in classical plasticity

In this work, an approach is proposed for the description of the plastic behavior of materials subjected to multiple or continuous strain path changes. In particular, although it is not formulated with a kinematic hardening rule, it provides a reasonable description of the Bauschinger effect when loading is reversed. This description of anisotropic hardening is based on homogeneous yield functions/plastic potentials combining a stable, isotropic hardening-type, component and a fluctuating component. The latter captures, in average, the effect of dislocation interactions during strain path changes. For monotonic loading, this approach is identical to isotropic hardening, with an expanding isotropic or anisotropic yield surface around the active stress state. The capability of this constitutive description is illustrated with applications on a number of materials, namely, low carbon, dual phase and ferritic stainless steel samples.

高張力鋼板のひずみ経路変化を含む張出し成形限界予測

高張力鋼板のひずみ経路変化を含む張出し成形限界予測

Prediction of sheet forming limits with Marciniak and Kuczynski analysis using combined isotropic–nonlinear kinematic hardening

The forming limit curve (FLC), a plot of the limiting principal surface strains that can be sustained by sheet metals prior to the onset of localized necking, is useful for characterizing the formability of sheet metal and assessing the forming severity of a drawing or stamping process. Both experimental and theoretical work reported in the literature has shown that the FLC is significantly strain-path dependent. In this paper, a modified Marciniak and Kuczynski (MK) approach was used to compute the FLC in conjunction with two different work-hardening models: an isotropic hardening model and a mixed isotropic–nonlinear kinematic hardening model, which is capable of describing the Bauschinger effect. Predictions of the FLC using the MK analysis have been shown to be dependent on the shape of the initial yield locus and on its evolution during work hardening; therefore the hardening model has an influence on the predicted FLC. In this investigation, published experimental FLCs of AISI-1012 low carbon steel and 2008-T4 aluminum alloy sheets that were subjected to various nonlinear loading paths were compared to predictions using both hardening models. The predicted FLCs were found to correlate quite well with experimental data and the effects of strain path changes and of the hardening model on predicted FLCs are discussed.

On crystal plasticity formability analysis for magnesium alloy sheets

Sheet metal formability is assessed in terms of the Forming Limit Diagram (FLD) for magnesium alloys with Hexagonal Close Packed (HCP) crystallographic structure. All simulations are based on the recently developed elastic–visco-plastic self-consistent (EVPSC) model and the classical Taylor model, in conjunction with the M–K approach. The role of crystal plasticity models and the effects of basal texture on formability of magnesium alloy AZ31B sheet are studied numerically. It is observed that formability in HCP polycrystalline materials is very sensitive to the intensity of the basal texture. The path-dependency of formability is examined based on different non-proportional loading histories, which are combinations of two linear strain paths. It is found that while the FLD in strain space is very sensitive to strain path changes, the Forming Limit Stress Diagram (FLSD) in stress space is much less path-dependent. It is suggested that the FLSD is much more favourable than the FLD in representing forming limits in the numerical simulation of sheet metal forming processes. The numerical results are found to be in good qualitative agreement with experimental observations.

Assessing the Validity of Original and Modified Failure Criteria to Predict the Forming Limit of Unwelded and Tailor Welded Blanks with Longitudinal Weld

The main objective of the work is to assess the validity of modified failure criteria proposed by Naik et al. [1] and original failure criteria in predicting the forming limit of unwelded and tailor welded blanks (TWBs) with longitudinal weld, during stretching and drawing operations. The four different failure criteria, namely, effective strain rate-based, major strain rate-based, thickness strain rate-based, and thickness gradient-based failure criteria, both in original and modified forms, are used to predict the forming limit strains of unwelded and welded blanks. In the case of unwelded sheet, the forming limit predictions are consistent with the experimental result in the drawing side, but considerable difference is observed in the stretching side of forming limit diagram (FLD). In the case of tailor welded blanks (TWB), whenever failure is seen near the weld region, the strain rate-based criteria are modified as RC1 ≥ 25, RC2 ≥ 32, RC3 ≥ 32 for failure to occur. TWB forming limit curve (FLC) predicted using the modified criteria show better accuracy than the original failure criteria in the stretching side of the FLD. In the drawing side, FLC predicted by original criteria is the same as that from modified criteria, where in strain path change is witnessed instead of limit strain improvement. Through this work, it is demonstrated that using modified failure criteria, forming limit of TWBs can be predicted with better accuracy during stretching operation, while original failure criteria are sufficient for a drawing operation or in the drawing side of FLD

Transient Yielding during Compression Tests on ECAP’ed AA1050 Aluminium

In most papers dealing with tension and/or compression tests, the conventional yield stress is determined either by an offset method (usually 0.2% strain) or by back extrapolation from the stress-strain curve. In our experiments on ECAP’ed Aluminium a transient hardening saturation (THS) is always observed during the compression tests, but not during the tensile tests. This THS occurs at a significantly lower stress than the conventional yield stress. The aim of the present paper is to determine which the “real” start of yielding is. Two different experimental approaches have been adopted, confirming that the THS stage is exactly the yielding stage. This is not unimportant because it increases the tension-compression asymmetry and hence the back-stress and kinematic hardening. The reason for this different behaviour between tension and compression can be ascribed to a different change in strain path with respect to the ECAP deformation.

Flow Behaviour of Commercial Purity Titanium Subjected to Equal Channel Angular Pressing

Commercial purity Ti was subjected to equal channel angular pressing (ECAP) for up to three passes at 400oC using a die with die angle of 120o. Compression testing of the ECAP specimens was carried out to determine the subsequent flow behavior. Two types of compression test specimen orientations, one parallel to the axis of ECAP and the other at 45o to the axis of the ECAP, were prepared from the specimens subjected to ECAP. Anisotropy in flow behaviour (as indicated by values of strength co-efficient, K and strain hardening exponent, n) was observed. The strain hardening rates were also calculated from the experimentally determined flow curves for the specimens tested in compression in the two orientations. The results have been interpreted in terms of the strain path change parameter between the two deformation steps (ECAP and compression). Strain hardening behaviour and microstructure evolution is discussed in terms of strain path change parameter. Specimens compressed in the direction parallel to the ECAP direction had lower strain hardening exponents while exhibiting higher initial flow stresses. The strain hardening rates were lower for specimens compressed at 45o to the ECAP direction compared to specimens compressed parallel to the ECAP direction.

Deformation, recrystallization and plastic anisotropy of asymmetrically rolled aluminum sheets

Materials processed under various thermo-mechanical conditions exhibit a different plastic anisotropy. Both conventional and asymmetric rolling processes were applied to a 6016 aluminum alloy for automotive application. A sequence of different rolling schedules bears an effect on the recrystallization and plastic behavior of the material through the annealing texture. The effect of strain path change and annealing conditions on the recrystallization texture is investigated and the experimental data are modeled with the help of crystal plasticity models. The plastic anisotropy is analyzed based on experimentally measured Lankford values and calculated limiting drawing ratios. The calculated limiting drawing ratio of ∼2.17 for asymmetrically rolled sheets represents a considerable improvement as compared to the conventionally produced materials with the highest limiting drawing ratio of ∼2.09.

A study of high strength steels undergoing non-linear strain paths—Experiments and modelling

Abstract This paper presents an evaluation of the constitutive behaviour, including plastic anisotropy and mixed isotropic-kinematic hardening of two high strength steels, Docol 600DP and Docol 1200M, during strain path changes. A series of tensile and shear tests was performed on both virgin and pre-strained materials. The initial anisotropy and work hardening parameters were obtained from tensile tests, shear tests and a bulge test of the virgin material, whereas the kinematic hardening parameters were identified by comparing numerical predictions to experimental results related to the pre-strained materials. Numerical predictions using the obtained parameters agree well with the experimental results, both in the case of proportional, and under non-proportional strain paths.

Influence of rolling ways on microstructure and anisotropy of AZ31 alloy sheet

Two rolling ways, unidirectional rolling and cross rolling, were carried out on twin roll cast AZ31 alloy sheet to study the influence of strain path change on the evolution of the rolling microstructure and texture as well as the anisotropic properties of AZ31 alloy sheet with microscopy, X-ray diffraction technique and tensile tests. It is found that cross rolling gives rise to more uniform microstructure and stronger texture intensities compared with unidirectional rolling. The differences in the microstructure and texture intensities are reflected in the anisotropy characterized by the difference in the yield stress and the fracture elongation that were measured along directions in the rolling plane at angles of 0°, 45° and 90° from the rolling direction.

Research on the drawing process with a large total deformation wires of AZ31 alloy

Magnesium and their alloys have been extensively studied in recent years, not only because of their potential applications as light-weight engineering materials, but also owing to their biodegradability. Due to their hexagonal close-packed crystallographic structure, cold plastic processing of magnesium alloys is difficult. The preliminary researches carried out by the authors have indicated that the application of the KOBO method, based on the effect of cyclic strain path change, for the deformation of magnesium alloys, provides the possibility of obtaining a fine-grained structure material to be used for further cold plastic processing with large total deformation.The main purpose of this work is to present research findings concerning a detailed analysis of mechanical properties and changes occurring in the structure of AZ31 alloy wire during the multistage cold drawing process. The appropriate selection of drawing parameters and the application of multistep heat treatment operations enable the deformation of the AZ31 alloy in the cold drawing process with a total draft of about 90%.

Influence of Strain Path Changes on Microstructure Inhomogeneity and Mechanical Behavior of Wire Drawing Products

Cold drawn low carbon steel wires are widely used in several engineering applications where a proper combination of strength and ductility is of the paramount importance. In the present paper, the multi-pass angular accumulative drawing (AAD) is proposed as a new forming process where the high strain accumulation is used as a way to achieve much higher microstructure refinement level compared to the conventional wire drawing process. This process is characterized by a complex strain path history, being an effect of wire diameter reduction, bending, tension and torsion, what directly affects the microstructure changes in the final product. This process also evolves high inhomogeneity of microstructure, that if properly controlled, can lead to further properties improvement - what can be especially beneficial for alloys that are not characterized by complex compositions. In the present paper, special emphasis is given on the inhomogeneity of both deformation and microstructure and resulted mechanical properties. After drawing and annealing (at 500oC) mechanical properties measurements and microstructure analysis on the longitudinal sections of the wires were performed to assess the differences existing with respect to the conventional wire drawing process.

The Material Flow Analysis in the Modified Orbital Forging Technology

The main aim of this work is the computer aided design of the new orbital forging process. The finite element model was developed and used in research on possibility of modification of the classical orbital forging technology based on the Marciniak press to obtain more effective process. Obtained numerical results from simulations of the new orbital process are compared with the experimental analysis, performed on the orbital press with the developed device. However, due to the novelty of the developed approach the investigation on direction of material flow during deformation is of particular interest in this work. Direction of material flow and strain path change effect due to incremental character of deformation is analyzed. Obtained results confirm good predictive capability of the FE model and are the basis for the comparison of the two processes and discussion on the effectiveness of the modified incremental forming process.

Investigation on the strain-path dependency of stress-based forming limit curves

Path-dependent forming limits have been computed for sheet metals undergoing various combinations of plane stress loading conditions. This paper presents a theoretical model for prediction of stress-based forming limit curves (SFLC) based on the Marciniak and Kuczynski (MK) model. Acceptable agreement was observed between calculated forming limit curves (FLC) and experimental data for AISI-1012 steel (Molaei 1999) and AA-2008-T4 alloys (Graf and Hosford Metallurgical Trans 24A:2503–2512, 1993). In this paper, the path dependency of SFLCs predicted for different non-proportional loading histories has been investigated. For a range of prestrain values in different bilinear loading paths, the SFLC remains practically unchanged. However, some strain path dependency is observed for large values of prestrain (\( \bar{\varepsilon } \geqslant 0.35 \) for AISI-1012 steel) and for abrupt changes in strain path. Nevertheless, the SFLC remains a good failure criterion for virtual forming simulations because the path dependency of SFLCs is much less significant than that of strain-based FLCs.

Three-dimensional flow characteristics of aluminum alloy in multi-pass equal channel angular pressing

Experiments with a square specimen made of commercially pure aluminum alloy (AA1050) were conducted to investigate deformation behaviour during a multi-pass Equal Channel Angular Pressing (ECAP) for routes A, Bc, and C up to four passes. Three-dimensional finite element numerical simulations of the multi-pass ECAP were carried out in order to evaluate the influence of processing routes and number of passes on local flow behaviour by applying a simplified saturation model of flow stress under an isothermal condition. Simulation results were investigated by comparing them with the experimentally measured data in terms of load variations and microhardness distributions. Also, transmission electron microscopy analysis was employed to investigate the microstructural changes. The present work clearly shows that the three-dimensional flow characteristics of the deformed specimen were dependent on the strain path changes due to the processing routes and number of passes that occurred during the multi-pass ECAP.