Abstract
Pressure sensitive asymmetric Drucker yield criterion is developed to deal with pressure dependent sheet metals for instance steels and aluminum alloys. The sensitivity to pressure is conserved by introducing three-dimensional anisotropic parameters in the first stress invariant; while the third deviatoric stress invariant is remained in odd function form to consider the strength differential effect (SDE). To describe the flow stress directionalities of metallic materials, the Drucker yield function is extended using two transformation matrix consisting of anisotropic parameters. The proposed Drucker yield criterion is utilized to predict the anisotropic yield and plastic deformation of aluminum alloys with weak SDE: AA 2090-T3 with face-centered cubic (FCC) crystal systems and AA 2008-T4 with body-centered cubic (BCC) crystal systems as well as metals with strong SDE: Zirconium clock-rolled plate with hexagonal close packing (HCP) crystal systems. The comparison between the predicted anisotropic behavior and experimental results reveals that the extended anisotropic Drucker yield criterion can precisely model the anisotropy for FCC, BCC and HCP metals. The proposed function is implemented into ABAQUS VUMAT subroutines to describe the four-point bending test which is used to consider the effect of various yield functions and material orientations on deformation behavior. The obtained contours of the cross-section, strain components distribution and also the shift of neutral layer indicate that the extended Drucker yield function can well predict the final geometric configuration of the deformed Zirconium beam.
Highlights
With the increasing demand for lightweight, fuel consumption and crashworthiness of automobiles, more and more lightweight materials such as aluminum alloys are increasingly demanded in the car industry to produce body parts in view of their excellent mechanical properties
In case of in-plane bending (IPB), where the c -axes are in accordance to the x-axis, the predicted contours of all yield functions well coincide with the experimental data, i.e., rectangular cross-section shown in Figure 17c, indicating correct prediction of the rigidity in the direction of hard-to-deform c -axes z /mm
IPB, where the hci-axes are in data accordance to athe x-axis, predicted contours of all and of compared with observed experimental obtained by local strain the measurement method yield functions well the and experimental cross-section determined by coincide dot-matrix with deposition mapping [34].data, Figurei.e., 18a isrectangular the case of through-thickness bending (TTB), where all the shown in yield criteria cancorrect predict similar plasticof strain the normalof orientation of Zirconium
Summary
With the increasing demand for lightweight, fuel consumption and crashworthiness of automobiles, more and more lightweight materials such as aluminum alloys are increasingly demanded in the car industry to produce body parts in view of their excellent mechanical properties. Bron and Besson et al [11] utilized two stress tensor transformations to substitute in expression the Karafillis and Boyce yield function [7], introducing twelve anisotropy coefficients to describe anisotropic materials Another alternative method to extend the existing isotropic yield function was done by Cazacu et al [12] who generalized the second and third invariants of deviatoric stress tensor of Drucker’s 3D yield criterion. Cazacu and Barlat [17] put forward anisotropic yield criterion expressed by the second and third invariants of the stress deviator and later extended it using the generalized invariants to describe SDE as well as the anisotropy of magnesium and its alloys. Four-point bending test is simulated on Zirconium clock-rolled plate to show its reliability of reflecting the SD effect and predicting the shift of the neutral plane
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