A dislocation density based elasto-plastic self-consistent model for the prediction of cyclic deformation: Application to AA6022-T4

Abstract

We develop a polycrystal plasticity constitutive law based on the elasto-plastic self-consistent (EPSC) theory for the prediction of cyclic tension-compression deformation. The crystallography based model integrates a dislocation based hardening model and accounts for inter-granular stresses and slip system level backstresses, which make it capable of capturing non-linear unloading and the Bauschinger effect (BE). Furthermore, the model features dissolution of dislocation population upon the load reversal, which enables it to predict the change in hardening rate during reverse loading from that during forward loading. To demonstrate these capabilities of the model, we investigate elasto-plastic behavior of AA6022-T4 sheets under in-plane cyclic tension-compression. From a set of carefully performed cyclic tests to several strain levels, we observe that the material exhibits (1) a typical decreasing hardening rate during forward loading, (2) a linear followed by non-linear unloading upon the load reversal, (3) a transient softening followed by rapid work hardening (the BE), and (4) a decrease in subsequent hardening rate during reverse loading (the permanent softening phenomenon). To predict these effects, we calibrate the model to establish a set of material parameters using a portion of the measured data. The remaining measured data is used for verification of the model. We show that using the single set of material parameters, the developed model is capable of predicting all the particularities pertaining to the cyclic deformation of the material with great accuracy. From the favorable comparison of the predictions and experimental data, we infer first that the non-linearity of unloading increases with the amount of pre-strain, next that the backstresses have a dominant effect in capturing non-linear unloading while both the backstresses and inter-granular stresses govern the BE, and finally that the inclusion of reversible dislocation motion is the key for capturing hardening rates during reverse loading.

Low‐cycle fatigue behavior of rolled WE43‐T5 magnesium alloy

“…Next, the material yields at a lower value of yield stress upon compression than the value reached upon prestrain in tension. This phenomenon is referred to as the Bauschinger effect . The lower yield upon the path reversal than the forward tension is attributed to a larger extent to the Bauschinger effect rather than to the tension versus compression asymmetry.…”

Anisotropic modeling of structural components using embedded crystal plasticity constructive laws within finite elements

“…Stored dislocation density can, however, serve to resist expansion of twin lamellae. More details of this dislocation density (DD) hardening model as it applies to α-U [13] as well as other metals, like FCC pure Cu [82], AA6022 [83], and Haynes 25 [84] or BCC Ta [85,86] and Nb [87] or HCP Zr [88][89][90], Be [10], and Mg [4], can be found in prior works. Below we provide an abbreviated review of this model.…”

Explicit incorporation of deformation twins into crystal plasticity finite element models

“…It is assumed that all slip and twin systems within the same deformation mode share the same values for critical resolved shear stress (CRSS). This hardening law has been successfully used to model deformation of several metals within mean-field self-consistent codes, differing in crystal structure, such as Haynes 25 [47], AA6022 [48], Nb [49,50], Ta [51,52], Mg [53][54][55], Zr [46,56,57], Be [10,58], and U [4,59,60]. Here, we integrate the same hardening law for U in CPFE and enable the existing CPFE to model the orthorhombic structure.…”