Prediction of asymmetric cyclic‐plastic behaviour for cyclically stable non‐ferrous materials

Abstract

Investigation on asymmetric cyclic‐plastic or ratcheting behaviour of non‐ferrous materials has received relatively little attention compared with ferrous materials. Ratcheting behaviour of materials is generally simulated using isotropic‐kinematic hardening models; however, for materials showing cyclically stable response, isotropic hardening is often not accounted for the constitutive modelling. A methodology based on Chaboche's isotropic‐kinematic hardening (CIKH) model with the consideration of genetic algorithm for optimization of initial estimates of the CIKH parameters is used in this study. The investigated plastic responses incorporate both symmetric strain‐controlled hysteresis loops and ratcheting behaviour. The suggested approach satisfactorily predicts the reported plastic response of cyclically stable non‐ferrous alloys based on aluminum, zirconium, and titanium.

Estimation of cyclic hardening/softening and ratcheting response of materials through an algorithm to optimize parameters in Chaboche's hardening rule

“…The adopted CIKH model considers a non‐linear isotropic hardening (IH) component along with a kinematic hardening (KH) part composed of four independent non‐linear backstress components; the fourth backstress incorporates a threshold term. Pertinent details of the methodology are already described in some earlier reports 59,69 . For the convenience of the current readers, the outline of the methodology and the modifications used for the present work are given here.…”

“…The parameter is the slope at the initial portion for the th backstress component, while the parameter is the dynamic recovery parameter controlling the rate of evolution of the th backstress component. The fourth backstress component ( ) contains an additional threshold term ( ) as proposed by Chaboche 40 ; the dynamic recovery for due to the parameter is activated only when the backstress has a magnitude greater than 40,47,59,69 …”

“…The preliminary estimate for the parameter , which controls the rate of the evolution of yield surface, is obtained from the variation of the size of the elastic zone with number of cycles under strain‐controlled loadings. A higher magnitude of parameter (>50) stabilizes the IH rapidly resulting in a cyclically stable response, while a low magnitude of (<10) is capable of replicating cyclic hardening or softening response 59,69 …”

“…The error function for the ratcheting simulations ( in Equation (10a)) considers an offset of 5% to the corresponding maximum magnitude of the experimental and the simulated strains. This is done to avoid the unreasonably large value of the error function due to the usually small magnitude of the ratcheting strains in the initial cycles, even when the absolute error is small following the previous reports 59,69 . The modified data points after consideration of the offsets are quantitatively represented by and as demonstrated in Figure 4B.…”

“…A methodology to simulate the cyclic‐plastic response of cyclically stable metallic materials based on the Chaboche isotropic‐kinematic hardening (CIKH) model has been recently proposed by Nath et al 59 The approach considers the estimation of parameters of the CIKH model using genetic algorithm optimization technique. The methodology has been demonstrated to suitably predict the cyclic‐plastic response of various cyclically stable ferrous and non‐ferrous alloys 59,68,69 under different strain‐controlled and stress‐controlled loading conditions. The novelty of this particular study lies in extending the proposed approach by Nath et al 59 earlier used for cyclic‐plastic simulations of cyclically stable materials towards predicting the stress‐strain response for cyclic hardening/softening materials under both strain and stress‐controlled loading; this is intended at the broader aim to assess the generalized nature of the proposed methodology by Nath et al 59 .…”