Ratcheting assessment of materials based on the modified Armstrong–Frederick hardening rule at various uniaxial stress levels

Abstract

The present study evaluates ratcheting response of materials by means of the Armstrong–Frederick (A–F) hardening rule, the modified A–F rule (Bower's model), and further modifications of the hardening rule based on new introduced coefficients. The implemented modifications on the A–F‐based hardening rule aims to address stages of ratcheting over stress cycles. The modified hardening rule predicts the ratcheting strain rate decay over stage I and the constant rate of strain accumulation during stage II. The modified hardening rule consisted of the coefficients of the hardening rule controlling stress–strain hysteresis loops generated over stress cycles during ratcheting process (Bower's modification on A–F rule) plus the coefficients controlling rates over stages of materials ratcheting deformation. Stress–strain‐dependent coefficients in the modified rule are responsible to compromise overprediction of ratcheting of A–F during stage I and the premature plastic shakedown beyond stage I induced by Bower's model. Ratcheting strain rate coefficients improved the hardening rule capability to calibrate and control the rate of ratcheting in stages I and II and enabled the modified hardening rule to predict ratcheting strain over a prolonged domain of stress cycles. The modified hardening rule was employed to assess ratcheting response of 304, 42CrMo, 316L steel and copper samples under uniaxial loading conditions. The predicted ratcheting values based on the modified hardening rule and the experimental ratcheting strains were found in good agreements.

Ratcheting of 304 stainless steel under multiaxial step-loading conditions

“…Modifications have been made to extend the capability of the A-V hardening rule [34,35] with the accumulated plastic strain increment, dp in the dynamic recovery term of the model. This enables the modified model (equation (8)) to follow different directions under multiaxial loading due to components p dε and a a .…”

“…Bari and Hassan [36] achieved better simulation of uniaxial ratcheting strain while the model with threshold over-predicted ratcheting strain for multiaxial loading conditions. Ahmadzadeh-Varvani [34,35] modified the dynamic recovery term in A-F kinematic hardening rule by means of limited number of coefficients to assess uniaxial ratcheting response of materials.…”

Ratcheting in pressurized pipes and equipment: A review on affecting parameters, modelling, safety codes, and challenges

“…The current literature has reported various loading conditions at which ratcheting progress and rate was highly influenced by loading spectra. 116 In pressurized pipes and vessels, hoop and axial stress components dominantly affected ratcheting response of materials at different directions. 99 Complexity in loading strain paths and step loading was investigated through experimental studies 28,86,[99][100][101][102][103][104][105][106][107][108][109][110][111] to reliably control ratcheting of components in service.…”

“…28,115,191,192 The backbone of these models is based on the A-F 193 kinematic hardening rule. 201 Different descriptions of the dynamic recovery term were proposed by Bower, 200 Ohno-Wang, 203,204 Jiang-Sehitoglu, 205,206 McDowell, 207 Abdel Karim-Ohno, 208,209 Chen et al, 113,114,210 and A-V. 116,[211][212][213][214][215][216] The progress of this class of hardening rules initiated by A-F 193 when first they modified Prager linear hardening model 217 by adding a nonlinear term as Strain range memorization was also added as new surface by Ohno.…”

The Chaboche hardening rule: A re-evaluation of calibration procedures and a modified rule with an evolving material parameter

“…Since this initial work of Armstrong and Frederick, the idea of describing the evolution of kinematic hardening variables in terms of nonlinear differential equations has been followed in many other studies such as those of Chaboche et al [10], Chaboche [11][12][13], Ohno and Wang [14], Voyiadjis and Basuroychowdhury [15], Bari and Hassan [16], Chen and Jiao [17], Dafalias et al [18], Krishna et al. [19], Abdel-Karim [20], Abdel-Karim and Khan [21], Kan and Kang [22], Chaboche et al [23], Ahmadzadeh and Varvani-Farahani [24], Jiang et al [25], Kourousis and Dafalias [26], Taleb [27], and Li et al [28] to name a few.…”