Modeling and characterization of cyclic relaxation and ratcheting using the distributed-element model

Abstract

Constitutive modeling of cyclic relaxation and ratcheting (cumulative inelastic deformation) is developed on the basis of the distributed-element model (DEM). Although the original DEM is capable of describing general, elastic-plastic behavior for cyclically stabilized materials, it has the inadequacy of not being able to account for the effect of cyclic relaxation and ratcheting. By introducing the nonlinear kinematic hardening rule proposed by Armstrong and Frederick into element behavior of the DEM, the model becomes effective in characterizing the behavior of cyclic relaxation and ratcheting. Validation of the modified DEM is conducted by simulating cyclic behavior of various metal materials, including CS 1018, heat-treated rail steel, and Grade 60 steel. The results show that the modified DEM demonstrates realistic behavior of materials in both uniaxial and biaxial cyclic relaxation and ratcheting. Furthermore, detailed investigation of element behavior in the model provides us with additional insight into complex behavior and characteristics of materials in cyclic relaxation and ratcheting.

A comprehensive thermo-viscoelastic experimental investigation of Ecoflex polymer

“…Hence, the peak stress decreases with repeated cycles. This behaviour is called the cyclic relaxation [15,16,17,18]. In contrast, the normal stress relaxation, where a specimen is held fixed after a certain strain, is called the static relaxation.…”

Concurrent ratcheting and stress relaxation at the notch root of steel samples undergoing asymmetric tensile loading cycles

“…They related the drop in stress over progressing cycles directly to plastic straining. Uniaxial ratcheting and stress relaxation in samples of mild steel, rail steel, and Grade 60 steel were studied by Chiang . He employed ratcheting and stress relaxation data collected through works of Jhansale and Topper, McDowell, and Dafalias and Popov to simulate the excess of plastic strain and drop in stress magnitude over loading cycles.…”

“…Uniaxial ratcheting and stress relaxation in samples of mild steel, rail steel, and Grade 60 steel were studied by Chiang. 7 He employed ratcheting and stress relaxation data collected through works of Jhansale and Topper, 5 McDowell, 18 and Dafalias and Popov 19 to simulate the excess of plastic strain and drop in stress magnitude over loading cycles. Samples of Al 7075-T6511 and Al 7249-T76511 were tested by Arcari and Dowling 20 to examine stress relaxation and ratcheting under variable amplitude loading conditions.…”

“…Literature cites a number of experimental studies conducted to assess ratcheting and stress relaxation on metallic components by Morrow and Sinclair, Wetzel, Landgraf, Stadnick and Morrow, Jhansale and Topper, Koh and Stephens, Chiang, Arcari and Dowling, Paul et al, Rice et al, Hassan and Kyriakides, Hu et al, Wang and Rose, Rahman and Hassan, Lee et al, and Varvani et al Among first research endeavors in ratcheting and stress relaxation is a series of tests performed on 4340 steel samples under asymmetric zero‐to‐tension cycles in 1950s by Morrow and Sinclair . Stress relaxation in steel samples was stabilized in lower number of cycles as stress amplitude increased in magnitude.…”

Analytical sensitivity matrix for the inverse identification of hardening parameters of metal sheets

“…is the stress for the constitutive parameters A j . In case of one dimensional loading with reversal, equation (8) can be analytically integrated to obtain the back-stress along the loading paths, X L , and the reverse loading paths X RL , respectively (Chiang, 2008)…”