Comparative analysis of optimisation methods for linking material parameters of exponential and power models: An application to cyclic stress–strain curves of ferritic stainless steel

Abstract

The four most commonly used optimisation methods for linking the material parameters of an exponential Armstrong–Frederick and a power Ramberg–Osgood model are compared for given cyclic stress–strain curves of a ferritic stainless steel EN 1.4512. These methods are the damped Gauss–Newton method, the Levenberg–Marquardt method, the Downhill Simplex method and a genetic algorithm. Globally optimal material parameters are obtained by parallel searches within the methods. The methods are tested for cyclic curves at 20 ℃, 300 ℃, 650 ℃ and 850 ℃. The optimal values of material parameters and R2 values are comparable, whereas the search paths, the numbers of steps to reach optimal solutions and the processing time of the methods differ.

Comprehensive Modelling of the Hysteresis Loops and Strain–Energy Density for Low-Cycle Fatigue-Life Predictions of the AZ31 Magnesium Alloy

“…In contrast, sliding requires the smallest activation energy in the body-centred and face-centred cubic crystal structures typical for steel and aluminium alloys, regardless of the loading direction [6]. On the macroscopic scale, a symmetrical stress–strain response is obtained for the body-centred and the face-centred cubic crystal structures if the material is loaded with an alternating strain [16]. The interchange of the three mechanisms in the hexagonal close-packed crystal structure causes an asymmetrical shape of the stress–strain curve, typically also observed for AZ31 [6].…”

A new approach to finite element modelling of cyclic thermomechanical stress-strain responses

“…The elastic region of the AF model is defined by one of the coefficients (R 0 ) which is searched for during the optimisation procedure. As a result of the optimisation, the cyclic curves can deviate in the initial plastic region if the two curves must minimally deviate over the whole region between the yield stress and the tensile strength [41]. On the contrary, the RO equation in its original form does not contain an explicit proportional limit.…”

“…The RO coefficients, tensile strengths and proportional limit stresses are given in Table 1. Table 1: Values of the RO coefficients, tensile strengths and proportional limit stresses [41]. As reference models available in Abaqus, the Besseling (Reference model 1) and the Armstrong-Frederick (Reference model 2) models have been used as they enable a temperature dependent elastoplastic material behaviour with either multilinear kinematic or combined isotropic-kinematic hardening, respectively.…”

“…The cyclic curve for the Besseling model has been discretised into the same number of segments as for the Prandtl model. The AF coefficients have been determined using the Downhill Simplex optimisation method with the additional condition that the kinematic hardening coefficient γ is equal for the input temperatures [41]. This ensured comparable RO and AF input curves (Fig.…”

“…These models enable either bilinear, multilinear or nonlinear material behaviour with several hardening laws. Besseling or Armstrong-Frederick models [7,27,28] are especially suitable for either a multilinear or a nonlinear description of the cyclic curve although they either do not match the RO equation completely as the constitutive equations can be based on different mathematical laws or the temperature influence can be considered variously between the models [41]. Moreover, an extensive amount of finite elements can also influence the computational times of simulations.…”