Micromechanical Modelling of the Cyclic Deformation Behavior of Martensitic SAE 4150—A Comparison of Different Kinematic Hardening Models

Abstract

A fundamental prerequisite for the micromechanical simulation of fatigue is the appropriate modelling of the effective cyclic properties of the considered material. Therefore, kinematic hardening formulations on the slip system level are of crucial importance due to their fundamental relevance in cyclic material modelling. The focus of this study is the comparison of three different kinematic hardening models (Armstrong Frederick, Chaboche, and Ohno–Wang). In this work, investigations are performed on the modelling and prediction of the cyclic stress-strain behavior of the martensitic high-strength steel SAE 4150 for two different total strain ratios (R ε = −1 and R ε = 0). In the first step, a three-dimensional martensitic microstructure model is developed by using multiscale Voronoi tessellations. Based on this martensitic representative volume element, micromechanical simulations are performed by a crystal plasticity finite element model. For the constitutive model calibration, a new multi-objective calibration procedure incorporating a sensitivity analysis as well as an evolutionary algorithm is presented. The numerical results of different kinematic hardening models are compared to experimental data with respect to the appropriate modelling of the Bauschinger effect and the mean stress relaxation behavior at R ε = 0. It is concluded that the Ohno–Wang model is superior to the Armstrong Frederick and Chaboche kinematic hardening model at R ε = −1 as well as at R ε = 0.

Micromechanical Modeling of Fatigue Crack Nucleation around Non-Metallic Inclusions in Martensitic High-Strength Steels

“…The mean values of the main alloying elements of the steel are given in Table 1. In the context of previous research on micromechanical modeling of lath martensitic microstructures, presented in [28,49], substantial experimental investigations were performed with respect to microstructural properties, cyclic effective deformation behavior and fatigue crack nucleation characteristics. The readers are referred to previous investigations [28,49], where the corresponding results are reported and discussed in detail.…”

“…The investigated lath martensite represents a fine-grained structure, whereby the observed blocks, laths and prior austenite grains show qualitatively heterogeneous size distributions. The prior austenite grains were reconstructed in a previous study [49] by the software package ARPGE [52] and the Nishiyama-Wassermann [53] orientation relationship.…”

“…Martensitic SVEs without defects were generated by multiscale Voronoi tessellations within a framework of the C++ software library voro++ (Version: 0.4.6) and python (Version: 2.7). This martensitic microstructure generator has been developed in a previous study by the authors and more details about the generation process are given in [49].…”

“…For the present work, three virtual SVEs were generated to represent a portion of the stochastic nature of metallic microstructures and the corresponding variability in fatigue crack initiation. For the accurate crystallographic representation of the lath martensitic structure of the investigated material, the different SVEs incorporate the Nishiyama-Wassermann orientation relationship [49]. The three different SVEs are build up on different numbers of prior austenite grains, crystallographic packets and blocks.…”

Modelling the Strain Range Dependent Cyclic Hardening of SS304 and 08Ch18N10T Stainless Steel with a Memory Surface

“…Some of the material models have been used to capture cyclic material behavior. To describe the cyclic behavior of SAE4150 martensitic steel [16], Schäfer et al considered three kinematic hardening models, i.e., the Chaboche [5], Armstrong-Frederick [4] and Ohno-Wang [6] models. They used these kinematic approaches to simulate the micromechanical behavior of the selected material.…”