Micro-mechanical investigation of fatigue behavior of Al alloys containing surface/superficial defects

Abstract

A crystal plasticity finite element (CPFE) simulation framework has been proposed in this study for the prediction of combined detrimental effect of mean stress and defects on the fatigue behavior of aluminum alloy. Experimental data for mean-stress effect on fatigue life and crack growth behavior was obtained on metal inter gas (MIG) welded joints of Al-5083/Al-5.8%Mg alloy plates and has been detailed in authors’ previous work, referred later. The present study focuses on its prediction using computational framework only. A 2D representative model for material’s microstructure was used for the simulations, generated using an anisotropic tessellation algorithm using the EBSD measurements data. A total of 10 different microstructure models were generated for each loading condition using six-node plane strain type quadratic triangular (CPE6) elements of mesh size 6 $\mathrm{\mu }$m. Two different types of cases were investigated: one without defect and other with a semi-circular surface defect. The simulated loadings at different stress ranges and stress ratios (R-ratio) were similar to the experimental conditions for the better comparison of the results. Significant heterogeneity in the distribution of R-ratios and the far-field applied R-ratio was observed. When defect was not considered, a clear deviation in the predicted fatigue lives from the experimental data was observed at different R-ratios: the predicted fatigue lives were higher than the experimentally observed fatigue lives. This was probably because of not considering the detrimental effect of defects on fatigue lives. But, when the defects were considered, the predicted results for different R-ratios were consistent with the experimental fatigue lives. The proposed CPFE simulation framework not only predicted well the effect of defects and mean stress on the fatigue lives, but also the scatter induced in them due to the defects.

Introduction

Failure of metallic components under high-cycle fatigue (HCF) conditions is generally controlled by the nucleation and propagation of micro-cracks, which are influenced by the local microstructure. Thus, the apparent random nature of fatigue behavior at the structure level is often related to the variability of local microstructural features i.e. grain size, crystal texture, defects, precipitates [1]. In real-life structures, defects in the form of pores, inclusions or notches due to poor surface roughness [2] act as stress raisers thereby resulting in decreased structural fatigue performances, when compared with the laboratory specimens. Accordingly, exhaustive experimental and simulation work is needed to statistically evaluate the fatigue performances and to determine the intrinsic process–structure–property relationships.

Several studies have been carried out to investigate and predict the role of these defects in the high cycle fatigue behavior of the structural components, specifically under mean tensile loads [3]. Murakami [4] proposed an empirical equation for estimating the effect of mean-stress on the endurance limit for the failures initiated from defects, based on the projected $\surd$area of the defect on the plane normal to the loading direction. Several approaches have also been proposed to predict the detrimental effect of the defects on fatigue lives and endurance limits by accounting for size, shape, position of the defects [5], [6], [7]. In a recent study, authors investigated the fatigue behavior of welded aluminum (Al) alloy containing multiple gas porosities of the size comparable to the grain size [8]. A shift from crystallographic crack initiation to defect-induced crack initiation was observed when transitioning from zero to positive mean-stresses. A macroscopic fatigue life model based on the modification of Walker’s model including the mean-stress effect was proposed. However, fatigue life predictions based on the application of empirical models (Basquin law, Miner’s rule, Goodman diagram) taking into account the macroscopic mechanical fields are structure-oriented methods and therefore material-specific, thus they do not account for the stochastic fatigue behavior due to the microstructural variabilities.

Crystal plasticity finite element method (CPFEM) has become a popular approach to predict the effect of particular microstructural attributes to the mechanical response of polycrystalline materials [9]. This method has been extensively applied in the field of fatigue for the past decades with an aim for providing insights and eventually predictions of the fatigue behavior and variability of metallic materials and thus accelerating the development of new alloys with improved fatigue performances. In particular, various mesoscopic fatigue criteria, often referred to as fatigue indicator parameters (FIP), have been proposed and investigated [10]. The FIP relates the location and time of crack initiation or propagation to the micro-mechanical fields and is believed to control the nucleation or growth of a fatigue crack. They are generally based on the critical plane approach by assuming that the local stresses [11], the accumulated plastic strain energy [12] or the mixed stress–strain fields [13] in a particular slip system are associated with the local driving forces responsible for the initiation and propagation of short fatigue cracks. Despite the difficulties to provide absolute predictions [14], this approach is attractive as a comparative means to isolate particular microstructural features through synthetically generated microstructures and to investigate their beneficial or detrimental behavior on the fatigue performance and its variability. In particular, it is found that the elastic anisotropy plays a major role on the stress and strain localization in body-centered cubic (BCC) [15], face-centered cubic (FCC) [16] and hexagonal close-packed (HCP) crystals [17], [18] due to local crystallographic orientations and misorientations which may lead to significant deviations when assuming elastic isotropy. In addition, the presence of notch [19], [20], surface defects [21], [22] and non-metallic inclusions [23] were systematically investigated using the CPFEM. However, most of the studies with the exception of few [24], only focuses on the crack initiation stage while in the high-cycle fatigue (HCF) regime, microstructurally short crack growth may account for the significant portion of the total fatigue life. Hence, to understand the effect of a particular microstructural attributes on the fatigue behavior, it is essential to get an estimation of the total fatigue life and not only of the nucleation life. However, the simulations of microstructurally and physically short crack propagation in a CPFE framework remains challenging as it requires the explicit modeling of a growing crack, either using the extended-FEM (X-FEM) approach [25], [26], cohesive zone modeling or meshing and remeshing of a crack by the introduction of duplicate nodes [27],…for a large number of cycles. Alternatively, the simplified approaches notably linking micro-mechanical fields in an undamaged polycrystal to driving forces for crack propagation have been shown to provide reliable predictions on the short crack growth behavior [28], [29].

In this paper, the authors aim to investigate the effect of mean-stress on the fatigue behavior of aluminum alloy containing pores by the simulation of synthetic polycrystalline aggregates using the Crystal plasticity finite element method (CPFEM). The remaining of the paper is organized as follows. In Section 2, the material and experimental procedures are described. The numerical methods including the synthetic microstructure, the crystal plasticity model and the fatigue life estimation approach are described in Section 3. The results are described and discussed in Section 4 starting with a mesh sensitivity analysis.