Keywords

• Crystal plasticity;
• Realistic microstructure;
• Cyclic deformation;
• Extended finite element;
• Crack growth

1. Introduction

Polycrystalline metals and alloys possess a heterogeneous nature of grain microstructure and exhibit anisotropic response during mechanical deformation. These crystallographic orientation effects cannot be captured by traditional isotropic homogeneous models. Therefore, physically-based crystal plasticity models were developed and have been successfully applied in literature to predict the anisotropic mechanical response of individual grains in polycrystalline materials. Combination of crystal plasticity and finite element method has the ability to model the global and local stress–strain response of crystalline materials under various types of loading regimes including fatigue [1], [2] and [3].

In the efforts to consider the effects of the material’s microstructure on the mechanical behaviour of nickel based superalloy, a large number of studies were conducted using crystal plasticity [4], [5] and [6]. These studies aimed to predict the global and local stress–strain response as well as grain texture evolution and micro-structural crack nucleation under various loading conditions. For example, Fedelich [7] employed a crystal plasticity model with implicit dependency on precipitate size and volume fraction to predict the influence of microstructural parameters such as lattice misfit on deformation behaviour of a single crystal nickel based superalloy. The model was also used to calculate the back stress as a function of local deformation state, i.e., distribution of plastic strain in the microstructure. Kumar et al. [8] adopted crystal plasticity-based finite element approach to study the effects of microstructural variability on cyclic deformation of a single crystal nickel base superalloy. This study considered the effect of size and volume fraction of the γ^′${\gamma }^{\prime }$ precipitates on fatigue resistance of the material. Shoney et al. [9] presented a microstructure sensitive crystal plasticity model which has the capability to capture the variation in stress–strain response with changes in grain size, distribution of precipitate size and precipitate volume fraction as well as dislocation density for each slip system. In this regard, Lin et al. [10] used 2D crystal plasticity model to study the effect of grain microstructure on localised stress–strain distribution of a polycrystalline nickel based superalloy. The study was subsequently extended to 3D to simulate the global stress–strain response of the material under fatigue loading [11]. In addition, effects of grain microstructure on crack tip deformation and crack growth path were also explored using the crystal plasticity model. However, these models were limited to the use of artificial grain microstructure generated by employing the Voronoi tessellation algorithm, and cannot capture the local stress and strain behaviour precisely, an important indicator for nucleation of fatigue cracks. In order to capture the actual localised stress–strain response, 2D model based on realistic microstructure were developed by Choi et al. [12] to predict the localised stress in polycrystalline Mg alloys using crystal plasticity finite element method. Similarly, Wang et al. [13] studied grain level heterogeneous deformation in polycrystalline α-Ti material using crystal plasticity model based on 2D realistic microstructure. However, the work is limited to simulation of local deformation, without consideration of global deformation. Also to our best knowledge, there is hardly any work devoted to prediction of fatigue crack growth in polycrystalline materials using the realistic grain microstructure and crystal plasticity model.

Fatigue failure in engineering materials has been an important subject for several decades. A number of computational techniques have been developed and used in the literature to predict fatigue crack initiation and propagation, especially the finite element method (FEM) [14]. However, the major shortcoming of FEM is that the crack surfaces need to be in line with the edges of the elements, which presents a challenge for FEM in modelling the growth of discontinuities and cracks. In order to overcome this difficulty, a novel approach, called extended finite element (XFEM), has been developed recently [15]. In this technique, the crack geometry is mesh-independent and there is no need for the re-meshing to accommodate the crack as it grows. This is achieved by incorporating the enrichment functions into standard finite element approximation space [16] and [17]. With an appropriate fracture criterion, crack propagation can be modelled without the introduction of a predefined crack growth path, a unique feature of the XFEM technique. In fact, the method has already been widely applied to model a variety of crack problems such as crack propagation in thin-walled structures, crack branching and dynamic crack growth [18], [19] and [20].