Stress intensity factors and crack propagation of metal-ceramic random microstructures

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Abstract

This paper is concerned with the crack analysis of RVE (representative volume element) microstructures of metal-ceramic phase composite. The detailed random RVE microstructure models of metal-ceramic phase composite are generated by a mathematical RMDF (random morphology description functions) micro modeling technology. The dispersion pattern and scale of random microstructure models are controlled by the volume fractions V of base materials and the total number N of Gaussian functions. The stress intensity factors (SIF) and the crack propagation trajectories are evaluated by the interaction integral and predicted by Paris law. These crack characteristics are investigated with respect to the model scale N and the initial crack length, and also compared with those of homogenization models. Through the numerical results, it is observed that both SIFs and crack propagation trajectories are remarkably influenced by the crack length, the model scale N and the dispersion pattern of RVE microstructure.

Introduction

Metal-ceramic phase composites are widely used for various engineering applications as advanced materials. Among the representative examples are advanced structural materials for aerospace engineering [1], bio-compatible artificial teeth [2], coating materials [3], electromagnetic materials [4], and nano and graphene composite materials [5,6]. These phase composites are a highly heterogeneous materials in which base constituents are mixed up in complex microstructure pattern [7,8]. When compared with general homogeneous materials, these heterogeneous materials with random microstructures provide superior performances because of only the excellent material properties of base constituents are combined. Furthermore, the target performance of these phase composites could be maximized when the major microscopic parameters, such as volume fractions of constituents, are optimally chosen. The most representative example can be a functionally graded materials (FGMs) in which the volume fraction distributions are optimally tailored to provide the best target performance [9,10].

Besides the randomness, the microstructure of dual-phase composites is characterized by several parameters such as the dispersion structure, the size and orientation of constituent particles, and volume fractions of base materials [11,12]. As a result, the thermomechanical responses of dual-phase composite become different for different microstructures, at the microscopic level, even when the geometry, loading and boundary conditions are kept the same. However, the numerical analysis and design of metal-ceramic phase composite is an extremely hard task because both the microstructure generation and the material characterization are highly painstaking. To avoid this difficulty, the use of more accessible homogenization model has been a main stream [8,13]. In homogenization model, the discrete microstructure is replaced with a volume fraction-equivalent macrostructure having spatially varying and continuous material properties.

Naturally, the crack analysis of metal-ceramic phase composites relied on the homogenization models. Traditionally, the elastic modulus has been assumed to vary exponentially in the thickness direction [14,15]. Hence, almost all the numerical studies on the stress intensity factor (SIF) and the crack propagation were carried out using these inhomogeneous homogenization models [[16], [17], [18], [19], [20]]. As a result, the effects of microscopic factors, except for the volume fraction distribution of constituents, such as the scale and pattern of microstructure could not be investigated. The major feature of these factors is randomness, so that SIF and the crack propagation trajectory of phase composites are not deterministic but stochastic. Nevertheless, the homogenization models provide the deterministic results which are affected only by the macroscopic volume fraction distribution of constituents. Hence, the employment of microscopic model is prerequisite for the stochastic crack analysis of metal-ceramic phase composites.

Fortunately, the advances in computer-aided modeling and image processing technologies enable one to generate the detailed microscopic models of dual-phase composites [21,22], even though restricted to the level of RVE. Among the advanced microscopic modeling technologies is a mathematical one called the random morphology description functions (RMDF). Being expressed by a linear combination of Gaussian functions, RMDF can generate a variety of random RVE microstructures with different volume fractions. The scale of microstructure models can be controlled by the total number of Gaussian functions. Thus, using this mathematical modeling technique, one can easily and quickly generate his own simulation models of RVE microstructures of metal-ceramic phase composites. And, one can investigate the fracture responses at the micro level with respect to the parameters associated with the microstructure.

In this context, this paper aims at the investigation of fracture mechanics characteristics of metal-ceramic phase composites at the microscopic level. The detailed solid and FEM models of metal-ceramic RVE microstructures are generated by a RMDF module which was developed in the previous work [8]. The mixed-mode stress intensity factors (SIFs) and the crack propagation trajectories are parametrically simulated to the scale and the dispersion pattern of microstructure and the initial crack length, in order to investigate the effects of randomness of microstructure and the trend to these key parameters. In addition, the numerical results are compared with those which are obtained using the volume-averaged homogenized model.

Section snippets

Construction of dual-phase RVE microstructures

This section briefly describes a generation of dual-phase RVE microstructures using random morphology description functions (RMDFs). In fact, a RVE is rarely defined for real dual-phase composites, but here we assume that it can be defined locally at least. First, a closed square domain Y=0,×0,2 occupied by a 2-D RVE is introduced, in which two base materials with the volume fractions V1 and V2 are mixed up in complex pattern. When y=y1,y2 be denoted by the local coordinates defined within

Linear fracture mechanics of heterogeneous materials

This section describes the evaluation of stress intensity factors (SIFs) and the prediction of crack propagation direction of dual-phase heterogeneous materials with an edge crack. Referring to Fig. 4(a), the material occupies a bounded domain Ω2 with the boundary Ω=ΓDΓNΓc¯, where ΓD denotes the displacement boundary, ΓN the traction boundary, and Γc=Γc+Γc¯ the crack surface. The Young’s modulus E and the Poisson’s ratio ν are not constant but variable within the material domain Ω. For

Stress intensity factors (SIFs)

Fig. 6(a) shows the geometry dimensions and the boundary conditions of a square RVE of metal-ceramic microstructures. The side length b is set by 1.0 mm, while the initial crack length a is set variable for the parametric investigation. The bottom side is completely clamped while the top side is subjected to uniform distributed load. Two loading cases are considered as following, the vertical distributed load Fy=1.0N for mode I and the horizontal one Fx=1.0N for mode II, respectively. Fig. 6(b)

Conclusion

In this paper, the characteristics of crack and crack propagation of metal-ceramic composites were numerically investigated at the microscopic level. The RVE microstructure models, called by RMDF models, were randomly generated by a mathematical RMDF micro modeling technology. The stress intensity factor (SIF), the crack trajectory and the tip stress of RMDF models were compared with those of the volume-averaged homogenized model and parametrically investigated with respect to the major factors

CRediT authorship contribution statement

J.R. Cho: Conceptualization, Formal analysis, Funding acquisition, Investigation, Methodology, Project administration, Resources, Supervision, Validation, Visualization, Writing - original draft, Writing - review & editing.

Declaration of Competing Interest

The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.

Acknowledgements

This research was supported by Basic Science Research Program through the National Research Foundation of Korea (NRF) funded by the Ministry of Education (Grant No. NRF-2017R1D1A1B03028879).

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