Investigating the Effective Fracture Toughness of Heterogeneous Materials
Heterogeneous materials are ubiquitous in nature, and are increasingly being engineered to obtain desirable mechanical properties. Naturally, the bulk properties of a heterogeneous material can be different from those of its constituents. Thus, one needs
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Investigating the Effective Fracture Toughness of Heterogeneous Materials Chun-Jen Hsueh, Guruswami Ravichandran, and Kaushik Bhattacharya Abstract Heterogeneous materials are ubiquitous in nature, and are increasingly being engineered to obtain desirable mechanical properties. Naturally, the bulk properties of a heterogeneous material can be different from those of its constituents. Thus, one needs to determine its overall or effective properties. For some of these properties, like effective elastic modulus, the characterization is well-known, while for other such as effective fracture toughness, it is a matter of ongoing research. In this paper, we present a method to measure the effective fracture toughness. For the method, we apply a time-dependent displacement condition called the surfing boundary condition. This boundary condition leads the crack to propagate steadily macroscopically but in an unconstrained manner microscopically. We then use the grid method, a non-contact full-field displacement measurement technique, to obtain the displacement gradient. With this field, we compute the macroscopic energy release rate via the area J-integral. Finally, we interpret the effective toughness as the peak of the energy release rate. Using this method, we investigate the influence of heterogeneity on effective fracture toughness. We find that the effective toughness can be enhanced due to the heterogeneity. Consequently, engineered heterogeneity may provide a means to improve fracture toughness in solids. Keywords Fracture toughness • Heterogeneous materials • Surfing boundary conditions • Grid method • Brittle materials
3.1
Introduction
Methods for measuring the toughness of homogeneous materials are well-established, but these methods do not extend to heterogeneous materials. While there are established methods for specific heterogeneous materials such as R-curve measurements for ceramics [1] and the double cantilever beam (DCB) method for the laminated materials [2], a general method for materials with complex heterogeneity is wanting. Similarly, a systematic understanding of the effective toughness, crack nucleation, deflection, and pinning in heterogeneous materials, and the dependence of toughness on microstructure are active research topics. Recently, Hossain et al. [3] proposed an approach to define the effective toughness and used it to study the role of microstructure on toughness. Here, we propose an experimental method to measure the effective toughness of heterogeneous materials based on the theoretical work of Hossain et al. [3]. The key idea is to enforce a steady and controlled crack growth at the macroscopic scale without constraining the microscopic scale.
3.2
Experimental Configuration
In this study, we developed an experimental configuration that enables macroscopically steady crack growth while allowing at the microscopic scale crack deflection and pinning, nucleation of distal cracks, etc. The experimental setup is shown in Fig. 3.1. A PMMA specimen which is 3.125 mm (1/800 ) thick is pre
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