A combined computational and experimental study of heterogeneous fracture

Abstract

Material property heterogeneity is present ubiquitously in various natural and man-made materials, such as bones, seashells, rocks, concrete, composites, and functionally graded materials. A fundamental understanding of the structure-property relationships in these material systems is crucial for the development of advanced materials with extreme properties. Well-developed homogenization schemes exist to establish such relationships in elasticity, electrostatics, magnetism, and other time- or history-independent material properties. Nevertheless, one’s understanding of the effective fracture properties of heterogeneous media is remarkably limited. The challenge here is that heterogeneous fracture, as a history-dependent process, involves complex interaction and negotiation of a discontinuity front with local heterogeneities. The determination of effective fracture properties necessitates a critical interrogation of this evolutionary process in detail. In this work, a combined experimental and modeling effort is made to examine and control fracture mechanisms in heterogeneous elastic solids. A two-phase laminated composite, which mimics the key microstructural features of many tough biological materials, is selected as a model material. In the computational part of this work, finite element analysis with cohesive zone modeling is used to model crack propagation and arrest in the laminated direction. A crack-tip-opening controlled algorithm is implemented to overcome the instability problems associated with inherently unstable crack growth. Computational results indicate that the mismatch of elastic modulus is an important factor in determining the fracture behaviors of the heterogeneous model material. Significant enhancement in the material’s effective fracture toughness can be achieved with appropriate modulus mismatch. Systematic parametric studies are also performed to investigate the effects of various material and geometrical parameters, including modulus mismatch ratio, phase volume fractions, T-stress, and cohesive zone size. Concurrently, a novel stereolithography-based additive manufacturing system is developed and used for fabricating heterogeneous test specimens with well-controlled structural and material properties. Fracture testing of each specimen is performed using the tapered double-cantilever beam (TDCB) test method. With optimized material and geometrical parameters, heterogeneous TDCB specimens are found to exhibit higher fracture toughness than their homogenous counterparts, which is in good agreement with the computational predictions. The integrative computational and experimental study presented here provides a fundamental mechanistic understanding of the fracture mechanisms in brittle heterogeneous materials and sheds light on the rational design of ultra-tough materials through patterned heterogeneities.