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Energy-based fracture criterion and interaction integral method for anti-plane cracks in nonhomogeneous micropolar materials
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DOI：10.1016/j.ijsolstr.2026.113950.png)
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Abstract
En 中文
This study extends both the maximum energy release rate criterion and the interaction integral (I-integral) method of linear elastic fracture mechanics (LEFM) within the framework of micropolar elasticity. The anti-plane fracture behavior of nonhomogeneous micropolar materials is systematically investigated. Through theoretical derivation, a closed-form expression is established to predict the crack kinking angles. This expression incorporates the influences of the nonlocal nature of material, micropolarity, along with the stress intensity factor (SIF) and couple-stress intensity factors (CSIFs). To accurately extract fracture parameters in nonhomogeneous micropolar materials with complex interfaces, a novel I-integral method is developed. This approach eliminates the need for calculating the derivatives of material properties and rigorously maintains domain-independence for material interfaces. By combining with the extended finite element method (XFEM), the numerical accuracy and domain-independence of the proposed I-Integral in anti-plane fracture problems are verified. Numerical studies reveal that the mode III SIF and the crack propagation angle are significantly influenced by the nonlocal nature of the material. Significant size-dependent behavior is observed, where the crack propagation angle gradually decreases as the specimen size increases. This trend confirms that the influence of non-locality weakens at larger scales, primarily attributed to the diminishing contribution of the local screwing mode (mode IV) and the local rolling mode (mode V) to the energy release rate. An increase in the internal characteristic length provides a shielding effect that suppresses microrotations, causing the crack propagation angle to asymptotically approach zero. Regarding functionally graded materials, gradients parallel to the crack direction significantly alter the crack trajectory by diminishing the tearing mode while enhancing the local rolling mode. Under pure mode III loading, the intensity factors (IFs) in particle-reinforced composites are strongly affected by particle size, location, and distribution patterns. Asymmetric particle distributions about the crack activate the local rolling mode, thereby inducing crack kinking.
Keywords:
Microrotation effects
Anti-plane crack
Fracture criterion
Interaction integral
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