On problems with the determination of the fracture resistance for materials with spatial variations of the Young’s modulus

Abstract

The paper considers the near-tip J-integral J tip , the far-field J-integral J far , and the experimental J-integral J exp in a material with sinusoidal variation of the Young's modulus E. The evaluations of J tip and J far are based on the concept of configurational forces; J exp is evaluated from the area below the load point displacement curve, as prescribed by the standard testing procedures. Analytic expressions and/or approximation formulae are derived, how J tip , J far and J exp depend on the system parameters of the material, i.e. wavelength and amplitude of the E-variation and its phase shift with respect to the crack tip position, and the global specimen dimensions. The analyses show that J tip and J far exhibit a strong dependency on the phase shift, but not the experimental J-integral J exp . This is the reason why the current procedures for fracture mechanics testing are not suitable to determine the

A computational framework for crack propagation in spatially heterogeneous materials

“…As expected, configurational forces are induced at the crack front under load and, as explained in §4a, these forces are influenced by the non-uniform density distribution. It is important to note that, in the case of heterogeneous materials, the stress intensity factors or J-integral are difficult to calculate or obtain experimentally [45]. Due to the inhomogeneities, the J-integral becomes path dependent and requires special correction terms to be computed [46,47].…”