Comparative analysis of computation methods for mixed-mode stress intensity factors of anisotropic materials
DOI:
https://doi.org/10.7242/1999-6691/2026.19.3.21Keywords:
cubic symmetry, inclined crack, mixed mode, stress intensity coefficients, displacement extrapolation method, stress extrapolation method, equivalent volume integration method, contour Jₖ-integralsAbstract
The article discusses the results of comparison of four numerical methods used to calculate stress intensity factors (SIFs) for anisotropic materials in problems of mixed-mode linear fracture mechanics: (i) displacement extrapolation method, (ii) stress extrapolation method, (iii) equivalent domain integral (EDI) method for computation of Jk-integrals (invariant integrals J1 and J2), and (iv) calculation of Jk-integrals using contour integration (by definition). The specific features of anisotropy in materials with cubic symmetry, which is inherent in single-crystal nickel-based alloys commonly used in the manufacture of blades of modern gas turbine units, are considered in detail. For this class of materials with arbitrary crack orientation and a mixed fracture mode, the analytical expressions for determining the SIF in terms of Jk-integrals are obtained using Lekhnitskii's formalism. The problem of uniaxial tension of an anisotropic plane with an inclined crack under the assumption of a plane stress state and admissibility of an analytical solution is considered as a test problem for a comparative analysis of the methods. The accuracy and convergence of the four considered methods for calculating the SIF are analyzed depending on the degree of domain discretization (number of finite elements), crack orientation with respect to the loading direction, and the degree of material anisotropy. The comparison is performed for three characteristic crack inclination angles: 15°, when the I mode (tension) dominates over the II mode (longitudinal shear); 45°, when the SIFs are equal to each other; 75°, when the II mode (longitudinal shear) dominates over the I mode (tension). The sensitivity of the errors in KI and KII to the errors in J1 and J2 is studied. This makes it possible to set limits on the scope of application of the methods for determining the SIF based on Jk-integrals.
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