Following previous works in the literature on the fracture of layered composites, semi-analytical expressions for energy release rate and mode-mixity phase angle in isotropic bi-material layers subjected to arbitrary end loadings are extended to materials characterized by a large elastic mismatch described by Dundurs’ parameters |α| ≤ 0.99 and |β| ≤ 0.4. The solutions depend on elementary bending, axial and shear loads acting at the crack tip cross section, elastic constants and relative thickness of the layers, and dimensionless coefficients describing the fracture parameters of single elementary loads. The coefficients associated to the shear forces are presented in the literature only for combinations with β = 0; here they are determined numerically for different values β not =0 to describe materials used in current applications. Simplified fitting formulae having general validity, as polynomials, which highlight the dependence on Dundurs’ parameters and are practical to support laboratory tests, are derived for layers with mid-thickness delaminations and thin layers on semi-infinite substrates. Applications to some mixed mode fracture specimens highlight the effects of β not = 0 on the fracture parameters and the limitations of estimates based on the commonly adopted assumption β = 0. As expected, the results for mid-thickness delaminations show that such effects are stronger on mode-mixity phase angle than on energy release rate.
Fracture mechanics solutions and operative formulae for isotropic bi-material layers with large elastic mismatch
Monetto I.;Barbieri L.;Massabo R.
2022-01-01
Abstract
Following previous works in the literature on the fracture of layered composites, semi-analytical expressions for energy release rate and mode-mixity phase angle in isotropic bi-material layers subjected to arbitrary end loadings are extended to materials characterized by a large elastic mismatch described by Dundurs’ parameters |α| ≤ 0.99 and |β| ≤ 0.4. The solutions depend on elementary bending, axial and shear loads acting at the crack tip cross section, elastic constants and relative thickness of the layers, and dimensionless coefficients describing the fracture parameters of single elementary loads. The coefficients associated to the shear forces are presented in the literature only for combinations with β = 0; here they are determined numerically for different values β not =0 to describe materials used in current applications. Simplified fitting formulae having general validity, as polynomials, which highlight the dependence on Dundurs’ parameters and are practical to support laboratory tests, are derived for layers with mid-thickness delaminations and thin layers on semi-infinite substrates. Applications to some mixed mode fracture specimens highlight the effects of β not = 0 on the fracture parameters and the limitations of estimates based on the commonly adopted assumption β = 0. As expected, the results for mid-thickness delaminations show that such effects are stronger on mode-mixity phase angle than on energy release rate.
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