Path dependence of the $$J_2$$ integral for rapid dynamic fracture
Source abstract
Abstract
Crack propagation can be analysed with the use of the well-known integrals (J_1) and (J_2), which are calculated by integrating a combination of the elastic and kinetic energy densities and the stress components along an arbitrary contour encompassing the moving crack tip. The first integral (J_1) can be expressed in terms of the squares of the dynamic stress intensity factors with coefficients that depend on the crack-growth speed. This integral corresponds to the energy release rate and is proven to be independent of the shape of the integration contour for both static and dynamic fracture. However, analytic calculation of the second integral (J_2) for different integration contours reveals a path dependence for situations with dynamic fracture. The resulting expressions do not only contain a mixed-mode term with the product (K_I KII) but also three terms with the squares of the stress intensity factors ((K_I^2), (KII^2) and (KIII^2)). The coefficients depend on the crack-growth speed, Poisson’s ratio and the shape of the integration contour. This path dependence is a novelty and poses fundamental questions as regards the interpretation and applicability of the (J_2) integral for the analysis of rapid dynamic fracture.
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Research context
OpenAlex topics: Fatigue and fracture mechanics · Rock Mechanics and Modeling · Numerical methods in engineering
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