Contours for planar cracks growing in three dimensions: Illustration for transversely isotropic solid

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Journal of Mechanics of Materials and Structures, ISSN: 1559-3959, Vol: 10, Issue: 4, Page: 481-495

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Brock, Louis Milton
Mathematical Sciences Publishers
Engineering; Mathematics; 3D; dynamic; criteria; analytic solution; crack contour; transverse isotropy; energy release; Mechanical Engineering
article description
Three-dimensional dynamic steady state growth of a semi-infinite plane crack in a transversely isotropic solid is considered. Growth takes place on a principal plane with the material symmetry axis as one tangent. Fracture is brittle, and driven by compressive loads that translate on the crack surfaces. Translation speed is constant and subcritical, but direction with respect to the principal axes is arbitrary. An analytical solution is obtained, and examined in light of the dynamic energy release rate criterion for the case of a translating compressive point force. Introduction of quasipolar coordinates leads to a nonlinear firstorder differential equation for the distance between force and crack edge. The equation depicts a crack edge that tends to the rectilinear away from the force. An analytical expression for the distance measured parallel to translation direction indicates a marked deviation from the rectilinear near the point force.