Dynamic fracture of a kane-mindlin plate

We study dynamic crack problems for an elastic plate by using Kane-Mindlin's kinematic assumptions. The general solutions of the Laplace transformed displacements and stresses are first derived. Path independent integrals for stationary cracks subjected to transient loads and steadily growing cracks are deduced. For a stationary crack in a very thin plate subjected to impact loads, the crack tip dynamic stress intensity factor (DSIF), K₁(t), is related to the far field plane stress one, K₁⁰(t), by where ν is Poisson's ratio. For a crack steadily growing with speed V, the crack tip DSIF, K₁(V), is given by where K₁⁰(V) is the plane stress DSIF and A(V) and B(V) are known functions of V. These results are applied to compute the DSIF for a semi-infinite stationary crack in an unbounded plate subjected to impact pressure on the crack faces. The results of DSIF for a finite crack in an infinite plate under uniform impact pressure on the crack surfaces show that for each plate thickness, the maximum DSIF is higher than that for the plane stress case.