ON A DYNAMICALLY ACCELERATING CRACK IN AN ACHENBACH-CHAO VISCOELASTIC SOLID

A closed form solution is presented for a dynamically accelerating, semi-infinite, anti-plane shear crack in a Achenbach-Chao linear viscoelastic solid in the limiting case of a vanishing equilibrium shear modulus. Simple expressions for the crack-face displacement and the stress intensity factor are constructed for arbitrary time dependent crack-face traction and crack-tip velocity, a(t), subject only to the restriction that 0 less-than-or-equal-to a(t) < c, where c is the short time (glassy) shear wave speed. The extent of material memory in the stress intensity factor and crack-face relative displacement during the transition from an initial accelerating crack growth phase to a constant crack speed regime are compared for loads travelling with the crack-tip and for stationary loads. The viscoelastic and elastic stress intensity factors are shown to exhibit the same degree of limited dependence upon the initial acceleration phase whereas the viscoelastic and elastic crack-face displacements behave quite differently with the former exhibiting a persistent and the latter a limited memory of the initial acceleration phase.