Circular arc crack under dynamic load: a generalized approach for energy release rate

In this work a new conservation integral Ĵ F consisting of path and area integrals derived from the appropriate energy balance expression has been proposed for a two-dimensional stationary circular arc crack subjected to rapidly varying loads. This integral is an outcome of the extension of the F-integral proposed by Lorentzon and Eriksson (Engg Fract Mech 66:423–439, 2000) in conjunction with the concept of Ĵ-integral introduced by Kishimoto et al (Engg Fract Mech 13:841–850, 1980). The present work considers effects of the material acceleration in addition to the work due to plastic deformation, body forces, thermal and initial strains applicable to the rate independent material constitutive law for deformation plasticity. It should, however, be pointed out that the present integral is different from integrals derived for straight crack dynamics in Bui (Advances in research on the strength and fracture of materials. (ICF4), vol. 3 Pergamon Press, Waterloo, Canada, pp. 91–95, 1977), Kishimoto et al. (Engg Fract Mech 13:841–850, 1980), Atluri (Engg Fract Mech 16(3):341–364, 1982), Nishioka and Atluri (Engg Fract Mech 18(1):1–22, 1983a), Nishioka and Atluri (Engg Fract Mech 18(1):23–33, 1983b), Atluri et al. (Engg Fract Mech 20(2):209–244, 1984), Kanninen and Popelar (Advanced fracture mechanics. Oxford University Press, New York, 1985), Freund (Dynamic fracture mechanics. Cambridge University Press, Cambridge 1990). Further, it is imperative that solution for the integral Ĵ F is amenable to suitable numerical schemes like finite element (or boundary element) method the description of which is outlined in brief.