Abstract :
In this work a new conservation integral
JˆF 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 Jˆ-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 andPopelar (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 JˆF is amenable to suitable numerical
schemes like finite element (or boundary element)
method the description of which is outlined in brief
