Dynamic analysis of non-symmetric problems for frictionless indentation and plane crack extension
Tóm tắt
Two-dimensional dynamic analyses of contact and stress loading problems associated with non-symmetric frictionless rigid indentation and plane crack extension under normal stress are presented. The extension rates of the contact strip/crack surfaces are assumed to be constant and sub-critical. Homogeneous function techniques are used to derive general mathematical solutions which are then fitted to the physical problem by matching the predicted and prescribed displacement/stress distributions on the contact strip/crack surfaces. By studying several examples, it is seen that coupling between inherently symmetric and antisymmetric components of the mathematical solutions complicates this procedure. Moreover, the relation between loading and solution behavior is not always physically obvious, especially with regard to symmetry/antisymmetry.
Tài liệu tham khảo
K. B.Broberg, The propagation of a brittle crack, Ark. Fys. 18 (1960) 159.
J. W.Craggs, Fracture criteria for use in continuum mechanics, in Fracture of solids (D. C. Drucker and J. J. Gilman, eds.) Wiley, New York 1963.
J. R. Willis, Self-similar problems in elastodynamics, Phil. Trans. Roy. Soc. (London A274) (1973) 435.
F. R.Norwood, Correction and extension of Broberg's results on brittle crack propagation, Int. J. Engng. Sci. 14 (1976) 477.
L. M.Brock, Non-symmetric extension of a plane crack due to tensile pre-stress and dilatational waves, Int. J. Engng. Sci. 13 (1975) 951.
L. M.Brock, Surface motions due to fault slip in the vertical mode with friction, Bull. Seism. Soc. Am. 65 (1975) 1653.
L. M.Brock, Non-symmetric extension of a small flaw into a plane crack at a constant rate under polynomial-form loadings, Int. J. Engng. Sci. 14 (1976) 181.
R. J.Bedding and J. R.Willis, The dynamic indentation of an elastic half-space, J. Elasticity 3 (1973) 289.
A. R.Robinson and J. C.Thompson, Transient stresses in an elastic half space resulting from the frictionless indentation of a rigid wedge-shaped die, Z. angew. Math. Mech. 54 (1974) 139.
G. P.Cherepanov and E. R.Anfanas'ev, Some dynamic problems of the theory of elasticity—a review, Int. J. Engng. Sci. 12 (1974) 665.
L. M.Brock, Symmetrical frictionless indentation over a uniformly expanding contact region—I. basic analysis, Int. J. Engng. Sci. 14 (1976) 191.
L. M.Brock, Symmetric indentation over a uniformly expanding contact region—II. perfect adhesion, Int. J. Engng. Sci. 15 (1977) 147.
F.Erdogan, Crack propagation theories, in Fracture, Vol. 2 (H. Liebowitz, ed.) Academic, New York 1968.