The Tip Field Of Mode Ⅲ Crack In Nonlinear Damage Materials

Material failure is an important consideration in the design of engineering structure. The near tip field solution provides insight into the selection of the failure criterion. This paper is concerned with an infinite slab containing a semi-infinite crack, which is subjected to the anti-plane shear loading condition. Based on the damage evolution formation depicted by Kachanov of brittle materials in unitary stress state, In this dissertation, the constitutive equation of nonlinear damage material is given, macroscopically, on the assumption thatdamage variable is exponential relation to strain, D = (Gy I K)" , where G is theshear module, K is the damage module and the y is the effective strain, D is damage variable and n is hardening exponent. When n=l, damage form of materials is linear strain damage model. When stress approach to critical, materials soften rapidly, unstable and destroyed. Formation of damage variable critical Dc is given by. this dissertation, Dc increasing with the increase of n, that is to say, the damage critical of tough materials is greater than that of brittle materials.Via the transform of coordinate, mode III crack problem in physical plane is inversed to stress plane to be investigated. Equilibrium equation and compatibility equation are deducted, in which (x, y) is expressed by unknownvariable 7^,7^,. Introducing strain function y/ , applying geometry equation ,compatibility equation and constitutive equation to deduct the basis equation satisfied by i// in mode III crack problem, for different n, small area damage solution of \i/ is obtained by means of calculation.Applying relevant formulae to deduct the formulation about shape of damage area, the shape of which being a series of circle is obtained, the center of circle and radius vary with D and n. In terms of the relation of coordinate of physical plane and strain plane, stress and strain field distribution curve expressed by polar coordinates in damage area is derived, when n=l,the result is same as that given by C.H.Popelar. When n>2, n influences the properties of the near tip crack field. If damage hardness equals to damage intensity, when n - , materials is elastic,then the radius of damage area is the same as the radius of ideal elastic-plasticitymaterials. The above provides theory bases for the establishment of failurecriterion.