The crack tip fields in strain gradient plasticity: the asymptotic and numerical analyses

An investigation of asymptotic crack tip singular fields and their domain o f validity is carried out for mode I cracks in solids characterized by the phenomenological strain gradient plasticity theory proposed by Fleck NA, Hu tchinson JW. (Strain gradient plasticity. In: Hutchinson JW, Wu TY, editors . Advances in applied mechanics, vol. 33. New York: Academic Press, 1997. p p. 295-361.) Separable near-tip singular fields are determined where fields quantities depend on the radial and circumferential coordinates (r, theta) according to r(p)f(theta). The singular field is completely dominated by t he strain gradient contributions to the constitutive law. In addition to th e asymptotic analysis, full field numerical solutions are obtained by a fin ite element method using elements especially suited to the higher order the ory. It is found that the singular field provides a numerically accurate re presentation of the full field solution only within a distance from the tip that is a tiny fraction of the constitutive length parameter. The constitu tive theory itself is not expected to be valid in this domain. Curiously, t he normal traction acting across the extended crack line ahead of the crack tip is found to be compressive in the singular field. The conclusion which must be drawn is that the singular field has a tiny domain of mathematical validity (neglecting crack face interaction), but no domain of physical va lidity. The significant elevation of tractions ahead of the crack tip due t o strain gradient hardening occurs at distances from the crack tip which ar e well outside this tiny domain in a region where the plasticity theory is expected to be applicable. The asymptotic singular fields are incapable of capturing the effect of traction elevation. (C) 1999 Elsevier Science Ltd. All rights reserved.