Pii: S0013-7944(99)00073-9

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