Finite Element Solutions for Plane Strain Mode I Crack with Strain Grading Effect

In this paper, a new phenomenological theory with strain gradient effects is proposed to account for the size dependence of plastic deformation at micro- and submicro-length scales. The theory fits within the framework of general couple stress theory and three rotational degrees of freedom omega(i) are introduced in addition to the conventional three translational degrees of freedom mu(i). omega(i) is called micro-rotation and is the sum of material rotation plus the particles' relative rotation. While the new theory is used to analyze the crack tip field or the indentation problems, the stretch gradient is considered through a new hardening law. The key features of the theory are that the rotation gradient influences the material character through the interaction between the Cauchy stresses and the couple stresses; the term of stretch gradient is represented as an internal variable to increase the tangent modulus. In fact the present new strain gradient theory is the combination of the strain gradient theory proposed by Chen and Wang (Int. J. Plast., in press) and the hardening law given by Chen and Wang (Acta Mater. 48 (2000a) 3997). In this paper we focus on the finite element method to investigate material fracture for an elastic-power law hardening solid. With remotely imposed classical K fields, the full field solutions are obtained numerically. It is found that the size of the strain gradient dominance zone is characterized by the intrinsic material length l(1). Outside the strain gradient dominance zone, the computed stress field tends to be a classical plasticity field and then K field. The singularity of stresses ahead of the crack tip is higher than that of the classical field and tends to the square root singularity, which has important consequences for crack growth in materials by decohesion at the atomic scale. (C) 2002 Elsevier Science Ltd. All rights reserved.

When Does a Polynomial Over a Finite Field Permute the Elements of the Field?

We present a class of indecomposable polynomials of non prime-power degree over the finite field of two elements which are permutation polynomials on infinitely many finite extensions of the field. The associated geometric monodromy groups are the simple ...

MODIFIED POLYSULFONES .1. SYNTHESIS AND CHARACTERIZATION OF POLYSULFONES WITH UNSATURATED END-GROUPS

Chloro-terminated polysulfones with various molecular weights were modified with poly(ethylene oxide) and poly[(ethylene oxide)(propylene oxide)] macromers carrying alpha-hydroxyl and omega-allyl end groups via classical polycondensation reactions. The pr

PENDANT FUNCTIONAL-GROUP COPOLYETHER SULFONES .1. SYNTHESIS AND CHARACTERIZATION OF NEW COPOLYETHER SULFONES WITH PENDANT ALDEHYDE GROUPS MODIFIED INTO PHENOLIC AZOMETHINE GROUPS

New functional copolyether sulfones with pendant aldehyde groups were synthesized by the classical polycondensation reaction between 4,4' -dichlorodiphenyl sulfone (I) and various bisphenols such as 5,5'-methylene bis-salicylaldehyde (II-2), 2,2-bis( 4-hydroxyphenyl)propane (III), and 2,6-bis(4-hydroxybenzylidene)cyclohexanone (IV). Condensation reaction with 4-aminophenol led to pendant phenolic azomethine groups containing copolyether sulfones. The structures of the resulting polymers were confirmed by IR, H-1-NMR spectra, and elemental analyses. The polymers were characterized by reduced viscosity, solubility, thermal stability, DSC, and x-ray diffraction measurements.