A path-independent integral and the approximate analysis of strain

  title={A path-independent integral and the approximate analysis of strain},
  author={John R. Rice},
  • J. Rice
  • Published 1 June 1968
  • Engineering
Abstract : An integral is exhibited which has the same value for all paths surrounding a class of notches in two-dimensional deformation fields of linear or non-linear elastic materials. The integral may be evaluated almost by inspection for a few notch configurations. Also, for materials of the elastic- plastic type (treated through a deformation rather than incremental formulation) , with a linear response to small stresses followed by non-linear yielding, the integral may be evaluated in… 

An integral associated with the state of a crack tip in a non-elastic material

An integral has been proposed for a non-elastic material whose value is determined by the magnitude of the singularities at the tip of a crack but which may be evaluated mainly far away from the

Non-linear analysis of shallow cracks in smooth and notched plates Part 1: Analytical evaluation

This is the first paper of two that deal with the non-linear analysis of shallow cracks. Simple formulae are given for estimating the J integral for a power-hardening elastic-plastic solid. The

Computation of the J‐integral for large strains

The phenomenon of failure by catastrophic crack propagation in structural materials poses problems of design and analysis in many fields of engineering. Cracks are present to some degree in all

Use of the J Contour Integral in Elastic-Plastic Fracture Studies by Finite-Element Methods:

In Part 1, a brief summary of the justification and advantages of the use of the J contour integral in elastic-plastic finite-element analysis is given. A more detailed appraisal is then made of its

The J-contour integral in peridynamics via displacements

Peridynamics is a nonlocal formulation of solid mechanics capable of unguided modelling of crack initiation, propagation and fracture. Peridynamics is based upon integral equations, thereby avoiding

On the Path-Dependence of the J-Integral Near a Stationary Crack in an Elastic-Plastic Material

The path-dependence of the J-integral is investigated numerically via the finite-element method, for a range of loadings, Poisson’s ratios, and hardening exponents within the context of J2-flow



The determination of the elastic field of an ellipsoidal inclusion, and related problems

  • J. D. Eshelby
  • Mathematics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1957
It is supposed that a region within an isotropic elastic solid undergoes a spontaneous change of form which, if the surrounding material were absent, would be some prescribed homogeneous deformation.

Contained plastic deformation near cracks and notches under longitudinal shear

An exact linear elastic-perfectly plastic solution is presented for the problem of a sharp notch (or, when the notch angle is zero, a crack) in a plane of finite width subjected to anti-plane

Representation of plasticity at notches by linear dislocation arrays

  • B. BilbyK. H. Swinden
  • Materials Science
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1965
Further work is reported on the use of linear dislocation arrays to represent plastic relaxation round notches. In previous papers the relaxation in an infinite medium by arrays collinear with the

On the Stress Distribution at the Base of a Stationary Crack

In an earlier paper it was suggested that a knowledge of the elastic-stress variation in the neighborhood of an angular corner of an infinite plate would perhaps be of value in analyzing the


Abstract : The development of the plastic strain in a V-grooved flat plate under longitudinal shear was followed from the elastic through the partially plastic to the fully plastic condition for a


Abstract : An experimental method of indentifying the plastic constraint ahead of a sharp crack loaded under plane-strain conditions is proposed. The method is based on the idea that the cleavage

Rupture of rubber. II. The strain concentration at an incision

The strain distribution around the tip of an incision in a thin test-piece of highly elastic material is considered. Using the results of a previous paper, relations between this strain distribution

Effects of root radius, stress, crack growth and rate on fracture instability

  • F. Mcclintock
  • Physics
    Proceedings of the Royal Society of London. Series A. Mathematical and Physical Sciences
  • 1965
Of various criteria for fracture at the root of a notch, the energy, local stress, and displacement criteria have limited validity. More appropriate is the history of both stress and strain over a