**Published:** Jan 1983

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**Source: **STP803V1-EB

The asymptotic near-tip stress and deformation fields for a Mode I plane-strain crack growing quasi-statically in an elastic-ideally plastic solid under small-scale yielding conditions are analyzed numerically by the finite-element method. The asymptotic analyses of Rice and Sorensen; Rice, Drugan, and Sham; and Drugan, Rice, and Sham predict that the crack opening rate ˙δ at a small distance *r* from the growing crack tip under contained yielding conditions is given by *a* is the crack length, *σ*^{0} the tensile yield strength, *E* Young's modulus, *J* the farfield value of the J-integral evaluated on contours in the elastic region, *β* = 5.462 (Drugan et al) for Poisson ratio *ν* = 0.3, and the parameters α and *R* are undetermined by the asymptotic analysis. The finite-element solutions generated are very detailed, with the maximum extent of the plastic zone being about 100 times the smallest element size. This high resolution in the finite-element solution enables correlation of the finite-element results with the asymptotic crack opening rate to be made and the expressions for the parameters α and *R* to be determined. Various crack growth histories are simulated by relaxing the nodal force at the crack tip and simultaneously increasing the external applied load in order to investigate the possible dependence of α and *R* on the crack growth history. The maximum amount of crack growth simulated is about 20 percent of the maximum extent of the plastic zone size. The numerical results reveal that a well-defined elastic unloading sector develops and moves with the advancing crack tip and its location coincides well that predicted by the asymptotic analysis. Estimation from the numerical results gives *β* = 5.46, which is in very good agreement with the asymptotic result. The parameter α is found to be independent of the crack growth histories examined and has a value of 0.58. An attempt to relate *R* to the quantity *EJ*/*σ*^{0}^{2} is made. However, it is found that the parameter *s*, defined by *s* ≡ *R*/(*EJ*/*σ*^{0}^{2}), varies in a range 0.113 to 0.133 for the crack growth histories simulated. Thus, the precise definition for *R* remains unclear.

**Keywords:**

elastic-plastic crack growth, ductile tearing fracture, asymptotic near-tip fields, embedded finite elements, plane strain, small-scale yielding, fractures (materials), quasi-static crack propagation, elastic-plastic fracture

**Author Information:**

Sham, T-L *Assistant professor, Department of Mechanical Engineering, Aeronautical Engineering and Mechanics, Rensselaer Polytechnic Institute, Troy, N.Y.*

**Committee/Subcommittee:** E08.08

**DOI:** 10.1520/STP37440S