**Published:** Jan 1980

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**Source: **STP700-EB

In an extension of earlier studies by Rice and Sorensen, a discussion is presented on the elastic-plastic stress and deformation fields at the tip of a crack which grows in an ideally plastic solid under plane strain, small-scale yielding conditions. The results of an asymptotic analysis suggest the existence of a crack-tip stress state similar to that of the classical Prandtl field, but containing a zone of elastic unloading between the centered fan region and the trailing constant stress plastic region. The near tip expression for the rate of opening displacement δ at distance *r* from the growing tip is found to have the same form suggested by Rice and Sorensen *ν* = 0.3). Here, *a* = crack length, *σo* = yield strength, *E* = elastic modulus, and *J* denotes the far-field value, namely, (1 − *ν*^{2})*K*^{2}/*E* for the small scale yielding conditions considered. The parameters *α* and *R* cannot be determined from the asymptotic analysis, but comparisons with finite element solutions suggest that, at least for small amounts of growth, *α* is approximately the same for stationary and growing cracks, and *R* scales approximately with the size of the plastic zone, being about 15 percent to 30 percent larger. For large scale yielding it is argued that a similar form applies with possible variations in *α* and *β*, at least in cases which maintain triaxial constraint at the crack tip, but in the fully yielded case *R* is expected to be proportional to the dimension of the uncracked ligament. The model crack growth criterion of Rice and Sorensen, requiring a critical *δ* at some fixed *r* from the tip, is reexamined in light of the more accurate solution. The results suggest that the *J* versus Δ*a* relation describing growth will be dependent on the extent of yielding, although it is suggested that this dependency might be small for highly ductile materials, provided that a similar triaxial constraint is maintained in all cases.

**Keywords:**

elastic-plastic crack mechanics, stable crack growth, ductile tearing fracture, fractures (materials), crack propagation

**Author Information:**

Rice, JR *Professor and research assistants, Division of Engineering, Brown University, Providence, R.I.*

Drugan, WJ *Professor and research assistants, Division of Engineering, Brown University, Providence, R.I.*

Sham, T-L *Professor and research assistants, Division of Engineering, Brown University, Providence, R.I.*

**Committee/Subcommittee:** E08.08

**DOI:** 10.1520/STP36972S