STP700: Elastic-Plastic Analysis of Growing Cracks

    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.

    Pages: 33    Published: Jan 1980


    Abstract

    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 ˙δ=α˙Jσo+β(σoE)˙aln(Rr) but now the presence of the elastic wedge causes β to have the revised value of 5.08 (for Poisson ratio ν = 0.3). Here, a = crack length, σo = yield strength, E = elastic modulus, and J denotes the far-field value, namely, (1 − ν2)K2/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 Δa 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


    Paper ID: STP36972S

    Committee/Subcommittee: E08.08

    DOI: 10.1520/STP36972S


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