### STP1220: Two-Parameter Characterization of Crack Tip Fields in Edge-Cracked Geometries: Plasticity and Creep Solutions

Sharma, SM

*Postdoctoral Fellow, Associate Professor and Graduate Student, University of Pennsylvania, Philadelphia, PA*

Aravas, N

*Postdoctoral Fellow, Associate Professor and Graduate Student, University of Pennsylvania, Philadelphia, PA*

Zelman, MG

*Postdoctoral Fellow, Associate Professor and Graduate Student, University of Pennsylvania, Philadelphia, PA*

Pages: 19 Published: Jan 1995

**Abstract**

Two-parameter descriptions of the crack tip stress fields in elastic-plastic materials are discussed in detail. It is shown analytically that the two-term asymptotic expansions for the near-tip stresses developed by Li and Wang [3] and Sharma and Aravas [4] can be represented in an alternative form in which the leading HRR-term can be replaced by the standard small-scale-yielding solution (with *T* = 0). A two-parameter characterization of the plane strain elastoplastic crack tip fields of edge-cracked geometries is presented. Detailed finite element calculations of edge-cracked bars loaded in tension (SENT) are carried out for different values of the crack length (*a*) to specimen width (*W*) ratio. The crack tip fields are characterized in terms of *J*-integral and the magnitude *Q*^{1} of the second term of the elastoplastic crack tip asymptotic solution. Comparison are made with the alternative pairs of parameters (*J, T*) and (*J, Q*) that have been suggested by Hancock and co-workers ([21, 22, 23, 24]) and O'Dowd and Shih ([7, 8]) respectively, where *T* is the so-called elastic-*T*-stress and *Q* is a measure of the crack tip stress triaxiality. Plane strain creep solutions are also obtained for a shallow-cracked SENT specimen with *a/W* = 0.05. It is found that, whereas the region of dominance of the HRR-like term is essentially zero, a two-term asymptotic expansion similar to that used in elastic-plastic materials provides an accurate description of the spatial and temporal variations of the crack tip stresses of the creeping solid.

**Keywords:**

Two-parameter characterization, asymptotic solution, J, -integral, shallow edge crack, plasticity, creep

**Paper ID:** STP14601S

**Committee/Subcommittee:** E08.08

**DOI:** 10.1520/STP14601S

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