SYMPOSIA PAPER Published: 01 January 1988

Three-Dimensional Transient Analysis of a Dynamically Loaded Three-Point-Bend Ductile Fracture Specimen


A transient three-dimensional full-field analysis of a three-point-bend fracture specimen dynamically loaded into the fully yielded plastic state has been carried out. The specimen is rapidly loaded by means of a concentrated transverse force applied at midspan on the uncracked surface of the specimen. It is assumed that the material is ductile and fracture initiation occurs after substantial plastic deformation has developed in the uncracked ligament. Furthermore, it is supposed that the crack-tip conditions are such that the J-integral may be adopted as a characterizing parameter. We derive an expression for the local energy flux appropriate to a three-dimensional crack front. Based on this fundamental crack-tip flux integral, a domain integral representation for J which is naturally compatible with finite-element analysis is obtained. Using the domain integral, accurate pointwise and local values of J along a three-dimensional crack front can be extracted from numerically determined field quantities. The effect of transient loading, geometry, and plastic deformation on the variation of J along the crack front is examined. A purpose of the present study is to determine conditions under which the value of J at initiation may be inferred from quantities that are directly measurable in a dynamic fracture experiment. In an earlier paper, a transition time was introduced to provide a practical bound on the time range over which conditions of J-dominance prevailed and the deep-crack formula was applicable under transient loadings. The transition time concept is further examined in this paper. With the full-field solutions in hand, we comment on the suitability of proposed surface locations for measurements of moment and rotation, the input measurements for application of the deep-crack formula for J. Implications for fracture testing of tough materials at relatively high-loading rates are discussed.

Author Information

Nakamura, T
State University of New York, Stony Brook, NY
Shih, CF
Brown University, Providence, RI
Freund, LB
Brown University, Providence, RI
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Developed by Committee: E08
Pages: 217–241
DOI: 10.1520/STP26778S
ISBN-EB: 978-0-8031-5063-8
ISBN-13: 978-0-8031-1174-5