Three Dimensional Effects Near a Crack Tip in a Ductile Three Point Bend Specimen. Part 1. A Numerical Investigation

Abstract
A simultaneous numerical and experimental investigation is undertaken to assess three dimensional effects and HRR dominance near a crack front in a ductile 3-point bend specimen. In parallel to the 3-D numerical calculations, a plane strain and a plane stress analysis of the same in-plane specimen geometry is performed to obtain upper and lower bounds for the 3-D calculation. The radial, angular and thickness variation of the stresses and displacements are studied in great detail from contained yielding, to fully plastic conditions. The results indicate that the plane strain HRR field prevails in the interior of the specimen very near the crack front even for moderate extents of yielding. On the other hand, for distances from the crack tip exceeding about half a specimen thickness, plane stress conditions are approached. The calculations presented here model a series of laboratory experiments involving three independent experimental techniques. Details regarding the experiments and comparisons of the experimental measurements with numerical calculations and theory are emphasized in Part II of this work.

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