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 plandIstrain 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 numercial calculations and theory are emphasized in Part II of this work.

A Three-dimensional Numerical Study of Mixed Mode (I and II) Crack Tip Fields in Elastic–plastic Solids

“…This figure along with Figure 7, which shows that σ θ and σ h have very little thickness variation for r/ h > 0.5, suggest that plane stress conditions are approached for radial distances from the crack tip exceeding half the plate thickness. A similar observation was made for pure mode I loading by Narasimhan and Rosakis (1990) and Nakamura and Parks (1990).…”

“…This disk is modeled using a finite element mesh comprised of eight-noded isoparametric hexahedral elements, which are focused at the crack tip (see Figure 1b). The crack front elements are formed by collapsing the eight-noded hexahedral elements to triangular prisms, while allowing for independent displacements of the nodes on the collapsed edge (as in Narasimhan and Rosakis, 1990).…”

“…Further, in engineering analysis, three-dimensional (3D) fracture problems are usually simplified by suitably assuming two-dimensional (2D) plane strain or plane stress conditions. However, in a thin plate containing a through crack, plane stress condition exists everywhere except in regions near the crack front where the stress state is 3D in nature Parks, 1988a, 1990;Narasimhan and Rosakis, 1990). Hence, the effects of ductility and 3D state of stress on mixed mode fracture are important and need to be addressed in detail to establish the suitability of 2D approximations.…”

“…Parks (1988a, 1990) performed a 3D boundary layer analysis of a thin ductile plate under mode I loading. Narasimhan and Rosakis (1990) and Zehnder and Rosakis (1988) carried out numerical (both 2D and 3D) and experimental investigations on a ductile three point bend specimen and found strong thickness variations of stress fields and J very near the crack front. Their results, and those reported by Nakamura and Parks (1990), revealed that strong 3D effects are present within a radial distance of about one-half plate thickness from the crack front.…”

Finite element simulations of notch tip fields in magnesium single crystals

“…The layers of nodes are located at X 3 / h = 0.0, 0.038, 0.084, 0.14, 0.20, 0.28, 0.38, 0.5. Thus, the layers become gradually thinner as the free surface (X 3 = 0) is approached in order to capture the strong through-thickness variation of the field quantities close to the notch root (Narasimhan and Rosakis 1990;Subramanya et al 2007). …”