This paper deals with a procedure to calculate the elastic stress intensity factors for arbitrary-shaped cracks in plane stress and plane strain problems. An assumed displacement.hybrid finite element model is employed wherein the unknowns in the final algebraic system of equations are the nodal displacements and the elastic stress intensity factors. Special elements, which contain proper singular displacement and stress fields, are used in a fixed region near the crack tip; and the interelement displacement compatibility is satisfied through the use of a Lagrangean multiplier technique. Numerical examples presented include: central as well as edge cracks in tension plates and a quarter-circular crack in a tension plate. Excellent correlations were obtained with available solutions in all the cases. A discussion on the convergence of the present solution is also included.
This study presents a rapid continuous process for grain refinement in metallic materials through severe plastic deformation (SPD). The principle is described and the process is applied to an Al-5056 alloy and an S45C carbon steel. The new process, designated in this study the severe torsion straining process (STSP), consists of producing a local heated zone in a rod and introducing torsion strain into the zone by rotating one end with the other. The process is continuous because the straining is achieved while the rod is moved so that the heated zone is shifted along the rod. The STSP does not require the use of any die and can be applicable to pipes or wires. Fine-grained structures produced with the STSP are confirmed using optical microscopy and transmission electron microscopy. Tensile properties are measured and compared with the unstrained fully annealed samples. The feasibility of the STSP is discussed with respect to the rotation speed and moving speed.
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