ASYMPTOTIC ANALYSIS OF GROWING CRACK STRESS DEFORMATION FIELDS IN POROUS DUCTILE METALS AND IMPLICATIONS FOR STABLE CRACK-GROWTH

Asymptotic stress and deformation fields near a quasi-statically growi ng plane strain tensile crack tip in porous elastic-ideally plastic ma terial, characterized by the Gurson-Tvergaard yield condition and asso ciated dow rule, are derived for small uniform porosity levels through out the range 0 to 4.54 percent. The solution configuration resembles that for crack growth in fully dense, elastically compressible, elasti c-ideally plastic Huber-Mises material for this porosity range, except that the angular extents and border locations of near-tip solution se ctors vary with porosity level, as do the stress and deformation field s within sectors. Increasing porosity is found to result in a dramatic reduction in maximum hydrostatic stress level, greater than that for a stationary crack; it also causes a significant angular redistributio n of stresses, particularly for a range of angles ahead of the crack a nd adjacent to the crack flank. The near-tip deformation fields derive d are employed to generalize a previously-developed, successful ductil e crack growth criterion. Our model predicts that for materials having the same initial slopes of their crack growth resistance curves, but different levels of uniform porosity, higher porosity results in a sub stantially greater propensity for stable crack growth.