Effect of the poisson ratio on the perfectly plastic stress field at a stationary plane-strain crack tip

Plane-strain crack-tip stress and strain fields are presented for materials exhibiting pressure-sensitive yielding and plastic volumetric deformation. The yield criterion is described by a linear combination of the effective stress and the hydrostatic stress, and the plastic dilatancy is introduced by the normality flow rule. The material hardening is assumed to follow a power-law relation. For small pressure sensitivity, the plane-strain mode I singular fields are found in a separable form similar to the HRR fields (Hutchinson, 1968a, b; Rice and Rosengren, 1968). The angular distributions of the fields depend on the material-hardening exponent and the pressure-sensitivity parameter. The low-hardening solutions for different degrees of pressure sensitivity are found to agree remarkably with the corresponding perfectly-plastic solutions. An important aspect of the effects of pressure-sensitive yielding and plastic dilatancy on the crack-tip fields is the lowering of the hydrostatic stress and the effective stress directly ahead of the crack tip, which may contribute to the experimentally-observed enhancement of fracture toughness in some ceramic and polymeric composite materials.

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A closed-form solution for the stress field in a rigid-perfectly plastic material under plane-strain conditions

Acta Mechanica ◽

10.1007/bf01178329 ◽

1989 ◽

Vol 77 (3-4) ◽

pp. 307-313 ◽

Cited By ~ 4

Author(s):

D. E. Panayotounakos ◽

N. P. Andrianopoulos

Keyword(s):

Stress Field ◽

Closed Form ◽

Plane Strain ◽

Plastic Material ◽

Closed Form Solution ◽

Form Solution ◽

Perfectly Plastic

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Influence of Porosity on Plane Strain Tensile Crack-Tip Stress Fields in Elastic-Plastic Materials: Part I

Journal of Applied Mechanics ◽

10.1115/1.2893760 ◽

1992 ◽

Vol 59 (3) ◽

pp. 559-567 ◽

Cited By ~ 6

Author(s):

W. J. Drugan ◽

Y. Miao

Keyword(s):

Stress Field ◽

Closed Form ◽

Normal Stress ◽

Plane Strain ◽

Plane Stress ◽

Entire Range ◽

Crack Tip ◽

Constant Stress ◽

Tensile Crack ◽

Stress Discontinuity

We perform an analytical first study of the influence of a uniform porosity distribution, for the entire range of porosity level, on the stress field near a plane strain tensile crack tip in ductile material. Such uniform porosity distributions (approximately) arise in incompletely sintered or previously deformed (e.g., during processing) ductile metals and alloys. The elastic-plastic Gurson-Tvergaard constitutive formulation is employed. This model has a sound micromechanical basis, and has been shown to agree well with detailed numerical finite element solutions of, and with experiments on, voided materials. To facilitate closed-form analytical results to the extent possible, we treat nonhardening material with constant, uniform porosity. We show that the assumption of singular plastic strain in the limit as the crack tip is approached renders the governing equations statically determinate with two permissible types of near-tip angular sector: one with constant Cartesian components of stress (“constant stress”); and one with radial stress characteristics (“generalized centered fan”). The former admits an exact asymptotic closed-form stress field representation, and although we prove the latter does not, we derive a highly accurate closed-form approximate representation. We show that complete near-tip solutions can be constructed from these two sector types for the entire range of porosity. These solutions are comprised of three asymptotic sector configurations: (i) “generalized Prandtlfield”for low porosities (0 ≤ f ≤ .02979), similar to the plane strain Prandtl field of fully dense materials, with a fully continuous stress field but sector extents that vary with porosity; (ii) “plane-stress-like field” for intermediate porosities (.02979 < f < .12029), resembling the plane stress solution for fully dense materials, with a ray of radial normal stress discontinuity but sector extents that vary with porosity; (iii) two constant stress sectors for the remaining high porosity range, with a ray of radial normal stress discontinuity and fixed sector extents. Among several interesting features, the solutions show that increasing porosity causes significant modification of the angular variation of stress components, particularly for a range of angles ahead of the crack tip, while also causing a drastic reduction in maximum hydrostatic stress level.

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