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

1992 ◽  
Vol 59 (3) ◽  
pp. 559-567 ◽  
Author(s):  
W. J. Drugan ◽  
Y. Miao

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.

1989 ◽  
Vol 56 (4) ◽  
pp. 786-790 ◽  
Author(s):  
John Dundurs

There is a strange feature of plane elasticity that seems to have gone unnoticed: The stresses in a body that contains rigid inclusions and is loaded by specified surface tractions depend on the Poisson ratio of the material. If the Poisson ratio in this stress field is set equal to +1 for plane strain, or +∞ for plane stress, the rigid inclusions become cavities for elastic constants within the physical range. The paper pursues this circumstance, and in doing so also produces several useful by-products that are connected with the stretching and curvature change of a boundary.


1973 ◽  
Vol 40 (1) ◽  
pp. 288-290 ◽  
Author(s):  
C. Atkinson

The exact solution is given for a line load acting on a half space of a power-law elastic material under conditions of plane stress. This solution is compared with the corresponding solution under plane-strain conditions; see Aruliunian [1]. A marked difference is found between the plane-stress and plane-strain fields for different values of the hardening exponent.


Author(s):  
Masataka Yatomi ◽  
Noel P. O’Dowd ◽  
Kamran M. Nikbin

In this work a computational study of creep crack growth in a carbon manganese steel is presented. The constitutive behaviour of the steel is described by a power law creep model and the accumulation of creep damage is accounted for through the use of a well-established model for void growth in creeping materials. Two dimensional finite element analyses have been performed for a compact tension specimen and it has been found that the predicted crack growth rate under plane strain conditions approaches that under plane stress conditions at high C* levels. Furthermore it has been shown, both experimentally and numerically, that an increase in test temperature causes the convergence of the cracking rate to occur at higher values of C*. This trend may be explained by the influence of crack-tip plasticity, which reduces the relative difference in constraint between plane stress and plane strain conditions. The constraint effect has been quantified through the use of a two-parameter characterisation of the crack tip fields under creep conditions.


1993 ◽  
Vol 60 (4) ◽  
pp. 883-889 ◽  
Author(s):  
Y. Miao ◽  
W. J. Drugan

This paper continues the investigation of Drugan and Miao (1992). There we studied analytically the influence of a uniform porosity distribution on the stress field near a plane strain tensile crack tip in ductile (elastic-ideally plastic) material, assuming that material very near the tip is at yield at all angles about the tip. Our solutions exhibited completely continuous stress fields for porosity f ≤ 0.02979, but for higher porosities they involved radial surfaces of radial normal stress jumps. Here we investigate whether, for this higher range of porosity, relaxing our assumption of yield at all angles about the tip will facilitate solutions exhibiting fully continuous stress fields. The answer to this is shown to be yes, with a single near-tip sector assembly providing such solutions for this entire higher porosity range. On either side of the crack symmetry plane, this solution configuration consists of a leading plastic sector possessing radial stress characteristics (“generalized centered fan ”), followed by a plastic sector of constant Cartesian components of stress, followed finally by a sector of purely elastic material adjacent to the crack flank. The angular extents of these sectors vary substantially with porosity level. In regions of purely elastic response, we have accounted for the influence of porosity on the overall, or effective, elastic moduli. Among the interesting features of these new solutions are a significantly enlarged generalized centered fan sector as compared to that of the fully plastic Part I solutions for the same f values, and for f values just slightly above the 0.02979 level, a narrow elastic sector exists in which stresses vary so rapidly with angle that they appear to be nearly discontinuous. This rapid variation spreads out as the elastic sector enlarges with increasing f, and, in contrast to the fully plastic solutions, the radial normal component of stress becomes negative near the crack flank.


2019 ◽  
Vol 24 (3) ◽  
pp. 549-576 ◽  
Author(s):  
M. Graba

Abstract The paper presents a comprehensive analysis of the stress field near a crack tip for a compact specimen dominated by the plane strain state using the finite element method. The analysis also includes the calculation of some parameters of in-plane constraints, both for small and large strain assumptions. It discusses the influence of the material characteristic, relative crack length and external load for the stress field, and the in-plane constraint parameter. The approximation formulas for some in-plane constraint parameters are presented.


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