Experimental checking of the ultimate equilibrium criterion for a crack or narrow slit in a plane stress field

1976 ◽  
Vol 8 (9) ◽  
pp. 1040-1043
Author(s):  
P. A. Pavlov ◽  
N. E. Nikulina
Keyword(s):  
Stress Field ◽  
Plane Stress ◽  
Narrow Slit ◽  
Ultimate Equilibrium

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
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.

A Complete Perfectly Plastic Solution for the Mode I Crack Problem Under Plane Stress Loading Conditions

2006 ◽  
Vol 74 (3) ◽  
pp. 586-589 ◽  
Author(s):  
David J. Unger
Keyword(s):  
Stress Field ◽  
Plane Stress ◽  
Plastic Material ◽  
Crack Problem ◽  
Yield Condition ◽  
Internal Crack ◽  
Mode I ◽  
Mode I Crack ◽  
Loading Conditions ◽  
Perfectly Plastic

A continuous stress field for the mode I crack problem for a perfectly plastic material under plane stress loading conditions has been obtained recently. Here, a kinematically admissible velocity field is introduced, which is compatible with the continuous stress field obtained earlier. By associating these two fields together, it is shown that they constitute a complete solution for the uncontained plastic flow problem around a finite length internal crack, having a positive rate of plastic work. The yield condition employed is an alternative criterion first proposed by Richard von Mises in order to approximate the plane stress Huber-Mises yield condition, which is elliptical in shape, to one that is composed of two intersecting parabolas in the principal stress plane.

Cavities vis-a`-vis Rigid Inclusions and Some Related General Results in Plane Elasticity

1989 ◽  
Vol 56 (4) ◽  
pp. 786-790 ◽  
Author(s):  
John Dundurs
Keyword(s):  
Stress Field ◽  
Plane Strain ◽  
Elastic Constants ◽  
Plane Stress ◽  
Poisson Ratio ◽  
Plane Elasticity ◽  
By Products

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.

A circular disc containing a radial edge crack opened by a constant internal pressure

1977 ◽  
Vol 81 (3) ◽  
pp. 497-521 ◽  
Author(s):  
R. D. Gregory
Keyword(s):  
Stress Concentration ◽  
Stress Field ◽  
Internal Pressure ◽  
Plane Stress ◽  
Edge Crack ◽  
Strain Energy ◽  
Circular Disc ◽  
Total Strain Energy ◽  
Significant Figures ◽  
Image Position

AbstractA circular disc of radius a, made of homogeneous, isotropic, linearly elastic material, contains a radial edge crack of length b(0 < b < 2a). The disc is in equilibrium in a state of generalized plane stress caused by loading the faces of the crack by a constant internal pressure. The problem of determining the resulting stress field throughout the disc is solved analytically in closed form. The principal results are that the stress concentration factor at the crack tip, the total strain energy W, and the opening U at the mouth of the crack, are given exactly bywhere A is a constant whose value correct to 6 significant figures isand , W0, U0 are normalising factors defined in section 6.

The Stress Field Due to a Line Load Acting on a Half Space of a Power-Law Hardening Material (A Comparison Between Plane Strain and Plane Stress)

1973 ◽  
Vol 40 (1) ◽  
pp. 288-290 ◽  
Author(s):  
C. Atkinson
Keyword(s):  
Exact Solution ◽  
Stress Field ◽  
Plane Strain ◽  
Half Space ◽  
Power Law ◽  
Elastic Material ◽  
Plane Stress ◽  
Strain Fields ◽  
Line Load ◽  
Hardening Material

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.

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