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

1993 ◽  
Vol 60 (4) ◽  
pp. 883-889 ◽  
Author(s):  
Y. Miao ◽  
W. J. Drugan
Keyword(s):  
Plane Strain ◽  
Plastic Material ◽  
Normal Component ◽  
Symmetry Plane ◽  
Crack Tip ◽  
Stress Fields ◽  
Elastic Response ◽  
Tensile Crack ◽  
Rapid Variation ◽  
Porosity Level

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.

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.

scholarly journals A Numerical Analysis of Selected Elastic-Plastic Fracture Parameters for DEN(T) Plates under Plane Strain Conditions

2017 ◽  
Vol 22 (1) ◽  
pp. 49-80 ◽  
Author(s):  
M. Graba
Keyword(s):  
Numerical Analysis ◽  
Fracture Mechanics ◽  
Plane Strain ◽  
Plastic Material ◽  
Crack Tip ◽  
Limit Load ◽  
Material Model ◽  
Crack Tip Opening Displacement ◽  
Opening Displacement ◽  
Elastic Plastic

Abstract This paper provides a numerical analysis of selected parameters of fracture mechanics for double-edge notched specimens in tension, DEN(T), under plane strain conditions. The analysis was performed using the elastic-plastic material model. The study involved determining the stress distribution near the crack tip for both small and large deformations. The limit load solution was verified. The J-integral, the crack tip opening displacement, and the load line displacement were determined using the numerical method to propose the new hybrid solutions for calculating these parameters. The investigations also aimed to identify the influence of the plate geometry and the material characteristics on the parameters under consideration. This paper is a continuation of the author’s previous studies and simulations in the field of elastic-plastic fracture mechanics [4, 6, 16, 17, 31].

Comparison of methods for obtaining crack-tip stress distributions in an elastic-plastic material

2005 ◽  
Vol 40 (5) ◽  
pp. 431-449 ◽  
Author(s):  
C. M Davies ◽  
N. P O'Dowd ◽  
K. M Nikbin ◽  
G A Webster ◽  
F Biglari
Keyword(s):  
Principal Stress ◽  
Plastic Material ◽  
Crack Tip ◽  
Maximum Principal Stress ◽  
Stress Fields ◽  
Good Representation ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Von Mises ◽  
Crack Tip Stress

Under linear elastic and elastic-plastic conditions the K field and the HRR (Hutchinson-Rice-Rosengren) field respectively are expected to provide an accurate representation of the stress field close to the crack tip in an elastic-plastic material. It has recently been proposed in French and UK defect assessment procedures that the Neuber method, originally developed for sharply curved notches, provides an alternative approach to estimate both notch and crack-tip stress fields, for use in conjunction with the sigma- d (σd) method to predict creep crack initiation times. In this work, the crack-tip stress fields under plane strain conditions, predicted from the Neuber approach, are compared with the HRR and K fields as well as those obtained from full-field finite element calculations. A compact tension and a single edge notched tension specimen have been examined; the material model used is the Ramberg-Osgood, power law plasticity model. As expected, the K field and HRR field have been found to provide a good representation of the near-tip fields at low and high loads respectively. Satisfactory solutions have also been obtained through the use of the reference stress to estimate the amplitude of the crack-tip stress in conjunction with the HRR field. The Neuber approach provides a good estimate of the equivalent (von Mises) stresses over the full range of load levels. However, but the use of the Neuber approach directly to predict the maximum principal stress in the plane of the crack provides a non-conservative prediction. A modified Neuber method, using an appropriate scaling function, has been proposed to determine the maximum principal stress in the plane of the crack from the equivalent (von Mises) stress predicted by the Neuber approach. Using the proposed method, a significantly improved estimate of the crack-tip stresses is obtained.

Stress Wave Radiation From a Crack Tip During Dynamic Initiation

1992 ◽  
Vol 59 (2) ◽  
pp. 356-365 ◽  
Author(s):  
V. Prakash ◽  
L. B. Freund ◽  
R. J. Clifton
Keyword(s):  
Fracture Mechanics ◽  
Plane Strain ◽  
Dynamic Fracture ◽  
Rear Surface ◽  
Crack Tip ◽  
Interparticle Spacing ◽  
Stress Fields ◽  
Wave Radiation ◽  
Normal Velocity ◽  
Square Root

Plate impact experiments are conducted to study the dynamic fracture processes which occur on submicrosecond time scales. These experiments involve the plane strain loading of a plane crack by a square tensile pulse with a duration of approximately one microsecond. The crack-tip loading rates achieved are K1 ˜ 108MPams−1, which are approximately two orders of magnitude higher than those obtained in other dynamic fracture configurations. Motion of the rear surface caused by waves diffracted from the stationary crack and by waves emitted by the running crack is monitored at four points ahead of the crack tip using a laser interferometer system. The measured normal velocity of the rear surface of the specimen agrees very well with the scattered fields computed using an assumed elastic viscoplastic model, except for the appearance of a sharp spike with a duration of less than 80 nanoseconds. This spike, which is not predicted by the inverse square root singular stress fields of linear elastic fracture mechanics, is understood to be related to the onset of crack growth and coincides with the abrupt and unstable ductile growth of a microstructural void to coalescence with the main crack. The crack initiation process is modeled as the sudden formation of a very small hole at the crack tip. This admits the possibility of dynamic crack-tip stress fields with crack-tip singularities stronger (˜r−3/2) than the inverse square root singular fields of fracture mechanics. The elastodynamic radiation resulting from the formation of a traction free hole at the crack tip is applied first to the case of antiplane shear deformation and then to the corresponding plane strain problem. The radiated fields predicted by the strongly singular solutions are found to be in good agreement with the spikes observed in the experiments. The radius of the hole, which appears as a parameter in the solution for the radiated field, agrees reasonably well with the interparticle spacing.

Sign in / Sign up

Export Citation Format

Share Document