A supplementary study of anisotropic plastic fields at a rapidly propagating plane-stress crack-tip (I)

1995 ◽  
Vol 16 (11) ◽  
pp. 1105-1115
Author(s):  
Lin Baisong
Keyword(s):  
Plane Stress ◽  
Crack Tip ◽  
Anisotropic Plastic

Plane stress dynamic fields near a propagating crack-tip in a power-law material

1988 ◽  
Vol 4 (1) ◽  
pp. 22-34 ◽  
Author(s):  
Zhang Zimao ◽  
Gao Yuchen
Keyword(s):  
Power Law ◽  
Plane Stress ◽  
Crack Tip ◽  
Propagating Crack

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.

Plane stress elastic-plastic fracture criteria and constraint intensity in crack tip regions

1990 ◽  
Vol 37 (3) ◽  
pp. 675-680 ◽  
Author(s):  
Jun Sun ◽  
Zengjie Deng ◽  
Mingjing Tu
Keyword(s):  
Plane Stress ◽  
Crack Tip ◽  
Fracture Criteria ◽  
Elastic Plastic

Computational Modelling of High Temperature Steady State Crack Growth Using a Damage-Based Approach

2003 ◽  
Author(s):  
Masataka Yatomi ◽  
Noel P. O’Dowd ◽  
Kamran M. Nikbin
Keyword(s):  
Crack Growth ◽  
Plane Strain ◽  
Plane Stress ◽  
Computational Study ◽  
Creep Crack Growth ◽  
Computational Modelling ◽  
Crack Tip ◽  
Creep Damage ◽  
Creep Model ◽  
Manganese Steel

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.

scholarly journals The stress field near the tip of a plane stress crack in a gel consisting of chemical and physical cross-links

2019 ◽  
Vol 475 (2227) ◽  
pp. 20180863 ◽  
Author(s):  
Jingyi Guo ◽  
Chung-Yuen Hui ◽  
Mincong Liu ◽  
Alan T. Zehnder
Keyword(s):  
Plane Stress ◽  
Crack Opening ◽  
Three Dimensional ◽  
Crack Tip ◽  
Stress Fields ◽  
Asymptotic Results ◽  
Constant Stretch ◽  
Cross Links ◽  
Theoretical Results ◽  
Gel Network

We study the time-dependent asymptotic stress fields near the tip of a mode I plane stress crack in a hydrogel. The analysis is based on a three-dimensional continuum model which describes the viscoelastic behaviour of a hydrogel gel with permanent and transient cross-links. The viscoelasticity results from the breaking and healing of the transient cross-links in the gel network. We show that the crack tip fields satisfy a local correspondence principle—that is, the spatial singularities of these fields are identical to a hyperelastic cracked body with the same but undamaged networks. Asymptotic results compare very well with finite-element simulations on a single-edge crack specimen loaded under constant stretch rate. We also compare the theoretical results (crack opening profile and crack tip strain field) with experiments and find excellent agreement.

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