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

Asymptotic Field near the Tip of a Mode I Quasi-Statically Propagating Crack in Rate-Sensitive Materials

2010 ◽  
Vol 452-453 ◽  
pp. 141-144
Author(s):  
Jia Lei Li ◽  
Bin Jia ◽  
Zhen Qing Wang ◽  
Bao Jun Pang
Keyword(s):  
Power Law ◽  
Crack Tip ◽  
Viscosity Coefficient ◽  
Mode I ◽  
Crack Tip Field ◽  
Plane Stress Condition ◽  
Propagating Crack ◽  
Power Law Function ◽  
Constitutive Mode ◽  
Hardening Coefficient

An elastic-viscoplastic constitutive mode was adopted to analyze asymptotically the tip field of a mode I quasi-statically propagating crack in rate-sensitive materials under plane stress condition. Under the assumption that the viscosity coefficient is a power law function of the rate of effective plastic strain, it was obtained through dimension match that the crack tip field possesses power law singularity. And the singularity exponent is uniquely determined by the power law exponent in the supposed viscosity coefficient. The elasticity, plasticity and viscosity of material at crack-tip only can be matched reasonably under linear-hardening condition. Variations of crack tip field characters according to each material parameter were discussed by means of numerical computation. The stress intensity is dominated by the material viscosity whereas the hardening coefficient has less significant influence on tip field. Furthermore, the solution can be transformed to the elastic-nonlinear-viscous one of Hui and Riedel if the limit case of zero hardening coefficient is considered.

The Elastic-Viscoplastic Field at the Mixed-Mode Crack-Tip under Compression and Shear

2011 ◽  
Vol 211-212 ◽  
pp. 364-368
Author(s):  
Zhen Qing Wang ◽  
Fang Liu ◽  
Wen Yan Liang
Keyword(s):  
Interface Crack ◽  
Power Law ◽  
Mixed Mode ◽  
Crack Tip ◽  
Viscosity Coefficient ◽  
Plastic Strain Rate ◽  
Crack Tip Field ◽  
Control Factors ◽  
Mixed Mode Crack ◽  
Propagating Crack

To further study the field of the mixed-mode interface crack tip under compression and shear, we analyze the problem on the quasi-static propagating of the interface crack theoretically and numerically.In this paper,we assumes that the artifical viscosity cofficient is in inverse proportion to power law of the plastic strain rate,and the stress of the interface crack possesses power law singularity. The viscosity of material,the friction touch effection of the crack-tip surface and the load hybrid parameter are considered. The asymptotic solution is established for elastic-viscoplastic field at the mixed-mode propagating crack-tip under comprission and shear.It is shown in numerical results and analysis that for the mixed-mode crack-tip field under compressing and shear is whole plastic without elastic unloaded section;viscosity effection is an important factor when propagating crack-tip field is studied; viscosity coefficient, mach number and singularity exponent are the control factors of singular field at the crack-tip.

scholarly journals On the nonlinear eigenvalue problems arising in fracturemechanics

2017 ◽  
Vol 21 (3) ◽  
pp. 125-139
Author(s):  
E.M. Yakovleva
Keyword(s):  
Power Law ◽  
Plane Stress ◽  
Shooting Method ◽  
Eigenvalue Problems ◽  
Crack Tip ◽  
Mode Ii ◽  
Static Mode ◽  
Nonlinear Eigenvalue Problems ◽  
Mode Ii Crack ◽  
Nonlinear Eigenvalue

In the article the stress-strain state near a Mode II crack tip under plane stress conditions in power-law materials is considered. It is noted that nowadays the whole eigenspectrum and orders of stress singularity at the crack tip for a power-law medium are of prevailing interest. Additional eigenvalues for the stress field at a static mode II crack under plane stress condition are numerically obtained for different values of the exponent n via the Runge-Kutta method in conjunction with the shooting method. However, in this case the shooting method is multi-parameter since it is necessary to select two parameters and, consequently, the results obtained require further verification and justification. For this purpose the technique developed in perturbation theory for study of nonlinear eigenvalue problems is offered and applied for eigenvalue problems arising from fracture mechanics analysis.

scholarly journals An approach to analysis of dynamic crack growth at bimaterial interface

2009 ◽  
Vol 36 (4) ◽  
pp. 299-327 ◽  
Author(s):  
R. Nikolic ◽  
Jelena Djokovic
Keyword(s):  
Asymptotic Analysis ◽  
Strain Field ◽  
Crack Tip ◽  
Optical Data ◽  
Bimaterial Interface ◽  
Dynamic Crack ◽  
New Approach ◽  
Shear Wave Speed ◽  
Propagating Crack

In this paper is presented the new approach to asymptotic analysis of the stress and strain fields around a crack tip that is propagating dynamically along a bimaterial interface. Through asymptotic analysis the problem is being reduced to solving the Riemann-Hilbert's problem, what yields the strain potential that is used for determination of the strain field around a crack tip. The considered field is that of a dynamically propagating crack with a speed that is between zero and shear wave speed of the less stiffer of the two materials, bound along the interface. Using the new approach in asymptotic analysis of the strain field around a tip of a dynamically propagating crack and possibilities offered by the Mathematica programming package, the results are obtained that are compared to both experimental and numerical results on the dynamic interfacial fracture known from the literature. This comparison showed that it is necessary to apply the complete expression obtained by asymptotic analysis of optical data and not only its first term as it was done in previous analyses.

Governing factors of the local tensile stress in the vicinity of a rapidly propagating crack tip in elastic-viscoplastic solids

2019 ◽  
Vol 218 ◽  
pp. 106548 ◽  
Author(s):  
Fuminori Yanagimoto ◽  
Kazuki Shibanuma ◽  
Toshiyuki Matsumoto ◽  
Katsuyuki Suzuki
Keyword(s):  
Tensile Stress ◽  
Crack Tip ◽  
Propagating Crack ◽  
Viscoplastic Solids

On Higher-Order Crack-Tip Fields in Creeping Solids

1999 ◽  
Vol 67 (2) ◽  
pp. 372-382 ◽  
Author(s):  
B. N. Nguyen ◽  
P. R. Onck ◽  
E. van der Giessen
Keyword(s):  
Power Law ◽  
Crack Tip ◽  
Small Strain ◽  
Higher Order ◽  
Single Edge ◽  
Constraint Effect ◽  
Scaling Properties ◽  
Crack Tip Fields ◽  
Asymptotic Development ◽  
Loading Parameter

In view of the near-tip constraint effect imposed by the geometry and loading configuration, a creep fracture analysis based on C* only is generally not sufficient. This paper presents a formulation of higher-order crack-tip fields in steady power-law creeping solids which can be derived from an asymptotic development of near-tip fields analogous to that of Sharma and Aravas and Yang et al. for elastoplastic bodies. The higher-order fields are controlled by a parameter named A2*, similar as in elastoplasticity, and a second loading parameter, σ∞. By means of the scaling properties for power-law materials, it is shown that A2* for a flat test specimen is independent of the loading level. Finally, we carry out small-strain finite element analyses of creep in single-edge notched tension, centered crack panel under tension, and single-edge notched bending specimens in order to determine the corresponding values of A2* for mode I cracks under plane-strain conditions. [S0021-8936(00)01202-2]

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