Case Criterion of Crack Onset in Orthotropic Bi-Material Notches

2011 ◽  
Vol 465 ◽  
pp. 157-160 ◽  
Author(s):  
Tomáš Profant ◽  
Jan Klusák ◽  
Michal Kotoul
Keyword(s):  
Energy Density ◽  
Crack Initiation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Local Minimum ◽  
Plane Elasticity ◽  
Mean Value ◽  
Density Factor ◽  
The Mean ◽  
Energy Density Factor

A bi-material notch composed of two orthotropic parts is considered. The stresses and displacements are expressed using the Stroh-Eshelby-Lekhnitskii formalism for plane elasticity. The potential direction of crack initiation is determined from the maximum mean value of the tangential stress or the local minimum of the mean value of the generalized strain energy density factor in both materials [1, 2]. The matched asymptotic procedure is introduced to derive the change of potential energy for the debonding crack and the crack initiated in the determined direction [3].

On the Crack Initiated from the Bi-Material Notch Tip

2010 ◽  
Vol 452-453 ◽  
pp. 441-444 ◽  
Author(s):  
Tomáš Profant ◽  
Jan Klusák ◽  
Michal Kotoul
Keyword(s):  
Energy Density ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Local Minimum ◽  
Plane Elasticity ◽  
Mean Value ◽  
Tangential Stresses ◽  
Density Factor ◽  
The Mean ◽  
Energy Density Factor

The bi-material notch composed of two orthotropic parts is considered. The radial and tangential stresses and strain energy density is expressed using the Stroh-Eshelby-Lekhnitskii formalism for the plane elasticity. The potential direction of the crack initiation is determined from the maximum mean value of the tangential stresses and local minimum of the mean value of the generalized strain energy density factor in both materials. Matched asymptotic procedure is used to derive the change of potential energy for the debonding crack and the crack initiated in the determined direction.

scholarly journals Prediction of Crack Initiation Direction for Surface Flaws Under Biaxial Loading

2003 ◽  
Vol 125 (1) ◽  
pp. 65-70 ◽  
Author(s):  
Abdennour C. Seibi ◽  
Sam Y. Zamrik
Keyword(s):  
Energy Density ◽  
Crack Initiation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Biaxial Stress ◽  
Crack Trajectory ◽  
Fracture Crack ◽  
Density Factor ◽  
Crack Angle ◽  
Energy Density Factor

This paper presents a simple method based on the strain energy density factor ΔS to study the fatigue characteristics of rhombic plates with induced angled flaws under biaxial stress field. The paper discusses in detail the procedures followed to predict the fracture crack initiation angle, θo, as a function of induced crack angle, β, the path of the crack trajectory at the initial stage of fracture and develop an expression for the crack growth rate. This method assumes that the crack extends in a radial direction and that the initial fracture crack angle, θo, is obtained by maximizing the hoop stress along a circumference of a radius r. Expressions for the stress-state near the crack tip were developed for computing the crack trajectory and the strain energy density factor. The crack trajectory path was estimated by computing the new values of the crack angle and a fictitious crack length. These computed values were in turn used to determine the strain energy density factor. The developed method revealed two important observations: i) The crack trajectory was in close agreement with the experimental data for the first 20% of the lifetime to failure, ii) the crack propagation rate is dependent on the crack angle using the stress intensity factor and exhibited no variation with respect to the crack angle when the strain energy density factor is used.

A Bi-Material Wedge – a Model for the Prediction of Failure Initiation at Shape and Material Discontinuities

2006 ◽  
Vol 324-325 ◽  
pp. 1305-1308
Author(s):  
Jan Klusák ◽  
Zdeněk Knésl
Keyword(s):  
Energy Density ◽  
Crack Initiation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Stress Concentrations ◽  
Singular Stress ◽  
Failure Initiation ◽  
Density Factor ◽  
Material Discontinuities ◽  
Energy Density Factor

Geometrical and material discontinuities in constructions lead to singular stress concentrations and consequently to a crack initiation. The model of a bi-material wedge makes it possible to analyse such construction points to assess their stability. The presented approach is based on the knowledge of the strain energy density factor distribution in the concentrator vicinity.

A Modified Strain-Energy Density Criterion Applied to Crack Propagation

1982 ◽  
Vol 49 (1) ◽  
pp. 81-86 ◽  
Author(s):  
P. S. Theocaris ◽  
N. P. Andrianopoulos
Keyword(s):  
Energy Density ◽  
Crack Initiation ◽  
Strain Energy Density ◽  
Strain Energy ◽  
Mean Value ◽  
Complex Functions ◽  
Slant Crack ◽  
Minimum Strain Energy ◽  
The Mean

An exact solution is presented to the problem of the crack-initiation direction by applying the minimum strain-energy density criterion in the case of a slant crack loaded uniaxially. The exact expressions of stresses, obtained from Muskhelishvili’s complex functions, are used in evaluating strain energy. Although the position of direction of the minimum density (ϑm) was accepted as the probable direction of the next kink of a propagating crack, the mean value of the strain-energy density is also introduced, instead of its minimum value, in the role of the critical quantity for crack initiation. Interesting results were derived for the behavior of this quantity concerning the phenomenon of bifurcation. The ratio of the mean-energy densities above and below the expected path of propagation is introduced as a second factor influencing the exact value of angle ϑm of propagation.

Sign in / Sign up

Export Citation Format

Share Document