Complex Variable Green’s Functions for Crack-Microcracks Interactions

2011 ◽  
Vol 465 ◽  
pp. 123-128 ◽  
Author(s):  
M. Chabaat ◽  
H. Ayas
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Main Crack ◽  
Green's Functions ◽  
Green’S Functions ◽  
Complex Variables ◽  
Mode I ◽  
Micro Cracks

In this study, interaction between a main crack and a surrounding layer of micro cracks is considered. A stress field distribution induced during these interactions is obtained using Muskhelshvili’s complex variables formalism which relies on the Green's functions. The effect of amplification and shielding on the resulting stress field is shown, herein, through a study of mode I Stress Intensity Factor (SIF). To quantify these effects, orientations as well as positions of microcracks with respect to the main crack is taken into consideration. Obtained results are compared and agreed with those of other researchers.

Interacting Crazing Patterns Near the Tip in the Damage Zone of a Crack

2010 ◽  
Vol 123-125 ◽  
pp. 555-558
Author(s):  
H. Seddiki ◽  
M. Chabaat
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Main Crack ◽  
Damage Zone ◽  
Numerical Approach ◽  
Mode I ◽  
The One ◽  
Linear Propagation

The present paper investigates interactions between a main crack and a surrounding layer of crazing patterns. Analysis of the stress field distribution as well as the energy induced during these interactions is based on the resolution of some equations along with appropriate boundary conditions and the use of a numerical approach. The effect of amplification and shielding on the resulting stress field is shown through a study of mode I Stress Intensity Factor (SIF). Besides, to quantify the effects of this damage on the main crack, it is shown that the Energy Release Rate (ERR) is defined as being a superposition of the energy released due to the linear propagation of the main crack as well as the one due to the translational change in the growth of the damage. It is also proven that crazes closer to the main crack dominate the resulting interaction effect and reflect an anti-shielding of the damage while a reduction constitutes a material toughness.

scholarly journals Calculation of Stress Intensity Factors at Both Ends of the Indenter under Eccentric Loads

2020 ◽  
Vol 2020 ◽  
pp. 1-12
Author(s):  
Xuefeng Yang ◽  
Yili Duo
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Stress Field ◽  
Rock Breaking ◽  
Rock Surface ◽  
Mode I ◽  
Singular Stress ◽  
Partial Load ◽  
Asymmetrical Mode

During rock breaking by drill, cone rolls on the rock surface and contact between gear teeth and surface is basically positive Mode-I plane indentation and bias Mode-I plane indentation. During bias action, there will be an asymmetrical Mode-I singular stress field at both ends of the indenter. The stress field singularity is of the same order as Mode-I crack tip and with the same function distribution. In this paper, based on the J2 integral conservation law, a new method is established for solving stress intensity factor of bias Mode-I plane indentation, which not only provides respective stress intensity factor of both ends of the indenter but also compares relations between eccentricity, partial load, and stress intensity factor. The study not only provides a method for establishment of new cone drill engineering design but also improves rock layer boring efficiency.

ELASTODYNAMIC STRESS INTENSITY FACTOR FOR A FINITE CRACK IN ELASTIC SOLID UNDER 3D TRANSIENT LOADING OF MODE I

2013 ◽  
Vol 05 (04) ◽  
pp. 1350044
Author(s):  
XIANHONG MENG ◽  
ZHAOYU BAI ◽  
MING LI
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Integral Transform ◽  
Elastic Solid ◽  
Scattered Wave ◽  
Mode I ◽  
Finite Width ◽  
Infinite Length ◽  
Distance Ratio

In this paper, the three-dimensional dynamic problem for an infinite elastic medium weakened by a crack of infinite length and finite width is analyzed, while the crack surfaces are subjected to mode I transient linear tractions. The integral transform approach is applied to reduce the governing differential equations to a pair of coupled singular integral equations, whose solutions can be obtained with the typical iteration method. The analytical solution of the stress intensity factor when the first wave and the first scattered wave reach the investigated crack tip is obtained. Numerical results are presented for different values of the width-to-longitudinal distance ratio z/l. It is found that the stress intensity factor decreases with the arrival of the first scattered longitudinal wave and increases with the arrival of the first scattered Rayleigh wave and tends to be stable. The static value considering both the first scattered wave and the first wave is about 50% greater than that considering only the first wave, and then the effect of the reflected wave is remarkable and deserves further study.

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