Moving Crack in an Infinite Plate of Orthotropic Anisotropy FGMs under Anti-Plane Shear

2010 ◽  
Vol 97-101 ◽  
pp. 928-931
Author(s):  
Xian Shun Bi ◽  
Feng Yang ◽  
Shuang Shuang Ma
Keyword(s):  
Crack Velocity ◽  
Characteristic Length ◽  
Crack Problem ◽  
Infinite Plate ◽  
Crack Tip ◽  
Shear Loading ◽  
Local Theory ◽  
Moving Crack ◽  
Plane Shear ◽  
Crack Tip Stress

The moving crack problem in an infinite plate of orthotropic anisotropy functionally graded materials (FGMs) subjected to an anti-plane shear loading is studied by making use of non- local theory. The shear modulus and mass density of FGMs are assumed to be of exponential form. Fourier transform is employed to solve the partial differential equation. The mixed boundary value problem is reduced to a pair dual integral equations which is solved by using Schmidt’s method. The semi-analytic solution of crack-tip stress is obtained, contrary to the classical elasticity solution, the crack-tip stress fields does not retains the stress singularity. The influences of the characteristic length, graded parameter, orthotropic coefficient and crack velocity on the crack-tip stress are analyzed. The numerical results show that the stress at the crack tip decrease as the characteristic length, crack velocity, graded parameter are increased and increase as the orthotropic coefficient is increased.

Mode III Yoffe Dynamic Crack Problem on the Interface between Dissimilar Materials

2007 ◽  
Vol 353-358 ◽  
pp. 42-45 ◽  
Author(s):  
Cheng Jin ◽  
Xin Gang Li ◽  
Li Zhang
Keyword(s):  
Crack Problem ◽  
Dynamic Stress Intensity Factor ◽  
Dissimilar Materials ◽  
Shear Loading ◽  
Dynamic Crack ◽  
Mode Iii ◽  
Moving Crack ◽  
Plane Shear ◽  
Shear Moduli ◽  
Laminated Material

A moving crack in a laminated structure with free boundary subjected to anti-plane shear loading is investigated in this paper. Using the bonding conditions of the interface between different media, all the quantities in our question have been represented with a single unknown function, and the problem is transformed into a dual integrated equation with the method of Fourier transform. The equation is solved using Schmidt method. Finally the numerical results show the relationships among the dynamic stress intensity factor and crack velocity, the height of different laminated material, shear moduli of different laminated material.

Nonlocal Theory Solution for Mode III in an Infinite Strip of FGMs

2006 ◽  
Vol 324-325 ◽  
pp. 955-958
Author(s):  
Xian Shun Bi ◽  
Bao Liang Liu
Keyword(s):  
Crack Velocity ◽  
Maximum Stress ◽  
Integral Transform ◽  
Characteristic Length ◽  
Mixed Boundary ◽  
Crack Tip ◽  
Shear Loading ◽  
Infinite Strip ◽  
Mode Iii ◽  
Dual Integral Equations

This article provides a theoretical and numerical treatment of a crack subjected to an anti-plane shear loading in an infinite strip of FGMs. The crack situated in the mid-plane of strip moves at a constant velocity. It is assumed that the shear moduli varies continuously in the thickness direction and is to be of exponential form. The mixed boundary value problem is reduced to a pair dual integral equations by means of nonlocal elasticity theory and integral transform method. The stress field and displacement field for the strip are solved near the tip of the crack by using Schmidt’s method. Then the influences of the characteristic length, graded parameters and crack velocity on the stress at crack tip are studied. Unlike the classical elasticity solution, the magnitude of stress at the crack tip is finite, and it is found that the maximum stress increases with the crack velocity as the strip length is decreased, and the maximum stress decreases with the characteristic length as the graded parameters is increased.

Crack-Tip Stress Fields in FGMs under Anti-Plane Shear Impact Loading Using the Non-Local Theory

2007 ◽  
Vol 348-349 ◽  
pp. 821-824
Author(s):  
Xian Shun Bi ◽  
Xue Feng Cai ◽  
Jian Xun Zhang
Keyword(s):  
Integral Equations ◽  
Impact Loading ◽  
Infinite Plate ◽  
Stress Singularity ◽  
Crack Tip ◽  
Functionally Graded ◽  
Local Theory ◽  
Dual Integral Equations ◽  
Plane Shear ◽  
Non Local

A crack in an infinite plate of functionally graded materials (FGMs) under anti-plane shear impact loading is analyzed by making use of non-local theory. The shear modulus and mass density of FGMs are assumed to be of exponential form and the Poisson’s ratio is assumed to be constant. The mixed boundary value problem is reduced to a pair dual integral equations through the use of Laplace and Fourier integral transform method. In solving the dual integral equations, the crack surface displacement is expanded in a series using Jacobi’s polynomials and Schmidt’s method is used. The numerical results show that no stress singularity is present at the crack tip. The stress near the crack tip tends to increase with time at first and then decreases in amplitude and the peak values of stress decreases with increasing the graded parameters.

The Crack Problem for Bonded Nonhomogeneous Materials Under Antiplane Shear Loading

1985 ◽  
Vol 52 (4) ◽  
pp. 823-828 ◽  
Author(s):  
F. Erdogan
Keyword(s):  
Stress Field ◽  
Shear Modulus ◽  
Crack Problem ◽  
Crack Tip ◽  
Shear Loading ◽  
Antiplane Shear ◽  
Intensity Factors ◽  
Finite Crack ◽  
Square Root Singularity ◽  
Crack Tip Stress

The main objective of this paper is the investigation of the singular nature of the crack-tip stress field in a nonhomogeneous medium having a shear modulus with a discontinuous derivative. The problem is considered for the simplest possible loading and geometry, namely the antiplane shear loading of two bonded half spaces in which the crack is perpendicular to the interface. It is shown that the square-root singularity of the crack-tip stress field is unaffected by the discontinuity in the derivative of the shear modulus. The problem is solved for a finite crack and extensive results are given for the stress intensity factors.

Asymptotic Crack-Tip Fields in Perfectly Plastic Solids Under Mixed Mode II/III Loading Conditions

2006 ◽  
Vol 129 (4) ◽  
pp. 664-669
Author(s):  
J. Pan ◽  
P.-C. Lin
Keyword(s):  
Mixed Mode ◽  
Crack Tip ◽  
Shear Loading ◽  
Mode Ii ◽  
Pure Mode ◽  
Loading Conditions ◽  
Mode Iii ◽  
Plane Shear ◽  
Crack Tip Fields ◽  
Perfectly Plastic

In this paper, governing equations and solutions for asymptotic singular and nonsingular crack-tip sectors in perfectly plastic materials are first summarized under combined in-plane and out-of-plane shear loading conditions. The crack-tip fields under mixed mode II/III loading conditions are then investigated. An assembly of crack-tip sectors is adopted with stress discontinuities along the border of the two constant stress sectors. The solutions of the crack-tip fields under pure mode II, mixed mode II/III, and nearly pure mode III loading conditions are presented. The trends of the angular variations of the mixed mode II/III crack-tip stresses agree with those of the available computational analysis and the asymptotic analysis for low strain hardening materials. The pure mode II crack-tip stresses are similar to those of Hutchinson, and the nearly pure mode III stresses are similar to those of the pure mode III crack-tip field of Rice.

scholarly journals Experimental Study on the Caustics of Moving Cracks and Elliptical Curvature under Impact Loading

2021 ◽  
Vol 2021 ◽  
pp. 1-12
Author(s):  
Haohao Luo ◽  
Renshu Yang ◽  
Yanbing Wang ◽  
Guoliang Yang ◽  
Chengxiao Li ◽  
...  
Keyword(s):  
Stress Intensity Factor ◽  
Stress Intensity ◽  
Intensity Factor ◽  
Impact Loading ◽  
Crack Tip ◽  
Test System ◽  
Moving Crack ◽  
Linear Elastic ◽  
Elastic Fracture ◽  
Crack Tip Stress

A dynamic caustics test system was used, and different moving cracks were analysed to study the interaction between the crack growth rate, stress intensity factor, and curvature of the elliptical end of a moving crack under impact loading. Based on the linear elastic fracture mechanics theory, linearly fitting of the crack tip stress intensity factor and the elliptical curvature were employed to obtain the specific functional expressions. ABAQUS software was used to numerically simulate the moving crack fracture process passing through different elliptical curvatures. The crack tip stress intensity factor was calculated by the stress extrapolation method. The stress intensity factor obtained from the numerical calculation and the caustics test was consistent. The test and numerical simulation results showed that the direction of moving cracks entering and passing through the elliptical defects shows a certain regularity. As the ellipse curvature increased, the moving crack stress intensity factor passing through the ellipse gradually decreased, and the moving crack also passed easily through oval defects.

Correspondence Relations for the Interface Crack in Monoclinic Composites Under Mixed Loading

1990 ◽  
Vol 57 (4) ◽  
pp. 894-900 ◽  
Author(s):  
Kuang-Chong Wu ◽  
Shyh-Jye Hwang
Keyword(s):  
Interface Crack ◽  
Crack Problem ◽  
Shear Loading ◽  
Antiplane Shear ◽  
Intensity Factors ◽  
Plane Shear ◽  
Applied Loading ◽  
As Stress ◽  
Crack Faces ◽  
Quantities Of Interest

A correspondence is established between the problem of an interface crack in mon-oclinic composites and that of an interface crack in isotropic composites. The interface crack considered is subjected to a combined tension-compression, in-plane shear and antiplane shear loading at the crack faces. Under the applied loading, the interface crack is assumed to be partially opened. Through the correspondence, quantities of interest such as stress intensity factors, sizes of the contact zones, for monoclinic composites can be obtained from the results of the isotropic interface crack problem.

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