scholarly journals Conservation laws in anisotropic elasticity II. Extension and application to thermoelasticity

1993 ◽  
Vol 443 (1917) ◽  
pp. 153-161 ◽  
Keyword(s):  
Stress Intensity ◽  
Conservation Laws ◽  
Stress Intensity Factors ◽  
Thermal Conditions ◽  
Anisotropic Elasticity ◽  
Integral Representations ◽  
Intensity Factors ◽  
Closed Form Solutions ◽  
Finite Crack ◽  
Crack Faces

The conservation laws in anisotropic elasticity developed in an accompanying paper are extended to include steady-state thermal elasticity. The conservation laws proposed in this paper lead to integrals that do not contain area integration and are path-independent. In addition to the extended J - and M -integrals of J. K. Knowels and E. Sternberg, also derived are path-independent contour integrals that yield directly the stress intensity factors when evaluated over contours enclosing a crack. The path-independent integral representations of the stress intensity factors are used to obtain closed form solutions for a finite crack in an unbounded thermoelastic medium subject to arbitrary thermal conditions on the crack faces.

Representations of Stress Intensity Factors by Path-Independent Integrals

1989 ◽  
Vol 56 (4) ◽  
pp. 780-785 ◽  
Author(s):  
Kuang-Chong Wu
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Body Force ◽  
Anisotropic Body ◽  
Crack Tip ◽  
Intensity Factors ◽  
Elastic Materials ◽  
Linear Elastic ◽  
Finite Crack

Stress intensity factors are represented by path independent integrals for linear elastic materials. Two types of representation are given. The first type of integrals are expressed by integration over contours surrounding a crack tip. Those of the second type are integrated over contours enclosing a finite crack. The path independent integrals are applied to determine the stress intensity factors due to a body force and a dislocation for a finite crack in an infinite anisotropic body.

Stress Intensity Factors for Finite Interface Cracks Between a Special Pair of Transversely Isotropic Materials

2002 ◽  
Vol 69 (3) ◽  
pp. 230-239 ◽  
Author(s):  
V. Boniface ◽  
L. Banks-Sills
Keyword(s):  
Finite Element ◽  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Transversely Isotropic ◽  
Complex Stress ◽  
Intensity Factors ◽  
Isotropic Materials ◽  
Analytic Expressions ◽  
Finite Crack ◽  
Transversely Isotropic Materials

An infinite bimaterial system made of two dissimilar, transversely isotropic materials bonded together (with the lower material being mathematically degenerate) and subject to remote loads is considered. An analytical expression for the complex stress intensity factor of a finite crack along the interface between these two materials is obtained. This result is extended to the case of an infinite array of collinear cracks along a similar interface. Next, the finite element method is employed to analyze these geometries for specific material properties. An area M-integral is used to extract stress intensity factors from the finite element results, which compare well with those obtained from the analytic expressions. Different types of loads are considered.

Stress Intensity Factors for Plate Bending and Shearing Problems

1994 ◽  
Vol 61 (3) ◽  
pp. 719-722 ◽  
Author(s):  
A. T. Zehnder ◽  
Chung-Yuen Hui
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Plate Theory ◽  
Infinite Plate ◽  
Bending Moment ◽  
Far Field ◽  
Intensity Factors ◽  
Arbitrary Angle ◽  
Cracked Plate ◽  
Finite Crack

Stress intensity factors for a finite crack in an infinite plate are calculated assuming Kirchhoff plate theory. Two problems are considered: a cracked plate subjected to uniform far-field shearing, and a cracked plate subjected to uniform far-field bending moment. In both cases the crack is oriented at an arbitrary angle to the axis of loading.

Electroelastic Fields Induced by Two Collinear and Energetically Consistent Cracks in a Piezoelectric Layer

2014 ◽  
Vol 30 (4) ◽  
pp. 361-372 ◽  
Author(s):  
X.-C. Zhong ◽  
K.-Y. Lee
Keyword(s):  
Stress Intensity ◽  
Boundary Conditions ◽  
Electric Fields ◽  
Stress Intensity Factors ◽  
Piezoelectric Layer ◽  
Intensity Factors ◽  
Crack Face ◽  
Closed Form Solutions ◽  
Electroelastic Fields ◽  
Crack Tips

AbstractWithin the framework of linear piezoelectricity, the problem of two collinear electrically dielectric cracks in a piezoelectric layer is investigated under inplane electro-mechanical loadings. The energetically consistent crack-face boundary conditions are utilized to address the effects of a dielectric inside the cracks on the crack growth. The Fourier transform technique is applied to solve the boundary-value problem. Under the consideration of two-case electromechanical loadings, the electroelastic fields near the inner and outer crack tips are obtained through the Lobatto-Chebyshev collocation method. The special case of two collinear energetically consistent cracks in an infinite piezoelectric solid is analyzed and the closed-form solutions of the crack-tip electroelastic fields are further determined. Numerical results show the variations of stress intensity factors and energy release rates near the inner and outer crack tips on the applied electric fields, the geometry of cracks and the width of the piezoelectric layer in graphics. The observations reveal that the stress intensity factors are dependent not only on the adopted crack-face boundary conditions, but also on the applied mechanical loading.

Effect of Orthotropy on Singular Stresses for a Finite Crack

1973 ◽  
Vol 40 (2) ◽  
pp. 491-497 ◽  
Author(s):  
T. Ohyoshi
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Stress Distributions ◽  
Intensity Factors ◽  
Singular Stress ◽  
Dynamic Stress Intensity Factors ◽  
P Waves ◽  
Finite Crack ◽  
Symmetric Surface ◽  
P And Sv Waves

The diffraction of P and SV-waves by a finite crack located on a symmetric surface of orthotropy is considered. By obtaining the singular stress distributions near the crack tip and dynamic stress-intensity factors, we show the influences of orthotropy on the stress distributions with orthotropic parameters, κα and κβ, and on the stress-intensity factors for P-waves in graph. The solution is presented in the form of integral equation having the kernel of a finite integration which is derived under some restrictions among the elastic constants. The conditions are satisfied for many orthotropic solids.

scholarly journals Short Subsurface Cracks Under Conditions of Slip and Stick Caused by a Moving Compressive Load

1985 ◽  
Vol 52 (4) ◽  
pp. 811-817 ◽  
Author(s):  
S. Sheppard ◽  
J. R. Barber ◽  
M. Comninou
Keyword(s):  
Stress Intensity ◽  
Stress Intensity Factors ◽  
Coulomb Friction ◽  
Compressive Load ◽  
Rolling Contact ◽  
Intensity Factors ◽  
Subsurface Cracks ◽  
Spalling Failure ◽  
Load Location ◽  
Crack Faces

The mechanism of spalling failure in rolling contact is modeled by an elastic half-plane with a subsurface crack parallel to the surface, loaded by a compressive normal force which moves over the surface. Coulomb friction at the crack faces reduces the Mode II Stress Intensity Factors and results in a number of history-dependent slip-stick configurations. The formulation used to study these involves a singular integral equation in two variables which must be solved numerically, and because of the history dependence, requires in an incremental solution. Only crack lengths and coefficients of friction that result in a maximum of two slip or stick zones for any load location are considered in this paper. It is found that the maximum range of stress intensity factors occurs at the trailing crack tip.

scholarly journals Bending by Concentrated Force of a Cantilever Strip Having a Through-thickness Crack Perpendicular to Its Axis

2020 ◽  
Vol 10 (6) ◽  
pp. 2037 ◽  
Author(s):  
Mykhaylo Delyavskyy ◽  
Viktor Opanasovych ◽  
Oksana Bilash
Keyword(s):  
Stress Intensity ◽  
Analytical Solution ◽  
Contact Area ◽  
Complex Variable ◽  
Stress Intensity Factors ◽  
Intensity Factors ◽  
Concentrated Force ◽  
Crack Location ◽  
Perfect Contact ◽  
Crack Faces

The article focuses on the bending problem for a cantilever beam with a straight through-thickness crack, perpendicular to its axis under bending by concentrated force. Depending on the crack location in relation to the axis, crack faces may be in three states: perfect contact, particular contact, or noncontact. Using the theory of functions of complex variable and complex potentials, the considered problem was reduced to a linear conjunction one. An analytical solution of the problem was obtained. In the case of particular contact, the length of the contact area and stress intensity factors were determined. The ultimate force that causes beam destruction was determined. Numerical analyses of the problem were also performed.

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