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1.
In this paper, the dynamic interaction between two collinear cracks in a piezoelectric material plate under anti-plane shear
waves is investigated by using the non-local theory for impermeable crack surface conditions. By using the Fourier transform,
the problem can be solved with the help of two pairs of triple integral equations. These equations are solved using the Schmidt
method. This method is more reasonable and more appropriate. Unlike the classical elasticity solution, it is found that no
stress and electric displacement singularity is present at the crack tip. The non-local dynamic elastic solutions yield a
finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis.
The project supported by the Natural Science Foundation of Heilongjiang Province and the National Natural Science Foundation
of China(10172030, 50232030) 相似文献
2.
In this paper, the dynamic behavior of a Griffith crack in a piezoelectric material strip subjected to the harmonic anti-plane shear waves is investigated by use of the non-local theory for impermeable crack surface conditions. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and the electric displacement near at the crack tip. By means of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations. These equations are solved using the Schmidt method. Contrary to the classical solution, it is found that no stress and electric displacement singularity is present near the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress near the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the thickness of the strip, the circular frequency of incident wave and the lattice parameter. 相似文献
3.
《International Journal of Solids and Structures》2003,40(3):747-762
In this paper, the dynamic behavior of two parallel symmetric cracks in piezoelectric materials under harmonic anti-plane shear waves is investigated by use of the non-local theory for permeable crack surface conditions. To overcome the mathematical difficulties, a one-dimensional non-local kernel is used instead of a two-dimensional one for the problem to obtain the stress occurs near the crack tips. By means of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations that the unknown variables are the jumps of the displacement along the crack surfaces. These equations are solved using the Schmidt method. Numerical examples are provided. Contrary to the previous results, it is found that no stress and electric displacement singularity is present near the crack tip. The non-local elastic solutions yield a finite hoop stress near the crack tip, thus allowing for a fracture criterion based on the maximum stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the frequency of the incident wave, the distance between two cracks and the lattice parameter of the materials, respectively. Contrary to the impermeable crack surface condition solution, it is found that the dynamic electric displacement for the permeable crack surface conditions is much smaller than the results for the impermeable crack surface conditions. The results show that the dynamic field will impede or enhance crack propagation in the piezoelectric materials at different stages of the dynamic load. 相似文献
4.
In this paper, the scattering of harmonic anti-plane shear waves by a finite crack in infinitely long strip is studied using
the non-local theory. The Fourier transform is applied and a mixed boundary value problem is formulated. Then a set of dual
integral equations is solved using the Schmidt method instead of the first or the second integral equation method. A one-dimensional
non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress occurring
at the crack tips. Contraty to the classical elasticity solution, it is found that no stress singularity is present at the
crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture
criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length,
the width of the strip and the lattice parameter.
Supported by the Post Doctoral Science Foundation of Heilongjiang Province, the Natural Science Foundation of Heilongjiang
Province and the National Foundation for Excellent Young Investigators. 相似文献
5.
《European Journal of Mechanics - A/Solids》2006,25(5):793-807
In this paper, the non-local theory of elasticity is applied to obtain the behavior of a Griffith crack in the piezoelectric materials subjected to a uniform tension loading. The permittivity of the air in the crack is considered. By means of the Fourier transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables are the jumps of the displacements across the crack surfaces. To solve the dual integral equations, the jumps of the displacements across the crack surfaces are expanded in a series of Jacobi polynomials. Numerical examples are provided to show the effects of the crack length, the materials constants, the electric boundary conditions and the lattice parameter on the stress and the electric displacement fields near the crack tips. It can be obtained that the effects of the electric boundary conditions on the electric displacement fields are large. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present at the crack tips. The non-local elastic solutions yield a finite hoop stress at the crack tips, thus allowing us to use the maximum stress as a fracture criterion. 相似文献
6.
Zhou Zhengong Wang Biao Sun Yuguo 《Acta Mechanica Solida Sinica》2003,16(1):52-60
The dynamic behavior ofa Griffith permeable crack under harmonic anti-plane shearwaves in the piezoelectric materials is investigated by use of the non-local theory.To overcome themathematical difficulties,a one-dimensional non-local kernel is used instead of a two-dimensionalone for the anti-plane dynamic problem to obtain the stress and the electric displacement near thecrack tips.By means of Fourier transform,the problem can be solved with a pair of dual integralequations that the unknown variable is the jump of the displacement across the crack surfaces.These equations are solved with the Schmidt method and numerical examples are provided.Con-trary to the previous results,it is found that no stress and electric displacement singularities arepresent at the crack tip.The finite hoop stress and the electric displacement depend on the cracklength,the lattice parameter of the materials and the circle frequency of the incident waves.Thisenables us to employ the maximum stress hypothesis to deal with fracture problems in a naturalway. 相似文献
7.
《International Journal of Solids and Structures》2006,43(5):887-898
In this paper, the interaction of two collinear cracks in functionally graded materials subjected to a uniform anti-plane shear loading is investigated by means of nonlocal theory. The traditional concepts of the nonlocal theory are extended to solve the fracture problem of functionally graded materials. To make the analysis tractable, it is assumed that the shear modulus varies exponentially with the coordinate vertical to the crack. By use of the Fourier transform, the problem can be solved with the help of a pair of triple integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is found that no stress singularity is present near the crack tips. The nonlocal elastic solutions yield a finite hoop stress at the crack tip, thus allowing us to use the maximum stress as a fracture criterion in functionally graded materials. The magnitude of the finite stress field depends on the crack length, the distance between two cracks, the parameter describing the functionally graded materials and the lattice parameter of the materials. 相似文献
8.
A.C. Eringen C.G. Speziale B.S. Kim 《Journal of the mechanics and physics of solids》1977,25(5):339-355
Solutions are presented for the one- and two-dimensional Griffith crack problems in non-local elasticity. The displacements and stresses are determined in an elastic plate, weakened by a sharpedged line crack. The plate is loaded by a uniform tension perpendicular to the line of the crack at infinity. The non-local elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum stress hypothesis. 相似文献
9.
Investigation of the Scattering of Harmonic Elastic Waves by Two Collinear Symmetric Cracks Using the Non-Local Theory 总被引:1,自引:1,他引:0
IntroductionThelastfourdecadeshavewitnessedtheinaugurationofanoveltheoryofmaterialbodies,namedthenon_localmechanics.ThiswasdoneprimarilyduetotheeffortsofEdelen[1],Eringen[2 ],GreenandRivlin[3].Accordingtothenon_localtheory ,thestressatapointXinabodydependsno… 相似文献
10.
In this paper, the dynamic behavior of two collinear cracks in the anisotropic elasticity material plane subjected to the
harmonic anti-plane shear waves is investigated by use of the nonlocal theory. To overcome the mathematical difficulties,
a one-dimensional nonlocal kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the
stress field near the crack tips. By use of the Fourier transform, the problem can be solved with the help of a pair of triple
integral equations, in which the unknown variable is the displacement on the crack surfaces. To solve the triple integral
equations, the displacement on the crack surfaces is expanded in a series of Jacobi polynomials. Unlike the classical elasticity
solutions, it is found that no stress singularity is present near crack tips. The nonlocal elasticity solutions yield a finite
hoop stress at the crack tips, thus allowing us to using the maximum stress as a fracture criterion. The magnitude of the
finite stress field not only depends on the crack length but also on the frequency of the incident waves and the lattice parameter
of the materials. 相似文献
11.
A non-local theory of elasticity is applied to obtain the dynamic interaction between two collinear cracks in the piezoelectric materials plane under anti-plane shear waves for the permeable crack surface boundary conditions. Unlike the classical elasticity solution, a lattice parameter enters into the problem that make the stresses and the electric displacements finite at the crack tip. A one-dimensional non-local kernel is used instead of a two-dimensional one for the anti-plane dynamic problem to obtain the stress and electric displacement near the crack tips. By means of the Fourier transform, the problem can be solved with the help of two pairs of triple integral equations in which the unknown variable is the jump of the displacement across the crack surface. The solutions are obtained by means of the Schmidt method. Crack bifurcation is predicted using the strain energy density criterion. Minimum values of the strain energy density functions are assumed to coincide with the possible locations of fracture initiation. Bifurcation angles of ±5° and ±175° are found. The result of possible crack bifurcation was not expected before hand. 相似文献
12.
Investigation of a griffith crack subject to uniform tension using the non-local theory by a new method 总被引:1,自引:0,他引:1
IntroductionInseveralpreviouspapers[1,2,3],Eringendiscussedthestateofstressnearthetipofasharplinecrackinanelasticplatesubjecttouniformtension,shearandanti_planeshear.Thefieldequationsemployedinthesolutionoftheseproblemsarethoseofthetheoryofnon_locale… 相似文献
13.
The nonlocal solution of two parallel cracks in functionally graded materials subjected to harmonic anti-plane shear waves 总被引:1,自引:0,他引:1
In this paper, the dynamic interaction of two parallel cracks in functionally graded materials (FGMs) is investigated by means
of the non-local theory. To make the analysis tractable, the shear modulus and the material density are assumed to vary exponentially
with the coordinate vertical to the crack. To reduce mathematical difficulties, a one-dimensional non-local kernel is used
instead of a two-dimensional one for the dynamic problem to obtain stress fields near the crack tips. By use of the Fourier
transform, the problem can be solved with the help of two pairs of dual integral equations, in which the unknown variables
are the jumps of displacements across the crack surfaces. To solve the dual integral equations, the jumps of displacements
across the crack surfaces are expanded in a series of Jacobi polynomials. Unlike the classical elasticity solutions, it is
found that no stress singularity is present at the crack tips. The non-local elastic solutions yield a finite hoop stress
at the crack tips. The present result provides theoretical references helpful for evaluating relevant strength and preventing
material failure of FGMs with initial cracks. The magnitude of the finite stress field depends on relevant parameters, such
as the crack length, the distance between two parallel cracks, the parameter describing the FGMs, the frequency of the incident
waves and the lattice parameter of materials.
The project supported by the National Natural Science Foundation of China (90405016, 10572044) and the Specialized Research
Fund for the Doctoral Program of Higher Education (20040213034).
The English text was polished by Yunming Chen. 相似文献
14.
《International Journal of Solids and Structures》1999,36(26):3891-3901
Field equations of the non-local elasticity are solved to determine the state of stress in a plate with a Griffith crack subject to the anti-plane shear. Then a set of dual-integral equations is solved using Schmidts method. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The significance of this result is that the fracture criteria are unified at both the macroscopic and the microscopic scales. 相似文献
15.
In this paper, the scattering of harmonic antiplane shear waves by two finite cracks is studied using the non-local theory.
The Fourier transform is applied and a mixed boundary value problem is formulated. Then a set of triple integral equations
is solved using a new method, namely Schmidt's method. This method is more exact and more reasonable than Eringen's for solving
this kind of problem. The result of the stress near the crack tip was obtained. Contrary to the classical elasticity solution,
it is found that no stress singularity is present at the crack tip, which can explain the problem of macroscopic and microscopic
mechanics. 相似文献
16.
Non-local theory solution for in-plane shear of through crack 总被引:5,自引:0,他引:5
A non-local theory of elasticity is applied to obtain the plane strain stress and displacement field for a through crack under in-plane shear by using Schmidt's method. Unlike the classical elasticity solution, a lattice parameter enters into the problem that make the stresses finite at crack tip. Both the angular variations of the circumferential stress and strain energy density function are examined to associate their stationary value with locations of possible fracture initiation. The former criterion predicted a crack initiation angle of 54° from the plane of shear for the non-local solution as compared with about 75° for the classical elasticity solution. The latter criterion based on energy density yields a crack initiation angle of 80° for a Poisson's ratio of 0.28. This is much closer to the value that is predicted by the classical crack tips solution of elasticity. 相似文献
17.
IntroductionTheclassicalconhnuummechanicshasbeenusedtosolvemanyproblemsinmacrofracturemechanics,butencountersdifficulheswhentheeffectofITilcrocharacteristicdimensionshouldbetakenintoaccount.Thestressfieldverynearthecracktipisstillnotclear.Somephenomenaofshortcrackscannotbeexplained["']andsomemechanismoffracturehasnotbeensolvedyet.Thenon-localelashcitytheoryseemsattractivetotheseproblems.Thetheoryofnon-localelasticity,establishedanddevelopedbyEringenetal[3),connectstheclassicalcontinuummechan… 相似文献
18.
19.
Using a proposed constitutive relation for materials with creep behavior, the stress and strain distribution near the tip of a Mode III growing crack is examined. Asymptotic equations of the crack tip field are derived and solved numerically. The stresses remain finite at the crack tip. Obtained qualitatively is the crack tip velocity and the local autonomy of the near tip field solution is discussed. 相似文献
20.
A constant moving crack in a magnetoelectroelastic material under in-plane mechanical, electric and magnetic loading is studied for impermeable crack surface boundary conditions. Fourier transform is employed to reduce the mixed boundary value problem of the crack to dual integral equations, which are solved exactly. Steady-state asymptotic fields near the crack tip are obtained in closed form and the corresponding field intensity factors are expressed explicitly. The crack speed influences the singular field distribution around the crack tip and the effects of electric and magnetic loading on the crack tip fields are discussed. The crack kinking phenomena is investigated using the maximum hoop stress intensity factor criterion. The magnitude of the maximum hoop stress intensity factor tends to increase as the crack speed increases. 相似文献