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We investigate the motion of a periodic system of rigid, isolated, parabolic dies along the surface of a half-space. The action of friction forces results in heat generation in the contact region. We assume that the surfaces of the dies are thermally insulated and the half-space is a heat conductor. We reduce the problem under consideration to a set of two integral equations for the contact temperature and pressure. We solve these equations numerically and investigate the influence of thermal deformation on the distributions of temperature and pressure and on the dimensions of the contact region. 相似文献
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This work is devoted to analyzing a thermal shock problem of an elastic strip made of functionally graded materials containing a crack parallel to the free surface based on a generalized fractional heat conduction theory. The embedded crack is assumed to be insulated. The Fourier transform and the Laplace transform are employed to solve a mixed initial-boundary value problem associated with a time-fractional partial differential equation. Temperature and thermal stresses in the Laplace transform domain are evaluated by solving a system of singular integral equations. Numerical results of the thermoelastic fields in the time domain are given by applying a numerical inversion of the Laplace transform. The temperature jump between the upper and lower crack faces and the thermal stress intensity factors at the crack tips are illustrated graphically, and phase lags of heat flux, fractional orders, and gradient index play different roles in controlling heat transfer process. A comparison of the temperature jump and thermal stress intensity factors between the non-Fourier model and the classical Fourier model is made. Numerical results show that wave-like behavior and memory effects are two significant features of the fractional Cattaneo heat conduction, which does not occur for the classical Fourier heat conduction. 相似文献
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V. V. Mykhas’kiv V. Z. Stankevych E. V. Glushkov N. V. Glushkova 《Journal of Mathematical Sciences》2011,176(4):590-599
We have considered the three-dimensional problem of harmonic loading of a circular crack in an elastic composite consisting
of two dissimilar half-spaces under sliding contact on the surface of their bonding. The defect is situated in one of the
half-spaces perpendicularly to the interface of materials. Using the representations of solutions in the form of Helmholtz
potentials, we have reduced the problem to a boundary integral equation for the function of dynamic defect opening. Based
on the numerical solution of this equation, we have obtained the frequency dependences of mode I stress intensity factor near
the crack for different relations between the elastic moduli of components of the composite and the depths of crack location
with respect to the interface. 相似文献
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We consider a plane strain problem for a piezoelectric/piezomagnetic bimaterial space with a crack in the region of the interface
of the materials. At infinity, tensile and shear stresses and heat, electric, and magnetic flows are set. Using representations
for all mechanical, thermal, and electromagnetic factors in terms of piecewise analytic functions, we formulate problems of
linear conjugation that correspond to a model of an open crack and models taking into account the contact zone in the vicinity
of a crack tip. Exact analytic solutions of the indicated problems are constructed. Expressions for stresses, the electric
and magnetic inductions, jumps of derivatives of displacements, and electric and magnetic potentials on the interface are
written. The coefficients of intensities of the indicated factors are presented. We derive a transcendental equation for the
determination of the real length of the contact zone. The dependences of this length and the coefficients of intensity on
the set external influences are investigated. 相似文献
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We constructed a closed solution for a bimaterial plane consisting of two dissimilar piezoelectric half-planes with a periodic
system of electrically permeable cracks at the interface between these materials. The presence of zones of smooth contact
of the crack lips near their tips was taken into account. By representing the characteristics of electromechanical fields
via piecewise analytic functions, we reduced the problem to a Dirichlet–Riemann periodic problem, which was solved exactly.
As a result of numerical analysis of the derived solution, we studied the dependence of the relative length of the contact
zones and stress intensity factors on the ratio between the crack length and period for different combinations of piezoelectric
materials. 相似文献
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Nano-tribology through molecular dynamics simulations 总被引:1,自引:0,他引:1
The solidification and interfacial slip in nanometer-scale lubricating films as well as the contact and adhesion of metal
crystals have been studied via molecular dynamics simulations. Results show that the critical pressure for the solid-liquid
transition declines as the film thickness decreases, indicating that the lubricant in the thin films may exist in a solid-like
state. It is also found that the interfacial slip may occur in thin films at relatively low shear rate, and there is a good
correlation between the slip phenomenon and the lubricant solidification. The simulations reveal that a micro-scale adhesion
may take place due to the atomic jump during the process of approaching or separating of two smooth crystal surfaces, which
provides important information for understanding the origin of interfacial friction. 相似文献
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A. O. Kamins’kyi M. F. Selivanov Yu. O. Chornoivan 《Journal of Mathematical Sciences》2011,176(5):616-630
We present results of an investigation of the development of a transverse shear crack in a composite material with linearly
viscoelastic components under external shear load. The solution is divided into the following two main stages: determination
of the time dependence of the crack tip opening displacement and determination of the crack-growth kinetics as a result of
the solution of integral equations. In the first stage, we use the solution of the corresponding elastic problem of determination
of the crack opening displacement and the problem of determination of the effective moduli of the composite reinforced with
unidirectional discrete fibers. Using the theoretically proved principle of elasto-viscoelastic analogy and the method of
Laplace inverse transformation, we obtain a solution in a time domain. In the second stage, using the criterion of critical
crack opening displacement for a transverse shear crack and an equation for the viscoelastic crack opening displacement of
this crack, we construct an equation of crack growth. We present results of the numerical solution, which illustrate the influence
of relations between the relaxation parameters of the materials of the components on the durability of the body with a crack. 相似文献
9.
An interaction of a tunnel conductive crack and a distant strip electrode situated at the interface between two piezoelectric semi-infinite spaces is studied. The bimaterial is subject by an in-plane electrical field parallel to the interface and by an anti-plane mechanical loading. Using the presentations of electromechanical quantities at the interface via sectionally-analytic functions the problem is reduced to a combined Dirichlet-Riemann boundary value problem. Solution of this problem is found in an analytical form excepting some one-dimensional integrals calculations. Closed form expressions for the stress, the electric field and their intensity factors, as well as for the crack faces displacement jump are derived. On the base of these presentations the energy release rate is also found. The obtained solution is compared with simple particular case of a single crack without electrode and the excellent agreement is found out. An auxiliary plane problem for open and closed cracks between two isotropic materials is also considered. The mathematical model of this problem is identical to the above one, therefore, the obtained solution is used for this model. It is compared with finite element solution of a similar problem and good agreement is found out. 相似文献
10.
We consider a problem of wedging of an elastic wedge by a rigid plate along an edge crack that is located on the axis of symmetry
of the wedge and reaches its vertex. The detachment of the crack faces from the surfaces of the plate is taken into account.
Using the Wiener–Hopf method, we obtain an analytic solution of the problem. The size of the detachment zone, the stress intensity
factor, the distribution of stresses on the line of continuation of the crack and in the contact domain, and circular displacements
of the crack faces are determined. 相似文献
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The linear crack located at the bimaterial interface between dissimilar homogeneous linearly elastic materials under normally incident harmonic tension-compression wave is considered in the study. The problem is solved by the method of boundary integral equations using an iterative algorithm. The dynamic stress intensity factors are computed as functions of the loading frequency taking the contact interaction of the opposite crack's faces into account. (© 2010 Wiley-VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
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弹性-幂硬化蠕变性材料Ⅱ型界面裂纹准静态扩展的渐近分析 总被引:1,自引:1,他引:0
建立了弹性-幂硬化蠕变性材料Ⅱ型界面裂纹准静态扩展的力学模型,求得了在裂纹表面自由和裂纹面有摩擦接触两种情况下,裂纹尖端应力场分离变量形式的渐近解.求解结果表明:Ⅱ型界面裂纹问题的应力、应变具有相同的奇异性;Ⅱ型界面裂纹尖端场不存在振荡奇异性;材料的幂硬化指数n和弹性模量比对裂纹尖端应力场幂硬化蠕变性材料区有着显著的影响,而弹性区仅受幂硬化指数n的影响,当n很大时,蠕变变形占主导地位,应力场趋于稳定,不随n的变化而变化;泊松比对裂纹尖端应力场的影响不明显. 相似文献
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Yu. L. Trakhinin 《Siberian Advances in Mathematics》2020,30(1):55-76
We study the free boundary problem for a contact discontinuity for the system of relativistic magnetohydrodynamics. A surface of contact discontinuity is a characteristic of this system with no flow across the discontinuity for which the pressure, the velocity and the magnetic field are continuous whereas the density, the entropy and the temperature may have a jump. For the two-dimensional case, we prove the local-in-time existence in Sobolev spaces of a unique solution of the free boundary problem provided that the Rayleigh-Taylor sign condition on the jump of the normal derivative of the pressure is satisfied at each point of the initial discontinuity. 相似文献
15.
《Journal of Applied Mathematics and Mechanics》2007,71(1):120-136
The contact deformation of the hub of a plunger pair is considered. It is assumed that, during the repeated reciprocating motion of the plunger, a crack is initiated and fracture of the materials of the elements of the contact pair occurs. The problem of the equilibrium of the hub of a friction pair with a crack nucleus reduces to solving a system of non-linear singular integrodifferential equations with a Cauchy-type kernel. The normal and shear forces in the zone where the crack originates are found from the solution of this system of equations. The condition for the appearance of a crack is formulated, taking account of the criterion of the limit traction of the bonds in the material. A problem for the plunger of a friction pair as applied to a borehole sucker rod pump is considered as an example. In conclusion, the case when there are several arbitrarily distributed rectilinear bridged cracks, with bonds between the crack faces in the end zone, close to the contact surface of the hub is investigated. 相似文献
16.
压电压磁复合材料中界面裂纹对弹性波的散射 总被引:5,自引:1,他引:4
利用Schmidt方法分析了压电压磁复合材料中可导通界面裂纹对反平面简谐波的散射问题.经过富里叶变换得到了以裂纹面上的间断位移为未知变量的对偶积分方程A·D2在求解对偶积分方程的过程中,裂纹面上的间断位移被展开成雅可比多项式的形式.数值模拟分析了裂纹长度、波速和入射波频率对应力强度因子、电位移强度因子、磁通量强度因子的影响A·D2从结果中可以看出,压电压磁复合材料中可导通界面裂纹的反平面问题的应力奇异性形式与一般弹性材料中的反平面问题应力奇异性形式相同. 相似文献
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W.T.Ang 《数学物理学报(B辑英文版)》1999,19(3)
1991MRSubjectClassification75M25,45E991IntroductionDuringthelasttenyearsorsojmanyresearchersinappliedmathematicsandmechanicshaveshownasurginginterestinformulatinglinearcrackproblemsillterlllsofsystel-alsofHadamardfillite-part(hypersingular)integralequations,e.g.Ioakimidis['],Lin'kovandMogilevskaya[']andAnal'].Anadvantageofsuchaformulationisthatthe11nkllowllfllnctionsaredirectlyrelatedtothejlllxlpillthedisplacementsacrossoppositeera(:kfaces.Oncetheyaredeterlttillied,crackparaliietersofinter… 相似文献
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We solve the problem of planar deformation of an isotropic plate fastened at one surface or symmetrically in its two surfaces to cover plates of a different material. As initial data we use the approximate relations of the two-dimensional formulation, which take account of the shear and the transverse compression of the plate. We study the dependence of the interlayer stresses on the ratio of the elastic moduli of the materials of the plate and the cover.Translated fromMatematicheskie Metody i Fiziko-Mekhanicheskie Polya, Issue 27, 1988, pp. 99–102. 相似文献
19.
An interface crack with an electrically permeable and mechanically frictionless contact zone in a piezoelectric bimaterial under the action of a remote mixed mode mechanical loading as well as thermal and electrical fields is considered in the first part of this paper. By use of the matrix‐vector representations of thermal, mechanical and electrical fields via sectionally‐holomorphic functions the problems of linear relationships are formulated and solved exactly both for an electrically permeable and an electrically impermeable interface crack. For these cases the transcendental equations and clear analytical formulas are derived for the determination of the contact zone lengths and the associated fracture mechanical parameters. A plane strain problem for a crack with a frictionless contact zone at the leading crack tip extending stationary along an interface of two semi‐infinite anisotropic spaces with a subsonic speed under the action of various loading is considered in the second part of this paper. By introducing of a moving coordinate system connected with the crack tip and by using the formal similarity of static and propagating crack problems the combined Dirichlet‐Riemann boundary value problem is formulated and solved exactly for this case as well and a transcendental equation is obtained for the determination of the real contact zone length. It is found that the increase of the crack speed leads to an increase of the real contact zone length and the correspondent stress intensity factors which increase significantly for a quasi‐Rayleigh wave speed. 相似文献
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We describe a method of determining the thermal conductance of a contact in simulation of contact thermoelasticity with regard for friction and heat generation. Using the results of numerical analysis, we construct the dependence of the thermal conductance of a contact on input parameters and show that some of them substantially affect this phenomenon. By the example of a one-dimensional nonstationary problem, we study the effect of the parameters of contacting surfaces on heat generation. 相似文献