Tstress solution of pennyshaped cracks in transversely. Modelling petroleum migration through microcrack propagation. List of research publications civil engineering mcgill. For the vertical transversely isotropic fractured sample under consideration with vertical symmetry z axis i. E p chen composites offer great promise as light weight and strong materials for high performance structures. The stress intensity factors for a periodic array of. The inclusion is assumed to be absolutely rigid and in perfect contact with the medium. The crack interaction factor is obtained using a recently developed model for stress intensity factors for an array of coplanar penny shaped cracks in a homogeneous material. Fiber reinforced composite materials have been characterized as a transversely isotropic medium having five elastic constants jones, 1975.
Pdf stress interference in axisymmetric torsion of a. Read a pennyshaped crack in transversely isotropic magnetoelectrothermoelastic medium subjected to uniform symmetric heat flux, international journal of solids and structures on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. This note contains some further discussion of the problem of a pennyshaped crack in a transversely isotropic solid. Poroelastic shear modulus dependence on porefluid properties arising in a model of thin isotropic layers. Micromechanics of composite materials george dvorak. It includes a pennyshaped crack in an infinite piezoelectric plate, a piezoelectric strip, a fiber embedded in a matrix, a piezoelectric cylinder with elastic coating. A pennyshaped microcrack filled by oil and gas in a transversely isotropic source rock driven by the excess pressure during kerogenpetroleum transformation. A model for pwave attenuation and dispersion in a porous. Note that for penny shaped cracks a crack density parameter oconnell and budiansky, 1974 is the proper choice. These conditions follow easily from the requirement that a rotation of the coordinate system in the x 1 x 2plane should not change the constants. Using a method of potential functions introduced successively to integrate the field equations of threedimensional problems for transversely isotropic. Micromechanics of composite materials george dvorak auth.
The axisymmetric problem of a concentric set of energetically consistent annular and pennyshaped cracks in an infinite piezoelectric body subjected to uniform far. Planar spatial correlations, anisotropy, and specific surface. Effective spring stiffness for a periodic array of. Interface cracks in piezoelectric materials iopscience. Because of the practical and fundamental importance of the problem, interface cracks in piezoelectric materials have been actively studied in the last few decades.
A transversely isotropic elastic solid with a pennyshaped or external crack. Particular attention is given to the interaction energy and the crack opening displacements. Based on the integral representation, explicit expressions of eshelby tensor will be present as the linear function of aspect ratio when the inclusion is lay on the isotropic plane of the transversely. Closedform solutions are obtained for a pennyshaped crack in a transversely isotropic elastic body, with the crack faces subjected to an arbitrary normal and shear loading. We use the concise notation of walpole l966a for transversely isotropic fourth order tensors. Pdf pennyshaped and halfplane cracks in a transversely. Hudsons model considers fractured rock as a single set of parallel pennyshaped cracks in an isotropic host solid figure 3.
The stress field created by a circular sliding contact on transversely isotropic spheres keer, l. Stress interference in axisymmetric torsion of a transversely. Associate professor baolin wang western sydney university. This paper presents explicit formulae of the tstress for a pennyshaped crack in a transversely isotropic, linearly elastic, infinite medium under remote triaxial.
May 01, 2014 read a penny shaped crack in transversely isotropic magnetoelectrothermoelastic medium subjected to uniform symmetric heat flux, international journal of solids and structures on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. An exact analysis of the modes ii and iii problems of a pennyshaped crack in a transversely isotropic piezoelectric medium is performed in this paper. Brannon sandia national laboratories albuquerque, nm 871850820 summary a mathematical framework is developed for the study of materials containing axisymmetric inclusions or flaws such as ellipsoidal voids, pennyshaped cracks. Civil and environmental engineering research output. Tsai used an integral equation approach and numerically obtained the harmonic sif for two characteristic transversely isotropic materials. Pdf a micromechanics inspired damage model for initially. The mechanical properties of platelet reinforced composites. Planar spatial correlations, anisotropy, and specific.
On wave propagation in elastic solids with cracks ch. Mott skip to main content accessibility help we use cookies to distinguish you from other users and to provide you with a better experience on our websites. A closedform solution of the tstress green s function for an isolated pennyshaped crack in a homogeneous, threedimensional, transversely isotropic, linearly elastic medium under a pair of selfequilibrated, unit normal concentrated forces acting on any location on the crack surface has been established. This book presents a broad exposition of analytical and numerical methods for modeling composite materials, laminates, polycrystals and other heterogeneous solids, with emphasis on connections between material properties and responses on several length scales, ranging from the nano and microscales to the macroscale. Pennyshaped crack in transversely isotropic piezoelectric. The present work is devoted to get the eshelby tensor of a penny. When a uniaxial stress is applied to such a material, some of the cracks will close depending on the angle of the crack normal with respect to the stress axis. Previous results in potential theory are then utilized to obtain. For a pennyshaped crack in a transversely isotropic material under uniform crack surface pressure, the volume of crack is determined to be tsai 1982. Journal of engineering materials and technology, 117, 412432. In this paper, the main objective is to investigate the interaction of a rigid disc in bonded contact with the surfaces of a penny shaped crack and an in nite transversely isotropic medium.
Inclusions, inhomogeneities and cavities springerlink. It is found that a broad class of natural and manmade ti materials have. Using a method of potential functions introduced successively to integrate the field equations of threedimensional problems for transversely isotropic piezoelectric materials, we obtain the socalled general solution in which the displacement components and electric potential functions are represented by a singular function satisfying some special partial differential equations of 6th order. Linear elastic transversely isotropic background medium permeated by inclined. We consider models based on two very different rock classes, granites and weakly consolidated granular systems. Large deformation analysis of axisylmmetric inhomogeneities including coupled elastic and plastic anisotropy r. The extended displacement discontinuity boundary integral equation eddbie and boundary element method is developed for the analysis of planar cracks of arbitrary shape in the isotropic plane of threedimensional 3d transversely isotropic thermomagnetoelectroelastic tmee media. Mixedmode fatigue crack propagation of pennyshaped cracks journal of engineering materials and technology, transactions of the asme.
Interaction energy for a pennyshaped crack in a transversely isotropic material consider an anisotropic linearly elastic solid with stressstrain relation a l where o is the stress tensor, c the linear strain tensor and l is the symmetric positive definite stiffness tensor. Skip to main content accessibility help we use cookies to distinguish you from other users and to provide you with a better experience on our websites. Helbig 1983 has emphasized that finely layered ti media virtually never display elliptical anisotropy. Analytical and numerical analyses for a pennyshaped crack. Sih, 9789024725595, available at book depository with free delivery worldwide. This leads to an undesired degradation of electrical and mechanical performance. By properties of integral transform methods, the generalized mixed boundaryvalue problem is formulated as a set of dual integral equations, which in turn, are reduced to a fredholm equation of the second kind. One of the major advantages of these materials as compared with metals is the basic way in which. Some problems of a rigid elliptical diskinclusion bonded inside a transversely isotropic space. Laws department of mechanical engineering, university of pittsburgh, pittsburgh, pa 15261, u.
In many cases, fracture occurs at interfaces as debonding and cracks. Threedimensional stress distributions in hexagonal aeolotropic crystals volume 44 issue 4 h. After mathematical preliminaries in section 2, the fundamental result for a dilute. The effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar pennyshaped cracks. A note on pennyshaped cracks in transversely isotropic materials. The wave is harmonic in time, impinging normally on the crack surfaces, which are assumed to remain separated during small deformation of the solidl. Stressinduced transverse isotropy in rocks lawrence m. Dynamic pennyshaped crack in a transversely isotropic. Threedimensional stresses around elliptical cracks in transversely. A pennyshaped crack in transversely isotropic magnetoelectrothermoelastic medium subjected to uniform symmetric heat. A note on pennyshaped cracks in transversely isotropic. Stressinduced transverse isotropy in rocks stanford university.
Exact electroelastic solutions for pennyshaped cracks. This letter provides an exact solution for a thermal pennyshaped crack in piezoelectric media. Among these, there is a special type of materials whose properties are variable only along one direction, defined as graded materials or functionally graded materials fgms. The first thing to note is that the platelets only alter the inplane moduli, i. Closedform expressions for the stress and electric displacement intensity factors at the crack border are given. Associate professor baolin wang academic course advisor, postgraduate mechanical and mechatronic engineering. The axisymmetric problem of a concentric set of energetically consistent annular and penny shaped cracks in an infinite piezoelectric body subjected to uniform farfield electromechanical loading is addressed.
Exact electroelastic solutions for pennyshaped cracks under. This research is concerned with the investigation of forced timeharmonic vertical vibration of a rigid disk enclosed in a transversely isotropic full space medium. The paper addresses the problem of contact of an elliptical inclusion in the form of a thin disk, bonded in the interior of a transversely isotropic space. A pennyshaped crack in transversely isotropic magneto. The solutions for estimating and predicting the mechanical responses are extremely difficult, in particular for nonhomogeneous materials. Berryman1 abstract the application of uniaxial pressure can induce elastic anisotropy in otherwise isotropic rocks.
C, c 33, c 44 and c 66, and in walpoles notation in general, a transversely isotropic tensor a with the symmetries a ijkl. However, for small uniaxial stresses, the present results show that both granular materials and systems with penny shaped cracks exhibit elliptical anisotropy in both the quasip and quasisv waves nur and simmons, 1969. Interaction of a pennyshaped crack and an external. Note that for either a pennyshaped or an elliptical crack with crack. Pennyshaped crack in transversely isotropic piezoelectric materials. This paper is concerned with the problem of a pennyshaped crack in an infinite transversely iso tropic elastic solid under uniform stress at infinity. Effective elastic properties of rocks with transversely. A penny shaped crack in a transversely isotropic material. Oct 14, 2004 this letter provides an exact solution for a thermal penny shaped crack in piezoelectric media. The scattering of a plane longitudinal wave by a pennyshaped crack in a transversely isotropic material is investigated in the present work. The problem of a pennyshaped crack in a transversely isotropic piezoelectric material loaded by both normal and tangential tractions and by electric charges is analyzed. For comparison, the sifs for isotropic materials are also calculated and shown in the gure. These models have been developed for a sparse concentration of pennyshaped cracks in a porous matrix. Surface and body waves generated by a point traction applied on transversely isotropic.
Coverage includes wave scattering problems by a single crack, a periodic array of collinear cracks in isotropic and transversely isotropic elastic solids, interface cracks with a periodic spacing, and randomly distributed microcracks. Jan 01, 20 the effect of crack interactions on stress intensity factors is examined for a periodic array of coplanar pennyshaped cracks. Brannon sandia national laboratories albuquerque, nm 871850820 summary a mathematical framework is developed for the study of materials containing axisymmetric inclusions or flaws such as ellipsoidal voids, penny shaped cracks. It deals with several topics on wave propagation in elastic solids with cracks. Aug 15, 20 the crack interaction factor is obtained using a recently developed model for stress intensity factors for an array of coplanar penny shaped cracks in a homogeneous material. Mechanics of materials 4 1985 209212 209 northholland short note a note on pennyshaped cracks in transversely isotropic materials n. An arbitrarily distributed temperature field applied on the crack faces is considered first.
Ebscohost serves thousands of libraries with premium essays, articles and other content including study on crack curving and branching mechanism in quasibrittle materials under dynamic biaxial loading. The crack is assumed to be subjected to uniformly distributed mechanical, electric and magnetic loads applied symmetrically on the upper and lower crack surfaces. For transversely isotropic materials, there are only five independent constants, although six constants appear in each of these matrices. Forced timeharmonic vertical vibration of a rigid disk. A simple and direct relationship is established between the limiting values of the. This chapter applies the formulation presented in the first two chapters to a range of piezoelectric problems containing pennyshaped cracks. Ifthe prestress fracture distribution is isotropic, the effective elastic properties ofsuch a material are then transversely isotropic due to the preferred alignment ofthe. Surface and body waves generated by a point traction applied on transversely isotropic solids journal of the acoustical society. Electrically impermeable cracks, electrically permeable cracks, and the permittivity of the. For uniform applied stress at infinity, the problem is solved using eshelbys method.
In this paper, an analytical solution for the axisymmetric interaction of a rigid disc inclusion embedded in bondedcontact with the surfaces of a penny shaped crack and a transversely isotropic medium is investigated. This paper presents a rigorous analytical formulation of a pennyshaped crack at the interface of a transversely isotropic elastic layer of finite thickness and a transversely isotropic elastic half space. Effective elastic properties of rocks with transversely isotropic. Letters in fracture and micromechanics 123 on an arbitrarily oriented crack in a transverselyisotropic medium felicia guerrero1, igor sevostianov1, and albert giraud2 1department of mechanical engineering, new mexico state university, las cruces, nm 88001, usa email. These results are important for investigating crack interactions. An unbounded transversely isotropic body of revolution containing two spheroidal cavities is subjected to torsion about its axis of elastic symmetry, which coincides with its axis of revolution. Thermal stresses in a transversely isotropic elastic solid weakened by an external circular crack 407 where a may 28, 2010 the present work is devoted to get the eshelby tensor of a penny. Oblate spheroids take the geometric form of thin pennyshaped cracks aspect ratios less than one. Crack shape adaptability in transversely isotropic solids, journal of the mechanics and physics of solids on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips. Modes ii and iii problems article pdf available in acta mechanica sinica 151. A micromechanics inspired damage model for initially transversely isotropic materials. A mathfree look at azimuthal surface seismic techniques. Extended displacement discontinuity boundary integral.
Axial translation of a rigid disc inclusion embedded in a. Pennyshaped crack in a transversely isotropic piezoelectric solid. For example, a transversely isotropic solid with x3 as the symmetry axis possesses five independent stiffness moduli, c i i. The potential theory method is employed based on the general solution of threedimensional piezoelasticity and the four harmonics involved are represented by one complex potential. Pennyshaped crack in a transversely isotropic piezoelectric. The problem of a pennyshaped crack embedded in an infinite space of transversely isotropic multiferroic composite medium is investigated. Some problems of a rigid elliptical diskinclusion bonded.
Tsai, 1988 determined the harmonic axisymmetric stress intensity factor for a penny shaped crack in a transversely isotropic material at low frequencies. Analytical and numerical analyses for a pennyshaped crack embedded in an infinite transversely isotropic multiferroic. Threedimensional stress distributions in hexagonal. Pennyshaped dugdale crack in a transversely isotropic.
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