It shows that the stresses and electrical displacements around the crack tips. An analytical model is developed for a functionally graded interfacial zone between two dissimilar elastic solids. Effect of material nonhomogeneities on the hrr dominance. Journal of theoretical and applied mechanics home icm. For homogeneous material plates and non homogeneous material plates, the cracktip field plays an important role in the research of fracture mechanics. Ahead of the crack tip, that is on the bond side, only the shear tractions are singular, exhibiting the squareroot type of singularity, regardless of the nature of the applied loads. Mode iii crack problems for two bonded functionally graded. The overall stress and strain distributions, which were obtained by pgnem, were smoothened and. Assessment was done based on the comparisons with analytical solutions and results from threedimensional crack tip finite element analysis. Evaluation of crack tip fields and stress intensity factors in. The cracktip higher order asymptotic fields for a mode iii. Furthermore, the generalized displacements are treated in a separationofvariable form, and the higherorder crack tip fields of the cracked fgm plate are obtained by the eigenexpansion method. The stress intensity factors at the crack tips are computed for mechanical loads.
Jin studied the singular crack tip fields in nonhomogeneous body under thermal stress and pointed out that the stress intensity factors sifs were still applicable in fracture problems of fg materials. It is first shown that the squareroot singular field still prevails in the crack tip region. The fracture behaviors near the interface crack tip for mode ii of orthotropic bimaterial are discussed. Nonfourier heat conduction of a functionally graded cylinder. Singular, hypersingular and singular free electromagnetic. Detection of crack locations in aluminum alloy structures. Crack tip singular fields in nonhomogeneous materials zhihe jin, zhihe jin. The energy release rate for a crack in fgm is given by 4 g 1 e. Past research faculty computational mechanics research. Experimental investigation of damage detection based on a.
Crack problems for bonded nonhomogeneous materials. Exact solution for functionally graded anisotropic elastic. On some crack problems for inhomogeneous elastic materials. Two dissimilar materials are joined along a straight edge with one or more cracks present. The crack problem for a nonhomogeneous plane request pdf. On the moving griffith crack in a nonhomo geneous orthotropic strip. The singular element has a builtin displacement field of the vr type with the two modes of stress intensity factors, k i and k ii, as unknowns. Jul 18, 2019 however, results for a nonhomogeneous cases are very scarce. 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. Surprisingly, a singular stress field of only several nanometers still governs. In fracture of nonhomogeneous materials, the use of auxiliary fields developed for homogeneous materials results in violation of one of the basic relations of mechanics, i. Sep 27, 2012 a new multilayered model is developed for the fracture analysis of a functionally graded interfacial zone with arbitrary material properties.
This finiteelement program uses four singular elements which surround the crack tip and regular elements which occupy the remaining region. A study on the crack control of a highspeed steel roll fabricated by a centrifugal casting technique, materials science. Boundary element method analysis for mode iii linear. Fracture mechanics, especially linear elastic fracture mechanics lefm, is a unique. This paper considers an antiplane moving crack in a nonhomo geneous material strip of finite thickness.
It is shown that the crack tip stresses are either bounded, asymptotic to r,0 crack contact mechanics for a coatingsubstrate system with functionally graded properties is performed, where the rigid flat punch slides over. Pdf crack tip fields in functionally graded materials with. Since fracture is a key failure mode of fgms, successful application of these materials depends on the understanding of their. Jin studied the singular crack tip fields in nonhomogeneous body under thermal stress and pointed out that the stress intensity factors sifs. The shear modulus and the mass density of the strip are considered for a class of functional forms for which the equilibrium equation has analytical solutions. Thermomechanical stress and displacement fields for a propagating crack in functionally graded materials fgms are developed using displacement potentials and asymptotic analysis. The fracture toughness and rcurve of functionally graded materials fgms are studied based on the crack. Nonhomogeneous material an overview sciencedirect topics. A spatially varying cohesive failure model is used to simulate quasistatic fracture in functionally graded polymers. Irwin called this coefficient the stress intensity factor sif. Department of mechanical engineering, shizuoka university, 351 johoku, hamamatsu, shizouka 432, japan. 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. Effect of microcracks in nonhomogeneous stress field on fracture instability in structural components.
Jul 24, 2019 the further development of fracture mechanics required analysis of eigenspectra and orders of singularity at a crack tip for power. The shear modulus, mass density, and coefficient of thermal expansion of the fgms are assumed to vary exponentially along the gradation direction. Singular and nonsingular approaches for predicting. The problem is solved by means of the singular integral equation technique.
Crack tip higher order stress and displacement fields for a mode iii crack along the direction of property variation in a functionally gradient material fgm, which has a power variation of shear modulus along the gradient direction, are obtained through the asymptotic analysis. The weak patch test for nonhomogeneous materials modeled with. A modified interaction energy integral method ieim is developed to obtain the mixedmode thermal stress intensity factors tsifs. An edge crack in a strip of a functionally graded material fgm is studied under transient thermal loading conditions.
Cohesive modeling of quasistatic fracture in functionally. Local cartesian and polar coordinates are introduced with origin at a crack tip and the negative xaxis 0 k t along the crack edges. Numerical analysis of cracktip fields in functionally graded. The stress functions are chosen which contain twelve undetermined coefficients and an unknown singularity exponent. A crack between orthotropic materials with a shear yield.
The governing equations of caustics method which is used to represent the opticsmechanics relation of the singular yield close to the external load are derived based on the exponential asymptotic expansion. The stress fields formed by a crack transport remotely applied elastic energy to the crack s tip, where the energy is dissipated by. Cracktip singular fields in nonhomogeneous materials journal. This work investigates crack tip asymptotic stress and deformation fields in elasticplastic nonhomogeneous materials and the effect of material nonhomogeneities on the size of the dominant zone of the singular fields. One cannot rule out the possibility that some secondary plastic strain does nevertheless occur on those systems, but they are ignored entirely here. Beom found singular crack tip fields and showed that these fields are uniquely characterized by realvalued stress intensity factors. Pdf thermal fracture of ceramics with temperaturedependent. Breakdown of continuum fracture mechanics at the nanoscale ncbi. Some aspects of thermal fracture mechanics of ceramics with temperaturedependent properties are studied.
Singular, hypersingular and singular free electromagnetic fields at wedge tips in metamaterials article in international journal of solids and structures 4716. Crack tip singular fields in nonhomogeneous materials. An opening mode crack in a nonhomogeneous elastic material by. Nonhomogeneous materials can be applied in many engineering fields such as aerospace and automobile industries. The simplest possible loading and geometry, the antiplane shear loading of two bonded half spaces in which the crack. It is assumed that the interfacial zone is divided into sublayers with the material properties of each sublayer varying in a powerlaw function. Compared with the previous ieim, the original point of this paper is.
Over 10 million scientific documents at your fingertips. Transient thermal stress analysis of an edge crack in a. The composite is loaded or restrained on the remote boundary,and the crack faces are free of load. Stress intensity relaxation at the tip of an edge crack in a functionally graded material subjected to a. By postulating a circular damage field at the cracktip represented by a power law function rm of. However, the governing equations become the system of the sixth order partial differential ones with the variable coefficients when the material gradient is perpendicular to the thickness direction of plates. Cracktip singular fields in nonhomogeneous materials. Gao et al and gao and wang considered periodic and collinear interface cracks in piezoelectric materials. The singular nature of the crack tip stress field in a nonhomogeneous medium with a shear modulus with a discontinuous derivative was investigated.
Fracture mechanics is now considered a mature subject and has become an important course in engineering curricula at many universities. Noda, crack tip singular fields in nonhomogeneous materials, journal of applied mechanics. Functionally graded materials fgms are regarded as one of the most promising candidates for future advanced composites in many engineering applications. The singular integral equations for impermeable and permeable cracks are derived. Evaluation of crack tip fields and stress intensity factors. A numerical evaluation of sifs of 2d functionally graded materials. A key aspect of this paper is that all mechanical properties and cohesive parameters entering the analysis are derived experimentally from fullscale fracture tests allowing for a fit of only the shape of the cohesive law to experimental data.
Nonfourier heat conduction of a functionally graded. Crack tip singular fields in nonhomogeneous materials,asme journal of applied mechanics, vol. Jan 15, 2012 a plane crack problem of nonhomogeneous materials with interfaces subjected to static thermal loading is investigated. Particulate functionally graded materials fgm made of glassfilled epoxy with edge cracks parallel to the direction of the elastic gradient. The stress intensity factor connects the global concepts. The fgm is assumed having constant youngs modulus and poissons ratio, but the thermal properties of the material vary along the thickness direction of the strip. However, results for a nonhomogeneous cases are very scarce. The effect of damping on dynamic stress intensity factors in. Based on the fact that an arbitrary curve can be approached by a continuous broken line, the interfacial zone with material properties varying continuously in an arbitrary manner is modeled as a multilayered medium with the elastic modulus varying linearly in each sublayer and. The electric field inside the cracks was analyzed and shown to be dependent on the material constants and. Journal of the brazilian society of mechanical sciences and engineering print version issn 16785878online version issn 18063691 j.
Material science research international, 2 1996, pp. In this connection, figure 1 shows a schematic representation of a bridge, wherein a nano crack cleavage is initially presented. The effect of material nonhomogeneities on the hrr dominance, however, has not been studied. The reissners plate bending theory with consideration of transverse shear deformation effects is adopted to study the fundamental fracture problem in functionally graded materials fgms plates for a crack perpendicular to material gradient. Based on the crack tip strain distributions, which were calculated by the extended finite element method xfem, the singular strain field near a crack tip was an important factor adopted to optimize fbg sensor placement. They can be classified as advanced materials characterized by variation in properties as the dimension varies. Dynamic cracktip stress and displacement fields under.
The higher order crack tip fields of exponential gradient. In that study, one material is assumed nonhomogeneous with its material properties varying through the thickness in a certain exponential manner and the interface crack problem is confronted by. Exact solutions are derived for threedimensional, anisotropic, linearly elastic, and functionally graded rectangular composite laminates under simply supported edge. Material failure occurs at small scales in the immediate vicinity of the tip of a crack. Consider a cracked nonhomogeneous material with continuous and piecewise differentiable youngs modulus e and poissons ratio here we assume there are only two differentiable pieces as shown in figure 10. In general, the fracture in materials usually initiates locally from a crack tip, which results in a global failure through crack propagation across the whole structure. Multiple fatigue crack growth modelling in nonhomogeneous.
Thus the material is elastically homogeneous but thermally nonhomogeneous. Department of engineering science and mechanics virginia polytechnic institute and state university blacksbulg, virginia, usa some aspects of thetmal fracture mechanics ceramics with temperaturedependent properties are studied. Analysis of cracktip fields and toughening mechanisms in. In previous studies, the elastic stress field near the crack tip was investigated by digital image correlation and the 2d intelligent hybrid method. Profile on researcherid representative publications a fracture mechanics t.
Crack tip singularity in damaged materials yan liu and sumio murakami department of mechanical engineering, nagoya university furocho, chikusaku, nagoya 46401, japan the effects of the preceding damage field on the stress singularity of a growing mode iii crack are investigated from the view point of continuum damage mechanics cdm. Methods of perturbation theory and their applications in. The application of fg materials can improve the bonding strength and toughness. The crack problem for bonded nonhomogeneous materials. Boundary element method analysis for mode iii linear fracture. The problem is formulated in terms of a system of cauchytype singular integral equations, which can be solved numerically. Hence, the inverse squareroot singular thermal flux and stress fields still prevail at the crack tip in a thermoelastic fgm, and the near tip hrr field exists for a powerlaw hardening fgm.
Higherorder crack tip fields for functionally graded. In this study, the 2d nonlinear hybrid method was developed to analyze the elasticplastic singular stress field near the crack tip from the displacement data obtained by digital image. An interaction energy integral method for nonhomogeneous. The model is used to study the crack problem in the functionally graded interfacial zone between two. Consistent formulations of the interaction integral method. In the framework of the assumption that the crack faces are free of stresses an exact analytical solution of the problem is given on basis of the complex potentials approach. Cracktip singularity in damaged materials sciencedirect. This solution possesses oscillating square root singularities in stresses and in the derivatives. One exception is a central crack subjected to a constant anti. Crack tip measurements are used to examine continuum models for fgms by treating the material as isotropic and nonhomogeneous at macroscales. Singular integral eqaution method for a moving crack. The crack problem for nonhomogeneous materials was studied by chan et al. The asymptotic behavior of the closed crack tip, comninoull, is unfamiliar and possibly disconcerting, fig.
On higher order parameters in cracked composite plates. Crack tip singular fields in nonhomogeneous materials, j. Situations where cracks are located on the compliant and the. This aspect enables the accurate representation of the elastic fields around the crack tip and simplifies the remeshing process during the crack propagation.
Particulate functionally graded materials fgm made of glassfilled epoxy with edge cracks parallel to the direction of the elastic gradient and subjected to pure bending have been studied. The singular stress and heat flux fields at the tip of the crack in a. A numerical method for the thermalshock crack problems of. Hence, we can come to the conclusion that the crack tip stress and displacement fields in nonhomogeneous materials have the same forms as those in homogeneous materials provided the material properties are continuous and piecewise differentiable. Damage estimation and stress singularity study using a. In order to fit the extreme working environment, nonhomogeneous materials, such as functionally graded materials fgms and thermal barrier coating tbc materials, should endure thermal shock perfectly in service. Based on the boundary conditions and linear independence, the system of twelve nonhomogeneous linear equations is derived. From the viewpoints of applied mechanics and heat conduction, functionally gradient materials are nonhomogeneous solids. Interface cracks in piezoelectric materials iopscience. Special focus is given to the determination of the higher order parameters of the crack tip asymptotic field, particularly the first non. This paper outlines a framework for evaluating the asymptotic crack tip field solution incorporating tz parameter in threedimensional crack problems.
In this work, three classes of mechanisms that can cause load sequence effects on fatigue crack growth are discussed. Antiplane shear behavior of an arbitrarily oriented crack. Department of mechanical engineering, shizuoka university, 351 johoku. Cracktip singular fields in functionally graded materials.
On the asymptotic stress field in angularly nonhomogeneous. International journal of engineering science 31 5, 793806, 1993. Hence, the linearelastic singular stress field near the crack tip can be obtained as 16 r11. The boundary between the two differentiable pieces is referred to as the weak property discontinuity line.
Journal of engineering and science in medical diagnostics and therapy. The singular stress and heat flux fields at the tip of the crack in. Sep 18, 2000 due to the regular singularity of the crack tip fields in fgm, the modemixity definition does not require an arbitrary length parameter in contrast to the bimaterial crack. The elastic stress and displacement fields near a crack tip in a twodimensional nonhomogeneous cracked body are derived utilizing an extension of the wiliams eigenfunction expansion technique. The crack tip higher order asymptotic fields of fgms plates are obtained by the asymptotic expansion method.
Effect of microcracks in nonhomogeneous stress field on. It is found that the analytic solutions degenerate to the corresponding fields of the isotropic homogeneous plate with reissners effect when the in. Erdogan lehigh university, bethlehem, pa 18015 abstract 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 fracture of materials is generally initiated locally from a crack tip, which. The existence of a crack in an otherwise perfect material dramatically amplifies applied stresses to values that approach a mathematical singularity at the crack s tip. It is assumed that the elastic properties of the material are exponential functions of the thickness coordinate. Fracture of nonhomogeneous materials, international journal of fracture, 34, pp. Some basic fracture mechanics concepts in functionally graded materials. The effects of material property gradients on the dominance of the crack tip singular fields are also discussed. International journal of solids and structures, 48. Oscillatory singularity behaviors near interface crack tip. Rice crack tip fields in crystals 319 the other ignored slip systems or combinations could not contribute to a crack tip strain singular ity.
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. Application of a matricitybased thermal conductivity model, engineering fracture mechanics vol. Instability criterion of inhomogeneous atomic system. The c3d8r hexahedron8node reduced integration elements were used to construct the crack tip mesh. A plane problem for a crack between two anisotropic semiinfinite spaces under remote tensileshear loading is considered. The elastic properties at the crack tip, however, should be used in the displacement field. Fully plastic asymptotic crack tip stress field solutions were provided by carrying out detailed full. The singular nature of the crack tip stress field in a nonhomogeneous medium having a shear modulus with a discontinuous derivative was investigated. A finite element program for fracture mechanics analysis. Meshfree analysis of cracks in isotropic functionally graded materials. It has also become a useful analysis and design tool to mechanical, structural, and material engineers. The general problem for an arbitrarily oriented crack in a. It is first shown that the squareroot singular field still prevaily in the crack tip.
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