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Vera Petrova - One of the best experts on this subject based on the ideXlab platform.
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revisit of antiplane shear problems for an Interface Crack does the stress intensity factor for the Interface mode iii Crack depend on the bimaterial modulus
Engineering Fracture Mechanics, 2019Co-Authors: Vera Petrova, S Schmauder, Mikael Ordyan, Alexander ShashkinAbstract:Abstract An overview of the results for Mode III Interface Crack problems available in the literature, as well as those obtained by the authors, is presented in the paper. The analytical and semi-analytical solutions for the main fracture characteristics (i.e. stress intensity factors and energy release rates) are discussed with respect to their dependency on bimaterial constants. Detailed formulation for the antiplane shear problem for an Interface Crack interacting with internal Cracks is presented using the methods of complex potentials and singular integral equations. Some particular solutions (e.g. for the problem of a singularity interacting with an Interface and for the Mode III Interface Crack) are obtained, and these can serve as benchmark solutions or as parts of other similar problems. The approximate closed-form solution is derived for a special case of the interaction between the Interface Crack and internal micro-Cracks. The resulting form of the solution for the stress intensity factors is rather simple and its structure is easily analyzed. A theoretical analysis of the explicit form of expressions for the stress intensity factors shows the conditions under which the solution for the Interface Crack depends on the bimaterial mismatch, and those under which it does not depend. This formula also allows to define the condition, when a small internal Crack does not influence the stress intensity factor of the Interface Crack (i.e. invisible for the Interface Crack).
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mathematical modelling and thermal stress intensity factors evaluation for an Interface Crack in the presence of a system of Cracks in functionally graded homogeneous bimaterials
Computational Materials Science, 2012Co-Authors: Vera Petrova, S SchmauderAbstract:Abstract The work is devoted to mathematical modeling of the fracture processes in the vicinity of an Interface Crack in functionally graded/homogeneous bimaterials with internal defects subjected to a thermal flux. A previously obtained solution (Petrova and Schmauder, 2009, 2011) [7] , [8] is used and supplemented with the additional possibility to take into account the Crack closure. The solution is based on the integral equation method and it is assumed that thermal properties of the functionally graded material (FGM) have exponential form. For a special case where an Interface Crack length is much larger than the internal Cracks in the FGM an asymptotic analytical solution of the problem is obtained as series of a small parameter (the ratio between sizes of the internal and Interface Cracks). Analyses of the effects of the location and orientation of the Cracks, the material non-homogeneity parameters and the Crack closure effects on the thermal stress intensity factors of the Interface Crack in FGM/homogeneous bimaterials are performed. Examples of some FGM/homogeneous bimaterial combinations (i.e., metal/metal, ceramic/metal) are discussed.
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mathematical modelling and thermal stress intensity factors evaluation for an Interface Crack in the presence of a system of Cracks in functionally graded homogeneous bimaterials
Computational Materials Science, 2012Co-Authors: Vera Petrova, S SchmauderAbstract:Abstract The work is devoted to mathematical modeling of the fracture processes in the vicinity of an Interface Crack in functionally graded/homogeneous bimaterials with internal defects subjected to a thermal flux. A previously obtained solution (Petrova and Schmauder, 2009, 2011) [7] , [8] is used and supplemented with the additional possibility to take into account the Crack closure. The solution is based on the integral equation method and it is assumed that thermal properties of the functionally graded material (FGM) have exponential form. For a special case where an Interface Crack length is much larger than the internal Cracks in the FGM an asymptotic analytical solution of the problem is obtained as series of a small parameter (the ratio between sizes of the internal and Interface Cracks). Analyses of the effects of the location and orientation of the Cracks, the material non-homogeneity parameters and the Crack closure effects on the thermal stress intensity factors of the Interface Crack in FGM/homogeneous bimaterials are performed. Examples of some FGM/homogeneous bimaterial combinations (i.e., metal/metal, ceramic/metal) are discussed.
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Crack Interface Crack interactions in functionally graded homogeneous composite bimaterials subjected to a heat flux
Mechanics of Composite Materials, 2011Co-Authors: Vera Petrova, S SchmauderAbstract:A bimaterial containing an Interface Crack and consisting of a homogeneous material and a functionally graded material (FGM) with a system of small internal Cracks is considered. The thermal fracture of the biomaterial under the action of a heat flux applied to it at infinity is investigated. The problem is studied in the case where the Interface Crack is much larger than the internal ones. It is assumed that the thermal properties of the FGM are continuous functions of the thickness coordinate. Asymptotic analytical formulas for the thermal stress intensity factors (TSIFs) at the tips of the Interface Crack are obtained as series in a small parameter (the ratio between sizes of the internal and Interface Cracks). Then, the critical heat fluxes and the angles of propagation direction of the Interface Crack are calculated using the criterion of maximum circumferential stress. A parametric analysis shows that the propagation direction of the Interface Crack depends on the location and orientation of the system of internal Cracks. The parameters of inhomogeneity of the FGM affect the value of TSIFs and, hence, the deflection angle of the Interface Crack.
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thermal Crack problems for a bimaterial with an Interface Crack and internal defects subjected to a heat source
International Journal of Fracture, 2004Co-Authors: Vera Petrova, K P HerrmannAbstract:The interaction between internal defects and an Interface Crack in a bimaterial subjected to a thermal load, in particular a heat source, is examined. Attention is focused on the construction of the associated integral equations.
Naoaki Noda - One of the best experts on this subject based on the ideXlab platform.
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effect of arbitrary bi material combination and bending loading conditions on stress intensity factors of an edge Interface Crack
International Journal of Structural Integrity, 2012Co-Authors: Kazuhiro Oda, Naoaki Noda, Xin Lan, Kengo MichinakaAbstract:Purpose – The purpose of this paper is to compute the stress intensity factors (SIFs) of single edge Interface Crack for arbitrary material combinations and various relative Crack lengths, and compare with those for the bonded plates subjected to tensile loading conditions. It aims to discuss the results of the shallow edge Interface Crack on the basis of the singular stress near the free‐edge corner without the Crack.Design/methodology/approach – In this study, the SIFs of Interface Crack in dissimilar bonded plates subjected to bending loading conditions are analyzed by the finite element method and a post‐processing technique. The use of post‐processing technique of extrapolation reduces the computational cost and improves the accuracy of the obtained result.Findings – The empirical expressions are proposed for evaluating the SIFs of arbitrary material combinations.Originality/value – Empirical functions can be used to obtain the SIFs for arbitrary material combinations for the bending loading conditio...
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single and double edge Interface Crack solutions for arbitrary forms of material combination
Acta Mechanica Solida Sinica, 2012Co-Authors: Xin Lan, Naoaki Noda, Yu Zhang, Kengo MichinakaAbstract:In this paper interfacial edge Crack problems are considered by the application of the finite element method. The stress intensity factors are accurately determined from the ratio of Crack-tip-stress value between the target given unknown and reference problems. The reference problem is chosen to produce the singular stress fields proportional to those of the given unknown problem. Here the original proportional method is improved through utilizing very refined meshes and post-processing technique of linear extrapolation. The results for a double-edge Interface Crack in a bonded strip are newly obtained and compared with those of a single-edge Interface Crack for different forms of combination of material. It is found that the stress intensity factors should be compared in the three different zones of relative Crack lengths. Different from the case of a Cracked homogeneous strip, the results for the double edge Interface Cracks are found to possibly be bigger than those for a single edge Interface Crack under the same relative Crack length.
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stress intensity factors for an edge Interface Crack in a bonded semi infinite plate for arbitrary material combination
International Journal of Solids and Structures, 2012Co-Authors: Naoaki NodaAbstract:Abstract Although a lot of Interface Crack problems were previously treated, few solutions are available under arbitrary Crack lengths and material combinations. In this paper the stress intensity factors of an edge Interface Crack in a bonded strip are considered under tension with varying the Crack length and material combinations systematically. Then, the limiting solutions are provided for an edge Interface Crack in a bonded semi-infinite plate under arbitrary material combinations. In order to calculate the stress intensity factors accurately, exact solutions in an infinite bonded plate are also considered to produce proportional singular stress fields in the analysis of FEM by superposing specific tensile and shear stresses at infinity. The details of this new numerical solution are described with clarifying the effect of the element size on the stress intensity factor. It is found that for the edge Interface Crack the normalized stress intensity factors are not always finite depending upon Dunders’ parameters. This behavior can be explained from the condition of the singular stress at the end of bonded strip. Convenient formulas are also given by fitting the computed results.
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stress intensity factor of an Interface Crack in a bonded plate under uni axial tension
Journal of Solid Mechanics and Materials Engineering, 2010Co-Authors: Naoaki Noda, Yu Zhang, Yasushi TakaseAbstract:Although a lot of Interface Crack problems were previously treated, few solutions are available under arbitrary material combination. This paper deals with a central Interface Crack in a bonded infinite plate and finite plate. Then, the effects of material combination on the stress intensity factors are discussed. A useful method to calculate the stress intensity factor of Interface Crack is presented with focusing on the stress at the Crack tip calculated by the finite element method. For the central Interface Crack, it is found that the results of bonded infinite plate under remote uni-axial tension are always depending on the Dunders’ parameters α, β and different from the well-known solution of the central Interface Crack under internal pressure that is only depending on β . Besides, it is shown that the stress intensity factor of bonded infinite plate can be estimated from the stress of Crack tip in the bonded plate when there is no Crack. It is also found that dimensionless stress intensity factor FI 0, FI >1 when (α+2β)(α-2β) <0, and FI =1 when (α+2β)(α-2β) =0.
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analysis of stress intensity factors of a ring shaped Interface Crack
International Journal of Solids and Structures, 2003Co-Authors: Naoaki Noda, Masayuki Kagita, Mengcheng Chen, Kazuhiro OdaAbstract:In this paper, numerical solutions of singular integral equations are discussed in the analysis of axi-symmetric Interface Cracks under torsion and tension. The problems of a ring-shaped Interface Crack are formulated in terms of a system of singular integral equations on the basis of the body force method. In the numerical analysis, unknown body force densities are approximated by the products of the fundamental density functions and power series, where the fundamental densities are chosen to express a two-dimensional Interface Crack exactly. The accuracy of the present analysis is verified by comparing the present results with the results obtained by other researchers for the limiting cases of the geometries. The calculation shows that the present method gives rapidly converging numerical results for those problems as well as for ordinary Crack problems in homogeneous material. The stress intensity factors of a ring-shaped Interface Crack are shown in tables and charts with varying the material combinations and also geometrical conditions.
Peter Schiavone - One of the best experts on this subject based on the ideXlab platform.
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a screw dislocation interacting with a semi infinite Interface Crack and two semi infinite Cracks perpendicular to the bimaterial Interface
Acta Mechanica, 2020Co-Authors: Xu Wang, Peter SchiavoneAbstract:Using conformal mapping and the image method, we derive an analytic solution to the problem of an isotropic elastic bimaterial involving a screw dislocation interacting with a semi-infinite Interface Crack, a semi-infinite Crack in the upper half-plane perpendicular to the Interface, and another semi-infinite Crack in the lower half-plane also perpendicular to the Interface. Closed-form expressions of the image force acting on the screw dislocation and the mode III stress intensity factors at the three Crack tips are derived.
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electric current induced thermal stress around a bi material Interface Crack
Engineering Fracture Mechanics, 2019Co-Authors: K Song, H P Song, Peter Schiavone, Cunfa GaoAbstract:Abstract In this paper we analyze the thermal stress distribution in the vicinity of an Interface Crack in a bi-material subjected to a remote electric current. We emphasize in particular, the influence of the electric current on the thermal stress intensity factors. Our results indicate that the electric current may either intensify or in fact neutralize the thermal stress intensity factors depending on the material parameters of the bi-material. Numerical analyses illustrate clearly that when the bi-material is described by particular combinations of material parameters, the electric current can effectively decrease the absolute value of mode I and mode II thermal stress intensity factors to the point where both are simultaneously nullified by the electric current. The fact that the thermal stress is generally a quadratic function of the prescribed electric current precludes the possibility of altering the effects of the electric current on the thermal stress intensity factors by simply adjusting the direction of the electric current itself.
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arc shaped permeable Interface Crack in an electrostrictive fibrous composite under uniform remote electric loadings
International Journal of Mechanical Sciences, 2016Co-Authors: Ming Dai, Cunfa Gao, Peter SchiavoneAbstract:Abstract We present a rigorous solution of the problem of an arc-shaped Interface Crack embedded between a circular electrostrictive fiber and a foreign matrix subjected to uniform remote electric loadings. The Crack faces are assumed to be permeable to an electric field. Mode-I and Mode-II stress intensity factors for the oscillatory singular stress field at the Crack tips are obtained using complex variable methods. We find that the stress intensity factors typically increase as the fiber becomes harder. For certain combinations of the arc length of the Crack and material constants of the fiber-matrix system, we show that remote electric loadings may actually prevent mode-I interfacial fracture. In particular, we show that when the fiber-matrix system degenerates to a homogeneous electrostrictive material and the medium inside the Crack is identical to that surrounding the material remotely, the application of remote electric loadings continue to have a significant influence on both mode-I and mode-II fracture.
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effect of surface elasticity on an Interface Crack in plane deformations
Proceedings of The Royal Society A: Mathematical Physical and Engineering Sciences, 2011Co-Authors: Chun Il Kim, Peter SchiavoneAbstract:We consider the effect of surface elasticity on an Interface Crack between two dissimilar linearly elastic isotropic homogeneous materials undergoing plane deformations. The bi-material is subjected to either remote tension (mode-I) or in-plane shear (mode-II) with the faces of the (Interface) Crack assumed to be traction-free. We incorporate surface mechanics into the model of deformation by employing a version of the continuum-based surface/Interface theory of Gurtin & Murdoch. Using complex variable methods, we obtain a semi-analytical solution valid throughout the entire domain of interest (including at the Crack tips) by reducing the problem to a system of coupled Cauchy singular integro-differential equations, which is solved numerically using Chebychev polynomials and a collocation method. It is shown that, among other interesting phenomena, our model predicts finite stress at the (sharp) Crack tips and the corresponding stress field to be size-dependent. In particular, we note that, in contrast to the results from linear elastic fracture mechanics, when the bi-material is subjected to uniform far-field stresses (either tension or in-plane shear), the incorporation of surface effects effectively eliminates the oscillatory behaviour of the solution so that the resulting stress fields no longer suffer from oscillatory singularities at the Crack tips.
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the effect of surface elasticity on a mode iii Interface Crack
Archives of Mechanics, 2011Co-Authors: Chun Il Kim, Peter SchiavoneAbstract:We study the contribution of surface elasticity to the anti-plane deformations of a linearly elastic bi-material with Mode-III Interface Crack. The surface elasticity is incorporated using a version of the continuum-based surface/Interface model of Gurtin and Murdoch. We obtain a complete semi-analytic solution valid throughout the solid (including the Crack tips) via a Cauchy singular, integro-differential equation of the first kind. Our solution demonstrates that the surface elasticity on the Crack face leads to finite stresses at the Crack tips and stress discontinuities across the material Interface.
Luca Di Stasio - One of the best experts on this subject based on the ideXlab platform.
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finite element solution of the fiber matrix Interface Crack problem convergence properties and mode mixity of the virtual Crack closure technique
Finite Elements in Analysis and Design, 2019Co-Authors: Luca Di Stasio, Zoubir AyadiAbstract:Abstract The bi-material Interface arc Crack has been the focus of interest in the composite community, where it is usually referred to as the fiber-matrix Interface Crack. In this work, we investigate the convergence properties of the Virtual Crack Closure Technique (VCCT) when applied to the evaluation of the Mode I, Mode II and total Energy Release Rate of the fiber-matrix Interface Crack in the context of the Finite Element Method (FEM). We first propose a synthetic vectorial formulation of the VCCT. Thanks to this formulation, we study the convergence properties of the method, both analytically and numerically. It is found that Mode I and Mode II Energy Release Rate (ERR) possess a logarithmic dependency with respect to the size of the elements in the Crack tip neighborhood, while the total ERR is independent of element size.
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Finite Element solution of the fiber/matrix Interface Crack problem: convergence properties and mode mixity of the Virtual Crack Closure Technique
2019Co-Authors: Luca Di Stasio, Zoubir AyadiAbstract:The bi-material Interface arc Crack has been the focus of interest in the composite community, where it is usually referred to as the fiber-matrix Interface Crack. In this work, we investigate the convergence properties of the Virtual Crack Closure Technique (VCCT) when applied to the evaluation of the Mode I, Mode II and total Energy Release Rate of the fiber-matrix Interface Crack in the context of the Finite Element Method (FEM). We first propose a synthetic vectorial formulation of the VCCT. Thanks to this formulation, we study the convergence properties of the method, both analytically and numerically. It is found that Mode I and Mode II Energy Release Rate (ERR) possess a logarithmic dependency with respect to the size of the elements in the Crack tip neighborhood, while the total ERR is independent of element size.
Kazuhiro Oda - One of the best experts on this subject based on the ideXlab platform.
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effect of arbitrary bi material combination and bending loading conditions on stress intensity factors of an edge Interface Crack
International Journal of Structural Integrity, 2012Co-Authors: Kazuhiro Oda, Naoaki Noda, Xin Lan, Kengo MichinakaAbstract:Purpose – The purpose of this paper is to compute the stress intensity factors (SIFs) of single edge Interface Crack for arbitrary material combinations and various relative Crack lengths, and compare with those for the bonded plates subjected to tensile loading conditions. It aims to discuss the results of the shallow edge Interface Crack on the basis of the singular stress near the free‐edge corner without the Crack.Design/methodology/approach – In this study, the SIFs of Interface Crack in dissimilar bonded plates subjected to bending loading conditions are analyzed by the finite element method and a post‐processing technique. The use of post‐processing technique of extrapolation reduces the computational cost and improves the accuracy of the obtained result.Findings – The empirical expressions are proposed for evaluating the SIFs of arbitrary material combinations.Originality/value – Empirical functions can be used to obtain the SIFs for arbitrary material combinations for the bending loading conditio...
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analysis of stress intensity factors of a ring shaped Interface Crack
International Journal of Solids and Structures, 2003Co-Authors: Naoaki Noda, Masayuki Kagita, Mengcheng Chen, Kazuhiro OdaAbstract:In this paper, numerical solutions of singular integral equations are discussed in the analysis of axi-symmetric Interface Cracks under torsion and tension. The problems of a ring-shaped Interface Crack are formulated in terms of a system of singular integral equations on the basis of the body force method. In the numerical analysis, unknown body force densities are approximated by the products of the fundamental density functions and power series, where the fundamental densities are chosen to express a two-dimensional Interface Crack exactly. The accuracy of the present analysis is verified by comparing the present results with the results obtained by other researchers for the limiting cases of the geometries. The calculation shows that the present method gives rapidly converging numerical results for those problems as well as for ordinary Crack problems in homogeneous material. The stress intensity factors of a ring-shaped Interface Crack are shown in tables and charts with varying the material combinations and also geometrical conditions.
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analysis of stress intensity factors of a ring shaped Interface Crack
Transactions of the Japan Society of Mechanical Engineers. A, 2003Co-Authors: Naoaki Noda, Masayuki Kagita, Mengcheng Chen, Kazuhiro OdaAbstract:In this paper, numerical solutions of singular integral equations are discussed in the analysis of axi-symmetric Interface Cracks under torsion and tension. The problems of a ring-shaped Interface Crack are formulated in terms of a system of singular integral equations on the basis of the body force method. In the numerical analysis, the unknown functions of the body force densities are approximated by the products of the fundamental density functions and power series, where the fundamental densities are chosen to express a two-dimensional Interface Crack exactly. The accuracy of the present analysis is verified by comparing the present results with the results obtained by other researchers for the limiting cases. The calculation shows that the present method gives rapidly converging numerical results for these problems as well as for ordinary Crack problems in homogeneous material. The stress intensity factors of a ring-shaped Interface Crack are shown in tables and charts with varying in material combination and also geometrical conditions.
