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H G Georgiadis - One of the best experts on this subject based on the ideXlab platform.
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plane strain Crack problems in microstructured solids governed by dipolar gradient elasticity
Journal of The Mechanics and Physics of Solids, 2009Co-Authors: P A Gourgiotis, H G GeorgiadisAbstract:Abstract The present study aims at determining the elastic stress and Displacement fields around the tips of a finite-length Crack in a microstructured solid under remotely applied plane-strain loading (mode I and II cases). The material microstructure is modeled through the Toupin–Mindlin generalized continuum theory of dipolar gradient elasticity. According to this theory, the strain-energy density assumes the form of a positive-definite function of the strain tensor (as in classical elasticity) and the gradient of the strain tensor (additional term). A simple but yet rigorous version of the theory is employed here by considering an isotropic linear expression of the elastic strain-energy density that involves only three material constants (the two Lame constants and the so-called gradient coefficient). First, a near-tip asymptotic solution is obtained by the Knein–Williams technique. Then, we attack the complete boundary value problem in an effort to obtain a full-field solution. Hypersingular integral equations with a cubic singularity are formulated with the aid of the Fourier transform. These equations are solved by analytical considerations on Hadamard finite-part integrals and a numerical treatment. The results show significant departure from the predictions of standard fracture mechanics. In view of these results, it seems that the classical theory of elasticity is inadequate to analyze Crack problems in microstructured materials. Indeed, the present results indicate that the stress distribution ahead of the Crack tip exhibits a local maximum that is bounded. Therefore, this maximum value may serve as a measure of the critical stress level at which further advancement of the Crack may occur. Also, in the vicinity of the Crack tip, the Crack-Face Displacement closes more smoothly as compared to the standard result and the strain field is bounded. Finally, the J-integral (energy release rate) in gradient elasticity was evaluated. A decrease of its value is noticed in comparison with the classical theory. This shows that the gradient theory predicts a strengthening effect since a reduction of Crack driving force takes place as the material microstructure becomes more pronounced.
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distributed dislocation approach for Cracks in couple stress elasticity shear modes
International Journal of Fracture, 2007Co-Authors: P A Gourgiotis, H G GeorgiadisAbstract:The distributed dislocation technique proved to be in the past an effective approach in studying Crack problems within classical elasticity. The present work aims at extending this technique in studying Crack problems within couple-stress elasticity, i.e. within a theory accounting for effects of microstructure. As a first step, the technique is introduced to study finite-length Cracks under remotely applied shear loadings (mode II and mode III cases). The mode II and mode III Cracks are modeled by a continuous distribution of glide and screw dislocations, respectively, that create both standard stresses and couple stresses in the body. In particular, it is shown that the mode II case is governed by a singular integral equation with a more complicated kernel than that in classical elasticity. The numerical solution of this equation shows that a Cracked material governed by couple-stress elasticity behaves in a more rigid way (having increased stiffness) as compared to a material governed by classical elasticity. Also, the stress level at the Crack-tip region is appreciably higher than the one predicted by classical elasticity. Finally, in the mode III case the corresponding governing integral equation is hypersingular with a cubic singularity. A new mechanical quadrature is introduced here for the numerical solution of this equation. The results in the mode III case for the Crack-Face Displacement and the near-tip stress show significant departure from the predictions of classical fracture mechanics.
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the mode iii Crack problem in microstructured solids governed by dipolar gradient elasticity static and dynamic analysis
Journal of Applied Mechanics, 2003Co-Authors: H G GeorgiadisAbstract:This study aims at determining the elastic stress and Displacement fields around a Crack in a microstructured body under a remotely applied loading of the antiplane shear (mode III) type. The material microstructure is modeled through the Mindlin-Green-Rivlin dipolar gradient theory (or strain-gradient theory of grade two). A simple but yet rigorous version of this generalized continuum theory is taken here by considering an isotropic linear expression of the elastic strain-energy density in antiplane shearing that involves only two material constants (the shear modulus and the so-called gradient coefficient). In particular, the strain-energy density function, besides its dependence upon the standard strain terms, depends also on strain gradients. This expression derives from form Il of Mindlin's theory, a form that is appropriate for a gradient formulation with no couple-stress effects (in this case the strain-energy density function does not contain any rotation gradients). Here, both the formulation of the problem and the solution method are exact and lead to results for the near-tip field showing significant departure from the predictions of the classical fracture mechanics. In view of these results, it seems that the conventional fracture mechanics is inadequate to analyze Crack problems in microstructured materials. Indeed, the present results suggest that the stress distribution ahead of the tip exhibits a local maximum that is bounded. Therefore, this maximum value may serve as a measure of the critical stress level at which further advancement of the Crack may occur. Also, in the vicinity of the Crack tip, the Crack-Face Displacement closes more smoothly as compared to the classical results. The latter can be explained physically since materials with microstructure behave in a more rigid way (having increased stiffness) as compared to materials without microstructure (i.e., materials governed by classical continuum mechanics). The new formulation of the Crack problem required also new extended definitions for the J-integral and the energy release rate. It is shown that these quantities can be determined through the use of distribution (generalized function) theory. The boundary value problem was attacked by both the asymptotic Williams technique and the exact Wiener-Hopf technique. Both static and time-harmonic dynamic analyses are provided.
P A Gourgiotis - One of the best experts on this subject based on the ideXlab platform.
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plane strain Crack problems in microstructured solids governed by dipolar gradient elasticity
Journal of The Mechanics and Physics of Solids, 2009Co-Authors: P A Gourgiotis, H G GeorgiadisAbstract:Abstract The present study aims at determining the elastic stress and Displacement fields around the tips of a finite-length Crack in a microstructured solid under remotely applied plane-strain loading (mode I and II cases). The material microstructure is modeled through the Toupin–Mindlin generalized continuum theory of dipolar gradient elasticity. According to this theory, the strain-energy density assumes the form of a positive-definite function of the strain tensor (as in classical elasticity) and the gradient of the strain tensor (additional term). A simple but yet rigorous version of the theory is employed here by considering an isotropic linear expression of the elastic strain-energy density that involves only three material constants (the two Lame constants and the so-called gradient coefficient). First, a near-tip asymptotic solution is obtained by the Knein–Williams technique. Then, we attack the complete boundary value problem in an effort to obtain a full-field solution. Hypersingular integral equations with a cubic singularity are formulated with the aid of the Fourier transform. These equations are solved by analytical considerations on Hadamard finite-part integrals and a numerical treatment. The results show significant departure from the predictions of standard fracture mechanics. In view of these results, it seems that the classical theory of elasticity is inadequate to analyze Crack problems in microstructured materials. Indeed, the present results indicate that the stress distribution ahead of the Crack tip exhibits a local maximum that is bounded. Therefore, this maximum value may serve as a measure of the critical stress level at which further advancement of the Crack may occur. Also, in the vicinity of the Crack tip, the Crack-Face Displacement closes more smoothly as compared to the standard result and the strain field is bounded. Finally, the J-integral (energy release rate) in gradient elasticity was evaluated. A decrease of its value is noticed in comparison with the classical theory. This shows that the gradient theory predicts a strengthening effect since a reduction of Crack driving force takes place as the material microstructure becomes more pronounced.
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distributed dislocation approach for Cracks in couple stress elasticity shear modes
International Journal of Fracture, 2007Co-Authors: P A Gourgiotis, H G GeorgiadisAbstract:The distributed dislocation technique proved to be in the past an effective approach in studying Crack problems within classical elasticity. The present work aims at extending this technique in studying Crack problems within couple-stress elasticity, i.e. within a theory accounting for effects of microstructure. As a first step, the technique is introduced to study finite-length Cracks under remotely applied shear loadings (mode II and mode III cases). The mode II and mode III Cracks are modeled by a continuous distribution of glide and screw dislocations, respectively, that create both standard stresses and couple stresses in the body. In particular, it is shown that the mode II case is governed by a singular integral equation with a more complicated kernel than that in classical elasticity. The numerical solution of this equation shows that a Cracked material governed by couple-stress elasticity behaves in a more rigid way (having increased stiffness) as compared to a material governed by classical elasticity. Also, the stress level at the Crack-tip region is appreciably higher than the one predicted by classical elasticity. Finally, in the mode III case the corresponding governing integral equation is hypersingular with a cubic singularity. A new mechanical quadrature is introduced here for the numerical solution of this equation. The results in the mode III case for the Crack-Face Displacement and the near-tip stress show significant departure from the predictions of classical fracture mechanics.
Lisa Zellmer - One of the best experts on this subject based on the ideXlab platform.
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determination of Crack Face Displacement by x ray tomography and digital volume correlation
Procedia Engineering, 2014Co-Authors: Angelika Bruecknerfoit, F. Zeismann, Lisa ZellmerAbstract:Physically small Cracks in a ferritic martensitic steel were analyzed in the SPring-8 synchrotron facility. Change in the Crack shape under static and cyclic loading could be determined in addition to the Crack shape by mounting micro-specimens in an in- beam loading stage. Additional information can be gained by comparing three-dimensional images of the Crack Faces using volumetric digital image correlation. The Displacement field on the Crack Faces is then available which, in turn, can be correlated to the microstructure determined by serial sectioning and orientation microscopy.
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xvii international colloquium on mechanical fatigue of metals icmfm17 determination of Crack Face Displacement by x ray tomography and digital volume correlation
2014Co-Authors: Angelika Bruecknerfoit, F. Zeismann, Lisa ZellmerAbstract:Abstract Physically small Cracks in a ferritic martensitic steel were analyzed in the SPring-8 synchrotron facility. Change in the Crack shape under static and cyclic loading could be determined in addition to the Crack shape by mounting micro-specimens in an in-beam loading stage. Additional information can be gained by comparing three-dimensional images of the Crack Faces using volumetric digital image correlation. The Displacement field on the Crack Faces is then available which, in turn, can be correlated to the microstructure determined by serial sectioning and orientation microscopy. © 2014 The Authors. Published by Elsevier Ltd. Selection and peer-review under responsibility of the Politecnico di Milano, Dipartimento di Meccanica. Keywords: X-ray tomography, fatigue Crack, COD, orientation microscopy 1. Introduction Crack growth in materials containing various phases is influenced by the microstructure well beyond the stage-I growth of microstructurally small Cracks, as hard phases c an block the Crack tip field even for fairly large physical ly small Cracks. This phenomenon was studied using a ferritic martensitic steel (carbon steel with Japanese designation JIS S15C) with fairly coarse microstructure (average size of ferrite grains 49μm, average size of martensite regions 32μm) as a model material. The mechanical properties w ere measured using standard round specimens and amounted to 392 MPa for the yield stress, 673 MPa for the ultimate tensile strength, and 13% for the fracture strain.
Xinglin Guo - One of the best experts on this subject based on the ideXlab platform.
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Weight Function Method for computations of Crack Face Displacements and stress intensity factors of center Cracks
Frattura ed Integrità Strutturale, 2015Co-Authors: Junling Fan, Dengke Dong, Li Chen, Chen Xianmin, Xinglin GuoAbstract:The weight function method provides a powerful and reliable tool for the determination of the stress intensity factor around the Crack tip in a linearly elastic Cracked solid subjected to arbitrary loading conditions. However, it is difficult to exactly compute the Crack Face Displacement whose partial derivative is responsible for the weight function calculation. In the present paper, only one reference stress intensity factor is used for the purpose of establishing a general expression of the Crack Face Displacement. Then, the generalized and simple expression is applied to calculate the weight function and the stress intensity factor of the center Crack configuration. The calculation of the weight function is reduced to the simple integration of the correction function and of the partial derivative of the Crack Face Displacement. It is shown that the present expressions for the computations of the Crack Face Displacement and its partial derivative are in good agreement with their exact solutions.
Mark E Mear - One of the best experts on this subject based on the ideXlab platform.
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analysis for t stress of Cracks in 3d anisotropic elastic media by weakly singular integral equation method
Computer Methods in Applied Mechanics and Engineering, 2019Co-Authors: Jaroon Rungamornrat, Naruethep Sukulthanasorn, Mark E MearAbstract:Abstract This paper proposes an efficient numerical procedure for computing T-stresses of Cracks in three-dimensional, linearly elastic, infinite media. The technique is established in a broad framework allowing a medium made of generally anisotropic materials and Cracks of arbitrary shape and under general loading conditions to be treated. A pair of weakly singular, weak-form, Displacement and traction boundary integral equations is utilized to formulate the key equations governing the unknown Crack-Face fields. Besides the basic benefits such as the reduction of spatial dimensions of the solution space and the efficient treatment of unbounded domains and remote boundary data, use of such integral equations in the formulation offers additional positive features including the computational simplicity resulting from the weakly singular nature of all involved integrals and the involvement of a complete set of Crack-Face Displacement fields. A weakly singular symmetric Galerkin boundary element method together with the special near-front approximation is utilized to solve for the unknown relative Crack-Face Displacement whereas the sum of the Crack-Face Displacement is obtained from the Displacement boundary integral equation for Cracks via the Galerkin technique. The latter step is one of the essential aspects of the present study that provides the direct means for determining the T-stress data in terms of the sum of the Crack-Face Displacement in the neighborhood of the Crack-front. An extensive numerical study is conducted for various scenarios and a selected set of results is reported to demonstrate both the accuracy and capability of the proposed technique.
