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Peter Schiavone - One of the best experts on this subject based on the ideXlab platform.
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A Screw Dislocation in a Monoclinic Tri-Material
Journal of Elasticity, 2020Co-Authors: Xu Wang, Peter SchiavoneAbstract:Employing primarily analytic continuation, we derive analytical solutions to the anti-plane problem associated with a Screw Dislocation located anywhere inside an anisotropic tri-material composed of an intermediate anisotropic elastic layer of finite thickness sandwiched between two semi-infinite anisotropic elastic media. All three phases of the tri-material are monoclinic with the symmetry plane at $x_{3}=0$ in a Cartesian coordinate system. We obtain explicit expressions for each one of the three analytic functions defined in its respective anisotropic elastic phase. This allows for the complete determination of the stresses and displacement in the tri-material. In addition, we present simple yet concise expressions for the image force acting on the Screw Dislocation. An interfacial Zener-Stroh crack in the tri-material is discussed using the analytical solution developed for an interfacial Screw Dislocation.
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A completely coated wedge crack interacting with a Screw Dislocation
International Journal of Solids and Structures, 2020Co-Authors: Xu Wang, Peter SchiavoneAbstract:Abstract We employ conformal mapping and analytic continuation to study the elastic field induced by a Screw Dislocation interacting with a completely coated semi-infinite wedge crack under mode III loading conditions. The Screw Dislocation can be located either inside the matrix or in the coating itself. Explicit expressions for the local wedge stress intensity factor and the image force acting on the Screw Dislocation are obtained. The Dislocation emission criterion from the completely coated wedge crack is established.
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Elastic interaction between a semi-infinite debonded anticrack and a Screw Dislocation
Meccanica, 2019Co-Authors: Xu Wang, Peter SchiavoneAbstract:We study the elastic interaction between a semi-infinite debonded anticrack lying on the negative real axis and a Screw Dislocation under the assumption of anti-plane mechanical loading. The lower side of the anticrack (or rigid line inclusion) is perfectly bonded to the surrounding material in contrast to its upper side which is fully debonded. A simple closed-form solution to this interaction problem is developed by means of conformal mapping and the method of images. Specifically, we obtain expressions for the image force acting on the Screw Dislocation, the two resultant stress intensity factors respectively characterizing the r ^−3/4 and r ^−1/4 type singularities at the tip of the debonded anticrack and the resultant material force on the debonded anticrack. The Dislocation emission criterion from the debonded anticrack in terms of two critical stress intensity factors is also established.
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Interaction between a completely coated semi-infinite insulating crack and a piezoelectric Screw Dislocation
Zeitschrift für angewandte Mathematik und Physik, 2019Co-Authors: Xu Wang, Peter SchiavoneAbstract:We derive analytic solutions to the problem of a completely coated semi-infinite insulating crack interacting with a Screw Dislocation under the assumption of anti-plane mechanical and in-plane electrical loading in a piezoelectric composite. The Screw Dislocation can be located either in the piezoelectric matrix or in the piezoelectric coating itself. We obtain explicit expressions for the resultant stress and electric displacement intensity factors, the resultant crack extension force and the image force acting on the Screw Dislocation. By employing orthogonality relations for two corresponding eigenvectors, we avoid tedious matrix operations in the development of the final expressions for the resultant field intensity factors, resultant crack extension force and image force.
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interaction between a completely coated semi infinite crack and a Screw Dislocation
Zeitschrift für Angewandte Mathematik und Physik, 2019Co-Authors: Xu Wang, Peter SchiavoneAbstract:Using complex variable methods, we derive analytic solutions to the problem of a Screw Dislocation interacting with a completely coated semi-infinite mode III crack. The crack and the parabolic coating–matrix interface have a common focus. The Screw Dislocation can be located either in the surrounding matrix or in the coating itself. Explicit expressions for the resultant stress intensity factor at the crack tip and the image force acting on the Screw Dislocation are obtained. Several special cases are discussed in detail to demonstrate the solutions and also to validate their correctness.
Xu Wang - One of the best experts on this subject based on the ideXlab platform.
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A Screw Dislocation in a Monoclinic Tri-Material
Journal of Elasticity, 2020Co-Authors: Xu Wang, Peter SchiavoneAbstract:Employing primarily analytic continuation, we derive analytical solutions to the anti-plane problem associated with a Screw Dislocation located anywhere inside an anisotropic tri-material composed of an intermediate anisotropic elastic layer of finite thickness sandwiched between two semi-infinite anisotropic elastic media. All three phases of the tri-material are monoclinic with the symmetry plane at $x_{3}=0$ in a Cartesian coordinate system. We obtain explicit expressions for each one of the three analytic functions defined in its respective anisotropic elastic phase. This allows for the complete determination of the stresses and displacement in the tri-material. In addition, we present simple yet concise expressions for the image force acting on the Screw Dislocation. An interfacial Zener-Stroh crack in the tri-material is discussed using the analytical solution developed for an interfacial Screw Dislocation.
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A completely coated wedge crack interacting with a Screw Dislocation
International Journal of Solids and Structures, 2020Co-Authors: Xu Wang, Peter SchiavoneAbstract:Abstract We employ conformal mapping and analytic continuation to study the elastic field induced by a Screw Dislocation interacting with a completely coated semi-infinite wedge crack under mode III loading conditions. The Screw Dislocation can be located either inside the matrix or in the coating itself. Explicit expressions for the local wedge stress intensity factor and the image force acting on the Screw Dislocation are obtained. The Dislocation emission criterion from the completely coated wedge crack is established.
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Elastic interaction between a semi-infinite debonded anticrack and a Screw Dislocation
Meccanica, 2019Co-Authors: Xu Wang, Peter SchiavoneAbstract:We study the elastic interaction between a semi-infinite debonded anticrack lying on the negative real axis and a Screw Dislocation under the assumption of anti-plane mechanical loading. The lower side of the anticrack (or rigid line inclusion) is perfectly bonded to the surrounding material in contrast to its upper side which is fully debonded. A simple closed-form solution to this interaction problem is developed by means of conformal mapping and the method of images. Specifically, we obtain expressions for the image force acting on the Screw Dislocation, the two resultant stress intensity factors respectively characterizing the r ^−3/4 and r ^−1/4 type singularities at the tip of the debonded anticrack and the resultant material force on the debonded anticrack. The Dislocation emission criterion from the debonded anticrack in terms of two critical stress intensity factors is also established.
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Interaction between a completely coated semi-infinite insulating crack and a piezoelectric Screw Dislocation
Zeitschrift für angewandte Mathematik und Physik, 2019Co-Authors: Xu Wang, Peter SchiavoneAbstract:We derive analytic solutions to the problem of a completely coated semi-infinite insulating crack interacting with a Screw Dislocation under the assumption of anti-plane mechanical and in-plane electrical loading in a piezoelectric composite. The Screw Dislocation can be located either in the piezoelectric matrix or in the piezoelectric coating itself. We obtain explicit expressions for the resultant stress and electric displacement intensity factors, the resultant crack extension force and the image force acting on the Screw Dislocation. By employing orthogonality relations for two corresponding eigenvectors, we avoid tedious matrix operations in the development of the final expressions for the resultant field intensity factors, resultant crack extension force and image force.
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interaction between a completely coated semi infinite crack and a Screw Dislocation
Zeitschrift für Angewandte Mathematik und Physik, 2019Co-Authors: Xu Wang, Peter SchiavoneAbstract:Using complex variable methods, we derive analytic solutions to the problem of a Screw Dislocation interacting with a completely coated semi-infinite mode III crack. The crack and the parabolic coating–matrix interface have a common focus. The Screw Dislocation can be located either in the surrounding matrix or in the coating itself. Explicit expressions for the resultant stress intensity factor at the crack tip and the image force acting on the Screw Dislocation are obtained. Several special cases are discussed in detail to demonstrate the solutions and also to validate their correctness.
Joseph Morillo - One of the best experts on this subject based on the ideXlab platform.
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Screw Dislocation in hcp ti dft Dislocation excess energies and metastable core structures
Modelling and Simulation in Materials Science and Engineering, 2014Co-Authors: Nathalie Tarrat, Lisa Ventelon, Magali Benoit, D Caillard, Nicolas Combe, Joseph MorilloAbstract:An extensive DFT search of (meta)stable structures of the a � 11 ¯ 20 � Screw Dislocation in hcp-Ti is presented. It reveals that the stable core structures are never basal but always prismatic. This prismatic core dissociates into two partial Dislocations in the same or neighboring prismatic planes depending on the initial position of the Dislocation line, leading to either a symmetric or an asymmetric core. An alternative way of defining the core region from an electronic structure point of view is also proposed. It evidences clearly the symmetric or asymmetric character of the cores. We then introduce an ansatz for a straightforward and fast calculation of the excess energy, per unit length of Dislocation, of a Screw Dislocation applicable to DFT calculations, in the cluster approach. The method is first validated on calculations of a a � 11 ¯ 20 � Screw Dislocation in hcp-Ti, performed with an EAM potential from which exact excess energies can be extracted. Then, it is shown that it does work in a DFT calculation, through its application to the same Screw Dislocation in hcp-Ti with an accuracy of 8.4 meV/A (1.8% of the excess energy for a cluster of 126 atoms per plane normal to the Dislocation line). The comparison of the excess energies of the symmetric and assymmetric cores, calculated with the proposed ansatz, reveals that their energy difference is within the uncertainty
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Screw Dislocation in hcp Ti : DFT Dislocation excess energies and metastable core structures
Modelling and Simulation in Materials Science and Engineering, 2014Co-Authors: Nathalie Tarrat, Lisa Ventelon, Magali Benoit, D Caillard, Nicolas Combe, Joseph MorilloAbstract:An extensive DFT search of (meta)stable structures of the a/3 〈112̄0〉 Screw Dislocation in hcp-Ti is presented. It reveals that the stable core structures are never basal but always prismatic. This prismatic core dissociates into two partial Dislocations in the same or neighboring prismatic planes depending on the initial position of the Dislocation line, leading to either a symmetric or an asymmetric core. An alternative way of defining the core region from an electronic structure point of view is also proposed. It evidences clearly the symmetric or asymmetric character of the cores. We then introduce an ansatz for a straightforward and fast calculation of the excess energy, per unit length of Dislocation, of a Screw Dislocation applicable to DFT calculations, in the cluster approach. The method is first validated on calculations of a a/3 〈112̄0〉 Screw Dislocation in hcp-Ti, performed with an EAM potential from which exact excess energies can be extracted. Then, it is shown that it does work in a DFT calculation, through its application to the same Screw Dislocation in hcp-Ti with an accuracy of 8.4 meV/Å (1.8% of the excess energy for a cluster of 126 atoms per plane normal to the Dislocation line). The comparison of the excess energies of the symmetric and assymmetric cores, calculated with the proposed ansatz, reveals that their energy difference is within the uncertainty of the method, which implies that the potential energy surface is very flat and that there could be many metastable core structures in hcp-Ti. © 2014 IOP Publishing Ltd.
Lisa Ventelon - One of the best experts on this subject based on the ideXlab platform.
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Screw Dislocation in hcp ti dft Dislocation excess energies and metastable core structures
Modelling and Simulation in Materials Science and Engineering, 2014Co-Authors: Nathalie Tarrat, Lisa Ventelon, Magali Benoit, D Caillard, Nicolas Combe, Joseph MorilloAbstract:An extensive DFT search of (meta)stable structures of the a � 11 ¯ 20 � Screw Dislocation in hcp-Ti is presented. It reveals that the stable core structures are never basal but always prismatic. This prismatic core dissociates into two partial Dislocations in the same or neighboring prismatic planes depending on the initial position of the Dislocation line, leading to either a symmetric or an asymmetric core. An alternative way of defining the core region from an electronic structure point of view is also proposed. It evidences clearly the symmetric or asymmetric character of the cores. We then introduce an ansatz for a straightforward and fast calculation of the excess energy, per unit length of Dislocation, of a Screw Dislocation applicable to DFT calculations, in the cluster approach. The method is first validated on calculations of a a � 11 ¯ 20 � Screw Dislocation in hcp-Ti, performed with an EAM potential from which exact excess energies can be extracted. Then, it is shown that it does work in a DFT calculation, through its application to the same Screw Dislocation in hcp-Ti with an accuracy of 8.4 meV/A (1.8% of the excess energy for a cluster of 126 atoms per plane normal to the Dislocation line). The comparison of the excess energies of the symmetric and assymmetric cores, calculated with the proposed ansatz, reveals that their energy difference is within the uncertainty
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Screw Dislocation in hcp Ti : DFT Dislocation excess energies and metastable core structures
Modelling and Simulation in Materials Science and Engineering, 2014Co-Authors: Nathalie Tarrat, Lisa Ventelon, Magali Benoit, D Caillard, Nicolas Combe, Joseph MorilloAbstract:An extensive DFT search of (meta)stable structures of the a/3 〈112̄0〉 Screw Dislocation in hcp-Ti is presented. It reveals that the stable core structures are never basal but always prismatic. This prismatic core dissociates into two partial Dislocations in the same or neighboring prismatic planes depending on the initial position of the Dislocation line, leading to either a symmetric or an asymmetric core. An alternative way of defining the core region from an electronic structure point of view is also proposed. It evidences clearly the symmetric or asymmetric character of the cores. We then introduce an ansatz for a straightforward and fast calculation of the excess energy, per unit length of Dislocation, of a Screw Dislocation applicable to DFT calculations, in the cluster approach. The method is first validated on calculations of a a/3 〈112̄0〉 Screw Dislocation in hcp-Ti, performed with an EAM potential from which exact excess energies can be extracted. Then, it is shown that it does work in a DFT calculation, through its application to the same Screw Dislocation in hcp-Ti with an accuracy of 8.4 meV/Å (1.8% of the excess energy for a cluster of 126 atoms per plane normal to the Dislocation line). The comparison of the excess energies of the symmetric and assymmetric cores, calculated with the proposed ansatz, reveals that their energy difference is within the uncertainty of the method, which implies that the potential energy surface is very flat and that there could be many metastable core structures in hcp-Ti. © 2014 IOP Publishing Ltd.
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Dislocation core field ii Screw Dislocation in iron
Physical Review B, 2011Co-Authors: Emmanuel Clouet, Lisa Ventelon, F. WillaimeAbstract:The Dislocation core field, which comes in addition to the Volterra elastic field, is studied for the $\ensuremath{\langle}111\ensuremath{\rangle}$ Screw Dislocation in $\ensuremath{\alpha}$-iron. This core field, evidenced and characterized using ab initio calculations, corresponds to a biaxial dilatation, which we modeled within the anisotropic linear elasticity. We show that this core field needs to be considered when extracting quantitative information from atomistic simulations, such as Dislocation core energies. Finally, we look at how Dislocation properties are modified by this core field by studying the interaction between two Dislocations composing a dipole, as well as the interaction of a Screw Dislocation with a carbon atom.
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Dislocation core field. II. Screw Dislocation in iron
Physical Review B: Condensed Matter and Materials Physics, 2011Co-Authors: Emmanuel Clouet, Lisa Ventelon, F. WillaimeAbstract:The Dislocation core field, which comes in addition to the Volterra elastic field, is studied for the Screw Dislocation in alpha-iron. This core field, evidenced and characterized using ab initio calculations, corresponds to a biaxial dilatation, which we modeled within the anisotropic linear elasticity. We show that this core field needs to be considered when extracting quantitative information from atomistic simulations, such as Dislocation core energies. Finally, we look at how Dislocation properties are modified by this core field, by studying the interaction between two Dislocations composing a dipole, as well as the interaction of a Screw Dislocation with a carbon atom.
Qihong Fang - One of the best experts on this subject based on the ideXlab platform.
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The interaction between a Screw Dislocation and a circular inhomogeneity in gradient elasticity
Meccanica, 2008Co-Authors: H.p. Song, Qihong Fang, Y.w. LiuAbstract:The interaction between a Screw Dislocation and a circular inhomogeneity in gradient elasticity is investigated. The Screw Dislocation is located inside either the inhomogeneity or the matrix. By using the Fourier transform method, closed analytical solutions are obtained when the inhomogeneity and the matrix have the same gradient coefficient. The explicit expressions of image forces exerted on Screw Dislocations are derived. The motion of the appointed Screw Dislocation and its equilibrium positions are discussed. The results show that the classical singularity is eliminated. Especially, for the case of a tiny inhomogeneity, the relation of Dislocations and inhomogeneities become quite different. The Screw Dislocation may be attracted by the stiff inhomogeneity and repelled by the soft inhomogeneity when it tends to the interface. So there is an unstable equilibrium position when a Dislocation tends to a tiny stiff inhomogeneity and there is a stable equilibrium position when a Dislocation tends to a tiny soft inhomogeneity.
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Analysis of a Screw Dislocation inside an inhomogeneity with interface stress
Materials Science and Engineering A-structural Materials Properties Microstructure and Processing, 2007Co-Authors: Y.w. Liu, Qihong FangAbstract:The problem of a Screw Dislocation inside a circular inhomogeneity incorporating interface stress is investigated. The analytical expressions of the complex potentials, stress fields and the image force acting on the Dislocation are obtained by means of the complex variable method. The image force acting on the Screw Dislocation is examined in detail. The results show that the influence of the interface stress on the movement and equilibrium positions of the Screw Dislocation inside the inhomogeneity may be significant when the radius of the inhomogeneity is reduced to nanometer scale. It can be seen that an additional repulsive force or attractive force acting on the Dislocation will be produced for considering the interface stress and the normalized image force depends on the size of the inhomogeneity which differs from the classical solution.
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size dependent elastic interaction of a Screw Dislocation with a circular nano inhomogeneity incorporating interface stress
Scripta Materialia, 2006Co-Authors: Qihong Fang, Y.w. LiuAbstract:Effect of interface stress upon the interaction between a Screw Dislocation and a nano-inhomogeneity is investigated. By using the complex variable method, the image force acting on the Screw Dislocation is obtained. The results indicate that the influence of interface stress on the motion of the Dislocation near the inhomogeneity becomes significant when the radius of the inhomogeneity is reduced to nanometer scale, leading to that the normalized image force depends on the inhomogeneity size which differs from the size-independent classical solution.
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a piezoelectric Screw Dislocation interacting with an interphase layer between a circular inclusion and the matrix
International Journal of Solids and Structures, 2004Co-Authors: Y.w. Liu, Qihong Fang, C P JiangAbstract:Abstract The interaction of a piezoelectric Screw Dislocation with an interphase layer between the circular inclusion and the piezoelectric matrix is dealt with. An efficient method for multiplying connected region is developed by combining the sectional holomorphic function, Cauchy-type integral and Laurent series expansion techniques, in terms of which the relation among the complex potentials for the three material regions is obtained. The functional equation in complex potentials for the interphase layer is derived, resulting in explicit series solutions for the two cases when piezoelectric Screw Dislocation is located in the matrix or in the inclusion. The image force acting on the piezoelectric Screw Dislocation is calculated by using the generalized Peach–Koehler formula. Three practical cases are provided to investigate the influence of the interphase layer parameters on the image force. The present solutions contain a number of novel and previously known results which can be shown to be special cases.
