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Nina Orlovskaya - One of the best experts on this subject based on the ideXlab platform.
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measurement of scratch induced residual stress within sic grains in zrb2 sic composite using micro raman spectroscopy
Acta Materialia, 2008Co-Authors: Dipankar Ghosh, Ghatu Subhash, Nina OrlovskayaAbstract:An analytical framework for determination of scratch-induced residual stress within SiC grains of ZrB2–SiC composite is developed. Using a ‘‘secular equation” that relates strain to Raman-peak shift for zinc-blende structures and the concept of sliding blister field model for scratch-induced residual stress, explicit expressions are derived for residual stress calculation in terms of phonon deformation potentials and Raman peak shift. It is determined that, in the as-processed composite, thermal expansion coefficient mismatch between ZrB2 and SiC induces compressive residual stress of 1.731 GPa within the SiC grains and a tensile tangential stress of 1.126 GPa at the ZrB2– SiC interfaces. With increasing scratch loads, the residual stress within the SiC grains becomes tensile and increases in magnitude with scratch load. At a scratch load of 250 mN, the calculated residual stress in SiC was 2.6 GPa. Despite this high value, no fracture was observed in SiC grains, which has been rationalized based on fracture strength calculations from Griffith Theory.
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Measurement of scratch-induced residual stress within SiC grains in ZrB2–SiC composite using micro-Raman spectroscopy
Acta Materialia, 2008Co-Authors: Dipankar Ghosh, Ghatu Subhash, Nina OrlovskayaAbstract:An analytical framework for determination of scratch-induced residual stress within SiC grains of ZrB2–SiC composite is developed. Using a ‘‘secular equation” that relates strain to Raman-peak shift for zinc-blende structures and the concept of sliding blister field model for scratch-induced residual stress, explicit expressions are derived for residual stress calculation in terms of phonon deformation potentials and Raman peak shift. It is determined that, in the as-processed composite, thermal expansion coefficient mismatch between ZrB2 and SiC induces compressive residual stress of 1.731 GPa within the SiC grains and a tensile tangential stress of 1.126 GPa at the ZrB2– SiC interfaces. With increasing scratch loads, the residual stress within the SiC grains becomes tensile and increases in magnitude with scratch load. At a scratch load of 250 mN, the calculated residual stress in SiC was 2.6 GPa. Despite this high value, no fracture was observed in SiC grains, which has been rationalized based on fracture strength calculations from Griffith Theory.
Dipankar Ghosh - One of the best experts on this subject based on the ideXlab platform.
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measurement of scratch induced residual stress within sic grains in zrb2 sic composite using micro raman spectroscopy
Acta Materialia, 2008Co-Authors: Dipankar Ghosh, Ghatu Subhash, Nina OrlovskayaAbstract:An analytical framework for determination of scratch-induced residual stress within SiC grains of ZrB2–SiC composite is developed. Using a ‘‘secular equation” that relates strain to Raman-peak shift for zinc-blende structures and the concept of sliding blister field model for scratch-induced residual stress, explicit expressions are derived for residual stress calculation in terms of phonon deformation potentials and Raman peak shift. It is determined that, in the as-processed composite, thermal expansion coefficient mismatch between ZrB2 and SiC induces compressive residual stress of 1.731 GPa within the SiC grains and a tensile tangential stress of 1.126 GPa at the ZrB2– SiC interfaces. With increasing scratch loads, the residual stress within the SiC grains becomes tensile and increases in magnitude with scratch load. At a scratch load of 250 mN, the calculated residual stress in SiC was 2.6 GPa. Despite this high value, no fracture was observed in SiC grains, which has been rationalized based on fracture strength calculations from Griffith Theory.
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Measurement of scratch-induced residual stress within SiC grains in ZrB2–SiC composite using micro-Raman spectroscopy
Acta Materialia, 2008Co-Authors: Dipankar Ghosh, Ghatu Subhash, Nina OrlovskayaAbstract:An analytical framework for determination of scratch-induced residual stress within SiC grains of ZrB2–SiC composite is developed. Using a ‘‘secular equation” that relates strain to Raman-peak shift for zinc-blende structures and the concept of sliding blister field model for scratch-induced residual stress, explicit expressions are derived for residual stress calculation in terms of phonon deformation potentials and Raman peak shift. It is determined that, in the as-processed composite, thermal expansion coefficient mismatch between ZrB2 and SiC induces compressive residual stress of 1.731 GPa within the SiC grains and a tensile tangential stress of 1.126 GPa at the ZrB2– SiC interfaces. With increasing scratch loads, the residual stress within the SiC grains becomes tensile and increases in magnitude with scratch load. At a scratch load of 250 mN, the calculated residual stress in SiC was 2.6 GPa. Despite this high value, no fracture was observed in SiC grains, which has been rationalized based on fracture strength calculations from Griffith Theory.
Ghatu Subhash - One of the best experts on this subject based on the ideXlab platform.
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measurement of scratch induced residual stress within sic grains in zrb2 sic composite using micro raman spectroscopy
Acta Materialia, 2008Co-Authors: Dipankar Ghosh, Ghatu Subhash, Nina OrlovskayaAbstract:An analytical framework for determination of scratch-induced residual stress within SiC grains of ZrB2–SiC composite is developed. Using a ‘‘secular equation” that relates strain to Raman-peak shift for zinc-blende structures and the concept of sliding blister field model for scratch-induced residual stress, explicit expressions are derived for residual stress calculation in terms of phonon deformation potentials and Raman peak shift. It is determined that, in the as-processed composite, thermal expansion coefficient mismatch between ZrB2 and SiC induces compressive residual stress of 1.731 GPa within the SiC grains and a tensile tangential stress of 1.126 GPa at the ZrB2– SiC interfaces. With increasing scratch loads, the residual stress within the SiC grains becomes tensile and increases in magnitude with scratch load. At a scratch load of 250 mN, the calculated residual stress in SiC was 2.6 GPa. Despite this high value, no fracture was observed in SiC grains, which has been rationalized based on fracture strength calculations from Griffith Theory.
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Measurement of scratch-induced residual stress within SiC grains in ZrB2–SiC composite using micro-Raman spectroscopy
Acta Materialia, 2008Co-Authors: Dipankar Ghosh, Ghatu Subhash, Nina OrlovskayaAbstract:An analytical framework for determination of scratch-induced residual stress within SiC grains of ZrB2–SiC composite is developed. Using a ‘‘secular equation” that relates strain to Raman-peak shift for zinc-blende structures and the concept of sliding blister field model for scratch-induced residual stress, explicit expressions are derived for residual stress calculation in terms of phonon deformation potentials and Raman peak shift. It is determined that, in the as-processed composite, thermal expansion coefficient mismatch between ZrB2 and SiC induces compressive residual stress of 1.731 GPa within the SiC grains and a tensile tangential stress of 1.126 GPa at the ZrB2– SiC interfaces. With increasing scratch loads, the residual stress within the SiC grains becomes tensile and increases in magnitude with scratch load. At a scratch load of 250 mN, the calculated residual stress in SiC was 2.6 GPa. Despite this high value, no fracture was observed in SiC grains, which has been rationalized based on fracture strength calculations from Griffith Theory.
Jean-jacques Marigo - One of the best experts on this subject based on the ideXlab platform.
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Variational Approach to Dynamic Brittle Fracture via Gradient Damage Models
2015Co-Authors: Jean-jacques Marigo, Daniel Guilbaud, Serguei PotapovAbstract:In this paper we present a family of gradient-enhanced continuum damage models which can be viewed as a regularization of the variational approach to fracture capable of predicting in a unified framework the onset and space-time dynamic propagation (growth, kinking, branching, arrest) of complex cracks in quasi-brittle materials under severe dynamic loading. The dynamic evolution problem for a general class of such damage models is formulated as a variational inequality involving the action integral of a generalized Lagrangian and its physical interpretation is given. Finite-element based implementation is then detailed and mathematical optimization methods are directly used at the structural scale exploiting fully the variational nature of the formulation. Finally, the link with the classical dynamic Griffith Theory and with the original quasi-static model as well as various dynamic fracture phenomena are illustrated by representative numerical examples in quantitative accordance with theoretical or experimental results.
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Application of the Dugdale model to a mixed mode loading of a semi infinite cracked structure
European Journal of Mechanics - A Solids, 2015Co-Authors: Hicheme Ferdjani, Jean-jacques MarigoAbstract:The Dugdale model was initially developed in the case of a mode I loading. It was extended to other modes and to the mixed mode case. The exact solutions were given for all these modes in the case of an infinite medium with a straight crack. This work is an application of the Dugdale model to a crack in a semi infinite structure submitted to a mixed mode loading. The coupled system of singular integral equations of the first kind corresponding to the elastostatic problem is solved semi-analytically. Particular attention is needed in the resolution because of jump discontinuities in the loading of the crack faces. The criteria of propagation are deduced from the revisited Griffith Theory (G. Francfort, J-J. Marigo, Journal of Mechanics and Physics of Solids (1998) 46:8 1319-1342). The presented results show the evolution of the applied load and critical stress with the crack length. The shape of the crack gap is also presented. A comparison with the problem of a crack in an infinite structure is performed.
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Damage localization and rupture with gradient damage models
Frattura ed Integrità Strutturale Fracture and Structural Integrity, 2012Co-Authors: Kim Pham, Jean-jacques MarigoAbstract:We propose a method of construction of non homogeneous solutions to the problem of traction of a bar made of an elastic-damaging material whose softening behavior is regularized by a gradient damage model. We show that, for sufficiently long bars, localization arises on sets whose length is proportional to the material internal length and with a profile which is also characteristic of the material. The rupture of the bar occurs at the center of the localization zone when the damage reaches there the critical value corresponding to the loss of rigidity of the material. The dissipated energy during all the damage process up to rupture is a quantity c G which can be expressed in terms of the material parameters. Accordingly, Gc can be considered as the usual surface energy density appearing in the Griffith Theory of brittle fracture. All these theoretical considerations are illustrated by numerical examples.
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Griffith Theory of brittle fracture revisited merits and drawbacks
Latin American Journal of Solids and Structures, 2005Co-Authors: Gilles A Francfort, Jean-jacques MarigoAbstract:A VARIATIONAL REFORMULATION OF GRI±TH'S Theory OF BRITTLE FRACTURE IS PROPOSED. AT THE EXPENSE OF A SLIGHT DEPARTURE FROM THE CLASSICAL Theory, THE NEW FORMULATION DECISIVELY ADDRESSES THREE MAJOR ISSUES: CRACK INITIATION, CRACK PATH, AND SMOOTHNESS OF THE CRACK EVOLUTION. THE NEW FORMULATION IS AMENABLE TO NUMERICAL IMPLEMENTATION; A SIMULATION QUALITATIVELY IN AGREEMENT WITH EXPERIMENTAL DATA IS PRESENTED. THAT COMPUTATION IS WELL BEYOND THE SCOPE OF THE CLASSICAL Theory AND DEMONSTRATES THE °EXIBILITY OF THE APPROACH. EXTENSIONS OF THE FORMULATION THAT CURE THE WEAKNESSES OF THE PROPOSED MODEL ARE SUGGESTED. IN THIS SHORT PAPER, WE ¯RST BRIE°Y DESCRIBE IN SECTION 1 THE VARIATIONAL FORMULATION THAT WE PROPOSE FOR QUASISTATIC BRITTLE FRACTURE EVOLUTION. OUR FORMULATION IS VERY CLOSE TO THE SPIRIT OF GRI±TH'S APPROACH TO BRITTLE FRACTURE [11], AND ONLY SLIGHTLY DEPARTS FROM THE CLASSICAL Theory. IN SECTION 2, WE PRESENT A COMPUTATION THAT ILLUSTRATES THE REACH OF THE MODEL. FINALLY, SECTION 3 ZEROES IN ON THE DRAWBACKS OF THE FORMULATION AND ON POSSIBLE REMEDIES; IT FOCUSSES ON THE USE OF OTHER SURFACE ENERGIES.
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Griffith Theory Revisited
Multiscale Modeling in Continuum Mechanics and Structured Deformations, 2004Co-Authors: Jean-jacques MarigoAbstract:Throughout the section, Ω denotes a bounded connected open domain of ℝ N , 1 ≤N ≤3, with smooth boundary ∂Ω the surface measure of which is finite and such that Ω is the interior of \(\bar \Omega \). As such, Ω represents the crack-free reference configuration of an elastic body.
Marigo Jean-jacques - One of the best experts on this subject based on the ideXlab platform.
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Dugdale model applied to a mixed mode loading of a semi infinite cracked structure
AFM Association Française de Mécanique, 2015Co-Authors: Ferdjani Hicheme, Marigo Jean-jacquesAbstract:The Dugdale model was initially developed in the case of {a} mode I loading. It was extended to other modes and to {the} mixed mode case. The exact solutions were given for all these modes in the case of an infinite medium with a straight crack. This work is an application of the Dugdale model to a crack in a semi infinite structure submitted to a mixed mode loading. The coupled system of singular integral equations of the first kind corresponding to the {elastostatic} problem is solved semi-analytically. Particular attention is needed in the resolution because of jump discontinuities in the loading of the crack faces. The criteria of propagation are deduced {from} the revisited Griffith Theory (G. Francfort, J-J. Marigo, Journal of Mechanics and Physics of Solids(1998) 46:8 1319-1342). The presented results show the evolution of the {applied load and critical stress with the crack length}. {The shape of the crack gap is also presented}. A comparison with the problem of a crack in an infinite structure is performe
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Application of the Dugdale model to a mixed mode loading of a semi infinite cracked structure
'Elsevier BV', 2015Co-Authors: Ferdjani Hicheme, Marigo Jean-jacquesAbstract:International audienceThe Dugdale model was initially developed in the case of a mode I loading. It was extended to other modes and to the mixed mode case. The exact solutions were given for all these modes in the case of an infinite medium with a straight crack. This work is an application of the Dugdale model to a crack in a semi infinite structure submitted to a mixed mode loading. The coupled system of singular integral equations of the first kind corresponding to the elastostatic problem is solved semi-analytically. Particular attention is needed in the resolution because of jump discontinuities in the loading of the crack faces. The criteria of propagation are deduced from the revisited Griffith Theory (G. Francfort, J-J. Marigo, Journal of Mechanics and Physics of Solids (1998) 46:8 1319-1342). The presented results show the evolution of the applied load and critical stress with the crack length. The shape of the crack gap is also presented. A comparison with the problem of a crack in an infinite structure is performed
