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Stephan Wojtowytsch - One of the best experts on this subject based on the ideXlab platform.
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The Effect of Forest Dislocations on the Evolution of a Phase-Field Model for Plastic Slip
Archive for Rational Mechanics and Analysis, 2019Co-Authors: Patrick W. Dondl, Matthias W. Kurzke, Stephan WojtowytschAbstract:We consider the gradient flow evolution of a phase-field model for crystal dislocations in a single slip system in the presence of forest dislocations. The model is based on a Peierls–Nabarro type energy penalizing non-integer slip and elastic stress. Forest dislocations are introduced as a perforation of the domain by small disks where slip is prohibited. The $${\Gamma}$$ Γ -limit of this energy was deduced by Garroni and Müller (SIAM J Math Anal 36(6):1943–1964, 2005 , Arch Ration Mech Anal 181(3):535–578, 2006 ). Our main result shows that the gradient flows of these $${\Gamma}$$ Γ -convergent energy functionals do not approach the gradient flow of the limiting energy. Indeed, the gradient flow dynamics remains a physically reasonable model in the case of non-Monotone Loading. Our proofs rely on the construction of explicit sub- and super-solutions to a fractional Allen–Cahn equation on a flat torus or in the plane, with Dirichlet data on a union of small discs. The presence of these obstacles leads to an additional friction in the viscous evolution which appears as a stored energy in the $${\Gamma}$$ Γ -limit, but it does not act as a driving force. Extensions to related models with soft pinning and non-viscous evolutions are also discussed. In terms of physics, our results explain how in this phase field model the presence of forest dislocations still allows for plastic as opposed to only elastic deformation.
Patrick W. Dondl - One of the best experts on this subject based on the ideXlab platform.
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The Effect of Forest Dislocations on the Evolution of a Phase-Field Model for Plastic Slip
Archive for Rational Mechanics and Analysis, 2019Co-Authors: Patrick W. Dondl, Matthias W. Kurzke, Stephan WojtowytschAbstract:We consider the gradient flow evolution of a phase-field model for crystal dislocations in a single slip system in the presence of forest dislocations. The model is based on a Peierls–Nabarro type energy penalizing non-integer slip and elastic stress. Forest dislocations are introduced as a perforation of the domain by small disks where slip is prohibited. The $${\Gamma}$$ Γ -limit of this energy was deduced by Garroni and Müller (SIAM J Math Anal 36(6):1943–1964, 2005 , Arch Ration Mech Anal 181(3):535–578, 2006 ). Our main result shows that the gradient flows of these $${\Gamma}$$ Γ -convergent energy functionals do not approach the gradient flow of the limiting energy. Indeed, the gradient flow dynamics remains a physically reasonable model in the case of non-Monotone Loading. Our proofs rely on the construction of explicit sub- and super-solutions to a fractional Allen–Cahn equation on a flat torus or in the plane, with Dirichlet data on a union of small discs. The presence of these obstacles leads to an additional friction in the viscous evolution which appears as a stored energy in the $${\Gamma}$$ Γ -limit, but it does not act as a driving force. Extensions to related models with soft pinning and non-viscous evolutions are also discussed. In terms of physics, our results explain how in this phase field model the presence of forest dislocations still allows for plastic as opposed to only elastic deformation.
Matthias W. Kurzke - One of the best experts on this subject based on the ideXlab platform.
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The Effect of Forest Dislocations on the Evolution of a Phase-Field Model for Plastic Slip
Archive for Rational Mechanics and Analysis, 2019Co-Authors: Patrick W. Dondl, Matthias W. Kurzke, Stephan WojtowytschAbstract:We consider the gradient flow evolution of a phase-field model for crystal dislocations in a single slip system in the presence of forest dislocations. The model is based on a Peierls–Nabarro type energy penalizing non-integer slip and elastic stress. Forest dislocations are introduced as a perforation of the domain by small disks where slip is prohibited. The $${\Gamma}$$ Γ -limit of this energy was deduced by Garroni and Müller (SIAM J Math Anal 36(6):1943–1964, 2005 , Arch Ration Mech Anal 181(3):535–578, 2006 ). Our main result shows that the gradient flows of these $${\Gamma}$$ Γ -convergent energy functionals do not approach the gradient flow of the limiting energy. Indeed, the gradient flow dynamics remains a physically reasonable model in the case of non-Monotone Loading. Our proofs rely on the construction of explicit sub- and super-solutions to a fractional Allen–Cahn equation on a flat torus or in the plane, with Dirichlet data on a union of small discs. The presence of these obstacles leads to an additional friction in the viscous evolution which appears as a stored energy in the $${\Gamma}$$ Γ -limit, but it does not act as a driving force. Extensions to related models with soft pinning and non-viscous evolutions are also discussed. In terms of physics, our results explain how in this phase field model the presence of forest dislocations still allows for plastic as opposed to only elastic deformation.
Wojtowytsch Stephan - One of the best experts on this subject based on the ideXlab platform.
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The effect of forest dislocations on the evolution of a phase-field model for plastic slip
'Springer Science and Business Media LLC', 2019Co-Authors: Kurzke Matthias, Dondl Patrick, Wojtowytsch StephanAbstract:We consider the gradient flow evolution of a phase-field model for crystal dislocations in a single slip system in the presence of forest dislocations. The model is based on a Peierls-Nabarro type energy penalizing non-integer slip and elastic stress. Forest dislocations are introduced as a perforation of the domain by small disks where slip is prohibited. The Γ-limit of this energy was deduced by Garroni and Müller (2005 and 2006). Our main result shows that the gradient flows of these Γ-convergent energy functionals do not approach the gradient flow of the limiting energy. Indeed, the gradient flow dynamics remains a physically reasonable model in the case of non-Monotone Loading. Our proofs rely on the construction of explicit sub- and super-solutions to a fractional Allen-Cahn equation on a flat torus or in the plane, with Dirichlet data on a union of small discs. The presence of these obstacles leads to an additional friction in the viscous evolution which appears as a stored energy in the Γ-limit, but it does not act as a driving force. Extensions to related models with soft pinning and non-viscous evolutions are also discussed. In terms of physics, our results explain how in this phase field model the presence of forest dislocations still allows for plastic as opposed to only elastic deformation
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The Effect of Forest Dislocations on the Evolution of a Phase-Field Model for Plastic Slip
'Springer Science and Business Media LLC', 2017Co-Authors: Dondl, Patrick W., Kurzke, Matthias W., Wojtowytsch StephanAbstract:We consider the gradient flow evolution of a phase-field model for crystal dislocations in a single slip system in the presence of forest dislocations. The model consists of a Peierls-Nabarro type energy penalizing non-integer slip and elastic stress. Forest dislocations are introduced as a perforation of the domain by small disks where slip is prohibited. The $\Gamma$-limit of this energy was deduced by Garroni and M\"uller (2005 and 2006). Our main result shows that the gradient flows of these $\Gamma$-convergent energy functionals do not approach the gradient flow of the limiting energy. Indeed, the gradient flow dynamics remains a physically reasonable model in the case of non-Monotone Loading. Our proofs rely on the construction of explicit sub- and super-solutions to a fractional Allen-Cahn equation on a flat torus or in the plane, with Dirichlet data on a union of small discs. The presence of these obstacles leads to an additional friction in the viscous evolution which appears as a stored energy in the $\Gamma$-limit, but it does not act as a driving force. Extensions to related models with soft pinning and non-viscous evolutions are also discussed. In terms of physics, our results explain how in this phase field model the presence of forest dislocations still allows for plastic as opposed to only elastic deformation
Yasushi Miyano - One of the best experts on this subject based on the ideXlab platform.
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Prediction of Fatigue Life of a Conical Shaped Joint System for Fiber Reinforced Plastics under Arbitrary Frequency, Load Ratio and Temperature
Mechanics of Time-Dependent Materials, 1997Co-Authors: Yasushi Miyano, Masayuki Nakada, R. MukiAbstract:A prediction method for the fatigue life of polymercomposites under arbitrary frequency, load ratio andtemperature was extended to that of polymer compositestructures. The method is based upon fourhypotheses: (a) the same mechanism applies to static,creep and fatigue failure, (b) the same time-temperaturesuperposition principle holds for all failure loads, (c) thelinear cumulative damage law applies to Monotone Loading, and(d) there exists a linear dependence of fatigue failure load uponload ratio. The tensile tests of a conically shapedjoint system for fiber reinforced plastics (FRP joint)for static, creep and fatigue Loadings were conductedat various temperatures. The validity of theproposed method and the applicability of thehypotheses for this FRP joint are discussed.
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Time and temperature dependence on the flexural fatigue strength in the transverse direction of unidirectional CFRP
International Conference on Experimental Mechanics: Advances and Applications, 1997Co-Authors: Masakazu Nakada, M. Maeda, T. Hirohata, M. Morita, Yasushi MiyanoAbstract:A prediction method of fatigue strength of polymer composites for an arbitrary frequency, stress ratio and temperature was proposed. The method is based upon the four hypotheses, (A) same failure mechanism for static, creep and fatigue failure, (b) same time-temperature superposition principle for all failure strengths, (C) linear cumulative damage law for Monotone Loading and (D) linear dependence of fatigue strength upon stress ratio. Flexural static, creep and fatigue tests at various temperatures were conducted in the transverse direction of two kinds of unidirectional CFRP laminates, which are T300/2500 and T300/PEEK. The validity of the prediction method and the applicability of the hypotheses for the flexural fatigue strength in the transverse direction of unidirectional CFRP laminates were discussed.