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S P Vyatchanin - One of the best experts on this subject based on the ideXlab platform.
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parametric Oscillatory Instability in gravitational wave laser detectors
Physics-Uspekhi, 2012Co-Authors: S P Vyatchanin, S. E. StriginAbstract:The nonlinear effect of parametric Oscillatory Instability in the gravitational wave laser detector (antenna) is considered as a factor that considerably reduces the sensitivity of the device. It is shown that in an antenna with a circulating power above a certain threshold value, excitation of Stokes optical modes occurs in Fabry-Perot resonators and of test mass elastic modes. Parametric Oscillatory Instability in gravitational wave interferometers of the second (LIGO, Virgo, LCGT, GEO-600) and third (ET — Einstein Telescope) generation with different types of pumps is examined. The effect discussed has been observed not only in gravitational wave laser interferometers, but also many times in other opto-mechanical systems. All current methods for suppressing parametric Oscillatory Instability in gravitational wave interferometers are also discussed, both passive and active.
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analysis of parametric Oscillatory Instability in fabry perot cavity with gauss and laguerre gauss main mode profile
Physics Letters A, 2010Co-Authors: S. E. Strigin, S P VyatchaninAbstract:Abstract We calculate the parametric instabilities in Fabry–Perot cavities of advanced VIRGO and LIGO interferometers with different main mode profiles. All unstable combinations of elastic and Stokes modes both for the case with TEM 00 and LG 33 as a carriers are deduced.
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numerical calculations of elastic modes frequencies for parametric Oscillatory Instability in advanced ligo interferometer
Physics Letters A, 2008Co-Authors: S Strigin, D G Blair, S Gras, S P VyatchaninAbstract:Abstract We discuss the importance of accurate numerical calculation of elastic modes in the mirrors of Advanced LIGO to enable precise predictions of the problem of parametric Oscillatory Instability. We propose accuracy estimations through use of analytical solutions based on Chree–Lamb modes. Small deviations from cylindrical test mass shape may produce splitting of non-axial symmetric elastic modes into doublets. This splitting may increase the possibility of parametric Oscillatory Instability.
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parametric Oscillatory Instability in ligo interferometer
Proceedings of SPIE the International Society for Optical Engineering, 2008Co-Authors: V B Braginsky, S. E. Strigin, S P VyatchaninAbstract:We present the analysis of a nonlinear effect of parametric Oscillatory Instability in power recycled LIGO interferometer with Fabry-Perot cavities in the arms. The basis for this effect is the excitation of the additional Stokes optical mode and the mirror elastic mode when the optical energy stored in the main Fabry-Perot cavity mode exceeds the certain threshold. We demonstrate that in the resonance case the parametric Oscillatory Instability will take place at the energy stored in the cavity of about five orders smaller than one planned for LIGO-II interferometer. The presence of anti-Stokes modes can depress parametric Oscillatory Instability. However, it is very likely that the anti-Stokes modes will not compensate the parametric Oscillatory Instability completely because of the existence of the mode combinations which interact with each other quite strongly.
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precursors of parametric Oscillatory Instability in ligo interferometer
JENAM-2007 "Our Non-Stable Universe", 2007Co-Authors: Ilya A Polyakov, S P VyatchaninAbstract:Abstract The basis of undesirable effect of parametric Oscillatory Instability in optical interferometer is provided by excitation of the additional (Stokes) optical mode having frequency ω 1 , and the mirror elastic mode, having frequency ω m . It appears when optical energy stored in the main mode, with frequency ω 0 , exceeds a certain threshold and the frequencies are related as ω 0 ≃ ω 1 + ω m . We analyze the time evolution of parametric Instability which allows predicting the characteristics of precursors of parametric Instability. Observation of such precursors may help avoid parametric Instability.
S. E. Strigin - One of the best experts on this subject based on the ideXlab platform.
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parametric Oscillatory Instability in gravitational wave laser detectors
Physics-Uspekhi, 2012Co-Authors: S P Vyatchanin, S. E. StriginAbstract:The nonlinear effect of parametric Oscillatory Instability in the gravitational wave laser detector (antenna) is considered as a factor that considerably reduces the sensitivity of the device. It is shown that in an antenna with a circulating power above a certain threshold value, excitation of Stokes optical modes occurs in Fabry-Perot resonators and of test mass elastic modes. Parametric Oscillatory Instability in gravitational wave interferometers of the second (LIGO, Virgo, LCGT, GEO-600) and third (ET — Einstein Telescope) generation with different types of pumps is examined. The effect discussed has been observed not only in gravitational wave laser interferometers, but also many times in other opto-mechanical systems. All current methods for suppressing parametric Oscillatory Instability in gravitational wave interferometers are also discussed, both passive and active.
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Parametric Oscillatory Instability in Fabry-Perot cavity with Gauss and Laguerre-Gauss pumping mode profiles
Gravitation and Cosmology, 2011Co-Authors: S. E. Strigin, Sergey P. VyatchaninAbstract:Parametric instabilities are calculated in the Fabry-Perot cavities of the gravitational-wave interferometers Advanced VIRGO and LIGO with Gauss and Laguerre-Gauss main mode profiles. We have revealed all unstable combinations of the elastic and Stokes’ optical modes for both the optical pumping mode TEM00 and for the Laguerre-Gauss pumping mode LG33.
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analysis of parametric Oscillatory Instability in fabry perot cavity with gauss and laguerre gauss main mode profile
Physics Letters A, 2010Co-Authors: S. E. Strigin, S P VyatchaninAbstract:Abstract We calculate the parametric instabilities in Fabry–Perot cavities of advanced VIRGO and LIGO interferometers with different main mode profiles. All unstable combinations of elastic and Stokes modes both for the case with TEM 00 and LG 33 as a carriers are deduced.
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parametric Oscillatory Instability in ligo interferometer
Proceedings of SPIE the International Society for Optical Engineering, 2008Co-Authors: V B Braginsky, S. E. Strigin, S P VyatchaninAbstract:We present the analysis of a nonlinear effect of parametric Oscillatory Instability in power recycled LIGO interferometer with Fabry-Perot cavities in the arms. The basis for this effect is the excitation of the additional Stokes optical mode and the mirror elastic mode when the optical energy stored in the main Fabry-Perot cavity mode exceeds the certain threshold. We demonstrate that in the resonance case the parametric Oscillatory Instability will take place at the energy stored in the cavity of about five orders smaller than one planned for LIGO-II interferometer. The presence of anti-Stokes modes can depress parametric Oscillatory Instability. However, it is very likely that the anti-Stokes modes will not compensate the parametric Oscillatory Instability completely because of the existence of the mode combinations which interact with each other quite strongly.
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Parametric Oscillatory Instability in a signal-recycled LIGO interferometer
Quantum Electronics, 2007Co-Authors: Sergey P. Vyatchanin, S. E. StriginAbstract:The undesirable effect of parametric Oscillatory Instability in a LIGO (Laser Interferometer Gravitational-Wave Observatory) laser gravitational-wave antenna with a signal-recirculation mirror is analysed in detail. The Instability is manifested in excitation of the Stokes optical mode and elastic mechanical mode of the mirror. It is shown that, if the eigenfrequencies of Fabry-Perot resonators in the interferometer arms are different, the parametric Instability is quite small due to a small passband band width. (fifth seminar in memory of d.n. klyshko)
Eran Bouchbinder - One of the best experts on this subject based on the ideXlab platform.
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Oscillatory and tip splitting instabilities in 2d dynamic fracture the roles of intrinsic material length and time scales
Journal of The Mechanics and Physics of Solids, 2021Co-Authors: Aditya Vasudevan, Eran Bouchbinder, Yuri Lubomirsky, Chihhung Chen, Alain KarmaAbstract:Abstract Recent theoretical and computational progress has led to unprecedented understanding of symmetry-breaking instabilities in 2D dynamic fracture. At the heart of this progress resides the identification of two intrinsic, near crack tip length scales — a nonlinear elastic length scale l and a dissipation length scale ξ — that do not exist in Linear Elastic Fracture Mechanics (LEFM), the classical theory of cracks. In particular, it has been shown that at a propagation velocity v of about 90% of the shear wave-speed, cracks in 2D brittle materials undergo an Oscillatory Instability whose wavelength varies linearly with l , and at larger loading levels (corresponding to yet higher propagation velocities), a tip-splitting Instability emerges, both in agreements with experiments. In this paper, using phase-field models of brittle fracture, we demonstrate the following properties of the Oscillatory Instability: (i) It exists also in the absence of near-tip elastic nonlinearity, i.e. in the limit l → 0 , with a wavelength determined by the dissipation length scale ξ . This result shows that the Instability crucially depends on the existence of an intrinsic length scale associated with the breakdown of linear elasticity near crack tips, independently of whether the latter is related to nonlinear elasticity or to dissipation. (ii) It is a supercritical Hopf bifurcation, featuring a vanishing oscillations amplitude at onset. (iii) It is largely independent of the phenomenological forms of the degradation functions assumed in the phase-field framework to describe the cohesive zone, and of the velocity-dependence of the fracture energy Γ ( v ) that is controlled by the dissipation time scale in the Ginzburg-Landau-type evolution equation for the phase-field. These results substantiate the universal nature of the Oscillatory Instability in 2D. In addition, we provide evidence indicating that the tip-splitting Instability is controlled by the limiting rate of elastic energy transport inside the crack tip region. The latter is sensitive to the wave-speed inside the dissipation zone, which can be systematically varied within the phase-field approach. Finally, we describe in detail the numerical implementation scheme of the employed phase-field fracture approach, allowing its application in a broad range of materials failure problems.
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Oscillatory and tip splitting instabilities in 2d dynamic fracture the roles of intrinsic material length and time scales
arXiv: Materials Science, 2020Co-Authors: Aditya Vasudevan, Eran Bouchbinder, Yuri Lubomirsky, Chihhung Chen, Alain KarmaAbstract:Recent theoretical and computational progress has led to unprecedented understanding of symmetry-breaking instabilities in 2D dynamic fracture. At the heart of this progress resides the identification of two intrinsic, near crack tip length scales -- a nonlinear elastic length scale $\ell$ and a dissipation length scale $\xi$ -- that do not exist in the classical theory of cracks. In particular, it has been shown that at a high propagation velocity $v$, cracks in 2D brittle materials undergo an Oscillatory Instability whose wavelength varies linearly with $\ell$, and at yet higher propagation velocities and larger loading levels, a tip-splitting Instability emerges, both in agreements with experiments. In this paper, using phase-field models of brittle fracture, we demonstrate the following properties of the Oscillatory Instability: (i) It exists also in the absence of near-tip elastic nonlinearity, i.e. in the limit $\ell\!\to\!0$, with a wavelength determined by the dissipation length scale $\xi$. This result shows that the Instability crucially depends on the existence of an intrinsic length scale associated with the breakdown of linear elasticity near crack tips, independently of whether the latter is related to nonlinear elasticity or to dissipation. (ii) It is a supercritical Hopf bifurcation, featuring a vanishing oscillations amplitude at onset. (iii) It is largely independent of the fracture energy $\Gamma(v)$ that is controlled by a dissipation time scale. These results substantiate the universal nature of the Oscillatory Instability of ultra-high speed cracks in 2D. In addition, we provide evidence indicating that the ultra-high velocity tip-splitting Instability is controlled by the limiting rate of elastic energy transport inside the crack tip region. Finally, we describe in detail the numerical implementation scheme of the employed phase-field fracture approach.
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Instability in dynamic fracture and the failure of the classical theory of cracks
Nature Physics, 2017Co-Authors: Chihhung Chen, Eran Bouchbinder, Alain KarmaAbstract:Cracks, the major vehicle for material failure^ 1 , undergo a micro-branching Instability at ∼40% of their sonic limiting velocity in three dimensions^ 2 , 3 , 4 , 5 , 6 . Recent experiments showed that in thin systems cracks accelerate to nearly their limiting velocity without micro-branching, until undergoing an Oscillatory Instability^ 7 , 8 . Despite their fundamental importance, these dynamic instabilities are not explained by the classical theory of cracks^ 1 , which is based on linear elasticity and an extraneous local symmetry criterion to predict crack paths^ 9 . We develop a two-dimensional theory for predicting arbitrary paths of ultrahigh-speed cracks, which incorporates elastic nonlinearity without extraneous criteria. We show that cracks undergo an Oscillatory Instability controlled by small-scale, near crack-tip, elastic nonlinearity. This Instability occurs above an ultrahigh critical velocity and features an intrinsic wavelength proportional to the ratio of the fracture energy to the elastic modulus, in quantitative agreement with experiments. This ratio emerges as a fundamental scaling length assumed to play no role in the classical theory of cracks, but shown here to strongly influence crack dynamics. Understanding crack formation is important for improving the mechanical performance of materials. A new theory is now presented for the description of cracks propagating at high speeds, with elastic nonlinearity as the underlying principle.
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dynamic crack tip equation of motion high speed Oscillatory Instability
Physical Review Letters, 2009Co-Authors: Eran BouchbinderAbstract:A dynamic crack tip equation of motion is proposed based on the autonomy of the near-tip nonlinear zone of scale 'nl, symmetry principles, causality, and scaling arguments. Causality implies that the asymptotic linear-elastic fields at time t are determined by the crack path at a retarded time t � � d, where the delay timed scales with the ratio of 'nl and the typical wave speed cnl within the nonlinear zone. The resulting equation is shown to agree with known results in the quasistatic regime. As a first application in the fully dynamic regime, an approximate analysis predicts a high-speed Oscillatory Instability whose characteristic scale is determined by 'nl. This prediction is corroborated by experimental results, demonstrating the emergence of crack tip inertialike effects. Introduction.—Fundamental puzzles in the dynamic fracture of brittle materials remain unresolved mainly due to the lack of a well-established equation of motion for a crack's tip. The study of dynamic fracture has focused on the central idea of linear-elastic energy flowing into the crack tip nonlinear and dissipative zone (1,2). While this approach is successful in determining the crack growth rate when its path is known a priori, it is fundamentally defi- cient in the general and most interesting case in which the crack's path is selected dynamically (e.g., instabilities (2,3)), without being supplemented with a path selection rule. This long-standing problem hampers the development of a predictive and complete theory of dynamic fracture. In this Letter we propose a dynamic crack tip equation of motion for isotropic materials under plane deformation, based on rather general physical considerations. A basic starting point is the concept of the autonomy of the crack tip nonlinear zone in the canonical theory of fracture, linear-elastic fracture mechanics (LEFM) (1). The idea is that the mechanical state within the small near-tip non- linear zone of scale 'nl (''inner problem''), where LEFM breaks down, is uniquely determined by the asymptotic linear-elastic fields surrounding it (''outer problem''), but is otherwise independent of the applied loadings and the geometric configuration (e.g., crack path) in a given prob- lem. Therefore, the near-tip nonlinear zone is coupled to the applied loadings and the geometric configuration through the asymptotic linear-elastic fields and the crack tip itself evolves according to the dynamics within the near-tip nonlinear zone. What role then plays the near- tip nonlinear zone in determining the path selected by a crack tip? The main idea of this Letter is that in the presence of a finite nonlinear near-tip zone, causality implies that the asymptotic linear-elastic fields at a given time t, which control the crack tip motion at that time, are determined by the crack path at a retarded time t � � d, where the delay timed scales with the ratio of 'nl and the typical wave speed cnl within the nonlinear zone. That is, we propose that the only essential properties of the near-tip nonlinear zone are its size 'nl and its typical wave speed cnl, and that these appear in a macroscopic continuum theory mainly through their causal effect. This physical effect is missing in LEFM since its basic tenet is that the nonlinear near-tip zone acts as an energy sink, but otherwise 'nl ! 0 can be assumed. The mathematical formulation of these ideas leads to a simple, continuum level, dynamic equation of motion for a crack's tip. This equation agrees with the well-known ''principle of local symmetry'' (4) in the quasistatic limit, but is shown to have novel implications in the fully dy- namic regime. As an example, we perform an approximate linear stability analysis of rapid mode I cracks. It predicts the existence of a spontaneous symmetry breaking, high- speed Oscillatory Instability whose characteristic scale is determined by 'nl. Using the recently developed weakly nonlinear dynamic fracture theory (5-7) to estimate 'nl, this prediction is shown to agree well with recent experi- ments (3). These results explicitly demonstrate the impor- tance of the length scale 'nl at high propagation speeds, as well as the emergence of crack tip inertialike effects. Crack tip dynamics.—The mathematical formulation of the ideas described above follows in three steps. Consider a
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Oscillatory Instability in two dimensional dynamic fracture
Physical Review Letters, 2007Co-Authors: Eran Bouchbinder, Itamar ProcacciaAbstract:The stability of a rapid dynamic crack in a two-dimensional infinite strip is studied in the framework of linear elastic fracture mechanics supplemented with a modified principle of local symmetry. It is predicted that a single crack becomes unstable by a finite wavelength Oscillatory mode at a velocity vc, 0:8cR < vc < 0:85cR, where cR is the Rayleigh wave speed. The relevance of this theoretical calculation to the Oscillatory Instability reported in the companion experimental Letter is discussed. Introduction.—High precision experiments on dynamic fracture in slabs of amorphous materials revealed very interesting instabilities in the form of microbranching. Above a critical velocity of about 0:4c R , where c R is the Rayleigh wave speed, a single, straight, rapidly moving crack is unstable against the appearance of small diameter side branches that affect both the morphology and the velocity of propagation (1). An important observation regarding this Instability is that although experiments are typically performed on quasi-two-dimensional samples (i.e., samples for which the third dimension is significantly smaller than the other two dimensions), the Instability is intrinsically three dimensional (2,3); at the onset of insta- bility the microbranches occupy only a small fraction of the small third dimension, barely misting the mirror quality of the main crack. Nevertheless, theoretically there were a number of at- tempts to explain this Instability in the context of linear elastic fracture mechanics (LEFM) in two dimensions, where the three-dimensional experimentally observed in- stability was interpreted as a macroscopic crack bifurcation in two dimensions. It was shown that above some critical velocity such a bifurcation is allowed on energetic grounds (4), but not necessarily realized dynamically. In the experi- mental companion paper (5) it was shown that in quasi-- two-dimensional systems (thin films loaded with a fixed grip) the first Instability is actually an Oscillatory mode rather than crack bifurcation. The aim of this Letter is to show that two-dimensional LEFM predicts indeed the existence of a dynamical Oscillatory Instability. We construct a theoretical model of a semi-infinite straight crack propagating at a constant velocity in an infinitely long two-dimensional strip under fixed-grip boundary con- ditions (6). The standard framework of LEFM is supple- mented with a modified principle of local symmetry (7,8), and see below for details. The analysis is based on a recently derived solution for the linear perturbation prob- lem of the dynamic stress intensity factors using the weight functions method (6,9,10). We find that an Oscillatory mode of finite wavelength becomes unstable above a criti- cal velocity vc, 0:8cR
time t is described by
Michael D Graham - One of the best experts on this subject based on the ideXlab platform.
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a mechanism for Oscillatory Instability in viscoelastic cross slot flow
Journal of Fluid Mechanics, 2009Co-Authors: Michael D GrahamAbstract:Interior stagnation-point flows of viscoelastic liquids arise in a wide variety of applications including extensional viscometry, polymer processing and microfluidics. Experimentally, these flows have long been known to exhibit instabilities, but the mechanisms underlying them have not previously been elucidated. We computationally demonstrate the existence of a supercritical Oscillatory Instability of low-Reynolds-number viscoelastic flow in a two-dimensional cross-slot geometry. The fluctuations are closely associated with the 'birefringent strand' of highly stretched polymer chains associated with the outflow from the stagnation point at high Weissenberg number. Additionally, we describe the mechanism of Instability, which arises from the coupling of flow with extensional stresses and their steep gradients in the stagnation-point region.
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a mechanism for Oscillatory Instability in viscoelastic cross slot flow
Journal of Fluid Mechanics, 2009Co-Authors: Li Xi, Michael D GrahamAbstract:Interior stagnation-point flows of viscoelastic liquids arise in a wide variety of applications including extensional viscometry, polymer processing and microfluidics. Experimentally, these flows have long been known to exhibit instabilities, but the mechanisms underlying them have not previously been elucidated. We computationally demonstrate the existence of a supercritical Oscillatory Instability of low-Reynolds-number viscoelastic flow in a two-dimensional cross-slot geometry. The fluctuations are closely associated with the 'birefringent strand' of highly stretched polymer chains associated with the outflow from the stagnation point at high Weissenberg number. Additionally, we describe the mechanism of Instability, which arises from the coupling of flow with extensional stresses and their steep gradients in the stagnation-point region.
Alain Karma - One of the best experts on this subject based on the ideXlab platform.
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Oscillatory and tip splitting instabilities in 2d dynamic fracture the roles of intrinsic material length and time scales
Journal of The Mechanics and Physics of Solids, 2021Co-Authors: Aditya Vasudevan, Eran Bouchbinder, Yuri Lubomirsky, Chihhung Chen, Alain KarmaAbstract:Abstract Recent theoretical and computational progress has led to unprecedented understanding of symmetry-breaking instabilities in 2D dynamic fracture. At the heart of this progress resides the identification of two intrinsic, near crack tip length scales — a nonlinear elastic length scale l and a dissipation length scale ξ — that do not exist in Linear Elastic Fracture Mechanics (LEFM), the classical theory of cracks. In particular, it has been shown that at a propagation velocity v of about 90% of the shear wave-speed, cracks in 2D brittle materials undergo an Oscillatory Instability whose wavelength varies linearly with l , and at larger loading levels (corresponding to yet higher propagation velocities), a tip-splitting Instability emerges, both in agreements with experiments. In this paper, using phase-field models of brittle fracture, we demonstrate the following properties of the Oscillatory Instability: (i) It exists also in the absence of near-tip elastic nonlinearity, i.e. in the limit l → 0 , with a wavelength determined by the dissipation length scale ξ . This result shows that the Instability crucially depends on the existence of an intrinsic length scale associated with the breakdown of linear elasticity near crack tips, independently of whether the latter is related to nonlinear elasticity or to dissipation. (ii) It is a supercritical Hopf bifurcation, featuring a vanishing oscillations amplitude at onset. (iii) It is largely independent of the phenomenological forms of the degradation functions assumed in the phase-field framework to describe the cohesive zone, and of the velocity-dependence of the fracture energy Γ ( v ) that is controlled by the dissipation time scale in the Ginzburg-Landau-type evolution equation for the phase-field. These results substantiate the universal nature of the Oscillatory Instability in 2D. In addition, we provide evidence indicating that the tip-splitting Instability is controlled by the limiting rate of elastic energy transport inside the crack tip region. The latter is sensitive to the wave-speed inside the dissipation zone, which can be systematically varied within the phase-field approach. Finally, we describe in detail the numerical implementation scheme of the employed phase-field fracture approach, allowing its application in a broad range of materials failure problems.
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Oscillatory and tip splitting instabilities in 2d dynamic fracture the roles of intrinsic material length and time scales
arXiv: Materials Science, 2020Co-Authors: Aditya Vasudevan, Eran Bouchbinder, Yuri Lubomirsky, Chihhung Chen, Alain KarmaAbstract:Recent theoretical and computational progress has led to unprecedented understanding of symmetry-breaking instabilities in 2D dynamic fracture. At the heart of this progress resides the identification of two intrinsic, near crack tip length scales -- a nonlinear elastic length scale $\ell$ and a dissipation length scale $\xi$ -- that do not exist in the classical theory of cracks. In particular, it has been shown that at a high propagation velocity $v$, cracks in 2D brittle materials undergo an Oscillatory Instability whose wavelength varies linearly with $\ell$, and at yet higher propagation velocities and larger loading levels, a tip-splitting Instability emerges, both in agreements with experiments. In this paper, using phase-field models of brittle fracture, we demonstrate the following properties of the Oscillatory Instability: (i) It exists also in the absence of near-tip elastic nonlinearity, i.e. in the limit $\ell\!\to\!0$, with a wavelength determined by the dissipation length scale $\xi$. This result shows that the Instability crucially depends on the existence of an intrinsic length scale associated with the breakdown of linear elasticity near crack tips, independently of whether the latter is related to nonlinear elasticity or to dissipation. (ii) It is a supercritical Hopf bifurcation, featuring a vanishing oscillations amplitude at onset. (iii) It is largely independent of the fracture energy $\Gamma(v)$ that is controlled by a dissipation time scale. These results substantiate the universal nature of the Oscillatory Instability of ultra-high speed cracks in 2D. In addition, we provide evidence indicating that the ultra-high velocity tip-splitting Instability is controlled by the limiting rate of elastic energy transport inside the crack tip region. Finally, we describe in detail the numerical implementation scheme of the employed phase-field fracture approach.
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Instability in dynamic fracture and the failure of the classical theory of cracks
Nature Physics, 2017Co-Authors: Chihhung Chen, Eran Bouchbinder, Alain KarmaAbstract:Cracks, the major vehicle for material failure^ 1 , undergo a micro-branching Instability at ∼40% of their sonic limiting velocity in three dimensions^ 2 , 3 , 4 , 5 , 6 . Recent experiments showed that in thin systems cracks accelerate to nearly their limiting velocity without micro-branching, until undergoing an Oscillatory Instability^ 7 , 8 . Despite their fundamental importance, these dynamic instabilities are not explained by the classical theory of cracks^ 1 , which is based on linear elasticity and an extraneous local symmetry criterion to predict crack paths^ 9 . We develop a two-dimensional theory for predicting arbitrary paths of ultrahigh-speed cracks, which incorporates elastic nonlinearity without extraneous criteria. We show that cracks undergo an Oscillatory Instability controlled by small-scale, near crack-tip, elastic nonlinearity. This Instability occurs above an ultrahigh critical velocity and features an intrinsic wavelength proportional to the ratio of the fracture energy to the elastic modulus, in quantitative agreement with experiments. This ratio emerges as a fundamental scaling length assumed to play no role in the classical theory of cracks, but shown here to strongly influence crack dynamics. Understanding crack formation is important for improving the mechanical performance of materials. A new theory is now presented for the description of cracks propagating at high speeds, with elastic nonlinearity as the underlying principle.