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A J Rosakis - One of the best experts on this subject based on the ideXlab platform.
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dynamic Crack deflection and penetration at interfaces in homogeneous materials experimental studies and model predictions
Journal of The Mechanics and Physics of Solids, 2003Co-Authors: Roy L Xu, Yonggang Huang, A J RosakisAbstract:Abstract We examine the deflection/penetration behavior of dynamic mode-I Cracks propagating at various Speeds towards inclined weak planes/interfaces of various strengths in otherwise homogeneous isotropic plates. A dynamic wedge-loading mechanism is used to control the incoming Crack Speeds, and high-Speed photography and dynamic photoelasticity are used to observe, in real-time, the failure mode transition mechanism at the interfaces. Simple dynamic fracture mechanics concepts used in conjunction with a postulated energy criterion are applied to examine the Crack deflection/penetration behavior and, for the case of interfacial deflection, to predict the Crack tip Speed of the deflected Crack. It is found that if the interfacial angle and strength are such as to trap an incident dynamic mode-I Crack within the interface, a failure mode transition occurs. This transition is characterized by a distinct, observable and predicted Speed jump as well as a dramatic Crack Speed increase as the Crack transitions from a purely mode-I Crack to an unstable mixed-mode interfacial Crack.
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the effect of bond strength and loading rate on the conditions governing the attainment of intersonic Crack growth along interfaces
Journal of The Mechanics and Physics of Solids, 1999Co-Authors: Alan Needleman, A J RosakisAbstract:Dynamic Crack growth along a bimaterial interface under impact shear loading is analyzed numerically. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the bond line and that allows for the creation of new free surface. The resistance to Crack initiation and the Crack Speed history are predicted without invoking any additional failure criterion. Full finite strain transient analyses are carried out. A plane strain model of the configuration used in experiments of Rosakis and co-workers is analyzed. Calculations are carried out for parameters characterizing a steel-PMMA bimaterial. For a sufficiently low impact velocity, the Crack Speed increases smoothly to the PMMA Rayleigh wave Speed, whereas above a sharply defined transition impact velocity, the Crack Speed reaches a value somewhat less than the PMMA dilational wave Speed. This high Speed Crack growth is associated with multiple Crack face contact, separated by discrete micro-Crack like openings behind the main shear Crack. The calculations reproduce, at least qualitatively, the type of Crack Speed histories and Crack tip fields seen in the experiments. They are also consistent with optical observations of finite multi-site contact occurring at intersonic Crack Speeds.
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the structure of the near tip field during transient elastodynamic Crack growth
Journal of The Mechanics and Physics of Solids, 1992Co-Authors: L. B. Freund, A J RosakisAbstract:Abstract T he process of dynamic Crack growth in a nominally elastic malerial under conditions of plane strain or plane stress is considered. Of particular concern is the influence of the transient nature of the process on the stress field in the immediate vicinity of the Crack tip during nonsteady growth. Asymptotically, the Crack tip stress field is square root singular at the Crack tip, with the angular variation of the singular field depending weakly on the instantaneous Crack tip Speed and with the instantaneous stress intensity factor being a scalar multiplier of the singular field. However, for a material particle at a small distance from the moving Crack, the local stress field depends not only on instantaneous values of Crack Speed and stress intensity factor, but also on the past history of these lime-dependent quantities. A representation of the Crack tip field is obtained in the form of an expansion about the Crack up in powers of radial coordinate, with the coefficients depending on the time rates of change of Crack tip Speed and stress intensity factor. This representation is used to interpret some experimental observations, with the conclusion that the higher-order expansion provides an accurate description of Crack tip fields under fairly severe transient conditions. In addition, some estimates are made of the practical limits of using a stress intensity factor field alone to characterize the local fields.
Dov Sherman - One of the best experts on this subject based on the ideXlab platform.
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the effect of reflected stress wave on Crack Speed in silicon crystal
Engineering Fracture Mechanics, 2020Co-Authors: Merna Shaheenmualim, Dov ShermanAbstract:Abstract The effect of reflected stress wave on Crack Speed during dynamic Crack propagation in brittle single crystal was investigated by cleavage fracture experiments and by Cracks dynamics theory. The specimens in the experimental program were quasi-statically loaded using the Coefficients of Thermal Expansion Mismatch (CTEM) method. Silicon crystal served as a model material where the Cracks were propagated on the ( 110 ) [ 1 1 ¯ 0 ] and (1 1 1)[1 1 2 ¯ ] low energy cleavage systems (LECSs) of the crystal. The effect of reflected stress wave was evaluated by comparing the experimental energy-Speed relationship and the theoretical Freund equation of motion. The experimental quasi-static energy release rate (ERR) was calculated by Finite Element Analysis (FEA) and the Crack Speed was measured by Potential Drop Technique (PDT). Since Freund equation of motion does not take into account the effect of reflected stress wave, any deviation found in the experimental results from the theoretical energy-Speed relationship, was identified as a possible effect of the reflected stress wave. We considered here the longitudinal wave, the horizontal shear wave, and the vertical shear wave. The time it takes for each wave to be reflected from the specimens' lateral boundaries back to the Crack tip was calculated and the Crack tip-wave front interaction was, accordingly, determined on the energy-Speed plot. It was found that the effect of reflected stress waves on the Crack Speed in silicon is minor. Finally, we found that the effect of the reflected stress waves on the Crack Speed differed slightly for Cracks with a different gradient of the driving force Θ = dG0/da which also affects the gradient of the Crack Speed, Φ = dV/da.
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the effect of reflected stress wave on Crack Speed in quasi statically loaded brittle crystal specimens
ECF21, 2016Co-Authors: Merna Shaheen Moalim, Dov ShermanAbstract:It is commonly accepted that when a dynamic Crack propagates at high Speed, the reflected stress wave is responsible for significant Crack Speed reduction. However, this assumption has not been yet fully verified experimentally, and in brittle single crystals in particular. We performed fast Crack cleavage experiments using a unique experimental setup that was developed in our lab. The method consists of quasi-static loading a brittle single crystal specimen adhered to an aluminum loading-frame by two thin layers of epoxy resin. Upon heating the assembly, the thermal expansion coefficient mismatch between the specimen and the loading frame used as a quasi-static driving force for Crack initiation and propagation. Crack Speed was evaluated by means of potential drop technique and measurements of the temperatures and strains during loading were used to evaluate the quasi-static strain energy release rate by means of finite element analysis. The energy Speed relationship formulated by Freund equation of motion, which does not account for stress wave reflection, was constructed. It is our claim that any deviations from Freund equation of motion point on the effect of reflected stress wave. We evaluated the experimental energy-Speed relationship of a Crack propagating on the (110)[1-10] low energy cleavage system of silicon crystal at high Crack Speeds (V max ~0.85C R ). Our experimental results show small variations in Crack Speed when compared to Freund equation of motion, meaning that the effect of reflected stress wave on Crack Speed in quasi-statically loaded brittle specimen is limited. We will present the experimental setup and findings including new experimental variables essential for evaluating the behavior at high Crack Speed.
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dynamic fracture instabilities in brittle crystals generated by thermal phonon emission experiments and atomistic calculations
Journal of The Mechanics and Physics of Solids, 2012Co-Authors: Fouad Atrash, Dov ShermanAbstract:Abstract Dynamic cleavage fracture experiments of brittle single crystal silicon revealed several length scales of surface and path instabilities: macroscale path selection, mesoscale Crack deflection, and nanoscale surface ridges. These phenomena cannot be predicted or explained by any of the continuum mechanics based equations of motion of dynamic Cracks, as presumably critical energy dissipation mechanisms are not fully accounted for in the theories. Experimentally measured maximum Crack Speed, always lower than the theoretical limit, is another phenomenon that is as yet not well understood. We suggest that these phenomena depend on velocity dependent and anisotropic material property that resists Crack propagation. The basic approach is that the bond breaking mechanisms during dynamic Crack propagation vibrate the atoms at the Crack front to generate thermal phonon emission, or heat, which provides additional energy dissipation mechanisms. This energy dissipation mechanism is a material property that resists Crack propagation. To evaluate this property, we combined the continuum based elastodynamic Freund equation of motion with molecular dynamics atomistic computer “experiments”. We analyzed the above experimental dynamic fracture instabilities in silicon with the obtained velocity dependent and anisotropic material property and show its importance in cleavage of brittle crystals.
Alan Needleman - One of the best experts on this subject based on the ideXlab platform.
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the effect of bond strength and loading rate on the conditions governing the attainment of intersonic Crack growth along interfaces
Journal of The Mechanics and Physics of Solids, 1999Co-Authors: Alan Needleman, A J RosakisAbstract:Dynamic Crack growth along a bimaterial interface under impact shear loading is analyzed numerically. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. A cohesive surface constitutive relation is also specified that relates the tractions and displacement jumps across the bond line and that allows for the creation of new free surface. The resistance to Crack initiation and the Crack Speed history are predicted without invoking any additional failure criterion. Full finite strain transient analyses are carried out. A plane strain model of the configuration used in experiments of Rosakis and co-workers is analyzed. Calculations are carried out for parameters characterizing a steel-PMMA bimaterial. For a sufficiently low impact velocity, the Crack Speed increases smoothly to the PMMA Rayleigh wave Speed, whereas above a sharply defined transition impact velocity, the Crack Speed reaches a value somewhat less than the PMMA dilational wave Speed. This high Speed Crack growth is associated with multiple Crack face contact, separated by discrete micro-Crack like openings behind the main shear Crack. The calculations reproduce, at least qualitatively, the type of Crack Speed histories and Crack tip fields seen in the experiments. They are also consistent with optical observations of finite multi-site contact occurring at intersonic Crack Speeds.
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Numerical simulations of dynamic interfacial Crack growth allowing for Crack growth away from the bond line
International Journal of Fracture, 1996Co-Authors: X P Xu, Alan NeedlemanAbstract:Dynamic Crack growth is analyzed numerically for a plane strain bimaterial block with an initial central Crack subject to impact tensile loading. The material on each side of the bond line is characterized by an isotropic hyperelastic constitutive relation. Potential surfaces of decohesion are interspersed in the material on either side of the bond line and along the bond line. The cohesive surface constitutive relation allows for the creation of new tree surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. The resistance to Crack initiation, the Crack Speed history and the Crack path are predicted without invoking any ad hoc failure criterion. Three calculations are carried out for a PMMA/Al bimaterial. The imposed loading and the properties of the adjacent materials are kept fixed, while the bond line strength is taken to be 1/4, 1/2, and 3/4 of the strength of PMMA. The nominal Crack Speed decreases with increasing bond line strength. When the bond line strength is 1/4 that of PMMA, the Crack remains on the bond line although there is an attempt at branching off the bond line. For the intermediate case, a bond line strength 1/2 that of PMMA, repeated branching of the main Crack off the bond line into the PMMA occurs, together with micro-Crack nucleation on the bond line. The Crack branches off the bond line into the PMMA when its strength is 3/4 that of PMMA, with the main direction of growth being parallel to the bond line, but with the Crack progressively drifting further into the PMMA.
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Numerical simulations of fast Crack growth in brittle solids
Journal of The Mechanics and Physics of Solids, 1994Co-Authors: Xiaopeng Xu, Alan NeedlemanAbstract:Dynamic Crack growth is analysed numerically for a plane strain block with an initial central Crack subject to tensile loading. The continuum is characterized by a material constitutive law that relates stress and strain, and by a relation between the tractions and displacement jumps across a specified set of cohesive surfaces. The material constitutive relation is that of an isotropic hyperelastic solid. The cohesive surface constitutive relation allows for the creation of new free surface and dimensional considerations introduce a characteristic length into the formulation. Full transient analyses are carried out. Crack branching emerges as a natural outcome of the initial-boundary value problem solution, without any ad hoc assumption regarding branching criteria. Coarse mesh calculations are used to explore various qualitative features such as the effect of impact velocity on Crack branching, and the effect of an inhomogeneity in strength, as in Crack growth along or up to an interface. The effect of cohesive surface orientation on Crack path is also explored, and for a range of orientations zigzag Crack growth precedes Crack branching. Finer mesh calculations are carried out where Crack growth is confined to the initial Crack plane. The Crack accelerates and then grows at a constant Speed that, for high impact velocities, can exceed the Rayleigh wave Speed. This is due to the finite strength of the cohesive surfaces. A fine mesh calculation is also carried out where the path of Crack growth is not constrained. The Crack Speed reaches about 45% of the Rayleigh wave Speed, then the Crack Speed begins to oscillate and Crack branching at an angle of about 29° from the initial Crack plane occurs. The numerical results are at least qualitatively in accord with a wide variety of experimental observations on fast Crack growth in brittle solids.
L M Brock - One of the best experts on this subject based on the ideXlab platform.
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interface Crack extension at any constant Speed in orthotropic or transversely isotropic bimaterials ii two important examples
International Journal of Solids and Structures, 2002Co-Authors: L M Brock, M T HansonAbstract:Abstract Part I [Int. J. Solids Struct., 39, 1165–1182] gives exact general solutions for steady dynamic extension by a semi-infinite Crack along the interface of dissimilar orthotropic/transversely isotropic half-spaces under in-plane loading. Crack Speed is any constant value, and results are valid for all six possible relations between the four body wave Speeds. These results are applied here to sub-critical interface Crack extension, and to debonding from a rigid half-space at any constant Speed. The former case demonstrates well-known phenomena––the minimum Rayleigh Speed is critical, and complex conjugate eigenvalues cause the Crack edge oscillatory/square-root singular behavior that implies interpenetration. Calculations for representative materials show that eigenvalue and stress intensity factor amplitude variation with Crack Speed is small except near the critical value. Results for the latter case complement those of other recent studies: Singular behavior vanishes for super-critical/sub-sonic Crack Speeds, although oscillations remain. For trans-sonic Crack Speeds, eigenvalues are real, singular behavior is no longer square-root, and interpenetration can still occur below a critical Speed. Lines of displacement gradient discontinuity radiate from the Crack edge, but can vanish at a critical Speed. Calculations show that eigenvalue variation with Crack Speed is more pronounced than in the first case.
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interface Crack extension at any constant Speed in orthotropic or transversely isotropic bimaterials i general exact solutions
International Journal of Solids and Structures, 2002Co-Authors: L M BrockAbstract:Abstract A semi-infinite Crack along the interface of two dissimilar half-spaces extends under in-plane loading. Each half-space belongs to a class of orthotropic or transversely isotropic elastic materials, the Crack can extend at any constant Speed, and all six possible relations between the four body wave Speeds are considered. A steady dynamic situation is treated, and exact full displacement fields derived. A key step is a factorization that produces, despite anisotropy, simple solution forms and compact Crack Speed-dependent functions that exhibit the Rayleigh and Stoneley Speeds as roots. These roots are calculated for various representative bimaterials. Closed-form Crack opening displacement gradient and interface stress fields are also derived from a general set of coupled singular integral equations. The equation eigenvalues can, depending on Crack Speed, be complex/imaginary conjugates, purely real, or zero. This suggests possibilities observed in other studies: oscillations and square-root singular behavior at the Crack edge, non-singular behavior, singular behavior not of square-root order, and the radiation of displacement gradient discontinuities at Crack Speeds beyond the purely sub-sonic range. These possibilities are explored further in terms of two important special cases in Part II of this study [Int. J. Solids Struct., 39, 1183–1198].
Markus J Buehler - One of the best experts on this subject based on the ideXlab platform.
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threshold Crack Speed controls dynamical fracture of silicon single crystals
Physical Review Letters, 2007Co-Authors: Markus J Buehler, Harvey Tang, Adri C T Van Duin, William A GoddardAbstract:Fracture experiments of single silicon crystals reveal that after the critical fracture load is reached, the Crack Speed jumps from zero to [approximate]2 km/sec, indicating that Crack motion at lower Speeds is forbidden. This contradicts classical continuum fracture theories predicting a continuously increasing Crack Speed with increasing load. Here we show that this threshold Crack Speed may be due to a localized phase transformation of the silicon lattice from 6-membered rings to a 5–7 double ring at the Crack tip.
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threshold Crack Speed in dynamic fracture of silicon
MRS Online Proceedings Library Archive, 2006Co-Authors: Markus J Buehler, Harvey Tang, Adri C T Van Duin, William A GoddardAbstract:We report a study of dynamic Cracking of a silicon single crystal in which the ReaxFF reactive force field is used for about 3,000 atoms near the Crack tip while the other 100,000 atoms of the model system are described with a simple nonreactive force field. The ReaxFF is completely derived from quantum mechanical calculations of simple silicon systems without any empirical parameters. This model has been successfully used to study Crack dynamics in silicon, capable of reproducing key experimental results such as orientation dependence of Crack dynamics (Buehler et al., Phys. Rev. Lett., 2006). Here we focus on Crack Speeds as a function of loading and Crack propagation mechanisms. We find that the steady state Crack Speed does not increase continuously with applied load, but instead jumps to a finite value immediately after the critical load, followed by a regime of slow increase. Our results quantitatively reproduce experimental observations of Crack Speeds during fracture in silicon along the (111) planes, confirming the existence of lattice trapping effects. We find that the underlying reason for this behavior is formation of a 5-7-double ring defect at the tip of the Crack, effectively hindering nucleation of the Crack at the Griffith load. We develop a simple continuum model that explains the qualitative behavior of the fracture dynamics.
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Hyperelasticity governs dynamic fracture at a critical length scale
Nature, 2003Co-Authors: Markus J Buehler, Farid F. Abraham, Huajian GaoAbstract:The elasticity of a solid can vary depending on its state of deformation. For example, metals will soften and polymers may stiffen as they are deformed to levels approaching failure. It is only when the deformation is infinitesimally small that elastic moduli can be considered constant, and hence the elasticity linear. Yet, many existing theories model fracture using linear elasticity, despite the fact that materials will experience extreme deformations at Crack tips. Here we show by large-scale atomistic simulations that the elastic behaviour observed at large strains—hyperelasticity—can play a governing role in the dynamics of fracture, and that linear theory is incapable of fully capturing all fracture phenomena. We introduce the concept of a characteristic length scale for the energy flux near the Crack tip, and demonstrate that the local hyperelastic wave Speed governs the Crack Speed when the hyperelastic zone approaches this energy length scale.