Academic literature on the topic 'Griffith's criterion'
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Journal articles on the topic "Griffith's criterion"
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NEGRI, MATTEO, and CHRISTOPH ORTNER. "QUASI-STATIC CRACK PROPAGATION BY GRIFFITH'S CRITERION." Mathematical Models and Methods in Applied Sciences 18, no. 11 (November 2008): 1895–925. http://dx.doi.org/10.1142/s0218202508003236.
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We consider the propagation of a crack in a brittle material along a prescribed crack path and define a quasi-static evolution by means of stationary points of the free energy. We show that this evolution satisfies Griffith's criterion in a suitable form which takes into account both stable and unstable propagations, as well as an energy balance formula which accounts for dissipation in the unstable regime. If the load is monotonically increasing, this solution is explicit and almost everywhere unique. For more general loads we construct a solution via time discretization. Finally, we consider a finite element discretization of the problem and prove convergence of the discrete solutions.
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Zhao, Yishu. "Griffith's criterion for mixed mode crack propagation." Engineering Fracture Mechanics 26, no. 5 (January 1987): 683–89. http://dx.doi.org/10.1016/0013-7944(87)90133-0.
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Akash, Tanmay Sarkar, Rafsan A. S. I. Subad, Pritom Bose, and Md Mahbubul Islam. "Nanomechanics of antimonene allotropes under tensile loading." Physical Chemistry Chemical Physics 23, no. 10 (2021): 6241–51. http://dx.doi.org/10.1039/d0cp05563h.
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Mechanical properties of monolayer antimonene been investigated with molecular dynamics simulations. A crackline stress distribution based fracture toughness calculation is established as a method to compare with Griffith's criterion for highly brittle 2D materials.
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Sato, Tamao, and Hiroo Kanamori. "Beginning of earthquakes modeled with the Griffith's fracture criterion." Bulletin of the Seismological Society of America 89, no. 1 (February 1, 1999): 80–93. http://dx.doi.org/10.1785/bssa0890010080.
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Abstract We present a source model for the beginning of earthquakes based on the Griffith's fracture criterion. The initial state is a critical state of pre-existing circular fault, which is on the verge of instability. After the onset of instability, the fault grows with a progressively increasing rupture speed, satisfying the condition of fracture energy balance at the crack tip. We investigate the difference in rupture growth patterns in two classes of models that are considered to represent end-member cases. In the first model (Spontaneous model), we assume that the surface energy varies smoothly as a function of position in the crust. In this model, faults with small initial dimensions grow in regions with small surface energy, and those with large initial dimensions, in large surface energy. The rupture velocity increases progressively until it reaches its limiting value. The synthetic velocity seismogram at far field shows a weak initial phase during the transitional stage to limiting velocity. The time taken to reach the limiting velocity is proportional to the initial length of pre-existing fault. Therefore, the duration of the weak initial phase scales with the initial length of fault. In the second model (Trigger model), we envisage that there are many pre-existing faults in the crust with various lengths. These faults are stable because they encounter some obstacle at their ends (e.g., fault segmentation, strong asperity, etc.). This situation is modeled with a local increase of surface energy near the ends of fault. An earthquake is triggered when the obstacle is suddenly removed (i.e., sudden weakening) or the stress is suddenly increased locally to overcome the obstacle. Once an earthquake is triggered, the fault growth is governed by the ambient surface energy. In this model, the rupture speed attains its limiting velocity almost instantly. The synthetic velocity seismogram at far field shows an abrupt, linear increase in amplitude without the weak initial phase that appears in the Spontaneous model. Both models can be unified using a trigger factor defined as a fractional perturbation of the surface energy at the ends of fault relative to the ambient surface energy. The Spontaneous model is characterized by a small trigger factor, and the Trigger model, by a large trigger factor. Thus, the seismic initiation phase with and without the slow initial phase can both occur depending on the trigger factor. The variability in the observed seismic initiation phase may represent a variation surface energy (strength) distribution surrounding the pre-existing cracks. A theoretical consideration of rupture arrest by barriers using the Griffith's fracture criterion does not support the scaling relation between the nucleation moment and the eventual size of earthquake.
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Popov, Valentin. "Energetic criterion for adhesion in viscoelastic contacts with non-entropic surface interaction." Reports in Mechanical Engineering 2, no. 1 (March 23, 2021): 57–64. http://dx.doi.org/10.31181/rme200102057p.
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We suggest a detachment criterion for a viscoelastic elastomer contact based on Griffith's idea about the energy balance at an infinitesimal advancement of the boundary of an adhesive crack. At the moment of detachment of a surface element at the boundary of an adhesive contact, there is some quick (instant) relaxation of stored elastic energy which can be expressed in terms of the creep function of the material. We argue that it is only this "instant part" of stored energy which is available for doing work of adhesion and thus it is only this part of energy relaxation that must be used in Griffith's energy balance. The described idea has several restrictions. Firstly, in this pure form, it is only valid for adhesive forces having an infinitely small range of action (which we call the JKR-limit). Secondly, it is only applicable to non-entropic (energetic) interfaces, which detach "at once" and do not possess their own kinetics of detachment.
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KNEES, DOROTHEE, ALEXANDER MIELKE, and CHIARA ZANINI. "ON THE INVISCID LIMIT OF A MODEL FOR CRACK PROPAGATION." Mathematical Models and Methods in Applied Sciences 18, no. 09 (September 2008): 1529–69. http://dx.doi.org/10.1142/s0218202508003121.
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We study the evolution of a single crack in an elastic body and assume that the crack path is known in advance. The motion of the crack tip is modeled as a rate-independent process on the basis of Griffith's local energy release rate criterion. According to this criterion, the system may stay in a local minimum before it performs a jump. The goal of this paper is to prove the existence of such an evolution and to shed light on the discrepancy between the local energy release rate criterion and models which are based on a global stability criterion (as for example the Francfort/Marigo model). We construct solutions to the local model via the vanishing viscosity method and compare different notions of weak, local and global solutions.
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Einav, Itai. "Fracture propagation in brittle granular matter." Proceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences 463, no. 2087 (August 28, 2007): 3021–35. http://dx.doi.org/10.1098/rspa.2007.1898.
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It is nearly a century since Alan Arnold Griffith developed his energy criterion for the fracture propagation of cracks in ‘near-continuous’ solids. Needless to say that his celebrated work has revolutionized the world of material science. In a very succinct way, Griffith connected between three important aspects of the fracture process: (i) the material, (ii) the stress level, and (iii) the geometry of the crack. Nothing similar was developed for brittle granular matter, although in these materials fracture propagates in the sense of comminution. Recently, I have developed an energy theory, called breakage mechanics, based on the concept of breakage. However, the analogy between the mechanics of breakage and fracture is missing. Here I establish this relation using energy principles and derive a critical comminution pressure for brittle granular materials. This critical pressure is surprisingly complementary to Griffith's critical tensile stress for near-continuous materials. This step enables for the first time to apply the principles of fracture mechanics to all disciplines dealing with confined particles comminution such as geophysics, geology, geotechnical engineering, mineral processing, agriculture and food industry, pharmaceutics and powder technology.
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MORI, Takahisa, and Hisashi TOKUTOMI. "TRIAXIAL AND BIAXIAL COMPRESSIVE STRENGTHS OF CONCRETE BY "MENNODO" CONCEPT APPLYING THE GRIFFITH'S FRACTURE CRITERION." Journal of Structural and Construction Engineering (Transactions of AIJ) 68, no. 569 (2003): 9–13. http://dx.doi.org/10.3130/aijs.68.9_4.
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Kendall, Kevin. "Energizing ASTM lap joint fracture standards." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 379, no. 2203 (June 21, 2021): 20200287. http://dx.doi.org/10.1098/rsta.2020.0287.
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Several ASTM standards on the fracture of glued and welded joints need attention because they do not consider the Griffith energy criterion of cracking which was proposed a century ago. It is almost as if Griffith never existed because the ASTM definition of failure is the stress criterion postulated by Galileo in 1638 in which stress at failure (i.e. strength = force/area) is defined as the determinant of fracture. Irene Martinez Villegas (Villegas, Rans 2021 Phil. Trans. R. Soc. A 376, 20200296. ( doi:10.1098/rsta.2020.0296 )) shows in this volume that attempts to use ASTM D5868 to standardize welded composite (carbon fibre reinforced polymer, CFRP) lap joints reveal major problems. First, the test is a low angle bend–peel test; not shear. Second, the energy required to break the joint is not emphasized so that joints may have high strength properties but also low toughness; third, the fracture force is not proportional to the lap joint area so the concept of strength independent of sample size is false; fourth, as the CFRP panels are made thicker, the strength rises at constant overlap area so the strength can be any value you want; fifth, the strength of larger joints goes down; this is the size effect noted in many bend-cracking tests, much as Galileo suggested for bent beam fracture in his famous book ‘the larger the machine, the greater its weakness'. The purpose of this paper is to demonstrate that poor ASTM ‘shear strength’ standards should be replaced by a definition of welded lap joint performance based on Griffith's energy conservation argument in which fracture surface energy is the main parameter resisting failure. The foundation of this Griffith-style lap joint analysis for long cracks goes back to 1975 but has been largely ignored until now because it does not fit the Griffith equation for cracked sheets, has no ‘stress intensity factor’, and travels at constant speed, not accelerating like the standard Griffith tension crack. This study of tensile delamination shows that a long lap crack is not driven by stress near the crack but by changes in stored elastic energy in the stretched strips remote from the crack tip, while strain energy release rate is negative. It would be more appropriate to call this lap failure a tensile delamination crack. This article is part of a discussion meeting issue ‘A cracking approach to inventing new tough materials: fracture stranger than friction’.
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Hong-Lam, DANG. "A study of tensile strength of fractured rock mass by phase field method in DEAL.II with local refinement technique." Transport and Communications Science Journal 71, no. 7 (September 30, 2020): 737–45. http://dx.doi.org/10.25073/tcsj.71.7.1.
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Cracking propagation in elastic and porous media is still challenge topics in mechanical, energy, and environmental engineering. In this paper, the phase field method will be used to model the cracking propagation at the small scale for elastic media. This method is doing well in DEAL.II with the help of local refinement technique which allows studying the tensile strength of fractured rock mass behavior without prior knowledge of cracking propagation path and reduction of computational consumption. This implementation is applied to model a fractured rock mass in which a plenty of explicit fractures are distributed though total energy released by Griffith's criterion. Through these applications, we demonstrate and highlight the performance of the phase field method with local refinement technique in modeling crack propagation as well as investigate the tensile strength of fractured rock mass dependency its crack orientation
Dissertations / Theses on the topic "Griffith's criterion"
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Racca, Simone. "Some models of crack growth in brittle materials." Doctoral thesis, SISSA, 2013. http://hdl.handle.net/20.500.11767/4809.
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This work is devoted to the study of models of fractures growth in brittle elastic materials; it collects the results obtained during my Ph.D., that are contained in [77, 76, 78]. We consider quasi-static rate-independent models, as well as rate-dependent ones and the case in which the first ones are limits of the second ones when certain physical parameters vanish. The term quasistatic means that, at each instant, the system is assumed to be in equilibrium with respect to its time-dependent data; this setting is typical of systems whose internal time scale is much smaller than that of the loadings. By rate-independent system we mean that, if the time-dependent data are rescaled by a strictly monotone increasing function, then the system reacts by rescaling the solutions in the same manner.
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Almi, Stefano. "Some results on the mathematical analysis of crack problems with forces applied on the fracture lips." Doctoral thesis, SISSA, 2016. http://hdl.handle.net/20.500.11767/4878.
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This thesis is devoted to the study of some models of fracture growth in elastic materials, characterized by the presence of forces acting on the crack lips. Working in the general framework of rate-independent processes, we first discuss a variational formulation of the problem of quasi-static crack evolution in hydraulic fracture. Then, we investigate the crack growth process in a cohesive fracture model, showing the existence of an evolution satisfying a weak Griffith's criterion. Finally, in the last chapter of this work we investigate, in the static case, the interaction between the energy spent in order to create a new fracture and the energy spent by the applied surface forces. This leads us to study the lower semicontinuity properties of a free discontinuity functional F(u) that can be written as the sum of a crack term, depending on the jump set of u, and of a boundary term, depending on the trace of u.
Book chapters on the topic "Griffith's criterion"
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Larsen, Christopher J. "Models for Dynamic Fracture Based on Griffith’s Criterion." In IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, 131–40. Dordrecht: Springer Netherlands, 2010. http://dx.doi.org/10.1007/978-90-481-9195-6_10.
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Bonnet, Marc. "Stability of Moving Fronts Under Griffith Criterion: A Computational Approach Using Integral Equations and Domain Derivatives." In Solid Mechanics and Its Applications, 269–76. Dordrecht: Springer Netherlands, 1999. http://dx.doi.org/10.1007/978-94-011-4738-5_32.
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Bažant, Zdeněk P., Jia-Liang Le, and Marco Salviato. "Overview of History." In Quasibrittle Fracture Mechanics and Size Effect, 260–69. Oxford University Press, 2021. http://dx.doi.org/10.1093/oso/9780192846242.003.0008.
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The last chapter briefly sketches the rich century-long history of fracture mechanics, with an additonal quasibrittle focus. The mainstream milestones were Griffith's 1921 introduction of energy criterion of crack propagation, Irwin's 1958 discovery of the relation of the energy release rate to the stress intensity factor of the near-tip singular stress field, Barenblatt's 1959 conception of the cohesive crack model, and Rice's 1966 discovery of the J-integral giving the energy flux into tip crack tip. Progress was spurred by the breakup of welded Liberty ships at sea and of Commet jetliners in flight, and later by many sudden shear failures of RC structures. At the interface with structural safety the main milestone was Weibull's 1939 introduction of his namesake distribution and statistical size effect in brittle failure. Hillerborg's 1976 fictitious crack model for concrete, essentially equivalent to the cohesive crack model, was a boost for computer simulation of concrete fracture. An even stronger impetus was, during 1984-1991, the gradual emergence, during 1976-87, of the crack band and nonlocal models which can capture the tensorial behavior of the FPZ, and of the energetic size effect law. Evolution of quasibrittle fracture mechanics continues until today (2020), e.g., with the recent disruption of established line-crack fracture concepts by the gap test documenting the strong effect of crack-parallel stresses. Fracture mechanics research will doubtless flourish for another century.
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Anand, Lallit, Ken Kamrin, and Sanjay Govindjee. "Energy-based approach to fracture." In Introduction to Mechanics of Solid Materials, 276–84. Oxford University PressOxford, 2022. http://dx.doi.org/10.1093/oso/9780192866073.003.0017.
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Abstract This chapter introduces the concept of energy release rate for linear elastic fracture mechanics. The classical Griffith fracture criterion, which is formulated in terms of the energy release rate and a critical value of the energy release rate for crack extension, is introduced. The relationship between the energy release rate and the stress intensity factor in Mode I is presented.
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Louchet, Francois. "Deformation, Fracture, and Friction Processes." In Snow Avalanches, 14–24. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198866930.003.0003.
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The main mechanical and physical quantities and concepts ruling deformation, fracture, and friction processes are recalled, with particular attention paid to the simplicity of the analysis, but without betraying the scientific validity of the arguments. We particularly discuss the difference between between elastic and plastic deformation, and quasistatic and dynamic loadings, essential in avalanche triggering mechanisms. The physical origin of Griffith’s rupture criterion that rules both fracture nucleation and propagation, and the transition between brittle and ductile failure processes, is thoroughly discussed. We also explain the physical meaning of the classical Coulomb’s friction law, showing why it can hardly apply to a non-conventional porous, brittle, and healable solid like snow.
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Anand, Lallit, and Sanjay Govindjee. "Energy-based approach to fracture." In Continuum Mechanics of Solids, 506–28. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198864721.003.0027.
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This chapter introduces the concept of energy release rates for linear elastic fracture mechanics. The concept of an energy release rate is defined and related to the criteria of Griffith with application in the context of bodies with point loads. Eshelby’s energy momentum tensor is also introduced and Rice’s path independent J-integral is derived, related to energy release rate, and applied to fracture problems.
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Sutton, Adrian P. "Cracks." In Physics of Elasticity and Crystal Defects, 179–220. Oxford University Press, 2020. http://dx.doi.org/10.1093/oso/9780198860785.003.0009.
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Loaded slit cracks are modelled as continuous distributions of dislocations with infinitesimal Burgers vectors. Cauchy-type singular integral equations for the density of Burgers vector in these distributions are solved using the theory of Chebyshev polynomials. The elastic fields of mode I elastic slit cracks are derived and the stress intensity factor is defined. Other defects may interact with cracks such as dislocations. This leads to the concepts of shielding and anti-shielding of cracks by dislocations. The Dugdale–Bilby–Cottrell–Swinden model of a mode I crack completely shielded by a plastic zone is derived. By introducing a dislocation free zone between the plastic zone and the crack tip the crack tip is only partially shielded, enabling more brittle tendencies to be described. Griffith’s energy criterion for the growth of an existing crack is seen as necessary but not sufficient. The Barenblatt crack introduces the influence of interatomic forces at the crack tip.
Conference papers on the topic "Griffith's criterion"
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Zheng, Bin, Han Liu, Samuel Jules, Hai Xie, and Kaikai Shi. "An Application of the Brittle Fracture Criterion Gp Method to a RPV Type Geometry – Towards the Industrialization of the Method." In ASME 2021 Pressure Vessels & Piping Conference. American Society of Mechanical Engineers, 2021. http://dx.doi.org/10.1115/pvp2021-61636.
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Abstract With the life extension of Nuclear Power Plants worldwide, new challenges have emerged in engineering calculations. These challenges often stem from the difficulty to demonstrate an adequate margin for some key components, which have gradually been ageing during the operation of the plant. In particular, the Reactor Pressure Vessel (RPV) is impacted by the irradiation, and the risk of brittle fracture under severe cold shocks must be assessed. In parallel to conventional approaches, a significant amount work has been performed over the past 20 years in France to adapt the historic Griffith energy release-rate approach to engineering space. The work was initiated by Francfort and Marigo[1]who set up a new elastic fracture theory, extended from the Griffith approach. Lorentz and Wadier[2][3] have since then improved the model which is based on several ingredients including the application of an energy minimization principle, the definition of a specific damage model and the use of a notch to represent the crack. Among other advantages, the Cleavage brittle fracture energy approach parameter (Gp) method has been developed as a true engineering approach and hence is relatively easy to implement in a FEA software: it has already been implemented into code_aster developed by EDF R&D [4]. Recently, CEA also implemented the method in Cast3M [5]. Beyond the application in France, and in the wake of a simple comparison benchmark launched in 2018 with CNNC/NPIC from China on a CT specimen [6], a calculation on a RPV type geometry was initiated. This is the second step of a larger effort aiming at working together on establishing a strong industrial basis to demonstrate applicability in engineering and structural integrity space. The paper provides the progress achieved in the benchmark work and the results obtained in the frame of the work jointly led with company B in the field.
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Chen, Deliang, Changping Chen, Yiming Fu, and Liming Dai. "Growth of Delamination for Laminates Circular Plates Subjected to Transverse Loads." In ASME 2009 International Mechanical Engineering Congress and Exposition. ASMEDC, 2009. http://dx.doi.org/10.1115/imece2009-10687.
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By using movable boundary variational principle, a set of nonlinear governing equations for the delaminated circular plate including the transverse shear deformation and contact effect between the delaminations subjected to transverse load are derived and the corresponding boundary and matching conditions are given. At the same time, according to the Griffith criterion, the formulas of total energy release rate and its individual mode components along the delamination front are obtained and the delamination growth is studied. In the numerical calculation, the delamination growth of axisymmetrical laminated circular plates with various delamination radiuses, delamination depths, and the different material properties are discussed.
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Medina, Hector E., and Brian Hinderliter. "Generation and Mechanical Analysis of Repeatable Random Rough Surfaces." In 2012 20th International Conference on Nuclear Engineering and the ASME 2012 Power Conference. American Society of Mechanical Engineers, 2012. http://dx.doi.org/10.1115/icone20-power2012-54951.
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Natural weathering and wear of structural materials in service nearly always generate surface roughness, and follow the Central Limit Theorem prediction for surface topology. This study couples experimental and statistical theory, to extend knowledge of life of materials from initial service surface conditions through surface damage accumulation. Statistical moments and other parameters were correlated with fracture locations probability (H/N), versus auto correlation length, and depth. As the surface grows to a full Gaussian, H/N increases its dependence on profile’s average and RMS roughness, and derived parameters. This dependence shows an asymptotic limit behavior that approaches agreeably Griffith’s crack criterion, though with multiple fracture locations. Importantly, a Transitional Region was observed, below which the probable location of fracture is uncorrelated to the parameters studied. This is because introduced roughness is insufficient to compete with impurities, internal and external manufacturing flaws, and scratches, due to handling and machining, on the samples.
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Jin, Xiaoqing, Leon M. Keer, and Qian Wang. "Behavior of a Fluid Filled Subsurface Crack Under Moving Hertzian Loading." In ASME/STLE 2007 International Joint Tribology Conference. ASMEDC, 2007. http://dx.doi.org/10.1115/ijtc2007-44449.
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Cracking of a fluid filled subsurface crack is studied by the distributed dislocation technique within the framework of two-dimensional linear elastic fracture mechanics. The opening volume of the horizontal Griffith crack is fully occupied by an incompressible fluid. In the presence of friction, a moving Hertzian line contact load is applied at the surface of the half plane. The induced hydrostatic fluid pressure inside the crack is calculated through an iterative scheme with the restriction that due to the fluid incompressibility there is no change of the crack-opening volume (COV). The stress intensity factors at the tips of the fluid filled crack are analyzed and the effective quadrature formulae are given for the evaluation of the COV. A hypothesis is introduced that the crack propagation is initiated when the elastic strain energy release rate reaches the critical fracture toughness and is arrested when the energy release rate is below the arrest toughness. Based on the energy criterion, predictions will be attempted for determining the load position where the crack propagation/kink commences as well as the growth increment of the branch crack before it is arrested. A step-by-step crack path is constructed for various loading conditions.
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Field, Brandon S., and Pega Hrnjak. "Adiabatic Two-Phase Pressure Drop of Refrigerants in Small Channels." In ASME 4th International Conference on Nanochannels, Microchannels, and Minichannels. ASMEDC, 2006. http://dx.doi.org/10.1115/icnmm2006-96200.
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The adiabatic pressure drop of two-phase refrigerant flow in small channels has been investigated. A rectangular channel with dh = 148.0 μm has been tested with four refrigerants: R134a, R410A, Propane (R290) and Ammonia (R717). This data has been combined with data taken from five different channels, with dh varying from 70 μm to 305 μm, of R134a. The measured pressure drops are compared to many published separated-flow and homogeneous pressure drop models. A new correlation for C, the Chisholm parameter, has been developed based on Reynolds number of the vapor phase (which contains the majority of the kinetic energy) and the dimensionless grouping ψ — a dimensionless ratio of viscous to surface tension effects taken from the analysis of capillary flow performed by Sou and Griffith (1964). This allows the new correlation to account for the varying fluid properties (including surface tension) that are found in the different refrigerants. The new correlation takes flow regime into account by means of a Weber number based flow transition criteria, following the flow map of Akbar et al. [10].
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Winiarski, B., and I. A. Guz. "The Effect of Cracks Interaction on the Critical Strain in Orthotropic Heterogeneous Material Under Compressive Static Loading." In ASME 2006 International Mechanical Engineering Congress and Exposition. ASMEDC, 2006. http://dx.doi.org/10.1115/imece2006-13688.
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Laminar composites due to their internal structure and manufacturing methods contain a number of inter- and intra- component defects which size, dispersion and mutual interaction alter significantly the critical compression strain level. The current paper is one of the first attempts to study the crack interaction in orthotropic materials compressed in a static manner along interlaminar defects. For laminated composites compressed along layers and, therefore, along the mentioned interfacial defects, the classical Griffith - Irvin criterion of fracture or its generalization are inapplicable and all stresses intensity factors and crack opening displacements are equal to zero. This fact emphasises the importance and the necessity of the most careful investigation of fracture due to specific mechanisms inherent to heterogeneous materials. The statement of the problem is based on the most accurate approach, the model of piecewise-homogenous medium. The moment of stability loss in the microstructure of material is treated as the onset of the fracture process. The behaviour of each constituent is described by the three-dimensional equations of solid mechanics, provided certain boundary conditions are satisfied at the interfaces. The complex non-classical fracture mechanics problem is solved by finite elements analysis, using linear buckling model. Numerical analysis is aided by the advanced FE analysis software - Abaqus 6.5. The results were obtained for particular cases of real composites for the typical dispositions of cracks. It was found that both cracks length and mutual position of cracks influence the critical strain of the composite.
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Karlsson, A. M. "Modeling the Debonding Behavior of Step-Tapered Patches: Analytical Solutions and Numerical Analysis of Selected Structures." In ASME 1999 International Mechanical Engineering Congress and Exposition. American Society of Mechanical Engineers, 1999. http://dx.doi.org/10.1115/imece1999-0517.
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Abstract A common method to strengthening or stiffening a weak part of an airplane structure is to adhere a patch over the inferior surface. Typically, this is done in order to prevent a crack from initiating, or to prevent an already existing crack from growing. Evaluation of the efficiency of the patch has traditionally been done with respect to the extent of crack growth, (e.g. Park et al. 1992, and Paul and Jones, 1992), which of course is of crucial interest. However, the integrity of the patched system needs to be considered as well, since the failure of the composite system (formed by the patch and the base structure) may lead to a rapid growth of the preexisting crack in the base structure and may have overall catastrophic consequences. In this study we are therefore interested in investigating the initiation of debonding between the patch and the base structure, as well as the extent and stability of the debonding. Early studies we conducted with respect to debonding suggested that relative long and relative compliant patches were preferred. Furthermore, an investigation regarding the effects of edge tapering on the debonding behavior showed that there are situations where a beveled edge may increase the propensity for debonding, requiring careful selection to achieve a suitable taper angle. In the present study, we investigate the integrity of the composite system for a base structure made from aluminum, and the patch made from aluminum or fiber reinforced epoxy, where both carbon and glass fiber are studied. In particular, we compare the materials selection in the patch, and for the case of a fiber-reinforced epoxy we also discuss the lay-up sequence. To model the debonding behavior, an analytical model developed previous is extended to allow for the current materials properties. This model is fully self consistent and includes a Griffith type fracture criteria which yields the condition for the propagating bond zone boundary. The model also considers the unbonded part of the patch, which has earlier been shown to be in either of three configurations: (i) full sliding contact between the unbonded part of the patch and the base structure, (ii) only the edge of the patch remains in sliding contact with the base structure, or (iii) the patch has totally lifted of the base structure. Results for both flat and curved structures are presented, as well as for a range of loading and boundary conditions. Among other results, it is seen that the degree of tapering is a more important parameter than the stacking sequence is with respect to the initiation and extent of debonding. Furthermore, a simplified testing method is discussed. In this method, the critical load for a case of simple boundary and loading conditions for a particular material system can be directly translated to the critical load for a more complicated structure.