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Journal articles on the topic 'Griffith's criterion'

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Published: 14 March 2023

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1

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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2

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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3

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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4

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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5

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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6

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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7

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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8

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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9

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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10

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

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11

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/10.47869/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

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12

DAL MASO, G., and R. TOADER. "A MODEL FOR THE QUASI-STATIC GROWTH OF BRITTLE FRACTURES BASED ON LOCAL MINIMIZATION." Mathematical Models and Methods in Applied Sciences 12, no. 12 (December 2002): 1773–99. http://dx.doi.org/10.1142/s0218202502002331.

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We study a variant of the variational model for the quasi-static growth of brittle fractures proposed by Francfort and Marigo.9 The main feature of our model is that, in the discrete-time formulation, in each step we do not consider absolute minimizers of the energy, but, in a sense, we look for local minimizers which are sufficiently close to the approximate solution obtained in the previous step. This is done by introducing in the variational problem an additional term which penalizes the L2-distance between the approximate solutions at two consecutive times. We study the continuous-time version of this model, obtained by passing to the limit as the time step tends to zero, and show that it satisfies (for almost every time) some minimality conditions which are slightly different from those considered in Refs. 9 and 8, but are still enough to prove (under suitable regularity assumptions on the crack path) that the classical Griffith's criterion holds at the crack tips. We also prove that, if no initial crack is present and if the data of the problem are sufficiently smooth, no crack will develop in this model, provided the penalization term is large enough.

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13

Louchet, F., J. Faillettaz, D. Daudon, N. Bédouin, E. Collet, J. Lhuissier, and A. M. Portal. "Possible deviations from Griffith’s criterion in shallow slabs, and consequences on slab avalanche release." Natural Hazards and Earth System Sciences 2, no. 3/4 (December 31, 2002): 157–61. http://dx.doi.org/10.5194/nhess-2-157-2002.

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Abstract. Possible reasons for deviations from Griffith’s criterion in slab avalanche triggerings are examined. In the case of a major basal crack, we show (i) that the usual form of Griffith’s criterion is valid if elastic energy is stored in a shallow and hard slab only, and (ii) that rapid healing of broken ice bonds may lead to shear toughnesses larger than expected from tensile toughness experiments. In the case of avalanches resulting from failure of multi-cracked weak layers, where a simple Griffith’s criterion cannot be applied, frequency/size plots obtained from discrete elements and cellular automata simulations are shown to obey scale invariant power law distributions. These findings are confirmed by both frequency/acoustic emission duration and frequency/size plots obtained from field data, suggesting that avalanche triggerings may be described using the formalism of critical phenomena.

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14

Li, S. "A multiscale Griffith criterion." Philosophical Magazine Letters 87, no. 12 (December 2007): 945–54. http://dx.doi.org/10.1080/09500830701647972.

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15

Li, Chun Guang, Xiu Run Ge, Hong Zheng, and Shui Lin Wang. "Two-Parameter Parabolic Mohr Strength Criterion and Its Damage Regularity." Key Engineering Materials 306-308 (March 2006): 327–32. http://dx.doi.org/10.4028/www.scientific.net/kem.306-308.327.

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A series of formulas about two-parameter parabolic Mohr strength criterion(2-PP Mohr criterion) are derived. Based on the results of uniaxial tension and uniaxial compression tests, the parameters involved in the criterion can be easily determined, then the criterion in terms of the major principal stress and the minor principal stress is derived, and the damage pattern is also discussed. At last, the formulas about the rupture angle and the friction angle are presented, and their relationship is also given. 2-PP Mohr criterion can describe not only shear but also tensile failure. In this criterion the ratio of the uniaxial compression strength and the uniaxial tension strength is not confined as in Griffith criterion. The formula about the rupture angle provides steady theoretical foundation for determining the direction of crack faces and damage patterns in the computation of macro crack propagation. In fact, Griffith criterion is only a special case of the two-parameter parabolic Mohr strength criterion proposed in this present paper.

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16

Lee, Younggi, Jeehoon Park, Junyeong Park, and Jaehyun Yim. "An algorithm for a lifted Massey triple product of a smooth projective plane curve." International Journal of Algebra and Computation 30, no. 08 (September 24, 2020): 1651–69. http://dx.doi.org/10.1142/s0218196720500587.

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We provide an explicit algorithm to compute a lifted Massey triple product relative to a defining system for a smooth projective plane curve [Formula: see text] defined by a homogeneous polynomial [Formula: see text] over a field. The main idea is to use the description (due to Carlson and Griffiths) of the cup product for [Formula: see text] in terms of the multiplications inside the Jacobian ring of [Formula: see text] and the Cech–deRham complex of [Formula: see text]. Our algorithm gives a criterion whether a lifted Massey triple product vanishes or not in [Formula: see text] under a particular nontrivial defining system of the Massey triple product and thus can be viewed as a generalization of the vanishing criterion of the cup product in [Formula: see text] of Carlson and Griffiths. Based on our algorithm, we provide explicit numerical examples by running the computer program.

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17

Yin, Hanqing, H. Jerry Qi, Feifei Fan, Ting Zhu, Baolin Wang, and Yujie Wei. "Griffith Criterion for Brittle Fracture in Graphene." Nano Letters 15, no. 3 (February 20, 2015): 1918–24. http://dx.doi.org/10.1021/nl5047686.

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18

Louat, N. P., and B. B. Rath. "Plastic flow and the Griffith fracture criterion." Acta Metallurgica 35, no. 12 (December 1987): 2921–27. http://dx.doi.org/10.1016/0001-6160(87)90291-4.

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19

Dégué, K. M., M. Soulié, and B. Ladanyi. "Extension of the Griffith's fracture criteria to saturated clays." International Journal for Numerical and Analytical Methods in Geomechanics 27, no. 4 (January 20, 2003): 275–88. http://dx.doi.org/10.1002/nag.271.

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20

Knees, Dorothee, and Matteo Negri. "Convergence of alternate minimization schemes for phase-field fracture and damage." Mathematical Models and Methods in Applied Sciences 27, no. 09 (May 23, 2017): 1743–94. http://dx.doi.org/10.1142/s0218202517500312.

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We consider time-discrete evolutions for a phase-field model (for fracture and damage) obtained by alternate minimization schemes. First, we characterize their time-continuous limit in terms of parametrized [Formula: see text]-evolutions, introducing a suitable family of “intrinsic energy norms”. Further, we show that the limit evolution satisfies Griffith’s criterion, for a phase-field energy release, and that the irreversibility constraint is thermodynamically consistent.

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21

Bartenev, G. M. "Thermofluctuation theory of strength and the Griffith criterion." Strength of Materials 21, no. 11 (November 1989): 1533–40. http://dx.doi.org/10.1007/bf01529408.

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22

Jarić, J. P., and E. S. Şuhubi. "Griffith criterion for brittle fracture in micropolar continuum." International Journal of Engineering Science 26, no. 5 (January 1988): 495–502. http://dx.doi.org/10.1016/0020-7225(88)90007-9.

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23

Hatzitrifon, N. K., and E. E. Gdoutos. "On the griffith criterion for three-dimensional cracks." International Journal of Engineering Science 26, no. 8 (January 1988): 833–36. http://dx.doi.org/10.1016/0020-7225(88)90033-x.

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24

Yuan, Mingqing, Haitao Zhao, Li Tian, Boming Zhang, Yanzhi Yang, Jia Chen, and Ji’an Chen. "Comparison of mixed mode fracture criteria in finite element analysis for matrix crack density estimation of laminated composites." Journal of Composite Materials 55, no. 2 (August 11, 2020): 277–89. http://dx.doi.org/10.1177/0021998320948246.

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A mixed mode crack density estimation method based on the finite element analysis (FEA) for laminated composites is proposed and verified in this paper. The damaged properties of cracked ply are obtained using semi-analytical micro-mechanical method for the first time. The piecewise functions of the mode I and mode II energy release rates involving crack density are given based on Griffith’s energy principle and discrete damage mechanics (DDM). Any mixed mode fracture criteria could be simply applied to the FEA of the structure to calculate the initiation and evolution of the micro-cracks in the laminate. Mode I criterion, power law and B-K criterion are applied in the numerical examples to compare their performances in the crack density estimation. It has been concluded that the accuracy of the fracture toughness is more important than the choice of fracture criterion in crack density estimation.

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25

Sumigawa, Takashi, Takahiro Shimada, Shuuhei Tanaka, Hiroki Unno, Naoki Ozaki, Shinsaku Ashida, and Takayuki Kitamura. "Griffith Criterion for Nanoscale Stress Singularity in Brittle Silicon." ACS Nano 11, no. 6 (June 2017): 6271–76. http://dx.doi.org/10.1021/acsnano.7b02493.

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26

Pirola, Gian Pietro, and Cecilia Rizzi. "Infinitesimal Invariant and vector bundles." Nagoya Mathematical Journal 186 (2007): 95–118. http://dx.doi.org/10.1017/s0027763000009375.

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AbstractWe study the Saito-Ikeda infinitesimal invariant of the cycle defined by curves in their Jacobians using rank k + 1 vector bundles. We give a criterion for which the higher cycle class map is not trivial. When k = 2, this turns out to be strictly linked to the Petri map for vector bundles. In this case we can improve a result of Ikeda: an explicit construction on a curve of genus g ≥ 10 shows the existence of a non trivial element in the higher Griffiths group.

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27

Yang, Q., L. G. Tham, and G. Swoboda. "Relationship between refined Griffith criterion and power laws for cracking." Mechanics Research Communications 31, no. 4 (July 2004): 429–34. http://dx.doi.org/10.1016/j.mechrescom.2004.02.002.

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28

Huang, Kai, Takahiro Shimada, Naoki Ozaki, Youhei Hagiwara, Takashi Sumigawa, Licheng Guo, and Takayuki Kitamura. "A unified and universal Griffith-based criterion for brittle fracture." International Journal of Solids and Structures 128 (December 2017): 67–72. http://dx.doi.org/10.1016/j.ijsolstr.2017.08.018.

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29

Nazarov, S. A. "The Irwin’s and Griffith’s criteria for a set of cracks." Doklady Physics 45, no. 7 (July 2000): 333–35. http://dx.doi.org/10.1134/1.1307083.

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30

Gontarz, Jakub, and Jerzy Podgórski. "Comparison of Various Criteria Determining the Direction of Crack Propagation Using the UDMGINI User Procedure Implemented in Abaqus." Materials 14, no. 12 (June 18, 2021): 3382. http://dx.doi.org/10.3390/ma14123382.

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This paper describes a method of predicting the direction of crack propagation implemented by user subroutines in the Simulia-Abaqus FEA system with the use of the extended finite element method (X-FEM). This method is based on displacements and stresses according to Westergaard’s solution of Griffith’s crack problem. During the calculations, in each crack increment, the algorithm reads the stresses and displacements in the model around the crack tip, calculates the criterion values at the read points, reduces them to a unit distance from the crack tip, fits a polynomial to these points, and finds the minimum of the function closest to the last propagation angle. The algorithm also decides when the crack grows, depending on a chosen criterion. Four criteria have been implemented to predict the direction of failure propagation: the maximum principal stress criterion, the Ottosen–Podgórski criterion, the new criterion described here based on the minimum component values of the displacement vector, and the maximum circumferential tensile stress (MTS). These criteria were verified in two tests: the three-point bending test of the notched beam and the anchor pull-out test. For these tests, the criterion built into Simulia Abaqus does not correctly define the crack path, which causes the crack propagation direction to “rotate” when simulating the fracture. The criteria developed here, in most cases, determine the crack path and the maximum force very well compared to real laboratory tests.

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31

Atkins, A. G. "Comments on ‘The Griffith-Orowan fracture theory revisited: The T-criterion’." International Journal of Mechanical Sciences 29, no. 4 (January 1987): 293–94. http://dx.doi.org/10.1016/0020-7403(87)90042-7.

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32

Liu, Feng, Qiheng Tang, and Tzu-Chiang Wang. "Intrinsic Notch Effect Leads to Breakdown of Griffith Criterion in Graphene." Small 13, no. 25 (May 16, 2017): 1700028. http://dx.doi.org/10.1002/smll.201700028.

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33

Kendall, K., N. McN Alford, S. R. Tan, and J. D. Birchall. "Influence of toughness on Weibull modulus of ceramic bending strength." Journal of Materials Research 1, no. 1 (February 1986): 120–23. http://dx.doi.org/10.1557/jmr.1986.0120.

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It is demonstrated both theoretically and experimentally that fracture toughness does not directly influence the Weibull modulus of ceramic bending strength for materials that obey the Griffith criterion for crack propagation. Weibull modulus remains unchanged as toughness is increased. However, toughness variations with crack length do affect the Weibull modulus. Thus materials that display R-curve behavior or Dugdale character give an increased Weibull modulus and appear more reliable.

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34

Zhang, Shuang, Hai Jun Wu, Zheng Jun Tan, and Feng Lei Huang. "Theoretical Analysis of Dynamic Spherical Cavity Expansion in Reinforced Concretes." Key Engineering Materials 715 (September 2016): 222–27. http://dx.doi.org/10.4028/www.scientific.net/kem.715.222.

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This paper aims to establish a model that considers the penetration resistance caused by the constraint effects of steel reinforcements on concrete. Firstly, based on the experiment phenomena that reinforcements increase the toughness and tensile strength of concretes, the fitting relational expression between toughness of reinforced concrete and ratio of reinforcement was used to improve the Griffith yield criterion for reinforced concrete. Then, the dynamic spherical cavity expansion analysis was developed using the improved Griffith yield criterion as constitutive model and the dilation equation as equation of state, and the response regions were consisted of six distinct zones: cavity, compaction zone, dilation zone, radially cracked zone, elastic zone and undisturbed zone. This dynamic analysis considered the compression and dilation of concretes at the same time and was applicable to the penetration problem of reinforced concrete target. At last, based on the theoretical model of this paper, the experiments of projectiles with different weights penetrating into reinforced concrete targets with different reinforcement ratios were calculated using penetration analysis method of rigid projectiles. The comparison results showed that the theoretical analysis model of this paper can be used to predict the depth of penetration and other physical parameters such as velocity and deceleration with certain rationality.

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35

Ballico, Edoardo, and Francesco Malaspina. "Qregularity and an extension of the Evans–Griffiths criterion to vector bundles on quadrics." Journal of Pure and Applied Algebra 213, no. 2 (February 2009): 194–202. http://dx.doi.org/10.1016/j.jpaa.2008.06.002.

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36

Makhutov, N. A., and Yu G. Matvienko. "Griffith theory and development of fracture mechanics criteria." Materials Science 29, no. 3 (1993): 316–19. http://dx.doi.org/10.1007/bf00558976.

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37

Aleksandrov, Anatoly, Natalya Aleksandrova, Vasiliy Chusov, and Aleksandr Riabov. "Ways of application of the provisions of mechanics of bodies with cracks to the calculation of asphalt concrete on strength and plasticity." MATEC Web of Conferences 239 (2018): 05018. http://dx.doi.org/10.1051/matecconf/201823905018.

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The report discusses the principles of two major theories of fracture mechanics of bodies with cracks, which include the theory of accumulation of damage Kachanov–Rabotnov and theory of brittle fracture Griffith–Irwin, including the invariant integral Cherepanov–Rice, describing the criterion of growth the crack. To assess the application of these theories to the calculation of asphalt concrete, laboratory test data are given and based on their analysis the appropriate conclusions.

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38

Lakirouhani, Ali, Mohammad Bahrehdar, Jurgis Medzvieckas, and Romualdas Kliukas. "COMPARISON OF PREDICTED FAILURE AREA AROUND THE BOREHOLES IN THE STRIKE-SLIP FAULTING STRESS REGIME WITH HOEK-BROWN AND FAIRHURST GENERALIZED CRITERIA." JOURNAL OF CIVIL ENGINEERING AND MANAGEMENT 27, no. 5 (June 10, 2021): 346–54. http://dx.doi.org/10.3846/jcem.2021.15020.

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Breakout is a shear failure due to compression that forms around the borehole due to stress concentration. In this paper, the breakout theory model is investigated by combining the equilibrium elasticity equations of stress around the borehole with two Hoek-Brown and Fairhurst generalized fracture criteria, both of which are based on the Griffith criterion. This theory model provides an explicit equation for the breakout failure width, but the depth of failure is obtained by solving a quartic equation. According to the results and in general, in situ stresses and rock strength characteristics are effective in developing the breakout failure area, As the ratio of in-situ stresses increases, the breakout area becomes deeper and wider. Because in the shear zone, the failure envelope of the Fairhurst criterion is lower than the Hoek-Brown failure criterion, the Fairhurst criterion provides more depth for breakout than the Hoek-Brown criterion. However, due to the same compressive strength of the rock in these two criteria, the same failure width for breakout is obtained from these two criteria. Also, the results obtained for the depth of failure from the theoretical model based on the Fairhurst criterion are in good agreement with the laboratory results on Westerly granite.

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Marsh, P. G., and W. W. Gerberich. "A microscopically-shielded Griffith criterion for cleavage in grain oriented silicon steel." Acta Metallurgica et Materialia 42, no. 3 (March 1994): 613–19. http://dx.doi.org/10.1016/0956-7151(94)90257-7.

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Meshkov, Yu Ya. "Griffith energy criterion in the fracture micro-and macromechanics of brittle bodies." Metal Science and Heat Treatment 38, no. 1 (January 1996): 28–32. http://dx.doi.org/10.1007/bf01153869.

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Zhou, Zhen Gong, and Lin Zhi Wu. "The Non-Local Theory Solution of a Crack in the Functionally Graded Piezoelectric Materials Subjected to the Harmonic Anti-Plane Shear Stress Waves." Key Engineering Materials 353-358 (September 2007): 258–62. http://dx.doi.org/10.4028/www.scientific.net/kem.353-358.258.

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In this paper, the non-local theory of elasticity was applied to obtain the dynamic behavior of a Griffith crack in functionally graded piezoelectric materials under the harmonic anti-plane shear stress waves. The problem can be solved with the help of a pair of dual integral equations. Unlike the classical elasticity solutions, it is found that no stress and electric displacement singularities are present at the crack tips, thus allows us to use the maximum stress as a fracture criterion.

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Eldred, Roger J. "Effect of Oriented Platy Filler on the Fracture Mechanism of Elastomers." Rubber Chemistry and Technology 61, no. 4 (September 1, 1988): 619–29. http://dx.doi.org/10.5254/1.3536208.

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Abstract Through an investigation of tension fatigue failure modes, oriented platy fillers have been found to provide elastomers with a unique failure mechanism which allows the elastomer to resist destructive crack growth. Samples of chlorosulfonated polyethylene containing talc as a reinforcing agent failed in an interlaminar shear mode, parallel to the applied stress. This fracture pattern resulted from diversion of the classical Griffith-type crack which would normally proceed perpendicularly to the stress. The theoretical criterion for diversion requires the adhesive fracture energy, Gad, in the plane of the diverted crack to be about one-tenth of the cohesive fracture energy, Gco, in the plane of the Griffith crack. Measured values of the fracture energies determined by 180° peel (Gad) tests and trouser tear (Gco) tests showed that the talc-filled elastomer satisfied the criterion. However, the criterion was met, not by the introduction of planes of weakness in the lateral direction (thereby reducing Gad), but by a more than five-fold increase in the cohesive fracture energy over that measured for a control containing carbon black as reinforcing agent. Examination of the fractured surfaces by scanning electron microscopy showed that the increase in Gco was due to the many energy absorbing fracture paths down which the tear was diverted as it advanced through the elastomer. Besides exhibiting high tear energies, the elastomer was found to be highly insensitive to stress risers such as razor cuts. The combination of tear resistance and insensitivity to flaws leads to a prediction that elastomers containing oriented platy fillers will exhibit increased strength and durability. This first practical system affording crack diversion has special application to hoses and topologically similar shapes such as boots and sleeves.

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Wang, E. Z., and N. G. Shrive. "On the griffith criteria for brittle fracture in compression." Engineering Fracture Mechanics 46, no. 1 (September 1993): 15–26. http://dx.doi.org/10.1016/0013-7944(93)90300-h.

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Xie, Y. J., Xiao Zhi Hu, and X. H. Wang. "A Theoretical Note on Mode I Crack Kinking and Branching." Advanced Materials Research 118-120 (June 2010): 314–18. http://dx.doi.org/10.4028/www.scientific.net/amr.118-120.314.

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An energy-based fracture mode has been derived for the mode I crack kinking and branching. The classic -integral has been further explored by a new partial integral path and the analytical solution of the energy release rate for crack kinking and branching from a mode-I crack tip has been established. The crack kinking/branching angle has also been analytically derived. It shows that the Griffith’s theorem and conservation law can be applied to both model I crack extension and model I crack kinking and branching. The branching mechanism for quasi-static mode-I crack has been theoretically investigated. The branching toughness and the K-based criterion for crack branching have been defined. The crack branching phenomena predicted by the present model are in well agreement with the experimental observations reported in the literatures.

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Jeulin, D. "Fracture Statistics Models and Crack Propagation in Random Media." Applied Mechanics Reviews 47, no. 1S (January 1, 1994): S141—S150. http://dx.doi.org/10.1115/1.3122809.

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Crack propagation in heterogeneous media is of primary interest for engineering purposes, in order to predict the overall toughness and the probability of fracture from data on the microstructure. Probabilistic models for mode I crack propagation in two dimensions are presented. They are developed for brittle elastic materials with a random distribution of fracture energy. These models enable us to calculate in a closed form the probability of fracture involving crack nucleation and propagation that differ from the usual fracture statistics models based on the weakest link model. The use of the Griffith’s crack arrest criterion is applied to random function models for the distribution of the fracture energy and for various loading conditions resulting in stable or unstable crack propagation. From the models are deduced some statistical size effects.

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Chen, Bin, Jing Hong Fan, J. Wang, X. Peng, and Xiao Lin Wu. "Research of Nanostructure of Bivalva Shell." Journal of Metastable and Nanocrystalline Materials 23 (January 2005): 83–86. http://dx.doi.org/10.4028/www.scientific.net/jmnm.23.83.

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Molluscan shells is a natural ceramic composite with excellent fracture strength and fracture toughness, which are attributed to their unique microstructures. Sanning electron microscope (SEM) observation on Bivalva shell showed that the shell consists of laminated aragonite and organic layers. These aragonite and organic layers are provided with the scale and characteristics of nanometer. The effect and function of these nanometer structures were analyzed based on Griffith criterion and energy-dissipation idea. The higher fracture strength and fracture roughness of bionanocomposite-molluscan shell were well explained with nanometer viewpoint.

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Dienes, J. K. "Comments on “a generalized griffith criterion for crack propagation” by L. G. Margolin." Engineering Fracture Mechanics 23, no. 3 (January 1986): 615–17. http://dx.doi.org/10.1016/0013-7944(86)90165-7.

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Almi, Stefano. "Quasi-static hydraulic crack growth driven by Darcy’s law." Advances in Calculus of Variations 11, no. 2 (April 1, 2018): 161–91. http://dx.doi.org/10.1515/acv-2016-0029.

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AbstractIn the framework of rate independent processes, we present a variational model of quasi-static crack growth in hydraulic fracture. We first introduce the energy functional and study the equilibrium conditions of an unbounded linearly elastic body subject to a remote strain {\epsilon\in\mathbb{R}} and with a sufficiently regular crack Γ filled by a volume V of incompressible fluid. In particular, we are able to find the pressure p of the fluid inside the crack as a function of Γ, V, and ϵ. Then we study the problem of quasi-static evolution for our model, imposing that the fluid volume V and the fluid pressure p are related by Darcy’s law. We show the existence of such an evolution, and we prove that it satisfies a weak notion of the so-called Griffith’s criterion.

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Keer, Leon M. "Mechanics of Contact Fatigue." Applied Mechanics Reviews 47, no. 6S (June 1, 1994): S194—S198. http://dx.doi.org/10.1115/1.3124405.

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Contact fatigue between typical machine elements such as gears, roller followers, bearings and other components involves many complex interacting features. There are the effects of geometry, mechanical properties, material properties and surface chemistry. The present discussion will center around analytical prediction techniques that are concerned only with the mechanical aspects of contact fatigue between two elements. Aspects related to the initiation of a crack under repeated loading will be discussed. The application of an approach developed by Mura, analogous to Griffith’s criterion for fracture, will be used to show how estimates of initiation life can be made and how these estimates are related to currently used ones. Once a crack has been initiated, then issues related to crack propagation become important. Some fracture mechanics based methods developed to calculate crack growth will be described along with estimates of crack propagation life.

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Marazzato, Frédéric, Alexandre Ern, and Laurent Monasse. "Quasi-static crack propagation with a Griffith criterion using a variational discrete element method." Computational Mechanics 69, no. 2 (November 3, 2021): 527–39. http://dx.doi.org/10.1007/s00466-021-02102-5.

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