Elastic Solids with Many Cracks and Related Problems

Kachanov, Mark

doi:10.1016/s0065-2156(08)70176-5

Cited by 744 publications

(571 citation statements)

References 133 publications

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“…This gives rise to elastic strain incompatibilities and microcracks are needed in order to accommodate plastic deformation. Both for AeWet and AeDry, the evolution of crack density was calculated from P wave velocities evolution (Figure 2) using two well-established Effective Medium theories: the NonInteracting Cracks [Kachanov, 1994] and the Extended Differential Self-Consistent (DEM) [Le Ravalec and Guéguen, 1996] methods. The DEM has been proven to be the most reliable method to calculate the effective elastic properties of cracked rocks [Orlowsky et al, 2003] as it takes into account the existing stress interactions between cracks.…”

Section: Discussionmentioning

confidence: 99%

Transient creep, aseismic damage and slow failure in Carrara marble deformed across the brittle‐ductile transition

Schubnel

Walker²,

Thompson

et al. 2006

Geophysical Research Letters

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[1] Two triaxial compression experiments were performed on Carrara marble at high confining pressure, in creep conditions across the brittle-ductile transition. During cataclastic deformation, elastic wave velocity decrease demonstrated damage accumulation (microcracks). Keeping differential stress constant and reducing normal stress induced transient creep events (i.e., fast accelerations in strain) due to the sudden increase of microcrack growth. Tertiary creep and brittle failure followed as damage came close to criticality. Coalescence and rupture propagation were slow (60 -200 seconds with $150 MPa stress drops and millimetric slips) and radiated little energy in the e x p e r i m e n t a l f r e q u e n c y r a n g e ( 0 . 1 -1 M H z ). Microstructural analysis pointed out strong interactions between intra-crystalline plastic deformation (twinning and dislocation glide) and brittle deformation (microcracking) at the macroscopic level. Our observations highlight the dependence of acoustic efficiency on the material's rheology, at least in the ultrasonic frequency range, and the role played by pore fluid diffusion as an incubation process for delayed failure triggering. Citation: Schubnel,

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Section: Discussionmentioning

confidence: 99%

Transient creep, aseismic damage and slow failure in Carrara marble deformed across the brittle‐ductile transition

Schubnel

Walker²,

Thompson

et al. 2006

Geophysical Research Letters

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“…4 shows that the self-consistent scheme predicts zero secant stiffness for a finite value of the crack density parameter, p = 9/16. This is contradicted by tests of concrete and other quasi-brittle materials which show that the post-peak softening diagram has a very long tail (Budiansky and O'Connell, 1976 ;Sayers and Kachanov, 1991 ;Kachanov, 1992;Kachanov, 1993).…”

Section: Equivalent Elastic Stiffness Predicted By the Self-consistenmentioning

confidence: 94%

“…2). Lest it be thought that the assumption of circular cracks might be overly restrictive, note that under certain conditions stated by Kachanov (Kachanov, 1993), circular cracks can be used as an approximation of elliptical cracks for the purpose of calculating the secant moduli. For that purpose, and for the case of the self-consistent scheme or the differential scheme, circular cracks of nonuniform radius can be approximated by uniform cracks for which the cube of the radius is the average of the cubes of the radii of the individual cracks.…”

Section: Equivalent Elastic Modulus Of a Materials With Uniforml Y Dismentioning

confidence: 99%

“…Approximate estimation of this function has been extensively reviewed by Kachanov and co-workers (Kachanov, 1992;Kachanov, 1993;Sayers and Kachanov, 1991;Kachanov et al, 1994). The incremental constitutive relation can be obtained by differentiation of (14), which yields (16) where L\ denotes small increments over a loading step.…”

Section: Equivalent Elastic Modulus Of a Materials With Arbitraril Y Omentioning

confidence: 99%

“…Crack arrays of various configurations have been analyzed. Variational bounds on the effective elastic moduli of crack materials have also been obtained (Kachanov, 1992(Kachanov, , 1993. Highly accurate numerical solutions for elastic bodies with various examples of specific crack configurations have been presented (Kachanov, 1992).…”

Section: Introductionmentioning

confidence: 99%

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Tangential stiffness of elastic materials with systems of growing or closing cracks

Prat

Bažant

1997

Journal of the Mechanics and Physics of Solids

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Although much has been learned about the elastic properties of solids with cracks, virtually all the work has been confined to the case when the cracks are stationary, that is, neither grow nor shorten during loading. In that case, the elastic moduli obtained are the secant moduli. The paper deals with the practically much more important but more difficult case of tangential moduli for incremental deformations of the material during which the cracks grow while remaining critical, or shorten. Several families of cracks of either uniform or random orientation, characterized by the crack density tensor, are considered. To simplify the solution, the condition of crack criticality, i.e. the equality of the energy release rate to the energy dissipation rate based on the fracture energy of the material, is imposed only globally for all the cracks in each family, rather than individually for each crack. Sayers and Kachanov's approximation of the elastic potential as a tensor polynomial that is quadratic in the macroscopic stress tensor and linear in the crack density tensor, with coefficients that are general nonlinear functions of the first invariant of the crack density tensor, is used. The values of these coefficients can be obtained by one of the well-known schemes for elastic moduli of composite materials, among which the differential scheme is found to give more realistic results for post-peak strain softening of the material than the self-consistent scheme. For a prescribed strain tensor increment, a system of N + 6 linear equations for the increments of the stress tensor and of the crack size for each of N crack families is derived. Iterations of each loading step are needed to determine whether the cracks in each family grow, shorten, or remain stationary. The computational results are qualitatively in good agreement with the stress-strain curves observed in the testing of concrete.

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Fatigue Behavior of Polymers

Lesser

2002

Encyclopedia of Polymer Science and Technology

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Polymers and polymer‐based composites are increasingly displacing more traditional materials in a wide variety of engineering applications, and as such characterization of their fatigue behavior is of utmost importance. This article presents a general overview of the fatigue behavior of polymers. After a brief introduction that includes general terminology, the effects of test conditions (sample geometry, loading frequency, etc) are discussed. The effects of these conditions are also discussed in relevance to both the high cycle and low cycle fatigue behavior. Current models for predicting fatigue life are also reviewed, including cumulative damage theories and fatigue crack propagation models. Morphological and environmental effects are then discussed over a broad range of semicrystalline, amorphous, and modified polymer systems.

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Elastic Solids with Many Cracks and Related Problems

Cited by 744 publications

References 133 publications

Transient creep, aseismic damage and slow failure in Carrara marble deformed across the brittle‐ductile transition

Transient creep, aseismic damage and slow failure in Carrara marble deformed across the brittle‐ductile transition

Tangential stiffness of elastic materials with systems of growing or closing cracks

Fatigue Behavior of Polymers

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