Fracture Kinetics of Crack Growth

Krausz, A. S.; Krausz, K.

doi:10.1007/978-94-009-1381-3

Cited by 75 publications

(64 citation statements)

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“…4. At the atomic lattice scale, it may be assumed, in general, that each jump is independent (i.e., the frequency of the jump is independent of the particular history of breaking and restoration sequences that brought the nanocrack to the current length) (20). The failure probability of the atomic lattice on sudden application of stress can thus be writ-…”

Section: )mentioning

confidence: 99%

Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics

Bažant

Bazant

2009

Proc. Natl. Acad. Sci. U.S.A.

105

110

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The failure probability of engineering structures such as aircraft, bridges, dams, nuclear structures, and ships, as well as microelectronic components and medical implants, must be kept extremely low, typically <10 −6 . The safety factors needed to ensure it have so far been assessed empirically. For perfectly ductile and perfectly brittle structures, the empirical approach is sufficient because the cumulative distribution function (cdf) of random material strength is known and fixed. However, such an approach is insufficient for structures consisting of quasibrittle materials, which are brittle materials with inhomogeneities that are not negligible compared with the structure size. The reason is that the strength cdf of quasibrittle structure varies from Gaussian to Weibullian as the structure size increases. In this article, a recently proposed theory for the strength cdf of quasibrittle structure is refined by deriving it from fracture mechanics of nanocracks propagating by small, activationenergy-controlled, random jumps through the atomic lattice. This refinement also provides a plausible physical justification of the power law for subcritical creep crack growth, hitherto considered empirical. The theory is further extended to predict the cdf of structural lifetime at constant load, which is shown to be size-and geometry-dependent. The size effects on structure strength and lifetime are shown to be related and the latter to be much stronger. The theory fits previously unexplained deviations of experimental strength and lifetime histograms from the Weibull distribution. Finally, a boundary layer method for numerical calculation of the cdf of structural strength and lifetime is outlined.cohesive fracture | crack growth rate | extreme value statistics | size effect | multiscale transition A comprehensive theory of the statistical strength distribution exists only for perfectly brittle structures failing at macrocrack initiation from a negligibly small representative volume element (RVE) of material. The objective of the present article is to extend recent studies (1-3) by developing a comprehensive and atomistically based theory for strength and lifetime distributions of structures consisting of quasibrittle materials. These materials, which include fiber composites, concretes, rocks, stiff soils, foams, sea ice, consolidated snow, bone, tough industrial and dental ceramics, and many other materials on approach to nanoscale, are characterized by a RVE that is not negligible compared with structure size D. The space does not allow commenting on previous valuable contributions made by Coleman (4), Zhurkov (5, 6), Freudenthal (7), Phoenix (8, 9) and others (10, 11) (for such comments, see, e.g., refs. 2, 3, 12, and 13).

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Section: )mentioning

confidence: 99%

Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics

Bažant

Bazant

2009

Proc. Natl. Acad. Sci. U.S.A.

105

110

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“…It seems reasonable to assume that the rate effect on each microplane component is of the same type as given by eqn. (2). Consequently the rate dependency for each microplane component reads (Bažant et al [1]): where c 0 and c 2 are material rate constants which have to be calibrated by fitting of the test data, ij ε = components of the macroscopic strain rate tensor (indicial notation).…”

Section: Rate Dependancy In the M2-o Microplane Modelmentioning

confidence: 99%

“…Here is for the rate dependency of the crack propagation adopted a model, which is applicable over many orders of magnitude of the loading rate. The model is based on the rate process theory (Krausz and Krausz [2]) of bond ruptures. It is coupled with the M2-O microplane model for concrete (Ožbolt et al [3]), which has been shown to be capable to realistically simulate failure of concrete structures for complex threedimensional stress-strain states (Ožbolt [4]).…”

Section: Introductionmentioning

confidence: 99%

Influence of loading rate on concrete cone failure

2006

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In the present paper the rate sensitive model, which is based on the energy activation theory of bond rupture, and its implementation into the M2-O microplane model for concrete are discussed. It is first demonstrated that the new model realistically predicts the influence of the loading rate on the uniaxial compressive behaviour of concrete. The new rate sensitive microplane model is then applied in a 3D finite element study of the pull-out of the headed stud anchors from a concrete block. In the study the influence of the loading rate on the pull-out capacity and on the size effect are investigated. The anchors are loaded with relatively high loading rates. The results of the study show that with the increase of the loading rate the nominal pull-out resistance increases. Moreover, it has been found that the size effect on the concrete cone capacity is stronger when the loading rate is higher. The result of numerical study implies that it must exist a problem dependent critical loading rate for which the size effect is minimal. INTRODUCTIONIt is well known that the loading rate influence significantly structural response. The material response depends on the loading rate through influence two different effects: (1) through the rate dependency of the growing microcracks and (2) through the creep of the bulk material between the cracks. Depending on the material, it dominates the first or the second effect. For quasibrittle materials, such as a concrete, which exhibit cracking and damage phenomena the first effect dominates for very high loading rates (impact loading). This is especially thru for the case of recently observed phenomena (Bažant et al. [1]) for which a sudden increase of the loading rate in softening leads to reversal of softening into hardening. However, for lower loading rates the second effect is more important.In the literature can be found a number of theoretical and experimental studies that deal with the problem of the rate effect for different materials (for literature review see Bažant et al. [1]). In most of these studies various stress-displacement relations, similar to the spring-dashpot models of viscoelasticity, were used. However, as pointed out by Bažant et al.[1] these models performs well only for one order of magnitude of the loading rate. Here is for the rate dependency of the crack propagation adopted a model, which is applicable over many orders of magnitude of the loading rate. The model is based on the rate process theory (Krausz and Krausz [2]) of bond ruptures. It is coupled with the M2-O microplane model for concrete (Ožbolt et al. [3]), which has been shown to be capable to realistically simulate failure of concrete structures for complex threedimensional stress-strain states (Ožbolt [4]).Experience, a large number of experiments as well as numerical studies for anchors of different sizes confirm that fastenings are capable to transfer a tension force into a concrete member without using reinforcement (Eligehausen et al. [5]). Provided the steel strength of the a...

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“…Healing could be considered by subtracting a healing rate function f heal from the dynamic function of damage, in a way similar to Krausz and Krausz [28],…”

Section: Healingmentioning

confidence: 99%

Anisotropic damage mechanics for viscoelastic ice

Pralong

Hutter

Funk

2006

Continuum Mech. Thermodyn.

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We present a formulation of continuum damage in glacier ice that incorporates the induced anisotropy of the damage effects but restricts these formally to orthotropy. Damage is modeled by a symmetric second rank tensor that structurally plays the role of an internal variable. It may be interpreted as a texture measure that quantifies the effective specific areas over which internal stresses can be transmitted. The evolution equation for the damage tensor is motivated in the reference configuration and pushed forward to the present configuration. A spatially objective constitutive form of the evolution equation for the damage tensor is obtained. The rheology of the damaged ice presumes no volume conservation. Its constitutive relations are derived from the free enthalpy and a dissipation potential, and extends the classical isotropic power law by elastic and damage tensor dependent terms. All constitutive relations are in conformity with the second law of thermodynamics.

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Fracture Kinetics of Crack Growth

Cited by 75 publications

References 0 publications

Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics

Scaling of strength and lifetime probability distributions of quasibrittle structures based on atomistic fracture mechanics

Influence of loading rate on concrete cone failure

Anisotropic damage mechanics for viscoelastic ice

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