Scaling Phenomena in Fatigue and Fracture

Баренблатт, Г. И.

doi:10.1007/s10704-006-0036-0

Cited by 48 publications

(34 citation statements)

References 24 publications

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“…two orders of magnitude, of values with practical significance. However, the underlying concept with great physical significance is that of 'intermediate asymptotics' (Barenblatt,[3], [25]). In order to illustrate the mathematical representation of the notion of 'intermediate asymptotics', let there be a phenomenon of interest with two limit values of a governing parameter x, say x 1 and x 2 , which differ substantially.…”

Section: The Role Of M 0 /M 1 Ratiomentioning

confidence: 99%

Dimensional analysis of the earthquake-induced pounding between inelastic structures

Dimitrakopoulos

Makris

Kappos

2010

Bull Earthquake Eng

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This is the accepted version of the paper.This version of the publication may differ from the final published version. Abstract In this paper the dynamic response of two and three pounding oscillators subjected to pulse type excitations is revisited with dimensional analysis. Using Buckingham's Π-theorem the number of variables that govern the response of the system is reduced by three. When the response is presented in the dimensionless Π-terms remarkable order emerges. It is shown that regardless of the acceleration level and duration of the pulse all response spectra become self-similar and follow a single master curve. This is true despite the realization of finite duration contacts with increasing durations as the excitation level increases. All physically realizable contacts (impacts, continuous contacts, and detachments) are captured via a linear complementarity approach. The study confirms the existence of three spectral regions. The response of the most flexible among the two oscillators amplifies in the low range of the frequency spectrum (flexible structures); whereas, the response of the most stiff among the two oscillators amplifies at the upper range of the frequency spectrum (stiff structures). Most importantly, the study shows that pounding structures such as colliding buildings or interacting bridge segments, may be most vulnerable for excitations with frequencies very different from their natural eigenfrequencies. Finally, by applying the concept of intermediate asymptotics, the study unveils that the dimensionless response of two pounding oscillators follows a scaling law with respect to the mass ratio, or in mathematical terms, that the response exhibits an incomplete selfsimilarity or self-similarity of the second kind with respect to the mass ratio. Permanent repository link

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Section: The Role Of M 0 /M 1 Ratiomentioning

confidence: 99%

Dimensional analysis of the earthquake-induced pounding between inelastic structures

Dimitrakopoulos

Makris

Kappos

2010

Bull Earthquake Eng

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“…2). The values of the critical scale l sc for various stages of crack propagation are presented in the table.Manifestations of the self similar nature of the fatigue crack growth were studied using methods of the theory of similarity and dimensionality [6,7]. The crack growth rate was defined as a = dl/dN (where l is the crack length and N is the number of cycles) and studied as for correlation with the following parame ters: a 1 = ΔK, stress intensity coefficient; a 2 = E, Young's modulus; a 3 = l sc , correlation scale in the ensemble of defects; a 4 = L pz , the scale related to the process zone.…”

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confidence: 99%

“…The crack growth rate was defined as a = dl/dN (where l is the crack length and N is the number of cycles) and studied as for correlation with the following parame ters: a 1 = ΔK, stress intensity coefficient; a 2 = E, Young's modulus; a 3 = l sc , correlation scale in the ensemble of defects; a 4 = L pz , the scale related to the process zone. β , we can reduce the scaling relation (3) to the following form analogous to the Paris law: (6) where α is a universal exponent.…”

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Scaling invariance of fatigue crack growth in gigacycle loading regime

et al. 2010

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is an open access repository that collects the work of Arts et Métiers ParisTech researchers and makes it freely available over the web where possible.This is an author-deposited version published in: http://sam.ensam.eu Handle ID: .http://hdl.handle.net/10985/10516To cite this version :V. OBORIN, M. BANNIKOV, O. NAIMARK, Thierry PALIN-LUC -Scaling invariance of fatigue crack growth in gigacycle loading regime -Tech. Phys. Lett. -Vol. 36, n°11, p.1061-1063 -2010 Any correspondence concerning this service should be sent to the repository Administrator : archiveouverte@ensam.euThe task of assessing the working resource of important structures, in particular, those for aircraft engines, poses qualitatively new basic problem related to evaluation of the reliability of materials under con ditions of cyclic loading in excess of 10 6 -10 10 cycles, which refer to the field of so called gigacycle fatigue. This interest is related to the fact that the resource of loading for many important parts operating under conditions of cyclic loading exceeds the so called multicycle range. the behavior of materials in the range of gigacycle fatigue reveals some qualitative changes in the laws governing both the nucleation of cracks (in the bulk of a sample) and their propagation, which are related to changes in the mechanisms of fatigue crack nucleation and propagation. In the range of gigacycle loading, the fatigue curve exhibits discon tinuities and the behavior shows evidence of a signifi cant increase in the role of environment, so that the problem acquires an interdisciplinary character.The stages of material fracture in the range of giga cycle loading are classified based on the structural signs of damage related to a broad spectrum of spatial scales, including persistent slip bands (PSBs), fatigue striations, microcracks (formed as a result of PSB crossing), and grain boundary defects. The main damage refers to the defect scales within 0.1 μm-1 mm, which are significantly smaller than those detected by the standard methods of nondestructive testing used for the conventional monitoring of reli ability, in particular, during the exploitation of build ings.An effective method for investigating the role of initial structural heterogeneity, monitoring the accu mulation of defects on various scales (dislocation ensembles, micropores, microcracks), and determin ing critical conditions for the transition from dispersed to macroscopic fracture is offered by the quantitative fractography. This technique reveals the characteristic stages of fracture (crack nucleation and propagation), thus providing a base for evaluating the temporal resource of materials and structures under conditions of gigacycle loading.The approach to characterization of the fracture surface morphology in terms of spatiotemporal invari ants was originally proposed by Mandelbrot [1]. This method is based on an analysis of the relief of a frac ture surface, which exhibits the property of self affin ity as manifested by the invariant characteristics of the surrace re...

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“…[1][2][3][4][5][6][7][8][9][10][11][12][13] In particular, the power-law divergence of the susceptibility in the vicinity of the point of material failure was one of the crucial aspects of this concept. Several studies attacked this problem utilizing different approaches: Quenched and annealed model formulations, thermal and non-thermal ensembles, different model dimensionalities.…”

Section: Introductionmentioning

confidence: 99%

Non-thermal quenched damage phenomena: The application of the mean-field approach for the three-dimensional case

Abaimov

Akhatov

2016

AIP Advances

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In this study, we apply the mean-field approach to the three-dimensional damage phenomena. The model approximates a solid as a polycrystalline material where grains are assumed isotropic. While the stiffness properties are considered homogeneous, the heterogeneous distribution of grains’ strengths provides the quenched statistical variability generating non-thermal fluctuations in the ensemble. Studying the statistical properties of the fluctuations, we introduce the concept of susceptibility of damage. Its divergence in the vicinity of the point of material failure can be treated as a catastrophe predictor. In accordance with this criterion, we find that damage growth in reality is much faster than it could be expected from intuitive engineering considerations. Also, we consider avalanches of grain failures and find that due to the slowing down effect the characteristic time of the relaxation processes diverges in the vicinity of the point of material failure.

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Scaling Phenomena in Fatigue and Fracture

Cited by 48 publications

References 24 publications

Dimensional analysis of the earthquake-induced pounding between inelastic structures

Dimensional analysis of the earthquake-induced pounding between inelastic structures

Scaling invariance of fatigue crack growth in gigacycle loading regime

Non-thermal quenched damage phenomena: The application of the mean-field approach for the three-dimensional case

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