Self-similarity and fractals in the Paris range of fatigue crack growth

Spagnoli, Andrea

doi:10.1016/j.mechmat.2004.04.003

Cited by 83 publications

(55 citation statements)

References 19 publications

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“…(8) can be regarded either as a structural-size dependent Paris' law (Carpinteri and Spagnoli 2004), or as a crack-size dependent fatigue crack growth law (Spagnoli 2005). Note that such an equation is formally identical to the classical Paris' law in Eq.…”

Section: Fractal Approaches To Fatiguementioning

confidence: 99%

“…In the case of large structural sizes where the transition from disorder to order takes place, d G → 0, and no size effects occur. This model was referred to as monofractal approach to size effect on fatigue crack growth in (Carpinteri and Spagnoli 2004;Spagnoli 2005). It was also noticed that it can be applied within a limited scale range.…”

Section: Fractal Approaches To Fatiguementioning

confidence: 99%

“…It was also noticed that it can be applied within a limited scale range. The use of a multifractal approach was also suggested in (Carpinteri and Spagnoli 2004;Spagnoli 2005) to model the propagation of both short and long fatigue cracks, although this possibility remained unexplored.…”

Section: Fractal Approaches To Fatiguementioning

confidence: 99%

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A unified fractal approach for the interpretation of the anomalous scaling laws in fatigue and comparison with existing models

Carpinteri

Paggi

2009

Int J Fract

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In this paper, a critical reexamination of the fractal models for the analysis of crack-size effects in fatigue is proposed. The enhanced ability to detect and measure very short cracks has in fact pointed out the so-called anomalous behavior of short cracks with respect to their longer counterparts. The cracksize dependencies of both the fatigue threshold and the Paris' constant C are only two notable examples of these anomalous scaling laws. In this context, a unified theoretical model seems to be missing and the behavior of short cracks can still be considered as an open problem. A new generalized theory based on fractal geometry is herein proposed, which permits to consistently interpret the short crack-related anomalous scaling laws within a unified theoretical framework. The proposed model is used to interpret relevant experimental data related to the crack-size dependence of the fatigue threshold in metals. As a main result, the model gives an explanation to the experimentally observed variability in the slope of the asymptote of the scaling law for the fatigue threshold in the short crack regime.

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Section: Fractal Approaches To Fatiguementioning

confidence: 99%

Section: Fractal Approaches To Fatiguementioning

confidence: 99%

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A unified fractal approach for the interpretation of the anomalous scaling laws in fatigue and comparison with existing models

Carpinteri

Paggi

2009

Int J Fract

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“…of a fracture surface as a fractal, has been further developed in [47,48]. Used was made of the renormalisation techniques to develop a growth law for an invasive lacunar fractal, viz.…”

Section: Cracks As Fractalsmentioning

confidence: 99%

“…tionship follows the form proposed in [47,48] and therefore has an underlying incomplete self-similarity, or self-similarity of the second kind. These findings It was revealed in [50] that:…”

Section: Cracks As Fractalsmentioning

confidence: 99%

A multi-scale approach to crack growth

Jones¹,

Barter²,

Molent³

et al.

Multiscaling in Molecular and Continuum Mechanics: Interaction of Time and Size From Macro to Nano

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This work first examines the fatigue crack growth histories (from microns to millimetres) of a range of test specimens and service loaded components and concludes that in most cases rack growth follows the generalised Frost and Dugdale crack growth law, i.e. as a first approximation there is a linear relationship between the log of the crack length or depth and the service history (number of cycles). It is then shown how the Frost and Dugdale crack growth law, incomplete self-similarity, the two parameter crack growth model, and fractal fatigue concepts are related. Also shown are how this law can be used to predict crack growth from sub microns to mm's in a range of full-scale aircraft fatigue tests and coupon tests, including aircraft fuselage lap-joints.

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Correlation Between Paris’ Law Parameters Based on Self-Similarity and Criticality Condition

Carpinteri

Paggi

Fracture of Nano and Engineering Materials and Structures

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Self-similarity and fractals in the Paris range of fatigue crack growth

Cited by 83 publications

References 19 publications

A unified fractal approach for the interpretation of the anomalous scaling laws in fatigue and comparison with existing models

A unified fractal approach for the interpretation of the anomalous scaling laws in fatigue and comparison with existing models

A multi-scale approach to crack growth

Correlation Between Paris’ Law Parameters Based on Self-Similarity and Criticality Condition

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