Fracture Mechanics

Miannay, D.

doi:10.1007/978-1-4612-1740-4

Cited by 61 publications

(27 citation statements)

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“…He argued that when the solutions given in [9] are converted to use polar coordinates, the resulting stress is a function of a stress intensity factor (SIF) and a series of trigonometric functions. By equating the work done to open the crack to the strain energy release rate, Irwin demonstrated the equivalence of the SERR and the SIF, which is now usually written as [10,11]:…”

Section: Historical Reviewmentioning

confidence: 99%

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On the relationship between disbond growth and the release of strain energy

Pascoe

Alderliesten

Benedictus

2015

Engineering Fracture Mechanics

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Current prediction methods for growth of disbonds under fatigue loading are generally based on a correlation with either the maximum strain energy release rate (SERR) or the SERR range. This paper highlights some issues with this approach. In particular, it is argued that the maximum SERR or the SERR range alone do not give sufficient information to uniquely characterize the driving force for crack growth. Furthermore it is argued that the relationship between crack growth rate and loss of strain energy should be considered on the scale of the entire load cycle. By means of disbond growth experiments it is shown that there is indeed a very strong correlation between the crack growth rate and the strain energy lost during a fatigue cycle. Unlike methods based on the SERR, this correlation is not affected by the R-ratio. Based on the found correlation a possible basis for a new approach to disbond growth prediction is suggested.

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Section: Historical Reviewmentioning

confidence: 99%

“…In the case of plane stress E = E, and for plane strain E = E/ 1 − ν 2 [10], where E is Young's modulus and ν is Poisson's ratio. Note that strictly speaking this equation only holds if K a = K a+∆a , i.e.…”

Section: Historical Reviewmentioning

confidence: 99%

On the relationship between disbond growth and the release of strain energy

Pascoe

Alderliesten

Benedictus

2015

Engineering Fracture Mechanics

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“…Traditional approaches given in popular textbooks (Anderson, 1995;Miannay, 1998) present the stress fields ahead of a crack tip as a combination of three modes, while the majority of the analytical or numerical studies deal only with two-dimensional problems.…”

Section: Introductionmentioning

confidence: 99%

Three-dimensional Correction of the Stress Intensity Factor for Plate with a Notch

et al. 2005

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International Journal of Fracture (2005) 136:75-98Abstract. The 3D effects of the 2D mode I stress intensity factor for the plate with a V-shaped straight through-thickness notch are investigated by the finite element method and three-dimensional thicknessdependent correction of SIF is suggested. The correction relies on the assumed relationship between the SIF and the constraint factor (out-of-plane degree of freedom). The 3D finite element mesh generator combining the 2D in-plane adaptive unstructured mesh with the structured through-thickness mesh Is developed and applied for the analysis purposes. Three-dimensionality was examined by using two independent indicators, namely, stress-or strain-based constraint factors. The three-point bend and tensile center-cracked plates are investigated. The results demonstrated that the developed 3D corrections may be treated as upper bound estimates of the SIF for three-point bend plate,while directly obtained numerical values are considered as lower bound estimates. Analysis of the tensile center-cracked plate demonstrated a different nature of the 3D SIF profile, which cannot be simply explained as a transitional state between plain strain and plain stress. Therefore, the suggested 3D correction concept is of a particular character.

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“…For Weibull statistics, the mean strength σ f and the associated SD δ(σ f ) then scale with sample size L as σ f ðLÞ ∼ δðσ f ÞðLÞ ∼ L −d=m . This approach has been successfully applied to the statistics of brittle failure strength under tension (7,13), with m in the range 6-30 (14). It implies a vanishing strength for L → +∞, although this decrease can be rather shallow, owing to the large values of m often reported.…”

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confidence: 99%

(Finite) statistical size effects on compressive strength

Weiss

Girard

Gimbert

et al. 2014

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

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The larger structures are, the lower their mechanical strength. Already discussed by Leonardo da Vinci and Edmé Mariotte several centuries ago, size effects on strength remain of crucial importance in modern engineering for the elaboration of safety regulations in structural design or the extrapolation of laboratory results to geophysical field scales. Under tensile loading, statistical size effects are traditionally modeled with a weakest-link approach. One of its prominent results is a prediction of vanishing strength at large scales that can be quantified in the framework of extreme value statistics. Despite a frequent use outside its range of validity, this approach remains the dominant tool in the field of statistical size effects. Here we focus on compressive failure, which concerns a wide range of geophysical and geotechnical situations. We show on historical and recent experimental data that weakest-link predictions are not obeyed. In particular, the mechanical strength saturates at a nonzero value toward large scales. Accounting explicitly for the elastic interactions between defects during the damage process, we build a formal analogy of compressive failure with the depinning transition of an elastic manifold. This critical transition interpretation naturally entails finite-size scaling laws for the mean strength and its associated variability. Theoretical predictions are in remarkable agreement with measurements reported for various materials such as rocks, ice, coal, or concrete. This formalism, which can also be extended to the flowing instability of granular media under multiaxial compression, has important practical consequences for future design rules.O wing to its importance for structural design (1), the elaboration of safety regulations (2), or the extrapolation of laboratory results to geophysical field scales (3), the size effects on strength of materials are one of the oldest problems in engineering, already discussed by Leonardo da Vinci and Edmé Mariotte (4) several centuries ago, but still an active field of research (5, 6). As early as 1686, Mariotte (4) qualitatively introduced the weakestlink concept to account for size effects on mechanical strength, a phenomenon evidenced by Leonardo da Vinci almost two centuries earlier. This idea, which states that the larger the system considered is, the larger the probability to find a particularly faulty place that will be at the origin of global failure, was formalized much later by Weibull (7). Considering a chain of elementary independent links, the failure of the chain is obtained as soon as one link happens to break. By virtue of the independence between the potential breaking events, the survival probability of a chain of N links is obtained by the simple multiplication of the N elementary probabilities. Depending on the properties of the latter, the global survival probability converges toward one of the three limit distributions identified by Weibull (7), Gumbel (8), and Fréchet (8), respectively. Together with Fisher and Tippett (9), t...

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Fracture Mechanics

Cited by 61 publications

References 0 publications

On the relationship between disbond growth and the release of strain energy

On the relationship between disbond growth and the release of strain energy

Three-dimensional Correction of the Stress Intensity Factor for Plate with a Notch

(Finite) statistical size effects on compressive strength

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