Modal analysis of the dynamic crack growth and arrest in a DCB specimen

Abdelmoula, Radhi; Debruyne, Gilles

doi:10.1007/s10704-014-9954-4

Cited by 6 publications

(14 citation statements)

References 10 publications

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“…Vibration may be one of the reasons why experiments used to measure initiation fracture toughness disagree on loading-rate effects [8]. Abdelmoula and Debruyne [9] investigated dynamic crack growth and arrest in a bimaterial DCB, using Euler-Bernoulli beams. Their theoretical model, which must be solved numerically, agrees well with the finite-element method (FEM).…”

Section: Introductionmentioning

confidence: 99%

Dynamic interfacial fracture of a double cantilever beam

Chen

Harvey

Wang

et al. 2020

Engineering Fracture Mechanics

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Assessment of the energy release rate (ERR) of layered material structures with account for dynamic and vibration effects is important for understanding and predicting fracture behavior in various engineering applications. In this work, the pure-mode-I interfacial fracture behavior of a symmetric double cantilever beam (DCB) under constant-rate opening displacement is studied using a dynamics and vibration analysis of Euler-Bernoulli beams, and the ERR is derived. Furthermore, a 'dynamic factor' that quantifies the dynamic effect in relation to the static component of ERR is defined. The resulting expressions are relatively short, mathematically elegant and convenient-to-use by engineers and researchers, which increases their usefulness. It is found that the dynamic factor is a function of the characteristic time only, and that this is an intrinsic property of DCB structures. An approximate method is also proposed to predict the crack extension. Predictions of ERR and crack extension are in good agreement with results from numerical results with finite-element method (FEM) simulations. Using only the first vibration mode is sufficient to capture the amplitude and frequency of ERR variation predicted by the FEM. Using higher-order vibration modes causes divergence in the amplitude of ERR oscillation; this is due to the limitation of Euler-Bernoulli beams in vibration analysis.

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Section: Introductionmentioning

confidence: 99%

Dynamic interfacial fracture of a double cantilever beam

Chen

Harvey

Wang

et al. 2020

Engineering Fracture Mechanics

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“…(1.28) Proposition 1.2 ensures that h (1) solves problem (1.21) in Ω T 1 . Now we can restart the argument from time…”

Section: Proposition 12 a Functionmentioning

confidence: 98%

“…By Lemma 1.4 the operator L maps Y ∩ C 0 (Ω T ) into itself. Now let h (1) , h (2) ∈ Y ∩ C 0 (Ω T ) and let (t, r) ∈ Ω T . Since h (1) , h (2) ∈ Y, one observes that in L[h (1) ] − L[h (2) ] there is a cancellation of the term H which only depends on the boundary conditions; hence,…”

Section: Proposition 12 a Functionmentioning

confidence: 99%

“…and that they satisfy the compatibility conditions h (1) (T 1 , 0) = z(T 1 ) and h (1) (T 1 , ρ 1 ) = 0. Arguing as before, we get the existence of a unique solution h (2) of (1.12) in Ω T 2 \ Ω T 1 with…”

Section: Proposition 12 a Functionmentioning

confidence: 99%

“…for every (h (1) , λ (1) ), (h (2) , λ (2) ) ∈ Z(M, T, y). Then by Lemma 3.4 and by the Ascoli-Arzelà Theorem, (Z(M, T, y), d) is a complete metric space.…”

Section: Now Definementioning

confidence: 99%

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Radial solutions for a dynamic debonding model in dimension two

Lazzaroni¹,

Molinarolo²,

Solombrino³

2020

Preprint

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In this paper we deal with a debonding model for a thin film in dimension two, where the wave equation on a time-dependent domain is coupled with a flow rule (Griffith's principle) for the evolution of the domain. We propose a general definition of energy release rate, which is central in the formulation of Griffith's criterion. Next, by means of an existence result, we show that such definition is well posed in the special case of radial solutions, which allows us to employ representation formulas typical of one-dimensional models.

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Crack Tip Equation of Motion in Dynamic Gradient Damage Models

Marigo

2016

J Elast

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International audienceWe propose in this contribution to investigate the link between the dynamic gradient damage model and the classical Griffith's theory of dynamic fracture during the crack propagation phase. To achieve this main objective, we first rigorously reformulate two-dimensional linear elastic dynamic fracture problems using variational methods and shape derivative techniques. The classical equation of motion governing a smoothly propagating crack tip follows by considering variations of a space-time action integral. We then give a variationally consistent framework of the dynamic gradient damage model. Owing to the analogies between the variational ingredients of these two models and under some basic assumptions concerning the damage band structuration, one obtains a generalized Griffith criterion which governs the crack tip evolution within the non-local damage model. Assuming further that the internal length is small compared to the dimension of the body, the previous criterion leads to the classical Griffith's law through a separation of scales between the outer linear elastic domain and the inner damage process zone

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Modal analysis of the dynamic crack growth and arrest in a DCB specimen

Cited by 6 publications

References 10 publications

Dynamic interfacial fracture of a double cantilever beam

Dynamic interfacial fracture of a double cantilever beam

Radial solutions for a dynamic debonding model in dimension two

Crack Tip Equation of Motion in Dynamic Gradient Damage Models

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