Williams meets von Karman: Mode coupling and nonlinearity in the fracture of thin plates

Chen, Hui; Zehnder, Alan T.; Potdar, Yogesh K.

doi:10.1007/978-94-017-2854-6_21

Cited by 8 publications

(12 citation statements)

References 17 publications

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“…• First, we are actually interested in situations with large geometric non-linearites, and the validity of this approach (based on linear plate equations) is not easy (Hui et al 1998), as well as the practical computation of the stress intensity factors from the imposed large scale loading. • A second question is to deduce the direction of propagation from the values of the stress intensity factor.…”

Section: Stress Intensity Factors In Thin Platesmentioning

confidence: 99%

Fracture path in brittle thin sheets: a unifying review on tearing

Roman

2013

Int J Fract

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We review several studies of crack path in brittle thin sheets where large out of plane bending is involved. Fracture path are observed to be very reproducible. We present a unifying framework based on an energetic point of view. A simplified description, where the sheet is considered to behave as an inextensible fabric, captures important features of experiments: the fact that fracture path seems to obey geometry. We quantify the possible effects of additional bending and stretching terms, and estimate the validity of the model.

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Section: Stress Intensity Factors In Thin Platesmentioning

confidence: 99%

Fracture path in brittle thin sheets: a unifying review on tearing

Roman

2013

Int J Fract

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“…How to extend the principle of local symmetry to this setting is not obvious (Roman, 2013). Furthermore, tearing is typically characterized by large geometric nonlinearity (Hamm et al, 2008;Bayart et al, 2010Bayart et al, , 2011Kruglova et al, 2011;Takei et al, 2013;Roman, 2013;Ibarra et al, 2016), and therefore it is not clear whether the crack tip fields of the linear theory characterized by the SIFs are meaningful (Hui et al, 1998) or if and how they determine crack propagation (Cohen and Procaccia, 2010). There have been attempts to develop theories that explain tearing in thin sheets including geometric nonlinearity (Cohen and Procaccia, 2010), which have focused on characterizing the stress state in the vicinity of the crack tip and have invoked a generalized principle of local symmetry.…”

Section: Accepted Manuscriptmentioning

confidence: 99%

A variational model of fracture for tearing brittle thin sheets

Millán

Torres-Sánchez

et al. 2018

Journal of the Mechanics and Physics of Solids

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Tearing of brittle thin elastic sheets, possibly adhered to a substrate, involves a rich interplay between nonlinear elasticity, geometry, adhesion, and fracture mechanics. In addition to its intrinsic and practical interest, tearing of thin sheets has helped elucidate fundamental aspects of fracture mechanics including the mechanism of crack path selection. A wealth of experimental observations in different experimental setups is available, which has been often rationalized with insightful yet simplified theoretical models based on energetic considerations. In contrast, no computational method has addressed tearing in brittle thin elastic sheets. Here, motivated by the variational nature of simplified models that successfully explain crack paths in tearing sheets, we present a variational phase-field model of fracture coupled to a nonlinear Koiter thin shell model including stretching and bending. We show that this general yet straightforward approach is able to reproduce the observed phenomenology, including spiral or power-law crack paths in free standing films, or converging/diverging cracks in thin films adhered to negatively/positively curved surfaces, a scenario not amenable to simple models. Turning to more quantitative experiments on thin sheets adhered to planar surfaces, our simulations allow us to examine the boundaries of existing theories and suggest that homogeneous damage induced by moving folds is responsible for a systematic discrepancy between theory and experiments. Thus, our computational approach to tearing provides a new tool to understand these complex processes involving fracture, geometric nonlinearity and delamination, complementing experiments and simplified theories.

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“…Using the large deflection von‐Karman plate theory (which assumes Kirchhoff‐like kinematics), Hui et al 13 . showed that the crack tip deformation fields can be described as a superposition of plane stress and Kirchhoff plate theory fields.…”

Section: Theorymentioning

confidence: 99%

“…In mixed‐mode problems, the crack tip fields can be described as a superposition of stress intensity factors from linear theories. However, in a fuselage, and in our test specimen, the deflection of the plate will be large, and thus non‐linear analyses are required 13 to correctly compute the stress intensity factors. In this work geometrically non‐linear analyses are used.…”

Section: Theorymentioning

confidence: 99%

Fatigue fracture in plates in tension and out‐of‐plane shear

Zehnder

Viz

Potdar

2000

Fatigue Fract Eng Mat Struct

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Straight cracks near a stiffening element, or curved cracks, in a pressurized shell can be subjected to out‐of‐plane tearing stresses in addition to normal tensile stresses due to the membrane stresses in the shell. To predict the rate of fatigue crack growth in such situations a theory and a crack growth rate correlation are needed. Such loadings are modelled as a superposition of plane stress tensile fracture (mode I) and Kirchhoff plate theory shearing fracture (mode 2). Finite element analyses using shell elements are used to compute the energy release rate and stress intensity factors associated with the loading. Three fatigue crack growth rate experiments were carried out on sheets of 2024‐T3 aluminium alloy loaded in tension and torsion. The first set of experiments is constant amplitude fatigue crack growth tests. The second consists of experiments where crack closure is artificially eliminated to determine the rate of crack growth in the absence of crack face contact. The third is a set of constant stress intensity factor amplitude tests. The results all show that as the crack grows extensive crack face contact occurs, retarding crack growth. In the absence of crack face contact, however, the addition of out‐of‐plane shear loading increases the crack growth rate substantially.

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Williams meets von Karman: Mode coupling and nonlinearity in the fracture of thin plates

Cited by 8 publications

References 17 publications

Fracture path in brittle thin sheets: a unifying review on tearing

Fracture path in brittle thin sheets: a unifying review on tearing

A variational model of fracture for tearing brittle thin sheets

Fatigue fracture in plates in tension and out‐of‐plane shear

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