A Normal Stress Criterion for Crack Extension Direction in Orthotropic Composite Materials

For isotropic materials, stress-and energy-based fracture criteria lead to fairly similar results. Theoretical studies show that the crack-path predictions made by these criteria are not identical in the presence of strong material anisotropy. Therefore, experiments are performed to ascertain which criterion may apply to anisotropic materials. Notched specimens made from sapphire, a microscopically homogeneous and brittle solid, are used for the experiments. An attempt is made to locate the notch on different crystallographic planes and thus to examine the fracture path along different cleavage planes. The experimental observations are compared with the numerical results of the maximum tensile stress and the maximum energy-release rate criteria. It is observed that most of the notched specimens are fractured where the tensile stress is maximum, whereas the energy criterion fails to predict the fracture path of most of the specimens. For the tensile-stress Žn.fracture criterion, a dimensionless parameter, A s 2p R s r g E , is introduced, where s and E , respectively, ' ' 0 n n a n n n n n n Ž are the tensile stress and Young's modulus in the direction normal to the cleavage plane specified by the angle a the . fracture surface energy of this plane is g and R is a characteristic length, e.g. the notch radius. Five out of six notched a 0 specimens which were tested, fractured at the point and along a cleavage plane where A Žn. is maximum. This parameter takes into account the effects of the surface energy of the corresponding cleavage plane, as well as the strength of the atomic bonds in the direction normal to the cleavage plane. It is suggested that for a specimen with a pre-existing crack, the Žc. maximum value of the parameter, A s K r g E , should be used as the measure of the fracturing condition, where ' nn a n n K is the hoop stress intensity factor in the direction normal to the cleavage plane. For the notched sapphire specimens, nn Laue-diffraction analysis, along with the considerations of the geometry of the unit cell of sapphire, shows that the weakest Ä 4 Ä 4 family of cleavage planes, 1012 and 1010 , are the fractured planes. q

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“…by Buczek and Herakovich 1985 . They suggest that Ž a crack kinks in the f-direction if the ratio R r , 0 .…”

Section: Comments On the Fracture Criterionmentioning

confidence: 93%

“…strain-energy-density function Sih, 1972 , the nor-Ž . mal-stress ratio Buczek and Herakovich, 1985 and Ž the tensor polynomial Tsai and Wu, 1971;Wu, . 1974 .…”

Section: Introductionmentioning

confidence: 99%

Experimental and computational study of fracturing in an anisotropic brittle solid

Azhdari

Nemat‐Nasser

1998

Mechanics of Materials

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“…To what extent a crack can propagate in the direction of maximal tensile stress-parallel to the substrate/film interface-rather than deviate into a plane of lower fracture energy is still a matter of debate. 25,26 A theoretical framework providing accurate predictions on the propagation direction of cracks in anisotropic media would lead to a clear determination of the systems as well as the crystallographic film orientations that can be obtained using the layer transfer technique. Work on this topic is currently in progress.…”

Section: Discussionmentioning

confidence: 99%

Competing failure mechanisms in thin films: Application to layer transfer

Ponson

Diest

Atwater

et al. 2009

Journal of Applied Physics

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We investigate the origin of transverse cracks often observed in thin films obtained by the layer transfer technique. During this process, two crystals bonded to each other containing a weak plane produced by ion implantation are heated to let a thin layer of one of the material on the other. The level of stress imposed on the film during the heating phase due to the mismatch of thermal expansion coefficients of the substrate and the film is shown to be the dominent factor in determining the quality of the transferred layer. In particular, it is shown that if the film is submitted to a tensile stress, the microcracks produced by ion implantation are not stable and deviate from the plane of implantation making the layer transfer process impossible. However, if the compressive stress exceeds a threshold value, after layer transfer, the film can buckle and delaminate, leading to transverse cracks induced by bending. As a result, we show that the imposed stress m -or equivalently the heating temperature-must be within the range − c Ͻ m Ͻ 0 to produce an intact thin film where c depends on the interfacial fracture energy and the size of defects at the interface between film and substrate.

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“…For a given α, the gap will propagate at the angle θ max that maximizes the ratio between stress and toughness (see, e.g., [17,18]),…”

Section: Modelmentioning

confidence: 99%

Circumferential gap propagation in an anisotropic elastic bacterial sacculus

Taneja

Levitan²,

Rutenberg³

2014

Phys. Rev. E

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We have modelled stress concentration around small gaps in anisotropic elastic sheets, corresponding to the peptidoglycan sacculus of bacterial cells, under loading corresponding to the effects of turgor pressure in rod-shaped bacteria. We find that under normal conditions the stress concentration is insufficient to mechanically rupture bacteria, even for gaps up to a micron in length. We then explored the effects of stress-dependent smart-autolysins, as hypothesised by Arthur L Koch [Advances in Microbial Physiology 24, 301 (1983); Research in Microbiology 141, 529 (1990)]. We show that the measured anisotropic elasticity of the PG sacculus can lead to stable circumferential propagation of small gaps in the sacculus. This is consistent with the recent observation of circumferential propagation of PG-associated MreB patches in rod-shaped bacteria. We also find a bistable regime of both circumferential and axial gap propagation, which agrees with behavior reported in cytoskeletal mutants of B. subtilis. We conclude that the elastic anisotropies of a bacterial sacculus, as characterised experimentally, may be relevant for maintaining rod-shaped bacterial growth.

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A Normal Stress Criterion for Crack Extension Direction in Orthotropic Composite Materials

Cited by 88 publications

References 6 publications

Experimental and computational study of fracturing in an anisotropic brittle solid

Experimental and computational study of fracturing in an anisotropic brittle solid

Competing failure mechanisms in thin films: Application to layer transfer

Circumferential gap propagation in an anisotropic elastic bacterial sacculus

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