Hoop stress intensity factor and crack-kinking in anisotropic brittle solids

Azhdari, Abbas; Nemat‐Nasser, Sia

doi:10.1016/0020-7683(95)00154-9

Cited by 29 publications

(8 citation statements)

References 19 publications

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“…Ž . 1995and Azhdari and Nemat-Nasser 1996a where additional references are also found. Fracture criteria should be based upon physical models and experimental observations, established from the knowledge of the fracturing mechanisms.…”

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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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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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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“…Due to the positive-definiteness of the elastic energy, the roots of Eq. 79 are always complex or purely imaginary and occur in conjugate pairs as 1 , 1 and 2 , 2 [108,109].…”

Section: Crack-tip Problem In Anisotropic Bodiesmentioning

confidence: 99%

“…For the purposes of this discussion, and in order to guarantee consistency among the results compared and corresponding to different materials, illustrative examples assume always anisotropic elasticity, with homogeneous and (directionally) uniform resistance to fracture. This is similar to the approach used in [108,116]. The simulations are performed considering a squaresymmetric material and a fully anisotropic material subjected to several mode mixity ratios K ranging from 0 • to 90 • .…”

Section: Crack Nucleation Kinking and Curvingmentioning

confidence: 99%

Anisotropic Continuum-Molecular Models: A Unified Framework Based on Pair Potentials for Elasticity, Fracture and Diffusion-Type Problems

Diana

2022

Arch Computat Methods Eng

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This paper presents a unified framework for continuum-molecular modeling of anisotropic elasticity, fracture and diffusion-based problems within a generalized two-dimensional peridynamic theory. A variational procedure is proposed to derive the governing equations of the model, that postulates oriented material points interacting through pair potentials from which pairwise generalized actions are computed as energy conjugates to properly defined pairwise measures of primary field variables. While mass is considered as continuous function of volume, we define constitutive laws for long-range interactions such that the overall anisotropic behavior of the material is the result of the assigned elastic, conductive and failure micro-interaction properties. The non-central force assumption in elasticity, together with the definition of specific orientation-dependent micromoduli functions respecting material symmetries, allow to obtain a fully anisotropic non-local continuum using a purely pairwise description of deformation and constitutive properties. A general and consistent micro-macro moduli correspondence principle is also established, based on the formal analogy with the classic elastic and conductivity tensors. The main concepts presented in this work can be used for further developments of anisotropic continuum-molecular formulations to include other mechanical behaviors and coupled phenomena involving different physics.

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“…The geometry of crack configuration yields: (13) Moreover, the constants km in Eq. (11) are also expressed by (14) where we see that km2 are the invariant constants, and Km the constants with respect to the rectangular coordinate systems (x, y).…”

Section: Statement Of Problem and Basic Equationsmentioning

confidence: 99%

“…Despite the significance of anisotropic elastic media in modern industry, the problem of kinked crack in anisotropic elastic media has received much less attention. The studies on the energy release rate [11,12] and the stress intensity factors [13] of the kinked cracks in homogeneous anisotropic elastic media have only been made. In [11][12][13], a method similar to that of Lo [14] for a infinitesimally small crack in homogeneous isotropic elastic media was employed.…”

Section: Introductionmentioning

confidence: 99%

A Crack Kinked at the Interface of Bonded Anisotropic Elastic Media under Longitudinal Shear Stresses

Kabeyasawa

Kobayashi

Sekine

2002

Int. J. Soc. Mater. Eng. Resour

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The stress intensity factors at the tips of a crack kinked at the interface of bonded anisotropic elastic media are analyzed. By using a singular point method, the problem is reduced to solving a system of singular integral equations with generalized Cauchy kernels. The characteristic equation that determines the stress singularity at the kink vertex is derived from the singular integral equations, and singular stress fields at the kink vertex are determined definitely. By taking into account of the stress singularity at the kink vertex, numerical results are given graphically for the stress intensity factors at the tips of the kinked crack.

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Hoop stress intensity factor and crack-kinking in anisotropic brittle solids

Cited by 29 publications

References 19 publications

Experimental and computational study of fracturing in an anisotropic brittle solid

Experimental and computational study of fracturing in an anisotropic brittle solid

Anisotropic Continuum-Molecular Models: A Unified Framework Based on Pair Potentials for Elasticity, Fracture and Diffusion-Type Problems

A Crack Kinked at the Interface of Bonded Anisotropic Elastic Media under Longitudinal Shear Stresses

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