A Modified Strain-Energy Density Criterion Applied to Crack Propagation

Theocaris, P. S.; Andrianopoulos, N. P.

doi:10.1115/1.3162075

Cited by 53 publications

(11 citation statements)

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“…According to the T-criterion [11][12][13] the total strain energy density is separated into two different parts. The volume densities of the two parts of the total energy are referred to as dilatational (Tv) and distortional (To) components, respectively.…”

Section: The Elastic Strain Energymentioning

confidence: 99%

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The variation of the dynamic modulus on crack propagation modes

Papadopoulos

Theocaris

1987

Int J Fract

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The variation of the elastic modulus due to the dynamic propagation of a crack and its influence on the instability of this dynamic process was studied, based on the theory of the T-criterion of failure of the material. Conditions for an eventual bifurcation of the moving crack were established according to this criterion. Furthermore, a comparison was undertaken between the results derived from the T-criterion and an improving modification of the S-criterion, called S 2-criterion, which Was based on the two-term expressions of the elastic stress field around the crack. While in the T-criterion the dilatational strain energy density, T~, was calculated on the respective Mises elastic plastic boundary where the distortional component of strain energy density was constant, in the S2-criterion the core region was defined by the respective initial curve of the dynamic caustic.It was shown that the changes of the dynamic modulus and Poisson's ratio, depending on the relative crack velocity, were the main factors creating these instability-and bifurcation-phenomena of the moving cracks. Nomograms of the critical relative velocities of bifurcation versus the dynamic modulus and Poisson's ratio were plotted and compared satisfactorily with experimental data. It was indicated that, while the T-criterion gave satisfactory results all over the range of velocities and moduli, the S 2-criterion gave comparable results only for brittle or semi-brittle cases. List of symbolsrl, 01, r:, 02, r, 0 = kl, ~ = E,, E, = Y, V i Cl~ C 2 t) = = zs,~ = dW/dV = ro = TD = (7 0 O=_ ~b = crack tip stresses referred to Cartesian coordinate system. polar coordinate system centered at crack tip. stress intensity factors. elastic moduli of the material. Poisson's ratios of the material. velocities of the longitudinal and the shear waves, respectively. crack velocity. the mass density of the material. parametric equations of caustics. elastic strain-energy density. dilatational strain-energy density. distortional strain-energy density. yield stress of the material. angle of birfucation.

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Section: The Elastic Strain Energymentioning

confidence: 99%

“…In this paper a theoretical investigation of crack branching was based on the study of the elastodynamic stress field developed in [8]. This stress field was applied separately to the T-criterion [11][12][13] and to the S2-criterion [14,15].…”

Section: Introductionmentioning

confidence: 99%

The variation of the dynamic modulus on crack propagation modes

Papadopoulos

Theocaris

1987

Int J Fract

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“…Therefore, investigating the crack initiation angle and the crack propagation path under the mixed loading mode are favorite subjects for researchers in the field of rock mechanics. There are a large number of theoretical models (Erdogan and Sih, 1963;Hussain et al, 1974;Nuismer, 1975;Palaniswamy and Knauss, 1972;Sih, 1974;Theocaris and Andrianopoulos, 1982) and experimental techniques (Grassl and Rempling, 2007;Isaksson and Ståhle, 2002;Lin et al, 2009;Song et al, 2004;Xeidakis et al, 1997) for investigating the mixed mode of crack growth in rock materials. Theoretical failure criteria such as the Maximum Tangential Stress (MTS) criterion (Erdogan and Sih, 1963), the minimum strain energy density criterion (Sih, 1974), and the maximum energy release rate criterion (Hussain et al, 1974) have been frequently used by researchers working on rock and geo-material fields in order to estimate the direction of the mixed mode in the crack growth process.…”

Section: Introductionmentioning

confidence: 99%

Determination of crack initiation and propagation in two disc shaped specimens using the improved maximum tangential stress criterion

Eftekhari

Baghbanan

Mohtarami

et al. 2017

jtam

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The crack initiation angle and propagation path for two different disc shaped test specimens (i.e., SCB and CBD specimen) are investigated experimentally and theoretically. The Maximum Tangential Stress (MTS) criterion does not calculate the crack initiation angle in SCB and CBD specimens correctly. Moreover, at the angles after occurrence of pure mode II, where the stress intensity factor of mode I becomes negative, this criterion is not applicable. Therefore, in this research work, Improved MTS (IMTS) criterion which has been implemented in the extended finite element method and is applicable under tensile and compressive loading conditions to examine the crack propagation path in the aforementioned disc shaped specimens. Furthermore, an experimental study on a cracked Brazilian disc specimen has been conducted at different angles. Results of IMTS criterion in these specimens show that the crack propagation path and the crack initiation angle can be predicted theoretically by using IMTS criterion.

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“…There are several models for crack extension in brittle media, such as the maximum principal tensile stress criterion ( Erdogan and Sih, 1963 ), the strain energy density criterion ( Sih, 1974 ), the maximum energy release rate criterion ( Palaniswamy and Knauss, 1978 ), and the modified strain energy density criterion ( Theocaris and Andrianopoulos, 1982;Wei, 2012 ). We use a simple cohesive-like model to describe crack extension.…”

Section: Model For Effective Mechanical Property Calculationsmentioning

confidence: 99%

The influence of crack-orientation distribution on the mechanical properties of pre-cracked brittle media

Zeng

Wei

2016

International Journal of Solids and Structures

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a b s t r a c tCracks in kerogen-rich shales and other brittle rock-like materials have a tremendous impact on their elastic properties and strength. In this paper, we investigate the effective mechanical properties of shale plates with pre-existing cracks. We employ the extended finite element method (XFEM) to investigate a pre-cracked medium with an elastic, isotropic and brittle shale matrix. We show how the mechanical properties of the orthotropic shale plates are dependent on the crack density and the standard deviation of crack angles. Both the Young's modulus and the Poisson's ratio of the cracked media exhibit a linear dependence on the standard deviation of crack angles, in contrast to the nonlinear dependence of the strength on the angle deviation. Finally, we propose mechanical models to capture the relationship between the mechanical properties and the distribution characteristics of pre-existing cracks in shales. These phenomenological models could be applied to estimate the fracking behavior of shales in engineering practice.

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A Modified Strain-Energy Density Criterion Applied to Crack Propagation

Cited by 53 publications

References 0 publications

The variation of the dynamic modulus on crack propagation modes

The variation of the dynamic modulus on crack propagation modes

Determination of crack initiation and propagation in two disc shaped specimens using the improved maximum tangential stress criterion

The influence of crack-orientation distribution on the mechanical properties of pre-cracked brittle media

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