Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model

Deshpande, V.S.; Evans, A.G.

doi:10.1016/j.jmps.2008.05.002

Cited by 138 publications

(125 citation statements)

References 40 publications

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“…Having determined l and a, the triaxial failure envelope (r 1 vs. r 3 at failure) was fit (at low confining stress) by varying the parameter b and the value of the initial damage D o as discussed further in a subsequent section. DESHPANDE and EVANS (2008) added a term to the strain energy density in Eq. 5 that represents the increase in elastic energy density associated with a pair of wing cracks each of length l…”

Section: Regime 3: Wing Cracks Nucleate and Grow From The Tips Of Thementioning

confidence: 99%

“…The formulations of ASHBY and SAMMIS (1990) and DESHPANDE and EVANS (2008) assume that the growing wing cracks are all parallel. We still assume all starter flaws are at the same angle W with respect to x 1 , but now assume that the components of their normal vectors in the x 1 and x 1 directions are randomly distributed as in Fig.…”

Section: Allowing Non-parallel Initial Flawsmentioning

confidence: 99%

“…In this paper, we explore a micromechanical damage mechanics originally formulated by ASHBY and SAMMIS (1990) and extended by DESHPANDE and EVANS (2008), which is based on the growth and interaction of tensile wing cracks nucleated at the tips of an initial distribution of microcracks. This model incorporates results from many studies of mode I wing cracks nucleated and driven by mode II sliding [for example see KACHANOV (1982a, b), NEMAT-NASSER and HORII (1982), ASHBY and HALLAM NÉE COOKSLEY (1986), JEYAKUMARAN and RUDNICKI (1995) and references therein].…”

Section: Introductionmentioning

confidence: 99%

“…While ASHBY and SAMMIS (1990) limited their analysis to the failure surface, DESHPANDE and EVANS (2008) extended their model by calculating the change in strain energy associated with the damage and using it to calculate strain as a function of loading stress. In this work, we calculate the strain energy associated with the growing wing cracks in a less approximate way than that used by DESHPANDE and EVANS (2008), and compare the resultant stress-strain curves with those measured for Westerly granite.…”

Section: Introductionmentioning

confidence: 99%

“…In this work, we calculate the strain energy associated with the growing wing cracks in a less approximate way than that used by DESHPANDE and EVANS (2008), and compare the resultant stress-strain curves with those measured for Westerly granite.…”

Section: Introductionmentioning

confidence: 99%

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The Micromechanics of Westerley Granite at Large Compressive Loads

Bhat

Sammis

Rosakis³

2011

Pure Appl. Geophys.

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Abstract-The micromechanical damage mechanics formulated by ASHBY and SAMMIS (Pure Appl Geophys 133(3) 1990) has been shown to give an adequate description of the triaxial failure surface for a wide variety of rocks at low confining pressure. However, it does not produce the large negative curvature in the failure surface observed in Westerly granite at high confining pressure. We show that this discrepancy between theory and data is not caused by the two most basic simplifying assumptions in the damage model: (1) that all the initial flaws are the same size or (2) that they all have the same orientation relative to the largest compressive stress. We also show that the stress-strain curve calculated from the strain energy density significantly underestimates the nonlinear strain near failure in Westerly granite. Both the observed curvature in the failure surface and the nonlinear strain at failure observed in Westerly granite can be quantitatively fit using a simple bi-mineral model in which the feldspar grains have a lower flow stress than do the quartz grains. The conclusion is that nonlinearity in the failure surface and stress-strain curves observed in triaxial experiments on Westerly granite at low loading rates is probably due to low-temperature dislocation flow and not simplifying assumptions in the damage mechanics. The important implication is that discrepancies between experiment and theory should decrease with increased loading rates, and therefore, the micromechanical damage mechanics, as formulated, can be expected to give an adequate description of high strain-rate phenomena like earthquake rupture, underground explosions, and meteorite impact.

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Section: Regime 3: Wing Cracks Nucleate and Grow From The Tips Of Thementioning

confidence: 99%

Section: Allowing Non-parallel Initial Flawsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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The Micromechanics of Westerley Granite at Large Compressive Loads

Bhat

Sammis

Rosakis³

2011

Pure Appl. Geophys.

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Rate‐ and strain‐dependent brittle deformation of rocks

et al. 2014

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Key Points:• Deformation by brittle creep requires less energy than by imposed strain rate • An empirical relation between creep rate and energy deficit is exhibited • A relation between our empirical law and stress corrosion laws is determined Abstract We develop a unifying framework to quantify rate-dependent deformation in the brittle field and establish links between the microscale time-dependent crack growth processes and the macroscopically observed rate dependency. Triaxial deformation experiments have been performed under both constant strain rate and constant stress (creep) conditions on three types of sandstone. The measured relative evolution of P wave speeds as a function of inelastic axial strain is similar for both types of test, despite differences in strain rate of up to 3 orders of magnitude. This similarity indicates that there exists a direct, time-independent link between the microstructural state (as reflected by the variations in P wave speed) and the inelastic axial strain. Comparison of applied stresses between constant strain rate and creep experiments as a function of inelastic strain indicates that creep deformation requires less mechanical work to bring the sample to failure. This energy deficit corresponds to a stress deficit, which can be related to a deficit in energy release rate of the microcracks. We establish empirically that the creep strain rate is given bẏ∝ exp(ΔQ∕ * ), where ΔQ is the stress deficit (negative) and * is an activation stress. This empirical exponential relation between creep strain rate and stress deficit is analogous to rate-and-state friction law. We develop a micromechanical approach based on fracture mechanics to determine the evolution of an effective stress intensity factor at crack tips during creep deformation and estimate the activation volume of the stress corrosion reaction responsible for brittle creep.

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Brittle creep and subcritical crack propagation in glass submitted to triaxial conditions

et al. 2015

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An experimental work is presented that aimed at improving our understanding of the mechanical evolution of cracks under brittle creep conditions. Brittle creep may be an important slow deformation process in the Earth's crust. Synthetic glass samples have been used to observe and document brittle creep due to slow crack‐propagation. A crack density of 0.05 was introduced in intact synthetic glass samples by thermal shock. Creep tests were performed at constant confining pressure (15 MPa) for water saturated conditions. Data were obtained by maintaining the differential‐stress constant in steps of 24 h duration. A set of sensors allowed us to record strains and acoustic emissions during creep. The effect of temperature on creep was investigated from ambient temperature to 70°C. The activation energy for crack growth was found to be 32 kJ/mol. In secondary creep, a large dilatancy was observed that did not occur in constant strain rate tests. This is correlated to acoustic emission activity associated with crack growth. As a consequence, slow crack growth has been evidenced in glass. Beyond secondary creep, failure in tertiary creep was found to be a progressive process. The data are interpreted through a previously developed micromechanical damage model that describes crack propagation. This model allows one to predict the secondary brittle creep phase and also to give an analytical expression for the time to rupture. Comparison between glass and crystalline rock indicates that the brittle creep behavior is probably controlled by the same process even if stress sensitivity for glass is lower than for rocks.

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Inelastic deformation and energy dissipation in ceramics: A mechanism-based constitutive model

Cited by 138 publications

References 40 publications

The Micromechanics of Westerley Granite at Large Compressive Loads

The Micromechanics of Westerley Granite at Large Compressive Loads

Rate‐ and strain‐dependent brittle deformation of rocks

Brittle creep and subcritical crack propagation in glass submitted to triaxial conditions

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