Explicit cross-property correlations for porous materials with anisotropic microstructures

Kachanov, Mark; Sevostianov, Igor; Shafiro, Boris

doi:10.1016/s0022-5096(00)00033-8

Cited by 72 publications

(35 citation statements)

References 16 publications

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“…At the same time, pores serve as nuclei for generation of cracks, the growth of which is the main mechanism of failure development in ceramics (Zimmermann and Röde, 1998). One of the standard approaches to describe the effect of porosity on the mechanical behaviour is to introduce effective elastic coefficients as functions of its level, obtained either experimentally or theoretically (Rice, 1998;Kachanov et al, 2001;Munro, 2001).…”

Section: Modelmentioning

confidence: 99%

Effect of material’s randomness on scaling of crack propagation in ceramics

Silberschmidt

2006

Int J Fract

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Crack propagation in real (quasi)brittle materials demonstrates various signs of stochasticity; a tortuous character of fracture surfaces, multiple cracking and crack branching observed in experiments are a vivid confirmation of it. Traditional approaches of fracture mechanics represent cracks as geometrically smooth objects with straight (or curved) crack fronts, thus usually neglecting morphology of real cracks. An introduction of a direct account for stochastic features of brittle materials into modelling schemes leads to a more adequate description of real fracture processes. The effect of the material's randomness on crack propagation in ceramics is studied based on the approach, combining these random features with continuum damage mechanics (CDM) and fracture mechanics. CDM describes a macroscopic manifestation of various failure processes developing at lower length scales. The numerical mode-I fracture analysis, based on discretization of a specimen's cross-section, containing a sharp notch, into rectangular elements, provides detailed information on slow crack propagation. A necessity to describe a crack with its length changing along the front presupposes a transition from a unique stress-intensity factor to a set of its local values. A computational procedure for simulation of crack-damage interaction and crack propagation in alumina specimens at tension is suggested on the basis of a modification of a lattice scheme unified with ideas of CDM and local stress-intensity factors. Inhomogeneity of material properties is modelled in terms of various random spatial distributions of the initial damage in the specimen's cross-section. Characterization of complicated morphology of cracks is implemented by means of scaling analysis of the crack-front shape.

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Section: Modelmentioning

confidence: 99%

Effect of material’s randomness on scaling of crack propagation in ceramics

Silberschmidt

2006

Int J Fract

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“…Following the approach described in [8], the effective stiffness of a fibre-reinforced composite containing cracks may be expressed if one considers a certain reference volume V of an infinite three-dimensional medium with an inclusion of volume V Ã (a region possessing elastic/conductive properties different from the ones of the surrounding material), the properties of the inclusion and of the matrix can be denoted by an asterisk and by ''0'', respectively. The stiffness contribution tensor N of an inclusion is defined by the following relation for the overall stress per volume V :…”

Section: Effective Stiffness Of a Fibre-reinforced Composite Containimentioning

confidence: 99%

“…Using the representations for tensors of elastic stiffness and compliance, Eshelby's tensor and unit tensor in terms of this basis yields the following relations for coefficients p i [8]:…”

Section: Effective Stiffness Of a Fibre-reinforced Composite Containimentioning

confidence: 99%

Environmental degradation using functionally graded material approach

Sevostianov

Sookay

Klemperer

et al. 2003

Composite Structures

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“…These considerations lead naturally to the concept of cross-property bounds and estimates [1][2][3][4][5][6][7]. Such ideas were applied very early to cold-worked metals by Bristow [8] in order to determine whether or not micro-cracking was an important issue.…”

Section: Introductionmentioning

confidence: 99%

Elastic and transport properties in polycrystals of cracked grains: Cross-property relations and microstructure

Berryman

2008

International Journal of Engineering Science

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Some arguments of Bristow (1960) concerning the effects of cracks on elastic and transport (i.e., electrical or thermal conduction) properties of cold-worked metals are reexamined. The discussion is posed in terms of a modern understanding of bounds and estimates for physical properties of polycrystals -in contrast to Bristow's approach using simple mixture theory. One type of specialized result emphasized here is the cross-property estimates and bounds that can be obtained using the methods presented. Our results ultimately agree with those of Bristow, i.e., confirming that microcracking is not likely to be the main cause of the observed elastic behavior of cold-worked metals. However, it also becomes clear that the mixture theory approach to the analysis is too simple and that crack-crack interactions are necessary for proper quantitative study of Bristow's problem. * JGBerryman@LBL.GOV

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Explicit cross-property correlations for porous materials with anisotropic microstructures

Cited by 72 publications

References 16 publications

Effect of material’s randomness on scaling of crack propagation in ceramics

Effect of material’s randomness on scaling of crack propagation in ceramics

Environmental degradation using functionally graded material approach

Elastic and transport properties in polycrystals of cracked grains: Cross-property relations and microstructure

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