Fractal Characteristics of Fracture Surfaces

Baran, George R.; Roques‐Carmes, C.; Wehbi, D.; Degrange, Michel

doi:10.1111/j.1151-2916.1992.tb05489.x

Cited by 24 publications

(6 citation statements)

References 19 publications

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“…for an infinitely thick sample, the mirror constant, A m , can be expressed as follows:

\underset{H \to \infty}{truelim} A_{normalm} = \underset{H \to \infty}{truelim} A_{md} = K_{IC} \frac{Y_{0}}{\sqrt{2} {(c_{normalo} / R_{normalm})}^{1 / 2}} \approx \frac{K_{IC} Y_{0}}{\sqrt{2 D^{*}}}

For an infinitely thick sample, the most likely shape for the initial flaw after subcritical crack growth is a/c = 0.85, as shown by Dwivedi et al ., corresponding to Y 0 ≈ 1.3. Various studies estimate the fractal exponent D * for SLG ( D * = 0.08), BSG ( D * = 0.07–0.10) and ASG 7 ( D * = 0.08). In all cases, only thick samples were considered in the estimation of D *.…”

Section: Discussionmentioning

confidence: 99%

Flexural Strength by Fractography in Modern Brittle Materials

Dugnani

Zednik

2013

J. Am. Ceram. Soc.

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Thin components made from advanced brittle glasses or ceramics are becoming increasingly important due to the widespread adoption of portable consumer products as well as other modern electronic and medical devices. The strength of these brittle materials is traditionally estimated from empirical relationships relating the stress at failure to characteristic lengths derived from the fracture surface's topography. One example is Orr's relationship, σf∙Rm1/2 = Am, which correlates the material strength, σf, to the radius of the “mirror‐mist boundary region,” Rm, through the empirical constant, Am. Although various studies have shown that, for flexural fractures (failed in bending), Am depends on the specimen's geometry, this effect has been generally neglected by arguing that the magnitude of Am is almost constant for thicker specimens. However, we show that this argument cannot be applied to thin geometries, and that by not accounting for the thickness of the sample, the flexural strength will be grossly underestimated. In this work, we introduce an expression based on an iterative fracture mechanics algorithm which yields more accurate estimates of flexural strength for thin brittle components in bending. The accuracy of the model is validated both through flexural strength tests on glass and by comparing our predictions to an extensive literature survey of experimental results.

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“…for an infinitely thick sample, the mirror constant, A m , can be expressed as follows:

\underset{H \to \infty}{truelim} A_{normalm} = \underset{H \to \infty}{truelim} A_{md} = K_{IC} \frac{Y_{0}}{\sqrt{2} {(c_{normalo} / R_{normalm})}^{1 / 2}} \approx \frac{K_{IC} Y_{0}}{\sqrt{2 D^{*}}}

Section: Discussionmentioning

confidence: 99%

Flexural Strength by Fractography in Modern Brittle Materials

Dugnani

Zednik

2013

J. Am. Ceram. Soc.

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“…Baran, Roques-Carmes et al (1992) examined the fractal dimension D of fractures and the fracture toughness K IC of glass and porcelain. K IC was measured by an indentation method, D by the Minkowski variational method applied to profiles.…”

Section: Brittle Fracturementioning

confidence: 99%

Fractal Surfaces

Russ

1994

409

175

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“…The glass phase was deduced as the key factor of service life for refractories at high temperatures. Irregular fracture surfaces could be characterized by using the fractal dimension based on self-similarity 28 . The correlation between fractal dimension and mechanical properties depended on the microstructure and phase of the materials 29,30 .…”

Section: Resultsmentioning

confidence: 99%

Investigation on Reliability of High Alumina Refractories

Yuan¹,

Zhu²,

Zhang³

et al. 2013

Mechanical Properties and Performance of Engineering Ceramics and Composites VIII

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Owing to their high refractoriness and slag resistance, high-alumina refractories are widely used in the lining of steelmaking furnaces, glass furnaces and cement rotary kilns in high-temperature industries. The impurities in the raw materials react to form the glass phase, which can melt into liquid at high temperatures. The modulus of rupture of refractories depends intensively on the content and composition of the glass phase. In this work, the cold and hot modulus of rupture for high-alumina bricks were investigated by means of fitting based on different theories. The effect of the glass phase on the modulus of rupture was analyzed by combining the phase composition, morphology of fracture surfaces and porosity for high-alumina refractories.

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Fractal Characteristics of Fracture Surfaces

Cited by 24 publications

References 19 publications

Flexural Strength by Fractography in Modern Brittle Materials

Flexural Strength by Fractography in Modern Brittle Materials

Fractal Surfaces

Investigation on Reliability of High Alumina Refractories

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