The Crack Problem for a Nonhomogeneous Plane

Delale, F.; Erdoğan, F.

doi:10.1115/1.3167098

Cited by 706 publications

(310 citation statements)

References 7 publications

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“…Gradual variation of material properties in FGMs, unlike abrupt changes encountered in discretely layered systems, is known to improve failure performance (Niino, et. al., 1987) Some of the early works on the fracture mechanics of FGMs include those by Atkinson and List (1978), and Delale and Erdogan (1983). An inverse Vr stress singularity at the crack in FGMs was suggested in these articles and was later confirmed by Eischen (1987) using asymptotic analysis.…”

Section: Introductionmentioning

confidence: 87%

Crack Tip Field Mapping and Failure Characterization of Functionally Graded Composites

Tippur¹

2001

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Section: Introductionmentioning

confidence: 87%

Crack Tip Field Mapping and Failure Characterization of Functionally Graded Composites

Tippur¹

2001

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“…An exponential spatial variation of the elastic modulus has been assumed in the analysis by Atkinson and List (1978), and Delale and Erdogan (1983). Further it has been shown (Erdogan et al, 1991;Erdogan, 1995) that assuming a smooth material property distribution at the interface between a material with constant properties and a functionally graded material, the anomalous phenomenon of either infinite or vanishing stress intensity factors is eliminated.…”

Section: Introductionmentioning

confidence: 99%

A model for graded materials with application to cracks

Jivkov

Ståhle

2003

International Journal of Fracture

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Abstract. Stress intensity factors are calculated for long plane cracks with one tip interacting with a region of graded material characteristics. The material outside the region is considered to be homogeneous. The analysis is based on assumed small differences in stiffness in the entire body. The linear extent of the body is assumed to be large compared with that of the graded region. The crack tip, including the graded region, is assumed embedded in a square-root singular stress field. The stress intensity factor is given by a singular integral. Solutions are presented for rectangular regions with elastic gradient parallel to the crack plane. The limiting case of infinite strip is solved analytically, leading to a very simple expression. Further, a fundamental case is considered, allowing the solution for arbitrary variation of the material properties to be represented by Fourier's series expansion. The solution is compared with numerical results for finite changes of modulus of elasticity and is shown to have a surprisingly large range of validity. If an error of 5% is tolerated, modulus of elasticity may drop by around 40% or increase with around 60%.

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“…the previous analytical fracture models, the material properties were usually assumed to be very particular functions (mainly exponential functions) (Delale & Erdogan 1983;Chen & Erdogan 1996;Erdogan & Wu 1997;Guo et al 2004Guo et al , 2005. Recently, Choi & Paulino (2008) investigated the thermoelastic contact problem of a FGM coating/substrate system, and the thermomechanical properties were assumed to be exponential functions so that the problem could be solved analytically.…”

Section: Introductionmentioning

confidence: 99%

A fracture mechanics model for a crack problem of functionally graded materials with stochastic mechanical properties

2012

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This study aimed to develop a method to build a 'bridge' between the macro fracture mechanics model and stochastic micromechanics-based properties so that the macro fracture mechanics model can be expanded to the fracture mechanics problem of functionally graded materials (FGMs) with stochastic mechanical properties. An analytical fracture mechanics model is developed to predict the stress intensity factors (SIFs) in FGMs with stochastic uncertainties in phase volume fractions. Considering the stochastic description of the phase volume fractions, a micromechanics-based method is developed to derive the explicit probabilistic characteristics of the effective properties of the FGMs so that the stochastic mechanical properties can be combined with the macro fracture mechanics model. A thought for choosing the samples efficiently is proposed so that the stable probabilistic characteristic of SIFs can be obtained with a very small sample size. The probability density function of SIFs can be determined by developing a histogram from the generated samples. The present method may provide a thought to establish an analytical model for the crack problems of FGMs with stochastic properties.

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The Crack Problem for a Nonhomogeneous Plane

Cited by 706 publications

References 7 publications

Crack Tip Field Mapping and Failure Characterization of Functionally Graded Composites

Crack Tip Field Mapping and Failure Characterization of Functionally Graded Composites

A model for graded materials with application to cracks

A fracture mechanics model for a crack problem of functionally graded materials with stochastic mechanical properties

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