×

A generalized Weibull approach to interface failure in bi-material ceramic joints. (English) Zbl 1271.74396

Summary: Due to the inherent brittleness of ceramics, the reliability of ceramic components is evaluated using the Weibull theory. Hence, the failure probability due to the presence of surface or volume flaws is calculated using a suitable fracture mechanics approach. In the following paper, the weakest link approach is generalized for the case of bi-material ceramic joints. Here, interface cracks need to be considered for causing failure. Interface failure probability is found to be a function of the crack tip mode-mixity state. This influence is assessed in the general loading case for a bi-material strip with an internal interface crack. Under certain conditions, a simplified analysis is possible, leading to a conservative assessment of the failure probability for interface cracks in a gradually varying remote stress field.

MSC:

74R10 Brittle fracture
74S60 Stochastic and other probabilistic methods applied to problems in solid mechanics
PDFBibTeX XMLCite
Full Text: DOI Link

References:

[1] Banks-Sills L.: Weight functions for interface cracks. Int. J. Fract. 60, 89–95 (1993)
[2] Batdorf S.B., Heinisch H.L.: Weakest link theory reformulated for arbitrary fracture criterion. J. Am. Ceram. Soc. 61, 355–358 (1978)
[3] Beremin F.M.: A local criterion for cleavage fracture of a nuclear pressure vessel steel. Metall. Trans. A 14, 2277–2287 (1983)
[4] Brueckner-Foit, A., Huelsmeier, P., Sckuhr, M., Riesch-Oppermann, H.: Limitations of the weibull theory in stress fields with pronounced stress gradients. In: Proceedings of ASME Turbo Expo, Munich, Germany, pp. 1–5 (2000)
[5] Charalambides P.G., Lund J., Evans A.G., McMeeking R.M.: A test specimen for determining the fracture resistance of bimaterial interfaces. J. Appl. Mech. 56, 77–82 (1989)
[6] Comninou M.: The interface crack. J. Appl. Mech. (Trans. ASME) 44, 631–636 (1977) · Zbl 0369.73092
[7] Dundurs J.: Effect of elastic constants on stress in a composite under plane deformations. J. Compos. Mater. 1, 310–322 (1967)
[8] England A.H.: A crack between dissimilar media. J. Appl. Mech. (Trans. ASME) 32, 400–402 (1965)
[9] Erdogan F.: Stress distribution in bonded dissimilar materials with cracks. J. Appl. Mech. (Trans. ASME) 32, 403–410 (1965)
[10] Evans A.G.: A general approach for the statistical analysis of multiaxial fracture. J. Am. Ceram. Soc. 61, 302–308 (1978)
[11] Evans A.G., Hutchinson J.W.: The thermomechanical integrity of thin films and multilayers. Acta Metall. Mater. 43, 2507–2530 (1995)
[12] Fett T., Munz D.: Stress Intensity Factors and Weight Functions. Computational Mechanics Publications, Southampton (1997) · Zbl 0946.74575
[13] Gaupta V., Argon A.S., Parks D.M., Cornie J.A.: Measurement of interface strength by laser spallation technique. J. Mech. Phys. Solids 40, 141–180 (2004)
[14] Govorukha V.B., Loboda V.V.: On the boundary integral equations approach to the semi-infinite strip investigation. Acta Mech. 128, 105–115 (1998) · Zbl 0902.73014
[15] He M.-Y., Hutchinson J.W.: Kinking of a crack out of an interface. J. Appl. Mech. (Trans. ASME) 56, 270–278 (1989)
[16] Herrmann K.P., Loboda V.V.: Special approach for the determination of fracture mechanical parameters at an interface crack tip. Arch. Appl. Mech. 68, 227–236 (1998) · Zbl 0911.73049
[17] Hutchinson J.W., Suo Z.: Mixed mode cracking in layered materials. Adv. Appl. Mech. 2, 63–191 (1992) · Zbl 0790.73056
[18] Lin T., Evans A.G., Ritchie R.O.: A statistical model of brittle fracture by transgranular cleavage. J. Mech. Phys. Solids 34, 477–497 (1986)
[19] Loboda V.V.: The problem of orthotropic semi-infinite strip with crack along the fixed end. Eng. Fract. Mech. 55(1), 7–17 (1996)
[20] Matsuo Y.: Probabilistic analysis of the brittle fracture loci under biaxial stress state. Bull. JSME 24, 290–294 (1981)
[21] Munz D., Fett T.: Ceramics: Mechanical Properties, Failure Behaviour, Materials Selection. Springer, Berlin (1999)
[22] Muskhelishvili N.I.: Some Basic Problems in the Mathematical Theory of Elasticity. Nordhoff, Groningen (1954) · Zbl 0057.16805
[23] Nemeth, N.N., Powers, L.M., Janosik, L.A., Gyekenyesi, J.P: CARES/LIFE Ceramics Analysis and Reliability Evaluation of Structures Life Prediction Program. NASA/TM-2003-106316, Cleveland, Ohio (2003)
[24] Neville D.J, Knott J.F.: Statistical distributions of toughness and fracture stress for homogeneous and inhomogeneous materials. J. Mech. Phys. Solids 34, 243–291 (1986)
[25] Poncelet M., Doudard C., Calloch S., Weber B., Hild F.: Probabilistic multiscale models and measurements of self-heating under multiaxial high cycle fatigue. J. Mech. Phys. Solids 58, 578–593 (2010)
[26] Rice, J.R.: Elastic fracture mechanics concepts for interfacial cracks. J. Appl. Mech. (Trans. ASME) (55), 98–103 (1988)
[27] Riesch-Oppermann H., Härtelt M., Kraft O.: STAU–a review of the Karlsruhe weakest-link finite element postprocessor with extensive capabilities. Int. J. Mater. Res. 99, 1055–1065 (2008)
[28] Suo Z.: Models for breakdown-resistant dielectric and ferroelectric ceramics. J. Mech. Phys. Solids 41, 1155–1176 (1993)
[29] Tranter C.J.: Integral Transforms in Mathematical Physics. Wiley, New York (1956) · Zbl 0074.31901
[30] Weibull W.: A statistical theory of the strength of materials. Ing. Vetenk. Akad. Handl. 151, 1–45 (1939)
[31] Wu S.J., Knott J.F.: On the statistical analysis of the local fracture stresses in notched bars. J. Mech. Phys. Solids 52, 907–924 (2004)
[32] Yahsi O.S., Gocmen A.E.: Contact problem for two perfectly bonded dissimilar infinite strips. Int. J. Fract. 34, 161–177 (1987)
[33] Zweben C., Rosen B.W.: A statistical theory of material strength with application to composite materials. J. Mech. Phys. Solids 18, 189–206 (1970)
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.