Ceramic fracture theory

D.P.H. Hasselman, R.M. Fulrath, Proposed Fracture Theory of a Dispersion Strengthened Glass Matrix,. Am. Ceram. Soc., 1966,... 

Hasselman, D.P.H. (1969), Unified theory of thermal shock fracture initiation and crack propagation in brittle ceramics , J. Am. Ceram. Soc., 52, 600-604. 

The classic Griffith-Orowan theory describes the relationship between strength and toughness of brittle materials such as ceramics (Griffith, 1920 Orowan, 1949). In the simple basic equation of the theory, the stress to fracture <7f is related to Youngs elastic modulus E, the fracture energy y and the critical crack length c by... 

The strength variability of ceramic materials can be evaluated using Weibull stahshc, which is based on the weakest-link theory, where the more severe flaw results in fracture propagation and determine the strength [69]. The Weibull two-parameter distribution is given by [14] ... 

It s a must to apply a material suitable module- and joining technique for the complex stress collective. For the ceramic components it s necessary to detect the in use mechanical, thermal and chemical loads. To analyze the stress field the FEA (Finite-Element-Analysis) is a suitable tool to calculate the particular stress distributions. In the next step the stress distributions (axial and torque loads) will be superposed to get an idea of the whole stress field. Furthermore with the FEA it s possible to calculate the tension stressed volume (VefO for these geometric complex components and offers the possibihty to calculate fracture probabilities according to the WeibuU-Theory. 

Polymers tend to have rather lower fracture strengths than materials such as metals or ceramics, but not concrete The theory of brittle fracture applies for polymers as for metals, but with greater emphasis on the development of a plastic zone around the tip of the growing crack (Fig. 4.5). The brittle mechanism is favoured in unmodified epoxies, and as a result of reducing the temperature, increasing the strain-rate or specimen thickness, and having sharp notches. Traditionally, susceptibility to brittle fracture has been assessed by some form of impact testing. 

Although this is a discussion on brittle materials, such as ceramics (glass is a perfect, brittle material), several researchers have developed theories of fracture based on dislocation models. More specifically, the shear stress created by dislocation pile-ups at some obstacle, specifically grain boundaries in polycrystaUine materials, reaches a sufficient value for crack formation. The following illustrates Stroh s [52] basic concept of microcrack formation, ultimately leading to the occurrence of fracture in brittle materials. 

As the name suggests, linear-elastic material behaviour is the precondition to allow applying the theory of linear-elastic fracture mechanics (lefm), discussed in this section. Strictly speaking, this precondition is fulfilled only in brittle materials like ceramics. In good approximation, it can also be used in ductile materials if the region of plastic deformation is restricted to the vicinity of the crack tip. Therefore, it can in many cases also be used to analyse metals. 

S. B. Batdorf, and H. L. Heinisch Jr., Weakest Link Theory Reformulated for Arbitrary Fracture Criterion. Journal of the American Ceramic Society, Vol. 61, No. 7 8, 1978, pp. 355 358. 

Methods for mechanical testing of materials are briefly introduced along with various strengthening mechanisms. The number and siu-face area of the slip systems in metals and in ceramics are shown to be responsible for the ductility (or the lack of it) and for ductile-to-brittle transitions. Griffith s theory of brittle fracture is used to introduce fracture mechanics and to develop the concept of fracture toughness. The viscoelastic behavior of polymers is briefly discussed. 

Ceramics and refractories are inherently brittle materials. The reason for this behavior is that the bonding in them is predominantly ionic or predominantly covalent. For plastic deformation, which is required for ductile fracture, there should be dislocation movement. In ionic compounds, formation of dislocation itself is difficult, because, for neutrality of the material, a pair of dislocations should simultaneously form. One should carry negative charge, and the other, positive. This is a difficult thing. If at all a dislocation forms, it requires simultaneous movement of the oppositely charged dislocations. This is still more difficult. In the case of covalent bonds, they are directional and strong. There is no question of any line defect, such as a dislocation, forming. Therefore, any question of dislocation movement does not arise. Ceramic and refractory materials fail by the sudden fracture of their atomic or ionic bonds. Hence, the failiue of ceramic and refractory materials can be discussed in terms of the failure of brittle materials. In other words, the theory of brittle materials fracture can be applied to ceramics and refractories. 

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