Flaw sensitivity

Effect of grain size on creep. (From W. R. Cannon and T. G. Langdon, /. Mater. Set., 18 1-50,1983.) 

Illustration of flaw sensitivity (a) Uniform stress when there is no flaw (b) stress concentration when a crack is created and (c) variation of stress with respect to interatomic distance. 

When the Oup reaches the fracture stress (Of) the failure takes place. It was mentioned that fracture stress is about one-tenth of the materials Young s modulus. When the applied stress reaches this value, fracture takes place. Thus Equation 15.46 can be written in terms of Of as  

Y is the Young s modulus. The following are the inferences from this equation  

The first inference means that sharp cracks are more vulnerable than blunt cracks. The two inferences have been proved experimentally. 

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Eurther heat treatment in excess of 2000°C is referred to as graphitization. Eiber stmcture further densifies as molecular packing and orientation increase. At temperatures of 3000°C or above, the fiber stmcture begins to approach a truly graphitic stmcture with three-dimensional order. Typically, fiber strain to failure decreases as the carbonization temperature exceeds 1500°C because of reaction of impurities with the carbon fiber and the development of an increasingly flaw-sensitive graphitic stmcture (31,34)... 

Flaws, their shape, and their propagation are the central themes of this chapter. The various aspects of brittle failure are discussed from several viewpoints. The concepts of fracture toughness and flaw sensitivity are discussed first. The factors influencing the strengths of ceramics are dealt with in Sec. 11.3. Toughening mechanisms are dealt with in Sec. 11.4. Section 11.5 introduces the statistics of brittle failure and a methodology for design. 

The toughness of a polymer can manifest itself in a complementary manner, in several different forms. In uniaxial tension of a smooth bar, the toughness is the plastic work required in order to fracture, per unit volume, which is given by the area under the stress-strain curve as shown in Fig. 13.1, where deformation under various strain rates e is terminated when the flow stress reaches a fracture strength fff that is flaw-sensitive but otherwise relatively insensitive to the deformation rate. 

The appropriateness of the Weibull analysis for a partially ductile material can also be justified fundamentally. Although the Weibull method of reliability analysis is formally developed for classically brittle materials (Kelly and Macmillan, 1986), i.e. materials that fail before they can exhibit a yield point, its use can be generalised for materials that exhibit flaw sensitivity. This generalisation can be arrived at simply by examining the equation (Simon and Bunsell, 1984 Chou, 1992) which is plotted to obtain a value... 

Fracture toughness is determined by the flaw sensitivity of the material. 

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