Fracture of Materials

The major purposes of comminution or size reduction operations can be summarized in four categories as shown in Table 2.2. Comminution is almost invariably performed in two or more stages. It starts with the crude mined or quarried product this is progressively taken to the desired final size by a step-by-step process. As the process of fracture is involved throughout this procedure, a brief discussion on the fracture of materials is appropriate at this point. 

The term fracture implies fragmentation of a solid body into two or more bodies under the action of stress. Two main types of fracture mode are observed in solids. The first is ductile fracture which is the failure of a material after it has undergone a considerable amount of plastic deformation. The other is brittle fracture which is the failure of a material without undergoing practically any plastic deformation. The type of failure which occurs depends largely on the nature of the material and its condition however, failure is also affected by 

The principle behind the phenomenon of fracture of materials can be described by having recourse to Griffith s theory. Alternatively, this can be done by introducing the concept of fracture toughness. 

This energy is considered to be supplied by the elastic strain energy, We, that is released per unit thickness by the formation of the crack and is given by 

The value of o obtained from this equation is the critical value of the applied tensile stress normal to the crack (also known as the Griffith stress) necessary to cause the crack to propagate and is given by 

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Besides Griffith s theory, the fracture of materials can be described in terms of a property known as fracture toughness. The fracture toughness of a material refers to its resistance to fracture in the presence of cracks or discontinuities. Fracture toughness is represented by... 

Therefore, the rate at which chemical bonds break increases with elastic shear stressing of the material. The rupture of chemical bonds, hence fracture of material, leads to its fragmentation into particles. This reduces the average particle size in powder as fractured particles multiply into even smaller particles. Equation (1.24) points to the importance of elastic shear strains in mechanical activation of chemical bonds for particle size refinement and production of nanoparticles. 

In some environments and under certain conditions, a microscopically brittle fracture of materials can occur at levels of mechanical stress that may be far below those required for general yielding or those that could lead to significant damage in the absence of an environment. This susceptibility also depends on the chemical composition and... 

Plastic Deformation and Fracture of Materials edited by H. Mughrabi. This book is Vol. 6 in the series Materials Science and Technology edited by R. W. Cahn, P. Haasen and E. J. Kramer, VCH Publishers, Inc., New York New York, 1993. Of especial interest concerning the present discussion see chap. 6 on the subject of solid solution strengthening by H. Neuhauser and C. Schwink and chap. 8 by B. Reppich on the subject of particle strengthening. 

In some environments and under certain conditions, a microscopically brittle fracture of materials can occur at levels of mechanical stress that may be far below the level required for general yielding or those that cause significant damage in the absence of an environment. The susceptibility also depends on the chemical composition and microstructure of the alloy. This form of corrosion requires an interaction between the electrochemical dissolution of the metal, hydrogen absorption, and the mechanical loading conditions (stress, strain, and stain rate) (73). The nature of these fracture modes varies from one class of material to another. However, all fracture modes are largely similar to one another. 

Landel, R.F., Fedors, RJL 1966. In Proceedings of the 1st International Conference on Fracture, Sendai, vol. 2. Japan. Soc. Strength and Fracture of Materials, Tokyo, p. 1247. 

The brittle fracture temperature of steel is a temperature below which its ductility has decreased so that brittle fracture of material is possible. Neutron flux irradiation of the reactor core causes damage in reactor pressure vessel (RPV) wall material and its brittle fracture temperature decreases. If the RPV is cooled below brittle fracture temperature, there is a danger of brittle fracture if there is an initial crack in the RPV wall material. The phenomenon is called pressurised thermal shock (PTS) and its worst consequence is a catastrophic failure of the RPV. PTS is more relevant for PWRs than for BWRs because PWRs generally have a narrower water gap between the reactor core and the RPV wall than BWRs. 

The crack-tip environment with its stress and plastic-strain concentration furnishes the means and driving forces for local fracturing of material, making the crack propagate to final fracture. The material separation in crack extension can occur by a variety of mechanisms in which a number of factors can play important roles, such as the structural constitution of the polymer, i.e., whether it is in unoriented or oriented glassy form or in semi-crystalline form, with a variety of morphologies. We consider first a selection of prominent forms of fracture in polymers and end with a short section on the fracture toughnesses of some prominent polymers. 

Bhattacharj ya D, Shield R, Friedrich K and Fakirov S (2006) Intern Workshop Fracture of Materials Moving Forwards , Sydney, Austraha, January 23-25. 

We have proposed a simpler model for systems involving charge separation during fracture. We have tested various aspects of this model on a number of materials.( 4,51,52) jhe basic features of this model as they relate to the fracture of materials in vacuum are the following ... 

H. Mughrabi, Plastic deformation and fracture of materials. Berlin Springer-Verlag . 

Figures 3 and 4 provide a consistent picture of this process. Fibers produced using the short-length die (L/D = 2.5) have a fine, readily fibrillated appearance Fig. 3a. This morphology is also revealed during failure in tensile testing. Unlike fracture of material produced with the longer dies, failure...

K. J. Wang, H. C. Lin, and K. Hua, Calculation of Stress Intensity Factors for Combined Mode Bend Specimens, pp. 123 133 in Advances in Research on the Strength and Fracture of Materials, Vol. 4, Edited by M. D. R. Taplin, ICF4, Waterloo, Canada (1977). 

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