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Fracture mechanics
It is a relatively new section of materials study under mechanical loading conditions. Using fracture mechanics concept it possible to determine whether a crack of given length in a material with known toughness is dangerous at a given stress level. This mechanics section can also provides guide lines for selection of materials and design against fracture failures.
Orowan modified equation is further modified by Irwin to replace the hard to measure plastic work term with other term that was directly measurable. New form of the equation

The above equation states that smaller the radius, higher is the stress enhancement. Another parameter, often used to describe fracture toughness is known as critical stress concentration factor, K, and is defined as follows for an infinitely wide plate subjected to tensile stress perpendicular to crack faces:


where ? is a parameter that depends on the specimen and crack sizes and geometries, as well as the manner of load application. For example, for a plate of width w loaded in tension with a centrally located crack of length 2c,

In this regard, it is important to realize that there are three basic modes of fracture, as shown in figure-8.4. Mode-I corresponds to fracture where the crack surfaces are displaced normal to themselves. This is a typical tensile type of fracture. In mode-II, crack surfaces are sheared relative to each other in a direction normal to the edge of the crack. In mode-III, shearing action is parallel to the edge of the crack. To indicate different modes, it is normal practice to add the corresponding subscript. The above example described is obviously of the mode-I. There are two extreme cases for mode-I loading. With thin plate-type specimens the stress state is plane stress, while with thick specimens there is a plane-strain condition. The plane-strain condition represents the more severe stress state and the values of K are lower than for plane-stress specimens. The fracture toughness measured under plane-strain conditions is obtained under maximum constraint or material brittleness. The plane strain fracture toughness is designated as KIc, and is a true material property.

While crack extension force, G, has more direct physical significance to the fracture process, the stress intensity factor K is preferred in working with fracture mechanics because it is more amenable to analytical determination. Both these parameters are related as: