Griffiths Theory on Fracture

The existence of flaws in the form of microcracks explains why the actual strength is lower than the theoretical strength. Crack formation requires energy to produce two new surfaces. Thus, Griffith s [22] approach to brittle failure is often called an energy balance theory . Observe the schematic illustration in Fig. 8.7 characterizing a crack. Here, the crack is shown at the center, though it may be at the sides of the specimen (half-cracks). 

Inglis [29] description of the crack (Fig. 8.7 is a plate) assumes that the applied stress, Ta is magnified at the end of the ellipse along the x axis (the major axis). The expression of this ellipse in the configuration shown in Fig. 8.7 is  

The stress concentration at the edge of the crack (the end of the major axis), where c is half the major axis and b = half the minor axis (i.e., half the dimensions of the crack), is given as  

For a static-crack system, the total energy is the sum of three terms  

Ue is the elastic energy. Us is the surface energy and Wl is the mechanical energy of the body or, alternatively, the amount of work done by the applied loads. A decrease in strain energy results from the formation of a crack. Thermodynamic equilibrium is reached when  

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