as to completely fracture the specimen, the crack will undergo further plastic deformation around the new crack tip, enlarging the zone of residual plastic stresses. This process further toughens and prolongs the life of the material because the new plastic zone is larger than what it would be under the usual stress conditions. This allows the material to undergo more cycles of loading. This idea can be illustrated further by the graph of Aluminum with a center crack undergoing overloading events. Limitations But a problem arose for the NRL researchers because naval materials, e.g., ship-plate steel, are not perfectly elastic but undergo significant plastic deformation at the tip of a crack. One basic assumption in Irwin's linear elastic fracture mechanics is small scale yielding, the condition that the size of the plastic zone is small compared to the crack length. However, this assumption is quite restrictive for certain types of failure in structural steels though such steels can be prone to brittle fracture, which has led to a number of catastrophic failures. Linear-elastic fracture mechanics is of limited practical use for structural steels and Fracture toughness testing can be expensive. Elastic–plastic fracture mechanics Most engineering materials show some nonlinear elastic and inelastic behavior under operating conditions that involve large loads. In such materials the assumptions of linear elastic fracture mechanics may not hold, that is, the plastic zone at a crack tip may have a size of the same order of magnitude as the crack size the size and shape of the plastic zone may change as the applied load is increased and also as the crack length increases. Therefore, a more general theory of crack growth is needed for elastic-plastic materials that can account for: the local conditions for initial crack growth which include the nucleation, growth, and coalescence of voids (decohesion) at a crack tip. a global energy balance criterion for further crack growth and unstable fracture. CTOD Historically, the first parameter for the determination of fracture toughness in the elasto-plastic region was the crack tip opening displacement (CTOD) or "opening at the apex of the crack" indicated. This parameter was determined by Wells during the studies of structural steels, which due to the high toughness could not be characterized with the linear elastic fracture mechanics model. He noted that, before the fracture happened, the walls of the crack were leaving and that the crack tip, after fracture,