Energy balance concepts in the physics of fracture

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Abstract
It is pointed out that there are a number of incompatible energy balances used in the study of fracture and fracture toughening. The original Griffith theory is based on the second law of thermodynamics and in the framework of this law a cracked body is in unstable equilibrium when the appropriate thermodynamic potential reaches a maximum value. This energy balance allows the identification of both the thermodynamic driving forces for crack extension and the forces resisting crack growth. A second, and widely used, energy balance is based on the first law of thermodynamics which is simply one of energy conservation and can yield no information about crack instability without further assumptions. The two energy balances are considered in relation to the effect of energy dissipating processes on fracture. It is shown that a crack extension force cannot be defined by dividing the sum of all the energy increments arising from all the processes accompanying crack extension by the increment of crack area since this gives rise to paradoxical results. It is concluded that the energy changes brought about by processes such as plastic deformation which accompany crack extension should not be included in the definition of a crack extension force. A local energy balance is used to define a crack extension force which yields results identical to crack shielding calculations in fracture toughening studies. It is shown that the work done by energy dissipating processes per unit area of crack surface does not act to increase the crack resistance or the `effective surface energy'. Energy dissipating processes have their effect on fracture by virtue of the fact that they alter the state of stress around the crack tip and thus reduce the thermodynamic driving force for crack growth.

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