Fracture mechanics energy balance approach

Sometimes the failure occurs by propagation of a crack that starts at the top and travels downward until the interface is completely debonded. In this case, the fracture mechanics analysis using the energy balance approach has been applied [92] in which P, relates to specimen dimensions, elastic constants of fiber and matrix, initial crack length, and interfacial work of fracture (W,). 

Fracture mechanics A J KINLOCH Basis energy balance and stress-intensity factor approaches... 

In his book, Maugis [20] describes the method which Irwin [21] used in 1957 for satisfying the energy balance when the stresses are known exactly around the crack tip. From this analysis, widely used in fracture mechanics, the limit of stress approaching the stress singularity is obtained to give the same answer as Eq. 18. 

Methods of analytical mechanics provide the natural basis to develop such a generalized approach. Within the bounds of quasistatic problems, methods of analytical statics are sufficient. The use of the principle of virtual work, instead of the energy balance equation, permits one to generalize the theory of fracture and fatigue to multi parametric problems and to omit restrictions on the potential character of external and internal forces. In this paper, only "non-healing" cracks are considered typical for most structural materials. Therefore, we consider mechanical systems with unilateral constraints. The principle of virtual work for such systems takes the form a system with ideal unilateral constraints stays in the equilibrium state if and only if the summed virtual work of all active forces on all small displacements compatible with the constraints is equal to zero or negative ... 

However, Gent and Hamed [104] have shown that the theory of small bending deformations used to derive Equation 6.24 is only valid to peel mechanics when )8pmp sin a, i.e. when Kp = 1. The results from these analyses have not been widely used in the interpretation of peel test data and the fracture mechanics approach, based upon an energy balance argument, which avoids the necessity for developing a detailed stress analysis has been far more widely applied. This approach is considered in Section 7.3.2. 

This approach is the most useful for engineering purposes since it expresses fracture events in terms of equations containing measurable parameters such as stress, strain and linear dimensions. It treats a body as a mechanical continuum rather than an assembly of atoms or molecules. However, our discussion can begin with the atomic assembly as the following argument will show. If a solid is subjected to a uniform tensile stress, its interatomic bonds will deform until the forces of atomic cohesion balance the applied forces. Interatomic potential energies have the form shown in Fig. 1 and consequently the interatomic force, whidi is the differential of energy with respect to linear separation, must pass throt a maximum value at the point of inflection, P in Fig. 1. 

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