Fracture mechanics energy balance

In the present section, attention will focus on the size of fragments created in a violent fragmentation event. The objective will be to explore some theoretical ideas which appear important to the dynamic fragmentation process. The two underlying phenomena that have dominated theoretical efforts in this area of dynamic fracture mechanics are the presence of an inherent flaw structure, and energy balance in the fracture process. 

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,). 

A final consequence of this reconciliation between the kinetic theory and fracture mechanics concepts, is that the effective surface energy S should vary somewhat as Regime I gives way to Regime II. In the former, the stress field is required to provide energy (in the absence of losses) of the order of AG upwards, since the balance of the activation energy G is provided by thermal fluctuations. In Regime II virtually the whole of G must be provided by the stress field so that we have. 

In the late forties, Irwin suggested the energy balance of Eq. (8.7) could be considered in a slightly different way. In Eq. (8.9), the mechanical energy terms, involving and f/, were coupled because they involve terms that act to promote crack extension, whereas the surface term was treated separately because it represents the resistance of the material to fracture. One can, therefore, define a parameter... 

Linear elastic fracture mechanics is no longer valid for dynamic fracture mechaiusms since continuous crack propagation addresses time dependent boundary conditions. The energy balance for the dynamic conditions can be written as... 

But infinite stress is always present in cracking problems and poses no difficulty if an energy-balance theory of crack equilibrium is used (see Fracture Mechanics). Applying this method to the above stress distribution gave the following equation, the so-called JKR equation, for the elastic contact spot diameter d of equal spheres, diameter D and... 

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

It is weU known that when evaluating the peel adhesion strength, only a part of mechanical work is consumed for real fracture of the adhesion bonds, whereas energy balance is spent on various by-processes. The part of energy spent on the deformation of polymer film during peeling is of special importance. 

The main emphasis of this chapter will be on the basic fracture mechanics concepts for cohesive and adhesive fracture with some extension to crack branching and crack nucleation from bimaterial comers. Most of the current fracture mechanics practice in testing adhesives and designing of adhesively bonded joints is limited to linear elastic fracture mechanics concepts. The development of the background material presented here will therefore be similarly constrained, except for the last section. Historically, fracture mechanics developed from energy balance concepts and examinations of stresses around crack tips. The adhesive fracture community has tended to favor the former, but both have useful features and will be carried forward in the discussions that follow. 

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. 

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