Critical elastic strain energy release rate

Griffith used an energy balance approach to predict the crack propagation conditions (see Williams, 1984). The driving force is the elastically stored energy in the notched samples, which can be used to create new surfaces. A parameter Gc, the critical elastic strain energy release rate [GIc in mode I], can be determined and expressed in J m-2. 

Fig. 1.78 Relationship between critical elastic strain energy release rate, G, and notch root radius, p a for PSZ b for Si3N4 [32]. With kind permission of Professor Toshiro Kobayashi...

The fracture behaviour of polymers, usually under conditions of mode I opening, considered the severest test of a material s resistance to crack initiation and propagation, is widely characterised using linear elastic fracture mechanics (LEFM) parameters, such as the plane strain critical stress intensity factor, Kic, or the critical strain energy release rate, Gic, for crack initiation (determined using standard geometries such as those in Fig. 1). LEFM... 

The critical strain energy release rate Gc is the energy equivalent to fracture toughness, first proposed by Griffith [Phil. Trans. Royal Soc., A221, 163 (1920)]. With an elastic modulus of , toughness and release rate are related by... 

Linear elastic fracture mechanics (LEFM) has been used successfully for characterization of the toughness of brittle materials. The driving force of the crack advance is described by the parameters such as the stress intensity factor (K) and the strain energy release rate (G). Unstable crack propagates when the energy stored in the sample is larger than the work required for creation of two fracture surfaces. Thus, fracmre occurs when the strain energy release rate exceeds the critical value. Mathematically, it can be written as... 

When a material obeys linear elastic fracture mechanics, its tendency to undergo crack initiation or propagation as a result of mechanical stress can be assessed in terms of fracture toughness parameters, such as (critical stress intensity factor) or Gj, (strain energy release rate). Analogous parameters can be used with thermally induced cracking. 

Keywords linear elastic fracture mechanics, critical strain energy release rate, precipitating elastomers, hyperbranched molecules, preformed rubber particles, core-shell latex particles, treated rubber, precipitating thermoplastic particles, preformed thermoplastic particles, crack bridging, shear banding, cavitation. 

The determination of the critical strain energy release rate (Gno) is important to evaluate the low velocity impact damage on some filament wound composite structures, such as pipes. The peak impact force, a major key material characteristic used for establishing the damage resistance in composite structures, can be predicted in some cases from the elastic and Gno material properties. In filament wound pipes, interlaminar fracture may occur associated to matrix cracking, leading to significant stiffness losses. 

When cracks extend in mode I loading in LEFM they release elastic strain energy in the surrounding stress field. The rate of release of such energy with crack extension can be considered as a generalized crack-driving force and is alternatively a direct representation of the work of fracture when a critical condition Gic for crack extension is reached. 

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