Brittle fracture energy

Figure 8.14. Strain-rate dependence of ideal brittle (fracture dominated) and ideal ductile (flow dominated) spall energies. A postulate of minimum fragmentation energy leads to a transition in spall behavior.

At strain rates below e, energy-limited spall is expected to proceed through a brittle (fracture dominated) spall mechanism while for strain rates greater than 8, a ductile (flow-dominated) mechanism is expected. 

Figure 9.3. Stress-strain curves for (a) rigid amorphous plastics material showing brittle fracture and (b) rubbery polymer. The area under the curve gives a measure of the energy required to break the...

If contact with a rough surface is poor, whether as a result of thermodynamic or kinetic factors, voids at the interface are likely to mean that practical adhesion is low. Voids can act as stress concentrators which, especially with a brittle adhesive, lead to low energy dissipation, i/f, and low fracture energy, F. However, it must be recognised that there are circumstances where the stress concentrations resulting from interfacial voids can lead to enhanced plastic deformation of a ductile adhesive and increase fracture energy by an increase in [44]. 

Hydrogen can decrease the strength of the metal-metal bond, thereby facilitating brittle fracture. Both the decohesion and surface energy models are based on this premise. 

The tensile strengths are about 55 MN/m, the elongations at break usually less than 10% and the modulus of elasticity about 2-7 GN/m Since the area under the curve provides a measure of the energy required to break the bonds, and since this area is small such polymers will have a low impact strength (which is closely related to energy to break) and will break with a brittle fracture. 

An example of a theory is the Griffith theory. It expresses the strength of a material in terms of crack length and fracture surface energy. Brittle fracture is based on the idea that the presence of cracks determines the brittle... 

This result indicates that the stress necessary to cause brittle fracture is lower, the longer the existing crack and the smaller the energy, P, expended in plastic deformation. The quantity Of represents the smallest tensile stress that would be able to propagate the crack of length 2 L. The term Of (tt L)°5 is generally denoted by the symbol K and is known as the stress-intensity factor (for a sharp elastic crack in an infinitely wide plate). Fracture occurs when the product of the nominal applied stress and the stress concentration factor of a flaw attains a value equal to that of the cohesive stress. 

The quantitative results of fracture energy, which are calculated from the total area under load-displacement curves, are presented in Fig. 50. It becomes obvious, that a brittle-tough transition exists at a volume fraction of around 10%. This brittle-tough transition is observed for solvent-modifled as well as semi-porous epoxies. A brittle behavior is observed in macroporous epoxies after complete solvent removal, thus giving low fracture energies similar to the neat epoxy for each porosity. 

Table 9. Critical strain energy release rates, G ., for common thermoplastics measured under impact loading promoting brittle fracture [92]...

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