Critical fracture strain rate, relation

The critical fracture strain rate (Cf) obeys the relation... 

The critical strain-energy release rate, Gp, in the specimen with notch-root radius, p, is indicated in Fig. 1.78 for both static and dynamic ceramic fracture. The linear relation of the lines in Fig. 1.78 are based on the Williams relation... 

The parameter determined by integration of the stress/strain history is the critical thermomechanical conversion factor, fic- As noted both in experiments [5] and in simulations [6], drawing is destabilised at a temperature of 50-60°C, i.e. within the range for which data were measured. Figure 4 shows that despite experimental and analytical uncertainties provides a very effective index for the plane stress fracture resistance Wpi they are related by a monotonic and, indeed, quite linear relationship. Figures 5 and 6 illustrate the robusmess of the procedure in that neither the initial temperature of the simulation nor the strain rate chosen to characterise plane stress separation unduly influences the result. 

The critical strain energy release rate is the energy equivalent to fracture toughness, first proposed by Griffith [Phil. Trans. Royal Soc., A22I, 163 (1920)]. They are related by... 

Somewhat more sophisticated instruments are frequently used for so-called instrumented impact tests. These instruments carry devices for measuring quantities such as the force applied to the sample and its displacement as a function of time and they allow the impact energy to be obtained more directly. Bending tests are, however, frequently carried out in a less sophisticated way using specimens without notches. The energy of fracture divided by the area of fracture is then called the impact strength. This quantity cannot be simply related to the quantities such as the critical strain-energy-release rate defined in fracture mechanics. 

On comparing Eqs. (10.3) and (10.6), we see that the critical stress intensity factor, Kc, and the fracture energy, or critical strain energy release rate, Gc, are related to each other and to the breaking stress at the crack tip, as follows ... 

The fracture toughness, a term defined by Irwin (1956, 1960) to characterize brittleness, provides a measure of the conditions required for catastrophic crack propagation in a material (see Section 1.6). One fracture toughness parameter is the surface fracture energy y, defined as one-half G, the critical strain energy release rate above which catastrophic failure occurs. In turn G is related to another convenient toughness parameter, the critical stress intensity factor a measure of the stress field at the crack tip. For fracture of an isotropic material in a plane strain modet (Baer, 1964, p. 946) ... 

The toughness of a material is related to the amount of energy dissipated during a fracture and can be described in terms of either a stress intensity factor K or a strain energy release rate G (82). Critical values of these terms (i.e., and Gc) define the fracture criterion for a given material. An opening mode I of fracture is assumed solely in this analysis and and G are the critical values of K and G in mode I fracture. Within the region of validity of LEFM, there is a simple relation between K and G ... 

Another commonly used method to determine fracture toughness of coatings is through the use of compliance fracture specimens, whereby the change in compliance of the specimen is measured or calculated as the crack propagates, and related to the mode I critical strain energy release rate, G c- Elementary fracture mechanics gives the required relationship [38] ... 

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