Stress Fractures

Similarly, the same equations combine to provide a strain-rate-dependent fracture stress criterion... 

The fracture stress and fragment size data in Fig. 8.11 are observed to... 

Figure 8.11. Fragment size and fracture stress dependence on tensile loading strain rate for oil shale.

The theoretieal fraeture parameters in (8.22) and (8.23), based on a model assuming an inherent power law fracture flaw distribution and a constant fracture growth velocity, can be determined with the strain rate dependent fracture data in Fig. 8.11 (Grady and Kipp, 1980). Using the fracture data for oil shale provides a value of m = 8 and a fracture stress dependence on strain... 

The parameters for the model were originally evaluated for oil shale, a material for which substantial fracture stress and fragment size data depending on strain rate were available (see Fig. 8.11). In the case of a less well-characterized brittle material, the parameters may be inferred from the shear-wave velocity and a dynamic fracture or spall stress at a known strain rate. In particular, is approximately one-third the shear-wave velocity, m has been shown to be about 6 for various brittle materials (Grady and Lipkin, 1980), and k can then be determined from a known dynamic fracture stress using an analytic solution of (8.65), (8.66) and (8.68) in one dimension for constant strain rate. 

Figure 15.7. Effect of period of loading on fracturing stress at 25°C of acrylic sheet (Perspex). (Reproduced by permission of ICI)...

Fig. 11. Fracture stress versus crack depth for small flaw fracture tests in IG-11 graphite.

The variability in fracture stress when small artificial flaws were controlling strength was particularly pronounced for H-451 graphite, as can be seen in Fig. 12. Here the crack dimensions and crack trip process zone dimensions are comparable to the microstructural dimensions. Consequently, local variations in microstmeture... 

This equation predicts that the fracture stress increases with the square root of the number of bonds to be broken and is inversely proportional to M. The percolation parameter p is in effect, the normalized bond density such that for a perfect net without defects, p = 1 and for a net that is damaged or contains missing bonds. 

The latter equation contains constants with well-known values and can therefore be used to predict the fracture stress of most polymers. For example, the bond dissociation energy Do, is about 80 kcal/mol for a C-C bond. For polystyrene, the modulus E 2 GPa, A. 4, p = 1.2 g/cm, = 18,000, and we obtain the fracture stress, o A1 MPa, which compares well with reported values. Polycarbonate, with similar modulus but a lower M. = 2,400 is expected to have a fracture stress of about 100 MPa. In general, letting E 1 GPa, p = 1.0 g/cm, and Do — 335 kJ/mol, the tensile strength is well approximated by... 

Vincent analyzed the tensile fracture stress o, of a broad range of polymers as a function of the number of backbone bonds per cross sectional area ( 2) and found a nearly linear relation, o 2, as shown in Fig. 12. 2 is related to via the theory of entanglements for random walk chains as [74]... 

The hot bond fracture stress Morse potential energy function by [1]... 

In a tensile test on an un-notched sample of acrylic the fracture stress is recorded as 57 MN/m. Estimate Ae likely size of the intrinsic defects in Ae material. 

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