Fracture behavior parameters

Thus, if the ratio AT//3 is constant, then the behavior shown in Fig. 12 could be described by the net solution. For many polymers, the characteristic ratio is around 7-10, the ratio Mo/j is the molecular weight per backbone bond (ca. 30-50) and will not vary extensively, b = 1.54 A and the density is about 1 g/cm such that the parameter is nearly constant. Since K is not very sensitive to the polymer properties, Eq. 6.5 is considered to describe the observed fracture behavior shown in Fig. 12. However, the data are not expected to fall on the straight line due to differences in K and j6 for each polymer. As a specific test case, consider... 

Strain rate sensitivity of (or the effect of press speed on) the formulation is of primary concern in scale-up. Whether the product development work was performed on a single-stroke press or a smaller rotary press, the objective in operations will be to increase efficiency, in this case the tablet output rate and, therefore, the speed of the press. For a material that deforms exclusively by brittle fracture, there will be no concern. Materials that exhibit plastic deformation, which is a kinetic phenomenon, do exhibit strain rate sensitivity, and the effect of press speed will be significant. One must be aware that although specific ingredients (such as calcium phosphate and lactose) may exhibit predominately brittle fracture behavior, almost everything has some plastic deformation component, and for some materials (such as microcrystalline cellulose) plastic deformation is the predominant behavior. The usual parameter indication is that target tablet hardness cannot be achieved at the faster press speed. Slowing the press may be the only option to correct the problem. 

Linear elastic fracture mechanics (LEFM) approach can be used to characterize the fracture behavior of random fiber composites. The methods of LEFM should be used with utmost care for obtaining meaningful fracture parameters. The analysis of load displacement records as recommended in method ASTM E 399-71 may be subject to some errors caused by the massive debonding that occurs prior to catastrophic failure of these composites. By using the R-curve concept, the fracture behavior of these materials can be more accurately characterized. The K-equa-tions developed for isotropic materials can be used to calculate stress intensity factor for these materials. 

The second condition to validate the scheme B is that embrittlement must correspond to a critical morphological state that is the only approach to explain its sudden character. The extensive and careful work of Kennedy et al. (//) on relationships between fracture behavior, molar mass and lamellar morphology, shows that this condition is fulfilled in the case of PE. Comparing various samples of different molar masses with different thermal histories, they found that the thickness of the amorphous layer (la) separating two adjacent lamellae is the key parameter (Fig. 6). As a matter of fact, there is a critical value lac of the order of 6-7 nm. For la > lac the samples are always ductile whatever their molar mass, whereas for U < laC the samples are consistently brittle. As a result, lac appears to be independent of the molar mass. Indeed, there is a specific molar mass, probably close to 70 kg.mof for PE below which crystallization is so fast that it is impossible to have la values higher than lac whatever the processing conditions. 

In a thermoplastic material it is, therefore, important to distinguish between the crack opening stretch (= COS) and the maximum craze width 2v. To characterize plastic deformation and fracture behavior of a thermoplastic material the maximum length of stretched fibrils and hence the maximum craze width 2v is a more fundamental parameter than the crack opening stretch. The latter, in addition, depends on the relaxation behavior of the broken remnants on the fracture surface. 

A molecular transition model involving the -relaxation in PMMA has been first put forward by Johnson and Radon They explained the transition in crack speed behavior based on a correlation between the temperature dependence of a time to failure inferred from fracture experiments and the temperature variation of the reciprocal frequency of the P-relaxation peak. They thus assumed that the crack transition is caused when the P-process is fully active. Also the fracture mechanics parameter K, governing the transition from slow to fast crack growth, shows a time and temperature dependence equal to that of the p-transition... 

A careful inspection of Tables 4 and 5 shows that changes, even limited, in the details of SAPA chemical structure may affect noticeably their fracture behavior. Although it has been carried out [1], a systematic study of their effects falls out of the scope of this article, because too many parameters are concerned. They include yield stress, p relaxation characteristics, tensile modulus, entanglement density, Mw / ratio, and also, in the high temperature range, the gap (Ta-T) between Ta and the test temperature T. Instead, emphasis will just be put here on two features whose explanation is quite simple. 

Testing Conditions and Analysis. The fracture behavior was investigated at room temperature at nominal piston velocities, from 10-4 m/s to 10 m/s. For test speeds higher than 10-1 m/s, the damped test procedure described in reference 15 was used. Quasi-static stress conditions therefore prevailed in the specimen, even at high loading rates. This fact allowed the analysis of fracture-mechanics parameters to be performed using a static approach. 

The evaluations of short fiber reinforced composites for fracture behavior includes studies with respect to material parameters such as the fiber content [42,103,120], fiber length and orientation [69,97,103,115], and fiber bundling [115.120] testing conditions such as the temperature [24,42,121,122] and the loading rate [121,123,124] and fractography [42,43,103,123], The influence of some of these parameters, e.g fiber content, rate of loading, and the test temperature on the fracture toughness of composites can be presented in the form of property maps [125,126],... 

In this chapter, the effects of various parameters on the fracture behavior of wood-plastic composites are discussed. Moreover, different methods of composite damage analysis are reviewed and the fracture analysis of WPG is presented. 

---