Fracture strain elongation

Og = fracture strain = elongation strain = strain at 50% elongation ... 

Consider now a polymer sample of current volume V responding by craze plasticity to an imposed current elongational strain rate e, developing a tensile (dilatational) flow resistance until a final fracture strain is achieved as shown in Fig. 1. The specific toughness W or the total deformational energy absorbed per unit volume for this polymer is the area under the stress strain curve, or... 

From the initial region of the stress-strain curve, Young s modulus E and the shear modulus G can be obtained. Both are a measure of the stiffness of a given material, which mirrors the resistance of an elastic body against deflection of an applied force. The point where the stress-strain curve abmptly falls down is known as the fracture point where the sample ruptures. Fracture stress and fracture strain are defined as the maximal stress and deformation (elongation or compression) that a sample can withstand. Material toughness can also be calculated from the area under the stress-strain curve up to ultimate fracture point. It is defined as amount of energy per unit volume required to cause a fracture in a material. 

Figure 5.17a represents tensile test specimens (compositions and designations in Table 5.1), before and after testing, obtained by optical micrographs, shown in Fig. 5.17b. As may be seen in 5.6a, grades B, C and D exhibit quite large strain, but specimens A, E, F and G fracture at elongations of less than 15 %. The effect of the strain rate on the tensile deformation is illustrated for specimen D (see Table) at 1600 and 1650 °C in Fig. 5.18a and that of the temperature at a constant strain rate is seen in Fig. 5.19b. The generally known fact that the temperature has an opposite effect on the flow curves and on strain hardening may also be seen in Fig. 5.18.

For ductile or superplastic ceramics, in the case of elongations of more than 10%, the fracture strain follows the empirical relationship proposed by Kim et al. [KIM 91],... 

Forming Limit Analysis. The ductihty of sheet and strip can be predicted from an analysis that produces a forming limit diagram (ELD), which defines critical plastic strains at fracture over a range of forming conditions. The ELD encompasses the simpler, but limited measures of ductihty represented by the percentage elongation from tensile tests and the minimum bend radius from bend tests. 

For smaller values of Vj, the behavior of the composite material might not follow Equation (3.84) because there might not be enough fibers to control the matrix elongation. That is, the matrix dominates the composite material and carries the fibers along for the ride. Thus, the fibers would be subjected to high strains with only small loads and would fracture. If all fibers break at the same strain (an occurrence that is quite unlikely from a statistical standpoint), then the composite material will fracture unless the matrix (which occupies only of the representative volume element) can take the entire load imposed on the composite material, that is. 

An important consideration is the effect of filler and its degree of interaction with the polymer matrix. Under strain, a weak bond at the binder-filler interface often leads to dewetting of the binder from the solid particles to formation of voids and deterioration of mechanical properties. The primary objective is, therefore, to enhance the particle-matrix interaction or increase debond fracture energy. A most desirable property is a narrow gap between the maximum (e ) and ultimate elongation ch) on the stress-strain curve. The ratio, e , eh, may be considered as the interface efficiency, a ratio of unity implying perfect efficiency at the interfacial Junction. 

Fig. 8.57 Strain rate reginres for studying stress corrosion cracking of 2 000, 5 000 and 7 000 series alloys . The ductility ratio is the ratio of elongation-to-fracture or reduction in area measured in solution to that measured in a control environment...

The first point of zero slope on the curve (point C) is identified with material yielding and so its coordinates are called the yield strain and stress (strength) of the material. The yield strain and stress usually decrease as temperature increases or as strain rate decreases. The final point on the curve (point D) corresponds to specimen fracture. This represents the maximum elongation of the material specimen its coordinates are called the ultimate, or failure strain and stress. Ultimate elongation usually decreases as temperature decreases or as strain rate increases. 

Although the creep behavior of a material could be measured in any mode, such experiments are most often run in tension or flexure. In the first, a test specimen is subjected to a constant tensile load and its elongation is measured as a function of time. After a sufficiently long period of time, the specimen will fracture that is a phenomenon called tensile creep failure. In general, the higher the applied tensile stress, the shorter the time and the greater the total strain to specimen failure. Furthermore, as the stress level decreases, the fracture mode changes from ductile to brittle. With flexural, a test specimen... 

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