Ductility strain

Samples were tested at room temperature in an Instron machine. Strain rates of 0.02%/sec were used initially, increasing to as high as 0.2%/sec for extended ductility. Strains up to 5% were measured with a clip-on strain gauge. Larger strains were determined by reassembling the broken pieces after failure. 

Fig. 9.4. Schematic representation of crack stability in ductile, strain-hardening material ...

As discussed in Section 2.0 (Exploration), the earth s crust is part of a dynamic system and movements within the crust are accommodated partly by rock deformation. Like any other material, rocks may react to stress with an elastic, ductile or brittle response, as described in the stress-strain diagram in Figure 5.5. 

Modified ETEE is less dense, tougher, and stiffer and exhibits a higher tensile strength and creep resistance than PTEE, PEA, or EEP resins. It is ductile, and displays in various compositions the characteristic of a nonlinear stress—strain relationship. Typical physical properties of Tef2el products are shown in Table 1 (24,25). Properties such as elongation and flex life depend on crystallinity, which is affected by the rate of crysta11i2ation values depend on fabrication conditions and melt cooling rates. 

Criteria of Elastic Failure. Of the criteria of elastic failure which have been formulated, the two most important for ductile materials are the maximum shear stress criterion and the shear strain energy criterion. According to the former criterion, from equation 7... 

This concept is explained by Figure 12 which shows the uniaxial stress— strain curve for a ductile material such as carbon steel. If the stress level is at the yield stress B or above, the problem is no longer a linear one. 

In (8.35) Y is the flow stress in simple tension (and may itself be a function of the temperature and strain rate) and is the critical volumetric strain at void coalescence (calculated within the model to equal 0.15 independent of material). Note that the ductile fragmentation energy depends directly on the fragment size s. With (8.35), (8.30) through (8.32) become, for ideal ductile spall fragmentation,... 

Figure 8.14 shows that a transition in spall mechanism is predicted to occur at a critical strain rate e, which corresponds to the intersection of the brittle and ductile fragmentation energy curves. By equating (8.39) and (8.43)... 

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. 

In the numerical calculations, an elastic-perfectly-plastic ductile rod stretching at a uniform strain rate of e = lO s was treated. A flow stress of 100 MPa and a density of 2700 kg/m were assumed. A one-millimeter square cross section and a fracture energy of = 0.02 J were used. These properties are consistent with the measured behavior of soft aluminim in experimental expanding ring studies of Grady and Benson (1983). Incipient fractures were introduced into the rod randomly in both position and time. Fractures grow... 

A void nucleation and growth fracture model embedded in a general viscoelastic-plastic material model is representative of approaches to ductile dynamic fracture (Davison et al., 1977 Kipp and Stevens, 1976). Other approaches include employing the plastic strain as a damage variable (Johnson and Cook, 1985) so that both spall and large strain-to-failure can be treated. 

Rubbers are exceptional in behaving reversibly, or almost reversibly, to high strains as we said, almost all materials, when strained by more than about 0.001 (0.1%), do something irreversible and most engineering materials deform plastically to change their shape permanently. If we load a piece of ductile metal (like copper), for example in tension, we get the following relationship between the load and the extension (Fig. 8.4). This can be... 

Plastic) strain after fracture, or tensile ductility. The broken pieces are put together and measured, and Cf calculated from (/ - IqI/Iq, where / is the length of the assembled pieces. 

Strain after fracture and percentage reduction in area are used as measures of ductility, i.e. the ability of a material to undergo large plastic strain under stress before it fractures. 

Sketch curves of the nominal stress against nominal strain obtained from tensile tests on (a) a typical ductile material, (b) a typical non-ductile material. The following data were obtained in a tensile test on a specimen with 50 mm gauge length and a cross-sectional area of 160 mm. ... 

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