Ductile materials, strain

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. 

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. ... 

A ductile material can be stretched uniformly only when stable flow occurs. The stable flow of materials has been investigated by Hart who described the transition from the stable to unstable flow. The beginning of geometrical instability and localisation of strain is the limit of the stable flow. At temperatures above 0.5 T (at equilibrium between recovery and hardening) the strain rate sensitivity parameter "m" may be derived from the expression ... 

One way of looking at the fracture characteristics of a ductile material is by measuring the amount of plasticity at a crack tip prior to crack propagation (Fig. 8.84). One test which measures this is the crack-tip opening displacement (CTOD), 5. Wells has found that 6 can be related to the strain energy release rate, G, by the formula ... 

At higher temperatures or lower strain rates, the stress-strain curve of the same material may exhibit a more gradual initial slope and a lower yield stress, as well as the drastic deviation from initial linearity and the higher failure stain characteristic of a ductile material. 

It should be recognized that tensile properties would most likely vary with a change of speed of the pulling jaws and with variation in the atmospheric conditions. Figure 2-14 shows the variation in a stress-strain curve when the speed of testing is altered also shown are the effects of temperature changes on the stress-strain curves. When the speed of pulling force is increased, the material reacts like brittle material when the temperature is increased, the material reacts like ductile material. 

FIGURE 15.34 A representative stress-strain diagram for a ductile material. 

More than 250 years ago it was observed that the strength of small-diameter wires increased proportionally as the diameter decreased (Musschen-broek, 1727). The inverse relationship between elastic strain and diameter has also been noted for whiskers of brittle or ductile materials of less than 20 micrometers in diameter (Evans, 1972). 

In terms of the mechanical behavior that has already been described in Sections 5.1 and Section 5.2, stress-strain diagrams for polymers can exhibit many of the same characteristics as brittle materials (Figure 5.58, curve A) and ductile materials (Figure 5.58, curve B). In general, highly crystalline polymers (curve A) behave in a brittle manner, whereas amorphous polymers can exhibit plastic deformation, as in... 

If the pressure in a thick-walled cylinder is raised beyond the yield pressure pei according to the equation (9), the yield will spread through the wall until it reaches the outer diameter [10]. For a perfectly elastic-plastic material the ultimate pressure for complete plastic deformation of the thick wall pCOmpi-pi, also called collapse pressure, can be calculated by equation (4.3-10). As the ductile materials used for high pressure equipment generally demonstrate strain... 

Mechanical Properties. The room temperature modulus and tensile strength are similar to those of other amorphous thermoplastics, but the impact strength and ductility are unusually high. Whereas most amorphous polymers arc glass-like and brittle below their glass-transition temperatures, polycarbonate remains ductile to about — 10°C. The stress-strain curve for polycarbonate typical of ductile materials, places it in an ideal position for use as a metal replacement. Weight savings as a metal replacement are substantial, because polycarbonate is only 44% as dense as aluminum and one-sixth as dense as steel. 

Plastic deformation (strain). When two surfaces of ductile materials are placed in contact and the load exceeds the elastic limit of one of the two materials, plastic deformation or strain occurs. The plastic deformation of one surface when two surfaces are in solid-state contact can occur in the presence or absence of lubricants. In fact, in some instances, the presence of lubricants can increase the deformability of the solid surfaces by a mechanism such as the Rehbinder effect. Plastic deformation of the solid surface is, therefore, observed in the presence of lubricants. Plastic deformation is accommodated by the generation of slip lines for dislocation flow in the solid surface. Dislocations are line defects in the solid and they are site of higher energy state on the surface. Thus, they interact or react more rapidly with certain chemical agents than do the bulk surfaces (Buckley, 1981 Lunarska and Samatowicz, 2000). 

In ductile materials the maximum in the stress-strain curve is the yield point. Two definitions of yield points are in use (see Fig. 13.68) ... 

Goodyear material with the same rubber content as the 13% American Cyanamid material exhibited more ductile stress-strain behavior. Possible reasons for this difference will be discussed later in the paper. Figure 6b shows the effect of rate on the behavior of the 13% American Cyanamid material. The yield stress increases with strain rate as was the case in all materials tested. Figure 6c shows the effect of temperature on the behavior of the same material. Again, as was the case in all materials tested, the yield stress decreases as the temperature is increased. 

FIGURE 13-19 Schematic plots of stress versus strain for brittle and ductile materials. 

FIGURE 13-35 Schematic plot of stress versus strain for a ductile material. 

The degree of fragmentation was found to diminish with smaller sieve fractions at the same compression load when several sieve fractions of unmilled crystalline a-lactose monohydrate was used. The authors concluded that particle fragmentation would reduce as porosity approached zero and elastic behavior would start to dominate the consolidation process (43). With a decrease in particle size, yield pressure decreased and the strain rate sensitivity index increased (44) which suggested a reduction in the extent of fragmentation. The transition from brittle to ductile material was thought to occur for a median particle size of around 20 pm (45). 

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