Luders band

Finally, mild steel can sometimes show an instability like that of polythene. If the steel is annealed, the stress/strain curve looks like that in Fig. 11.10. A stable neck, called a Luders Band, forms and propagates (as it did in polythene) without causing fracture because the strong work-hardening of the later part of the stress/strain curve prevents this. Luders Bands are a problem when sheet steel is pressed because they give lower precision and disfigure the pressing. 

Large plastic deformation can be identified by the accumulation of slips at the macroscopic scale as well as at the atomic scale. During tensile deformation, metal blocks slip on slip planes and rotate, as schematically illustrated in Fig. 1. Increasing plastic deformation results in numerous cross slips. Such slips can be observed as Luders bands in annealed low-carbon steel subjected to tensile deformation. 

Discontinuous or inhomogeneous yielding and flow by Luder s band formation and propagation has long been a nuisance and is sometimes an unacceptable problem in the fabrication of complex shapes such as automobile doors and bumpers from low-carbon steels because of the surface appearance marred by Luder s lines. However, discontinuous yielding has sometimes been proven to be advantageous, as in machining of low-carbon steels. 

The elastic-plastic tensile instability point in mild steel has received much attention and many explanations. Some polymers, such as polycarbonate, exhibit a similar phenomenon. Both steel and polycarbonate not only show an upper and lower yield point but visible striations of yielding, plastic flow or slip lines (Luder s bands) at an approximate angle of 54.7° to the load axis also occur in each for stresses equivalent to the upper yield point stress. (For a description and an example of Luder s band formation in polycarbonate, see Fig. 3.7(c)). It has been argued that this instability point (and the appearance of an upper and lower yield point) in metals is a result of the testing procedure and is related to the evolution of internal damage. That this is the case for polycarbonate will be shown in Chapter 3. For a discussion of these factors for metals, see Drucker (1962) and Kachanov (1986). 

What is a Luder s band At what angle do they occur Name two materials in which they are known to occur. 

As the electrical strain gage is located outside of the neck, the strain measurement given by curve 1 in Fig. 3.7(d) does not provide a useful measure of strain beyond the point of Luder s band formation. The average... 

As mentioned earlier, there have been many attempts to develop mathematical models that would accurately represent the nonlinear stress-strain behavior of viscoelastic materials. This section will review a few of these but it is appropriate to note that those discussed are not all inclusive. For example, numerical approaches are most often the method of choice for all nonlinear problems involving viscoelastic materials but these are beyond the scope of this text. In addition, this chapter does not include circumstances of nonlinear behavior involving gross yielding such as the Luder s bands seen in polycarbonate in Fig. 3.7. An effort is made in Chapter 11 to discuss such cases in connection with viscoelastic-plasticity and/or viscoplasticity effects. The nonlinear models discussed here are restricted to a subset of small strain approaches, with an emphasis on the single integral approach developed by Schapery. 

The yield stress (Luder s band formation) vs. creep to yield time from Eig. 11.12 is shown in Eig. 11.16 and compared to Eq. 11.35. The constants A, B and C in Eq. 11.35 were determined from the creep to yield data. Poisson s ratio was assumed to be 0.4 and all other parameters were determined for the modified Bingham model. A similar procedure was used to obtain the creep to yield behavior of a rubber-toughened adhesive (Brinson, et ah, (1975)). 

In experiments for both polycarbonate and polysulfone Luder s bands formed. In polycarbonate the Luder s band was a precursor to yielding but in polysulfone the Luder s bands were a precursor to rupture that occurred... 

What is a Luder s band and what stress is it s formation associated with ... 

Figure 3, which is a replot of the data of Fig. 1, was included to focus attention on the deformational behavior of these steels as measured by elongation. At 70 F, these steels deform by localized necking and extensive reduction of area, followed by fracture in the necked area (see Fig. 10). At -320 and -423°F, these same steels deform by a much more uniform elongation and reduction of area over the entire reduced section (see Fig. 10). This condition is most pronounced in the 62 cold-worked samples. At low temperature, the increase in strength in the reduced section due to plastic strain and associated martensite formation more than offsets the increase in stress due to the reduction in cross-sectional area (i.e., necking down) hence, the sample elongates over the entire reduced section prior to failure. At -423 F this elongation frequently occurs in a discontinuous manner, accompanied by audible clicks, serrations in the stress—strain curve, and striations in the sample, whose appearance is not unlike Luder s bands. The cross section of such a striation is shown in Fig. 12. These striations have been observed in other alloys by other investigators, and have been variously attributed to catastrophic twinning, thermal instability, and the burst-type formation of dislocations [1]. In this material another possibility exists, namely, the formation of martensite. This transformation is known to occur by an instantaneous shear mechanism and yields a volume increase which could account for the serrated stress—strain curve [5]. These effects demonstrate again that the...

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