Displacement ductility

Connections structural steel members are generally designed to develop the full strength of the member. With regard to ductility evaluations for connections, explicit checks are generally not made. It is presumed that satisfaction of the gross member displacement ductility criteria ensures the integrity of the member connections. 

In Equation 2.27, the value of psfyh shall be limited to 0.35 ksi. Figure 2.13 shows value of Factor 1 that varies over the range of displacement ductility demand ratios, pj. 

FIGURE 2.13 Factor 1 versus displacement ductility demand ratio,... 

Inside the plastic hinge zones (assume displacement ductility = 5) ... 

Ductility is the ability of a structure, its components, or the materials used therein, to maintain resistance in the inelastic domain of response. It includes the ability to sustain large deformations and the capacity to absorb energy by hysteretic behavior. Displacement ductility is defined as the ultimate strain of the material divided by its yield strain. For an anchor in tension, it may be taken as the elongation of the anchor at maximum tension load divided by the elongation at yield. 

The most important displacive transformation is the one that happens in carbon steels. If you take a piece of 0.8% carbon steel "off the shelf" and measure its mechanical properties you will find, roughly, the values of hardness, tensile strength and ductility given in Table 8.1. But if you test a piece that has been heated to red heat and then quenched into cold water, you will find a dramatic increase in hardness (4 times or more), and a big decrease in ductility (it is practically zero) (Table 8.1). 

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 ... 

Yielding is a manifestation of the possibility that some of the atoms (or molecules) in the stressed material may slip to new equilibrium positions due to the distortion produced by the applied tensile force. The displaced atoms can form new bonds in their newly acquired equilibrium positions. This permits an elongation over and above that produced by a simple elastic separation of atoms. The material does not get weakened due to the displacement of the atoms since they form new bonds. However, these atoms do not have any tendency to return to their original positions. The elongation, therefore, is inelastic, or irrecoverable or irreversible. This type of deformation is known as plastic deformation and materials that can undergo significant plastic deformation are termed ductile. 

To summarize, we can say that granulated materials should behave in a brittle manner, similar to a ceramic, in the sense of having small yield strains and small critical displacements but their behavior should also be ductile, similarto polymers, in the sense of having large process zones. The consequence of having large process zones is important since it implies that... 

The stress intensification factors in Appendix D of ASME B31.3 have been developed from fatigue tests of representative piping components and assemblies manufactured from ductile ferrous materials. The allowable displacement stress range is based on tests of carbon and austenitic stainless steels. Caution should be exercised when using eqs. (la) and (lb) (para. IP-2.2.10) for allowable displacement stress range for some nonferrous materials (e.g., certain copper and aluminum alloys) for other than low-cycle applications. 

With Cu-Zr, in an interval of 1000°C it amounts to 1 %. If initial dimensions, LCu and LZr, are 1 cm each, then the relative displacement of the phases is 100 pm which value is close on the order of magnitude to layer thicknesses encountered in reaction-diffusion experiments. With brittle compound layers formed and insufficiently ductile initial phases, this appears to be more than sufficient to cause any couple to rupture. 

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