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Objectives:

When you finish this module (especially the appropriate textbook sections and problems), you will be able to:
· Define cold working, hot working, and annealing
· Compute the strain-hardening coefficient
· Explain the strain-hardening mechanisms for various materials
· Compute % cold work and design an annealing process
· Determine the electrical conductivity and yield strength of copper given the percentage of cold work
· Explain how to design a fatigue-resistant shaft
· Explain what happens to a cold-worked metal when it is welded
· Define superplasticity and explain the conditions that are required

Reference: §7.1 - 7.11 of The Science and Engineering of Materials, 3^rd Edition, Askeland, PWS Publishing Co.

Definitions and Concepts:

When a material is cold worked (e.g., an ingot is rolled at room temperature to produce a sheet), the shape is changed. That means that the stress had to exceed the yield strength. In other words, the material has entered the plastic region. Figure 7-1a (page 176) shows the application of a stress beyond the yield stress ; when the stress is removed, the material return elastically and has a permanent offset. Cold working increases the yield strength (and also increases the brittleness). Figure 7-1b shows that the new yield stress is ; now we cold work it some more using a new stress , remove the stress again and get a new offset, and so on. How many times this can be done without cracking depends on the material and the stress used.

Suppose a rod is drawn through a die to produce a wire.  The die must be smaller than the diameter desired!  That's because, when the wire emerges from the die, it returns elastically to zero stress on the stress-strain plot to produce the offset discussed above.  But in doing so, its diameter expands!

What happens during cold working determines the number of times this cycle can be repeated. For metals, cold working increases the number of dislocations. Ceramics are usually so brittle that cold working cannot be applied at low temperatures. Some polymers strengthen when they are deformed but dislocations are not the reason; their long chains are becoming aligned (see Fig. 7-4 page 179). Various deformation processes are shown in Figure 7-5, page 180.

The percent cold work is defined as the reduction in area:

For rolling processes, the width of the plate usually does not change. For such cases (see Fig. 7-7 page 181) the % cold work (% CW) can be given by

Note from Example 7-1 that the %CW is determined over the entire process, not by the sum of the steps!

Speaking of metals, various grain textures are produced by drawing, extruding, and rolling. Sometimes these are desirable. They represent residual stresses that have developed during the deformation. It may be that further processing is needed but the material is too brittle. Annealing (maintaining the sheet, or machine part at an elevated temperature for a given time) is a way to remove these residual stresses by recrystallization. Then the material is cold worked again. Example 7-6 (page 193) outlines a five-step process of cold working/annealing to produce a product with the desired properties.

Figure 7-12 (page 187) shows that cold working increases the yield strength but adversely affects the conductivity.  It also causes the material to become more brittle.  The three stages of annealing - recovery, recrystallization, and grain growth are well explained on pages 189 -191.  But I think that too much has been crowded into the plots in Figure 7-15 and make it difficult to read.  I suggest a careful reading of Problem 7-19 and my solution.

Hot working is plastic deformation at elevated temperatures. No strengthening occurs. This is useful for HCP metals, since there are more slip systems at higher temperatures.