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Discussion: After performing the experiments it is helpful to create tables and graphs to analyze the data and find any trends that occur during the procedure. This will help create a better understanding of the theory that was discussed in the introduction. The graph in Figure 4 displays the relationship between hardness and percent cold work. By analyzing the data it is clear that the theory of cold work strengthening a material is supported. The copper specimen after the cold work has almost a fourfold increase in hardness. For the specimen with 37.315 ​± ​0.067% cold work the initial hardness was 24.3 ​± ​3.35 and was ​88.16 ​± ​1.925 ​ after it was strain hardened. The introduction talked about how during strain hardening the average distance between dislocations decreases and since dislocations hinder each other’s motion their movement becomes limited. This explains why there is an increase in hardness as the material was cold worked. Figure 5 shows data from all the specimens that were used in the lab; each of them experienced a different percentage of cold work. With increasing amount of cold work, less heat was needed to reduce their hardness and return them to their pre cold-worked state. The theory that less activation energy is necessary to start the annealing process of higher cold worked materials is supported by the results of this procedure. The statistical analysis shows that we reject the null hypothesis, which state that the means are equal, because P-value is less than 0.05 This actually means that the averages of hardness changes as the annealing temperature change. The 24 pairs out of 28 ​mean of hardness values were significantly different from each other. Both of these results mean ​there is a significant difference between the eight means. However, as ​noted from the StatGraphics software, there is a risk of 5% of calling each pair of means significantly different when they are not. With a 5% error, there are 24 ​± ​1.4 pairs which will not change the final conclusion about rejecting the null hypothesis. There are many errors addressed in this experiment, some of them are ​quantified and some are not. The only noticeable error is the hardness reading for 4% CW after annealing process which is appear in Figure 5 at 200 and 400 ​∘ ​C. One reason that might yield to this error is that the sample brushed too hard, cutting grooves into the sample. However, the overall trends were the same for all the data; therefore, the final conclusion is not affected by this anomaly or any other error that was discussed previously. Conclusion: In conclusion this experiment shows the strong relationship between cold work, annealing temperature, and hardness. The first part of the experiment shows that an increase in cold work correlates to an increase in hardness while in the second part of the experiment shows a decrease in hardness with an increase of annealing temperature. It is also shown that the recrystallization temperature is inversely proportional to the amount of cold work done on a sample. This can be explained by the internal strain energy in the material increasing as the amount of cold work increases, requiring less thermal energy to start recrystallization. The results from this experiment could be extrapolated out to other metals, though other metals should be tested as well. Knowing how cold work and annealing affects the hardness of metal is extremely useful for engineers. If a metal needs to be more flexible (e.g. in copper wires or the crumple zones of cars) the material can be annealed to allow more ductility. If a metal needs to be harder (e.g. for scratch resistant surfaces or a race car’s roll cage) the material can be cold worked to increase its hardness. In cases where a specific material hardness is needed, the hardness can be fairly precisely manipulated through a combination of cold work and annealing to achieve the desired hardness. This data was not completely consistent. There were two data points from the 4% CW sample that were anomalous from the rest of the data, at 200C and 450C. It is very likely that there was some sort of experimental error since they don’t follow the same trend as the rest of the data and that the 450C 4%CW sample’s measured hardness is much softer from every other measured hardness at any point during the experiment suggesting error when measuring the hardness of the sample. References: [1] Callister, W., and Rethwisch, D., 2007, “Materials Science and Engineering: An Introduction,” 9th ed., John Wiley & Sons, New York, pp. 191-195, Chap. 6. [2] G. Sachs and K. R. Van Horn, Practical Metallurgy, 1940, “Applied Metallurgy and the Industrial Processing of Ferrous and Nonferrous Metals and Alloys,” Reproduced by permission of ASM International, Materials Park, OH. [3] 2.5.3.2. Material inhomogeneity. (n.d.). Retrieved November 03, 2016, from http://www.itl.nist.gov/div898/handbook//mpc/section5/mpc532.htm