Final answer:
The percent increase in yield strength of aluminum, magnesium, and copper due to strain hardening can differ due to their crystal structures and material properties. Metals with a face-centered cubic (fcc) structure like aluminum and copper typically have high ductility and can be strain-hardened significantly. The hexagonal close-packed (hcp) structure of magnesium results in usually less ductility, affecting its ability to strain and harden as much as fcc metals.
Step-by-step explanation:
The student is interested in the percent increase in yield strength of commercially pure annealed aluminum, magnesium, and copper by strain hardening and the differences observed among them. Strain hardening, also known as work hardening, is a process that increases the strength of metals by plastic deformation. This process involves applying stress to a material, which exceeds its yield strength, causing it to deform plastically, and thus introducing dislocations and defects within the material's crystal structure, resulting in a harder and stronger material.
Each metal responds to strain hardening differently due to its crystal structure and bonding characteristics. In general, metals with a face-centered cubic (fcc) structure like aluminum tend to have high ductility and can undergo a significant amount of strain hardening. This is because the fcc structure has a large number of slip systems that allow for extensive plastic deformation before the material fractures. Magnesium, with its hexagonal close-packed (hcp) structure, tends to be less ductile than fcc metals and thus can be more challenging to strain harden as it has fewer slip systems. Copper, also an fcc metal, will behave similarly to aluminum, but differences in chemical composition and initial microstructure can lead to varying degrees of strain hardening.
The observed differences in percent increase in yield strength due to strain hardening can be attributed to the metals' crystal structures, purity levels, initial dislocation density, and the presence of alloying elements. To compare their specific increases, one would need to conduct tensile tests and generate stress-strain curves for each material, both before and after strain hardening, and calculate the percentage increase in yield strength from the respective yield points.