Final answer:
The Hall-Petch relationship describes the relationship between the yield strength of a material and its grain size. To show that the yield strengths of the steel and aluminum alloy obey the Hall-Petch relationship, perform tensile and compressive tests and measure average grain sizes.
To determine σ0 and ky for each material, plot stress against √(grain size) and analyze the data. Additionally, measure hardness and thermal conductivity for each material.
Step-by-step explanation:
The Hall-Petch relationship describes the relationship between the yield strength of a material and its grain size. According to the Hall-Petch equation, the yield strength (σ) of a material is inversely proportional to the square root of its average grain size (d). The equation is given by σ = σ0 + ky √(d), where σ0 is the initial yield strength, ky is a constant specific to the material, and d is the grain size.
a) To show that the yield strengths of the steel and aluminum alloy obey the Hall-Petch relationship, you would need to perform tensile tests on both materials and measure their average grain sizes. Then, you can plot σ against √(d) and check if the data points follow a linear trend, indicating that they obey the Hall-Petch relationship.
b) Similarly, you can conduct compressive tests on both materials and measure their average grain sizes. Then, plot the compressive stress against √(d) and check if the data points follow a linear trend.
c) To determine the hardness for steel and aluminum, you can measure the hardness using a hardness testing method such as the Rockwell hardness test or the Vickers hardness test.
d) To analyze the thermal conductivity for steel and aluminum, you can measure their thermal conductivities using a thermal conductivity testing method such as the hot wire method or the laser flash method.