Question

The yield strength for an alloy that has an average grain diameter of 5.1x10^-2 mm is 115 mpa. at a grain diameter of 8.0x10^-3 mm the yield strength increases to 275 mpa. at what grain diameter in mm will the yield strength be 227 mp

Answer 1

To find the grain diameter at which the yield strength will be 227 MPa, you can use the concept of the Hall-Petch relationship and solve for x in the equation sqrt(115 MPa / x) = sqrt(275 MPa / 8.0x10^-3 mm). The grain diameter at which the yield strength is 227 MPa is 1.75x10^-2 mm.

Step-by-step explanation:

To find the grain diameter at which the yield strength will be 227 MPa, we can use the concept of the Hall-Petch relationship. This relationship states that the yield strength of a material is inversely proportional to the square root of the average grain diameter. We have two data points: (5.1x10^-2 mm, 115 MPa) and (8.0x10^-3 mm, 275 MPa).

Using this data, we can set up the equation:

sqrt(115 MPa / x) = sqrt(275 MPa / 8.0x10^-3 mm)

Solving for x, the grain diameter at which the yield strength is 227 MPa, we find x = 1.75x10^-2 mm. Therefore, at a grain diameter of 1.75x10^-2 mm, the yield strength will be 227 MPa.

This is a commonly encountered principle in materials science courses at the college level, which deals with understanding and manipulating the properties of various materials for engineering applications.