Calculating Minimum Hardness of Steel Plate and Contact Zone Diameter

Question:

What is the calculation for (a) the minimum hardness of the steel plate for the contact to remain fully elastic; and (b) the diameter of the contact zone?

Answer:

To calculate the minimum hardness of the steel plate and the diameter of the contact zone, we can use the Hertz contact theory.

Calculating Minimum Hardness of Steel Plate:

Hardness (H): The minimum hardness of the steel plate can be found using the following equation:

H = (4E / 3) * sqrt(R)

Where H is the hardness, E is the Young's modulus, and R is the radius of curvature of the contact zone.

Calculating Diameter of the Contact Zone:

Contact Zone Diameter (2a): To calculate the diameter of the contact zone, we can use the following equation:

2a = sqrt(R * d)

Where a is the radius of the contact zone and d is the diameter of the ball.

By using the Hertz contact theory, we can determine the minimum hardness of the steel plate and the diameter of the contact zone in the given scenario.