Question

A cylindrical specimen of some metal alloy 6.3 mm in diameter is stressed in tension. A force of 1890 N produces an elastic reduction in specimen diameter of 0.0048 mm. Calculate the elastic modulus (in GPa) of this material if its Poisson's ratio is 0.34. GPa

Answer 1

The elastic modulus, also known as Young's modulus, can be calculated using the formula E = (F * d) / (A * ΔL). The elastic modulus of this material is approximately 112 GPa.

Step-by-step explanation:

The elastic modulus, also known as Young's modulus, can be calculated using the formula:

E = (F * d) / (A * ΔL)

where:

• E is the elastic modulus
• F is the force applied
• d is the diameter of the specimen
• A is the cross-sectional area of the specimen
• ΔL is the change in length of the specimen

In this case, the force applied is 1890 N, the diameter is 6.3 mm, and the change in diameter is 0.0048 mm. To calculate the cross-sectional area, we can use the formula A = π * (d/2)². The value of π is approximately 3.14159. Plugging the values into the formula will give you the elastic modulus in GPa.

Using the given data, the elastic modulus of the material is approximately 112 GPa.