To answer this question, we need to use the Basquin's law, which is a power law that describes the relationship between stress amplitude and the number of cycles to failure in a material subjected to cyclic loading. The equation is:

Sa = σ'f * (2N)^b

where:
Sa is the stress amplitude,
σ'f is the fatigue strength coefficient,
2N is the number of reversals to failure (2N = 2 * number of cycles),
b is the fatigue strength exponent.

We have two points on the S-N curve, so we can use them to solve for σ'f and b.

First, let's convert the cycles to reversals:
(700; 2*10^3) and (250; 2*10^6)

Then, we can set up two equations and solve for σ'f and b:

700 = σ'f * (2*10^3)^b
250 = σ'f * (2*10^6)^b

Solving these equations, we get σ'f ≈ 2023.6 MPa and b ≈ -0.097.

Now, we can use these values to find the number of reversals to failure at a stress amplitude of 220 MPa:

220 = 2023.6 * (2N)^-0.097

Solving for N, we get N ≈ 2.2 * 10^6 cycles.

Therefore, the endurance at a completely reversed rotating bending stress range of 220 MPa for 50 % probability of survival falls in the interval [2.0 × 10^6 ; 2.5 × 10^6), so the correct answer is B.

Question

To answer this question, we need to use the Basquin's law, which is a power law that describes the relationship between stress amplitude and the number of cycles to failure in a material subjected to cyclic loading. The equation is:

Sa = σ'f * (2N)^b

where:
Sa is the stress amplitude,
σ'f is the fatigue strength coefficient,
2N is the number of reversals to failure (2N = 2 * number of cycles),
b is the fatigue strength exponent.

We have two points on the S-N curve, so we can use them to solve for σ'f and b.

First, let's convert the cycles to reversals:
(700; 2*10^3) and (250; 2*10^6)

Then, we can set up two equations and solve for σ'f and b:

700 = σ'f * (2*10^3)^b
250 = σ'f * (2*10^6)^b

Solving these equations, we get σ'f ≈ 2023.6 MPa and b ≈ -0.097.

Now, we can use these values to find the number of reversals to failure at a stress amplitude of 220 MPa:

220 = 2023.6 * (2N)^-0.097

Solving for N, we get N ≈ 2.2 * 10^6 cycles.

Therefore, the endurance at a completely reversed rotating bending stress range of 220 MPa for 50 % probability of survival falls in the interval [2.0 × 10^6 ; 2.5 × 10^6), so the correct answer is B.

Knowee AI · Accepted Answer