Design for Dynamic Load

Dynamic loads and fatigue

A time-varying load can produce inertia forces, vibration and cyclic stress. Fatigue cracks can initiate and grow at stresses below monotonic yield strength. Impact, low-cycle plastic fatigue and high-cycle elastic fatigue need different models.

Define the stress cycle

For a uniaxial cycle, sigma_m = (sigma_max + sigma_min)/2 and sigma_a = (sigma_max - sigma_min)/2. Hence sigma_max = sigma_m + sigma_a and sigma_min = sigma_m - sigma_a. The sum is the maximum stress, not a separate universal “dynamic stress”. Stress ratio R = sigma_min/sigma_max when the denominator is nonzero.

Mean-stress design

A common high-cycle design approximation for nonnegative tensile mean stress is the modified Goodman relation:

sigma_a/S_e + sigma_m/S_ut <= 1/n.

S_e is the corrected component endurance strength for the specified conditions, S_ut is ultimate tensile strength and n is the required safety factor for proportional scaling of both stress components. This is an approximate design model, not a universal life prediction. A Soderberg line substitutes yield strength S_y for S_ut and is generally more conservative. Also check maximum stress against yielding. Do not extrapolate tensile-mean-stress rules indiscriminately into compression.

Worked example

A component has sigma_a = 150 MPa, sigma_m = 50 MPa, corrected S_e = 200 MPa, S_ut = 500 MPa and S_y = 300 MPa. The stress ranges from -100 to 200 MPa and R = -0.5.

Goodman utilization = 150/200 + 50/500 = 0.85. The proportional-load Goodman factor is 1/0.85 = 1.176. It passes a factor-of-one check but does not meet a required factor of 1.5 because 0.85 > 1/1.5. The separate peak-stress yielding factor is 300/200 = 1.5. Yielding and fatigue checks are different.

Finite-life calculations

An S–N curve must specify stress amplitude, mean-stress conditions, units and applicable cycle range. For an illustrative fully reversed test fit sigma_a = 1000 N^(-0.1) MPa, where N is cycles to failure, sigma_a = 316.228 MPa gives N ≈ 100000 cycles. Solve N = (sigma_a/1000 MPa)^(-10). Do not use an arbitrary positive power of a stress ratio to claim a fraction-of-a-cycle fatigue life. This illustrative fit is not material data for the previous component.

Design workflow

1. Obtain the actual stress history, including inertia and dynamic amplification where relevant.
2. Determine mean and alternating local stresses using appropriate fatigue concentration factors.
3. Select fatigue data consistent with material, surface, size, temperature and reliability.
4. Check fatigue and static yielding separately; consider variable-amplitude damage only with its assumptions stated.
5. Check stiffness and resonance independently. A slowly changing load can cause fatigue even when vibration is negligible.

Quick check

For stress varying from 20 to 100 MPa, the mean is 60 MPa and the amplitude is 40 MPa. Amplitude is half the range, not the maximum stress.