Design for Creep

Creep in design

Creep is time-dependent inelastic deformation under sustained load. It is especially important for metals at elevated homologous temperatures; some polymers creep significantly near room temperature. A short-duration tensile test cannot establish long-duration deformation or rupture resistance.

Stages and design limits

Primary creep has a decreasing strain rate, secondary creep an approximately steady rate, and tertiary creep an accelerating rate associated with damage and possible rupture. Check both permissible accumulated strain and creep-rupture life for the specified temperature, stress and service duration. Stress relaxation under constrained total strain is related but differs from constant-stress creep.

A model for secondary creep

A common calibrated form is strain_rate = A sigma^n exp(-Q/(RT)), where T is absolute temperature, Q is activation energy and R is the gas constant. The coefficient's units depend on the chosen stress and time units. This is a strain-rate relation, not a universal equation for “creep stress”. It describes a fitted regime and must not be extrapolated across changes in mechanism, stress or temperature without evidence. See Sandia's power-law creep model.

Worked strain calculation

For an illustrative material at a fixed specified temperature and stress of 150 MPa, suppose a test fit for the interval of interest is epsilon_total = sigma/E + A_t sqrt(t), with E = 200 GPa, A_t = 5.0e-7 s^(-1/2), and t measured in seconds. The fit includes elastic plus time-dependent strain and is supplied for this exercise only.

At t = 10000 h = 36000000 s, sqrt(t) = 6000 s^(1/2).

Elastic strain = 150e6/200e9 = 0.00075. Creep strain = (5.0e-7)(6000) = 0.00300. Total strain = 0.00375 = 0.375%.

A 1 m uniform bar therefore extends 3.75 mm in this simple constant-stress model. Of this, 0.75 mm is the elastic contribution. This time-power fit is not the steady-rate secondary-creep law above and supplies no rupture life.

Common errors

• Using Celsius in an Arrhenius exponential.
• Changing hours to seconds without also using a coefficient calibrated for seconds.
• Treating stress-dependent coefficients as valid at a different stress.
• Equating a strain limit with rupture, or using a room-temperature modulus at high temperature without justification.
• Confusing constant load with constant true stress when cross-sectional area changes appreciably.

Quick check

For a measured constant secondary creep rate of 2e-8 per second over a 100-hour interval, additional creep strain is 2e-8 × 360000 = 0.0072 = 0.72%, provided the rate remains applicable throughout that interval.