Creep Model

Creep is a time dependent strain produced under a state of constant stress.

Creep is observed in most engineering materials especially metals at elevated temperatures, high polymer plastics, concrete, and solid propellant in rocket motors. Since creep effects take long time to develop, they are usually neglected in dynamic analysis.

The creep curve is a graph between strain versus time. Three different regimes can be distinguished in a creep curve; primary, secondary, and tertiary. Usually primary and secondary regimes are of interest.

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The Bailey-Norton Classical Power Law for Creep based on an “Equation of State” approach is implemented. The law defines an expression for the uniaxial creep strain in terms of the uniaxial stress and time.

Classical Power Law for Creep (Bailey-Norton law)

and

where:

T = Element temperature (Kelvin)

CT = A material constant defining the creep temperature-dependency

C0 is the Creep Constant 1 you enter in the Properties tab of the Material dialog box.

The units of the Creep Constant 1 must be entered in the SI unit system. The conversion factor is equal to 1/ (stress ^ (C1) * time^(C2)). The stress units are in N/m2 and time is in seconds.

C1 is the Creep constant 2, and C2 is the Creep constant 3 in the material properties dialog box.

The classical power law for creep represents primary and secondary creep regimes in one formula. Tertiary creep regime is not considered. “t” is the current real (not pseudo) time and sigma is the total uniaxial stress at time t.

To extend these laws to multiaxial creep behavior, the following assumptions are made:
  • The uniaxial creep law remains valid if the uniaxial creep strain and the uniaxial stress are replaced by their effective values.
  • Material is isotropic
  • The creep strains are incompressible

For a numerical creep analysis, where cyclic loading may be applied, based on the strain hardening rule, the current creep strain rates are expressed as a function of the current stress and the total creep strain:

: effective stress at time t
:total effective creep strain at time t
: components of the deviatoric stress tensor at time t

Deriving Creep Constants from Reference Data

In this example, you derive creep constants from reference data for a Stainless Steel material.

From the Classical Power Law for Creep (Bailey - Norton law), the creep strain at time t, when no temperature variation is considered, is given by:



In the Material dialog box, the constants C0, C1, and C2 are labeled as:

C0 = Creep Constant 1, C1 = Creep Constant 2, and C2 = Creep Constant 3

In the above equation: the Creep Constant 1 ( C0) is calculated in the SI unit system ( stress in N /m 2 and time in sec), Creep Constant 2 ( C1 >1) is unitless, and Creep Constant 3 (C2) is between 0 and 1.

From the reference creep data below, you calculate the creep constants for the equation of creep state. The table references constant stress values at constant temperatures that can develop a creep strain of 1% over an extented period. These data refer to Stainless Steel - Grade 310.
Temperature (C) Stress (MPa) Stress (MPa)
time = 10,000 hr time = 100,000 hr
550 110 90
600 90 75
650 70 50
700 40 30
750 30 20
800 15 10
Select the stress data for temperature 550 C. Assuming C2 =1, from the creep state equation above, you have a system of 2 equations with 2 unknowns C0 and C1. First you calculate C1. The two equations to the state of creep are:

0.01 = C0 * 110 C1* 10,000 (Eq.1)

0.01 = C0 * 90 C1* 100,000 (Eq.2)

Equating the two equations and using logarithmic functions:

C1 * log (110) = C1 * log (90) +1 (Eq.3)

From (Eq.3), you calculate C1 = 11.47.

You can use either (Eq.1) or (Eq.2) to calculate C0. C0 is calculated in the SI units, so you need to apply conversion factors.

C0 = 0.01 / ( (90E6)11.47 * 100000 *3600) = 1.616E-102

You enter the three creep constants in the Material dialog box:

Creep Constant 1 = 1.616E-102 , Creep Constant 2 = 11.47, Creep Constant 3 = 1

In the Material dialog box, select Include Creep Effect to activate the creep calculation for the selected material model. Creep calculations are considered only for nonlinear studies. Creep effect is not available for the linear elastic orthotropic and viscoelastic material models.

Solver Settings for Creep Calculations

  • In the Material dialog box, select Include Creep Effect to activate the creep calculation for the selected material model. Creep calculations are supported only for nonlinear studies with solid mesh. Creep effects are not supported for shells or beams. Creep consideration is not available for the linear elastic orthotropic and viscoelastic material models.
  • When you consider creep effects in a nonlinear study, select option Automatic (autostepping) to improve chances of convergence (Nonlinear study dialog box). The solver calculates an original value for the creep strain εorg, and if εorg exceeds 1.0, the solution terminates. If the solver exceeds the maximum equilibrium iterations required to reach convergence, the solution terminates, and the solver issues appropriate error messages with corrective actions.
  • For Solver, select Automatic Solver Selection.
  • Enter End time in seconds (Nonlinear study dialog box).