Creep is the inelastic, irreversible deformation of structures during time. It is a life limiting factor and depends on stress, strain, temperature and time. This dependency can be modeled as followed:

Creep can occur in all crystalline materials, such as metal or glass, has various impacts on the behavior of the material and can ultimately lead to following problems: [NAFEMS_HT21]

Disproportionate deformation leads to buckling or failure. In machines with moving parts this can reduce the size of gaps and lead to frictional abrasion.

The connection of bolted parts can loosen over time, because of relaxations of the pre-stressing. This relaxation can also occur in cables, gaskets and flanges.

Excessive heat and load cycles can favor the propagation of cracks, which can lead to damage and ultimately to failure of the part.

Because of these extremely different factors the effects of creep in certain situations can be highly complex. By undertaking creep analysis the influence of these effects can be evaluated and the life time of parts can be estimated. Especially in the hot section of turbines of commercial and military plains this can be a crucial factor for the design process and save a lot of money.

Three stages of creep

Creep can be divided in three different stages: primary creep, secondary creep and tertiary creep

Primary creep (0<m<1

$0<m<1$

) starts rapidly with an infinite creep rate at the initialization. Here is m

$m$

the time index. It occurs after a certain amount of time and slows down constantly. It occurs in the first hour after applying the load and is essential in calculating the relaxation over time.

Secondary creep (m=1

$m=1$

) follows right after the primary creep stage. The strain rate is now constant over a long period of time.

The strain rate in the tertiary creep stage is growing rapidly until failure. This happens in a short period of time and is not of great interest. Therefore only primary and secondary creep are modeled on the SimScale platform.

Calculating the creep strain

The creep strain equations are based on an additive strain decomposition:

The choice of the formulation to be used varies from problem to problem and depends on the data of the temperature and stress field of the problem.

Important remarks

The creep formulation parameters (A,m,n)

$(A,m,n)$

and (ϵc0,σ0)

$({\u03f5}_{0}^{c},{\sigma}_{0})$

are defined in the sense of the above equations with respect to the rate form of the creep laws.

It is important to have a consistent unit system when converting parameters found in literature or material supplier or test data. Often the creep parameters are are given relate to length measure in mm, stresses in MPa and time in hours.

An example of how to convert the parameter A of the Time Hardening or Strain Hardening formulation would be: ASI=13600⋅13600m⋅1106n⋅AMPah

Especially when primary creep is observed it is very important to refine the time stepping sufficiently to capture the creep behavior correctly. Therefore it is advised to use the Field Change criteria of the Automatic Time Stepping available for Code_Aster.

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