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Tips and Tricks for FEA Modeling of Creep
What do cracks in 75-year-old English lead pipes, the Boston "Big Dig” roof failure and the collapse of the New York World Trade Center towers have in common? Creep played a major role in all three failures. Do you need to determine if creep is an issue with your design? Are you having problems getting your creep analysis to converge? This post provides tips for enhancing the accuracy and convergence of your creep simulation.
Low strain-rate, time-dependent deformation of materials characterized by creep (or stress relaxation) material laws exhibit the following characteristics:
- Creep, like plasticity, is an irreversible (inelastic) strain.
- Creep strain is generally assumed to be incompressible under creep flow.
- Creep, unlike rate-independent plasticity, has no yield surface at which inelastic strains occur. Hence, creep does not require a higher stress value for more creep strain to occur.
- Creep strains are assumed to develop at all non-zero stress values.
- In crystalline materials, such as metals, creep mechanism is linked to micro-mechanical behavior such as diffusional flow of vacancies and dislocation movement.
- Creep deformation is typically modeled in the following form, where creep strain rate can be a function of stress, strain, time, and temperature:
- There are three main stages of creep seen in most materials subjected to constant loading (Figure 1, above). In the primary stage, the strain rate decreases with time. This tends to occur over a short period. The secondary stage has a constant strain rate associated with it. In the tertiary stage, the strain rate increases rapidly until failure (rupture).
Obtaining both an accurate and converged solution in any nonlinear finite element analysis is a challenge. Here are my top tips in order of importance specifically associated with modeling creep.
1) Material Testing: Accurate material test data is a must when modeling time dependent deformation associated with creep. Calibration between test and computer modeling requires the selection of the most robust material model that accurately portray the range of strains expected in the simulation. Equivalent creep strain or creep strain rate material data vs. time is needed and is typically also a function of stress and temperature. Determining which of these parameters has the biggest impact on the creep strain will also help in the selection of the most appropriate creep material law.
The test data should represent as close as possible the in-situ material response. Since creep strain typically occurs over long periods of time, this makes actual testing impractical. Material test data is often accelerated via higher stress and/or temperatures. A sample procedure for extrapolating creep strains to longer time intervals is cited in Reference 1. The procedure was based on applying time-shift factors to creep strain curves at elevated temperatures to establish a master strain curve for longer time intervals.
2) Material Law Selection: There are many materials laws available to simulate creep strains using finite elements. These range from the simple stress dependent Power law to many different Strain or Time Hardening laws, which often contain Norton’s stress dependent constant as well as temperature effects. Selecting the best material law plays a crucial role in the success of your analysis. Select a material law with the best curve fit over the range of expected stresses and strains. Often the creep laws were developed for just one of the three stages of creep strain discussed above. Selecting the best material law can be a bit of trial and error process using test data curve fit compatibility and solution robustness (see item 3 below) as selection criteria.
I would suggest starting with the simpler laws first, such as the Norton Power law. Be cognitive of the expected strain levels in your simulation. For example, if you don’t expect any strains to exceed 5%, there is no reason to look to match strains at 30% since these will never be encountered in the real problem. Some FEA codes have regression based curve fitting capabilities that can be used to quickly test a number of different laws and automatically determine the necessary law coefficients. ANSYS Mechanical APDL curve fitting is illustrated in Figure 2.
Figure 2 Example Creep Curve Fitting using ANSYS Mechanical APDL
Some key tips to creep curve fitting:
- A successful curve fit depends greatly on the initial coefficient values.
- The more parameters a model has, the more difficult it is to get the solution to converge.
- Models with many parameters will sometimes converge more easily if you fix some of the coefficients
- Make sure you use enough significant figures when transferring the creep constants into the analysis. Small errors or typos in creep coefficients often lead to erroneous or un-converged solutions.
- Define temperature dependence using the Arrhenius law in the creep equation instead of multiple temperature-dependent creep constants which generally use unrealistic linear based interpolation rather than the more accurate log based solution illustrated below:
3) Test the Material Law: The one element test case should be used to determine the robustness of the material model by imposing force (for creep) or displacement (for relaxation) loads at different stress and temperature levels. Comparing the convergence efficiency between multiple material models on the single element model can be the deciding factor when more than one material law might fit the strain or strain rate test data adequately. The right choice can save significant CPU time and convergence headaches with the real model.
4) Load Stepping: Since most creep or stress relaxation typically occurs at early times in the analysis, using several load steps with successive increases in auto time steps produces the most accurate and robust solutions. Develop the load stepping procedures with the one-element model and then copy these over to the full analysis.
5) Creep Strain Limits: Once creep strains exist, they can never be removed. The creep strain increment at each time step must be carefully monitored so that it stays within reasonable limits. ANSYS allows the user to set a creep strain ratio limit (creep strain increment divided by the elastic strain) such that If the calculated maximum creep ratio exceeds the defined creep ratio limit, the solution is automatically bisected until the creep limit is satisfied or the minimum time step is reached.
Reference 1: Farrag, K., "Development of an Accelerated Creep Testing Procedure for Geosynthetics, Part II: Analysis," Geotechnical Testing Journal, Vol. 21, No. 1, 1998, pp. 38-44,http://dx.doi.org/10.1520/GTJ10423J. ISSN 0149-6115
by: Chris Mesibov
by: Chris Mesibov
by: Chris Mesibov
by: Chris Mesibov
by: Peter Barrett
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