Creep failure occurs in a material when it is subjected to constant load over prolonged periods of time. This is permanent deformation occurring in the material due its inherent atomic or molecular structure. This failure occurs when the stresses are well below the yield stress of the material. Understanding and accounting for creep behavior is very important in design phases to ensure reliability of many products.
As described in the previous article there are three stages for creep: Primary, steady state and tertiary creep. Primary and tertiary creep depend on stress level, temperature and time, whereas the secondary creep depends only on stress level and temperature. This secondary creep is the major part of the whole creep process. Usually, numerical models which capture the creep behavior focus on the primary and secondary stages.
Standard Creep Laws
Numerical models provide engineers with a practical means to simulate creep behavior over extended periods within a manageable timeframe and computational resources. The table below summarizes some common creep laws that are used in Abaqus for modeling secondary stage creep.
Other models, such as Anand, double power, and Darveaux, are not included in the table above. These models are tailored for specific material applications.
Example Creep Problem
In this article, the creep behavior of the example structure is analyzed in Abaqus under the specified constant stress state as described below.
Problem Definition
The creep behavior of the rectangular beam (100mm X 20mm X 20 mm) is analyzed in this below. The beam is assumed to be made of carbon steel andC3D8R elements are used to discretize the model. The beam is fixed in all DOF on the left side and is subjected to constant negative pressure loads of 5 MPa, 2 MPa and 1 MPa on rectangular faces as shown in the figure below.
Material Model
The material assumed for the rectangular bar here is carbon steel. Elastic properties (young’s modulus and Poisson’s ratio) are needed to calculate the structure’s static response to the applied loads. Creep material constants are needed to evaluate creep strain generated in the structure during the second Visco step. Time hardening creep law is used in this example which is formulated as shown below.
where, A is power law multiplier with units 1/h, n and m are stress and time orders.
The figure below shows the material card to enter creep parameters in Abaqus. We can also enter temperature-dependent creep data as per requirement.
Step Setup
To perform a thorough creep analysis, two key steps are required: the Static step and the Visco step.
In the Static step, the initial stress state of the structure is evaluated using a standard algorithm to establish baseline conditions that reflect the actual loads and constraints the material will encounter.
Following the Static step, the obtained stress state is imported into the visco step. This step is focused on assessing the creep behavior of the structure over an extended duration of 1,000 hours. By using the stress data from the Static step, the Visco step simulates the time-dependent deformation of the material. The visco step setup is shown in the figure below.
Results
The figure below shows the displacement results from the analysis after static step, 120 hours, 600 hours and 1000 hours. The displacement in the rectangular bar increases with an increase in the time of the analysis.
The graph below shows the nonlinear evolution of creep strain magnitude over a time period of 1000 hours.
Final Thoughts
Creep is a gradual deformation process that occurs over time in materials subjected to constant stress and elevated temperatures. Given that creep can lead to structural failure over time, it is important to accurately predict its effects. Hopefully this article has provided insights into different creep laws, their usage and limitations.
If you have questions regarding creep in your structure or FEA in general, get in touch with us today!
