1. What is creep?

Creep is a time-dependent deformation of materials occurring at elevated temperatures and within the range of stresses below the elastic limit of the material. In practice, the tensile properties of metals are often nearly independent of time at room temperature. However, at high temperatures, the dependence of strength on loading rate and time becomes evident, resulting in material undergoing creep.

The temperature at which creep occurs is material-dependent, meaning that a temperature that is high for one material may not be high for another material to experience creep. This temperature is generally related to the material's melting point. Typically, creep occurs at temperatures higher than half the melting point. In creep analysis, numerous factors come into play, and now we intend to examine these factors.

Figure 1: The turbine blade is damaged due to creep

2. Creep lifetime

As mentioned, creep occurs under long-term loading and at high temperatures. The conditions for creep commonly exist in various industries such as power generation plants, chemical factories, and aerospace industries. Therefore, designers and engineers must consider creep analysis in the design and construction of industrial components. Estimating the creep lifetime is necessary to prevent unforeseen and catastrophic events. Hence, estimating the creep lifetime is a crucial parameter in creep analysis. Generally, creep lifetime refers to the duration that a component can withstand creep before failure occurs. There are various models available for estimating creep lifetime, and we will examine some of the most well-known ones.

• Larson Miller estimation model

This model estimates creep lifetime based on the Larson-Miller parameter. This parameter is derived from the creep rupture data and expresses a relation between temperature and the time required for creep rupture. Eq (1) expresses the time to creep rupture (t_r) in terms of the Larson-Miller parameter (P_LM), the Larson-Miller constant (C_LM), and temperature (T).

Figure 6: Larson-Miller parameter values ​​based on stress

As mentioned, in this method, the Larson-Miller parameter is obtained using empirical data.

• Orr-Sherby-Dorn estimation model

Similar to the Larson-Miller model, the Sherby-Dorn model estimates creep lifetime based on the Sherby-Dorn parameter. This parameter is also derived from empirical data. In the equation of this model, the time to creep rupture is expressed in terms of the Sherby-Dorn parameter (P_OSD), temperature (T), activation energy (Q), and the universal gas constant (R).

• Polynomial estimation models

In creep analysis, there are models that estimate creep lifetime based on other models. These models are polynomial models. For example, the polynomial Larson-Miller model operates based on the Larson-Miller model. The difference in this approach is that instead of using empirical data to obtain the Larson-Miller parameter, a polynomial is used.

There are numerous methods for estimating creep lifetime that can assist us in creep analysis. However, these models, especially polynomial models, can also be used in creep analysis in Abaqus using the Abaqus creep subroutine, as they are based on theoretical relations.

3. Abaqus Creep models

One of the methods for creep analysis is simulation and creep analysis in Abaqus. Abaqus is a powerful finite element simulation software that is highly efficient in analyzing and studying phenomena such as creep. Creep is a time-consuming phenomenon therefore, its analysis and investigation in experimental tests are challenging and costly. However, Abaqus software provides users with the capability to perform creep analysis with less time and cost. So far, numerous models have been developed for creep analysis, and Abaqus creep incorporates some of the best creep analysis models. In the following sections, we will introduce some of these models.

3.1. Time Hardening law

When the temperature or stress conditions vary during loading, hardening conditions should be considered. One of these conditions is hardening proportional to time. In this case, relations for creep strain variations over time can be obtained. One of the models provided by Abaqus creep for creep analysis is the time hardening law. This model accounts for hardening based on time and its relation is as follows:

3.2. Time Power law

The time-hardening model mentioned cannot accurately predict creep when stress changes. Additionally, using this method in Abaqus software sometimes faces computational problems. For these reasons, the time power law has been developed as an alternative to the time hardening law, which does not pose computational issues for Abaqus software. This model utilizes the following relation to predict creep:

3.3. Strain Hardening law

Similar to the time hardening law, this model is also used when creep is accompanied by hardening. However, this model is particularly suitable for situations where stress changes over time and generally at low-stress levels. The relation for predicting creep according to this law is as follows:

3.4. Creep power law

creep analysis in Abaqus using the strain hardening law, such as the time hardening law, there are computational issues present in Abaqus, and sometimes Abaqus is unable to solve the creep problem using this model. For this reason, you can utilize the creep power law. This law, similar to the strain hardening law, can predict creep in situations where strain hardening relation exists due to stress changes. Moreover, there are no computational issues associated with using the creep power law. The creep power law is recognized as one of the best and most practical models for predicting creep. The following relation is used to predict creep using the creep power law:

4. Abaqus creep subroutine

Abaqus is a highly powerful finite element software, but sometimes users have needs that are not preconfigured in Abaqus. To address this issue, Abaqus recommends using subroutines. Users can fulfill their specific requirements by utilizing subroutines in a predetermined format. Various models have been provided in the Abaqus for creep analysis, some of which we have reviewed in previous sections. Occasionally, Abaqus users may require the use of specialized or advanced models for creep analysis. For this category of users, Abaqus recommends using the Abaqus creep subroutine. Utilizing the Abaqus creep subroutine can also assist users in simulating complex creep analysis problems within Abaqus.

As you have already noticed, creep is a highly important phenomenon in engineering. Therefore, understanding this phenomenon, creep analysis, identifying its influential factors, and finding ways to predict and simulate it are of great significance. One way to predict creep in components with low cost is through creep analysis in Abaqus. However, as you know, this also comes with its own complexities. For this reason, our team has decided to address all your needs in the form of a tutorial training package.

The "Abaqus creep analysis tutorial" package can provide answers to all your questions regarding simulation and creep analysis. If you want to familiarize yourself with the mentioned Abaqus creep prediction models in this article, as well as other models available in Abaqus, or learn how to work with the Abaqus creep subroutine, consider acquiring this package. In addition, this package includes two examples of simulations in Abaqus software.