## Introduction

There are many (>10) creep models available in Ansys Mechanical. These models are mainly use for metals, but there is nothing inherent about these models that prevent them from also being used for polymers. In this article I will explore the different creep models, and answer questions like: **How do they work? Which one should you use?** Also, if you are an Abaqus user, then check out our article on creep models for Abaqus.

Here’s an example APDL material definition that is using a linear elastic-plastic with creep material model:

` ````
```MP, DENS, matid, 1e-09
MP, EX, matid, 10
MP, NUXY, matid, 0.4
TB, CREEP, matid,1,, 1
TBDATA, 1, 0.01
TBDATA, 2, 2
TBDATA, 3, -0.5
TBDATA, 4, 0
TB, PLAS, matid, 1, 3, MISO
TBPT, , 0, 10
TBPT, , 0.01, 11
TBPT, , 0.02, 12

The traditional way to teach creep behavior of materials is to divide the creep response into 3 different regions. In the primary region the creep strain rate decreases with time, in the secondary (or steady-state) creep region the creep rate is linear with time, and in the tertiary region the creep rate is increasing with time. Note that in this figure is plotting **linear time**, but for polymers the creep rate is often proportional to the logarithm of the creep time (not linear).

In the next few sections I will go through a number of the most common Ansys creep models.

## Creep Model 1: Strain Hardening

Creep equation: \( \dot{\varepsilon}_c = C_1\, \sigma^{C_2}\, \varepsilon_c^{C_3}\, e^{-C_4/T} \). No explicit time dependence, which is good. The following figure shows the influence of the strain exponent C3. If C3 < 0 then the creep strain rate decreases with time, which is typical for primary creep. This is one of my favorite creep models in Ansys.

## Creep Model 2: Time Hardnening

Creep equation: \( \dot{\varepsilon}_c = C_1\, \sigma^{C_2}\, t^{C_3}\, e^{-C_4/T} \). Note that the creep rate in this model depends explicitly on the time. This means that any simulated part will change its properties with time even if there is no applied stress. This is not how materials behave. **I do not recommend using a creep model with explicit time dependence unless you really have to.** The following figure shows the influence of the creep parameter C3. If C3 < 0 then the creep strain rate decreases with time.

## Creep Model 3: Generalized Exponential

Creep equation: \( \dot{\varepsilon}_c = C_1\, \sigma^{C_2}\, r\, e^{-rt} \), where \(r = C_5 \sigma^{C_3} e^{-C_4/T}. \) Note that the creep rate explicitly depends on the time. This means that any simulated part will change its properties with time even if there is no applied stress.

## Creep Model 4: Generalized Graham

Creep equation: \( \dot{\varepsilon}_c = C_1\, \sigma^{C_2} \left( t^{C_3} + C_4 t^{C_5} + C_6 t^{C_7} \right) e^{-C_8/T}

\). Note that the creep rate explicitly depends on the time. This means that any simulated part will change its properties with time even if there is no applied stress.

## Creep Model 5: Generalized Blackburn

Creep equation:\( \dot{\varepsilon}_c = f(1-e^{-rt})+gt \), where \(f = C_1 e^{C_2\sigma}\), \(r = C_3 \displaystyle\left( \frac{\sigma}{C_4}\right)^{C_5}\), and \(g= C_6 e^{C_7 \sigma}\). If you study this equation carefully you will see that the creep rate will become equal to C6 when there is no applied stress. This seem odd to me. There should not be any creep if the applied stress is 0.

## Creep Model 6: Modified Time Hardening

Creep model: \( \varepsilon_c = C_1 \sigma^{C_2} t^{C_3+1}e^{-C_4/T} / (C_3+1) \). This is functionally identical to the Time Hardening model. I don’t see any particular reason to use this model. Note that the equation is written in terms of creep strain, not creep strain rate.

## Creep Model 7: Modified Strain Hardening

## Creep Model 8: Generalized Garofalo

## Creep Model 9: Exponential Form

## Creep Model 10: Norton

Creep equation: \(C_1 \sigma^{C_2} e^{-C_3/T}\). This is a simplified version of the Strain Hardening model. I prefer the strain hardening model since it allows for strain dependence of the creep rate.

## Creep Model 11: Combined Time Hardening

Creep equation: \( \varepsilon_c = \displaystyle \frac{C_1}{C_3+1} \sigma^{C_2}t^{C_3+1}e^{-C_4/T} + C_5 \sigma^{C_6}t \, e^{-C_7/T} \). This seems like a reasonable creep model, except that it is too complicated for my liking. I prefer the Strain Hardening model instead. Note that the equation is written in terms of creep strain, not creep strain rate.

## Summary

- These creep models are mainly used for metals
- For polymers I recommend: Strain Hardening, Generalized Garofalo
- Try to avoid using a creep equation with explicit time dependence
- The creep models can be combined with linear elastic, and elastic-plastic components
- The creep models are not great at predicting the response of polymers