AbstractThe energy demand of human being is ever increasing. The naturally available energy resources are in a crude form and need conversion to one which is readily available for end use. Power plants play the role of this conversion process. Majority of the conversion processes take place at severe conditions of very high temperature and high pressure. Hence, power plant components always exhibit inelastic behaviours like creep and fatigue. The design of such components should take these inelastic behaviours in to consideration. This work focuses on modelling the creep behaviour of superheater materials. Specifically, creep constitutive model of T91 steel which is commonly used for constructing superheater tubes is developed and validated with results from experimental work. Then a material user subroutine has been written to incorporate the model in commercial software ABAQUS

Altenbach, Holm

Tibba, Getachew Shunki

Elsevier - Publisher Connector 

1876-6102 © 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of RERIS 2016
doi: 10.1016/j.egypro.2016.07.170 
 Energy Procedia  93 ( 2016 )  197 – 202 
ScienceDirect
Africa-EU Renewable Energy Research and Innovation Symposium, RERIS 2016, 8-10 March 
2016, Tlemcen, Algeria 
Modelling creep behaviour of superheater materials 
Getachew Shunki Tibbaa*, Holm Altenbachb 
aJimma University, Jimma Institute of Technology, Jimma 378, Ethiopia 
bOtto-von-Guericke Universitaet Magdeburg, Universitaetsplatz 2 G10-058, Magdeburg 39106, Germany  
Abstract 
The energy demand of human being is ever increasing. The naturally available energy resources are in a crude form and need 
conversion to one which is readily available for end use. Power plants play the role of this conversion process. Majority of the 
conversion processes take place at severe conditions of very high temperature and high pressure. Hence, power plant components 
always exhibit inelastic behaviours like creep and fatigue. The design of such components should take these inelastic behaviours 
in to consideration. This work focuses on modelling the creep behaviour of superheater materials. Specifically, creep constitutive 
model of T91 steel which is commonly used for constructing superheater tubes is developed and validated with results from 
experimental work. Then a material user subroutine has been written to incorporate the model in commercial software ABAQUS. 
 
© 2016 The Authors. Published by Elsevier Ltd. 
Peer-review under responsibility of the organizing committee of RERIS 2016. 
Keywords: Creep; constitutive model; Material User Subroutine; T91 Steel; ABAQUS. 
1. Introduction 
To fulfil the ever increasing energy demand of human being, energy conversion is being intensively performed 
throughout the world [1, 2, and 3]. About 80% of these energy conversion processes involve heat transfer [4] which 
need high temperature operation to obtain higher efficiency. Such processes are challenging for materials of 
components involved in the conversion. Different materials with better properties are being engineered to overcome 
the challenges. Advanced steels are among materials developed for this purpose. This work deals with explanation 
 
 
* Corresponding author. Tel.: +251911386973; fax: +251478112144. 
E-mail address: getachew.shunki@ju.edu.et 
Available online at www.sciencedirect.com
© 2016 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license 
(http://creativecommons.org/licenses/by-nc-nd/4.0/).
Peer-review under responsibility of the organizing committee of RERIS 2016
198   Getachew Shunki Tibba and Holm Altenbach /  Energy Procedia  93 ( 2016 )  197 – 202 
of the need for high temperature operations, modelling creep behaviour of superheater tube material, implementing 
the model in computational software and performing simulation of stress distribution in the superheater. 
2. Methodology 
The mechanical loads, which are commonly in the range of 100 to 200MPa, experienced by power plant 
components are quite low as compared to the yield strength of the components’ materials and may not result in 
immediate failure of the components. But as these loads act for a long period of time, fluctuating in nature, and 
accompanied by high temperature conditions, they force the components to exhibit time dependent inelastic 
behaviour like creep and fatigue. The objective of this work is to model this to model this behaviour. 
2.1. Modelling the Inelastic Behaviour  
In this work, the mixture constitutive model [5, 6] will be used with aid of conceptual model shown in Figure 1. 
This modelling assumes that a material consists of hard and soft constituents. The volumes of these constituents 
evolve with stress and strain. The deformation of the constituents is iso-strain type. 
Both constituents show elastic and inelastic behaviour. The elastic properties of the two constituents are assumed 
to be similar. There is non-uniform distribution of stresses in the two constituents (ߪ௦  in the soft and ߪ௛  in the hard). 
As deformation progresses, the volume fraction of the hard constituent is assumed to decrease to a certain saturation 
value due to the physical phenomena that take place in the material. The total stress ߪ acting in the material can be 
written in terms of stresses developed in the constituents as 
ߪ ൌ ߪ௦ሺͳ െ ߟ௛ሻ ൅ ߪ௛ߟ௛  (1) 
where ߟ௛  is the volume fractions of hard constituent. 
Fig. 1. Material Hard and Soft Constituent Assumption Model: a) Conceptual Physical Model for Uni-Directional Test, b) Maxwell-Type Elastic-
Inelastic Soft Constituent Model, c) Iso-Strain Connection of Creep-Soft and Creep-Hard Constituents. 
 Getachew Shunki Tibba and Holm Altenbach /  Energy Procedia  93 ( 2016 )  197 – 202 199
The variations of the strains in the constituents for uni-axial stress state are assumed to be governed by (2) as 
given in [5]. 
ߝሶ௦ ൌ ఙሶଽ௄ ൅
ఙሶ ೞ
ଷீ ൅ ݂ሺȁߪ௦ȁሻ
ఙೞ
ȁఙೞȁ ǡ ߝሶ௛ ൌ
ఙሶ
ଽ௄ ൅
ఙሶ ೓
ଷீ ൅
ఙ೓ିఙ
ఙ೓כିఙ ȁߝሶ
௖ȁ (2) 
where K and G are the bulk and shear modulus of the material, respectively, ε˙c is the average creep rate of the 
mixture and σhѽ is the saturation value of the stress in the hard constituent. To incorporate the physical phenomena in 
the development of the model, it is necessary to consider the nature of the creep curves of Advanced Steels. The 
main phenomena are hardening, softening and damage [5]. 
The total strain is split into elastic and inelastic parts in the usual way as,  
ߝሶ ൌ ఙሶா ൅ ߝሶ௖   (3) 
Combining (1) through (3) and incorporating the three evolution variables representing the physical phenomena 
(hardening, softening and damage), the general constitutive equation that governs the inelastic behaviour of the 
material can be given by 
ߝሶ௖ ൌ ݂ ቀȁఙିఉ௰ȁଵିఠ ቁ
ఙିఉ௰
ȁఙିఉ௰ȁ  (4) 
where ݂ is a function, β, Γ and ω are the evolution variables that govern the hardening, softening and damage 
processes, respectively, of the material. 
The model equations of the evolution variables are given in (5), (6), and (7), respectively [5]. 
ߚሶ ൌ ଷீ௖೓ ቀߝሶ
௖ െ ȁߝሶ௖ȁ ఉఉכቁ   (5) 
߁ሶ ൌ ܣ௦ሺ߁ כ െ߁ሻ ȁߝሶ௖ȁ  (6) 
ሶ߱ ൌ ቀఙାȁఙȁଶఙ ቁ݉
ఠ
೘షభ
೘
ఌכ  ȁߝሶ௖ȁ  (7) 
where ܿ௛is material parameter dependent on reference value of the volume fraction of the hard constituent, ܣ௦is 
a constant material parameter, m and ߝכ are material parameters. ݉ is a constant while ߝכis stress dependent. 
2.2. Computational Implementation 
Once the model parameters are identified and the model is validated, computational implementation is performed 
to show the success of integrating the model in a computational software. In this work, fluid-structure-interaction 
analysis of a superheater tube, Figure 4 a), has been made with the main aim of implementing the constitutive model 
developed into a computational software. The temperature distribution in the component has been determined by 
performing computational fluid dynamics analysis in ANSYS FLUENT. The structural analysis of the component 
has been made in ABAQUS by using ANSYS FLUENT result temperature distribution as a predefined field. 
200   Getachew Shunki Tibba and Holm Altenbach /  Energy Procedia  93 ( 2016 )  197 – 202 
Fig. 2. Variation of Creep Rate with Creep Strain at 6000 C-Separate Equations (Data source: [7]). 
3. Results and Discussion 
The modelling procedure begins with finding an appropriate function ݂  to be used in (4). The Generalized 
Garofalo model has been found to fit better for T91 steel experimental data. After a rigorous curve fitting activity, a 
model that incorporates all the evolution equations, shown in Figure 2, is obtained.  
After accepted accuracy of a constitutive model has been achieved, it has to be validated with data of different  
Fig. 3. Variation of Creep Strain with Time at 6000 C (Data source: [7]) Shown here for Validation Purpose. 
 Getachew Shunki Tibba and Holm Altenbach /  Energy Procedia  93 ( 2016 )  197 – 202 201
tests for the same material. Figure 3 shows the validation of the model against experimental data, at 6000C, of 
creep strain with time. The very good fit observed indicates the accuracy and appropriate- ness of the mixture model 
for modelling creep. As it can be witnessed by the curve-fits shown, the model has very high accuracy compared to 
other models so far used for the same purpose. The result can also be compared with works in [8].  
The creep constitutive model developed in the previous section has been implemented in ABAQUS through the 
user material subroutine, UMAT. The distribution of stress before and after creeping of the component has been 
shown in Figure d) and e). The result shows a decrease in the maximum stress and an increase in the minimum stress 
with time. Here the fixed parameters are the loads (temperature and pressure), not stress. Therefore, the material 
undergoes stress redistribution, resulting in narrowing of stress range. The results witness the successful 
implementation of the creep model in to ABAQUS. 
Fig. 4. a) Picture of Superheater Tube, b) Computational Model, c) Temperature Distribution, K, d) Von Mises stress Distribution(Time=0), Pa, 
e) Von Mises Stress Distribution. 
202   Getachew Shunki Tibba and Holm Altenbach /  Energy Procedia  93 ( 2016 )  197 – 202 
4. Conclusion 
In this work the inelastic (creep) behaviour of superheater tube material, T91 Steel, used in thermal power plants 
has been modelled. The mixture constitutive equation was used in the modelling. The modelling was done 
successfully by calibrating the material constants through optimization using available experimental data from 
literature. The results are very satisfactory as validations with experimental data and comparisons with results of 
other constitutive models show. 
References 
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[3] Goswami DY, Kreith F. Handbook of Energy Efficiency and Renewable Energy. London: Taylor & Francis; 2007.  
[4] Wang L. Advances in Transport Phenomena. Heidelberg: Springer; 2011.  
[5] Naumenko K, Altenbach H, Kutschke A. A combined model for hardening, softening, and damage processes in advanced heat resistant 
steels at elevated temperature. International Journal of Damage Mechanics 2011;20(4):578–97.  
[6] Besseling JF, Van Der Giessen E. Mathematical Modelling of Inelastic Deformation. London: Taylor & Francis; 1994. 
[7] Kimura K, Kushima H, Sawada K. Long-term creep deformation property of modified 9Cr-1Mo steel.  Materials Science and Engineering; 
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[8] Takahashi Y.  Study on creep–fatigue evaluation procedures for high chromium steels–part II: Sensitivity to calculated deformation. 
International Journal of Pressure Vessels and Piping 2008; 85(6): 423–40. 


Modelling Creep Behaviour of Superheater Materials 

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Modelling Creep Behaviour of Superheater Materials

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