- Researchers from the University of Liège, Fraunhofer IWM and IMDEA Materials have developed a modelling framework that may dramatically accelerate the characterisation of creep behaviour in high-temperature materials
The European research team behind AID4GREENEST has developed a mathematical framework that could significantly reduce the time required to assess how materials deform under prolonged mechanical loads and elevated temperatures.
Published in the International Journal of Solids and Structures, the new approach enables researchers to reconstruct the intrinsic long-term creep behaviour of materials from accelerated testing methods, reducing total testing time by up to 76.7%.
The breakthrough addresses one of the major challenges associated with creep testing, which is used to understand how materials gradually and permanently deform when subjected to sustained stresses over long periods.
Accurate creep characterisation is essential for materials used in demanding applications such as power generation turbines, where components must operate safely under high temperatures and mechanical loads for years.
However, conventional creep testing is notoriously time-consuming. Establishing a material’s long-term performance typically requires multiple samples to be tested independently under different stress levels, where experiments can last months or even years.
One of the most promising characterisation methods for accelerating this process is the Stepped Isostress Method (SSM). Instead of performing separate tests at each stress level, SSM progressively increases the stress applied to a single specimen, allowing creep behaviour under multiple loading conditions to be investigated within a single experiment.
Due to their previous loading conditions, however, experiments have consistently shown that creep strain rates measured during stepped testing are systematically higher than those obtained from conventional constant-stress tests under otherwise identical conditions.
This loading-history effect alters the internal state of the material, meaning SSM data cannot be directly interpreted as representing the material’s intrinsic creep behaviour.
To address this issue, the research team developed a history-dependent constitutive model that quantifies and corrects the influence of prior loading conditions.
The framework keeps track of the material’s loading history, accounting for the combined effects of stress and time throughout the test. This history changes the material’s resistance to further viscoplastic deformation, represented by a quantity called the “drag stress”.
The model successfully reproduces the behaviour observed in both conventional constant-stress creep tests and stepped isostress experiments, including the characteristic increase in creep strain rate following stress increments.
More importantly, the researchers developed an inverse methodology capable of working backwards from stepped-test measurements to reconstruct the intrinsic minimum creep strain rate that would be obtained from standard constant-stress testing.
When validated against conventional creep experiments, the predicted values remained within the experimental scatter observed across different temperatures and loading paths, demonstrating the reliability of the approach.
The study showed that the framework can reduce total testing time from 290 days to just 68 days, corresponding to a saving of 76.7%. In addition, the methodology can substantially reduce experimental resources, lowering the number of required specimens and tests by 65.6%, from 32 conventional tests to only 11 stepped tests.
The model was successfully validated using 30CrMoNiV5-11 martensitic steel, a heat-resistant alloy widely used in turbine rotors and shafts for power-generation applications.
While the framework provides a practical approach to accelerated creep characterisation, it remains phenomenological, meaning it captures loading-history effects without explicitly modelling the underlying microstructural changes in the material.
Future research could explore links between the model’s history variable and measurable microstructural features, as well as its extension to more complex loading conditions and other materials.
“We believe this approach could contribute to faster qualification of advanced metallic materials for energy applications, supporting the development of safer and more efficient industrial components”, said the research team behind the study, which included researchers Fan Chen, Carlos Rojas-Ulloa, Laurent Duchene and Anne Marie Habraken from the University of Liège, Alexander Kott, Lukas Morand and Maxim Zapara from Fraunhofer IWM and Christina Schenk from IMDEA Materials Institute.
The authors acknowledge support from Horizon Europe, Project No. 101091912 (AID4Greenest). Anne Marie Habraken acknowledges support from the F.R.S.\u2013 FNRS (Fonds de la Recherche Scientifique, Belgium; Walloon Region). The authors would like to thank Ilchat Sabirov (IMDEA Materials Institute) for his valuable suggestions regarding the SSM testing programme and Carlos Llovo Vidal (Reinosa Forgings & Castings) for providing the turbine-shaft material used for the SCT and SSM experiments.