Thermo-mechanical fatigue

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Thermo-mechanical fatigue (short TMF) is the overlay of a cyclical mechanical loading, that leads to fatigue of a material, with a cyclical thermal loading. Thermo-mechanical fatigue is an important point that needs to be considered, when constructing turbine engines or gas turbines.

Contents

Failure mechanisms

There are three mechanisms acting in thermo-mechanical fatigue

Each factor has more or less of an effect depending on the parameters of loading. In phase (IP) thermo-mechanical loading (when the temperature and load increase at the same time) is dominated by creep. The combination of high temperature and high stress is the ideal condition for creep. The heated material flows more easily in tension, but cools and stiffens under compression. Out of phase (OP) thermo-mechanical loading is dominated by the effects of oxidation and fatigue. Oxidation weakens the surface of the material, creating flaws and seeds for crack propagation. As the crack propagates, the newly exposed crack surface then oxidizes, weakening the material further and enabling the crack to extend. A third case occurs in OP TMF loading when the stress difference is much greater than the temperature difference. Fatigue alone is the driving cause of failure in this case, causing the material to fail before oxidation can have much of an effect. [1]

TMF still is not fully understood. There are many different models to attempt to predict the behavior and life of materials undergoing TMF loading. The two models presented below take different approaches.

Models

There are many different models that have been developed in an attempt to understand and explain TMF. This page will address the two broadest approaches, constitutive and phenomenological models. Constitutive models utilize the current understanding of the microstructure of materials and failure mechanisms. These models tend to be more complex, as they try to incorporate everything we know about how the materials fail. These types of models are becoming more popular recently as improved imaging technology has allowed for a better understanding of failure mechanisms. Phenomenological models are based purely on the observed behavior of materials. They treat the exact mechanism of failure as a sort of "black box". Temperature and loading conditions are input, and the result is the fatigue life. These models try to fit some equation to match the trends found between different inputs and outputs.

Damage accumulation model

The damage accumulation model is a constitutive model of TMF. It adds together the damage from the three failure mechanisms of fatigue, creep, and oxidation.

where is the fatigue life of the material, that is, the number of loading cycles until failure. The fatigue life for each failure mechanism is calculated individually and combined to find the total fatigue life of the specimen. [2] [3]

Fatigue

The life from fatigue is calculated for isothermal loading conditions. It is dominated by the strain applied to the specimen.

where and are material constants found through isothermal testing. Note that this term does not account for temperature effects. The effects of temperature are treated in the oxidation and creep terms..

Oxidation

The life from oxidation is affected by temperature and cycle time.

where

and

Parameters are found by comparing fatigue tests done in air and in an environment with no oxygen (vacuum or argon). Under these testing conditions, it has been found that the effects of oxidation can reduce the fatigue life of a specimen by a whole order of magnitude. Higher temperatures greatly increase the amount of damage from environmental factors. [4]

Creep

where

Benefit

The damage accumulation model is one of the most in-depth and accurate models for TMF. It accounts for the effects of each failure mechanism.

Drawback

The damage accumulation model is also one of the most complex models for TMF. There are several material parameters that must be found through extensive testing. [5]

Strain-rate partitioning

Strain-rate partitioning is a phenomenological model of thermo-mechanical fatigue. It is based on observed phenomenon instead of the failure mechanisms. This model deals only with inelastic strain and ignores elastic strain completely. It accounts for different types of deformation and breaks strain into four possible scenarios: [6]


The damage and life for each partition is calculated and combined in the model

where

and etc., are found from variations of the equation

where A and C are material constants for individual loading.

Benefit

Strain-Rate Partitioning is a much simpler model than the damage accumulation model. Because it breaks down the loading into specific scenarios, it can account for different phases in loading.

Drawback

The model is based on inelastic strain. This means that it does not work well with scenarios of low inelastic strain, such as brittle materials or loading with very low strain. This model can be an oversimplification. Because it fails to account for oxidation damage, it may overpredict specimen life in certain loading conditions.

Looking forward

The next area of research is attempting to understand TMF of composites. The interaction between the different materials adds another layer of complexity. Zhang and Wang are currently investigating the TMF of a unidirectional fiber reinforced matrix. They are using a finite element method that accounts for the known microstructure. They have discovered that the large difference in the thermal expansion coefficient between the matrix and the fiber is the driving cause of failure, causing high internal stress. [7]

Related Research Articles

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Linear elasticity is a mathematical model of how solid objects deform and become internally stressed by prescribed loading conditions. It is a simplification of the more general nonlinear theory of elasticity and a branch of continuum mechanics.

<span class="mw-page-title-main">Fatigue (material)</span> Initiation and propagation of cracks in a material due to cyclic loading

In materials science, fatigue is the initiation and propagation of cracks in a material due to cyclic loading. Once a fatigue crack has initiated, it grows a small amount with each loading cycle, typically producing striations on some parts of the fracture surface. The crack will continue to grow until it reaches a critical size, which occurs when the stress intensity factor of the crack exceeds the fracture toughness of the material, producing rapid propagation and typically complete fracture of the structure.

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The work of a force on a particle along a virtual displacement is known as the virtual work.

<span class="mw-page-title-main">Coble creep</span>

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<span class="mw-page-title-main">Rock mass plasticity</span>

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Solder fatigue is the mechanical degradation of solder due to deformation under cyclic loading. This can often occur at stress levels below the yield stress of solder as a result of repeated temperature fluctuations, mechanical vibrations, or mechanical loads. Techniques to evaluate solder fatigue behavior include finite element analysis and semi-analytical closed-form equations.

<span class="mw-page-title-main">Crack growth equation</span>

A crack growth equation is used for calculating the size of a fatigue crack growing from cyclic loads. The growth of a fatigue crack can result in catastrophic failure, particularly in the case of aircraft. When many growing fatigue cracks interact with one another it is known as widespread fatigue damage. A crack growth equation can be used to ensure safety, both in the design phase and during operation, by predicting the size of cracks. In critical structure, loads can be recorded and used to predict the size of cracks to ensure maintenance or retirement occurs prior to any of the cracks failing. Safety factors are used to reduce the predicted fatigue life to a service fatigue life because of the sensitivity of the fatigue life to the size and shape of crack initiating defects and the variability between assumed loading and actual loading experienced by a component.

Anelasticity is a property of materials that describes their behaviour when undergoing deformation. Its formal definition does not include the physical or atomistic mechanisms but still interprets the anelastic behaviour as a manifestation of internal relaxation processes. It is a behaviour differing from elastic behaviour.

References

  1. Nagesha, A et al. "A comparative study of isothermal and thermomechanical fatigue on type 316L(N) austenitic stainless steel" Materials Science and Engineering: A, 2010
  2. Changan, Chai et al. "Recent Developments in the Thermomechanical Fatigue Life Prediction of Superalloys", JOM, April 1999
  3. "Thermo Mechanical Technical Background"
  4. Heckel, T. K. et al. "Thermomechanical Fatigue of the TiAl Intermetallic Alloy TNB-V2" Experimental Mechanics, 2009
  5. Minichmayr, R.; Riedler, M.; Winter, G.; Leitner, H.; Eichlseder, W. (2008). "Thermo-mechanical fatigue life assessment of aluminium components using the damage rate model of Sehitoglu". International Journal of Fatigue. 30 (2): 298–304. doi:10.1016/j.ijfatigue.2007.01.054.
  6. Zhuang, W. Z. et al. "Thermo-mechanical fatigue life prediction: A critical review" Defence Science and Technology Organisation Publications, 1998
  7. Zhang, Junqian and Fang Wang "Modeling of Damage Evolution and Failure in Fiber-Reinforced Ductile Composites Under Thermomechanical Fatigue Loading" International Journal of Damage Mechanics, 2010