Thermo-mechanical fatigue

Key takeaways

Thermo-mechanical fatigue belongs to physics; place it in that map before memorising details.
Learn the definition first, then one example that makes the definition concrete.
Connect Thermo-mechanical fatigue to a quantity you can measure, compute or draw — that is where exam questions come from.
Reproduce the core statement of Thermo-mechanical fatigue from memory before moving on to harder problems.

Reference excerpt

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.

Failure mechanisms There are three mechanisms acting in thermo-mechanical fatigue

Creep is the flow of material at high temperatures Fatigue is crack growth and propagation due to repeated loading Oxidation is a change in the chemical composition of the material due to environmental factors. The oxidized material is more brittle and prone to crack creation. 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. 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.

1 N f = 1 N f f a t i g u e + 1 N f o x i d a t i o n + 1 N f c r e e p {\displaystyle {\frac {1}{N_{f}}}={\frac {1}{N_{f}^{fatigue}}}+{\frac {1}{N_{f}^{oxidation}}}+{\frac {1}{N_{f}^{creep}}}}

where N f {\displaystyle N_{f}} 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.

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

Δ ϵ m 2 = C ( 2 N f f a t i g u e ) d {\displaystyle {\frac {\Delta \epsilon _{m}}{2}}=C(2N_{f}^{fatigue})^{d}}

where C {\displaystyle C} and d {\displaystyle d} 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.

… excerpt ends here. Continue reading the full article.

Worked examples

Example 1 — a first encounter with Thermo-mechanical fatigue

Start with the simplest possible case. Write down what Thermo-mechanical fatigue claims or describes in one sentence, then invent the smallest concrete situation in which that sentence is true. In physics, the smallest case is usually a single object, a single equation or a single measurement. Check that every symbol or term in your sentence has a meaning in that case.

Example 2 — changing one variable

Take the situation from Example 1 and change exactly one quantity: double it, halve it, or set it to zero. Predict what should happen to Thermo-mechanical fatigue before you calculate. Comparing your prediction with the result is the fastest way to find out whether you understand the idea or only the words.

Example 3 — an exam-style question

Typical questions about Thermo-mechanical fatigue ask you to (a) state it precisely, (b) apply it to given data, and (c) explain a limitation. Practise writing all three answers in under five minutes; the third part is what separates a full-mark answer from an average one.

Applications of Thermo-mechanical fatigue

In research: Thermo-mechanical fatigue appears in physics research whenever the underlying quantities have to be modelled precisely. Papers usually cite it as a starting assumption and then explore where it breaks down.
In technology and industry: Engineering practice reuses Thermo-mechanical fatigue in design rules, simulations and safety margins. Knowing the idea lets you read a specification sheet and understand why the numbers look the way they do.
In the classroom: Thermo-mechanical fatigue is common in secondary-school and first-year university syllabi. It links to neighbouring topics Fracture mechanics, Mechanical engineering, so understanding it makes those chapters shorter.
In everyday life: Look for Thermo-mechanical fatigue outside the textbook — in sport, cooking, traffic, electronics or the sky above you. An example you found yourself is remembered far longer than one you were given.

How to study Thermo-mechanical fatigue in 20 minutes

Read the reference excerpt below once, without taking notes.
Close the page and write down what Thermo-mechanical fatigue means in your own words.
Compare your version with the excerpt and mark what you missed.
Work through the three examples above with pen and paper.
Explain Thermo-mechanical fatigue out loud to somebody else — or to Teacher Smith in the lgStudy chat.

Frequently asked questions

What is Thermo-mechanical fatigue in simple terms?

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.

Why does Thermo-mechanical fatigue matter?

Because it connects several physics ideas at once: it gives you a definition you can apply, a quantity you can calculate, and a way to check whether a result is plausible.

How should I study Thermo-mechanical fatigue?

Read the excerpt, restate it from memory, then work through the examples and applications listed on this page. The five-step study plan above takes about twenty minutes.

What does this page cover?

It gives you a compact reference excerpt plus original lgStudy explanations, examples, applications and study material on Thermo-mechanical fatigue.