Thermomechanical Fatigue
Thermomechanical fatigue (TMF) — the simultaneous cycling of both mechanical strain and temperature, in-phase and out-of-phase cycling, the role of thermal gradients, the strain-temperature phasing and the life implications compared to isothermal fatigue.
What is thermomechanical fatigue?
Thermomechanical fatigue (TMF) is fatigue under simultaneous cyclic mechanical loading and cyclic temperature variation. In contrast to isothermal fatigue (where the temperature is constant and only the mechanical strain cycles), in TMF both the mechanical strain and the temperature cycle simultaneously. TMF is the realistic loading condition for many high-temperature components — turbine blades, combustion chambers, brake discs, exhaust manifolds — where the mechanical load and the temperature change together during each operating cycle. The simultaneous cycling introduces effects that are not captured by isothermal fatigue testing: the phasing of the strain and temperature cycles matters, the thermal gradients introduce additional stresses, and the material properties change continuously during the cycle.
In-phase and out-of-phase cycling
The phasing of the mechanical strain and the temperature cycle defines two fundamental TMF modes. In in-phase (IP) TMF, the maximum strain occurs at the maximum temperature and the minimum strain at the minimum temperature. In out-of-phase (OP) TMF, the maximum strain occurs at the minimum temperature and the minimum strain at the maximum temperature. The two modes produce different damage mechanisms and different lives. In IP TMF, the tensile strain at high temperature promotes creep damage (tensile creep at the peak temperature). In OP TMF, the compressive strain at high temperature may promote creep damage in compression, and the tensile strain at low temperature promotes fatigue damage. The TMF life depends on the phasing, the material and the temperature range. IP and OP TMF lives may differ by factors of several.
The total strain range
In TMF, the total strain range is the sum of the mechanical strain range and the thermal strain range. The thermal strain is the product of the CTE and the temperature range. For components with constrained thermal expansion, the thermal strain contributes to the total strain and hence to the fatigue damage. The total strain range is the parameter that governs the TMF life, analogous to the strain range in isothermal fatigue. However, the TMF life is not simply the isothermal fatigue life at the mean temperature — the simultaneous temperature cycling and the phasing effects make the TMF life different (usually shorter) than the isothermal life at any single temperature in the range. The TMF life must be assessed from TMF tests or from a validated TMF life model.
Total strain in TMF: eps_total = eps_mechanical + eps_thermal eps_thermal = alpha(T) * (T - T_ref) Delta_eps_total = Delta_eps_mechanical + Delta_eps_thermal where: eps_total = total strain [dimensionless] eps_mechanical = mechanical (applied) strain eps_thermal = thermal strain from CTE * delta T Delta_eps_total = total strain range per cycle alpha(T) = coefficient of thermal expansion [1/K] T = temperature [K or °C] T_ref = reference temperature For constrained thermal cycling (no external mechanical load), the mechanical strain is zero and the total strain equals the thermal strain (which is converted to stress by the constraint).
Thermal gradients and through-thickness stress
In a component with through-thickness thermal gradients (e.g. a blade wall with hot gas on one side and cooler cooling air on the other), the thermal cycling produces through-thickness stresses. During a temperature transient, the surface temperature changes faster than the interior, producing thermal stress. The surface may be in compression during heating (the surface expands first, constrained by the cooler interior) and in tension during cooling. These thermal stresses add to the mechanical stresses and contribute to the TMF damage. The through-thickness stress distribution depends on the thermal gradient, the transient rate, the material properties and the constraint. A coupled thermal-structural analysis is needed to compute the TMF strain and stress history at the critical locations.
Life implications
TMF life is generally shorter than isothermal fatigue life at the mean temperature, for the same mechanical strain range. The reasons are several: the simultaneous temperature cycling introduces additional thermal strain, the phasing of strain and temperature affects the creep and fatigue damage, the thermal gradients introduce additional stress, and the material properties change continuously during the cycle. TMF life prediction requires either TMF test data at representative conditions or a validated TMF life model. Using isothermal fatigue data with a simple temperature correction is not adequate for components with significant TMF. The TMF assessment should identify the critical location, the strain-temperature history at that location, and the applicable TMF life model or data.
Comparison with isothermal creep-fatigue
TMF is related to but distinct from isothermal creep-fatigue. In isothermal creep-fatigue, the temperature is constant and the hold period produces creep damage. In TMF, the temperature cycles and the creep damage is produced during the high-temperature portion of the cycle. The two approaches give different results for the same component — the TMF assessment captures the effect of temperature cycling that the isothermal assessment misses. For components with significant temperature cycling (e.g. turbine blades with thermal transients), TMF is the more realistic assessment. For components with predominantly steady temperature and cyclic mechanical load (e.g. a pressure vessel with pressure cycles), isothermal creep-fatigue may be adequate. The choice should be based on the actual service conditions.
TMF analysis workflow and phasing fidelity
A reliable TMF assessment starts with the transient temperature field, because spatial gradients and thermal lag determine the local mechanical strain history. The thermal solution should be verified first, then transferred to the structural model with temperature-dependent elastic, plastic and creep properties as required. At each candidate location, extract temperature, total strain, mechanical strain and stress as synchronised time histories. Plotting the local strain-temperature loop is a powerful check: it immediately shows the actual phase relationship and whether the assumed in-phase or out-of-phase classification is too simplistic. Real components often exhibit phase lags that vary through the section or across the transient, so the local history should take precedence over a nominal system-level label.
Cycle stabilisation and model scope
The first thermal cycle is not always representative of long-term TMF behaviour. Plasticity, creep relaxation and residual stress can alter the response over successive cycles. Where these effects are significant, analyse enough repeated cycles to determine whether the local hysteresis loop stabilises, ratchets or progressively changes. The required model scope depends on the question: an elastic thermal-stress screening model may be adequate to identify candidate hot spots, but life prediction near yield or with long high-temperature dwells requires an appropriate inelastic material description. The selected constitutive model should be supported by data over the temperature and strain-rate range traversed by the cycle.
Thermomechanical fatigue is not the same as isothermal fatigue at the mean or peak temperature. The simultaneous cycling of strain and temperature, the phasing and the thermal gradients introduce effects that isothermal testing cannot capture. Use TMF test data or a validated TMF model for components with significant simultaneous strain and temperature cycling.