Hold-Time Effects in High-Temperature Fatigue

The hold time in cyclic loading

In high-temperature fatigue, the load cycle may include a hold time (dwell period) at the peak load, peak strain or peak temperature. The hold time represents the steady-state operation between transients — for example, a turbine blade that experiences a thermal transient during start-up, then operates at steady conditions for hours, then experiences another transient during shutdown. The hold time is the period of steady high-temperature operation. During the hold, the material creeps (if the load is held constant) or the stress relaxes (if the strain is held constant). The hold time has a profound effect on the fatigue life — longer hold times generally reduce the life, because more creep damage accumulates. The hold time effect is one of the defining features of creep-fatigue interaction.

Stress relaxation during the hold

In a strain-controlled fatigue test (fixed total strain range), the hold period is at a fixed strain. During the hold, the stress relaxes as creep strain replaces elastic strain. The stress relaxation is governed by the same creep constitutive law that governs constant-load creep. The relaxed stress at the end of the hold is lower than the peak stress at the start. The stress relaxation reduces the effective stress range for the subsequent cycle, but it also means that the stress at the start of the next reversal is lower, which changes the hysteresis loop shape. The accumulated creep strain during the hold contributes to the creep damage. The stress relaxation rate depends on the creep properties, the temperature and the hold time — faster creep (higher temperature, higher stress) gives faster relaxation.

Stress relaxation during hold (strain-controlled):

  eps_total = eps_elastic + eps_plastic + eps_creep = constant

  dsigma/dt = -E(T) * eps_dot_creep(sigma, T)

  dsigma/dt = -E(T) * A * sigma^n * exp(-Q/(R*T))

where:
  sigma = stress during hold [Pa] (decreasing)
  E(T) = elastic modulus at temperature [Pa]
  eps_dot_creep = creep strain rate [1/s]
  t_hold = hold time [s]

The creep strain accumulated during the hold:
  eps_creep_hold = integral from 0 to t_hold of eps_dot_creep dt

This creep strain contributes to the creep damage
for the cycle.

Creep damage accumulation during the hold

The creep strain accumulated during the hold period contributes to the creep damage for that cycle. The creep damage per cycle is the creep strain divided by the rupture strain, or (in the time-fraction approach) the hold time divided by the rupture life at the hold stress and temperature. The total creep damage over the component life is the creep damage per cycle multiplied by the number of cycles. Longer hold times give more creep damage per cycle and fewer cycles to failure. The creep damage is concentrated at the grain boundaries (where voids nucleate and grow), while the fatigue damage is associated with cyclic slip bands. The two damage mechanisms operate at different microstructural sites but interact through the stress and strain fields.

Tensile vs compressive holds

The position of the hold within the cycle matters. A tensile hold (hold at peak tensile strain) is generally more damaging than a compressive hold (hold at peak compressive strain). The reason is that creep voids grow under tensile stress — during a tensile hold, the material is under tensile stress and voids nucleate and grow. During a compressive hold, the stress is compressive and voids do not grow (they may even close). However, a compressive hold may cause other effects — the compressive creep strain may change the mean stress and the subsequent tensile stress range. Some materials show a significant difference between tensile and compressive holds; others show less. The test programme should include both hold types if the service cycle includes both. The balance between tensile and compressive hold damage depends on the material and the conditions.

Effect on crack initiation

The hold time affects the fatigue crack initiation life. The creep damage accumulated during the hold provides preferential sites for crack initiation — the creep voids and grain boundary damage act as crack nucleation sites. The crack initiation life is reduced compared to pure fatigue (no hold). The reduction is more pronounced at longer hold times and higher temperatures. In some materials, the crack initiation mode changes from transgranular (typical of pure fatigue) to intergranular (typical of creep) as the hold time increases. This transition reflects the shift from fatigue-dominated to creep-dominated damage. The crack initiation life is an important part of the total life for smooth components; for components with pre-existing defects, the crack growth life may dominate.

Effect on crack growth

The hold time also affects the fatigue crack growth rate. During the hold period at peak load, the crack may grow by creep crack growth (time-dependent crack extension under sustained load) in addition to the fatigue crack growth (cycle-dependent crack extension). The total crack growth per cycle is the sum of the fatigue crack growth (from the cyclic part) and the creep crack growth (from the hold). The creep crack growth rate depends on the creep properties, the temperature and the stress intensity factor at the crack tip. The combined crack growth rate is higher than the pure fatigue rate. For components with pre-existing defects or where crack growth dominates the life, the hold time effect on crack growth is critical.

• Creep-Fatigue Interaction Fundamentals
• Fatigue & Damage Tolerance

Waveform fidelity and test correlation

Hold-time behaviour is highly sensitive to the complete cycle waveform. Ramp rate, strain range, strain ratio, temperature, hold position and control mode can all affect the amount of relaxation and the resulting damage mechanism. A tensile hold in a strain-controlled laboratory test is not automatically equivalent to a nominally similar dwell in a load-controlled structure. When using published or programme-specific test data, compare the test waveform with the local FEA history rather than matching only the peak temperature and nominal hold duration. If the service cycle contains multiple ramps or dwells, identify which part of the local hysteresis loop is represented by the available data and where extrapolation is being made.

Structural consequences of relaxation during a dwell

In a constrained component, stress lost by relaxation at one location is not necessarily lost from the structure. It may be transferred to a neighbouring section, fastener, weld or material region. The local fatigue consequence must therefore be interpreted alongside the component-level redistribution. On unloading or reversal, the relaxed region can also experience a different stress range and mean stress than would be predicted by a purely elastic cycle. For complex geometries, examine the complete stress-strain loop over several cycles and confirm whether the response stabilises, ratchets or continues to redistribute. This is particularly important when a hold period is introduced into an existing fatigue assessment that was originally based on elastic ranges alone.

The hold time is the key parameter in creep-fatigue interaction. Longer hold times increase the creep damage per cycle and reduce the total life. Always assess the effect of hold time on both crack initiation and crack growth, and distinguish between tensile and compressive holds — tensile holds are generally more damaging.