Technology / Technical guide
Mean Stress Correction in Wind Turbine Fatigue
Two stress cycles can have the same amplitude but different tensile means. A mean-stress correction maps those different cycle conditions to a reference fatigue relation; it does not create missing material data.
Separate the centre of a cycle from its alternating part.
The correction belongs to a stated fatigue model and stress measure. Understanding that boundary matters more than choosing a familiar curve name.
01 / Cycle quantities
One cycle has more than one stress descriptor.
For a scalar stress cycle, σm = (σmax + σmin)/2 and σa = (σmax −σmin)/2.
For a scalar stress cycle, σm = (σmax + σmin)/2 and σa = (σmax −σmin)/2. The first locates the centre of the cycle; the second gives its half-range. They are not interchangeable, even when both are expressed in MPa.
A hypothetical cycle from 20 to 60 MPa has mean 40 MPa and amplitude 20 MPa. A second cycle from −20 to 20 MPa has the same amplitude and zero mean. Comparing only their ranges discards this difference. These are illustrative scalar cycles, not measured blade or flange stresses.
02 / Reference state
A fatigue curve already has conditions.
A stress-life relation associates a defined stress quantity and cycle condition with an observed or modelled number of cycles.
A stress-life relation associates a defined stress quantity and cycle condition with an observed or modelled number of cycles. The reference may be specified by mean stress or by a load ratio R = σmin/σmax. R is undefined when its denominator is zero.
Mean-stress correction is needed only in relation to that reference. If the fatigue data already capture the relevant dependence, applying another correction can count the same effect twice. The same local stress definition must be used for both the cycle and the reference curve.
03 / Haigh diagram
Read mean and amplitude as two coordinates.
A Haigh diagram places mean stress on one axis and amplitude on the other.
A Haigh diagram places mean stress on one axis and amplitude on the other. A chosen constant-life contour describes combinations assigned the same life under that model. Its shape is a material and model question, not a consequence of drawing the axes.
A vertical change increases amplitude at fixed mean; a horizontal change shifts mean at fixed amplitude. Moving along a contour differs from moving toward a static tensile limit. This geometric distinction prevents an ultimate-strength intercept from being mistaken for an endurance limit.
04 / Linear correction
What a Goodman-type relation assumes.
For one conventional tensile-mean, linear Goodman model, let Su be an assumed ultimate tensile strength and Sa0 a reference amplitude at zero mean.
For one conventional tensile-mean, linear Goodman model, let Su be an assumed ultimate tensile strength and Sa0 a reference amplitude at zero mean. The contour σa/Sa0 + σm/Su = 1 gives the equivalent zero-mean amplitude σa,eq = σa/(1 −σm/Su).
With the hypothetical values σa = 20 MPa, σm = 40 MPa and Su = 200 MPa, σa,eq is 25 MPa. The result follows from the assumed line. It is not a measured fatigue penalty, a MARSTON strength value or proof that the model is appropriate for a composite blade.
05 / Other relations
Changing a curve changes the mapping.
A linear tensile-mean relation and a curved interaction relation assign different equivalent amplitudes to the same point.
A linear tensile-mean relation and a curved interaction relation assign different equivalent amplitudes to the same point. Agreement at a zero-mean intercept does not make their predictions identical away from it. The chosen relation needs evidence for the material and loading regime.
Even within the linear example, a denominator approaching zero makes the mapping grow without bound. This signals the limit of that idealised construction near the static intercept; it does not justify extrapolating to an actual life. Compressive means and multiaxial stresses require their own treatment.
06 / Life boundary
A corrected amplitude is only one input.
An equivalent amplitude must still be related to an appropriate fatigue curve.
An equivalent amplitude must still be related to an appropriate fatigue curve. A variable history also needs a cycle interpretation and a damage model. Fatigue cycle counting identifies cycles; it does not independently establish their mean-stress sensitivity.
GFRP confirmation alone supplies neither a directional fatigue curve nor a validated correction relation. Fibre orientation, stress state and failure mechanism matter. The correction explained here therefore remains a conditional model, separate from product lifetime, reliability and composite failure criteria.
Related technical guides: Cyclic Bolt Loading and Flange Fatigue · Composite Blade Failure Criteria Explained · Adhesive Joint Peel and Shear Mechanics.
General background: COMSOL — Mean stress correction. These references explain industry concepts; they are separate from the applicable MARSTON product and project documents.
Key concepts and conditions.
Read each quantity with its reference, units and stated conditions. A general relation does not establish a model-specific value.
| Concept / quantity | Meaning / relation | Conditions / limits |
|---|---|---|
| Mean stress | (σmax + σmin)/2 | Cycle centre |
| Stress amplitude | (σmax −σmin)/2 | Half of the scalar stress range |
| Load ratio | R = σmin/σmax | Requires a nonzero maximum |
| Haigh contour | Mean–amplitude relation | Assigned life under specified conditions |
| Equivalent amplitude | Model-dependent mapping | Not life or a material property by itself |
Engineering questions.
Can equal stress amplitudes have different fatigue effects?
Yes. Mean stress can differ, and its effect depends on the material and loading conditions.
Does a Goodman correction predict life directly?
No. It maps a cycle to a reference amplitude within a chosen model; an appropriate fatigue relation is still needed.
Is ultimate tensile strength an endurance limit?
No. They describe different responses and cannot be substituted for each other.
Can I apply the tensile-mean equation to every compressive cycle?
No. The stated example does not validate that extension.
Does GFRP identify a universal mean-stress correction?
No. Composite fatigue depends on directional structure, stress state and failure mechanism.
Should mean stress be corrected twice?
No. First establish whether the reference data or model already include the relevant dependence.
Technical enquiry
Discuss the technical question.
Two stress cycles can have the same amplitude but different tensile means. Share the model and applicable operating or design information for an engineering discussion.