Technology / Technical guide
Composite Creep, Stress Relaxation & Time-Dependent Response
A time-dependent material can continue deforming under an unchanged stress, or reduce its stress while its strain is held fixed. These are different conditions. A modulus measured at one time scale cannot automatically describe every sustained or changing load history.
Fix the controlled quantity before interpreting time dependence.
Creep compliance and relaxation modulus represent different relationships. A spring–dashpot model makes the distinction visible, but its simple parameters and ideal long-time response do not identify a real blade material or lifetime.
01 / Creep
An unchanged stress can accompany changing strain.
In a linear one-dimensional representation under a stress step held at σ0, creep compliance J(t) gives ε(t) = J(t)σ0.
In a linear one-dimensional representation under a stress step held at σ0, creep compliance J(t) gives ε(t) = J(t)σ0. J has inverse-pressure units. Increasing compliance over time means increasing strain under that defined constant-stress condition.
Constant external force only corresponds to constant stress when the relevant area and stress distribution remain suitably fixed. A changing geometry or multiaxial load state adds distinctions. The term creep should therefore identify the controlled quantity and the material representation rather than simply mean any slow motion.
02 / Relaxation
An unchanged strain can accompany changing stress.
For a strain step held at ε0 in a compatible linear model, relaxation modulus Erel(t) gives σ(t) = Erel(t)ε0.
For a strain step held at ε0 in a compatible linear model, relaxation modulus Erel(t) gives σ(t) = Erel(t)ε0. This has pressure units. COMSOL’s viscoelasticity theory separately defines relaxation and creep through the respective histories.
A decreasing stress in that representation does not mean the material has disappeared or the imposed strain became zero. The boundary constraint remains fixed while the internal response changes. A real assembly can combine changing forces and displacements, rather than exactly reproducing either elementary condition.
03 / Simple model
A Maxwell element has a defined limited response.
An ideal Maxwell element places a linear spring and viscous dashpot in series.
An ideal Maxwell element places a linear spring and viscous dashpot in series. Its one-dimensional relation is εdot = σdot/E + σ/η, with spring modulus E and dashpot viscosity η. The elements share stress while their strains add.
At constant strain after the ideal step, σ(t) = σ0 exp(−t/τ), with τ = η/E. At constant stress, the model has an immediate spring strain plus a strain increasing as σ0t/η. These are consequences of the chosen element, not a universal law for every composite.
04 / Time scale
A relaxation time does not name a service life.
For a hypothetical τ = 10 s, the ideal Maxwell relaxation at t = τ is about 36.8% of its initial stress.
For a hypothetical τ = 10 s, the ideal Maxwell relaxation at t = τ is about 36.8% of its initial stress. This says nothing about a wind blade’s time constant, allowable stress or remaining life. The model’s initial loading convention must also stay explicit.
More general models can retain an elastic long-time branch or a distribution of relaxation times. Their long-time behaviour differs from the single Maxwell element. One data point or a convenient exponential curve cannot uniquely identify all of those physical or fitted model components.
05 / Other mechanisms
Time dependence differs from cycle accumulation.
Fatigue describes effects associated with a load-cycle history; creep and relaxation concern time-dependent response under their conditions.
Fatigue describes effects associated with a load-cycle history; creep and relaxation concern time-dependent response under their conditions. They can interact, but counting cycles does not automatically describe sustained-load deformation. The fatigue guide addresses that separate representation.
Viscoelastic strain can include recoverable delayed response and dissipative behaviour depending on the model. It should not be renamed permanent damage merely because it changes with time. Damage, plasticity and thermal changes require their own assumptions rather than being hidden inside one unexplained time coefficient.
06 / Composite scope
Constituents and directions can have different histories.
A composite combines reinforcement, matrix and interfaces, so time-dependent response can depend on direction, temperature and constituent behaviour.
A composite combines reinforcement, matrix and interfaces, so time-dependent response can depend on direction, temperature and constituent behaviour. A complete representation must preserve that scope. The constituent guide distinguishes the underlying material roles.
No MARSTON resin model, creep compliance, relaxation spectrum or time-dependent strength is established here. GFRP confirmation does not provide these parameters. This article offers no accelerated-life extrapolation, operating-duration limit or procedure for loading or altering a blade.
Related technical guides: Sandwich Composite Mechanics: Face Sheets, Core & Interfaces · Laminate Orientation, Symmetry & Bend–Twist Coupling · Bolted Joint Stiffness: Load Sharing & Contact Separation.
General background: COMSOL: creep, relaxation and spring–dashpot model conditions · MIT OCW: elementary Maxwell model and relaxation conditions. 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 |
|---|---|---|
| Creep compliance | J(t) in Pa⁻¹ | Defined constant-stress representation. |
| Relaxation modulus | Erel(t) in Pa | Defined constant-strain representation. |
| Dashpot viscosity | η in Pa s | Parameter of the stated ideal model. |
| Maxwell time | τ = η/E in s | Not a service-life quantity. |
| Fatigue | Load-cycle history | Different from the elementary sustained-load conditions. |
Engineering questions.
Are creep and relaxation the same imposed condition?
No. One fixes stress; the other fixes strain in the stated ideal cases.
Is constant force always constant local stress?
No. Geometry and the stress distribution can change.
Does τ describe a blade’s lifetime?
No. It is a time scale in the chosen constitutive model.
Is every composite described by one Maxwell element?
No. Other models and material mechanisms can be required.
Does all time-dependent deformation prove damage?
No. The response mechanism and recoverability depend on the model and material.
Are the ten-second example values MARSTON properties?
No. They are assumed values illustrating ideal relaxation.
Technical enquiry
Discuss the technical question.
A time-dependent material can continue deforming under an unchanged stress, or reduce its stress while its strain is held fixed. Share the model and applicable operating or design information for an engineering discussion.