Time and repetition: creep, relaxation and fatigue

Creep is deformation that continues to grow while the stress stays constant. Hang a weight on a wire and leave it: the extension you measure a year later is larger than the one you measured on the day, even though the load never changed.

Creep is strongly temperature-dependent. For steel it is negligible at ordinary temperatures and becomes a governing consideration in fire and in high-temperature plant. For concrete, timber and most polymers it matters at everyday temperatures, and long-term deflections in concrete can be two or three times the immediate ones.

The classic creep curve has three stages:

1. 1.Primary creep — the strain rate starts high and decreases as the material hardens.
2. 2.Secondary creep — a long, roughly straight portion at a steady, minimum strain rate. This is the stage design calculations are usually based on, because it dominates the service life.
3. 3.Tertiary creep — the rate accelerates as internal damage accumulates, ending in rupture.

Relaxation is the same underlying process seen from the other side. Instead of holding the stress and watching strain grow, hold the strain and watch the stress fall.

The practical case is prestressing. A tendon stretched to a set extension and locked off will lose force over time — the steel relaxes — and the concrete around it creeps and shrinks as well, shortening the member and slackening the tendon further. Prestress losses of this kind are not a defect; they are predicted and allowed for from the start, and a design that ignored them would end up with far less prestress than intended.

The distinction is worth keeping crisp:

• Creep: stress constant, strain increases.
• Relaxation: strain constant, stress decreases.

Fatigue is failure under repeated loading, and it is the one that catches people out, because it happens at stresses well below yield and gives very little warning.

The mechanism has three phases:

1. 1.Initiation. A microscopic crack forms, almost always at a point of stress concentration — a weld toe, a bolt hole, a sharp re-entrant corner, a surface scratch.
2. 2.Propagation. Each load cycle advances the crack a tiny amount. The crack faces rub, and the fracture surface develops the characteristic smooth, banded appearance.
3. 3.Final fracture. The remaining uncracked area becomes too small to carry the peak load, and the member fails suddenly.

What drives fatigue is the stress range Δσ = σ_max − σ_min, not the peak stress. A member cycling between 200 and 190 N/mm² is under a far higher peak stress than one cycling between 0 and 100, but the second is in much greater danger.

Fatigue data is presented on an S–N curve: stress range against the number of cycles to failure, both on log scales, so the relationship plots as a straight line. Some steels show an endurance limit — a stress range below which the life is effectively unlimited — but the presence of welds, corrosion or a corrosive environment can remove it.