Spring fatigue: stress ratio, cycles and material choice

What fatigue failure looks like

A spring that fails in fatigue usually starts at a surface defect or a point of high stress on the inside of a coil. The crack grows across the wire section over many cycles and the spring breaks suddenly, often with little visible deformation. The fracture face may show a smooth origin and a rougher final zone, but the appearance alone does not prove the cause.

The important point for a designer is that fatigue is a cycle-by-cycle process. A spring that holds its load in a single static test can still fail after a few thousand cycles at the same stress. The static check and the fatigue check answer different questions.

Fatigue also interacts with corrosion, fretting and temperature. A spring that would survive in a dry test rig may fail sooner in a damp enclosure or against a moving seat. The environment belongs in the specification, not in a footnote.

Stress ratio and mean stress

The stress ratio, usually written R, is the minimum stress divided by the maximum stress in a cycle. A spring that is compressed from zero stress to a working stress has a ratio of zero. A spring that cycles between two positive loads has a ratio between zero and one. A fully reversed cycle has a ratio of minus one.

Most compression springs work with a positive minimum stress, because the spring is installed under preload. The cycle then has a mean stress and an alternating stress. The mean stress matters because a high mean stress reduces the stress range that the material can tolerate. A Goodman or Gerber diagram is the usual way to combine them.

The practical consequence is that two springs with the same maximum stress can have very different lives. The one with the lower minimum stress has the larger range and the shorter life. When a drawing gives only a maximum load, it leaves the most important fatigue variable unstated.

Cycles and the S-N curve

The S-N curve plots stress range against the number of cycles to failure. For steels, the curve tends to flatten at a high cycle count, which is often treated as an endurance limit. Non-ferrous materials such as phosphor bronze do not show the same clear limit, so a finite life target has to be used.

A design target should state the number of cycles, the stress ratio and the acceptable failure probability. A target of one million cycles with a safety factor on stress is a different requirement from a target of ten million cycles at the same stress. The drawing should say which one applies.

For a variable load history, a simple damage rule such as Miner's rule can combine blocks of cycles at different stress levels. The rule is an approximation, but it is better than designing for the worst block alone. It also forces the designer to write down the load history rather than guess it.

Material choice

Music wire offers high strength and good fatigue resistance at a low cost, and it is the default for small springs in a dry environment. Oil tempered wire extends the available diameter range and is common for larger springs. Chrome silicon and chrome vanadium are used for high duty springs where toughness and temperature resistance matter.

Stainless steel 302 is the general purpose corrosion resistant choice. It has a lower modulus and a different fatigue response from music wire, and it is not immune to corrosion in chloride environments. Stainless 316 improves the corrosion resistance at a further cost in strength. Precipitation hardening grades such as 17-7PH are used where higher strength and corrosion resistance are both needed.

Phosphor bronze and beryllium copper appear where conductivity, non-magnetic behaviour or a marine environment matters. They have different fatigue characteristics and generally lower allowable stresses than steel. Do not carry a steel stress limit across to a copper alloy without checking the material data.

Shot peening, stress relief and set

Shot peening introduces a compressive residual stress at the surface. That compressive layer opposes the tensile stress that drives a fatigue crack, so it can raise the fatigue life for a given stress range. The benefit depends on the intensity, the coverage and the condition of the surface before peening.

Stress relief after forming reduces the residual stress from coiling and bending. It can improve dimensional stability and fatigue life, but the temperature and time have to suit the material. An over-high temperature can soften a spring temper wire and reduce the load.

Set, or presetting, compresses the spring beyond its working length to remove some initial deformation. It stabilises the free length and can introduce a favourable residual stress pattern. It is not a substitute for a fatigue check, and it changes the load at first compression, so the load test has to follow the set.

Setting a cycle target

The cycle target should come from the application, not from a generic table. A valve spring, a contact spring and a latch spring see very different histories. Write down the number of cycles per operation, the operations per day and the life of the equipment, then add a margin for surge, misalignment and test variation.

The table below is an illustrative starting point for the conversation. It is not a material limit and it is not a substitute for a fatigue calculation.

Design checks before release

A fatigue check needs more than a rate calculation. It needs the stress at the installed length, the stress at the working length, the stress ratio, the cycle target and the material data for the actual condition. It also needs a view of the surface and the environment.

• Calculate the stress at both ends of the cycle, not only the maximum
• State the stress ratio and the cycle target on the drawing
• Check the spring index and apply the curvature correction
• Confirm the wire grade, temper and surface condition
• Decide whether shot peening or stress relief is required
• Check the seat and the guide for fretting and wear
• Agree the load test and the fatigue test, if one is required