Spring Fatigue: How to Design for Long Life Under Cyclic Load

Every spring that works in repeated cycles — opening and closing a valve thousands of times per minute, absorbing impacts in a suspension, or returning an actuator on an automation line — is subject to fatigue. Fatigue is the progressive degradation of the material under loads that vary over time, and it is the dominant cause of failure in dynamic springs. What surprises many designers is that fatigue rupture happens at stresses well below the static strength of the steel: a spring that would comfortably carry a load applied once can crack after a few million repetitions of that same load.

Designing against fatigue is therefore different from designing against peak load. It is not enough to keep the peak stress below the yield strength; you must control the stress amplitude, the mean stress, and the number of cycles expected over the spring's life. This guide walks through the essential concepts — crack initiation, cyclic stresses, the S-N curve, the Goodman, Gerber and Sines criteria, and the treatments that most extend life — and ends with a fully worked valve-spring example.

What fatigue is and why the crack starts on the inner coil

Fatigue develops in three stages. First, initiation: under repeated loading, the cyclic slip of crystal planes forms micro-cracks at the surface, almost always starting from a defect — a drawing scratch, a non-metallic inclusion, a corrosion pit, or a handling mark. Then propagation: with each cycle the crack advances a fraction of a millimetre, leaving the characteristic fatigue striations. Finally the sudden, brittle-looking final fracture, when the remaining section can no longer carry the load.

In a helical spring, the critical point is always the inner face of the coil. The wire works essentially in torsion, but the curvature of the helix concentrates the stress on the inside of the winding. This effect is captured by the Wahl factor (Kw), which corrects the nominal shear stress and grows as the spring index (C = D/d) drops. Low indices, below 5, produce high inner-surface stress peaks and drastically cut fatigue life. That is why most fatigue cracks in springs are born on that inner surface — and why protecting it, with a good finish and compressive residual stresses, is the most direct route to a durable spring.

Cyclic loading: mean stress, alternating stress and stress ratio

A dynamic spring rarely swings between zero load and maximum load. Typically it is pre-compressed at assembly and works between a minimum load (F_min) and a maximum load (F_max), producing a shear stress that varies between τ_min and τ_max. To analyse fatigue, we split this oscillation into two parts: the component that stays constant and the component that varies.

The mean stress (τ_m) is the central value about which the stress oscillates; the alternating stress or amplitude (τ_a) is half of the total swing between peak and valley. The stress ratio R relates the valley to the peak and describes the type of cycle: R = 0 is a pulsating cycle starting from zero, and R near 1 is a small oscillation about a high mean. Fatigue depends strongly on both components: raising the amplitude is always more damaging, but a high mean stress also shortens life and cannot be ignored.

The S-N (Wöhler) curve and the endurance limit

A material's fatigue strength is summarised by the S-N curve, or Wöhler curve, which relates the applied stress amplitude to the number of cycles to failure, usually on a logarithmic scale. The larger the amplitude, the fewer cycles the material survives. The curve drops steeply in the finite-life region — between a few thousand and about one million cycles — showing that small reductions in amplitude buy many cycles of life.

Steels have a valuable feature: below a certain amplitude, the curve goes flat. That plateau is the endurance limit (or fatigue limit), reached typically between 10⁶ and 10⁷ cycles. If the working alternating stress stays below this limit, the spring has, in practice, infinite life — it can cycle indefinitely without cracking. This boundary separates two design regimes: finite life, when we accept a defined number of cycles (for example, 200,000 openings of a gate), and infinite life, required in applications such as automotive valve springs that must survive billions of cycles.

Design criteria: modified Goodman, Gerber and Sines

Once τ_a and τ_m are known, we need a criterion that combines the two into a single safety check, because the material fails through an interaction of amplitude and mean. The modified Goodman criterion is the most used in spring engineering because it is simple and conservative. It draws a straight line between the shear endurance limit (S_se, on the alternating-stress axis) and the ultimate shear strength (S_su, on the mean-stress axis); any combination of τ_a and τ_m that falls inside that line is safe.

The Goodman safety condition appears in the formula below, where n is the desired safety factor. There are alternatives: the Gerber criterion uses a parabola instead of a straight line and tends to predict experimental data better for tensile mean stresses, being less conservative. The Sines criterion is widely used in multiaxial fatigue and treats mean stress in a specific way. In spring practice, modified Goodman is the safe starting point; Gerber is used when you want to make fuller use of the material with test data to back it up.

The biggest fatigue-life improvers

Fatigue life is governed by the surface, so almost every gain comes from improving the surface condition of the wire or introducing compressive residual stresses that make it harder for cracks to open. The factors below are in rough order of impact:

• Shot peening: blasts the surface with steel shot, leaving a layer of compressive residual stress that must be overcome before any crack can open. It is the single largest fatigue gain, often raising life by 20% to well over 100%, and is standard on valve and suspension springs.
• Good surface finish: scratches, tool marks and roughness are crack-initiation sites. Smooth, polished wire has a noticeably higher endurance limit than wire with a rough surface.
• Avoiding decarburization: the loss of carbon in the outer layer during heat treatment weakens exactly the most-stressed region. Quality spring wire tightly controls decarburization.
• Avoiding inclusions: internal non-metallic inclusions act as micro-notches. Clean-melt steels (for example, vacuum-refined) perform far better in fatigue.
• Presetting (scragging): compressing the spring beyond yield once, before service, creates favourable residual stresses and stabilises the free length, increasing load capacity and resistance to set.
• Correct index: keeping C between 6 and 10 limits the Wahl factor and, with it, the stress peak on the inner coil where fatigue starts.

Worked example: a valve-type spring

Consider this guide's preset spring: chrome-silicon wire with d = 3 mm, a 24 mm outer diameter and therefore a mean diameter D = 21 mm and index C = 7. It cycles between a minimum load F_min = 120 N (assembly preload) and a maximum load F_max = 300 N on each valve opening. Let us estimate the stresses and check for fatigue.

With C = 7, the Wahl factor is approximately Kw = 1.21. The corrected shear stress is computed with the formula below, applied at each load extreme. Substituting the values, the geometric factor 8·D/(π·d³) works out to about 1.98 MPa per newton, so τ ≈ 1.21 · 1.98 · F ≈ 2.40 · F (with F in N).

For F_min = 120 N we get τ_min ≈ 288 MPa; for F_max = 300 N, τ_max ≈ 719 MPa. From these two values we compute the fatigue components: the alternating stress τ_a = (719 − 288)/2 ≈ 216 MPa and the mean stress τ_m = (719 + 288)/2 ≈ 503 MPa. The stress ratio is R = 288/719 ≈ 0.40.

Now the modified Goodman check. For peened chrome-silicon, we take a shear endurance limit S_se ≈ 450 MPa and an ultimate shear strength S_su ≈ 1300 MPa (about 0.67 of the tensile strength for this wire size). Substituting: τ_a/S_se + τ_m/S_su = 216/450 + 503/1300 ≈ 0.48 + 0.39 ≈ 0.87. The reciprocal is the safety factor: n ≈ 1/0.87 ≈ 1.15.

The engineering reading is direct: the 216 MPa amplitude sits comfortably below the 450 MPa endurance limit, but the high mean stress of 503 MPa consumes much of the margin. A safety factor of 1.15 points to a spring that should reach essentially infinite life if peened and well finished, but with little slack — reducing the peak load, slightly increasing the wire or coil diameter, or ensuring shot peening are the levers to widen the margin.

Materials for fatigue

The material choice sets the ceiling for fatigue performance. For demanding cyclic applications, the champions are chrome-silicon wire (CS) and oil-tempered valve-spring wire. Both combine high tensile strength with a clean, uniform microstructure, tight control of decarburization, and a low-roughness surface — exactly the attributes that raise the endurance limit.

Chrome-silicon stands out further for holding its properties at higher temperatures and for resisting set well, which makes it the standard material for engine valve springs, suspension springs and clutches. Oil-tempered valve-spring-quality wire is an economical option for high volumes with excellent fatigue life. For general use with moderate cycling, music wire offers a great finish and good performance; stainless steels prioritise corrosion resistance, at a slightly lower endurance limit. The rule of thumb: the more severe the cycle and the higher the required cycle count, the more it pays to invest in valve-spring-quality wire and shot peening.

How molas.app.br estimates stresses and safety

When you build your spring in the molas.app.br designer, you can set two operating points — the minimum and maximum load (or height) of the cycle. For each point, the tool computes the Wahl-corrected shear stress and, from those, derives the mean and alternating stresses; it then compares these components against the endurance limit and strength of the chosen material, showing the safety margin. This way you can see instantly whether the design trends toward infinite or finite life, and adjust wire size, diameter or load before manufacturing.