Design Stresses and Fatigue

§1Why springs fail below the elastic limit

A spring can break at a stress far below the level that would bend it once. Understanding why is the whole basis for choosing a safe working stress.

The puzzle occupied engineers for a century: why should a spring stressed well within its elastic limit eventually fail? Many wrong theories came and went. The most persistent is the crystallisation theory — the folk belief that a broken spring "crystallised", pointed to whenever a fracture shows coarse grains. It is simply untrue. Steel is crystalline from the moment it solidifies; the coarse grains at a fatigue fracture are no different from those anywhere else in the section. The small, smooth grains near where the crack began are burnished by rubbing together, sometimes thousands of times, before the remaining section lets go.

The correct account is Wood's: fatigue is the conversion of cyclic deformation first into fine slip, then into coarse slip, which grows into a minute crack that propagates until the part breaks. Fine slip occurs at low stress, coarse slip at higher stress, and in cold-worked material — the material of cold-coiled springs — coarse-slip groups can pile up so that several coils fail almost together. No formula will ever say exactly when a given spring will break, but fatigue curves derived from thousands of tests give sound recommended design stresses. A handful of definitions anchor the rest of this sheet: fatigue life is the number of cycles to failure at a given stress; fatigue strength (or endurance strength) is the stress causing failure after a stated number of cycles; and the elastic limit — the stress a spring can take without permanent set — is used in tension for bending springs and in torsion for compression and extension springs.

§2The three service classes

Every recommended design stress hangs on one question: how many times will the spring deflect? Three classes divide the answer.

For each material the handbook gives three design-stress curves for compression and extension springs and three for torsion springs. Which curve applies depends on the service class — the number of deflections the spring must survive. Light service, 1000 to 10 000 deflections, covers static and seldom-used springs — bomb fuses, projectiles, shock absorbers, safety devices — and may be designed almost up to the minimum elastic limit. Average service, 100 000 to 1 000 000 deflections, covers most springs in machines, brakes, motors and switches at normal frequencies below 300 cycles per minute. Severe service, over 1 000 000 deflections, covers engine valve springs, pneumatic hammers, presses and hydraulic controls; the stress is taken from the lowest curve and lowered a further 10 % to reach 10 million cycles, generally regarded as infinite life.

The curves assume springs deflecting from 25 to 75 % of their total deflection, at room temperature, at normal index, without buckling, and properly stress-relieved. They may be raised 20–30 % for springs that are baked, set-relieved and shotpeened. The compression curves serve extension springs if the values are reduced 10–15 % and the hook bending stresses are checked separately against the torsion curves.

§3Reading the design-stress curves

Each curve set is read the same way: run up from the wire diameter and read off the safe stress for each class.

The curves cover the popular materials across their commercial wire diameters — they are not for square, rectangular or shaped wire, nor for spiral, clock, flat, volute or hot-rolled springs, which need their own fatigue testing. To use them, run a vertical line from the wire diameter and read where it crosses each of the three curves. For music wire at 2.16 mm, for instance, the line meets the lowest curve at 710 MPa (severe service), the middle at 860 MPa (average) and the top at 950 MPa (light). All values are given in both inch-pound and metric SI units, rounded to sensible figures — the handbook is explicit that 100 000 psi is really 689.5 MPa but is written 690, and that temperatures are rounded too, 480 °F standing for 250 °C.

The design tables carry oil-tempered MB steel as the baseline; for other materials the deflection of one coil is scaled by a fixed factor that captures the difference in torsional modulus. Those factors are a compact way to compare materials at a glance.

A phosphor-bronze spring, then, deflects nearly twice as far as an identical oil-tempered steel one under the same stress, because its torsional modulus is lower — a direct consequence of the moduli tabulated for each alloy elsewhere in this section.

§4The endurance limit

For a spring that must last indefinitely, the governing number is not a single stress but the range between the first load and the last.

The endurance limit is the highest stress, or range of stress, that can be repeated indefinitely without failure. Ten million deflections is taken as infinite life and used to establish it, though springs surviving three million cycles usually reach ten million, and some testers now stop there. The key insight is that the endurance limit is set by the range of stress — the gap between the initial and final stress in each cycle — not by the peak alone: the narrower the range, the longer the life. An oil-tempered MB compression spring worked between 117 and 493 MPa, for example, should have unlimited life. Stress-relieved hard-drawn steels, music wire and 300-series stainless gain a further 2 to 3 points of Rockwell C hardness, and a matching rise in minimum elastic limit, which adds assurance that the curves will be met.

§5Curvature correction

The calculated stress in a coiled spring is not the real stress. Curvature crowds the shear onto the inside of the wire, and the calculation must be corrected before it is compared with any curve.

Coiling a wire raises the stress on the inside of the section above the value the simple formula gives, because the shear is unevenly distributed across a curved wire. The correction is a factor K, read from the proper curve against the spring index — the mean diameter divided by the wire diameter — and multiplied into the calculated stress. The correction is largest at small index and falls toward unity as the index grows: at an index of 7.3 the factor is about 1.21, so the true stress is 21 % above the calculated value. The corrected stress is what you compare with the design-stress curves; it must not be fed back into the deflection formulas, where it would cause errors.

§6Fatigue testing in practice

Where the curves do not cover a case, springs are tested — and the testing has its own discipline, starting with speed.

Testing in a fatigue machine is the surest way to know how long a spring will last, but it must be done carefully. Test at least five similar springs together, record every characteristic, and hold the speed between 200 and 350 cycles per minute — 300 is best. Fast cycling generates heat, over-deflects the first coils and causes early breakage; running a spring at an 1800 rpm motor speed can drive it to eleven times its natural frequency, effectively 19 800 cycles per minute, and premature fatigue. Determine each batch's life by discarding the highest and lowest results and averaging the two closest. True fatigue cracks start on the inside of a coil, where the stress is highest; breaks elsewhere point to tool marks, inclusions or poor wire.

The last row carries a warning: rotary-straightened wire lasted a fraction as long, because cold drawing aligns tensile strength along the wire while rotary straightening works it transversely, lowering the elastic limit. Straightened wire should never be used where long fatigue life is required.

§7Causes of spring failure

The Spring Manufacturers Institute ranks the causes of failure by how often they occur. The order is itself a design checklist.

Most failures come from high stress caused by large deflections and heavy loads — which is why high stress belongs only to static springs, and low stress lengthens life. After that come a cluster of avoidable process faults, then a set of occasional causes tied to environment and detail design.

Two entries deserve emphasis. Hydrogen embrittlement from electroplating or acid cleaning without a prompt baking treatment is a frequent cause of failure in spring steel — and nonferrous springs are immune to it. Shock loading raises stresses far above what the formulas predict, and high-carbon steels tolerate it less well than alloy steels. Low temperature turns the same point around: carbon steels lose the ability to take shock as they cool, so below freezing the answer is stainless, nickel or nonferrous.

§8Quick reference