How is the long-term creep of a spring determined?

Question

Spring Design

In spring design, there a a variety of parameters to consider. Some of the parameters are solely physical (wire diameter, coil diameter, length, etc.) and some are determined from the physical dimensions in combination with the material properties (spring constant, allowable stress, etc.).

Spring Set

One physical characteristic of a spring is whether or not it will experience set. This is a permanent deformation of the spring after it has been compressed. Whether or not set is an issue depends on the level of stress that the spring undergoes versus the material's tensile strength.

The common rule of thumb is that set is not a concern if the spring only experiences 40% or less of its tensile stress. If the spring experiences between 40% to 60% of its tensile stress, then the set can be compensated for during manufacturing. Above 60% of the tensile stress, set cannot be controlled.

The reason that spring set can be compensated for is that it occurs after only a few cycles and then the full amount of set has been reached.

Creep

Creep is a separate phenomenon from set. Set happens immediately, but creep happens with constant load over time. Since the metal is under stress, it should exhibit creep. Creep is also affected by temperature.

I want to know how a spring is affected by long-term constant load. I have not been able to find any information about creep in springs or how to calculate it during spring design.

How is the long-term creep of a spring determined?

Answer 1

Your question is insufficiently constrained.

The short answer is that you haven't provided enough information to give a complete answer: creep is complicated enough for a single material, however there are a variety of mechanisms depending on the material, temperature, normalised stress, time etc etc. In a "generic metal" the below diagram is a fair place to start for determining which mechanism you are working with, but those breakpoints will still change with the material. Obviously something like aluminium stops behaving like a solid metal well below 3000 deg C.

Some nickel superalloys experience less creep at higher temps, although these are exotic and extremely expensive.

If your question truely is "How is this determined for a specific spring of a specific material?" then the answer is disappointingly simple: put your spring in a constant temp oven for a range of very long times and a range of loads and measure what happens. It doesn't matter by which mechanism it is creeping, all you want to know is how it will respond in time to that load at that temp.

Edit: following your comment I feel I understand that what you are asking slightly better so should revise the answer accordingly. Whilst it is always best to test your parts creep is particularly nasty in that you can't get your answers quickly and it tends to be expensive. A material would help more than anything else here, but here is a suggested design method (I am not familiar with the design of springs to alleviate creep, this is just a common sense set of suggests from a fellow engineer):

1. Decide yourself the operating conditions you expect it to take: load, duration of load and temperature. You ought to know this all.
2. (optional) Decide what kind of spring response you want and design the spring accordingly. Different springs respond to load fundamentally differently.
3. Find some equation for estimating the stress distribution in a spring; you haven't specified what type of spring you are designing but based on the mention of compressive load I would assume a steel coil spring but it could be one of many. If that is the case then I don't have an equation for the stress distribution, which is likely to be complex as coil springs probably have a combination of axial and shear loads when they deform. Either way, find some stress distribution, I'd imagine because of continuity a mean stress would do which at first glance would just be a function of angle of coil relative to direction of compression.
4. Decide whether creep is seriously a consideration for you. Most springs operate no where near the UTS of the material they are made from and if you are orders smaller then I'd question whether creep is something you need to worry about at all. Your car sits on its springs for decades and doesn't lose appreciable ride height. Even if you do get some change, does it influence on your design at all if your spring grows fractionally shorter over the space of a decade?
5. Decide on how important weight saving is to you and choose your material to give you the desired spring constant whilst reducing cost as best you can.
6. Use a table similar to the one below to find the region of creep which you are operating in, given the material, and calculate your rate of creep from an equation which applies to that region and constants appropriate to your material. You can find this all online.
7. Figure out whether this rate is acceptable.

Please consider that the first step that one would take to alleviate creep (decreasing the normalised stress) will change the characteristics of your spring which likely restricts you to a material change or a different spring design.

Answer 2

The contents below are extracted from the linked wiki article that seems to contain the clues to your question.

"Creep behavior can be split into three main stages. In primary, or transient, creep, the strain rate is a function of time. In Class M materials, which include most pure materials, strain rate decreases over time. This can be due to increasing dislocation density, or it can be due to evolving grain size. In class A materials, which have large amounts of solid solution hardening, strain rate increases over time due to a thinning of solute drag atoms as dislocations move.[4]

In the secondary, or steady-state, creep, dislocation structure and grain size have reached equilibrium, and therefore strain rate is constant. Equations that yield a strain rate refer to the steady-state strain rate. Stress dependence of this rate depends on the creep mechanism.

In tertiary creep, the strain rate exponentially increases with stress. This can be due to necking phenomena, internal cracks, or voids, which all decrease the cross-sectional area and increase the true stress on the region, further accelerating deformation and leading to fracture.

Deformation mechanism maps

Deformation mechanism maps provide a visual tool categorizing the dominant deformation mechanism as a function of homologous temperature, shear modulus-normalized stress, and strain rate. Generally, two of these three properties (most commonly temperature and stress) are the axes of the map, while the third is drawn as contours on the map.

To populate the map, constitutive equations are found for each deformation mechanism. These are used to solve for the boundaries between each deformation mechanism, as well as the strain rate contours. Deformation mechanism maps can be used to compare different strengthening mechanisms, as well as compare different types of materials.[6]

At high stresses (relative to the shear modulus), creep is controlled by the movement of dislocations. For dislocation creep, Q = Q(self diffusion), m = 4–6, and b is less than 1. Therefore, dislocation creep has a strong dependence on the applied stress and the intrinsic activation energy and a weaker dependence on grain size. As grain size gets smaller, grain boundary area gets larger, so dislocation motion is impeded.

Dislocation creep

Some alloys exhibit a very large stress exponent (m > 10), and this has typically been explained by introducing a "threshold stress," σth, below which creep can't be measured. The modified power law equation then becomes:

where A, Q and m can all be explained by conventional mechanisms (so 3 ≤ m ≤ 10), R is the gas constant. The creep increases with increasing applied stress, since the applied stress tends to drive the dislocation past the barrier, and make the dislocation get into a lower energy state after bypassing the obstacle, which means that the dislocation is inclined to pass the obstacle. In other words, part of the work required to overcome the energy barrier of passing an obstacle is provided by the applied stress and the remainder by thermal energy."

https://en.wikipedia.org/wiki/Creep_(deformation)