Understanding Fatigue

Subtle and unappreciated, metal fatigue has been the root cause of many a disaster. From experience we know that fatigue is often overlooked in engineering designs, and consistent, predictable performance and behaviour are lost. As part of our Quality Management System, and Value Proposition, we have a design and manufacturing risk assessment that from once being an internal QA input, now sees us spending time in the heart of our customerś operations. Very often, we find issues where the root cause is metal fatigue.

Fatigue occurs when the base metal of a structure or component becomes weak from repeated stress cycles. Metal fatigue begins with the crack initiation (imperceptible to the naked eye) and its subsequent propagation due to the cyclic loading and unloading. Those who have chipped a windscreen know the inevitability of the process, as they watched the slow march of the developing crack, that might take weeks to develop and finally fail. But fail it always does!

Ubiquity of Fatique

It is not unusual for us to pick up an issue in the operations of our customers by taking note of either the frequency with which a particular size is ordered, or taking note of the number of spares required or observing their frequency of urgent breakdowns. In these instances, when we conduct an investigation, we invariably find disc springs being used incorrectly in machinery that is applying them in a sub-optimal manner. The point to note is that without exception, metal fatigue has been either the root cause or contributing factor, and hence the focus of any remediation.

When we investigate, this involves us joining our customer´s plant managers and maintenance teams and dismantling machines in situ, (this can be a messy business!!)) and conducting our failure analysis. This includes:

an analysis of the disc springs themselves - material composition, hardness & hardening, contact flats, radii, dimensions etc
the installation of the disc springs - clearances, alignment, lubrication etc
the actual physical dynamics of the stack - pre-load and final design load and travel etc
a verification of the engineering design - stresses, loads etc

So by being curious and caring about our customers, we ask the right questions, provide solutions and add great value from 1) greatly reducing unscheduled downtime, 2) reducing waste and rework, and 3) reducing maintenance costs. To re-iterate and emphasize the point metal fatigue is always either the root cause or contributing factor, and must be the focus of any remediation.

The intention of this page is thus to:

Build awareness with our customerś of the importance of understanding fatigue
Introduce some concepts that are useful in understanding the problem
Provide some tools that allow us to quantify objectively, consistent and predictable operating lifespans
Explain some of the gaps, short-comings and consequences that manufacturers conveniently neglect to share regarding fatigue
Differentiate ourselves from the rest of the market

Useful Concepts & Terminology

Elasticity is the tendency of solid objects and materials to return to their original shape after the external forces (load) causing a deformation are removed. An object is elastic when it returns to its original size and shape when the load is no longer present. Elastic behavior varies vastly between materials and depends on the microscopic structure of the material.

Plasticity is a behavior that occurs when stress is greater than the materialś´ elastic limit. In the plastic region, the object or material does not return to its original size and shape when the loading stress dissipates but instead acquires a permanent deformation. Plastic behavior ends at the breaking point.

The Yield strength of a material is defined as the point at which, as stress is applied to the material, plastic deformation starts to occur as the material is being loaded.

There is no definite point on the curve where elastic strain ends and plastic strain begins, the yield strength is chosen to be that strength when a definite amount of plastic strain has occurred. Yield strength is chosen when 0,2 percent plastic strain has taken place. The 0.2% yield strength or the 0.2% offset yield strength is calculated at 0.2% offset from the original cross-sectional area of the sample. As with stress, which we denote with the Greek small letter sigma - σ, Yield Strength is measured in MPa or N/mm².

Strain relates to deformation of a material from stress. It is simply a ratio (so it appears as a % on graphs) of the change in length to the original length. Deformations that are applied perpendicular to the cross section are normal strains, while deformations applied parallel to the cross section are shear strains.

Stress is the measure of applied force F (or load) to a cross section area and is defined as "force per unit area". Tensile stress tends to stretch or lengthen the material - acts normal to the stressed area, whilst compressive stress tends to compress or shorten the material. We denote the difference between the two by a positive (tensile)) or negative (compressive) sign.

Base Material

We purposefully use Spring Steels in the manufacture of disc springs because of these metals´ physical and mechanical properties of durability, pliability, toughness, and longevity (once heat treated properly!!). All of properties relate to the spring attribute property of reacting to loading by elastic deformation. There are instances where requirements such as non-magnetism, the ability to operate in elevated ambient temperatures or highly corrosive environments, require the use of alternative materials. In these instances, the published product data which relates to Spring Steel should not be used. For more on this subject. please go to our detailed discussion on materials used in the manufacture of disc springs.

Stress Strain Diagrams

We can graph the relationship between stress and strain on a stress-strain diagram. Each material has its own characteristic strain-stress curve

Fig 1.1 - Generic Stress Strain Curve.

In the accompanying diagram we can see that in the region between O and A, the curve is linear. Hence, Hooke’s Law obeys in this region. In the region from A to B, the stress and strain are not proportional. However, if we remove the load, the body returns to its original dimension.

The point B in the curve is the Yield Point or the elastic limit and the corresponding stress is the Yield Strength (Sy) of the material. Once the load is increased further, the stress started exceeding the Yield Strength. This means that the strain increases rapidly even for a small change in the stress.

This is shown in the region from B to D in the curve. If the load is removed at, say a point C be-tween B and D, the body does not regain its original dimension. Hence, even when the stress is ze-ro, the strain is not zero and the deformation is called plastic deformation.

Further, the point D is the ultimate tensile strength (Su) of the material. Hence, if any additional strain is produced beyond this point, a fracture can occur (point E). Note that if:

The ultimate strength and fracture points are close to each other (points D and E), then the material is brittle.
The ultimate strength and fracture points are far apart (points D and E), then the material is ductile.

Estimating Fatigue

The key points on a disc spring where stress must be considered, are referred to by convention, as σ_I-IV as depicted in the diagram below. Of these we typically provide data on σ_I-III

Fig 1.2 - Stress Points on a Disc Spring.

The tensile stresses at points σ_II and σ_III in Fig. 2 above, are used in estimating disc spring fatigue life. These points on the disc spring are where fatigue cracks will originate. Estimation of fatigue life requires working out the maximum stress differences between the preload and final design load for points II and III. The highest stress differential pair is chosen, and the corresponding upper (final design load stress) and lower (preload stress value) are used to estimate fatigue life measured in cycles.

Fig 1.3 - Modified Goodman Diagrams for Group 1 Disc Springs.

These stress values, the fatigue life charts (Modified Goodman Diagrams) are used to estimate the fatigue life of the disc spring. We take the difference in final design load and preload stresses for points II and III, we then see which has the biggest difference, the two stresses that make up this difference are then mapped on to the modified Goodman diagram. To use the chart, draw a vertical line drawn on the X axis representing the minimum stress at the designated location and draw a horizontal line on the Y axis representing the maximum stress at the designated location. The intersection of these two lines is used to compare to the nearest fatigue lines, which are an estimation of the expected fatigue life.

There is a lot to interpret in a Goodman Fatigue Diagram, and the diagram below attempts to make this all clear.

Fig 1.3 - The different regions of a Goodman Diagram.

We have different regions(Red, Purple, Green, Yellow, Red & Blue) on the Diagram, which are bounded by lines A to E.

A - The upper stress threshold - anything mapped above here (RED region), means that under dynamic load, the disc spring will crack and break
B - Here there is no difference between the Preload and Design Load, so there is no real dynamic load, anything above this line but below line C - 2 million, (GREEN region), will have a life measured in millions of cycles.
D - 1/2 million line - Anything below this line and above the 2 million line, (YELLOW Region) will have a lifespan of 100ś of thousands of cycles
E - 100,000 line - Anything above (BLUE Region) will have a limited life measured in 1000ś of cycles, any thing below but above the 1/2 million line (BROWN Region) will have a life of 10s of thousands of cycles
Purple Region - This cannot be a valid region as this would infer a preload stress greater than the final load stress - which is impossible

It is important to note the following:

There is a separate Goodman diagram for Group I,II and III disc springs
There are no Goodman diagrams published for disc springs other than Spring Steel
These diagrams are not strictly valid for stack values of i>10 and/or n>2

Worked Example

For example, let’s say we needed to estimate the fatigue life of a Series B, Group 2 disc spring with an outside diameter of 50 millimeters, an inside diameter of 25.4 millimeters, and a thickness of 2 millimeters. The preload is 15 percent of the spring’s initial height, and the final position is 75 percent of its initial height.

Using the specification chart shown in Table 1, at 15 percent of the spring’s initial height, the stress at location II (σII) is 128 newtons per square millimeter (N/mm2) and the stress at location III (σIII) is 264 N/mm2. Similarly, at 75 percent of the spring’s initial height, the stress at σII is 923 N/mm2 and the stress at σIII is:

1,140 N/mm2. Now, we can calculate the differences between the stresses at each location.

Location II: 923 – 128 = 795 N/mm2.
Location III: 1,140 – 264 = 876 N/mm2.

The calculations indicated the maximum differential in stress occurs at location III. Therefore, we will use the stress values from location III, and the fatigue life charts to estimate the fatigue life of the disc spring.

To use the chart, draw a vertical line drawn on the X axis representing the minimum stress at location III and draw a horizontal line on the Y axis representing the maximum stress at location III. (See Chart 1.) The intersection of these two lines is the estimated fatigue life. Thus, in our example, the line on the X axis is drawn at 264 N/mm2, and the line on the Y-axis is drawn at 1,140 N/mm2. The intersection is slightly above the 100,000 cycle line, so the estimated fatigue life of the spring would be slightly less than 100,000 cycles.

Reality Check

Do not assume that all disc springs on the popular commercial lists are equal. It is amazing to see how mistakes made on one list manage to migrate across the world to other businesses. Someone is having a laugh! Mistake or malicious intent? The point that should sober you up is that there are legacy disc springs on the commercial lists that need to be used with caution. This is why we provide a red flag on our product lists, and a single star to subtly indicate our views, based on our observations and experiences.

The product data we provide with each disc spring is useful and should be carefully considered when selecting a disc spring. But do not rely on data that appears on any list (not even ours), verify yourself using this simple online calculation tool for Disc Spring Stresses and Loads

Fig 1.4 - Example Product Data for Larger Group 3 Disc Springs.

Letś look at the first column above, a 127x250x16 Reduced Thickness Disc Spring with Contact Flats. This is a popular disc spring used in a specific generation of arc furnace applications. They are used in stacks of 14 in series, to hold the crucible, that contains more than 500 Tons of molten ore, in place.

Now, what is the preload to final design load working range, that can be accommodated by these disc springs under a dynamic load? We will allow you to verify using the tools provided, that for this seemingly robust disc spring, weighing in at 4.7kgs, that it cannot be used in any application beyond 50% of S/h₀! and you thought that 75% was the recommended limit. Ok, then what of a static load? Look at the stress on location point I, which will hint at the fact that this is a disc spring that if not properly manufactured will experience relaxation and setting within hours of use. Now that becomes a problem when installed on an arc furnace, which every hour of down time costs $$$$!

There are other monsters lurking in the lists out there, be careful, let us help you.