Introduction to durability analysis

Structural durability analysis is a tool for evaluating a design's structural worthiness, or its durability, under the cumulative effect of simple or complex loading conditions.

Durability analysis in this software consists of strength analysis and fatigue analysis.

• Strength analysis evaluates if the model can structurally instantaneously withstand the maximum static or transient stresses applied to it. This static strength evaluation serves to determine if a fatigue evaluation is required. For example, if peak stresses exceed the material ultimate strength a fatigue evaluation is required. The strength evaluation also serves to determine which stress or strain life criterion should be used in the fatigue evaluation. See Understanding the strength evaluation for more information.

• Fatigue analysis evaluates the fatigue life of the model from stress or strain time histories.

Generally speaking, fatigue life can be defined as the number of cycles to "failure due to repeated load (...) involving the initiation and propagation of a crack or cracks to final fracture" NOTE. Simcenter 3D Durability can predict the portion of this process associated with crack initiation, and in the context of this documentation, fatigue failure is taken to mean crack initiation. Results of a fatigue analysis are displayed as contour plots that show the number of fatigue cycles the structure can undergo before crack initiation occurs.

Fatigue analysis uses the cumulative damage approach to estimate fatigue life from stress or strain time histories. Estimation is accomplished by reducing data to a peak/valley sequence, counting the cycles, and calculating fatigue life.

Basic concepts of fatigue analysis

The following figure illustrates the basic concepts of fatigue loading.

Experimental fatigue life estimation

The process of estimating fatigue life for experimentally obtained data can be separated into three steps:

1. Peak/valley reduction

2. Cycle counting

3. Damage estimation

Peak/valley reduction

The peak/valley reduction process attempts to remove data that has little or no effect on the life prediction. First, all data points between the peaks and valleys are removed. This leaves only the data points that correspond to either peaks or valleys.

Next, peak/valley pairs that are insignificant can be removed. There are several ways to do this. One way is to specify a tolerance and remove peak/valley pairs with a difference within this tolerance. In the following figure, pairs less than 150 microstrain are removed.

If a tolerance of 150 is used on the data shown, points 2 and 3, and points 5 and 6 can be removed, since the range for both pairs is 100.

Cycle counting

After the data is reduced to a peak/valley sequence, cycle counting occurs. If the data was generated from simple cyclic loading, then cycles and the corresponding ranges can be determined by visual inspection. Finding cycles in experimental data is not as easy. Extensive research on this subject has resulted in a variety of algorithms that count cycles for experimentally obtained data.

A reversal is half a cycle, and an amplitude is half a range. When a cycle is counted, it may in fact be that a reversal has been found, depending on the algorithm. Along with each cycle or reversal comes a corresponding range or amplitude.

A simple method of counting cycles is to identify each successive peak/valley pair as a range.

For the data shown, points 1-2, 2-3, 3-4, and 4-5 are all ranges using this counting method.

Other methods of counting cycles include:

• Range pair

• Rainflow counting

Range pair

The range pair algorithm finds a reversal, and therefore a range, for two different cases.

For the positive slope range, point 1 must be less than or equal to point 3, and point 2 must be less than or equal to point 4. For the negative slope range, point 1 must be greater than or equal to point 3, and point 2 must be greater than or equal to point 4.

When two points have been determined to be a range, they are excluded from further counting. In the examples shown, points 2 and 3 would be dropped from further counting, while points 1 and 4 could be used again.

Rainflow counting

Rainflow counting is the most popular counting method in fatigue life estimation because it follows the stress-strain hysteresis loop. This counting method was named rainflow by its inventors, M. Matsuishi and T. Endo, because graphically it looks similar to rain flowing down a pagoda roof NOTE.

The rules that govern rainflow counting are as follows:

• Order the history so that the largest magnitude occurs as the first peak and the last valley.

• Starting with the first peak or valley, allow the rain to drip down until a cycle is closed, as described in step 3; or until the rain is stopped, as in step 4.

• If you start at a peak, a cycle is closed when you come opposite a peak that is greater than or equal to the starting peak. This is demonstrated by points 5-6-7. Starting at 5, the rain runs down to point 6, and then drips straight down to point 7. It is stopped opposite to 7 because the magnitude of peak 7 is higher than peak 5. A cycle is indicated in the figure with a short horizontal line where the rain stops. If you start at a valley, a cycle is closed when you come opposite a valley that is less than or equal to the starting valley. This is demonstrated by points 2-3-4. Starting at 2, the rain runs down to point 3, and then drips straight down to point 4. It is stopped opposite to 4 because the magnitude of valley 4 is less than valley 2.

• The rain is stopped when it runs into rain falling down from one of the above roofs. This is demonstrated by the rain, which runs from point 3 toward point 4. It is stopped before it gets to point 4 by rain falling down from point 2. The short vertical line at the end of the line running from 3 toward 4 indicates the rain was stopped.

• After a cycle is closed, or the rain is stopped for the first point, move to the second point and allow the rain to drip down. Repeat this until each point has been processed.

Rainflow counting with mean stress

In order to accurately predict fatigue life in structures that have pre-loads or offsets in their strain or stress histories, you need to include mean stress in the calculations. Mean strain cannot be converted to mean stress directly through the cyclic stress-strain equation. Consider the following hysteresis loop.

The small loops (4-5-4 and 1-2-1) within the large loop (0-3-6) have equal strain ranges. Using the cyclic stress-strain equation, the strain ranges can be converted to stress ranges that are equal to one another. The mean strain for the two loops is also the same. The mean stress, however, is different for the two loops, as one is positive and one is negative.

A method is needed that simulates traversing the hysteresis loop so that the proper mean stress can be obtained from an input strain history.

This can be achieved fairly efficiently by breaking the largest hysteresis loop into discrete elements placed end to end. Instead of performing conversions on each strain value to determine the corresponding stress values, a matrix of strain values and their corresponding stresses can be built up ahead of time. The more elements that are used, the better the approximation of the hysteresis loop.

After the strain or stress ranges and the corresponding mean stresses are located, the fatigue life may be estimated. The stress-life and strain-life equations can be modified to include mean stress effects.

Accumulating damage

There are two methods for proceeding with the experimental fatigue life estimation:

• All cycles are counted, after which all damage is estimated.

• Cycle counting and damage estimation occur simultaneously.

Simcenter 3D Durability uses the first method to accumulate damage from all cycles and events.

Look up more details

Understanding the strength evaluation

Strength calculations for orthotropic failure criteria

Fatigue evaluation on element free faces

Fatigue life criteria

Biaxial fatigue evaluation on element free faces

Using a notch factor for modeling the local plastic behavior

Understanding cyclic stress-strain behavior

Understanding the fatigue safety evaluation

Cumulative damage

Random fatigue methods

Strain and stress calculations from strain gage leg data

Strain gage transverse corrections for rosette legs

Scientific literature references for durability

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Introduction to durability analysis, Simcenter 3D 2021.1 Series

© 2020 Siemens

H.O. Fuchs, R.I. Stephens, “Metal Fatigue in Engineering”, Wiley, 1980.

Matsuishi, M., and Endo, T., “Fatigue of Metals Subjected to Varying Stress”, Japan Society of Mechanical Engineers, March, 1968.

Endo, T., et. al., “Damage Evaluation of Metals for Random or Varying Loading”, Proceedings of the 1974 Symposium on Mechanical Behavior of Materials, Volume 1, Society of Materials Science, Japan, 1974. pp. 371-380.

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