In my last article I discussed the importance of failure analysis and work cycle quantification. To perform these analyses there are several software programs and many methods to choose from, but they all share a similar philosophy. Several names in failure research including Murakami, Raju, Newman, and Paris have come up with formal methods to go from a regular stress analysis to a failure analysis to a work cycle number.

## First build a virtual product

To begin, you model your part in CAD, mesh it and apply working conditions to it. Then, the software allows you to export the visual model to a data file that can be processed by a solver. Solvers, such as Nastran or Samcef, will evaluate several matrices and equations to come up with results displaying where stress is most critical, or where or when deformation reaches a breaking point. Using this information, you can therefore calculate how long your part will work without breaking, or how many work cycles it will perform before showing signs of wear.

These practices focus on hypothetical defects and how they spread within a finished definite plane. According to their equations, once the crack reaches the border of a plane with critical stress value, calculations should stop and the work cycles that were reached before fracture are the first quantification you can use.

To give a better insight into the theory, let’s walk through a simplified example….

## Calculate the working life of a frying pan

Let’s say we have a frying pan and we would like to understand how many work cycles (defined as heating the pan for 15 minutes) it can endure before failure. Let’s assume a basic static analysis has been conducted, and the meshed CAD of the pan has been submitted to work conditions over the span of one working cycle. We get the following results:

- Critical stress
- Deformation

## Test, test and test again

We will now take a look at the step-by-step process of calculating the working life of our new frying pan:-

## Step 1: Define the critical regions

These regions can be assessed through expertise or analysis. Depending on your own experience, you might already be able to tell which regions of your part likely suffer the most damage or are prone to deformation. Using analysis, the critical regions are the ones where stress concentration or deformation is at its highest. Once you define the first location, remove it from the analysis and move to the next one. Define as many as necessary. Usually, we stop defining regions once we reach one with stress less than the average admissible.

## Step 2: Define crack hypothesis

What is the defect’s basic shape? What are its dimensions? What is the hypothesis of the material? How will the crack spread be studied? This will help in picking one of the formulas available to conduct failure stress. Each formula comes with sets of hypotheses and equations to calculate the stress concentration coefficient, its development through work cycles and resulting stress at the end of each work cycle. In the picture below, the main crack types adopted by industries are displayed along with their classic dimensions.

## Step 3: Define critical stress component

Within every critical region, you will find a specific element with the highest stress value. This element needs to be studied. The resulting stress should be dissected into its main components. The component with the highest value will be the one to conduct the rest of the study.

## Step 4: Define the finite plane

This is one more hypothesis that is available with the formula. You must choose the location of the plane. Let’s say the component with the highest stress value is X and the one with the second highest stress is Z. The crack will most likely diffuse through X on a XZ plane.

## Step 5: Launch iterations

This step will likely require software help since it’s an iterative calculation with data accumulation within each step. Once you have put your crack on the plane and used a formula, all that is left is to submit the crack to a series of work cycles (heating the pan, cooling, heating, cooling), until the crack reaches the end of the definite plane or failure stress value. When this event occurs, iterations should stop and work cycles should be counted.

## Step 6: Average the work cycles

The operation described should be conducted on more than one region. You will most likely find that the critical region has the smallest work cycle value. Certain circumstances might lead to a different result but this will generally be the case. You now have a conservative estimate of work cycle life. Now your industry’s security coefficient and acceptable stress results should be considered.

## Step 7: Be aware of the perspectives available

Once you have worked through your first failure analysis according to a set of hypothesis, you can improve the analysis and get a more accurate and defendable number of work cycles by developing your hypothesis or adopting new ones. We assumed the pan will be heated for 15min but this might not be the case. Also, a sudden change of temperature (for example putting the pan under cold water right after taking it off the stove) could be a significant factor. Likewise, many boundary conditions might have been overlooked in the first static analysis, or other defects’ shapes would be more accurate with the pan’s material or working dispositions. It’s important to consider multiple hypotheses and keep track of experimental results.

## Conclusion

To summarise, failure analysis is extremely versatile and specific to each and every industry. However, its formulas and the defect hypotheses upon which it relies are easy to assimilate and can be used by anyone who is willing to do the work and the calculation. The result of all this effort is a competitive benefit to the company…most people would be more inclined to buy a pan knowing exactly how many work cycles can be expected over one that is unknown.

*Picture and hypothesis source*: STRESS-INTENSITY FACTOR EQUATIONS FOR CRACKS IN THREE-DIMENSIONAL FINITE BODIES SUBJECTED TO TENSION AND BENDING LOADS (*Newman and Raju*)