Mechanical Engineering Internship: Volvo Trucks

Project Goal 

To research and analyze various mean stress correction models for the fatigue analysis of polymers and composites and to recommend the best model.

My Role(s): 

Technical Skills: Non-technical Skills: 

Results

Successfully determined the best mean stress correction model for the fatigue analysis of polymers and composites using a detailed literature review and internal data analysis. Developed a Python script with an integrated graphical user interface (GUI) capable of applying this model to the company's internal material fatigue database.

Key Takeaways

Project Overview & Process

Over their lifetimes, trucks experience cyclic loading on many of their components. Volvo designs its parts to withstand these fatigue loads by simulating how they would behave using finite element analysis.

To accurately simulate the fatigue behavior of materials, we would need the fully reversed fatigue data for the material, where the average mean stress of a given cycle is zero. However, most of the data that original equipment manufacturers receive is not in the fully reversed form: there is some amount of pre-loaded tension or mean stress. This is because fully reversed fatigue tests are difficult to conduct because applying a compressive force on a sample introduces a risk of buckling.

Therefore, when we receive non-fully reversed data, we need to apply a mean stress correction model to transform it into a fully reversed format, and several models can accomplish this, such as the Walker equation, the Goodman equation, and the Gerber equation. To determine which model provided the best mean stress correction for polymers, I used two methods:

An example of one stress cycle where the figure on the left represents a zero mean stress and the figure on the right shows a positive mean stress. For a given stress amplitude, a sample is cycled until failure and this process is repeated for different stress amplitudes until there are enough data points to construct a stress amplitude vs. number of cycles to failure (S-N) curve (see figure below).

An example set of S-N curves to illustrate the effect of mean stress on fatigue life predictions. The red curve (representing a non-zero mean stress) would predict shorter lifetimes for a component than the blue curve (representing a zero mean stress).

Results & Discussion

Based on my literature review, it was conclusive that the Walker model provided the best mean stress correction for polymers and composites. However, the value of the best-fit parameter that gave the best correction varied largely between different materials, ranging from 0.28 for PLA to 0.6 for certain grades of PC/ABS.

Based on the literature review and my analysis of the fatigue data that we had for PC/ABS and PC/ASA, I determined that the Walker equation was the best mean stress correction model for polymers and composites. The next major question involved the best-fit parameter: what parameter values would yield the best results? If this value varies largely between different materials (even between different grades of the same material), how do you determine what value to use?

 To help answer these questions, I performed a sensitivity analysis on the Walker best-fit parameter: I varied the parameter from 0 to 1 with increments of 0.01 and determined how well each corrected curve correlated with the fully reversed data. I found that the S-N curves were not very sensitive to changes in the Walker best-fit parameter; for the PC/ABS, values ranging from ~0.4 to ~0.8 produced an S-N curve that had an R^2 value of 0.9 or greater when correlated with the fully reversed curve. I saw similar results in the PC/ASA data when varying the best-fit parameter from ~0.2 to ~0.4.

Based on these results, my final recommendation was the Walker mean stress correction model with a best-fit parameter value of 0.55. This value was chosen because it is backed up by literature and it was shown to provide a good mean stress correction for the PC/ABS material we investigated. The downside is that, for materials that are very sensitive to the mean stress effect such as the PC/ASA (whose best-fit parameter was 0.28), using 0.55 would yield a conservative result.

However, it is important to remember that we are trying to recommend a best-fit parameter for all of our polymers and composites because we rarely receive fully reversed fatigue data for these materials. Because of this, we need a parameter that will provide a good correction in the best of cases and a conservative correction in the worst of cases so that we don't design components that fail before they are predicted to fail.

The Walker mean stress correction model, where gamma is the best-fit parameter, the stress amplitude and mean stress are denoted by the subscripts a and m respectively, and the corrected stress amplitude is denoted by the subscript ao.

S-N curves for a) PC/ABS and b) PC/ASA, including the fully reversed and the non-fully reversed curves.

S-N curves including the mean stress corrections for a) PC/ABS and b) PC/ASA, where the best model would yield a curve that merges with the fully reversed curve.