## Fracture Mechanics

I had an interesting problem to solve last week. It was concerning fatigue failure. A simple element after sucessive stress solicitations breaks apart (nothing new). It starts with a small scratch/crack and after a few million cycles and voilá the part breaks.

I initially made the traditional fatigue analysis but discovered that it is possible to go one step ahead! Using crack analysis directly in my model. Well I know this is around since at least 2014 so says Ansys.

My traditional approach involved a two way analysis where I calculated my maximum stresses for a dynamic input load measured through lab tests. After this I used standard fatigue analysis techniques to calculate the fatigue strenght. To do this I also required a wohler curve.

An alternative way is to include the crack into the finite element model and calculate what happens after a few cycles. Some software packages allow this type of calculation making our lives simpler.

I will go more indeph on fracture mechanics and fatigue in the future but for now I just want to give some good references to get started fast in this subject.

A good example of what to do, to give you a guide for your first steps on fracture mechanics can be seen in the following link.

https://caeai.com/resources/fracture-mechanics-workbench-v145-e-learning-presentation

A good example of a fatigue fracture can be seen in the Wikipedia

https://commons.wikimedia.org/wiki/File:Pedalarm_Bruch.jpg

https://en.wikipedia.org/wiki/Fatigue_(material)

https://en.wikipedia.org/wiki/Fatigue_(material)#The_S-N_curve

https://commons.wikimedia.org/wiki/File:Strain-N.png

## The meshing dilema uncovered

Finally I got the time to wrap up this subject and uncover this mystery. Actually none of the curves I presented was correct. Let me recap.

1. I used the default mesh – option 1,
2. I used a course mesh with general surface refinement – option 2
3. I used a bit finer mesh with local surface refinement – option 3

I got the above graph. Next I decided to cut the solid but shared the boundary conditions so that it was a single entity just sectioned. On my target edge/surface I defined a volume mesh (more refined) and on top of that near the edge I was studying and measuring I place a volume refinement. I got just about as much elements as before but now they were concentrated on my target zone.

The final mesh had the following

And the final result:

And here you go. The yellow curve has nothing to do with the blue curve which was my starting point and eventually converged with my previous 2 attempts.

Lessons learned:

Carefull usage of meshes, it is always good practice to verify mesh sensitivity. This example applies to any thing you do in simulation, it is always good to verify if the result we have in hand are actually trustable.

Comments to the starter: When ever your boss demands results immediately it is always tempting not to do a sensitivity analysis to rush and give something. If for instance this was a professional case (which it’s not) and one feed the blue line there would be some opportunity for mistakes. It is always important to verify how accurate a result the requester desires. On some clients the blue line would be wonderful for others it would be useless.

Ultimately the simulation result needs to fit the expectations of the requester. And the simulation effort, accuracy and time should fit those expectations.

## The mystery of the train seat uncovered

Will the train seat withstand 120Kg? was I seeing things? Maybe the weight was more since the person had a backpack. But the load was extreme.

I calculated 5 mm deformation on the cushion. Could I have seen it? Well maybe. Stresses were far away from the plasticity limit, however the structure feels loaded.

From my analysis the structure could take even more load and wobble even more. Maybe the squeaking sound over exaggerated my notion of wobbling.

The light blue image is the deformed state,  we can see the deformation direction, which moves in a expected direction.

In this close up we can see a slight displacement. But very small.

So my conclusions:

The heavy train traveller was safe, the seat could stand a few extra Kg’s of weight with some more camping equipment.

The design seems fairly robust, however it actually wobbles.

## What is a model?

What is a model?

According to google it is “a thing used as an example to follow or imitate” and or a “three-dimensional representation of a person or thing or of a proposed structure, typically on a smaller scale than the original”.

For Merriam the definition is more explored where in point 12 we get a more compatible definition of modelling. “a system of postulates, data, and inferences presented as a mathematical description of an entity or state of affairs; also :  a computer simulation based on such a system” Merriam dictionary

Representing our world objects, processes, states as mathematical expressions. These can be developed, visualised and used in CAD, CAE, Excel, Matlab, any capable programable environment software. A good day to day example offered in Merriam dictionary is the Weather model. There are a set of mathematical equations that are calibrated through many real life weather stations that deliver predictions of what the weather will be in the future and what occurred in the past which we did not measure. So basically a model is a means to study a future state or recap a past state through a lot of math. Looks simple.