Photo: Joachim Rode

Doctoral dissertation: the secret behind fractures and cracks

Tuesday 19 Jun 18
by Søren Ravn


Brian Nyvang Legarth
Associate Professor
DTU Mechanical Engineering
+45 45 25 42 57
Sometimes fractures and cracks develop in an unpredictable way. In a new doctoral dissertation, Brian Nyvang Legarth has studied why this is the case.

“There are fractures and cracks in almost all materials, and the fractures can be found everywhere—probably also in the last plane you flew on. I can guarantee you it had cracks somewhere,” says Brian Nyvang Legarth with a smile, before adding:

“The question is, however, whether the cracks are dangerous.”

That’s definitely a good question, and Brian Nyvang Legarth is no doubt the right person to ask.

He is an associate professor at DTU Mechanical Engineering, from where he is also a graduate. He is now also a doctor after having defended his doctoral dissertation as the culmination so far of a long-standing fascination with and immersion into ‘the non-linear behaviour of anisotropic materials’, which is part of the title of his dissertation.

"How big mistakes do you make when you think that the material behaves in a certain way, and it then turns out to behave in another? "
Brian Nyvang Legarth

In the dissertation, he concludes on his studies of where and when materials break and, not least, how, e.g., a crack develops. Because the more you can predict, the better you can prevent cracks and fractures and prepare for them.

But the behaviour of some materials is more difficult to predict than that of others, which is the case for, e.g., anisotropic materials. They are special materials with different properties in different directions. Anisotropic materials can, for example, crack slightly in one direction instead of another. It can be wood, metals, plastic, or different composite materials.

Popularly speaking, anisotropic materials are unpredictable and contain more secrets than isotropic materials, which behave in a more predictable—and boring—way, at least if you are a researcher with Brian Nyvang Legarth’s temperament.

The major difference

Isotropic materials are, however, to a large extent a prerequisite for his research.

“Metals are—as a main rule—seen as isotropic. I have studied the difference of assuming the material is isotropic when it in reality is anisotropic. How big mistakes do you make when you think that the material behaves in a certain way, and it then turns out to behave in another? This applies to standard calculations on the dimensioning of materials used everywhere, e.g. in mobile phones, car, bridges, houses, wind turbines, or, yes, a plane.”

What have the studies shown you?

“We have isotropy as a reference point, and then we have anisotropy as a more realistic variation of it. I can see that anisotropy can either accelerate a fracture or crack, which is rarely good, or postpone it, in which case you have been really lucky. Or it can completely change how the fracture or crack occurs. And you are really in trouble, if you believe that now I have figured it out, but I’ve assumed that it’s isotropic. When I then use the material in real life, the anisotropy triggers the fracture or crack to take place somewhere completely different. That’s a problem.”


“Then there is a risk that the stresses in the materials, which we want to find and understand, are growing inappropriately somewhere else. This means that a fracture or crack occurs in a place or at a time you had not expected. And if it happens in a plane, which has often been the case, it can of course be catastrophic. It is all about predicting a stress scenario. So since the material behaves in a certain way, where will the fracture or crack then occur. My research is very much a question of becoming as good as possible at predicting it.”

In order to pursue that ambition, Brian Nyvang Legarth has developed new numerical calculations using computer codes and simulations that are to a far greater extent than previously can reveal which properties materials have in the different directions, which stresses the materials can withstand, and how the fractures or crack will develop once they have occurred and the materials are deformed. But the simulations cannot stand alone.

“The simulations go hand in hand with experiments. The numerical simulations have the advantage that they are much cheaper. You can make a huge range of different scenarios. Doing it in a lab is very costly and time-consuming. One could say that my primary work is to develop theoretical models and ways to incorporate them in a computer program and then do some virtual tests.”

Cracks can grow without stress

What is the most difficult about predicting when and where a fracture or crack develops?

“If I get a structure from a design engineer, it’s rarely difficult to find out if it breaks or when. The hard part is to monitor fractures or cracks when they occur and see if they become serious—especially if more than one occurs at the same time as a result of anisotropy. A fracture or crack changes the structure’s stiffness, because the crack cannot withstand the stress. That is up to the remaining intact material.

So it’s a very unstable calculation when things start to break. When materials start to crack, the stress is redistributed completely, and some of my studies have shown that cracks grow despite the fact that the stress does not increase. And it’s quite difficult to calculate this in practice. You often need to use some tricks, which I’ve also done."

Why is it important to be able to monitor the crack? Can’t you just repair it when it occurs?

“Yes, and now we’re back to the fact that not all cracks are dangerous. We can live with some cracks. Not everything needs to be repaired. There are lots of cracks in structures that are acceptable. The question is how much and how you can put stress on the structure. If you know that and keep within the limits, you are on the safe side. And then there is also the fact that when repairing a structure, e.g. a plane, you introduce new errors in the structure, and then it may be the repair itself that causes the plane to crash.”

Can be used everywhere

Brian Nyvang Legarth’s research is essentially basic research with a longer time horizon. But, fully in line with DTU’s spirit, he places great emphasis on a technological purpose—with focus on usefulness and applications. And knowledge of the behaviour of anisotropic materials is relevant to all engineers and companies in the high-tech mechanical industry—not least the ship and wind turbine industry as well as the aerospace industry, where the materials are subjected to gigantic stresses, and where the consequences of fractures or cracks can be fatal. But the results can also be used in less critical scenarios of a more financial nature.

What is it that keeps you enthusiastic about this field of research?

“There are several things. The materials look harmless, but once you start doing something with them, they start behaving in a way that I hadn’t expected. Something secret takes place in there, which I can’t see, but I can see the effect of it. That’s what I find fascinating.

Brian Nyvang Legarth’s doctoral dissertation is entitled: The non-linear mechanics of anisotropic materials—fractures and harmonization. The defence took place on 18 June 2018.