Category Archives: Materials Science

About Tsai-Wu failure criterion

Predicting material failure is always a challenge, especially when it comes to composites and advanced materials. There are plenty of theories that try to provide a numerical approach to solve this complex problem, such as Maximum Stress/Strain Theories,  Hashin, Tsai-Hill or Tsai-Wu. Although all of them brought something valuable to the table, some of them don’t seem to be that precise when accurate results are needed. In these terms, Tsai-Wu is my least favourite criterion and I’ll explain the reasons for that.


First of all, Tsai-Wu is an interactive failure criterion for composite materials. This means that the theory takes into account the interaction of different stress components in order to predict failure. Basically, the criterion uses equation 1 (subjected to the condition given by equation 2) to calculate an index and, if its value is one, then it means the material is failing. Please note that i,j=1,2,…,6, where subindices 1 to 3 represent normal stress components and 4 to 6 are shear stress components. In the original publication, authors explain how the different coefficient can be determined through experimental tests (e.g. compression, tension, biaxial…). So far, so good.

01

Equation 1

02

Equation 2

Problems start when people adapt this approach to introduce failure in Finite Element (FE) analyses. This theory does not include any damage evolution, so if you define failure as soon as the index reaches 1, then elements will be deleted from the model straight away. To be fair, if you are just trying to get estimations for composites, this is not that bad, since they are supposed to fail as soon as they reach a certain level of stress. The main issue is when users use this interactive failure criterion for other materials. For example, for a three dimensional case, equation 1 can be rewritten as follows:

06

Equation 3

Now consider a material which has similar strengths in the 3-principal axes and assume that the positive and negative shear strengths are equal. Then, using the expressions from equation 4 (where the parameters represent the tensile, compressive and shear strengths), we know that: F1=F2=F3; F11=F22=F33; F4=F5=F6=0; F44=F55=F66.

03

Equation 4

There are an infinite number of ways to determine the interactive coefficients so, how do we solve this problem? Some people suggests biaxial tests but another effective way to overcome this issue is to make the following assumption (as suggested in literature):

04

Equation 5

Firstly, this assumption satisfies the stability condition (equation 2) and secondly, it proves to be quite satisfactory for composite materials. Generalising this idea, we find the following:

05

Equation 6

Okay, so now consider that our material exhibits an elastic-perfectly plastic behaviour in compression. This would mean that the specimen should keep deforming under constant load after the yield (or maximum) compressive stress was reached. Hence, the criterion would predict failure once that value was reached, and no plastification prior to failure would be considered. For instance, consider uniaxial compression once the yield stress is reached, as shown in Figure 1:

Capture

Figure 1

Using all the equations which were introduced before, we have:

07

Equation 7

Therefore, in FEA elements would be deleted after that point, whereas in reality we would expect the material to keep deforming. That being said, more problems appear in cases where the structure is subjected to mixed loading conditions, since the criterion would then predict premature failure.

This post does not intend to state categorically that this theory is useless, that is not what I mean at all! But lately I have seen companies offering FE services using this type of approach, not taking into account that the material under consideration might not be compatible with the assumptions made for this criterion. I just needed to highlight this bad practice that I’ve noticed, so sorry if I’ve offended anyone!

Spanish university to collaborate with the development of intelligent materials

The University of Alicante (Spain) is taking part in a project that will develop intelligent materials for aerospace, automotive and transportation industries. The main aim will be to improve the safety of occupants and the durability of the components.


Researchers from the Department of Civil Engineering from the University of Alicante and the tech company Applynano Solutions are carrying out this project known as MASTRO, which stands for Intelligent Bulk Materials for Smart Transport Industries. The project is part of the Horizon 2020 programme, which is the biggest investment system for R&D in Europe.

Their goal is to develop intelligent materials for the transportation sector. In particular, the aerospace and automotive industries will be the main targets. Amongst other innovations,  these materials will be able to monitor their own deformations and they will also be capable of heating and defrosting their surfaces. Besides, thanks to their capability to repair and protect themselves from damage, they will improve their efficiency, their durability and users’ safety. At the same time, manufacturing and maintenance costs will be reduced, as well as emissions.

In order to develop these materials, different matrices will be used, including polymers, concrete and carbon nanomaterials. Their functions will be based on three processes: the variation of electric resistivity when a material is subjected to a mechanical load, the relation between the heat that is generated and the electric flux, and electrostatic discharge.

One the one hand, the Spanish university will work on the development of the function related to perception of strain and damage on structures made of reinforced concrete. In addition, the previously mentioned institution will also focus on the heating of surfaces made of asphalt and concrete in order to avoid the formation of ice.

On the other hand, Applynano Solutions will work on the development of the carbon nanomaterials, the manufacturing of composites and the production of prototypes.

These are exciting news for the European research community, since not only Spain but also institutions from United Kingdom, Portugal, Italy, France, Germany and Sweden will collaborate with the MASTRO project. Hopefully, we’ll see encouraging results in the near future! I’ll keep you updated!

The Secret Science of Superheroes

Do you like science? Are you a comic geek? If your answer to both questions is “yes”, then “The Secret Science of Superheroes” is your book!


Last August I got myself an autographed copy of “The Secret Sicence of Superheroes”, thanks to Dr David Jesson and Dr Mark Whiting (University of Surrey) and I must say I don’t regret it at all! The book is distributed by the Royal Society of Chemistry and it was edited by Mark Lorch and Andy Miah. When I first heard about this book, Dr David Jesson told me that the whole thing was completed in just one weekend during an event in Manchester and that each chapter was written by a different author and it related a specific superheroe topic with the author’s field of expertise. Interesting, right?

I would review every single chapter, I really would, but… then you wouldn’t read the book! So, I’m just going to talk very briefly about the things I enjoyed the most. Basically, the text is written for a general audience, introducing the scientific concepts as the authors try to make their point. Read more

Introduction to Impact Dynamics: the ideal collision when playing pool

While I was playing pool the other day, I remembered a lesson that I learned during my time at the University of Seville as well as at Cranfield University. It is related to the quite complicated subject of Impact Dynamics… But don’t be afraid, today I’ll just cover a simple case as an introduction. In particular, I’m going to write about how the ideal collision between the white ball and the other ball that we are aiming to move.


First of all, we need to differentiate between different types of collisions, depending on the loss of translational kinetic energy or, in other words, the conversion of kinetic energy to rotations, vibrations or heat. For this case, let’s consider two bodies: one in motion (impactor) and another in stationary conditions. Hence, we can distinguish between the following categories:

  • Elastic collision: all the energy is transmitted from one body to another, i.e. the impactor stops and the stationary mass starts moving at the same speed as the initial one from the moving mass.
  • Completely inelastic collision: the moving mass stops after hitting the stationary body. The stationary mass remains as it was.
  • Inelastic collision: the impactor suffers a decrease in speed after the collision, whereas the stationary mass starts moving at a certain speed.
  • Superelastic collision: if additional energy is provided to the stationary body during the impact, then it will start moving at a higher speed than the one at which the impactor hit it.

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Graphene-based composite nanomaterial can prevent the overheating of lithium-ion batteries

Although the performance of lithium-ion batteries (LIBs) have been remarkably improved in the past decades, there is a big risk in the use of this type of battery: they can catch fire when they are subjected to abuse. Researchers from Stanford University have developed a nanocomposite material which can be included into the electrodes in order to prevent the explosion of the battery.


To perform in an efficient way, LIBs require operation conditions which are within a specific range of current density, voltage and temperature. Nevertheless, when they are subjected to abuse conditions, exothermic reactions can take place, leading to a fast increase in internal temperature and pressure. What does it mean? Well, our battery is likely to explode!

Current LIBs include external sensors to prevent overheating and overpressure but, unfortunately, temperature and pressure inside the cells can actually increase much faster than they can be detected by those external sensors. Because of that, several alternatives have been developed in order to include internal components to solve the problem. For example, ceramic coating has been proven to be an effective way to shut down the battery and improving the thermal tolerance. However, after the battery is shut down, it cannot be used again. Using solid-state electrolytes can be another option, but the overall performance of the battery is decreased due to their low ionic conductivity. Read more

Mechanics of composites

A while ago, I wrote a simple document for undergraduates in order to explain that composite materials can fail in different ways. This was created as a high level document which could be used to find useful references with regards to failure modes, basic failure criteria and damage propagation models. I wanted to share this with you in case you are new in this field or just if you simply want to learn some basics of composites!


A composite can be defined as a material which is composed of two or more constituents of different chemical properties, with resultant properties different to those of the individual components. They usually consist of a continuous phase (matrix) and a distributed phase (reinforcement). These reinforcements can be fibrous, particulate or lamellar and they are usually stiff and strong, so that they are responsible for providing the stiffness and the strength of the composite. On the other hand, the matrix provides shear strength, toughness and resistance to the environment.

Fibre reinforced composites are considered as the strongest and sometimes also the stiffest, due to:

  • Alignment of molecules or structural elements.
  • Very fine structures.
  • Elimination of defects.
  • Unique structures.
  • Statistical factors.

With regards to fibre reinforced composite materials, their main failure modes are:

  • Fibre failure induced by tension in fibre direction.
  • Fibre failure induced by compression in fibre direction.
  • Matrix fracture induced by tension.
  • Matrix fracture induced by compression.
  • Delamination

It is remarkable that fibre failure typically caused composite failure, whereas matrix failure may not cause the same drastic effect. Read more

Recycling of Carbon Fibre Reinforced Polymers

The use of carbon fibre reinforced polymers (CFRP) is increasing every day. This type of material have been used in aerospace and automotive industries (amongst others) for years, but now the cost of manufacturing components made of carbon fibre is becoming more accessible for mass production and more companies are introducing CFRP parts in their products because of their good mechanical properties, energy absorption capability and low weight. However, since a large increment in the production is observed, companies need to be aware of the different recycling techniques that are currently available for these materials.



Nowadays there are different ways to recycle composite materials and some of them are more developed than others. However, the use of recycled carbon fibres (rCF) is not that common in industry, mainly because of the lack of confidence in their performance when compared to virgin carbon fibres (vCF). In addition, there is a clear disadvantage: rCFs cannot be used for the same applications as what they were originally designed for. Because of this, I want to introduce some of the recycling techniques which are currently available for composites.

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