When using Finite Element Analysis (FEA) for studying composite materials, one of the most used failure criterion is the one which was proposed by Hashin in 1980. This theory is included in all the main FEA packages and, probably, you are more than familiar with this particular model. However, what you might not know is that the failure criteria that you are defining is not exactly the Hashin’s one. If you want to know why, this is your place.
Since the available failure criteria at that point presented some inconsistencies, in 1980 Hashin developed a new criteria which differentiated between failure modes. His theory considered four different ways in which the material could fail:
Failure criteria for composite materials are usually classified in two categories: non-interactive and interactive theories. In literature, you can find that the main non-interactive failure criteria are the Maximum Stress Theory and the Maximum Strain Theory. However, one question arises: is the second one a non-interactive theory in reality? Let’s figure it out.
To begin with, a non-interactive failure criterion is that one which only takes into account the effect of one stress or strain component for each failure condition. In other words, it does not consider any interaction between the different components. For example, the Maximum Stress Theory considers that the material fails when one of the stress components reaches a maximum value. Hence, considering a sample loaded in tension:
Where subindex 1 refers to the fibre direction and 2 corresponds to the transverse direction. When the stress reaches the limit value (measured experimentally under uniaxial stress conditions), the material fails. It is clear how in that failure criterion only one stress component is considered for each condition.
Every time you use Finite Element Analysis you need to assign a material model to all the components. Since there are plenty of them, one question arises: which one should you use for your particular case?
To begin with, there might be more than one material model which can provide an accurate solution to your problem. However, it is likely that one of them will present some advantages when compared to the others, such as computational time or the number of parameters which have to be defined. When you have spent time working with a certain kind of material (e.g. metals) you will have gained some experience that will help you choosing between different options whenever you face a similar Finite Element model. But, what happens when you are new and you don’t know where to start?