# Fracture Energy for JH2 Model (Ceramics and FEA)?

Ozen
This is a bit of a multi-part question on impact engineering and FEA usage.

I am working on making my Alumina ceramic model as accurate as possible in ANSYS for impact simulations. But I am noticing a common theme, while using model parameters in scientific journals I am not getting any cracking in the simulation. The ceramic has localized failure but there are no cracks or wide spread failure. This does not seem to be accurate because Alumina does shatter into fragments from a bullet impact. Yet is I run the model against a soft core bullet, there will be cracking or breaking, it will fully repel the bullet. The material parameters are correct, I've looked them over many times, and the values used are the standard set by a peer reviewed journal. So I am left with two ideas: 1) according to the impact engineering book my professor sent me pictures of, in compression ceramics are more resistant to the micro cracks already in the structure and the addition of new micro cracks doesn't effect the compression strength. This allows the compression strength to be much closer to the theoretical strength of a perfect ceramic. 2) Perhaps adding a crack softening failure model into the material properties could give more realistic simulations.

I believe 2) is the correct path, but I may be wrong and the simulation could be accurate and just unable to simulate fractures like in reality.

The second part of this question/problem, is the value to use for the crack softening failure model. It wants a fracture energy (strain energy release rate) but I only have fracture toughness values. I have a fracture toughness value of 3.0 MPA m^1/2, which is K_IC. The only equations I found linking fracture energy (G) is G = (K_I)^2 / E. E is for if E is given as plain strain, therefore E = E / (1 - v^2). K_I >/= K_IC. K_I is the Mode I stress intensity factor.

So, would I just use K_IC = K_I since I have no other data? How reliable would this be? Furthermore, I would have to calculate E according to the equation, right? Since you can't measure plane stress but you can measure plane strain, and that would be the value I get from the Shear Modulus and Bulk Modulus.

What do y'all think of this odd situation? Is option 1) or 2) correct? And how would I calculate the fracture energy G?

FEAnalyst
I have some experience with simulations involving dynamic fracture of ceramics but I use Abaqus. That software has a built-in brittle cracking model (known as Hillerborg's model in the literature). With VUMAT subroutine it's also possible to implement other models, such as the crack delay model proposed by J. Pelfrene (check his article "Fracture Simulation of Structural Glass by Element Deletion in Explicit FEM", it can be useful for you). Thanks to the element deletion functionality in Abaqus it's possible to simulate the actual fracture where the sample breaks into pieces after impact.

I don't know what features Ansys offers for such analyses but with its acquisition of LS-Dyna simulations like that shouldn't be a big problem. I know for sure that element deletion is implemented in this software and I'm just not sure what material models it offers.

Ozen
I have some experience with simulations involving dynamic fracture of ceramics but I use Abaqus. That software has a built-in brittle cracking model (known as Hillerborg's model in the literature). With VUMAT subroutine it's also possible to implement other models, such as the crack delay model proposed by J. Pelfrene (check his article "Fracture Simulation of Structural Glass by Element Deletion in Explicit FEM", it can be useful for you). Thanks to the element deletion functionality in Abaqus it's possible to simulate the actual fracture where the sample breaks into pieces after impact.

I don't know what features Ansys offers for such analyses but with its acquisition of LS-Dyna simulations like that shouldn't be a big problem. I know for sure that element deletion is implemented in this software and I'm just not sure what material models it offers.
Thanks for the source, I'll check it out when I have time!

In ANSYS, I use Explicit Dynamics (AutoDyn) instead of LS-DYNA. While I have a key for LS-DYNA, it is confusing to work in while I can use explicit dynamics directly in workbench and streamline my work. The material models I use are the Johnsom-Holmquist 2 strength and failure model and the Polynomial EOS. The JH2 models the ceramic strength, damage, and failure behavior. When an element fails, it gets automatically deleted from the model.

Here is a link showing an alumina plate penetrated: , skip to 9:00 min. Below is the alumina model.

This model is the only one that has the back side failure larger than the front side. But it erodes the SiC tip much faster, so i question its accuracy (SiC is stronger and much harder than Alumina). The other models show a through hole with additional elements deleted around it. But none of the models look like the hole in the video. Hence why I think the material model may be incomplete with just JH2 and Poly EOS.