Greetings Qiaobing Xu,

Thank you!

My model is aimed specifically at describing the ductile failure mechanism. This mechanism is characterized by large amounts of plasticity and is common for many structural metals (e.g., aluminum and steel). However, some metals (e.g., tungsten) are more brittle and do not fail by the same mechanism, which means that my model would not describe its failure well. For the range of metals that do undergo ductile failure, my model is simply applied by changing the matrix properties and initial void volume fraction of the micro-scale model.

There are many models used to describe the failure of metals:
-Models that specifically tackle ductile failure include: the Brown-Embury model, the Thomason (limit load) model, and modifications to the Gurson model to account for failure (most notably the work by Nahshon and Hutchinson). The advantage to using my model instead of the aforementioned models is that my model offers a robust and complex description of failure that does not use any fitting parameters (i.e., my model makes predictions based solely on the observable microstructure).
-Other models, such as the Mohr-Coulomb failure model, could be used for more brittle materials.

Additionally, the entire field of fracture mechanics is devoted to these type of problems. Specifically, linear elastic fracture mechanics are commonly used for brittle materials. Non-linear fracture mechanics are more complex and are needed for applications to ductile materials.

Let me know if you are interested in knowing more about any of the models in a more specific context,
-Geoffrey

Hello Aparna Baskaran,

Thanks!

To clarify, the macroscopic model does also include an elastic-plastic material response (based on the Gurson constitutive model).

The large scale model in general is relevant for elements on the “structural component” level. More exactly, the notched bar I show in my video and poster has dimensions in the millimeter range. Larger sizes are also relevant here. Because an underlying assumption in my macro-scale model is that many voids contribute to failure, the macro-scale model must be much larger than the void size.

The size of the micro-scale model is on the order of 10s of microns. Yes, you are indeed correct that as we approach smaller scales other atomistic effects become important. In fact, other members of my research group have investigated this more closely. They found, through atomistic simulations, that sub-micron sized voids are resistant to growth until very high stresses or temperatures are reached.

On the scale of my void models, however, other effects may be still be important. Because my micro-scale models are on the order of the grain size (at least for my test material), the isotropic plasticity model I use may be too simple. Other researchers have shown that anisotropic plasticity affects the growth and coalescence of voids. Therefore, we may consider the use of a plasticity model, which can better account for crystal orientation in the future.

Finally, I use the word ‘multiscale’ to mean that I am using simulations conducted at a micro-scale to inform my simulation at the macro-scale. In essence, my model uses information from two different simulations, each of which corresponds to a different scale. This is what I meant by ‘multiscale.’

Let me know if I can further clarify anything,
-Geoffrey

Hi Natalia Noginova,

The colors in the videos of the macro-scale model (like the cover image of my video) represent damage i.e., how close an element is to failure. You’ll notice that at the beginning of loading all elements are blue (undamaged) and that just before each element fails it is red.

We do not take into account the possibility of self heating or any other temperature effects. Our assumption is that at our slow strain rates (quasi-static) and at stresses on the order of 100MPa that temperature effects will be small.

Finally, because the plasticity models we chose for our micro- and macro-scale models are rate independent, our results assume a quasi static loading. In order for us to match experimental results that show the rate sensitivity of failure, we could change our plasticity models to a rate dependent formulation. Inertial effects of void growth would already be included in our model because of our use of an explicit dynamic FE framework. This is an option for future refinement of the model, though we hope to better match results at quasi-static rates before we venture down that path.

Thanks,
-Geoffrey

Hello Qi-Huo Wei,

Yes, we do assume that elastic properties of the material is independent of loading (i.e., that the material response is elastically isotropic). On the macro-scale model we base this assumption on the fact that the grain size is small compared to our elements and that the grains would be randomly oriented. On the micro-scale this assumption does not hold because the size our entire micro-scale model is about the same as the grain size (specifically for our aluminum test material). But because our test material is aluminum and the elastic anisotropy factor is relatively close to 1, the assumption is still valid. The role of anisotropic plasticity is believed to be much more important; I addressed this briefly in my response to Aparna Baskaran’s question in case you are interested.

Defects do play a role in ductile failure. It is from micro-scale defects such as inclusions, precipitates, and even grain boundaries that voids nucleate. Larger scale defects, such as cracks, also effect ductile failure based on how they change loading (e.g., stress concentrations).

Thank you for the questions,
-Geoffrey

Greetings Hyunjoon Kong,

The voids considered in our model are on the order of 10 microns.

I sure hope so! Because lack of material heterogeneity is the main source of error in our model, we hope to tackle this first.
We have done tests on unit cells with different sized voids and saw that we would need to increase the size of the voids by 400% in order to match experimental results. These tests still assumed a constant void size (for each simulation) but we think it represents a rough estimate of the effect of void size.

There are some experimental and a few computational works in the literature that lead us to believe the heterogeneous spacing of the voids is actually more important that void size effects.

We may at some point try to model cells with multiple voids (of varying sizes) at once and see how this effects our results. But first, we would like to look more closely at void spacing effects.

Thanks and let me know if you have any more questions,
-Geoffrey

Thanks Eamonn!

-The sizes of the microvoids I simulate are on the order of 10s of microns. And yes, I assume that the voids are ‘pre-existing’ in the material; this assumption is based on the fact that voids normally nucleate from inclusions/precipitates and that they nucleate early in loading. At this scale we do not have to worry about molecular effects.

-Yes, I assume constant microvoid size/distribution in the macro-scale model.

-The latter case. I use the micro-scale models to construct a failure criterion which relates stress state to failure.

-I have done a few simulations on cells with 2 and 3 voids, but I have not done a systematic comparison. There are two main problems with increasing the number of voids: 1) the computations become computationally demanding, and 2) the methods needed for these larger simulations add an element of error (which grows with number of voids) to the results.

-I’m happy to answer questions. Please let me know if there is anything else you are curious about.

Hey Asal,

So the first thing to understand is that the voids often initiate from particles in the material. For instance in some aluminum alloys you might add magnesium, but as you load the material, included magnesium particles can create voids (either by particle cracking or by separation from the aluminum matrix).

The addition of these alloying particles can improve many mechanical properties of the metal (such as increasing yield stress) but may decrease its resistance to failure. So we actually have to strike a balance between the positive and negative effects of the particles. I believe my research will be useful in finding this balance.

And yes, temperature as well as deformation will affect void growth. Creep and fatigue will contribute to void evolution as well.

Thanks for the questions!

Hello Elizabeth,

I believe my response to Asal’s question above will be helpful in answering some of your questions.

In general, voids can initiate at any place in the material that is not homogeneous. The voids initiate because deformation of the material is not constant. This usually comes in the form of particle inclusions that are harder or softer than the material around them.

Yes, their number has been investigated in several materials, but it is most often referred to by the volume fraction. Volume fractions of .5% to a 5% would be normal for many structural metals. One of the newer ways to find this information is by use of X-ray tomography, which is similar to giving a chunk of metal a CT scan.

Thank you for the interest in the topic, and let me know if you are still curious about anything else.

thanks! it is very clear. Fascinating stuff to attract students and encourage them to go into materials science and related topics. Hope that you get an award!

Good question Carlos,

The traditional cup-cone fracture surface occurs for many reasons. One of which is that as the crack propagates, the stress state in the remaining material changes dramatically. This effect is specifically what my research hopes to quantify. In essence, you see two failure modes occurring: one occurring due to normal stresses (near the center) and the other due to shear stresses (on the ‘sides’ of the cup). Based on the specific material in question the amount of the material that fails due to each mode changes.

The material that I model in my video/poster will exhibit cup cone behavior; however, due to the geometry (i.e., the notch) in the test specimen I show, it occurs only slightly very near the surface. In my research I am more concerned with the initiation of the crack, but in theory if I were to try to capture this phenomenon I could simply refine my mesh in that surface region.

Very cool, thank you for the edification!

Voids, as I refer to them, here are regions of empty space on the order of 10 microns large.
Dislocations, which are defects in the crystal structure, are much much smaller (approximately 100,000 times smaller). And while it is possible for many dislocations to pile up and create larger voids, it is unlikely to see that play a part on the scales I look at.

No, Jeffrey, unfortunately no one in my group currently works on in-situ characterization of voids. Some of the data that I have used in setting up my model has come from published works using xray imaging; however, the published data is usually quite limited. For this reason I also believe that a collaboration with that field would be invaluable and I may start looking for collaborators in the near future.