Brittleness and material behaviours

[Nanako]

hi all, I'm creating a physics based game. My design works by pre-fracturing objects into distinctive chunks at authortime, to prevent extensive processing later (some realtime fracturing will also occur, but that's unrelated).

So i have lots of walls that are made up of lots of little chunks, and my intention is to simulate things as such that the wall doesn't behjave like it's made of discrete chunks, just as one large piece of material (that conveniently fractures along those lines)

Anyways that's just context.

I want to ask for a 101 explanation of three different physical behaviours, and i also want to know how the property of Brittleness relates to them, and what other properties i might need to model these behaviours convincingly:1. Cumulative damage.
If you hit a steel beam hard (but not hard enough to bend it) with a sledgehammer, then you'll have no real appreciable effect. The impact is dissipated away, probably through vibration or minor deformation or somesuch, and the piece of steel is more or less unchanged.

But if you smack a lump of concrete with a sledgehammer (not hard enough to shatter it), it will typically lose little chunks, gain cracks, and generally decrease in structural integrity./ Making it easier to destroy with more hits of the same force.

Briefly explain this to me?2. Localisation of impacts
As far as I'm aware, when you hit an object ( say, a brick wall) the impact is dissipated across the surface/volume of the object, and thusly may cause lots of cracks along that wall until it eventually crumbles.

But when you hit that same object really really hard in a small area (for example, by firing an AP tank shell at it) you'll tend to punch a small hole right through, and leave most of the rest of the wall relatively undamaged.

How does this work, that harder impacts seem to do less overall damage to an object than ones it can successfully resist? And also why does this happen. Why for example, does the brick wall not implode inwards in an attempt to dissipate the incoming force evenly, and crumble into little shards of rubble.3. Reverberation.
Probably not a correct term, and probably strongly related to #2. Is there any way to meaningfully determine how likely/how far a material will spread out incoming forces? If I'm going to hit the middle of a wall with a million pascal, is there any way to meaningfully determine in then physical makeup of that wall, whether i want a hole punched through the middle, or i want the whole thing to resist and implode towards the impact point?

In terms of the context of my simulation, how can i meaningfully determine how much of the force applied to a chunk, should be transferred to the chunks it touches, and how should this force curve falloff with distance? how large muist a wall be for one part of it to feel nothing from an impact at the other end?
The concept of brittleness fits in here somewhere, I'm sure. But I'm not entirely clear on where.

Would an especially brittle material
Be more, or less capable of resisting cumulative damage?
Would it be more likely to have holes punched through it, or to collapse under massive stress on a small area?

Are there other material properties besides brittleness that govern these behaviours ? What are they?

 

[DEvens]

You need to do some homework. You could start with Wikipedia and go from there if that's not enough.

For starters, look up such terms as elastic deformation, plastic deformation, strain failure, fracture failure, crack propagation, and work hardening.

 

[Nanako]

hi x thank you, i have been doing lots of independant research, and will continue that, but I'm also here for more of a human touch. Accurately simulating every detail of physical interactions is of course, impossible. I mostly require assistance in translating real physics into efficient approximations. i'll read up on those topics

 

[ArthurMK]

For a better answer than what I can give read "The new science of strong materials: or why don't you fall through the floor?" by Jim Gordon, its a masterpiece and contians all the theory you need to know to explain this. Also, fair warning this may be a long reply.

Things underlined are things you should also look into yourself for more detail.

1. Metals have a different microscopic structure to concrete:

• Metals have a crystalline lattice structure which is ordered, within this structure there are defects such as dislocations and vacancies.
• Concrete is a ceramic so has an amorphous structure, with no clear order, and therefore no defects!

This means that when enough stress (force over a given area) is applied to a metal the defects mentioned above can move through the ordered lattice (think of it as train tracks) so can relieve the stress as they allow the metal to plastically deform into the shape that the stress trying to pull them in (e.g. bent or dented), this means that steel is tough,

Concrete on the other hand has no such mechanism to relieve stress, as atoms cannot move past each other in the way that dislocations and vacancies allow for, when you apply stress you are pulling the atoms themselves apart rather than moving them around. So once enough stress is applied the concrete simply cracks or breaks in a brittle manner rather than plastically deforming. So concrete is brittle.

Why I place emphasis on the word enough is that to plastically deform/break something you first have to deform it elastically any additional stress applied after its elastic limit will push a sample into it's plastic region, where metals deform (and eventually break too!) and concrete gives up and takes a break (sorry, too good to pass up on!).

Successive impacts will have a cumulative effect of the force each one exerts on the sample is above the elastic limit as the plastic deformation will remain. Once a metal sample is plastically deformed to an extent that there can be no more atomic shifting around it will break in the same manner as concrete.

It is also important to bear in mind that steel has a higher ultimate strength than concrete. It is a common mistake to get brittle/tough behaviours mixed up with the strength of a material. Brittle and tough are concepts related to the amount of deformation something can undergo without breaking. Strength is a measure of how much stress (force) something can withstand before breaking:

• Blu-tack is tough, but weak.
• Glass is brittle, but strong (relative to blu-tack).

2+3. NOTE: this is the limit of what has been taught to me/ I have learned, therefore I cannot offer any source material for the next two bullet points, but I am applying concepts I know well and see no reason for this to be untrue.

This can be explained by applying the concept of ultimate strength (how much stress a material can take without breaking), take the impact point of each blow (weak and AP tank shell) to be a single point on a wall of uniform material and density (specifically, not a brick wall, this will be explained):

• If the stress induced in the wall at the point of the hit is less than the ultimate strength of the material, then at that point the wall won't break. As the point is still intact some of this stress will be dissipated throughout the material. But it will be greatest at the point of impact, imagine it as a stereotypical mountain with the impact at the peak where stress is greatest and all around it the stress decreases with radius from the peak. This means that nowhere on the 'stress mountain' will there be a place where the material will break, as the impact point is the point of greatest stress and it's still standing.

• If the stress is greater than the US of the material at the impact then the material will break there, but it will not break instantly, so the stress will still be dissipated in the rest of the material in the same manner as before. The edge of the hole created is the radius at which the height of 'stress mountain' falls below the materials US. so with an AP tank shell there is a hole AND the wall is structurally damaged in the same way as above.

Why no brick wall? A brick wall is a composite, and the mortar is weaker than the brick. This means the mortar is basically an outline of where the wall is most likely to break so the whole 'stress mountain' uniform concept is more complicated and depends on the brick wall in question.

3 is too specific and i won't pretend to know what the relationship is, and in your research to ind out you may discover what I've said in the above 2 bullet points to be total rubbish! But that's science.

End questions:

• A brittle material is more susceptible to successive impacts, as they have a MUCH lower capacity for plastic deformation than tough materials.
• Answered by mixing 1 and 2 together.
• STRENGTH, STRESS, STRAIN, DEFORMATION (PLASTIC AND ELASTIC), BRITTLE/TOUGH. The last pair especially.

I hope that helps, again sorry for the long windedness!

AK

 

[Nanako]

Wow thank you arthur, I am still reading this, but i have a specific question

• If the stress induced in the wall at the point of the hit is less than the ultimate strength of the material, then at that point the wall won't break. As the point is still intact some of this stress will be dissipated throughout the material. But it will be greatest at the point of impact, imagine it as a stereotypical mountain with the impact at the peak where stress is greatest and all around it the stress decreases with radius from the peak. This means that nowhere on the 'stress mountain' will there be a place where the material will break, as the impact point is the point of greatest stress and it's still standing.

• If the stress is greater than the US of the material at the impact then the material will break there, but it will not break instantly, so the stress will still be dissipated in the rest of the material in the same manner as before. The edge of the hole created is the radius at which the height of 'stress mountain' falls below the materials US. so with an AP tank shell there is a hole AND the wall is structurally damaged in the same way as above.

This is a pretty nice answer, it's mostly what i suspected. However, it is missing the key detail. That is, How exactly does this "mountain" decline? Is it's slope a constant angle? Or must i define a maximum radius and have it decay linearly over that?Or should it decay exponentially?

 

[ArthurMK]

Thats where my knowledge ends unfortunately! although you won't go too far wrong with an exponential relationship. As long as stronger hits spread out more than weaker ones!