So what is the precise role that thickness plays in the resistance of a specimen to deformation or fracture during a collision?

[Physicist-Writer]

From Stress-Strain curves in static loading conditions, we know the stress in force/cross-sectional area that's needed to deform a material. So with a bigger specimen, there's also a bigger cross-sectional area so you need a bigger force to generate the necessary stress. This same concept should apply in dynamic loading/impact strength tests I believe. But thickness should matter too in terms of how much energy can be absorbed. Penetrating through 100 mm thick steel should be harder than going through just 10 mm steel. So where does this fit into the equation?

 

[Baluncore]

what is the precise role that thickness plays in the resistance of a specimen to deformation or fracture during a collision?

Thickness is important in absorbing energy by deformation. The rigidity of a material, and the force needed to deform it, is proportional to the cube of the thickness. By definition, too thick or too thin is a bad thing. Energy absorbed is equal to force required, multiplied by distance deformed.

From the point where deformation exceeds the elastic limit, the material yields, so crumpling of the material absorbs the energy of the impact. There needs to be a mix of rigidities, so impacts of different energies are absorbed. The aim is to maximise the time it takes for the impact to complete, since that reduces the deceleration suffered by the occupants or contents.

 

[Frabjous]

A stress-strain curve can be viewed as a material property (like an equation of state). Penetration involves the flow behavior of the material in which one needs to apply a force to keep expanding the bottom of the crater. For a thicker target, you need to apply this force for a longer time because you are going through more material. For most situations, this force is larger than the one one would expect from the stress-strain curve.

 

[Physicist-Writer]

Thickness is important in absorbing energy by deformation. The rigidity of a material, and the force needed to deform it, is proportional to the cube of the thickness. By definition, too thick or too thin is a bad thing. Energy absorbed is equal to force required, multiplied by distance deformed.

When would thickness be a bad thing aside from weight or cost concerns? I remember seeing a formula that related stiffness as the inverse of length, K= AE/L is that what you are referring to? I was a bit confused by that too now that you mention it. But thanks for mentioning that other formula regarding stiffness being proportional to the cube of thickness, that helps a lot.

From the point where deformation exceeds the elastic limit, the material yields, so crumpling of the material absorbs the energy of the impact. There needs to be a mix of rigidities, so impacts of different energies are absorbed. The aim is to maximise the time it takes for the impact to complete, since that reduces the deceleration suffered by the occupants or contents.

Ah yes, car crumple zones are indeed used to weaken the average force of the collision. Formerly people made cars that were too rigid, which protected the car but then what's the good of protecting the car if the occupants weren't kept safe.
But I guess for most inanimate objects where people aren't involved, wouldn't rigidity be generally better?

For a thicker target, you need to apply this force for a longer time because you are going through more material. For most situations, this force is larger than the one one would expect from the stress-strain curve.

Ah, so it's a combination of increased thickness to overcome and also naturally have to maintain that force for a longer time just to get through the length of the thick material.

 

[Baluncore]

This discussion is too general, there are too many unspecified equations.

When would thickness be a bad thing aside from weight or cost concerns?

When the material is so thick that it remains elastic, the impactor bounces off the target, which reverses the velocity of the impactor, and so doubles the impactor acceleration. Only structural material that reaches the plastic zone can yield and absorb the energy of a collision.

But I guess for most inanimate objects where people aren't involved, wouldn't rigidity be generally better?

Paper wraps rock.

Alternating sheets of different material are often better than one thick layer. There is an acoustic reflection from each change in material properties.

Ah, so it's a combination of increased thickness to overcome and also naturally have to maintain that force for a longer time just to get through the length of the thick material.

It is a matter of absorbing energy in a continuous way that maximises the deceleration time.

Energy, or work done, is force times distance. The distance is the dimension of the crumple zone, while the force is proportional to the cube of the thickness of the material that is being bent in that zone.

 

[Physicist-Writer]

This discussion is too general, there are too many unspecified equations.

Then we can specify it more. The gist is I'm trying to get an overview of what happens in a collision between objects when accounting for both material and shape quality, a mental model I can then use for any situation.

For example, say there's a cubic block of gold and a cubic block of iron, and you toss both at each other, who wins that clash and in what way(s)? Well gold is weaker than iron in almost every way, but if we assume the gold block is much thicker than the iron block, then it's gonna be much heavier in mass (gold denser than iron as it is) and presumably if they were thrown at the same speed but from opposite directions at each other, the gold block would push away the iron block, but then my question mark would be who gets deformed more, when factoring in that the gold block is thicker.

When the material is so thick that it remains elastic, the impactor bounces off the target, which reverses the velocity of the impactor, and so doubles the impactor acceleration. Only structural material that reaches the plastic zone can yield and absorb the energy of a collision.

Ah, gotcha, thanks for clarification.

Alternating sheets of different material are often better than one thick layer. There is an acoustic reflection from each change in material properties.

Oh, so that reduces energy more?

 

[Baluncore]

... but then my question mark would be who gets deformed more, when factoring in that the gold block is thicker.

Your gold block would "mushroom" out slightly at the contact with the iron, like the head of a chisel that you hit with a hammer. The size of the mushroom will depend on the mass of the materials and the square of the speed difference.

Following the collision, the heavier gold would continue moving in the same direction, initially carrying the smaller iron block with it, but then pushing the iron ahead as the remaining elastic energy in both materials is released.

 

[Physicist-Writer]

Your gold block would "mushroom" out slightly at the contact with the iron, like the head of a chisel that you hit with a hammer. The size of the mushroom will depend on the mass of the materials and the square of the speed difference.

Following the collision, the heavier gold would continue moving in the same direction, initially carrying the smaller iron block with it, but then pushing the iron ahead as the remaining elastic energy in both materials is released.

Yes I see, but as you raise the speeds though, there comes a point where the materials may begin to plastically deform.

 

[Baluncore]

Yes I see, but as you raise the speeds though, there comes a point where the materials may begin to plastically deform.

Elastic deformation will leave no trace, as that part of the collision is elastic.
I was writing about the plastic deformation.

The thin layer of gold against the contact, has the most weight behind it, so will deform most. That permanent "mushroom" is the result of plastic deformation, close to the face impacted by the hammer or iron block.

https://en.wikipedia.org/wiki/Chisel#Cold_chisel
"The head of the chisel is chamfered to slow down the formation of the mushroom shape caused by hammering and is left soft to avoid brittle fracture splintering from hammer blows."

 

[Physicist-Writer]

Elastic deformation will leave no trace, as that part of the collision is elastic.
I was writing about the plastic deformation.

The thin layer of gold against the contact, has the most weight behind it, so will deform most. That permanent "mushroom" is the result of plastic deformation, close to the face impacted by the hammer or iron block.

https://en.wikipedia.org/wiki/Chisel#Cold_chisel
"The head of the chisel is chamfered to slow down the formation of the mushroom shape caused by hammering and is left soft to avoid brittle fracture splintering from hammer blows."

Ah gotcha, sorry misunderstood a bit. But what about the iron, how much is it's deformation at higher speeds? All else equal I'd expect the iron to take less deformation than gold, but in this case the gold block is supposed to be the thicker overall object, so I'm still a bit confused on that.

 

[Baluncore]

All else equal I'd expect the iron to take less deformation than gold, but in this case the gold block is supposed to be the thicker overall object, so I'm still a bit confused on that.

It takes less force to deform gold than iron, so iron may be protected by the gold. A copper hammer protects the steel objects it hits, by deforming first.

The concept of a "thicker overall object" is quite meaningless in a technical discussion. I assumed the contact took place between the ends of two prisms having the same section, just that the gold weighed more, and could be a longer prism.

 

[Physicist-Writer]

It takes less force to deform gold than iron, so iron may be protected by the gold. A copper hammer protects the steel objects it hits, by deforming first.

The concept of a "thicker overall object" is quite meaningless in a technical discussion. I assumed the contact took place between the ends of two prisms having the same section, just that the gold weighed more, and could be a longer prism.

So yes, the cross-sectional areas of the iron and gold would be equal if the gold is a longer prism, but i thought being longer meant being thicker. so what does thickness really refer to and not refer to in non-colloqiual language here? For example you mentioned that formula that stress is proportional to the cube of the thickness earlier.

 

[Baluncore]

For example you mentioned that formula that stress is proportional to the cube of the thickness earlier.

That is the force needed to bend a sheet of material, having that thickness.
The body panel of a vehicle, or a sheet of paper that is being wrapped around a rock.

 

[Physicist-Writer]

That is the force needed to bend a sheet of material, having that thickness.
The body panel of a vehicle, or a sheet of paper that is being wrapped around a rock.

I see, but still not quite understanding the difference, if the gold block is thicker, and has the same length and width as the iron block then why would the thickness (what you referred to as being a longer prism) not matter?

 

[Baluncore]

If the gold prism is longer, it will weigh more, and so have more kinetic energy. But you are not bending the gold prism like a sheet of material, you are flattening and spreading one end only.

The cubic function is related to bending sheets or bars, not mushrooming the ends.

This subject is too big to discover by trial and error.

 

[Physicist-Writer]

If the gold prism is longer, it will weigh more, and so have more kinetic energy. But you are not bending the gold prism like a sheet of material, you are flattening and spreading one end only.

The cubic function is related to bending sheets or bars, not mushrooming the ends.

I see, that helped clarify it.

This subject is too big to discover by trial and error.

Is it? I'm just looking for an overview to form a conceptual mental model. You've clarified most of it I think There's always more nuances to learn that I'm sure even experts in the field are still learning. So a conceptual, common sense understanding is fine, but I still need to see what the whole forest looks like from a helicopter view, even if I can't see every detail of the trees and leaves from that distance, if you catch my metaphor.

 

[Baluncore]

You've clarified most of it I think.

https://en.wikipedia.org/wiki/Dunning–Kruger_effect

 

[Physicist-Writer]

https://en.wikipedia.org/wiki/Dunning–Kruger_effect

No? There's a difference with accepting you're not gonna be an expert on something, but still having a middleground, common sense understanding

I'm not claiming to know everything to know more than I do, just that most of it should be clarified for a common sense understanding, unless you're holding back more info. Where would you draw the line here?

I'm not ever gonna be a Ph.D. in this subject, so does that mean I can't become competent enough to understand on a basic level what are the most important variables for most collisions I may see in every day life or may want to write a fiction about.

 

[Baluncore]

You cannot know what you do not know.
You are confused and do not yet have a common sense understanding.
You are overconfident.

Where would you draw the line here?

Where you say: "I need to read more before trusting my head or my hand".

 

[Physicist-Writer]

You cannot know what you do not know.
You are confused and do not yet have a common sense understanding.
You are overconfident.

And even experts with graduate degrees don't know everything. So again, where are you drawing this line? When is a common sense understanding reached?

Where you say: "I need to read more before trusting my head or my hand".

How much more needs to be done? I asked you if you were holding back the forest, or more information and you don't seem to be addressing the point.

 

[Baluncore]

And even experts with graduate degrees don't know everything.

The experts know how little they know, and doubt everything.
When referred to as experts, they shrink like imposters.

I asked you if you were holding back the forest, or more information and you don't seem to be addressing the point.

I did when I wrote:

This subject is too big to discover by trial and error.

We have only scratched the surface of your minimum single case.

I don't have the time to rein you in, on a continued rampage into the subject. You need to read the books and demonstrate humility.

 

[Physicist-Writer]

The experts know how little they know, and doubt everything.
When referred to as experts, they shrink like imposters.

And they are still experts though, enough to be considered knowledgeable in the field and have an advanced understanding even if there are gaps or nuances that are subject of further investigation.

We have only scratched the surface of your minimum single case.

You need to read the books and demonstrate humility.

How much??? I'm not getting a degree in this subject, that does not mean a person cannot gain a "common sense " understanding. Just as like someone can have the "common sense" about how magnetism works even if you can always learn more and more nuance the full story since quantum mechanics is a thing, but for a "common sense" understanding, quantum mechanics is not necessary. Why does everything need to be a deep dive to have a general conceptual understanding? The people who became experts in a field sacrificed time learning about everything else, but that does not mean they don't have common sense. I barely know any of the intricate details of a car works, I'm not a mechanic, but that still doesn't stop me from knowing basics.

I don't have the time to rein you in, on a continued rampage into the subject.

Then just say that then instead of expecting someone to just drop everything and get a whole 4 year degree in the subject, which is not realistic for everyone. Most people are content with the limited education they got in high school, I just asked for a little more than that to understand a relatively simple example.

This is not my primary field of study, but I wished to learn a bit more, and felt I'm at a satisfactory point for my requested level of understanding, if there's something more high-level I'm missing, sure, I'd want to know, but I'm not doing a deep dive, I don't have the time to do that, if I did I'd just sign for the course and go through it all and do another 4 years of college.