I've read that the strength of a material is unaffected by thickness - the amount of force per unit area it can withstand before failing is only dependent on the material in question, and not how thick it is. Is this really true? It certainly seems counter-intuitive, and if it is true, why do submarine hulls for example need to be thick? Wouldn't a thin sheet be able to provide the same strength? Or is the thickness just needed to provide rigidity (i.e. a thin hull would collapse under the pressure, but would still keep the water out)?
It really depends on the material in question and what kind of stress it experiences. There's also different metrics of strength: compressive strength, flexural strength, tensile strength, etc. Submarines are under a lot of pressure. More material does mean more rigidity and therefore modifies its strength properties (you'll have to google flexural strength to see the mathematical relationship).
Think of breaking a thin piece of glass, like a microscope slide. It's pretty easy to do. Now picture glass with the same aspect ratio, but significantly thicker -- it would be harder to break.
I think you mean length, not thickness, the Pa it can withstand is generally proportional to its thickness even if just because its mass per unit area is proportional to its thickness
Assuming you had a uniaxial force and your definition of strength was the yield strength, then yes, this is not dependent on the thickness of the material.
However, a submarine would have to be completely flat for this to mean what you seem to think it means.
>However, a submarine would have to be completely flat for this to mean what you seem to think it means.
Would a submarine in the shape of a rectangular or triangular prism count as "completely flat"?
>the Pa it can withstand is generally proportional to its thickness
I don't think it is. Yielding happens at the microstructural level, and each part of the object will be experiencing the same pressure, so I don't see how the mass per unit area or thickness comes to play in that.
However, there are other considerations for material properties other than yield strength, some of which do depend on e.g. the volume, like the ability to withstand impact and dissipate energy without fracture.
Not the anon you're replying to, but no. If the shell encases a cavity of air, then under compression there's an increased degree of freedom for the material to collapse into, and fail. Flat *sides* on something like a prism would compromise the structural integrity of the system because at the center of each side, the material will be the most susceptible to failure under stress (external forces are not applied evenly) and the material will want to collapse inward. Spheres and ellipsoids behave well under compression because they're largely uniform and external forces are distributed more evenly -- like the old trick where squeezing an egg in the palm of your hand doesn't result in breaking.
No, I meant flat as in a single plane.
Do keep in mind that, if your object is hollow, then the sides must withstand the force on the top and bottom faces, at which point you do want significant side thickness to make sure there's enough area there to not exceed pressures at which yielding occurs.
It actually has a DECREASING fracture strength with increasing thickness, due to statistical effects; a thicker piece of material is more likely to have a defect that will cause a stress concentration, leading to crack initiation sooner.
If you assume a perfect material, then yes, strength is independent of thickness.
Mechanical Engineer in his final semester here, you're all misunderstanding the basic concept here. I'm going to word this as generally as I can because I don't feel like getting into deeper detail.
Force per unit area is stress. It's also pressure, but for the purposes of mechanical failure, we refer to it as stress.
Materials have many properties. One of these is the point of deformation where yield occurs, and another is the point of deformation where ultimate failure occurs. Deformation here is referred to as strain, which is simply any change in shape/size. In other words, how much a material can be stretched/bent/compressed before it breaks is a material property.
Strain occurs when a material undergoes a stress. How much much strain occurs for a given stress is a material property, and, for the purposes of a basic explanation is mostly a linear relation up until yielding, which we refer to as Young's Modulus. The relation is defined as Stress = Strain * Young's Modulus. Young's Modulus is a material property. Stress is how much force per unit area the structure is experiencing, and strain is how much it changes shape as a response to this. If strain becomes to large, the structure fails.
>Why does a submarine need thickness then?
Because crudely drawn pic related.
(continuing to part two)
Let's say you have two 6in long samples of annealed 302 stainless steel. One sample is 1/2in in diameter, the other is 5/8in.
The tensile strength of the MATERIAL is 75,000psi. This does not change with the thickness.
The tensile strength of the SAMPLES are 18,750lb and 29,297 respectively.
If you made a diving board really thin, it would break upon a person standing on it.
If you made a diving board at the current normal thickness of diving boards, it'd noticeably flex (which is strain) under a person using it, but do not yield nor fail.
If you made a diving board really thick, it would experience very little strain under a person's weight, and wouldn't noticeably flex at all.
Submarines feeling waterpressure is the same idea. The force is staying the same, and while the outer surface area is staying the same, the stress is not, because the outer surface area isn't the area being affected by the force. This is because you are bending it. The surface area shown facing you in the top picture is the area that the force is being applied over, not the outside. So making it thicker increases the surface area, decreases the stress, thus decreasing the strain, thus preventing failure.
Now this can be a bit confusing in the case of a submarine since it's a water pressure being applied, so let me elaborate the best that I can.
You have a given water pressure for your depth. This pressure is defined as force per unit area of the outside of the hull. This means that any area X will have the same force applied on it. This force is trying to bend that area inwards. As such, the stress here is a function of the thickness. More thickness means less stress, less stress means less strain, less strain means we it doesn't fail.
I apologize if I explained this poorly in my rambling. I'd recommend just reading about Statics as a whole if you want to know more. I purposefully avoided more complex topics like what yielding actually is, or comparing engineering stress&strain to true stress&strain.
I honestly only skimmed the thread, but it legitimately sounds like a lot of people here are using words that are mostly correct without understanding what they're talking about.
>it really depends on the material in question
The material would never change what dimensions matter, the material only determines what those dimensions need to be.
>I don't see how thickness comes into play
I've already explained thoroughly that thickness defines the cross sectional area, is one of two parameters (alongside the outside force) that defines the stress here.
The Young's modulus and yield strain of a material are material properties. These two define the yield stress, which is then effectively a material property. This is not dependent on any dimensions of the material, nor does it depend at all on the force being applied, because it is a property.
Stress here is a function of the cross sectional surface area, of which the thickness is a dimension. This means that a thinner submarine will give a greater stress with the same force being applied.
I'm honestly a bit unsure what you're trying to convey with this completely flat thing. A flat piece of material would still undergo compression underwater and the thickness would still matter, most materials just happen to have higher yield strengths under this sort of compression that they do under bending. A theoretical planar material with zero thickness would fail instantly.
Also, yield is not the end all, a material can yield without failing, it's just generally desirable to not yield, especially in the case of something like a submarine.
Actually, I think I misworded that last part, let me be more clear.
The stress perpendicular to a plane (red) would not be a function of the thickness.
The stress in blue would approach infinity as the thickness approached 0 since we have Force / Height*Thickness.
The stress in green would approach infinite as the thickness approached 0 since we have Force / Length*Thickness.
The plane would fail instantly underwater, where force occurs from all sides.
I said the material matters because it does. Certain materials have physical structures which make it best for handling tension or compression, etc. Like bending a piece of glass. The concave side does fine under compression, but the surface features of the convex side propagate cracking under tension and therefore failure. Maybe that tidbit was largely irrelevant to OP's question, but I was just trying to highlight the variability in reference frame of these kinds of questions.
The material matters in determining whether or not the structure will fail, absolutely.
The stresses are only functions of the force and dimensions. The material does not matter in defining the stress, only in defining what stress is acceptable, and what the results of the stress are, including the strain experienced from these stresses, and whether or not yield/failure occurs.
The material might change what the LIMITING dimensions of failure are, if that's what you're implying. I didn't understand that clearly from your original post.
For example, concrete is good under compression, but worse under tension. Steel on the other hand, handles both compression and tensions similarly. But neither material defines what dimensions are relevant in determining the amount of compression/tension being experienced. The material determines the results of the stress.
But for the purposes of saying that your original post is "wrong", no material would ever make it such that the thickness of a submarine didn't matter. Material determines what the thickness needs to be, but only an infinitely strong material would allow for a 0 thickness.
>the amount of force per unit area it can withstand before failing is only dependent on the material in question, and not how thick it is. Is this really true?
That's obviously absurd. A one atom thick material doesn't resist the same force as a 2 inch thick sample of the same material. This notion is grounded in simplified, ideal cases of material science which do not actually exist in nature. I think the only cases where this is may actually true are with monatomic crystalline salts, where the rigid, completely non-malleable structure cannot be warped and only breaks.
>the amount of force per unit area it can withstand before failing is only dependent on the material in question
>if it is true, why do submarine hulls for example need to be thick
force PER UNIT AREA is constant and independent of thickness and geometry
does "normalized quantity" ring any bells?
>A one atom thick material doesn't resist the same force as a 2 inch thick sample of the same material
no shit sherlock
you have to multiply the cross sectional area with the force per unit area to get the actual force which the geometry of the given material can withstand