# Force required to indent a volume of material

• I
• Physics quest
In summary, the conversation discusses a theoretical physics question about the force required to create an indentation of a certain size in an object. The question involves visualizing 3 4 meter by 4 meter cubes made of granite, brass, and iron, and determining the factors and formula needed to calculate the force needed to send a chisel with an area of 43 square inches into each block 7 inches deep. The conversation also mentions a formula provided by an acquaintance, but notes that it only gives the required force to indent, not the force to create a certain volume of indentation or factor in the material inside the blocks. The discussion also touches on the complexity of the problem and compares it to piercing armor. Later, the conversation delves into
Physics quest
Hello folks and happy holidays!

So I have a theoretical physics question for everyone, I am simply very interested in this subject and would like to know more about how to find, mathematically speaking the force required to create an indentation of a certain size in an object based on known numbers or estimates on the material, the area and volume etc.

For this theoretical question I have visualized before me 3 4 meter by 4 meter cubes, one is made of granite, the other is brass and yet another is iron.

Now, what factors do I require, and what formula would be most efficient for a laymen (in math and physics in general) such as myself to find out how much force I need to send a chisel with an area of 43 square inches into each object 7 inches deep? The Chisel has a volume of 71 inches cubed.

Taking into account all the material I have to move inside these solid blocks to get that many inches in, and the force required to succeed in one attempt. So to summarize, a chisel of previously mentioned dimensions is being struck 7 inches into a solid 4 meter by 4 meter block of granite, brass and iron and I want to know how much force that would be required in Newtons.

I thought I would also include some things I have found out by myself and others can correct me on my workings so far, as I said I am not that experienced at this sort of thing. An acquaintance of mine gave me a formula that goes as follows;

area (43 inches square) transferred into meters square and multiplied by the hardness of a material, my contact said 490 MPa for Iron, 200 MPa for brass would give me a figuire that when multiplied by 1 million would leave me with Newtons required to indent an area of said material.

But unless I am mistaken, this would only give me the required force to indent to begin with, not the required force to create an indentation of a certain volume, nor would it factor in the material inside the solid blocks that may be moved by moving said volume/area of material?

If anyone has a formula or a source on how to work this out I would be very much appreciated. The general request can be simplified down to if anyone has a good formula or calculation to find force required for such an impact on said materials. The visual aid of blocks and a chisel is just my way of considering the problem.

Many thanks to all, and happy holidays again!

Last edited:
Oh wow. This is not a simple problem to answer at all. Some aspects such as the pressure at the tip of the chisel can be calculated at least approximately in closed form. However many aspects, in particular the way the material gives way are both empirical, and nonlinear. They are modeled as coupled differential equations and "solved" (or perhaps modeled is a better word) numerically using finite element analysis.

FactChecker
Most chisels achieve hardness at the expense of being brittle. The chisel would soon break.

Technically, the problem you state is similar to a military weapon piercing armor. Research armor piercing to learn more.

it also sounds like this http://fable.wikia.com/wiki/The_Sword_in_the_Stone

Cutter Ketch said:
Oh wow. This is not a simple problem to answer at all. Some aspects such as the pressure at the tip of the chisel can be calculated at least approximately in closed form. However many aspects, in particular the way the material gives way are both empirical, and nonlinear. They are modeled as coupled differential equations and "solved" (or perhaps modeled is a better word) numerically using finite element analysis.

So the problem is extremely hard to even estimate would you say? oh bother, unfortunate. Do you not need force to calculate pressure?

Thank you for your response all the same.

anorlunda said:
Most chisels achieve hardness at the expense of being brittle. The chisel would soon break.

Technically, the problem you state is similar to a military weapon piercing armor. Research armor piercing to learn more.

it also sounds like this http://fable.wikia.com/wiki/The_Sword_in_the_Stone

Ah yes haha, in the case of my question though for the sake of argument let's say the Chisel does not break or have any damage to it perceivable after it has impacted the material.

Thanks Nidum, looked over your thread and found those posts quite informative. So concerning my question in my opening post, what information would I need to work out force required to indent a volume of metal in one hit?

The press machines mentioned in your thread seemed somewhat like what I am considering. To be more specific, let's discuss a single scenario since I gave a few in my opening post, let's go with a a "press" with an area of 43 inches square making an indentation equal to its volume (71 inches cubed) 7 inches into a solid iron block with a volume of 64 meters cubed. I guess the press could have a cone/rhino horn sort of shape to it, with the point going into the metal.

Imagine if you will the block is a perfect cube of iron, and this press machine is stamped quickly, within a few seconds into the block to create the indentation mentioned. For arguments sake, the press is strong enough to do this without being damaged, the cube itself does not move at all and is on a flat surface.

What further information would I need to try and find the force the press machine is exerting on the cube to succeed in its indentation?

Thank you again, and happy holidays dude.

The situation you describe would be near impossible to replicate in reality .

Let us have a look at some simpler problems pro tem .

If you had a plate of mild steel and you wanted to punch a round hole right through it what do you think the practical set up would look like and what forces would be involved ?

Assume the plate to be relatively thin compared to the diameter of the hole .

Nidum said:
The situation you describe would be near impossible to replicate in reality .

yes I expect so, but I am interested in the required forces.
If you had a plate of mild steel and you wanted to punch a round hole right through it what do you think the practical set up would look like and what forces would be involved ?

If I had to guess I would say you would put the plate on a surface with the hole in the middle and the press would strike the area of steel over the hole. Not too different from the image in the other thread you posted.

Yes but how much force would be needed to punch the hole ? When you can work this out we can move on to more complex problems .

Well a google search tells me mild steel has an MPa of 250, so if the hole you want to make in the steel is say 28 mm in area (just pulled this number out of the air) then using the formula in my OP I suspect it should take 7067.5 N to permanently indent the metal and make the hole. Course, my issue in my OP is I do not know force required for volume of a material or any other such factors so that is just the basic force required to indent mild steel over the area I gave.

Hey Nidum, I hope you had some merry days over the holiday season

I was wondering if what I did above is correct, or if you know of a more accurate formula if it is not, cheers!

You need to start drawing sketch diagrams to aid your thinking .

To punch a hole in a flat plate you basically have to cut a cylinder of metal from the plate and push it downwards and out .

What forces are acting on that cylinder during the punching process ?

How big is the cylinder and how big is the object that is cutting it out?

## 1. What is the definition of "force required to indent a volume of material?"

The force required to indent a volume of material refers to the amount of pressure or force needed to penetrate or deform a material by a specific amount, usually measured in units of newtons (N).

## 2. How is the force required to indent a volume of material measured?

The force required to indent a volume of material can be measured using a variety of instruments such as a hardness tester or a universal testing machine. These instruments apply a controlled force to the material and measure the resulting indentation or deformation.

## 3. What factors affect the force required to indent a volume of material?

The force required to indent a volume of material can be influenced by various factors including the type of material, its composition, hardness, and thickness. Other factors such as temperature, humidity, and the shape of the indenter can also impact the force required.

## 4. How does the force required to indent a volume of material relate to its mechanical properties?

The force required to indent a volume of material is closely related to its mechanical properties, such as hardness, elasticity, and plasticity. The higher the force required to indent a material, the harder and more resistant it is to deformation, and the stronger its mechanical properties are.

## 5. What is the significance of understanding the force required to indent a volume of material?

Understanding the force required to indent a volume of material is important in various industries and fields, such as engineering, manufacturing, and materials science. It allows for the evaluation and comparison of different materials, as well as the prediction of their behavior under certain conditions, which is crucial for designing and selecting materials for specific applications.

• Mechanical Engineering
Replies
24
Views
3K
• Mechanics
Replies
2
Views
257
• Mechanical Engineering
Replies
1
Views
746
• Classical Physics
Replies
12
Views
273
• Classical Physics
Replies
11
Views
2K
• Introductory Physics Homework Help
Replies
11
Views
649
• Engineering and Comp Sci Homework Help
Replies
1
Views
1K
• Calculus
Replies
5
Views
564
• Mechanical Engineering
Replies
3
Views
638
• Other Physics Topics
Replies
8
Views
2K