Mathematical description of a ball hitting a glass plate and causing damage

[mohammed El-Kady]

Summary: damage on glasses plate by hitting ball

If a ball hit a rectangular plate of glass and it cause a damage "but it didn't broken" how can i represent this damage using mathematics?
I'll tell you my idea about it: let the ball move horizontally and hit the plate perpendicularly with momentum mv then the damage will be described as stress or strain tensor. This my idea if it's wrong tell me the truth.

 

[Dale]

You are correct that the stress and strain tensors are used to represent the material properties of materials. What you are probably interested in is the yield stress. At this point the material will begin to permanently deform. The ultimate stress would be the stress at which it breaks entirely. For materials like steel there is a fairly large difference between the yield stress and the ultimate stress, but for brittle materials like glass they are fairly close.

 

[mohammed El-Kady]

You are correct that the stress and strain tensors are used to represent the material properties of materials. What you are probably interested in is the yield stress. At this point the material will begin to permanently deform. The ultimate stress would be the stress at which it breaks entirely. For materials like steel there is a fairly large difference between the yield stress and the ultimate stress, but for brittle materials like glass they are fairly close.

thank you for your response but can you give me a site to see an example?
another question: is yield stress the material not broken, ultimate stress the material is broken? like the body on rough plane and a force affect on it, if its not large enough to move the body the friction force not limiting, if its make it about to move the friction force is limiting? true?

 

[PhanthomJay]

Now that’s a question that would take a textbookCourse! In brief one can calculate the force on the glass plate knowing the Velocity of the ball and convert it to kinetic energy. The force, based on the stiffness, can be used to determine the contact stress and if high enough exceeding the strength of the glass it will cause a crack but it will not propagate through and break as it is very local.However at the back of the plate where the bending stress is in tension if that stress exceeds the ultimate then it will crack and break this time because it is not local anymore. The strength of the glass is dependent on the initial flaw size in the glass. It can vary anywhere between 1000 PSI and 40,000 PSI depending on the depth of the initial flaw. Glass, without the flaw, has a ridiculously high breaking strength.

 

[mohammed El-Kady]

Now that’s a question that would take a textbookCourse! In brief one can calculate the force on the glass plate knowing the Velocity of the ball and convert it to kinetic energy. The force, based on the stiffness, can be used to determine the contact stress and if high enough exceeding the strength of the glass it will cause a crack but it will not propagate through and break as it is very local.However at the back of the plate where the bending stress is in tension if that stress exceeds the ultimate then it will crack and break this time because it is not local anymore. The strength of the glass is dependent on the initial flaw size in the glass. It can vary anywhere between 1000 PSI and 40,000 PSI depending on the depth of the initial flaw. Glass, without the flaw, has a ridiculously high breaking strength.

Brilliant answer. Thank you