Fracture Mechanics Problem: Max Slit Length Without Fracture

[Rastanking]

Hi everyone,

I have a problem that I hope someone can help me with, the question is.

A mass of 500kg induces a tensile stress in a glass sheet restrained at the top. Given that the fracture strength of sound glass is 170MPa what is the maximum length of slit that can be tolerated without fracture.

The mass is 200mm wide, 2mm deep and has a crack of 2a in the centre

so using the formula = δ√∏a = √EGc

I get this δ = (500 x 9.81) / 200 x 2

So first question is because the mass is suspended at the top I'm assuming that the 9.81 is gravity and if so the second question appears, from the formula how do I know which figures to use?

To me the formula states ∏xa, I'm assuming that's area and E = Youngs Modulus of Elasticity and Gc is Critical energy release rate.

Any help would be appreciated.

 

[eljose79]

Hi there,

Thank you for posting your question on this forum. I would be happy to help you with this problem.

Firstly, you are correct in your assumption that the 9.81 in the formula represents gravity. This is because the mass is acting downwards due to the force of gravity, which is inducing the tensile stress on the glass sheet.

To answer your second question, the formula you are using is known as the Griffith's theory of brittle fracture. In this theory, δ represents the tensile strain induced by the applied stress, ∏ represents the length of the crack, and a represents the radius of the crack. E represents the Young's Modulus of Elasticity, which is a measure of the stiffness of a material, and Gc represents the Critical Energy Release Rate, which is a measure of the energy required to propagate a crack in a material.

In order to solve this problem, you will need to use the values given in the question, such as the mass, width, depth, and fracture strength of the glass. You will also need to determine the value of Gc for sound glass, which can be found in reference materials or calculated using experimental data. Once you have all the necessary values, you can plug them into the formula and solve for ∏, which will give you the maximum length of slit that can be tolerated without fracture.

I hope this helps. Please let me know if you have any further questions or need clarification on any of the concepts. Good luck with your problem!