What are some approaches for estimating the work done up to fracture?

[ralden]

Good day everyone! i have a problem dealing with the fracture analysis. We all know that the work done per unit volume is equal to the area under the curve of stress-strain curve or we can express it in terms of integral form, and if we're looking at necking point stress can be express in this terms of stress = constant*(strain)^n
where n is the work-hardening, but if we extend it up to fracture i don't know the expression for the stress and strain. So guys please help me figure out the work done up to fracture. Thank you!

 

[Achy47]

Hello, thank you for bringing up this important topic regarding fracture analysis. I understand the importance of understanding the work done up to fracture.

Firstly, it is important to note that the stress-strain curve is a representation of the mechanical properties of a material. It shows the relationship between the applied stress and the resulting strain. The area under the curve represents the work done per unit volume, as you mentioned.

When it comes to the fracture point, the stress and strain values can vary greatly depending on the material and the conditions under which it is being tested. However, there are a few general approaches that can be used to estimate the work done up to fracture.

One approach is to use the fracture toughness, which is a measure of a material's resistance to fracture when a crack is present. This can be calculated by measuring the stress and strain at the point of fracture and using a fracture toughness equation, such as the Griffith or Irwin equation.

Another approach is to use the strain energy density, which is a measure of the energy stored in a material under stress. This can be calculated by integrating the stress-strain curve up to the point of fracture.

It is also important to consider the type of fracture that has occurred, as this can affect the work done up to fracture. For example, a brittle fracture will have a different work done compared to a ductile fracture.

In conclusion, there is no one specific expression for the stress and strain at the point of fracture, as it can vary depending on the material and conditions. However, by using concepts such as fracture toughness and strain energy density, we can estimate the work done up to fracture. I hope this helps in your analysis. Thank you.