Notched specimen under constant K and temperature gradient

[YohannM]

Hello all,

It seems like a fairly straightforward question but I cannot find any information in the literature.

Let's suppose we apply a crack driving force K1=45 MPa.m^0.5 to a notched specimen with an upper shelf fracture toughness K_mat = 50 MPa.m^0.5 at room temperature T0=20 oC.

Under a constant K1=45 MPa.m^0.5 (let's ignore the effect of thermal expansion here), the temperature drops to T1=-10 oC and the fracture toughness of the material is now K_mat=40 MPa.m^0.5 (now lower shelf).

Is the specimen going to fail ? Intuitively I would think that it is the case but some people argued that if the loading occurs prior to the drop in toughness the specimen will NOT fail.

Could you please suggest some references describing similar experiments/theoretical analyses ?

Thanks for your help,

Yohann

 

[Achy47]

Dear Yohann,

Thank you for your question. To answer it, we need to consider the concept of fracture toughness and how it relates to crack propagation. Fracture toughness is a material property that describes the resistance of a material to crack propagation. It is typically represented by the symbol K, and has units of MPa.m^0.5.

In your scenario, the notch in the specimen acts as a pre-existing crack. When a force, represented by K1, is applied to the specimen, it creates a driving force for the crack to propagate. The fracture toughness of the material, represented by K_mat, determines how resistant the material is to crack propagation. In this case, K_mat=50 MPa.m^0.5 at room temperature T0=20 oC.

Now, when the temperature drops to T1=-10 oC, the fracture toughness of the material decreases to K_mat=40 MPa.m^0.5. This means that the material is now less resistant to crack propagation than at room temperature. However, the applied force K1 remains the same. This means that the driving force for crack propagation is greater than the resistance of the material to crack propagation. In other words, the crack will continue to propagate and the specimen will ultimately fail.

This is supported by the concept of the Griffith criterion, which states that a material will fail when the applied stress exceeds the critical stress required to propagate an existing crack. In your scenario, the applied stress (represented by K1) remains constant, while the critical stress (represented by K_mat) decreases. Therefore, failure is inevitable.

I hope this helps to answer your question. For further reading on this topic, I recommend the following references:

1. "Fracture Mechanics: Fundamentals and Applications" by T.L. Anderson
2. "Introduction to Fracture Mechanics" by D.R. Harington
3. "Fracture and Fatigue Control in Structures: Applications of Fracture Mechanics" by R.W. Hertzberg

Best of luck with your research.