Greetings,

I have some confusion about the fracture toughness equation as below:

K_IC^′=K_IC^o+2σ_R (C/π)^(1/2)

K_IC^o is the material toughness without given stress (so the value is constant)

K_IC is the material toughness after given stress

σ_R is residual stress

C is crack length

from this paper

https://www.sciencedirect.com/science/article/abs/pii/S0261306903000220

we can see that after post treatment the crack length is reduced, stress become more compressive. and, can we say that the material toughness after given stress K_IC becomes higher? However, the as mentioned, the crack length is shorter, in the math form, shorter crack length will give lower toughness.

Please help me explain this. Thank you in advance.