The stress at crack tip is formally unbound. Therefore the SIFs are introduced to get a finite value, which can be compared.

Dear Ajay Kumar,

The stress intensity factor is arrived based on the stress only, even in some standard software it is defined as stress ratio i.e. shear strength/shear stress. The degree of failure can be classified using stress ratio, if it is 1 then at the verge of failure, if more than 1 then the material behaviour is within elastic and less than 1 material failed. This kind study is very useful to understand the stability of ground during deep excavation during metro tunnel construction etc..ok all the best in your research..

The theories of material failure that predict rupture are valid only at small stress concentration factors and cannot predict failure at high stress-concentration factors such as those occurring at the tip of a crack. Hence an alternative failure criteria based on fracture mechanics such as stress intensity factor, J-integral, etc are used.

First and foremost:

Stress Intensity Factor (SIF) ≠ Stress Concentration Index ≠ Failure Index

All 3 have different meanings and applications and they are not synonyms.

The SIF is born in the field of Linear Elastic Fracture Mechanics (LEFM), although it can be ported and applied in extensions of the latter, such as Elasto-Plastic Fracture Mechanics, Finite Fracture Mechanics, ... I'll base my discussion on LEFM, as the theoretical base of the SIF is mainly rooted in this field.

In LEFM, the material is considered to be perfectly elastic and to present some notch of predefined geometry. The reference case, and also the first one to have been solved, is the infinite plate with a centered finite sharp crack, i.e. a segment, under constant stress applied at infinity. We do NOT use any damage criterion, neither for initiation nor for propagation. There's no damage, discrete or diffuse, of which we're calculating the onset or the propagation. We just have a piece (a plate in this case) with a notch of some geometry placed somewhere (a sharp crack in the center) under some kind of loading condition (constant stress at infinity).

The question we want to answer is the following: how does the stress field behave in the neighborhood of the crack tip?

In LEFM, it always presents a singularity which, in polar coordinates centered at the crack tip, is of the type r^(-1/2), i.e. an inverse square root. In the case of a crack placed between two materials with mismatching elastic properties, the stress is also oscillating in the vicinity of the crack tip and a sin(r) is superposed to the r^(-1/2) function. The solution of the stress field is fully characterized when the divergent function is multiplied by an amplitude, which depends on the global geometry, the crack geometry and the type and magnitude of the applied load.

From the mathematical point of view, you can regard it as the amplitude of the function or as a stretching of the r^(-1/2) function and it is referred to as the "strength of the singularity".

From the physical point of view, it allows us to write the local stress field as

sigma(r) = A(global geometry, crack geometry, type and magnitude of applied load) * r^(-1/2) + lower order terms

The amplitude function A() is what is called "Stress Intensity Factor". Notice that the SIF is a function of global parameters only, which can be controlled or measured in an experiment.

So, how does failure enter the stage? Failure initiation is always defined in terms of some combination of stresses or strains. J-integral and Energy Release Rates can only be used in propagation. Their applicability is not dependent on the level of applied or local stress. Let's assume that we use a simple maximum stress criterion: failure will occur if

sigma(r=0) > sigma_critic

where sigma_ critic is some critical value defining the onset of damage.

We now that we can write the previous relation as:

lim(r->0)(SIF(global geometry, crack geometry, type and magnitude of applied load) * r^(-1/2)) > sigma_critic

where the SIF can be taken out of the limit as it is independent of the local coordinate

SIF(global geometry, crack geometry, type and magnitude of applied load)*lim(r->0)(r^(-1/2)) > sigma_critic

In a not very mathematically orthodox way, we can divide by r^(-1/2) both terms and obtain

SIF(global geometry, crack geometry, type and magnitude of applied load) > sigma_critic / lim(r->0)(r^(-1/2))

What has appeared on the left side of the equation? The definition of the (critical) Stress Intensity Factor. Thus we can rewrite our maximum stress criterion as a maximum SIF criterion.

SIF(global geometry, crack geometry, type and magnitude of applied load) > SIF_critic

Why is the latter better than the original stress formulation? Stress is local, while SIF is global and can be related to quantities that are accessible to mechanical tests.

thank you so much Luca Di Stasio , Karthigeyan . S , Mir Aamir Abbas, Jonathan Hahn

To answer your question simply - yes, the stress intensity factor has more meaning than directly the stress. It is a measure of crack tip driving force and expressed as SIF it becomes geometry and crack length independent. Hence for a given material-environment system one can determine the expected crack growth rate in a component based on laboratory generated data. Hence it is useful from the point of life prediction of a component that has cracks detected during inspection. For uniformly loaded specimen without crack stress is appropriate. For a notched specimens or components with stress concentrations, knowledge of Kt and notch root radius, one can determine the fatigue life - see our recent paper available here on 'Does a nucleated crack grow?' published in Eng. Frac. Mech. 2017.