This is a difficult question. This comes of elastic equilibrium of solid in presence of a crack. In absence of a crack a uniform stress distribution can keep it in equilibrium. In the presence of a crack a redistribution of stress takes place resulting in higher stresses at the crack tip. To actually derive this one has to use elasticity theory.
Sir in griffens formula we use sigma a (ie the applied stress component perpendicular to crack major axis),shoudnt we use sigma max there to decide wheather the crack will propogate or not in case of stress concentration?
Sir in Callister book, different formula is written for maximum stress ... Maximum stress = applied stress(2under root crack length/radius) So which one is correct ...
Sir excellent explanation.However I do not understand one thing.The crack that exists at the central location of the specimen is elliptical in shape.On first place why did we take an elliptical shape as assumption?We could have taken any other shape and secondly why have we devised that formula(just an intuition is it an approximation of an infinite series)?
Elliptical shape is a nice smooth shape without sharp corners. Sharp corners create problems in mathematical solutions as the radius of curvature goes to zero at these points and thus stress tends to infinity. Among smooth shapes ellipse is more general. For equal major and minor axes it becomes a circle. Thus the formula gives that the stress at the tip of circular holes is three times the applied stress. For very large major to minor axis ratio the ellipse approximates a sharp crack. The formula was first derived by a civil engineer C.E. Inglis in 1913. Under the assumption of liner elasticity it is an exact formula. A website giving more details is www.fracturemechanics.org/ellipse.html
@@rajeshprasad101 Sir what is "relaxed volume" in the Griffth Criterion?I have seen this term being mentioned in Meyer and Chawla also How is K different from K_{IC}?
Due to crack, there is a region around crack faces where the stress is lower than the applied stress. This region can be called relaxed volume. Difference between K and KIc: I will explain with an analogy. Stress is what you apply on the material. It can have any value. It is not a material property. But yield stress is the critical value of stress at which yielding begins. It is a material property. Similarly, K is what you apply. it can have any value and is not a material property. KIc is the critical value at which crack propagates. It is a material property.
@@introductiontomaterialsscience Sir, in the equation at 3:18 in the video, is σₐ equal to 'F/ cross sectional Area of the specimen without hole' or 'F/cross sectional area of the specimen with hole'? if 'F' is the applied force.
Sir in Callister book, different formula is written for maximum stress ... Maximum stress = applied stress(2under root crack length/radius) So which one is correct ...
The formula of Callister is an approximate one. The formula given here is more accurate. Usually, (2under root crack length/radius) is much larger than 1 due to small crack tip radius. So 1 in the formula given here can be neglected and Callister's formula is obtained. However, you can see that for zero crack length Callsiter's formula will predict zero maximum stress. This is obviously unreasonable. The formula given here will predict maximum stress equal to the applied stress which is reasonable.
