A hole, sharp corner, crack etc. act as points of high stress concentration. Is it just because of the lower surface area they provide, or is there another explanation?
Stress Concentration Factor mainly depends upon the geometry of the notch.
If the fillet radius is small, the change in shape is abrupt, then the internal stresses do not get enough space to get redistributed evenly.
Thus the actual stress becomes more than the theoretical stress.
This increase in stress due to sudden change of geometric shape is called stress concentration.
So, A hole, sharp corner, cracks etc. act as points of high stress concentration not just because of the very less surface area they provide. It is because of the abrupt change in the surface area. This is the reason why we provide sufficient fillet radius, to allow redistribution evenly.
I think it is rather because of disturbances in force transfer. For example if you have a shaft with changing sections, and each section separately will not exceed the permissible stress level it is still possible that in the place where the diameter changes you will get big stresses. You can even find some other examples like drilling additional hole in plate to make it symmetrical because it is even better to have two symmetrical hole than one out of the symmetry. However, in that plate case is rather related to the center of the second moment of area but actually we are getting back to the load transfer anyway.
Dear researcher just think that you are applying load on a notched specimen and assume it is consists of certain segments. Now the state of stress is not equal at every sections and the higher cross section have lower effective stress. On the other hand the sharp corner/ notch have lower cross sectional area and with application of same level of load due to lower cross section area effective level of stress is much higher. Hence these regions are stress concentration regions. Please let me know if you think that my answer is fair enough...
Your question is very much elaborately answer in R.S Khurmi book of machine design in the section of fillets and radii.
It may help in envision the example of a plate under uniaxial tension, in which you can imagine a uniform stress "flow" through the sample, basically transferring the tensile stress applied to the two ends through the sample. Now imagine putting a small hole in the middle of the plate in between two of these "stress flows" and gradually start enlarging the hole. As the hole is enlarged it will start pushing the "stress flow" lines together on each side, with the flow being the most dense near the imperfection (hole). Thus if you measure local stress in that region it will be much higher than far field uniform stress in the sample. This is referred to as stress concentration. (this link sort of describes this: http://upload.wikimedia.org/wikipedia/commons/f/fc/HoleForceLines.svg)
Please note that this example was rather crudely describes for the purpose of clarity. The same discussion can be extended to adding other types of geometric imperfections in a sample, such as sharp corners and notches.
I hope this explanation helped!
Stress Concentration Factor mainly depends upon the geometry of the notch.
If the fillet radius is small, the change in shape is abrupt, then the internal stresses do not get enough space to get redistributed evenly.
Thus the actual stress becomes more than the theoretical stress.
This increase in stress due to sudden change of geometric shape is called stress concentration.
So, A hole, sharp corner, cracks etc. act as points of high stress concentration not just because of the very less surface area they provide. It is because of the abrupt change in the surface area. This is the reason why we provide sufficient fillet radius, to allow redistribution evenly.
Its easy to understand this with a molecular view point. Imagine a hollow cylinder with considerable thickness. Atoms of the element will be distributed evenly throughout the volume (to have even density). Now, when we intend to roll it out to make it flat, the outer circumference will receive more atoms fighting each other to secure a spot, which results in molecular level friction and dislocations, ultimately stress. Similarly, the atoms in the inner circumference will relax and there are chances of rupture due to low concentration of atoms (Important concepts are the electronic energy distribution and force components acting on each atoms - Mere finite element analysis wont give you a comfortable picture)!! Enjoy!!
Sharp corners do not act as stress raisers or stress concentration points because they are defined as such, as explained in Machine Elements books.
Dear Saransh,
All the above comments are right. So argue the same is lead.
There is the concept of "flow lines of force" that is the basis of all previous explanations.
However, you want to share a fact that may help to understand the phenomenon physically. If you look at the image of the femur in longitudinal section, you will see that this cavity is formed by a lattice of plates (trabeculae), which are those that transmit force from the hip to the tubular bone from the knee.
In all sections where there is an expansion / contraction of these plates (lines) separate / combine to allow adequate flow of force. That is, in the femur of the human body, top designer, considered large radii of curvature so that the lines do not concentrate efforts and therefore the effort associated with this region does not increase its value by a factor representing the hub value efforts.
When you visualize a part that is under some kind of load (axial, torsional, bending stress), stress 'fringes' are seen where the size of the fringe area relates to the amount of stress in that region of the part. Where there are sharp (right) angles, there are more stress lines seen and thats where the loadings are highest. The best graphic and explanation that I have seen on this (old school of course - 1935) is on page 11, 12, and 13 of the document at the link below. The entire document is extremely useful in my opinion.
https://www.ideals.illinois.edu/bitstream/handle/2142/4463/engineeringexperv00000i00276.pdf?sequence=3
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