# Notch strengthening of bar in tension

• jstluise
The figure plots stress vs. strain for a material with a notch in it, and it clearly shows that while the nominal stress is still below yield, the stress at the notch is much higher. So, the notch does indeed strengthen the material.I guess my question boils down to: if I know the geometry of the notch (and thus, the stress concentration factor Kt), how do I know when the member will fail? This seems to be a material property, so I'm guessing the only way to figure it out would be through experiments?You could calculate the notch tensile strength based on the stress concentration factor, but it would be more complicated than

#### jstluise

I was looking at some tensile testing data of some round bars with grooves machined into them, and based on the geometry of the groove I could not figure out how it was possible to withstand the high loads that it was seeing. I was stumped, but by some blind luck I saw a property listed on Matweb as "Notched Tensile Strength" which was much higher than the regular tensile strength (e.g. Titanium 6al-4v, 170 ksi vs. 225 ksi with Kt=6.7). That lead me to notch strengthening, something I've never seen or explored before. The whole idea of stress concentration rings a bell, but it has been quite a while since I have looked at it.

I really only found one source that did a decent job of briefly explaining it (see section 7.5): http://www.omegaresearchinc.com/Publications/getpub.cfm?pub_id=18

But, other than that I haven't found much. I was hoping someone here could help drive home the concept. I guess the main thing I am hung up on is calculating the notch tensile strength.

Can the notched tensile strength be calculated based on the stress concentration factor of the groove (http://analysischamp.com/StressBook/TABA2513.htm)? Or is it something that can only be determined experimentally? What does the "notched tensile strength" in the Matweb specs do for me if every notch has a different Kt?

Any help is appreciated! Also, if you know of any sources that discuss this, that would be great!

Are they, the video, referring to the stress at the notch?
( Which is different than the nominal stress on the member. )
Load not the same thing as stress.
A stress concentration will decrease the load that can be applied to a member. ( Or so I always thought ).
Are you saying that the video states a notch in a member can increase the load that can be applied to it before failure, than an un-notched member.

256bits said:
Are they, the video, referring to the stress at the notch?
( Which is different than the nominal stress on the member. )
Load not the same thing as stress.
A stress concentration will decrease the load that can be applied to a member. ( Or so I always thought ).
Are you saying that the video states a notch in a member can increase the load that can be applied to it before failure, than an un-notched member.

Thanks for the reply. The data I was looking at was a simple force vs. displacement curve, and based on the original geometry of the groove/notch (specifically, the minimum cross-sectional area at the center of the notch) I calculated the maximum stress at the notch. It turned out to be much higher than the ultimate tensile strength of the material, which is why I was puzzled. The nominal stress in the member was still below yield.

Yes, it is important to realize the difference between stress and load. While the maximum stress at the notch is greater due to the notch strengthening effect, the maximum load that the member can withstand is still less than if the notch was not present; the rod will always be strongest without a notch. So yes, a stress concentration will decrease the load that can be applied to a member.

I guess my question boils down to: if I know the geometry of the notch (and thus, the stress concentration factor Kt), how do I know when the member will fail? This seems to be a material property, so I'm guessing the only way to figure it out would be through experiments?

Well, I think it still stands that one does not want, in a general sort of way, a notch in a brittle material, but with a ductile material one can work around it by using Kt.

If you look at fig 1.12 of this site, it gives a representation of engineering stress-strain curve ( using the nominal area ) vs the true stress-strain curve ( ie using the actual necked region area ), perhaps that will give you some insight. One can see that the actual stress on the sample increases up to E' being much larger than the engineering ultimate stress. Since you used the notched area,..., then again maybe it is more complicated than just that.

Here is what some people are doing, recent 2014,
http://www.jmst.org/article/2014/1005-0302-30-6-599.html
They have a good question at the end of the first paragraph, does a notch strengthen or weaken a material, with a few notes on what we know, and what we don't.

Last edited:
Thanks for the link. That figure does a good job of showing how how true stress/strain compares to engineering stress/strain.

I think the situation I am talking about is bit more complicated than that. I was able to dig up the plot that I was referring to:

The material is Titanium 6Al-4V STA and the rod has a nominal diameter of 0.163". The minimum diameter at the center of the notch is 0.079".

Using the minimum area at the notch (and not considering any notch strengthening effects), I would expect the rod to fail in tension around 833 lbf (170 ksi * pi/4 * .079"^2). Without the notch, the rod should fail around 3500 lbf. However, we see that the bolt actually fails at 1500 lbf. Not considering any reduction of area due to necking, that gives a maximum stress of around 309 ksi, 1.8x the specified tensile strength of the member.

Even if we consider true stress, we would expect the member to fail at a even lower force (<833 lbf) because of the slight reduction of area during the deformation (i.e. higher stress).

Looking at the Matweb data, there is a "Notched Tensile Strength" of 225 ksi (Kt = 6.7), which tells me there is some sort of notch strengthening effect going on.

Does that make more sense?

The surface of a rod will have scratches that form the start of cracks leading to tensile failure. I suspect that the notch radius and surface finish of the notch is better than the natural surface of the rod. The neck moves surface forces into the body of the rod, away from the unreliable chilled surface. That prevents excessive stress concentration at the end of surface cracks.

There is a parallel technique I have seen used on truck axles. Long ago I was told that by machining a rounded notch close to the spline, after breaking an axle at the notch, the spline can be more easily pulled from the differential and the axle replaced without dismantling the entire assembly. Also, that if the rounded notch is cut, the axle is less likely to break because of Murphy's Law. Now I see that it may not be Murphy's Law, (human perception bias), but “notch strengthening” that is having the paradoxical effect.

Baluncore, I was wondering if there was an application for this type of "technology", and I guess there is.

jstluise said:
Using the minimum area at the notch (and not considering any notch strengthening effects), I would expect the rod to fail in tension around 833 lbf (170 ksi * pi/4 * .079"^2). Without the notch, the rod should fail around 3500 lbf. However, we see that the bolt actually fails at 1500 lbf. Not considering any reduction of area due to necking, that gives a maximum stress of around 309 ksi, 1.8x the specified tensile strength of the member.

Even if we consider true stress, we would expect the member to fail at a even lower force (<833 lbf) because of the slight reduction of area during the deformation (i.e. higher stress).

Looking at the Matweb data, there is a "Notched Tensile Strength" of 225 ksi (Kt = 6.7), which tells me there is some sort of notch strengthening effect going on.

Does that make more sense?

Thanks for the graph and calculations. Very interesting how the load is affected.
The reason I did say it was probably more complicated, is that the usual graphs one sees for stress-strain take into account only the one dimension, using only the axial load ( which one knows ) and the area of the specimen ( which one knows ). For machine design that should be adequate in a majority of cases, and one does not have to go further in stress analysis.

In fact, though, a small element dx,dy,dz of the material is never under just one single stress. On each face, there could be an axial load and shear ( in each direction by the way ). You will notice that moving out from an element located at the centerline of the specimen, all elements are bounded by another element, except the one at the surface.
If I recall correctly ( which maybe I do not ), the outmost elements first experience plastic deformation, which then extends into the specimen as the load continues. For the specimen to change volume, an element, call it A, has to move from its original location to another location. But, as there is another element in the way, A can thus have a tensile or compressive stress on its other faces orthoginal to the axial load. With compression this might be easier to see, as for as element A attempts to "squish" out of its original loacation due to the stress on its axial face, it is bounded by an inner element that is also pushing it outwards radially and by an outer element that is pushing it inwards. In the tangential direction the same stresses are occurring.

For the notched ductile specimen, the notch would want to deform plastically, but being bound by the main part of the speciment, which is still elastic, it can't.

Hope that makes some sense.