Sunil:

I'm not sure about S/N fatigue but there is no standard four-point bending test to my knowledge for fatigue crack propagation in metallic materials - the ASTM specifies the compact-tension, center-crack sheet (middle-cracked tension) or the three-point bending test. Nevertheless, in most of my early fatigue work before the standard was ever written, I always used the four-point bending test as it offers a state of pure bending from the constant bending moment between the inner two loading points. Because of this, I also prefer it to cantilever or three-point bending for small fatigue crack studies as it offers a larger statistical sampling volume (or surface). Finally the double-notched four-point bend test is particularly useful for discerning whether a fracture process is stress- or strain-controlled and in identifying the precursor processes in the development of the fracture. This is because as both notches see the same bending moment, when fracture occurs at one notch, the other (unbroken) one is at the point of fracture. The vicinity around this unbroken notch can then be examined metallographically to see what damage processes proceed the fracture. If the initial crack or void forms at the notch root, it is a strain-controlled fracture as this is where the local strain is highest; conversely, if the initial crack forms ahead of the notch, it is a stress-controlled fracture as the local stress is at a maximum ahead of a notch at the boundary of the notch plastic zone, or fractionally before it. If you're interested, an example of this is shown in the attached paper.

ROR

Sunil:

I'm not sure about S/N fatigue but there is no standard four-point bending test to my knowledge for fatigue crack propagation in metallic materials - the ASTM specifies the compact-tension, center-crack sheet (middle-cracked tension) or the three-point bending test. Nevertheless, in most of my early fatigue work before the standard was ever written, I always used the four-point bending test as it offers a state of pure bending from the constant bending moment between the inner two loading points. Because of this, I also prefer it to cantilever or three-point bending for small fatigue crack studies as it offers a larger statistical sampling volume (or surface). Finally the double-notched four-point bend test is particularly useful for discerning whether a fracture process is stress- or strain-controlled and in identifying the precursor processes in the development of the fracture. This is because as both notches see the same bending moment, when fracture occurs at one notch, the other (unbroken) one is at the point of fracture. The vicinity around this unbroken notch can then be examined metallographically to see what damage processes proceed the fracture. If the initial crack or void forms at the notch root, it is a strain-controlled fracture as this is where the local strain is highest; conversely, if the initial crack forms ahead of the notch, it is a stress-controlled fracture as the local stress is at a maximum ahead of a notch at the boundary of the notch plastic zone, or fractionally before it. If you're interested, an example of this is shown in the attached paper.

ROR

The maximum bending moment and so the max. bending stress will not be at one section (at the middle section of the 3-points bending specimen), but the maximum will be at all sections between the inner two loading points. This increases the probability of failure as all defects between the loading points will be subjected to a maximum bending stress .

Dr. Al-Ethari:

My apologies but I beg to differ. What you have described, that the maximum stress will be at all sections between the inner two loading points, pertains to four-point bending, not three-point bending, and in any event it's not for all sections but only those at the top surface that is in tension.

ROR

Robert O Ritchie

I mean at one section (middle section) for 3-point bending and at all section for 4-point bending. In both cases the max. stress will be at the outer fiber (at the surface). The probability of failure for 4-point still higher.

Now you're correct!

Dear Robert O Ritchie,

Thank you for the three points:

1. It offers a state of pure bending

2. Sampling volkume/surface is larger

3. It helps discern whether fracture process is tress or strain controlled

The attachement is particularly useful as well and my thx for that as well.

Eventhough, theoretically, we should be expecting a state of pure bending everywhere along the inner loading span, I believe that this would be slightly violated in the practical case, as a consequence of Saint-Venant's principle, atleast in regions very close or close to the inner supports.

What I would like to ask you is:

Firstly, is this belief of mine reasonable? and

Secondly, if so, has there been any study regarding this, which tells what portion of the inner span would be under pure bending.

Thirdly, I would also like to ask you that at loads high enough to result in huge contact stresses at the loading line (which I can approximate as the line contact in cylinder and solid body (neglecting thicknewss of course, and hence leading to approximations) ), is there any corrections that are avaiable in the vast body of literature to take into account the actual state of stress in the case of a 4-point bending, or even a 3-point bending for that matter.

Your feedback will be very valuable and enlightening for me. Thanks again Sir.

Merry Christmas :)