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State of stress in a Uniaxial Tensile Test
Hello Mechanicians,
I have a doubt regarding Uniaxial Tensile Test which has bugged me for quite some time. It may be a trivial one, but it goes like this:
Why is a "Uniaxial" Tensile test called so, when we know from solid mechanics that at a point inside the bulk of tensile specimen there would be stress in all the three directions (Consider a point inside a cylindrical uniaxial tensile test specimen. Now if you section it through x,y, z planes, considering y axis is the direction of loading, there is always material on the other side undergoing relative displacements to pull or push it and thus there should be stress in all the three direction). Why is then Uniaxial Tensile Test called "Uniaxial" as majority of the specimen is experiencing triaxial sress? Why is it then, its often mentioned in some materials science text books that necking sets in the triaxial state of stress and before necking its uniaxial stress state?
In such a scenario what would be a utility of such a test?
Kindly let me know if I may be missing out something here in understanding. A detailed explanation shall be highly appreciated.
Also, it will be very helpful if anyone can point a literature explaining State of Stress in a cylindrical Tensile Test from a solid mechanics point of view.
Thanks,
Danish
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Comments
An idealization
I believe that the uniaxial stress state is an idealization and very hard to obtain i reality.
However, if you ensure that the specimen ends are not restricted against transverse deformation is possible (e.g. by using bolts in a slightly large hole through the specimen) and align the applied force perfectly with the speciment, the (macroscopic) state of stress should be very close to uniaxial as long as the deformation is uniform in the guage area (the part of the speciment where you measure deformations).
On the other hand, the microscopic state of stress, i.e. on the scale of the microstructure, would generally not be in a state of uniaxial stress. For dual phase steels (that I see you're focusing on:) the stress state in each phase is triaxial after initial (local) plastic yield, and very much so after "macroscopic" yielding.
Even for an idealized homogeneous material the stress state is triaxial when the deformation is no longer uniform, i.e. when a neck starts to form. A standard form of "correction" to the longitudinal stress is the so-called Bridgeman correction which takes the radius of curvature of the nack into account.
- Espen
PS: all of the above relates to isotropic materials only!
Dear Espen,
Dear Espen,
Thanks a lot for your response. I undertsand that tensile test is an attemp to reach the ideal case of uniaxial tensile test.
However my doubt is a bit different. From the way I understand there should be triaxial state of stress in the tensile specimen before the start of necking even at contnuum scale (not microstrucutre state). For e.g Consider a point inside a cylindrical uniaxial tensile test specimen. Now if you section it through x,y, z planes, y axis being the direction of loading, apart from the pull experienced by it along y axis due to external loading, there will be also be pull/push on this point by the material present on the other side along x and y axis as the material will be contarcting along x and z direction due to transverse strain. Wont this push/pull cause stress on this point even in x and z direction? As long as the point is inside the cylinder there should be triaxial stress. On surface however the normal stress would become zero.
Kindly let me know where am i going wrong in the understanding.
Thanks,
Danish
I meant " by the material
I meant " by the material present on the other side along x and z axis as" in the above comment on 6h line . Sorry for the typo