von mises henkey theorem
TRANSCRIPT
Tumukunde Dan
Uganda Petroleum Institute - Kigumba
Email: [email protected]
What are von mises stresses exactly?
Von Mises Stress is actually a misnomer. It refers to a theory called the "Von Mises - Hencky
criterion for ductile failure".
In an elastic body that is subject to a system of loads in 3 dimensions, a complex 3 dimensional
system of stresses is developed (as you might imagine). That is, at any point within the body
there are stresses acting in different directions, and the direction and magnitude of stresses
changes from point to point. The Von Mises criterion is a formula for calculating whether the
stress combination at a given point will cause failure.
There are three "Principal Stresses" that can be calculated at any point, acting in the x, y, and z
directions. (The x,y, and z directions are the "principal axes" for the point and their orientation
changes from point to point, but that is a technical issue.)
Von Mises found that, even though none of the principal stresses exceeds the yield stress of the
material, it is possible for yielding to result from the combination of stresses. The Von Mises
criteria is a formula for combining these 3 stresses into an equivalent stress, which is then
compared to the yield stress of the material. (The yield stress is a known property of the material,
and is usually considered to be the failure stress.)
The equivalent stress is often called the "Von Mises Stress" as a shorthand description. It is not
really a stress, but a number that is used as an index. If the "Von Mises Stress" exceeds the yield
stress, then the material is considered to be at the failure condition.
The formula is actually pretty simple, if you want to know it:
(S1-S2)^2 + (S2-S3)^2 + (S3-S1)^2 = 2Se^2
Where S1, S2 and S3 are the principal stresses and Se is the equivalent stress, or "Von Mises
Stress". Finding the principal stresses at any point in the body is the tricky part.
OR
For an element subject to principal stresses σ1,σ2,σ3 this theory states that yielding begins
(σ1-σ2)^2 + (σ2-σ3)^2 + (σ1-σ3)^2 = 2((σyp)^2
where σyp is the yield point of the material.
Then, σyp = √(σ1−σ2)^2 + (σ2−σ3)^2 + (σ1−σ3)^2
2
The theory states that a ductile material starts to yield at a location when the von Mises stress
becomes equal to the stress limit. In most cases, the yield strength is used as the stress limit.
However, the ultimate tensile or set your own stress limit.
σyp ≥ σlimit
Yeild strength is a temperature dependant property. This specified value of the yield strength
should consider the temperature of the component. The factor of safety at a location is calculated
from:
Factor Of Safety(FOS) = σlimit
σyp
σyp can also be termed von mises stress
arge factors of safety in a region indicate that you can save material from that region.
o A factor of safety less than 1.0 at a location indicates that the material at that location has
failed.
o A factor of safety of 1.0 at a location indicates that the material at that location has just
started to fail.
o A factor of safety larger than 1.0 at a location indicates that the material at that location is
safe.
o The material at a location will start to fail if you apply new loads equal to the current
loads multiplied by the resulting factor of safety.