Differential Yield Stress and Von Mises Criterion

[1350-F]

If I have the differential yield stress σ_d=(σ₁-σ₃) for a material, what can I derive from that for use with the von mises criterion? Do I have k=0.5×(σ₁-σ₃) or σ_y in axial tension, where σ₃ = 0? Essentially is my axial yield stress = σ_d or √3 × σ_d /2? (in plane stress)

 

[Chestermiller]

See this: http://en.wikipedia.org/wiki/Von_Mises_yield_criterion

 

[1350-F]

See this: http://en.wikipedia.org/wiki/Von_Mises_yield_criterion

Reading this confirmed my suspicions that the axial yield would equal the differential yield and from there you would divide by √3 to get k. For tresca k would equal σ_d/2. In that case why report it as a differential stress? I think that's what was throwing me off. Assuming we would know to add the axial yield to any hydrostatic stress to get our maximum principal stress why give σd?

 

[Chestermiller]

Reading this confirmed my suspicions that the axial yield would equal the differential yield and from there you would divide by √3 to get k. For tresca k would equal σ_d/2. In that case why report it as a differential stress? I think that's what was throwing me off. Assuming we would know to add the axial yield to any hydrostatic stress to get our maximum principal stress why give σd?

The reason differential stress is used is that people out-of-the-know can relate to it easily.

Chet

 

[alphy]

Differential yield stress (σd) is a measure of the difference between the maximum and minimum principal stresses in a material. It can be used to determine the material's ability to withstand different types of stress, such as tension and compression.

The von Mises criterion is a mathematical model that predicts the failure of materials under complex stress conditions. It takes into account the magnitudes of all three principal stresses, rather than just the maximum and minimum, to determine the likelihood of failure.

To use the von Mises criterion, the value of σd can be substituted for the difference between the maximum and minimum principal stresses (σ1-σ3). This results in a value of √3×σd/2, which can then be compared to the material's yield stress (σy) to determine its safety factor.

In axial tension, where σ3 = 0, the von Mises criterion simplifies to k=0.5×(σ1-σ3), which is equivalent to σd. Therefore, in this case, the axial yield stress would be equal to σd.

In plane stress, the von Mises criterion can be expressed as k=√(3/2)×(σ1-σ3), which is equivalent to √3×σd/2. So in this case, the axial yield stress would be equal to √3×σd/2.

In summary, the differential yield stress (σd) can be used in the von Mises criterion to determine the material's safety factor and predict its failure under complex stress conditions. The specific equations used will depend on the type of stress being analyzed (axial tension or plane stress).