Von Mises Stress: Yielding & SF Criterion Equation

In summary, Von Mises stress is a measure of the stress experienced by a material at a specific point, taking into account both normal and shear stresses. It is calculated using the Von Mises yield criterion equation and is used to determine if a material will deform or fail under a given load. The relationship between Von Mises stress and yielding is that if the stress exceeds the yield strength, the material will deform, but if it is below the yield strength, it will remain elastic. The stress concentration factor takes into account the effect of stress concentrations on the Von Mises stress, and the safety factor is used to account for uncertainties and calculate the risk of failure for the material.
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Hi, just wanted to ask for the von Mises criterion equation, is the equation without the SF (the one I circled in blue) only applicable when yielding has FIRST occurred? (i.e when SF=1)? and is the equation including the SF (one I circled in orange) applicable to all cases? (i.e whether the material has yielded or not)
thank you
 
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sorry the images didn't upload on my original post:
 

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1. What is Von Mises stress?

Von Mises stress is a measure of the stress state at a point within a material. It takes into account the three principal stresses and combines them into a single value that represents the equivalent stress at which the material will yield.

2. How is Von Mises stress calculated?

Von Mises stress is calculated using the yield criterion equation, which takes into account the three principal stresses (σ1, σ2, and σ3) and the yield strength (σy) of the material. The equation is: σv = √(σ1^2 + σ2^2 + σ3^2 - σ1σ2 - σ2σ3 - σ1σ3)

3. What is the significance of yielding in materials?

Yielding is the point at which a material begins to permanently deform under stress. This is an important consideration in engineering and design, as it determines the maximum load a material can withstand before failure.

4. What is the significance of the safety factor (SF) in the Von Mises stress equation?

The safety factor (SF) is a multiplier used to account for uncertainties in material properties, loading conditions, and other factors that may affect the yield strength of a material. It is included in the Von Mises stress equation to ensure a margin of safety in design and prevent failure.

5. How is the Von Mises stress criterion used in engineering?

The Von Mises stress criterion is used to determine the maximum stress a material can withstand before yielding. It is commonly used in engineering design and analysis to ensure that structures and components are designed to withstand expected loads without failure.

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