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The three directions of Tensile Stress are labelled here as sx, sy, and sz. By convention,

tension is a positive number, (and so a negative number means compression). The three

directions of Shear Stress are labelled using the symbol t. Shear does not act in a single

simple direction, it acts within a plane; that’s why it takes two indicies to label each shear

stress. txy is the same as tyx. This is also why there seem to be 6 shear stresses labeled,

but there are really only three – the Red, Green, and Blue vectors are used to show which

pairs of Shear are really just the symmetric members.

Yield Criteria

We need to be able to look at a complex, 6­dimensional state of stress, and somehow compare it to our reported Yield

Strength in a simple, 1­dimensional state of stress, and ask: “Is this complex case worse – yes or no ?”

Consider the linkage element pictured below. This part is restrained on the large bore at the bottom, and undergoes a vertical

(+Y) tug on the top face of 4600 lbs. (pink). There is a 450 lb. force acting in the –Z direction, (purple) on the front boss face,

and a torque of 1200 in­lb. (red) on the two small horizontal arms, about the vertical axis. Finally, an 800 in­lb. torque (orange)

acts on the central bore (the one with the keyway) about the –X direction.

The FEA must compute all 6 components of stress, at every element. How would it plot all 6 values at once, at every point?

And, even if it could, how would you LOOK at them? Certainly, we can plot each component of stress one­at­a­time, and try to

locate any weaknesses in our design that way.

Clearly we need some way of combining these 6 stress components into a single number that we can compare to our test of

the Yield strength. That is exactly what the Von Mises stress calculation attempts to do.

You can think of the Von Mises stress as a sort of “credit score” for each finite­element in your part. Certainly, your own

financial status has MANY dimensions – how much liquid cash in your pocket? How much in your bank accounts? How about

your house – Own it? Above Water? Still paying on a car loan? And yet, somehow, with all of the complexity and subtly that

could go into computing your net worth…. The credit card companies routinely boil you down to a single number. Less than

500? Misery. Greater than 720? Banks love you. Do you want to know the exact formula the credit card companies use to do

this magic?

Me, neither. But for the purists out there, the formula for computing a single, scalar Von Mises stress, s from your 6

components is: (x=dir 11, y=dir22, z=dir33, and shear on xy plane is dir 12, etc).

u

OK, glad we got that out of the way.  What does all that mean?  Simply stated, Von Mises says that only the stresses which act 

to distort the shape of the part, will matter when checking for yield.  If you were to mold a cube, like our stress­cube pictured 2 

pages ago, but out of solid glass – and then you dropped it in the deepest trench in the ocean, 7 miles down – the pressure on 

each face of the glass would be enormous.   But the Von Mises stress would be zero, because the pressure would act 

everywhere equally, in all directions, the cube would simply shrink, but would otherwise not flex.   (Unless you had some 

molding defects, like air bubbles in the glass or variations in the density, the glass should survive any depth).

The Von Mises equation computes the net energy stored by element distortion, and then backs that value out as an equivalent 

stress.  Unlike the 6 components of stress that feed into it, V.M stress has no direction, only a magnitude.  We compare this 

number to our uni­axial Tension test, and there you have it – your yes­no criterion!

So let’s get back to that linkage arm for which we listed all the stress 

components – the plot of each element’s Von Mises stress is shown at right.  

Even though 3 other components of stress were all located in one (other) 

place, the most highly­distorted element is located inside the intersection of 

two holes, (which is also where the Y­axial stress was the greatest).  

Interestingly, the peak Y­component of stress was over 28,000 psi, but the Von 

Mises stress in the same area is less, about 27,600 psi.

This must mean that the other 5 components of stress in this immediate area 

must be acting such that they cancel out, to a small degree, some of the Y­axis 

distortion.

Other Yield Theories

It should be stated right here, that Richard Von Mises stress is not the only kid on the block.  Other theories exist about how to 

evaluate the total state of stress.  Especially, if you have a brittle material like glass, or concrete, then you should instead 

compare the material Yield Strength to the Mohr­Coulomb stress, or often just ‘Coulomb Stress’.

Coulomb stated that most things fail in shear.  Once you transpose the coordinate system in which you view the part, to that 

orientation which produces the plane of worst­case shear, you just assume THAT shear is the value that is going to cause a 

crack to appear.  It turns out that Coulomb’s theory is more conservative than Von Mises, and most engineers will use the 

Coulomb criterion for brittle materials, and Von Mises criterion for ductile materials like steel, aluminum, most plastics, etc.

Of course, material properties are not tabulated for the estimated engineering shear stress at which a test specimen fails, they 

are tabulated only for the engineering tensile stress.  So if our material is brittle, we need to know the equivalent tensile­stress 

magnitude, corresponding to the worse­case shearing plane, as experienced by each finite­element.   In Solidworks Simulation 

you do this by choosing the plot type:

“INT: Stress Intensity (P1­P3)”

And what, you might ask, are “P1” and “P3”?   Good question!  But not nearly as important a question as “what is Von Mises 

stress”.   And the majority of engineering materials qualify as ‘ductile’ for our purposes, so that is why Solidworks creates a 

Nodal plot of Von Mises stress, as the default output, for every linear, static study.   And this article has gotten too long 

already, so we’ll pick up the topic of other Directional stress components, for the next installment of KAP’s Corner.

Posted in KAP's Corner | Tagged FAQ, Frequently Asked Questions, KAP's Corner, Simulation, Tech Tips, Von Mises Stress

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