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von
Mises, an applied mathematician forced to leave Germany in 1933, came to
Harvard in 1939. He gave the first university course on powered flight
in 1913, and made and piloted a 600- horsepower aircraft for the
Austrian army.
von
Mises developed a criterion for the yield stress of ductile materials that
employs the total distortional strain energy in the sample. Originally
developed for mathematical convenience, the model provides a better fit
to data obtained on ductile samples than the Tresca criterion. Written
in terms of the principal stresses this criterion states that yield will
occur when:
sM
= (1/2[(s1
- s2)2
+ (s1
- s3)2
+ (s2
- s3)2]
)0.5.
The
value of sM
can be obtained from a uniaxial yield stress determination since for uniaxial
tension s1
= sy
= yield stress, and s2
=
s3
=
0, so that sM
= sy
. The term in the square root is also proportional to the shear stress
on the octahedral planes of the coordinate system defined by the principal
axes. |
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