Question

The leakage limit of an aluminum alloy to uniaxial tensile is Y = 320 MPa. The same material also leaks into a complex load described by the tensile state [σij]:

330 95 0 Съ-| 95 70 01 MPa 00150

Consider what leakage criterion (Treska or Mises) best describes the behavior of the material.

Answer 1

Comparing with the matrix

xx	xy	xz
yx	yy	yz
zx	zy

We get

_xy=_yx= 95

_xz=_zx= 0

_yz=_zy= 0

_xx= 330

_yy= 70

_zz= 150

maximum principle stress is given by

=(_xx+_yy)/2+(((_xx-_yy)/2)²+_xy²)^1/2

This gives

₁=361

₂=180

₃=330

and corresponding max shear stresses are :

₁=161

₂=40

₃=90

Now Von mises stress is given by :

therefore = 167.66

Now tresca's criteria states that if the principal stresses are arranged in decreasing order then

thus

Now factor of safety

for von mises is 320/167.66 = 1.91

for Tresca is (320/2)/90.5 = 1.77....... (For isotropic material, Shear stress limit is half that of tensile strength)

Thus Factor of safety for tresca's criteria is less and thus it best describes the behavior of the material.