Page 168 - Biaxial Multiaxial Fatigue and Fracture

Fatigue Limit of Ductile Metals Under Multiaxial Loading 153

Table 1. Coefficients AQ for the calculation of equivalent mean stresses, x = O,,, y = Ora and z

= 5ya

j
1 1 2 3
2
4x2+3y2-4xy+7z2 3x2+4y2-4xy+7z2 2x2+2y2-3~+3z
1
2
2
3z
32
y2
x2 + y2 - xy i x2 i - ry +32 2 x2 + y2 - xy i
7x2 + 7 y2 - 6xy + 86r2 10~z-6~~ -6xzi l0yz
2 2 2 x2 + y2 - xy i3z 2 2
y2
x iy2-xy+3z x2 i -xy + 32
5x2 + y2 i 2xy i 422 x2 + 5y2 + 2xy + 4z2 -k Y )z
2 3x2+3y2+2xy+4z 2
3y2
3x2 i + 2xy + 422 3x2 + 3y2 + 2xy + 42
1-
=xyad=w 0.8-

0.6- 130 test results

0.4- steel (bending&torsion)
0 steel (tension&torsion)
0.2 - AI-alloy
- equation
ellipse
0 I , I 1
0 0.2 0.4 0.6 0.8 1
axad*w

Fig. 3. Fatigue limit under alternating normal and shear stresses

If one combines the eIIipticaI equation with coIIected test resuIts [25] to yield a standardised
diagram, Fig. 3, Eq. (19) then agrees with the test results.
For the case of an alternating nom1 stress with a superposed static shear stress, the
fatigue limit is decreased by the superposed static shear stress, Fig. 4. Up to a static shear stress
zVm which is lower than the yield strength RPo.2, the influence of the superposed shear stress is
correctly described by the SIH. Beyond this value, however, the influence of the superposed
shear stress is overestimated. With rxrm > Rpo.2, severe plastic deformations occur;
consequently, this case is defined by a static strength design, and is of no importance for
practical applications.