Can anybody through some light on material fatigue theory ... Von Misses Stress etc?

Question

Can anybody through some light on material fatigue theory ... Von Misses Stress etc?

Answer 1

A very good account of what you want is in Wikipedia. It starts like this:

The von Mises yield criterion[1] suggests that the yielding of materials begins when the second deviatoric stress invariant \ J_2 reaches a critical value \ k. For this reason, it is sometimes called the \ J_2-plasticity or \ J_2 flow theory. It is part of a plasticity theory that applies best to ductile materials, such as metals. Prior to yield, material response is assumed to be elastic.

In material science and engineering the von Mises yield criterion can be also formulated in terms of the von Mises stress or equivalent tensile stress, \ \sigma_v \,, a scalar stress value that can be computed from the stress tensor. In this case, a material is said to start yielding when its von Mises stress reaches a critical value known as the yield strength, \ \sigma_y. The von Mises stress is used to predict yielding of materials under any loading condition from results of simple uniaxial tensile tests. The von Mises stress satisfies the property that two stress states with equal distortion energy have equal von Mises stress.

Because the von Mises yield criterion is independent of the first stress invariant, \ I_1, it is applicable for the analysis of plastic deformation for ductile materials such as metals, as the onset of yield for these materials does not depend on the hydrostatic component of the stress tensor.

Although formulated by Maxwell in 1865, it is generally attributed to von Mises (1913).[2] Huber (1904), in a paper in Polish, anticipated to some extent this criterion.[3] This criterion is referred also as the Maxwell–Huber–Hencky–von Mises theory.