Failure theories and fatigue

Mechanics of materials is the spine of the Machine Design & Materials exam — about a quarter of it — and failure prediction is where a lot of those points live. You need both the static theories and the fatigue approach, and you need to know which one the problem is asking for.

Static failure theories

• Ductile materials: the maximum-shear-stress (Tresca) theory and the distortion-energy (von Mises) theory. Von Mises is the less conservative and the usual default; Tresca is simpler and more conservative.
• Brittle materials: maximum-normal-stress theory.
• Everything ties back to a factor of safety against the relevant strength (yield for ductile, ultimate for brittle).

Fatigue

• Cyclic loading is described by mean and alternating stress. The S-N curve gives life vs. stress amplitude; steels show an endurance limit.
• Mean-stress lines — Goodman, Soderberg, Gerber — combine mean and alternating stress against the material's strengths to predict whether a part survives.
• Stress concentrations matter far more in fatigue than in static loading; a fatigue stress-concentration factor amplifies the alternating stress.
• Real endurance limits get knocked down by surface finish, size, loading, and reliability factors before you use them.

Where people lose points

• Picking the wrong theory — applying a ductile theory to a brittle part, or vice versa.
• von Mises arithmetic on combined stress states.
• Mean-stress confusion — plotting the wrong point on a Goodman line, or using yield where ultimate belongs.
• Ignoring stress concentration in a fatigue problem.

How to study it

First, train the decision: static or fatigue? ductile or brittle? That routing is half the battle. Then drill von Mises on combined stress states and Goodman-line problems until the steps are automatic. This is dense, high-value territory — exactly where focused, diagnosed practice pays off.

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