# Fatigue

### Index

### General

In certain cases materials subjected to cyclical loads break also if their yield strength was never reached during service; this phenomenon is known as "fatigue".

The life span of a mechanical component subjected to cyclic loada depends in general on the following main factors:

- Material used to manufacture the component
- Type and value of operational stress
- GShape of component, and in particular presence of stress raisers(notches)
- Operational environment (more or less aggressive)
- Surface condition (roughness, surface stresses if any)
- Frequency of loading cycle.
- The recent approach to the problem of fatigue distinguishes the subject in a first phase of incubation of the fatigue crack and a second phase of propagation of the crack, and concentrate on the latter.

The classical approach is based on the number of loading cycles required to reach fracture of a standard test piece, and brought in the past to define, for some families of materials (hardening and tempering steels) the concept of "fatigue limit".

### Definitions

US definitions, drawn from MIL-HDBK-5, are used.

- Maximum stress Smax: maximum value of stress reached during fatigue cycle
- Minimum stress Smin: minimum (algebraic) value of stress reached during fatigue cycle
- Stress ratio R = Smin/Smax; in detail R=-1 for alternatinng stress and R=0 for pulsing stress
- Cycles to failure N: number of fatigue cycles at which the rupture of the test piece happens; in many cases in the fatigue plots instead than the value of N the relevant decimal logarithm is shown.
- Notch factor or stress intensity factor Kt: factor by which the local mean stress is intensified due to presence of notches; for unnotched test pieces Kt=1
- Crack propagation rate da/dN, where 2a is the crack length at a certain moment of the propagation phase.
- Stress Intensity Factor Range Δ K = Y (Smax - Smin) √a, where Y is a numerical constant and a the crack length

### Presentation of data

In general the fatigue properties of a material are determined experimentally on test pieces and shown as plots in form of

Fatigue curves (diagrams Smax versus N or versus log(N)), that show the number of cycles to rupture versus the maximum stress; these plots should report the type of stress applied (tensile, bending, etc.), the stress intensity factor, the stress ratio, the test environment, (if different from air in normal conditions of temperature and relative humidity), the frequency of application of load (if different from those normally used for testing, for which the experimental values are deemed not to be influenced by frequency) and, for aluminium alloys and other non isotropic materials, the metallurgical direction.

Crack propagation diagrams (diagrams da/dN versus Δ K), showing the speed at which the crack propagates as a function of level of applied stress.

### Stress intensifiers

The mechanical components contain in general abrupt changes in sections, holes, fillets, grooves that, under load, produce locally stress levels higher than the average stress levels computed on the basis of the nominal cross section.

Such local stresses depend on the shape of the part and the type of material.

The geometrical stress intensity factor or notch factor Kt is defined as the ratio of the local maximum stress and the average stress referred to the nominal cross section; the value of this factor can be drawn from the relevant manuals, or experimentally by use of photoelastic analysis, or using brittle lacquers, or with finite elements computing techniques.

As an example the data for a cylindrical part stressed in tension are shown.

### Design criteria

For the design of a fatigue stressed part the following should be considered:

Selection of material: some aluminium alloys, specially those typical of aerospace, have been detailed investigated for fatigue, and the relevant data are available in bibliography. In general the alloys with the higher static allowables show the best fatigue properties.

Shape of part: particular care shall be given to stress raisers, in particular sharp corners and sharp slots shall be avoided wherever possible.

Surface conditions: the data of the fatigue curves are generally drawn out of test pieces ground with fine sand paper; rough finishing decreases consistently fatigue strength; the same as far as deep scratches and notches are involved. In the most critical cases local treatments of pre-compression of surfaces (shot peening or cold rolling) can be applied.

Surface protection: shall be adequate to the operating environment of the component, since possible corrosive attack can start building of fatigue cracks; pay attention that, specially for low cycle fatigue, anodising (and particularly hard anodising) reduces fatigue strength.