Mechanical Engineering Design Notes

Design Contents

Preliminary Matters
Design Methodology
..brain storming
..evaluation matrix
Statistical Considerations
..variability in materials
..variability in dimensions
..variability in loading
..preferred sizes
Design Factor
Introduction to Failure
Failure Theories
Application of von Mises
..criterion in 2 D

Stress Concentration
..and notch sensitivity
Failure Under Combined Loading
..combined bending and torsion
Failure Under Cyclic Loading
..fracture mechanics
Instability - Buckling
Concentrically Loaded Strut
..slender columns
..Euler formula
..effective length
..short and intermediate columns
Eccentrically Loaded Strut
.. theory
Shock Loading

FAILURE UNDER CYCLIC LOADING - Fatigue, Fracture and Crack Growth Rates

1 Fatigue - Involves crack initiation followed by crack growth

Requires cyclic - repeated stressing - normally cracks only develop under tensile stresses.
Fatigue is only a problem when the failure is unexpected
Fatigue contributes to 80 - 90 % of all failures
Offshore fatigue contributes to 20 - 25% of failures

Fatigue has been recognised and researched for 120 years - so - why is it still a problem?

A major reason is that it is complex.
Welding now used extensively - and is a potent source of defects
Higher mechanical efficiency is being required, leading to more highly stressed components.

Comparatively recent techniques enable calculations to be made predicting the life or remaining life of a structure containing defects.

There are two stages in fatigue: crack initiation and crack growth. For some materials, ferrous metals being an important group, low cyclic stresses, below the 'threshold limit', do not lead to crack initiation.

Fatigue damage normally starts where cyclic stresses are most severe, this will often be at somewhere on a component surface where there is some imperfection or notch. For smooth specimens with a gradually changing section impurities or inhomogeneities in the grain structure provide crack initiation points. For these reasons it is important to take care when designing components which contain changes in section and features such as - key ways, screw threads, 'O' ring grooves, etc. to ensure that their effects are properly assessed. For components subjected to very high cyclic stresses, high purity steels may be used to minimise potential crack initiation locations, an example of this is the steel used by some manufacturers of ball and roller bearings.

2 Design philosophies:

2.1 Safe life:
Developed in the late 1950s and 1960s for the aircraft industry.
Still widely used, based on S-N curves, but although mean values are available for many materials, experimental curves contain a lot of scatter.
Some effects are important and fairly well understood, effects of surface roughness, components size, notches.
The effects of mean stress may need to be considered as most data has been generated for R = - 1 (zero mean stress) a little data is available for R = 0 ( zero - tension loading). (R = minimum stress/maximum stress). For different loadings, it is necessary to carry out a transformation using:
Goodman Line, Goodman criterion "Calculator" Gerber Parabola, Soderberg Line or Smith Curve.

There were however two significant problems with this approach:

  • The structure was not protected if it contained a manufacturing or maintenance induced defect.
  • Owing to the spread of results, a conservative safety factor was required and many components were prematurely retired. Even testing to 4 times the required life did not prevent some aircraft losses.

2.2 Fail Safe:
Developed in the 1960s for aircraft design to overcome limitations of the 'Safe Life' methodology.
The idea is to multiple load path structures, such that if an individual element should fail, the remaining elements would have sufficient structural integrity to carry the additional loads from the failed element until until the damage is detected through scheduled maintenance.
Designers and operators live safely with cracks. This was not a feasible approach until the 1960's when fracture mechanics started to be able to provide a quantative description of the residual life of a cracked component.

In addition to the multiple load paths, crack stoppers are often used. These may consist of materials with a high fracture toughness used to supplement the residual strength of the surrounding structure and to prevent cracks propagating to failure.
An example of a crack stopper is a stringer in a pressurised aircraft fuselage.

2.3 Defect (or Damage) Tolerant Approach:
Developed in the 1970s for aircraft design and based upon fracture mechanics techniques.
This is useful for complex structures with inherent defects, it is assumed that all structures contain growing cracks and failure can occur when actual conditions are different to those modelled.
For this approach to be used facilities must be available for measuring crack lengths. Generally defects need to be bigger than the grain size of the metal for the fatigue strength to be lowered.

For aircraft the objective is to detect cracks in 'Principal Structural Elements' (PSE) before they propagate to failure. By establishing inspection intervals for the PSEs based on the time it takes for a crack to grow from an initial detectable size to the critical crack length, safe operation can be maintained. This computation is quite complex and will involve working from the detailed usage programme of the plane.
Having determined the number of flight hours to failure, this is normally divided by two to give an inspection interval, this means that should a PSE develop a crack it should be inspected at least once before the crack propagates to failure.

This methodolgy means that undamaged components are not retired and factors of safety can be reduced as fracture mechanics provides a more precise characterisation of crack behaviour, the large scatter factors associated with fatigue results and methods are not required.

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