Failure Modes - Principles of Human Joint Replacement - page 37

˃ f = ˃ m + ˃ r S y /S n (4)
Where the mean stress ˃ m and the range stress σ r are:
˃ m = (˃ max + ˃ min )/2 (5)
˃ r = (˃ max - ˃ min )/2 (6)
where ˃ f is the failure stress, ˃ max is the maximum stress at a point during the
fluctuation and ˃ min is the minimum stress.
For typical implant or instrument S n is replaced by S m and a part is assumed
safe against fatigue, if:
S m /N < ˃ m + ˃ r S y /S m (7)
where N is the factor of safety.
2.2.4 Factor of Safety
The factor of safety, occasionally called the factor of ignorance, is used to account
for the fact that all estimates of safety against fracture are approximations and in
most cases the expected loads are only estimates. Among the factors used are
those that reflect the level of control over the materials and manufacturing process
used, the accuracy of the computational methods used, the knowledge of what
loading to expect and the degree of safety required. Where human safety is
involved a factor of safety of 2 is normally used [5].
2.3 Stress Computation
In order to use the equations above one must, of course have an estimate of the
stresses within or on a body. These stresses are obtained by “Stress Analysis”.
Classically, designers used either methods based on the Strength of Materials
approach or elasticity methods. Today the Strength of Materials approach has little
benefit in the analysis of implants since accurate analysis is critical. It can,
however, be of use in the analysis of instruments due to the often simple shapes
involved. The software package “MathCAD” can be used for such computation
and contains a number of subroutines for computation using strength of material
methods.
The advent of computer based solid modeling and inexpensive numerical
methods based on the theory of elasticity, however, make Finite Element Analysis
(FEA), the most commonly used approach. Since this method is based on the
classical linear theory of elasticity [3], occasionally modified to include nonlinear
effects, an understanding of this theory is essential in understanding the use and
results of FEA methodology and software.