Basic Materials Properties for Materials Selection - Medical Device Design: Innovation from Concept to Market - page 339

Cross-sectional area A

Force F

Extension e Original length l

Figure E.1
Rod under stress.

force

stress =

cross - sec tional area

(E.2)

F
A

N
m

σ =

2

The rod will extend in the direction of the force applied. The measurement for this is called strain ;
its symbol is the Greek character epsilon, ε . It is defined as the ratio of the extension of the rod to
the original length of the rod. It therefore has no units - it is a dimensionless quantity.

extension
original length
e
l

strain

(E.3)

m
m

ε

Hooke found that these two properties were interlinked for all solid materials. Indeed he
found that for all solids the relationship between stress and strain is linear; this is called
Hooke's Law. If we plot a graph of stress versus strain, for any given material, the graph
produced is very characteristic - see Figure E.2 .

Figure E.2 illustrates an example stress-strain curve for a ductile material. The yield stress ( σ y )
is the elastic limit of the material. If you deform a component to stress levels below this value
the material will deform, but will return to the original shape after the load is released. If you
load the component above this value the component will deform plastically, that is, some of the
deformation will be permanent and your component has failed. All safety factors are related to the
yield stress. A safety factor of 2, for example, means your maximum stress does not exceed σ y /2.

For some materials the yield point is not easily identifiable. In this case a common estimate for
yield stress is the proof stress. This is defined as the stress required to obtain a specific amount
of permanent deformation. Often this is 0.1% permanent deformation and it is then called σ 0.01 .

The yield stress and proof stress of a specific material is not constant. It is highly dependent
on how the material is treated (e.g., how it is processed and/or heat treated).