Mechanical properties - Orthopaedic Biomaterials in Research and Practice - page 55

(true stress), again for easy experimental determination. Modern
handbooks and tables cite true values of σ m . This value is given
rather than the stress at failure (σ u ) since σ m is either equal to or
greater than σ u and it is assumed in actual applications that if
external loads are sufficient to produce σ m , they will be sustained
and lead to rapid post-necking fracture.

4. Elongation at fracture (or elongation to failure). Again based on
laboratory tests, this is the amount of deformation remaining after
failure and thus is a measure of ductility. Frequently expressed
as a percentage, it is then called percent elongation . It is usually
determined by placing marks 1 to 2 inches apart on the tensile
specimen before testing. This dimension is called the gage length
and may be quoted in the data table. After testing to failure, the
two parts of the specimen are reapproximated and the separation
between the gage marks is measured. Then, the elongation is cal-
culated as follows:

Percent elongation Final lengthGage length
Gag

−
e length

= × 100 .

This is a strain; thus, it has no dimensions and is equal to ε u − ε r ,
where ε r is the elastic strain at failure (= σ u / E ) (see Figure 3.1).

For highly ductile materials, percent elongation is an excellent,
but still slightly low , estimate of ε u (expressed as a percentage). If
it is cited as “percent elongation before (or at ) failure,” then it is
measured intraexperimentally and is explicitly equal to ε u , without
allowance for elastic recovery after fracture.

5. Reduction in area. This is another measure of ductility, which is
easy to obtain experimentally in highly ductile materials. Frequently
expressed as a percentage, it is then called percent reduction. No
gage length or specimen marking is required. A circular cross-
section tensile specimen is used, and its diameter is measured ini-
tially and after failure. Then,

2 2

(( original diameter )( − final diameter ))

Percent reduction = × 100

.

2

( original diameter )

For incompressible materials (υ = 0.5), this will be the same
as percent elongation but will be less than that if υ < 0.5. It may
also be measured intraexperimentally, with some difficulty, and
then the value is cited as “percent reduction before (or at ) fail-
ure” and is related to percent elongation obtained under the same
conditions.

6. Toughness . This is the ability to absorb energy before failure and
is especially important for applications involving impact, such as
the striking face of a surgical mallet or impactor. As previously