A “Toolbox” for Forensic Engineers

112 Forensic Materials Engineering: Case Studies
Figure 4.16 Microstructures of commercially pure (CP) titanium obtained by
thermal treatment (magnification: 400¥).
one surface is deformed into a convex shape and the material here is in
tension, while the opposite surface is deformed into a concave shape where
it is under compression. It is often thought that forensic work, being scientific
by nature, must always be accompanied by long mathematical arguments.
However, this is not the case as simple logic matched against the evidence is
the only way in which causation is determined. Nevertheless, there are occasions
where quantitative evaluation becomes valuable. A simple equation
used for evaluating stresses and strains on beams in bending is the “engineer’s
bending equation”:
M/I = s /y = E/R
where M is the moment on the beam, I the second moment of area of the
beam section, s the stress at a distance y across the beam section, E the tensile
modulus of the beam material and R the radius of curvature of the bent
beam (Figure 4.17). Some of these variables become constant when a single
type of beam is considered under two different loading conditions. Thus E
is constant (same material) and I is constant (same section shape).
A particular case that required calculation of strain on the outside of a
bend occurred when a manufacturer encountered a problem when forming