Material strain is proportional to material stress.
The ratio of the stress applied to a body to the strain produced.
When sound travels in a solid material, one form
of wave energy can be transformed into another form. For example,
when a longitudinal waves hits an interface at an angle, some
of the energy can cause particle movement in the transverse direction
to start a shear (transverse) wave. Mode conversion occurs when
a wave encounters an interface between materials of different
acoustic impedances and the incident angle is not normal to the
interface. From the ray tracing movie below, it can be seen that
since mode conversion occurs every time a wave encounters an interface
at an angle, ultrasonic signals can become confusing at times.
In the previous section, it was pointed out that when sound waves
pass through an interface between materials having different acoustic
velocities, refraction takes place at the interface. The larger
the difference in acoustic velocities between the two materials,
the more the sound is refracted. Notice that the shear wave is
not refracted as much as the longitudinal wave. This occurs because
shear waves travel slower than longitudinal waves. Therefore,
the velocity difference between the incident longitudinal wave
and the shear wave is not as great as it is between the incident
and refracted longitudinal waves. Also note that when a longitudinal
wave is reflected inside the material, the reflected shear wave
is reflected at a smaller angle than the reflected longitudinal
wave. This is also due to the fact that the shear velocity is
less than the longitudinal velocity within a given material.
Snell's Law holds true for shear waves as well as longitudinal
waves and can be written as follows.
VL1 is the longitudinal wave velocity
in material 1.
VL2 is the longitudinal wave velocity
in material 2.
VS1 is the shear wave velocity in
VS2 is the shear wave velocity in
In the applet below, the shear (transverse) wave ray path has
been added. The ray paths of the waves can be adjusted by clicking
and dragging in the vicinity of the arrows. Values for the angles
or the wave velocities can also be entered into the dialog boxes.
It can be seen from the applet that when a wave moves from a slower
to a faster material, there is an incident angle which makes the
angle of refraction for the longitudinal wave 90 degrees. As mentioned
on the previous page, this is known as the first critical angle
and all of the energy from the refracted longitudinal wave is
now converted to a surface following longitudinal wave. This surface
following wave is sometime referred to as a creep wave and it
is not very useful in NDT because it dampens out very rapidly.
Beyond the first critical angle, only the shear wave propagates
into the material. For this reason, most angle beam transducers
use a shear wave so that the signal is not complicated by having
two waves present. In many cases there is also an incident angle
that makes the angle of refraction for the shear wave 90 degrees.
This is known as the second critical angle and at this point, all
of the wave energy is reflected or refracted into a surface following
shear wave or shear creep wave. Slightly beyond the second critical
angle, surface waves will be generated.
Note that the applet defaults to compressional velocity in the
second material. The refracted
compressional wave angle will be generated for given materials
and angles. To find the angle of incidence required to generate
a shear wave at a given angle complete the
Set V1 to the longitudinal wave velocity of material 1. This material could be the transducer wedge or
the immersion liquid.
Set V2 to the shear wave velocity (approximately one-half
its compressional velocity) of the
material to be inspected.