When the geometry of the part is relatively uncomplicated and
the orientation of a flaw is well known, the length (a)
of a crack can be determined by a technique known as tip diffraction.
One common application of the tip diffraction technique is to
determine the length of a crack originating from on the backside
of a flat plate as shown below. In this case, when an angle beam
transducer is scanned over the area of the flaw, the principle
echo comes from the base of the crack to locate the position of
the flaw (Image 1). A second, much weaker echo comes from the
tip of the crack and since the distance traveled by the ultrasound
is less, the second signal appears earlier in time on the scope
Crack height (a) is a function of the ultrasound
velocity (v) in the material, the incident
and the difference in arrival times between the two signal
(dt). Since the incident angle and the thickness of the
material is the same in both measurements, two similar right triangle
are formed such that one can be overlayed on the other. A third
similar right triangle is made, which is comprised on the crack,
the length dt and the angle Q2.
The variable dt is really the difference
in time but can easily be converted to a distance by dividing
the time in half (to get the one-way travel time) and multiplying
this value by the velocity of the sound in the material. Using
trigonometry an equation for estimating crack height from these
variables can be derived as shown below.
Solving for "a" the equation becomes
The equation is complete once distance dt is calculated by dividing
the difference in time between the two signals (dt) by two and
multiplying this value by the sound velocity.