6. Moire methods (In Plane)

Question 1

What is the moire effect?

Answer 1

Interference of light by a network of lines / array of dots, concentric circles or radial lines.

Question 2

How is the moire effect useful to us in stress analysis?

Answer 2

It visually magnifies motions and displacements, and fringes are produced which are contours of distortion. Strains or shapes then, can be deduced from measuring such displacements.

Question 3

Notate these rotated motifs (superimposed equidistant straight lines) according to standard geometric moire theory.
Assume slightly different pitch (p does not equal q).

Answer 3

Number the lines, fringes and mark the origin.

Question 4

We can see that for the vertical lines x=lp
given that mq=xcostheta + ysintheta
rearrange for y for the second family of lines.

Finding a relationship for N from the graph, substitute your x and y equations into that relationship, and rearrange the final equation for Nq, assuming small theta.

This, written in terms of epsilon_x, is the moire fringe equation. How can we write it using this term?

Answer 4

we know that the pitch changes (from p to q) due to strain.

This strain in the x direction (epsilon_x) is equivalent to (p-q)/p

Question 5

A fringe shift is used as a device to measure the factors which the moire fringe equation shows the fringe order to be dependant on.

So tell me james, what is it measuring?

Answer 5

change of pitch (strain) (p,q)
change of relative position (translation) (x,y)
change of relative orientation (rotation) (theta)

Question 6

Using the diagram for aid, explain how a fringe pattern is produced

Answer 6

Light passes through specimen grating and undeformed master
Some areas, light is blocked
Eye averages data (acts as a low-pass filter)
Resulting fringe pattern

Question 7

More simply, derive epsilon_x using knowledge from the strength of materials.

Answer 7

As p is constant, a moire fringe is a locus of points of constant displacement

Question 8

Explain and comment on direct superimposition as an observation technique for in plane motion

Answer 8

one grating on specimen
master grating attached (via corner clamp or oil)

+ eliminates distortional effects
+ best on transparent materials
- contact must be maintained between motifs, or else fringe visibility suffers

Question 9

Explain and comment on double-exposure as an observation technique for in plane motion

Answer 9

grating on specimen
first exposure, unloaded
second exposure, loaded

+ Two photographic plates can be used
to reduce effect of rigid body motions
-Concerning distortions, film shrinkage affects both gratings
- Real-time viewing is not possible
- Technique is limited by photographic resolution

Question 10

A two dimensional strain field benefits from increased accuracy. Suggest two methods and give the equation for the stress.

Answer 10