Aim Of Experiment:

The aim of the experiment is to locate the stress concentration areas (notches) in some structural elements. We also have to measure stress in notch areas and determine shape factors (
) based on measurement results.

Experimental Stand:

A reflection polariscope is the measurement instrument used. See diagram on figure 5,the polariscope can be used in both circular and linear version.

Polarizer P
, and analyzer A
, are placed in clamping rings attached on bearings to polariscope housing. The analyzer is capable of rotating because it is fixed in movable ring P within clamping rings. Two quarter-wave plates, C
and C
, fixed in their own rings within the clamping rings, are coupled by a separate gear, which ensures that both of them can be turned simultaneously by angle of 45 degrees left or right, and rotation angle is limited by guard finger K. The polariscope Is equipped with a source of white light with a halogen light-bulb.

In the image, appearing in the circular polariscope, one can see and observe interference fringes, called isochromatic lines, whose distribution is strictly related to stress field distribution (and, at the same time, to strain distribution) in the region where the coating is bounded on the examined object. On the free edge of the object, e.g. where the so-called bottom of notch is located, the normal stress, whose direction is perpendicular to the edge line, equals zero,
= 0. Equation (20) simplifies in these conditions to the form which makes it possible to directly determine the value of normal stress
of direction tangent to the edge line(see Equation 20)

The value of normal stress
of direction tangent to the edge line:

(20)

Where C is the correction coefficient depending on the proportion between rigidity of coating material and rigidity of object material.

In the case of plane state stress, the coefficient can be expressed by formula:

C

Where E
=
(Young's modulus of coating's material).

E
=
(Young's modulus of A1 alloy duralumin).

=10,7mm (thickness of the coating's material).

= 7,7mm(thickness of the Object.

= 0,32 (Poisson's ratio of A1 alloy duralumin ).

= 0,00128 (model constant).

N- The order (or number) of isochromatic line.

The linear regression of the measured data

Once we had read the order of fringes from the model, we applied linear regression model in order to determine the corrected value of the fringe order. With use of this approach, we removed the systematic error of the measurement.

The relation between N and P is assumed linear and computed with use of the linear regression method.

The coefficients
and
are computed with the use of the following equations (the result from the assumption of the linearization of the data and minimizing the RMS error).

(Part I, section5,3)

No. Of model:		1	2	3		4		5
N		1	1,5	2		2,5		3
P[N]		35	50	70		89		105
		1,03	1,45	2,01		2,54		2,98
N -		-0,03	0,05	-0,01		-0,04		0,02
N		0,98	1,39	1,95		2,48		2,93
[ ]		70,167	100,239	140,335		178,426		210,502
[ ]		540,289	771,841	1080,578		1373,877		1620,867
[ ]		7,1	10,1	14,1		18,0		21,2
S( )		-	0,07	0.04		0,03		0,02
a	9,883		9,925	9,953	9,913		9,929

Records of measurements and elaboration of results (Table 8.1

a₀= 0,054 a₁= 0,028

The standard deviation of random variable
according to (42) - is S(
)=
= 3,67*10

The error analysis

Stress
on free edge of The notch, determined from (8.2), is the realization of a random variable in indirect measurements.

The estimate of variance of variable
- according to formule (50) In section 5.2 of part I - equals

The value of S(
) from formula (45) see part 1, section 5.1.2 is

The isochromatic fringe orders reading error for assumed confidence level
are:

(Part1 section5,1,2 Table3)

=0,056

The limiting error of measurement of The determined stress
is then

The error of mesurement of The shape factor
can be calculated using The formula (48c):

.

The scatter Plots based on Table (8.1)

REMARKS AND CONCLUSIONS:

When a photo elastic material is subjected to a load and illuminated with polarized light from the measurement instrumentation (called a reflection polariscope), patterns of color appear which are directly proportional to the stresses and strains within the material.

Loading beyond a order 5 fringe will risk elastic deformation or fracture of the specimen.

The transition lines seen between the red and green bands are known as "fringes." The stresses in the material increase proportionally as the number of fringes increases. Closely spaced fringes means a steeper stress gradient, and uniform color represents a uniformly stressed area. Hence, the overall stress distribution can easily be studied by observing the numerical order and spacing of the fringes.

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