Polariscope: Practical Design

16
CENTRAL MECHANICAL ENGINEERING RESEARCH INSTITUTE (CMERI) COUNCIL OF SCIENTIFIC AND INDUSTRIAL RESEARCH (CSIR) INDIA

description

The presentation will enable you to design a polariscope: an instrument used for experimental stress analysis at very low cost

Transcript of Polariscope: Practical Design

Page 1: Polariscope: Practical Design

CENTRAL MECHANICAL ENGINEERING RESEARCH INSTITUTE (CMERI)COUNCIL OF SCIENTIFIC AND INDUSTRIAL RESEARCH (CSIR)

INDIA

Page 2: Polariscope: Practical Design

At the end of the talk, you would be able to-

Design Your Own Polariscope At A Cost Within $50.

Page 3: Polariscope: Practical Design

Definition of mechanical stress: Internal forces acting inside a deformable body.

Reasons for such internal forces:-Due to applied external forces.-Atomic forces.-Forces generated due to thermal expansion of the body.-Due to vibrations ………………. And many MORE.Consequences:-Material fatigue.-Fracture.-Degradation in material strength.Stress is a tensor quantity Has magnitude and multiple directions (more than one).

Fig 1. Shear Stress

Stress is a tensor quantity Has magnitude and multiple directions (more than one).Types of stresses Principal Stresses and Shear Stress.Principal stresses are the stresses acting on the principal axes of the body. Principal axis isdefined as the axes at which magnitude of shear stress is zero.As stress is a tensor, it is denoted by a matrix called Cauchy’s matrix and the matrix gives thestress components in different directions. In 3-D analysis the matrix is given as:

The eigen values of the matrix corresponds to principal stresses and the eigenvectors gives the directions in which these principal stresses act and so called principal directions.Shear stress can be physically understood as the stress component coplanar with the body. Figure 1 shows its physical significance.

Page 4: Polariscope: Practical Design

Birefringence in physics is defined as a property of some materials like Calcite, Glass, Plasticsto exhibit double refractive indices when stress is present in the material. In other words, astressed birefringent material shows different refractive indices to a beam of light in differentdirections and hence light will be subjected to different phase retardation along different directions. The effect in mechanics is known as photo-elasticity.

The effect of birefringence can be felt if polarized light is incident on such materials.If monochromatic polarized light source is used to illuminate such stressed birefringent objecta pattern with dark and white fringes are observed. In case a white light source is used, coloredpatterns are seen. Figure 2 shows such effect.The stress optic law which relates principal stresses andthe induced phase retardations is given by:

Fig 2. Birefringence Demonstration

the induced phase retardations is given by:

where R is the induced retardation, C is the stress optic coefficient, t is the specimen thickness, σ11 is the first principal stress, and σ22 is the second principal stress.

Page 5: Polariscope: Practical Design

A polariscope is an instrument for analysis of stress in a birefringent material. If the material isnot birefringent, say for example metals, the material is coated with a thin layer of knownbirefringent material. Different types of polariscope are available in theory and in market. Wehave designed and developed a Gray field polariscope (GFP) for stress analysis, as it is very simpleand includes least complex mathematics.

Figure 3 shows a commercially availableGFP schematic. However, as seen here ithas a rotating section, in order to orientit in particular orientation before imagecapturing. This feature limits its applicationcapturing. This feature limits its applicationin dynamic stress analysis, i.e. whenstress on an object changes very rapidly ina short period and its not possible to rotate the required part in that shortinterval.

So, instead of the rotating part, we useda beam splitter here and pasted linearpolarizing plates at required orientations. Figure 3

Page 6: Polariscope: Practical Design

Figure 4

Page 7: Polariscope: Practical Design

S.No Material Cost Website

1 Linearly polarizing plate (A4 size)Product No: P210

Polarizer 210x300mm

$10+ 5 (shipping)

http://www.3dlens.com/shop/polarizer-210x300mm.php

2 Circularly polarizing filters $8 http://www.ebay.in/itm/52MM-CPL-FILTER-CIRCULAR-

POLARIZER-4-NIKON-D3100-D5100-

/270923037183?pt=LH_DefaultDomain_203&hash=item3ultDomain_203&hash=item3f144579ff#ht_2737wt_958

3 Beam SplitterProduct No: 408

Multi Image Fresnel Lens

$2 http://www.3dlens.com/shop/multi-image-fresnel-

lens.php

4 Light source (LED with a reflector) found at local electronic shops

$1

5 Plexiglass sheets for making stands and base found at local

hardware stores.

$10

Contd…

Page 8: Polariscope: Practical Design

For static stress analysis (i.e. when stress does not change with time), normal good qualityCameras can be used to capture the images like Sony CyberShot DSC-W610 or BenQ 14 MP Point & Shoot Digital Camera which is available within $70. For dynamic stress analysis, a camera with high frame rate is required. Such cameras arealthough costly but are affordable. We have used Casio EXILIM ZR-200 at 1000fps movie modefor dynamic stress analysis. The cost of such cameras lies in range of $400.

In this way, we can design a polariscope at throw away price.

Page 9: Polariscope: Practical Design

Side view Top view

Base Plate

Light Source

Sliders

Linear Polarizer

Circular Polarizer

4 image Beam Splitter

Linear polarizing plates at 0, 45, 90 and 135 with respect to polarizer

Page 10: Polariscope: Practical Design

For a Gray field polariscope/poledioscope the measured value of light intensity from the image/image detection unit is given by Equation:

2

1 sin sin 2( )2

aI cos 2 sin 2a c sI I I I

WhereI is the intensity of the image pixel under consideration procured from detection unit ofpolariscope.Ia = a2/2 is the average light intensity collected by detector unit.α is the orientation of linearly polarizing plates in the analyzer.

2

( sin )sin 22c

aI

2

( sin )cos 22s

aI

Where 2 2Wherea is the amplitude of circularly polarized light.β is the orientation of fast axis or equivalently orientation of first principal strain with reference.Δ is the amount of phase lag for the slow axis compared to the fast axis.

In the mentioned experimental set up images were captured at 4 different orientations of the analyzer unit i.e. (α= 0, 45, 90 and 135 degrees). For each of these values of α, Equation 4 can be written as Equations

1 1 sin sin 2aI I

2 1 sin cos2aI I

3 1 sin sin 2aI I

4 1 sin cos 2aI I

Page 11: Polariscope: Practical Design

Solving the equations:

1

2 2 2

3 1 4 2

1

2 a

I I I II

1 1 3

4 2

1tan

2

I I

I I

11 22

2 (2 )C t

Using stress optic law

Where,C is the stress optic coefficient.t is the specimen thickness. (2t is used as light travels through the coating twice in reflectionphoto-elasticity).photo-elasticity).σ11 and σ22 are the principal stresses.λ is the wavelength of light used.

12 11 22( ) tan 2 The shear stress can be found by Mohr circle as

In order to evaluate stress optic coefficient of the material under consideration, we impose a material of known shape to known stress. We imposed a disk coated with birefringent materialEthylene Vinyl-Acetate (EVA) under known stress. The EVA material is inexpensive and is availableat local electronic shops in form of Glue gun sticks. Its low melting point enables us to melt it and coat the target material with it of uniform coating thickness.

Page 12: Polariscope: Practical Design

EVA coated disk

The solutions for the normal stresses along the horizontal diameterare given by:

22 2

11 2 2

2 4

4x

P D x

hD D x

4

22 22 2

2 41

4y

P D

hD D x

4 2 2

11 22 22 2

8 4

4

P D D x

hD D x

Schematic for diskunder compression

Where, P is the applied load, h and D are the sample thickness and diameter respectively. The values of Δ (phase lag) on X axis of the disk were scanned with respect to position of the point on the axis. The stress optic law was compared with the mathematical equation to find stress optic coefficient.

Page 13: Polariscope: Practical Design

0 45 Obtained fringepatterns

90 135

Page 14: Polariscope: Practical Design

0

45

MATLAB

90

135

MATLAB

Stress in Pascals

Page 15: Polariscope: Practical Design

A very low costly polariscope for accurate and complete stress analysis is thus presented.

The design is useful for amateurs, hobbyists, students as well as researchers who are keen toPursue experimental stress analysis at least cost.

Page 16: Polariscope: Practical Design

In case of any design related queries feel free to contact at:[email protected]@cmeri.res.in

For algorithm related queries contact at:[email protected]