Photoelasticity determination of a deformation or stress field

• US 4,914,487 A
• Filed: 02/19/1988
• Issued: 04/03/1990
• Est. Priority Date: 02/19/1987
• Status: Expired due to Fees

• Current Assignee: M A T R A
• Original Assignee: Matra
• Inventors: Croizer, Pierre, Dessendier, Philippe
• Primary Examiner(s): Rosenberger, Richard A.
• Application Number:
  US07/158,804
• Time in Patent Office: 774 Days
• Field of Search: 356/364, 356/366, 356/367, 356/33, 356/34, 356/35
• US Class Current: 356/35
• CPC Class Codes: G01L 1/241 by photoelastic stress analysis

Abstract

A method for photoelasticity examination of a stress or strain field comprises successive steps. A two dimensional image of a test-piece is formed which has isochromatic fringes in the form of an array of pixels and the grey level of each pixel is stored as a digital value. From the isoclinals, the orientation of the main stresses σI and σII is determined at each pixel and the angle of orientation is stored for obtaining each pixel; from the stored pixels, the law of variation of brightness is worked out along at least three lines parallel to an arbitrary direction chosen by the operator and passing completely through the test-piece; from a condition at the limits and by finite differences then integration, a value is determined representative of σI and σII at each point of the median line among the three lines and σI and σII are derived from the stored digital values and from the computed values of σI and σII. A device for carrying out the method includes a polarizer and an analyzer whose relative angle may be modified, an imaging system and a computer for carrying out the successive computation steps.

Claims

1. Method for photoelasticity determination of the distribution of principal stresses along a straight line segment across a loaded test-piece of a material exhibiting induced birefringence, comprising the steps of:

(a) directing polarized monochromatic light on the test-piece, forming a two-dimensional image of said test-piece as a two-dimensional array of pixels under conditions causing isochromatic fringes to appear while eliminating isoclinals and storing a brightness value for each of said pixels in digital form;

(b1) directing light having a first angular direction of linear polarization onto said test-piece, forming a two-dimensional image of said test-piece as a two-dimensional array of pixels under conditions which provide isoclinals and storing data including only those pixels which are located on said isoclinals with said first angular direction of polarization at least in a part of interest of said image including said straight line segment and two lateral straight line segments located on either side of the first-named straight line segment, at the same distance thereof and parallel thereto;

(b2) repeating step (b1) with a plurality N-1 of other and mutually different angular directions of linear polarization, N being an integer greater than 1, whereby a table is obtained storing a respective angular direction of polarization for each of said pixels in the part of interest;

(c) deriving the value of the difference between the respective principal stresses at each pixel along said straight line segment from said stored brightness values,

(d) computing a partial derivative of the variation of the stresses along a predetermined direction at each point of said first-named straight line segment from the stored values of the difference between the principal stresses at locations of the pixels of said lateral straight line segments, using finite difference approximations;

(e) computing the sum of the principal stresses at each pixel along said first-named straight line segment by integration of said derivative and using the stored values of the difference between the principal stresses along said first-named straight line segment;

(f) and computing the principal stresses from said sums and differences.

2. Method according to claim 1, wherein said isoclinals are found by comparing the light intensity transmitted through a polarizer, the test-piece and an analyser to a predetermined light intensity threshold for a plurality of angular positions of said polarizer and analyser.

3. Method according to claim 1, wherein computation of the values of σ

I+σ

II on the first-named straight line segment includes indicating a zero order fringe on said first-named straight line segment, deriving σ

I-σ

II from the brightness variation from the zero order fringe, repeating the same steps for the lateral straight line segments, computing the value of τ

xy for each pixel of the first-named straight line segment, approximating the successive values of δ

τ

/δ

y by finite difference between said lateral straight line segments, determining the partial derivative of σ

x from the partial derivative of τ and

computing σ

by integration.

4. Method according to claim 1, wherein, during step (a), the two-dimensional array of pixels is formed by:

obtaining a first picture by passing said linearly polarized monochromatic light which is linearly polarized through a polarizer having a predetermined direction of polarization,

storing values of the pixels of said first picture,

obtaining a second picture by passing said linearly polarized monochromatic light through a polarizer having a direction of polarization at 45°

from the direction of polarization for forming the first picture,

storing values of the pixels of the second picture, and

summing the two values for each pair of corresponding pixels in the two pictures for forming said two-dimensional image.

5. Apparatus for photoelasticity determination of the distribution of principal stresses along a straight line segment across a loaded test-piece of a material exhibiting induced birefringence, comprising:

polarizer means directing polarized monochromatic light on the test-piece and analyser means for receiving said light from said test piece and forming a two-dimensional image of said test-piece as a two-dimensional array of pixels,

means operatively associated with said polarizer and analyser to cause isochromatic fringes to appear in said image while eliminating isoclinals and storing a brightness value for each of said pixels in digital form;

means for optional modification of the polarizer and analyser to form sucessive two-dimensional images of said test-piece as two-dimensional arrays of pixels under conditions which provide successive sets of isoclinals and storing data including only those pixels which are located on said isoclinals for each said angular direction of polarization, and

computer means for successively computing the values of the difference between the respective principal stresses at each pixel along said straight line segment from said stored brightness values;

computing a partial derivative of the variation of the stresses along a predetermined direction at each point of said straight line segment from the stored values of the difference between the principal stresses at locations of the pixels of lateral straight line segments located on either side of the first-named straight line segment, at the same distance thereof and parallel thereto, using finite difference approximations;

computing the sum of the principal stresses at each pixel along said first-named straight line segment by integration of said derivative and using the stored values of the difference between the principal stresses along said first-named straight line segment; and

computing the principal stresses from said sums and differences.