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Half-fringe photoelasticity for orthotropic materials
Fibre Science and Technology 21 (1984) 341-351
Half-Fringe Photoelasticity for Orthotropic Materials Arkady S. Voloshin and Christian P. Burger Department of Engineering Science and Mechanics, Engineering Research Institute, Iowa State University, Ames, Iowa 50011 (USA)
SUMMARY The objective of this paper is to establish a completely new approach to tile photoelastic analysis ~f photo-orthotropic models. A new technique has been developed that utilizes digital image analysis procedures to resolve small differences in the low level bire[~'ingence of photoorthotropic materials. This approach allows model materials to be selected not Jbr their high bireJringence response, but rather Jbr their ability to model prototype behavior accurately. Another advantage of the proposed system is the possibility of using low loads, thus eliminating problems associated with nonlinear behavior and creep. The half-J~'ingephotoelasticity system is briefly described, and its capabilities are outlined. Results J,br an orthotropic halJ:plane loaded by a concentrated load and Jot a disk under diametral compression are also presented.
INTRODUCTION Photoelasticity has traditionally been the workhorse for experimental studies of elastic stress fields in solids. Many of its traditional roles are now performed more efficiently by means of different numerical techniques, but photoelasticity has moved on to address new problems. Its potential for future use is great, for despite extensive work in complementary optical methods, no alternate experimental system has been able to replace the full field capability and the sensitivity of photoelasticity. 341
Fibre Science and Technology 0015-0568/84/$03.00 © Elsevier Applied Science Publishers Ltd, England, 1984. Printed in Great Britain
342
Arkady S. Voloshin, Christian P. Burger
With the increased use of fiber-reinforced materials (FRM) in critical industrial applications, the need has arisen for adequate stress analysis. Since analytical techniques are as yet unequal to the task, a good experimental procedure is needed. Some research has produced photoelastic model materials which are orthotropic in nature, yet transparent enough to be of value in optical techniques. 1-3 The measurement and interpretation of artificial stress birefringence and corresponding procedures are fairly well established and described elsewhere. 1- 5 Unfortunately, current model materials are quite complicated and expensive to produce; in addition, one must apply considerable external loads to produce enough fringes, so that the classical approach of counting may then be utilized. Such loading may lead to nonlinear response, creep, and other undesirable effects. To overcome this limitation, a system has been developed that works with materials which have low birefringence response and/or with low loading. It utilizes modern digital image analysis techniques in conjunction with classical whole field photoelasticity. The half-fringe-photoelasticity system described here takes advantage of the ability of modern digital image analysis techniques to resolve small changes in gray levels (light intensity) over a full field of view in order to perform an accurate photoelastic analysis at low levels of birefringence. Thus, the proposed method overcomes the main disadvantages of contemporary photo-orthotropic elasticity--the necessity of applying large loads with their consequent large deformations--as well as the need for special model materials with high birefringence response.
THE SYSTEM The described technique is based on the ability of commercially available image analysis systems to acquire rapidly information on light intensity over a whole field and to transfer this information into a digital storage device. Later this information may be accessed by computer and processed to improve resolution and to yield a stress field. The system is called half-fringe photoelasticity (HFP) because it operates effectively with less than one-half wavelength of relative retardation. The system is best visualized as a traditional polariscope setup, consisting of a radiation source, a polarizer plus quarter-wave
Half-fringe photoelasticity for orthotropic materials
343
plate, a model, a quarter-wave plate plus analyzer, and a means of recording the image. In place of the classical camera or the more recent photodiodes, a wholly new computer-based image analysis system now exists. This system includes: 1.
2.
3.
4.
An 'Eyecom' scanner which uses a special vidicon television camera tube to scan the chosen image area. The picture is divided into 480 lines, and each line is divided into 640 parts. The brightness (Z-value) is converted into a video signal with an 8-bit resolution. A real-time digitizer which can digitize the video signal in 1/30 s and transfer the data to the Refresh Memory where it may be accessed later by the computer. A display system or monitor which visualizes the information and acts as a graphics/numeric terminal for data processing, program development, and graphical data displays. A LSI-11/2 computer and peripherals.
This approach has been used successfully for isotropic photoelasticity 6 and experimental fracture mechanics. 7
D A T A ANALYSIS The basic equations of orthotropic photoelasticity are the stress optic law 1'4 and the equations for the transmitted light in a circular polariscope, s These are generally given in the following form: The orthotropic stress optic law for linear elastic behavior may be represented as
Nii= Qijklakl
(i, j, k, l = 1, 2, 3)
(1)
where Nij = birefringence tensor of second rank; QijkZ= photoelastic stress-optic properties tensor of fourth rank; and aij = stress tensor of second rank. Reducing eqn (1) for two-dimensional problems and aligning fibers with a coordinate system, results in a simplified relationship between the applied state of stress and observed birefringence:
LkA,
+ \ f,= ) _J
(2)
344
Arkady S. Voloshin, Christian P. Burger
where A = relative retardation; aij = in-plane stress tensor (i,j = 1, 2); h = thickness of photoelastic model in direction of light propagation; f u = components of the stress-optic tensor (i,j = 1,2) related to Qijkt; and the observed fringe order is
(3)
N = A/2rc
that is, the relative retardation in terms of complete cycles of retardation. In a circular polariscope (dark field setup) the intensity of the transmitted light I emerging from the analyzer is v I = K sin2 _A 2
(4)
where Kis a constant, A is the phase difference, and I = 0 when A/2 = nrc for n = 0, 1, 2, 3. For these values N = A/2rt = 0, 1,2 . . . . , n. The light intensity distribution for eqn (4) is given in Fig. 1.
I
0
w/2
~
3 v/2
2w
0
I/2
1
3/2
2
~
A/2 N
Fig. 1. Relation between the transmitted light intensity and fractional fringe value.
Since resolution of the 'Eyecom' scanner is 8-bit, the image analysis system distinguishes between 256 gray levels in any interval from 0 to re/2, ~/2 to re, and so on. It cannot identify the interval, nor can it identify which half fringe it is reading, as can be seen from Fig. 1. The parameters in eqn(2) must, therefore, be chosen so that 0 < A/2 < re/2 and, consequently, 0 < N < 1/2. This condition is. however, an advantage and not a restriction, since it is easily satisfied by applying low loads. On the other hand, some simple changes in the procedure allow use of the system for a range greater than one-half of the fringe (this will be reported elsewhere). The digitization of the intensity plot in Fig. 1 occurs on the I
Half-fringe photoelasticity for orthotropic materials
345
axis, so that equal gray level divisions represent uneven (a 1 -02) increments. In order to keep N < 1/2, the parameters h,f~s, and aij must be selected accordingly. This requires that one or all of the following be true: 1. 2. 3.
Low stresses in the models. This usually means that the model loads will be low. High f~j, i.e. low stress birefringence in the model material. Small h, i.e. thin models.
The first and last requirements are desirable in all photoelastic work. Low loads mean small deformations, reduced nonlinearity and creep, and better modeling of prototype response. Thin models approximate plane stress better and make it easier to meet the requirement that the stress field should not vary through the thickness of the model or slice. Highf~s (i.e. lower sensitivity to loads) has generally been abandoned by photoelasticians as an undesirable characteristic. With insensitive materials, high fringe order can only be obtained by using high loads and thick models. For HFP, a highJl ~ does not present a restriction. Now consider eqn (4) as rewritten to incorporate the reference intensity (Io) for a particular nonloaded model/polariscope combination: I = I o sin z 2
,(5)
Equation (2) then becomes n N =/rh~( 0"11 L\fll
0-22~2
(20.12"~211/2 arc sin N//~o~/o (6) ~-2// + \ J]2 J J The digital optical system described here is able to measure light intensity with 8-bit resolution. =
Calibration of the system
Since the system described here measures light intensity which is related to the fringe order, a procedure for calibration was developed. Equation (6) may be rewritten in the form using eqn (2) and is fully described in Ref. 6. Calibrations were performed on two beams under pure bending. In the first case the fibers were parallel, and in the second they were normal to the longitudinal direction of the beam. The model material used was a plate of unidirectional FRM (2 mm thick), produced by I. M. Daniel at IITRI. z
346
Arkady S. Voloshin, Christian P. Burger
FIBER DIRECTION
~
~
125-
I00
~ ~ .AI, . , , .
,~,.L.,.,~,~., AI J "
O.500
-
0.375
75
z
0.250
~ 50
25
o FRINGE ORDER (TARDY METHOD) D FRINGE OR~R (CALCULATED) - - L E A S T SQUARE FIT
I 0
I
~
I
0.125
^
Ie
25 50 75 lO0 POSITION ACROSS THE BEAM FROM FREE EDGES (IN PIXELS)
0.000
Fig. 2. Calibrationcurve. The beam has been incrementally loaded, corresponding light intensities have been recorded, and resultant partial fringe order has been evaluated by using the traditional Tardy compensation technique. 6 The corresponding theoretical fringe order distribution is, of course, a straight line for the beam in pure bending. The result of this calibration is presented in Fig. 2. The continuous line represents the best fit in least square sense through all fringe order points. The difference between measured and calculated partial fringe order was within 3 ~o for each point considered.
C O N C E N T R A T E D LOAD ON A S E M I - I N F I N I T E O R T H O T R O P I C PLATE The half-fringe-photoelasticity technique was applied to the problem of the concentrated load on a semi-infinite plate. The edge of an orthotropic plate 0.10 x 0.10 x 0.002 m was loaded by a concentrated load through a steel cylinder. The resultant optical response was observed through a transmission polariscope by the video analyzer. This primary image is contaminated with electrical and optical noise, which includes imperfections of the light source, polarizers, quarter-wave plates, lenses, and the model. The random noise caused by electronics may be dramatically
347
Halffringe photoelasticity for orthotropic materials
reduced by taking 16 consecutive pictures of the same photoelastic field and averaging the results. This operation is performed by means of a built-in hardware function. After this averaging, the picture was stored in the Refresh Memory. From here it could be recalled, viewed on the display monitor, and accessed by the computer for processing. Figure 3(a) shows the resultant birefringence in the photo-orthotropic plate loaded by contact load, as it is seen through the dark field transmitted polariscope with circular setting. Not much information can yet be gathered by applying the usual approach of fringe courting. The bright area near the loading point represents one-half of the full fringe order. As the surface is approached, the fringe value increased from 0.5 to 1, which can be identified by the narrow black semi-ellipse. After that, the highest fringe values are indistinguishable. The attempt to increase the number of full fringes by increasing the load resulted in 2.5 fringes (Fig. 3(b)). After unloading it was found that a relatively large contact area sustained permanent damage as can be seen in Fig. 4. This simple exercise proves the importance of using relatively low loads which will not
iiiiiii iiiii ~ i!! :iiii: ~
(a)
iii iiii~i ¸¸¸ i ¸ :
I' " 2
(b)
Fig. 3. Contactload on the plate in the circularpolariscope(dark field).(a) Photoelastic response under low level load. (b) Photoelasticresponse under maximum load.
348
Fig. 4.
Arkady S. Voloshin, Christian P. Burger
Damage zone after maximum loading.
Fig. 5.
Bit map of the equal intensity areas.
damage the model, but will result in low birefringence (Fig. 3(a)). The information about fringe order is present in this picture and several techniques are available to extract and represent it. The built-in hardware function allows the so-called bit map (which is the last two bits of each pixel) to be seen. The result is shown in Fig. 5. However, it has to be kept in mind that these lines are lines of equal light intensity and not fringe values. This function does not convey any direct stress information but serves as a valuable technique for discovering, for example, lack of symmetry of loading, stress gradients, and the like. Figure 5 shows that slight lack of symmetry exists; the attempted repeated loading did not cure this problem. One may compare the clarity of this information with the foggy appearance of the original picture (Fig. 5 versus Fig. 3(a)). To visualize the acquired information, the light intensity of each pixel is transformed to the corresponding fractional fringe order according to the calibration curve (Fig. 2). All pixels with values from 0 to 0.125 are assigned the particular value from the gray scale (0-255); the pixels with values in the range 0.125-0.250 are assigned different values and so on.
Half-fringe photoelasticity for orthotropic materials
Fig. 6. Fractional fringe orders. Area with fringe order in the range of(l) 0"00 to 0.10; (2)0.10 to 0.20; (3)0.20 to 0.30; (4) 0.30 to 0.40; (5) 0.40 to 0.50.
Fig. 7.
349
Contour map of equal fringe values.
The resulting picture (Fig. 6) shows five regions, each one containing the pixels with particular values. The calculated relative retardation values can be used to produce a contour map of the constant fringe order (Fig. 7). The contour lines are at equal fringe increments (0-04 fringe in this case). Another example represents the case of an FRM disk under diametral compression with fibers normal to the direction of the applied load. Figure 8 shows row data. Each contour line corresponds to the partial fringe order; the increment is 0"08 of the full fringe order. In both examples image enhancement has not been attempted. No digital filtering to remove high frequency noise was done, nor was an attempt made to adjust for slight nonsymmetry of loading. Unimproved data are presented to illustrate the very fundamental quality of the images obtained. It is important to note that no photographic procedures were used
350
Arkady S. Voloshin, Christian P. Burger
Fig. 8.
Disk under diametral compression---contourmap.
anywhere in this analysis. Everything was done in real time, on line, with Figs 3-8 as the final output. CONCLUSIONS The described method, together with several examples, illustrates two major changes in the usual photoelastic procedure as applied to photoorthotropic media: 1.
2.
Relatively small loads were used in such a way that the problems of nonlinear behavior and creep of a fiber-reinforced material model were reduced. A full field, automated photoelastic procedure was established.
While this paper reports the preliminary results for the new approach to photoelasticity of the orthotropic materials, it is already clear that the speed, efficiency, and resolution of the half-fringe-photoelasticity technique will place it in the forefront of future developments in experimental stress analysis applied to composite materials. ACKN O W L E D G E M E N T S This research was partially funded through NSF Grant CME 80 14066. The encouragement of Dr Clifford Astill from the National Science
Half-fringe photoelasticity for orthotropic materials
351
Foundation and the support of both the Department of Engineering Science and Mechanics and the Engineering Research Institute at Iowa State University are gratefully acknowledged.
REFERENCES 1. A. S. Voloshin, M. Arcan and Z. Hashin, 'Interlaminar Shear Stress Distribution in FRM Photoelastic Coupons', Proceedings, Sixth International Conference on Experimental Stress Analysis, Munich, West Germany, Sept. 18-22, 1978. 2. I. M. Daniel, T. Niiro and G. M. Kaller, Development of the Orthotropic Birefringence Material for Photoelastic Stress Analysis, NASA CR 165709, May, 1981. 3. R. Prabhakaran, Separation of principal stresses in photo-orthotropic elasticity, Fiber Sci. Technol., 13 (1980), pp. 245-53. 4. C. E. Knight and N. Pih, Shear difference method and application in orthotropic photoelasticity, J. Eng. Mater. Technol., 98 (1976), pp. 368-74. 5. R. C. Sampson, A stress-optic law for photoelastic analysis of orthotropic composites, Exp. Mech., 10 (1970), pp. 210-16. 6. A. S. Voloshin and C. P. Burger, Half-fringe photoelasticity: A new approach to whole field stress analysis, Exp. Mech., 23 (1983), pp. 304-13. 7. C. P. Burger and A. S. Voloshin, 'Stress Intensity Factors in Glass and Polycarbonate by Half-Fringe Photoelasticity', Proceedings of the Ninth Canadian Congress of Applied Mechanics (CANCAM 83), Saskatchewan, Saskatoon, Canada, May 30-June 3, 1983, pp. 915-16. 8. A. Kuske and G. Robertson, Photoelastic Stress Analysis, John Wiley and Son, London, 1979, pp. 100-2.
Half-Fringe Photoelasticity for Orthotropic Materials Arkady S. Voloshin and Christian P. Burger Department of Engineering Science and Mechanics, Engineering Research Institute, Iowa State University, Ames, Iowa 50011 (USA)
SUMMARY The objective of this paper is to establish a completely new approach to tile photoelastic analysis ~f photo-orthotropic models. A new technique has been developed that utilizes digital image analysis procedures to resolve small differences in the low level bire[~'ingence of photoorthotropic materials. This approach allows model materials to be selected not Jbr their high bireJringence response, but rather Jbr their ability to model prototype behavior accurately. Another advantage of the proposed system is the possibility of using low loads, thus eliminating problems associated with nonlinear behavior and creep. The half-J~'ingephotoelasticity system is briefly described, and its capabilities are outlined. Results J,br an orthotropic halJ:plane loaded by a concentrated load and Jot a disk under diametral compression are also presented.
INTRODUCTION Photoelasticity has traditionally been the workhorse for experimental studies of elastic stress fields in solids. Many of its traditional roles are now performed more efficiently by means of different numerical techniques, but photoelasticity has moved on to address new problems. Its potential for future use is great, for despite extensive work in complementary optical methods, no alternate experimental system has been able to replace the full field capability and the sensitivity of photoelasticity. 341
Fibre Science and Technology 0015-0568/84/$03.00 © Elsevier Applied Science Publishers Ltd, England, 1984. Printed in Great Britain
342
Arkady S. Voloshin, Christian P. Burger
With the increased use of fiber-reinforced materials (FRM) in critical industrial applications, the need has arisen for adequate stress analysis. Since analytical techniques are as yet unequal to the task, a good experimental procedure is needed. Some research has produced photoelastic model materials which are orthotropic in nature, yet transparent enough to be of value in optical techniques. 1-3 The measurement and interpretation of artificial stress birefringence and corresponding procedures are fairly well established and described elsewhere. 1- 5 Unfortunately, current model materials are quite complicated and expensive to produce; in addition, one must apply considerable external loads to produce enough fringes, so that the classical approach of counting may then be utilized. Such loading may lead to nonlinear response, creep, and other undesirable effects. To overcome this limitation, a system has been developed that works with materials which have low birefringence response and/or with low loading. It utilizes modern digital image analysis techniques in conjunction with classical whole field photoelasticity. The half-fringe-photoelasticity system described here takes advantage of the ability of modern digital image analysis techniques to resolve small changes in gray levels (light intensity) over a full field of view in order to perform an accurate photoelastic analysis at low levels of birefringence. Thus, the proposed method overcomes the main disadvantages of contemporary photo-orthotropic elasticity--the necessity of applying large loads with their consequent large deformations--as well as the need for special model materials with high birefringence response.
THE SYSTEM The described technique is based on the ability of commercially available image analysis systems to acquire rapidly information on light intensity over a whole field and to transfer this information into a digital storage device. Later this information may be accessed by computer and processed to improve resolution and to yield a stress field. The system is called half-fringe photoelasticity (HFP) because it operates effectively with less than one-half wavelength of relative retardation. The system is best visualized as a traditional polariscope setup, consisting of a radiation source, a polarizer plus quarter-wave
Half-fringe photoelasticity for orthotropic materials
343
plate, a model, a quarter-wave plate plus analyzer, and a means of recording the image. In place of the classical camera or the more recent photodiodes, a wholly new computer-based image analysis system now exists. This system includes: 1.
2.
3.
4.
An 'Eyecom' scanner which uses a special vidicon television camera tube to scan the chosen image area. The picture is divided into 480 lines, and each line is divided into 640 parts. The brightness (Z-value) is converted into a video signal with an 8-bit resolution. A real-time digitizer which can digitize the video signal in 1/30 s and transfer the data to the Refresh Memory where it may be accessed later by the computer. A display system or monitor which visualizes the information and acts as a graphics/numeric terminal for data processing, program development, and graphical data displays. A LSI-11/2 computer and peripherals.
This approach has been used successfully for isotropic photoelasticity 6 and experimental fracture mechanics. 7
D A T A ANALYSIS The basic equations of orthotropic photoelasticity are the stress optic law 1'4 and the equations for the transmitted light in a circular polariscope, s These are generally given in the following form: The orthotropic stress optic law for linear elastic behavior may be represented as
Nii= Qijklakl
(i, j, k, l = 1, 2, 3)
(1)
where Nij = birefringence tensor of second rank; QijkZ= photoelastic stress-optic properties tensor of fourth rank; and aij = stress tensor of second rank. Reducing eqn (1) for two-dimensional problems and aligning fibers with a coordinate system, results in a simplified relationship between the applied state of stress and observed birefringence:
LkA,
+ \ f,= ) _J
(2)
344
Arkady S. Voloshin, Christian P. Burger
where A = relative retardation; aij = in-plane stress tensor (i,j = 1, 2); h = thickness of photoelastic model in direction of light propagation; f u = components of the stress-optic tensor (i,j = 1,2) related to Qijkt; and the observed fringe order is
(3)
N = A/2rc
that is, the relative retardation in terms of complete cycles of retardation. In a circular polariscope (dark field setup) the intensity of the transmitted light I emerging from the analyzer is v I = K sin2 _A 2
(4)
where Kis a constant, A is the phase difference, and I = 0 when A/2 = nrc for n = 0, 1, 2, 3. For these values N = A/2rt = 0, 1,2 . . . . , n. The light intensity distribution for eqn (4) is given in Fig. 1.
I
0
w/2
~
3 v/2
2w
0
I/2
1
3/2
2
~
A/2 N
Fig. 1. Relation between the transmitted light intensity and fractional fringe value.
Since resolution of the 'Eyecom' scanner is 8-bit, the image analysis system distinguishes between 256 gray levels in any interval from 0 to re/2, ~/2 to re, and so on. It cannot identify the interval, nor can it identify which half fringe it is reading, as can be seen from Fig. 1. The parameters in eqn(2) must, therefore, be chosen so that 0 < A/2 < re/2 and, consequently, 0 < N < 1/2. This condition is. however, an advantage and not a restriction, since it is easily satisfied by applying low loads. On the other hand, some simple changes in the procedure allow use of the system for a range greater than one-half of the fringe (this will be reported elsewhere). The digitization of the intensity plot in Fig. 1 occurs on the I
Half-fringe photoelasticity for orthotropic materials
345
axis, so that equal gray level divisions represent uneven (a 1 -02) increments. In order to keep N < 1/2, the parameters h,f~s, and aij must be selected accordingly. This requires that one or all of the following be true: 1. 2. 3.
Low stresses in the models. This usually means that the model loads will be low. High f~j, i.e. low stress birefringence in the model material. Small h, i.e. thin models.
The first and last requirements are desirable in all photoelastic work. Low loads mean small deformations, reduced nonlinearity and creep, and better modeling of prototype response. Thin models approximate plane stress better and make it easier to meet the requirement that the stress field should not vary through the thickness of the model or slice. Highf~s (i.e. lower sensitivity to loads) has generally been abandoned by photoelasticians as an undesirable characteristic. With insensitive materials, high fringe order can only be obtained by using high loads and thick models. For HFP, a highJl ~ does not present a restriction. Now consider eqn (4) as rewritten to incorporate the reference intensity (Io) for a particular nonloaded model/polariscope combination: I = I o sin z 2
,(5)
Equation (2) then becomes n N =/rh~( 0"11 L\fll
0-22~2
(20.12"~211/2 arc sin N//~o~/o (6) ~-2// + \ J]2 J J The digital optical system described here is able to measure light intensity with 8-bit resolution. =
Calibration of the system
Since the system described here measures light intensity which is related to the fringe order, a procedure for calibration was developed. Equation (6) may be rewritten in the form using eqn (2) and is fully described in Ref. 6. Calibrations were performed on two beams under pure bending. In the first case the fibers were parallel, and in the second they were normal to the longitudinal direction of the beam. The model material used was a plate of unidirectional FRM (2 mm thick), produced by I. M. Daniel at IITRI. z
346
Arkady S. Voloshin, Christian P. Burger
FIBER DIRECTION
~
~
125-
I00
~ ~ .AI, . , , .
,~,.L.,.,~,~., AI J "
O.500
-
0.375
75
z
0.250
~ 50
25
o FRINGE ORDER (TARDY METHOD) D FRINGE OR~R (CALCULATED) - - L E A S T SQUARE FIT
I 0
I
~
I
0.125
^
Ie
25 50 75 lO0 POSITION ACROSS THE BEAM FROM FREE EDGES (IN PIXELS)
0.000
Fig. 2. Calibrationcurve. The beam has been incrementally loaded, corresponding light intensities have been recorded, and resultant partial fringe order has been evaluated by using the traditional Tardy compensation technique. 6 The corresponding theoretical fringe order distribution is, of course, a straight line for the beam in pure bending. The result of this calibration is presented in Fig. 2. The continuous line represents the best fit in least square sense through all fringe order points. The difference between measured and calculated partial fringe order was within 3 ~o for each point considered.
C O N C E N T R A T E D LOAD ON A S E M I - I N F I N I T E O R T H O T R O P I C PLATE The half-fringe-photoelasticity technique was applied to the problem of the concentrated load on a semi-infinite plate. The edge of an orthotropic plate 0.10 x 0.10 x 0.002 m was loaded by a concentrated load through a steel cylinder. The resultant optical response was observed through a transmission polariscope by the video analyzer. This primary image is contaminated with electrical and optical noise, which includes imperfections of the light source, polarizers, quarter-wave plates, lenses, and the model. The random noise caused by electronics may be dramatically
347
Halffringe photoelasticity for orthotropic materials
reduced by taking 16 consecutive pictures of the same photoelastic field and averaging the results. This operation is performed by means of a built-in hardware function. After this averaging, the picture was stored in the Refresh Memory. From here it could be recalled, viewed on the display monitor, and accessed by the computer for processing. Figure 3(a) shows the resultant birefringence in the photo-orthotropic plate loaded by contact load, as it is seen through the dark field transmitted polariscope with circular setting. Not much information can yet be gathered by applying the usual approach of fringe courting. The bright area near the loading point represents one-half of the full fringe order. As the surface is approached, the fringe value increased from 0.5 to 1, which can be identified by the narrow black semi-ellipse. After that, the highest fringe values are indistinguishable. The attempt to increase the number of full fringes by increasing the load resulted in 2.5 fringes (Fig. 3(b)). After unloading it was found that a relatively large contact area sustained permanent damage as can be seen in Fig. 4. This simple exercise proves the importance of using relatively low loads which will not
iiiiiii iiiii ~ i!! :iiii: ~
(a)
iii iiii~i ¸¸¸ i ¸ :
I' " 2
(b)
Fig. 3. Contactload on the plate in the circularpolariscope(dark field).(a) Photoelastic response under low level load. (b) Photoelasticresponse under maximum load.
348
Fig. 4.
Arkady S. Voloshin, Christian P. Burger
Damage zone after maximum loading.
Fig. 5.
Bit map of the equal intensity areas.
damage the model, but will result in low birefringence (Fig. 3(a)). The information about fringe order is present in this picture and several techniques are available to extract and represent it. The built-in hardware function allows the so-called bit map (which is the last two bits of each pixel) to be seen. The result is shown in Fig. 5. However, it has to be kept in mind that these lines are lines of equal light intensity and not fringe values. This function does not convey any direct stress information but serves as a valuable technique for discovering, for example, lack of symmetry of loading, stress gradients, and the like. Figure 5 shows that slight lack of symmetry exists; the attempted repeated loading did not cure this problem. One may compare the clarity of this information with the foggy appearance of the original picture (Fig. 5 versus Fig. 3(a)). To visualize the acquired information, the light intensity of each pixel is transformed to the corresponding fractional fringe order according to the calibration curve (Fig. 2). All pixels with values from 0 to 0.125 are assigned the particular value from the gray scale (0-255); the pixels with values in the range 0.125-0.250 are assigned different values and so on.
Half-fringe photoelasticity for orthotropic materials
Fig. 6. Fractional fringe orders. Area with fringe order in the range of(l) 0"00 to 0.10; (2)0.10 to 0.20; (3)0.20 to 0.30; (4) 0.30 to 0.40; (5) 0.40 to 0.50.
Fig. 7.
349
Contour map of equal fringe values.
The resulting picture (Fig. 6) shows five regions, each one containing the pixels with particular values. The calculated relative retardation values can be used to produce a contour map of the constant fringe order (Fig. 7). The contour lines are at equal fringe increments (0-04 fringe in this case). Another example represents the case of an FRM disk under diametral compression with fibers normal to the direction of the applied load. Figure 8 shows row data. Each contour line corresponds to the partial fringe order; the increment is 0"08 of the full fringe order. In both examples image enhancement has not been attempted. No digital filtering to remove high frequency noise was done, nor was an attempt made to adjust for slight nonsymmetry of loading. Unimproved data are presented to illustrate the very fundamental quality of the images obtained. It is important to note that no photographic procedures were used
350
Arkady S. Voloshin, Christian P. Burger
Fig. 8.
Disk under diametral compression---contourmap.
anywhere in this analysis. Everything was done in real time, on line, with Figs 3-8 as the final output. CONCLUSIONS The described method, together with several examples, illustrates two major changes in the usual photoelastic procedure as applied to photoorthotropic media: 1.
2.
Relatively small loads were used in such a way that the problems of nonlinear behavior and creep of a fiber-reinforced material model were reduced. A full field, automated photoelastic procedure was established.
While this paper reports the preliminary results for the new approach to photoelasticity of the orthotropic materials, it is already clear that the speed, efficiency, and resolution of the half-fringe-photoelasticity technique will place it in the forefront of future developments in experimental stress analysis applied to composite materials. ACKN O W L E D G E M E N T S This research was partially funded through NSF Grant CME 80 14066. The encouragement of Dr Clifford Astill from the National Science
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Foundation and the support of both the Department of Engineering Science and Mechanics and the Engineering Research Institute at Iowa State University are gratefully acknowledged.
REFERENCES 1. A. S. Voloshin, M. Arcan and Z. Hashin, 'Interlaminar Shear Stress Distribution in FRM Photoelastic Coupons', Proceedings, Sixth International Conference on Experimental Stress Analysis, Munich, West Germany, Sept. 18-22, 1978. 2. I. M. Daniel, T. Niiro and G. M. Kaller, Development of the Orthotropic Birefringence Material for Photoelastic Stress Analysis, NASA CR 165709, May, 1981. 3. R. Prabhakaran, Separation of principal stresses in photo-orthotropic elasticity, Fiber Sci. Technol., 13 (1980), pp. 245-53. 4. C. E. Knight and N. Pih, Shear difference method and application in orthotropic photoelasticity, J. Eng. Mater. Technol., 98 (1976), pp. 368-74. 5. R. C. Sampson, A stress-optic law for photoelastic analysis of orthotropic composites, Exp. Mech., 10 (1970), pp. 210-16. 6. A. S. Voloshin and C. P. Burger, Half-fringe photoelasticity: A new approach to whole field stress analysis, Exp. Mech., 23 (1983), pp. 304-13. 7. C. P. Burger and A. S. Voloshin, 'Stress Intensity Factors in Glass and Polycarbonate by Half-Fringe Photoelasticity', Proceedings of the Ninth Canadian Congress of Applied Mechanics (CANCAM 83), Saskatchewan, Saskatoon, Canada, May 30-June 3, 1983, pp. 915-16. 8. A. Kuske and G. Robertson, Photoelastic Stress Analysis, John Wiley and Son, London, 1979, pp. 100-2.