Abstract

In transmission photoelasticity, stresses and strains are not directly measured on the real piece, but on a photoelastic model. To improve accuracy, the photoelastic material type, size of the model, its thickness, and the applied load must be chosen properly. In this paper, the influence of selectable parameters in a photoelastic transmission analysis has been studied through the evaluation of measurement uncertainties. The experimental data and further study of a generic functional relationship, representative of a stress-separation technique, show that, for a given photoelastic material, the model of minimum uncertainty of measurement is the one whose ratio load/dimension is the maximum allowed by the data- acquisition technique used. The thickness affects only the amount of material used. Therefore, any size of the model can achieve maximum accuracy, provided that it is subjected to the greatest possible load within its elastic range.

© 2011 Optical Society of America

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References

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  1. M. Solaguren-Beascoa Fernández, “Towards uncertainty evaluation in photoelastic measurements,” J. Strain Anal. Eng. Des. 45, 575–587 (2010).
    [CrossRef]
  2. “Calibration and assessment of optical strain measurements systems—Part I: reference material for optical methods of strain measurement,” VAMAS TWA26, Draft VAMAS TWA26 pre-standard (Standardisation Project for Optical Techniques of Strain Measurement, University of Sheffield, 2007).
  3. “Calibration and assessment of optical strain measurements systems—Part II: Standardised test materials for optical methods of strain measurement systems,” VAMAS TWA26, Draft VAMAS TWA26 pre-standard (Standardisation Project for Optical Techniques of Strain Measurement, University of Sheffield, 2007).
  4. “Calibration and assessment of optical strain measurements systems—Part III: Good practice guide to (1) geometric moiré for in-plane displacement/strain analysis, (2) grating (moiré) interferometry for in-plane displacement/strain analysis, (3) image correlation for in-plane displacement/strain analysis, (4) thermoelastic stress analysis, (5) reflection photoelasticity, (6) transmission photoelasticity, (7) electronic speckle pattern interferometry for displacement/strain analysis,” VAMAS TWA26, Draft VAMAS TWA26 pre-standard (Standardisation Project for Optical Techniques of Strain Measurement, University of Sheffield, 2007).
  5. K. Ramesh, Digital Photoelasticity—Advanced Techniques and Applications (Springer-Verlag, 2000).
  6. Vishay Measurements Group Inc., “Selecting photoelastic coatings,” Technical Note 704 (Vishay Measurements Group Inc., Raleigh, NC, USA, 2005).
  7. P. Siegmann, D. Backman, and E. A., “A robust demodulation and unwrapping approach for phase-stepped photoelastic data,” Exp. Mech. 45, 278–289, 2005.
    [CrossRef]
  8. M. N. Pacey and R. A. Tomlinson, “Complete two-dimensional principal stress separation by the photoelastic oblique incidence method,” Appl. Mech. Mater. 3–4, 229–234 (2005).
    [CrossRef]
  9. M. A. Herrador Morillo, A. G. Gonzalez Gonzalez, and A. Garcia Asuero, “Estimation of the uncertainty of indirect measurements from the propagation of distributions by using the Monte-Carlo Method: an overview,” Chemom. Intell. Lab. Syst. 79, 115–122, 2005.
    [CrossRef]
  10. M. Solaguren-Beascoa Fernández, J. M. Alegre-Calderón, and P. M. Bravo Díez, “Implementation in MATLAB of the adaptive Monte Carlo method for the evaluation of measurement uncertainties,” Accredit. Qual. Assur. 14, 95–106, 2009.
    [CrossRef]
  11. M. Solaguren-Beascoa Fernández, J. M. Alegre Calderón, P. M. Bravo Díez, and I. I. Cuesta Segura, “Stress separation techniques in photoelasticity—a review,” J. Strain Anal. Eng. Des. 45, 1–17, 2010.
    [CrossRef]
  12. ISO—International Organization for Standardization, “Uncertainty of measurement—part 3: Guide to the expression of uncertainty in measurement,” ISO/IEC Guide 98-3:2008 (ISO, Geneva, 2008).
  13. ISO—International Organization for Standardization, “Propagation of distributions using a Monte Carlo method,” ISO/IEC Guide 98-3/Suppl.1:2008 (ISO, Geneva, 2008).
  14. M. Solaguren-Beascoa Fernández, “Data acquisition techniques in photoelasticity,” Exp. Tech., doi:10.1111/j.1747-1567.2010.00669.x (to be published).
    [CrossRef]

2010 (2)

M. Solaguren-Beascoa Fernández, “Towards uncertainty evaluation in photoelastic measurements,” J. Strain Anal. Eng. Des. 45, 575–587 (2010).
[CrossRef]

M. Solaguren-Beascoa Fernández, J. M. Alegre Calderón, P. M. Bravo Díez, and I. I. Cuesta Segura, “Stress separation techniques in photoelasticity—a review,” J. Strain Anal. Eng. Des. 45, 1–17, 2010.
[CrossRef]

2009 (1)

M. Solaguren-Beascoa Fernández, J. M. Alegre-Calderón, and P. M. Bravo Díez, “Implementation in MATLAB of the adaptive Monte Carlo method for the evaluation of measurement uncertainties,” Accredit. Qual. Assur. 14, 95–106, 2009.
[CrossRef]

2005 (3)

P. Siegmann, D. Backman, and E. A., “A robust demodulation and unwrapping approach for phase-stepped photoelastic data,” Exp. Mech. 45, 278–289, 2005.
[CrossRef]

M. N. Pacey and R. A. Tomlinson, “Complete two-dimensional principal stress separation by the photoelastic oblique incidence method,” Appl. Mech. Mater. 3–4, 229–234 (2005).
[CrossRef]

M. A. Herrador Morillo, A. G. Gonzalez Gonzalez, and A. Garcia Asuero, “Estimation of the uncertainty of indirect measurements from the propagation of distributions by using the Monte-Carlo Method: an overview,” Chemom. Intell. Lab. Syst. 79, 115–122, 2005.
[CrossRef]

Alegre-Calderón, J. M.

M. Solaguren-Beascoa Fernández, J. M. Alegre-Calderón, and P. M. Bravo Díez, “Implementation in MATLAB of the adaptive Monte Carlo method for the evaluation of measurement uncertainties,” Accredit. Qual. Assur. 14, 95–106, 2009.
[CrossRef]

Bravo Díez, P. M.

M. Solaguren-Beascoa Fernández, J. M. Alegre-Calderón, and P. M. Bravo Díez, “Implementation in MATLAB of the adaptive Monte Carlo method for the evaluation of measurement uncertainties,” Accredit. Qual. Assur. 14, 95–106, 2009.
[CrossRef]

Gonzalez Gonzalez, A. G.

M. A. Herrador Morillo, A. G. Gonzalez Gonzalez, and A. Garcia Asuero, “Estimation of the uncertainty of indirect measurements from the propagation of distributions by using the Monte-Carlo Method: an overview,” Chemom. Intell. Lab. Syst. 79, 115–122, 2005.
[CrossRef]

Herrador Morillo, M. A.

M. A. Herrador Morillo, A. G. Gonzalez Gonzalez, and A. Garcia Asuero, “Estimation of the uncertainty of indirect measurements from the propagation of distributions by using the Monte-Carlo Method: an overview,” Chemom. Intell. Lab. Syst. 79, 115–122, 2005.
[CrossRef]

A., E.

P. Siegmann, D. Backman, and E. A., “A robust demodulation and unwrapping approach for phase-stepped photoelastic data,” Exp. Mech. 45, 278–289, 2005.
[CrossRef]

Alegre Calderón, J. M.

M. Solaguren-Beascoa Fernández, J. M. Alegre Calderón, P. M. Bravo Díez, and I. I. Cuesta Segura, “Stress separation techniques in photoelasticity—a review,” J. Strain Anal. Eng. Des. 45, 1–17, 2010.
[CrossRef]

Backman, D.

P. Siegmann, D. Backman, and E. A., “A robust demodulation and unwrapping approach for phase-stepped photoelastic data,” Exp. Mech. 45, 278–289, 2005.
[CrossRef]

Bravo Díez, P. M.

M. Solaguren-Beascoa Fernández, J. M. Alegre Calderón, P. M. Bravo Díez, and I. I. Cuesta Segura, “Stress separation techniques in photoelasticity—a review,” J. Strain Anal. Eng. Des. 45, 1–17, 2010.
[CrossRef]

Cuesta Segura, I. I.

M. Solaguren-Beascoa Fernández, J. M. Alegre Calderón, P. M. Bravo Díez, and I. I. Cuesta Segura, “Stress separation techniques in photoelasticity—a review,” J. Strain Anal. Eng. Des. 45, 1–17, 2010.
[CrossRef]

Fernández, M. Solaguren-Beascoa

M. Solaguren-Beascoa Fernández, J. M. Alegre Calderón, P. M. Bravo Díez, and I. I. Cuesta Segura, “Stress separation techniques in photoelasticity—a review,” J. Strain Anal. Eng. Des. 45, 1–17, 2010.
[CrossRef]

M. Solaguren-Beascoa Fernández, “Towards uncertainty evaluation in photoelastic measurements,” J. Strain Anal. Eng. Des. 45, 575–587 (2010).
[CrossRef]

M. Solaguren-Beascoa Fernández, J. M. Alegre-Calderón, and P. M. Bravo Díez, “Implementation in MATLAB of the adaptive Monte Carlo method for the evaluation of measurement uncertainties,” Accredit. Qual. Assur. 14, 95–106, 2009.
[CrossRef]

M. Solaguren-Beascoa Fernández, “Data acquisition techniques in photoelasticity,” Exp. Tech., doi:10.1111/j.1747-1567.2010.00669.x (to be published).
[CrossRef]

Garcia Asuero, A.

M. A. Herrador Morillo, A. G. Gonzalez Gonzalez, and A. Garcia Asuero, “Estimation of the uncertainty of indirect measurements from the propagation of distributions by using the Monte-Carlo Method: an overview,” Chemom. Intell. Lab. Syst. 79, 115–122, 2005.
[CrossRef]

Pacey, M. N.

M. N. Pacey and R. A. Tomlinson, “Complete two-dimensional principal stress separation by the photoelastic oblique incidence method,” Appl. Mech. Mater. 3–4, 229–234 (2005).
[CrossRef]

Ramesh, K.

K. Ramesh, Digital Photoelasticity—Advanced Techniques and Applications (Springer-Verlag, 2000).

Siegmann, P.

P. Siegmann, D. Backman, and E. A., “A robust demodulation and unwrapping approach for phase-stepped photoelastic data,” Exp. Mech. 45, 278–289, 2005.
[CrossRef]

Tomlinson, R. A.

M. N. Pacey and R. A. Tomlinson, “Complete two-dimensional principal stress separation by the photoelastic oblique incidence method,” Appl. Mech. Mater. 3–4, 229–234 (2005).
[CrossRef]

Accredit. Qual. Assur. (1)

M. Solaguren-Beascoa Fernández, J. M. Alegre-Calderón, and P. M. Bravo Díez, “Implementation in MATLAB of the adaptive Monte Carlo method for the evaluation of measurement uncertainties,” Accredit. Qual. Assur. 14, 95–106, 2009.
[CrossRef]

Appl. Mech. Mater. (1)

M. N. Pacey and R. A. Tomlinson, “Complete two-dimensional principal stress separation by the photoelastic oblique incidence method,” Appl. Mech. Mater. 3–4, 229–234 (2005).
[CrossRef]

Chemom. Intell. Lab. Syst. (1)

M. A. Herrador Morillo, A. G. Gonzalez Gonzalez, and A. Garcia Asuero, “Estimation of the uncertainty of indirect measurements from the propagation of distributions by using the Monte-Carlo Method: an overview,” Chemom. Intell. Lab. Syst. 79, 115–122, 2005.
[CrossRef]

Exp. Mech. (1)

P. Siegmann, D. Backman, and E. A., “A robust demodulation and unwrapping approach for phase-stepped photoelastic data,” Exp. Mech. 45, 278–289, 2005.
[CrossRef]

J. Strain Anal. Eng. Des. (2)

M. Solaguren-Beascoa Fernández, J. M. Alegre Calderón, P. M. Bravo Díez, and I. I. Cuesta Segura, “Stress separation techniques in photoelasticity—a review,” J. Strain Anal. Eng. Des. 45, 1–17, 2010.
[CrossRef]

M. Solaguren-Beascoa Fernández, “Towards uncertainty evaluation in photoelastic measurements,” J. Strain Anal. Eng. Des. 45, 575–587 (2010).
[CrossRef]

Other (8)

“Calibration and assessment of optical strain measurements systems—Part I: reference material for optical methods of strain measurement,” VAMAS TWA26, Draft VAMAS TWA26 pre-standard (Standardisation Project for Optical Techniques of Strain Measurement, University of Sheffield, 2007).

“Calibration and assessment of optical strain measurements systems—Part II: Standardised test materials for optical methods of strain measurement systems,” VAMAS TWA26, Draft VAMAS TWA26 pre-standard (Standardisation Project for Optical Techniques of Strain Measurement, University of Sheffield, 2007).

“Calibration and assessment of optical strain measurements systems—Part III: Good practice guide to (1) geometric moiré for in-plane displacement/strain analysis, (2) grating (moiré) interferometry for in-plane displacement/strain analysis, (3) image correlation for in-plane displacement/strain analysis, (4) thermoelastic stress analysis, (5) reflection photoelasticity, (6) transmission photoelasticity, (7) electronic speckle pattern interferometry for displacement/strain analysis,” VAMAS TWA26, Draft VAMAS TWA26 pre-standard (Standardisation Project for Optical Techniques of Strain Measurement, University of Sheffield, 2007).

K. Ramesh, Digital Photoelasticity—Advanced Techniques and Applications (Springer-Verlag, 2000).

Vishay Measurements Group Inc., “Selecting photoelastic coatings,” Technical Note 704 (Vishay Measurements Group Inc., Raleigh, NC, USA, 2005).

ISO—International Organization for Standardization, “Uncertainty of measurement—part 3: Guide to the expression of uncertainty in measurement,” ISO/IEC Guide 98-3:2008 (ISO, Geneva, 2008).

ISO—International Organization for Standardization, “Propagation of distributions using a Monte Carlo method,” ISO/IEC Guide 98-3/Suppl.1:2008 (ISO, Geneva, 2008).

M. Solaguren-Beascoa Fernández, “Data acquisition techniques in photoelasticity,” Exp. Tech., doi:10.1111/j.1747-1567.2010.00669.x (to be published).
[CrossRef]

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Figures (4)

Fig. 1
Fig. 1

Standard uncertainty and fringe order against the force applied to the model.

Fig. 2
Fig. 2

Standard uncertainty and fringe order against the size of the model.

Fig. 3
Fig. 3

Standard uncertainty and fringe order against the thickness of the model.

Fig. 4
Fig. 4

Graphical representation for the selection of the photoelastic material and its thickness in a transmission analysis (for materials supplied by the firm Vishay).

Tables (1)

Tables Icon

Table 1 Data in a Transmission Analysis with the Stress-Separation Technique by Oblique Incidence

Equations (13)

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σ p = σ m ( F p F m ) ( L m L p ) ( t m t p ) .
f required = ( ε 1 ε 2 ) max N max = γ max N max = expected strain level maximum number of fringes .
f = λ t m · K .
σ 1 m = E m 1 + ν m λ cos ξ t m K sin 2 ξ ( N ξ N cos ξ ) , σ 2 m = E m 1 + ν m λ t m K sin 2 ξ ( N ξ cos ξ N ) ,
Y = f ( X 1 , X 2 , X N ) = c i = 1 N x i p i = c · X 1 p 1 · X 2 p 2 · X N p N ,
u ( y ) = i = 1 N [ c i u ( x i ) ] 2 ,
c i = f X i | X 1 = x 1 , , X N = x N = p i y x i .
u ( y ) = i = 1 N [ p i y x i u ( x i ) ] 2 = y i = 1 N [ p i w ( x i ) ] 2 w ( y ) = i = 1 N [ p i w ( x i ) ] 2 .
w ( y ) = i = 1 M [ p i u ( x i ) x i ] 2 + i = M + 1 N [ p i w ( x i ) ] 2 = i = 1 M [ p i u ( x i ) K i · x i ] 2 + i = M + 1 N [ p i w ( x i ) ] 2 = i = 1 M [ p i w ( x i ) K i ] 2 + i = M + 1 N [ p i w ( x i ) ] 2 .
σ m N t m K .
σ m F m L m t m .
N F m L m K .
( F m L m ) optimum = σ m σ p ( F p L p ) ( t m t p ) .

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