Abstract

An optical system for measuring the coefficient of thermal expansion (CTE) of materials has been developed based on electronic speckle interferometry. In this system, the temperature can be varied from −60°C to 180°C with a Peltier device. A specific specimen geometry and an optical arrangement based on the Michelson interferometer are proposed to measure the deformation along two orthogonal axes due to temperature changes. The advantages of the system include its high sensitivity and stability over the whole range of measurement. The experimental setup and approach for estimating the CTE was validated using an Aluminum alloy. Following this validation, the system was applied for characterizing the CTE of carbon fiber reinforced composite (CFRP) laminates. For the unidirectional fiber reinforced composites, the CTE varied with fiber orientation and exhibits anisotropic behavior. By stacking the plies with specific angles and order, the CTE of a specific CFRP was constrained to a low level with minimum variation temperature. The optical system developed in this study can be applied to CTE measurement for engineering and natural materials with high accuracy.

© 2018 Optical Society of America under the terms of the OSA Open Access Publishing Agreement

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References

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  1. U. Onen and T. Boyraz, “Microstructural characterization and thermal properties of aluminium titanate/spinel ceramic matrix composites,” Acta Phys. Pol. A 125(2), 488–490 (2014).
    [Crossref]
  2. A. K. Mukhopadhyay and D. G. Zollinger, “Development of dilatometer test method to measure coefficient of thermal expansion of aggregates,” J. Mater. Civ. Eng. 21(12), 781–788 (2009).
    [Crossref]
  3. L. O. Heflinger, R. F. Wuerker, and H. Spetzler, “Thermal expansion coefficient measurement of diffusely reflecting samples by holographic interferometry,” Rev. Sci. Instrum. 44(5), 629–633 (1973).
    [Crossref]
  4. Y. Morita, K. Arakawa, and M. Todo, “Experimental analysis of thermal displacement and strain distributions in a small outline J-leaded electronic package by using wedged-glass phase-shifting moiré interferometry,” Opt. Lasers Eng. 46(1), 18–26 (2008).
    [Crossref]
  5. F. Pignatiello, M. De Rosa, P. Ferraro, S. Grilli, P. De Natale, A. Arie, and S. De. Nicola, “Measurement of the thermal expansion coefficients of ferroelectric crystals by a moiré interferometer,” Opt. Commun. 277(1), 14–18 (2007).
    [Crossref]
  6. K. Zhang, W. He, L. Zhang, X. Zhao, and Y. Tian, “Measuring the thermal expansion coefficient of the carbon fiber optical tube by heterodyne laser interferometry,” Proc. SPIE 10141, 10141l (2016).
  7. C. T. Meng, C. C. Cheng, C. C. Hsu, and C. C. Wu, “Effective thermal expansion coefficient measurement of holographic material using total internal reflection heterodyne interferometry,” Opt. Eng. 54(9), 094105 (2015).
    [Crossref]
  8. C. Dudescu, J. Naumann, M. Stockmann, and S. Nebel, “Characterization of thermal expansion coefficient of anisotropic materials by electronic speckle pattern interferometry,” Strain 42(3), 197–205 (2006).
    [Crossref]
  9. ASTM E289–04, “Standard Text Method for Linear Thermal Expansion of Rigid Solids With Interferometry,” http://www.astm.org .
  10. C. M. Vest, Holographic Interferometry (Wiley, 1979).
  11. B. Liu, Q. Wei, J. Tu, D. Arola, and D. Zhang, “Inspection of the interior surface of cylindrical vessels using optic fiber shearography,” Meas. Sci. Technol. 28(9), 095202 (2017).
    [Crossref]
  12. W. W. Macy., “Two-dimensional fringe-pattern analysis,” Appl. Opt. 22(23), 3898 (1983).
    [Crossref] [PubMed]
  13. K. Hayat and S. K. Ha, “Non-contact measurement of the coefficient of thermal expansion of Al 6061-T6 with fiber Bragg grating sensors,” J. Mechanical Sci. Technol. 28(2), 621–626 (2014).
    [Crossref]
  14. M. H. Song, G. H. Wu, N. Wang, and G. Y. Zhang, “Coefficient of thermal expansion and compute of carbon fibre reinforced magnesium composites,” Rare Met. Mater. Eng. 38(6), 1043–1047 (2009).

2017 (1)

B. Liu, Q. Wei, J. Tu, D. Arola, and D. Zhang, “Inspection of the interior surface of cylindrical vessels using optic fiber shearography,” Meas. Sci. Technol. 28(9), 095202 (2017).
[Crossref]

2016 (1)

K. Zhang, W. He, L. Zhang, X. Zhao, and Y. Tian, “Measuring the thermal expansion coefficient of the carbon fiber optical tube by heterodyne laser interferometry,” Proc. SPIE 10141, 10141l (2016).

2015 (1)

C. T. Meng, C. C. Cheng, C. C. Hsu, and C. C. Wu, “Effective thermal expansion coefficient measurement of holographic material using total internal reflection heterodyne interferometry,” Opt. Eng. 54(9), 094105 (2015).
[Crossref]

2014 (2)

U. Onen and T. Boyraz, “Microstructural characterization and thermal properties of aluminium titanate/spinel ceramic matrix composites,” Acta Phys. Pol. A 125(2), 488–490 (2014).
[Crossref]

K. Hayat and S. K. Ha, “Non-contact measurement of the coefficient of thermal expansion of Al 6061-T6 with fiber Bragg grating sensors,” J. Mechanical Sci. Technol. 28(2), 621–626 (2014).
[Crossref]

2009 (2)

M. H. Song, G. H. Wu, N. Wang, and G. Y. Zhang, “Coefficient of thermal expansion and compute of carbon fibre reinforced magnesium composites,” Rare Met. Mater. Eng. 38(6), 1043–1047 (2009).

A. K. Mukhopadhyay and D. G. Zollinger, “Development of dilatometer test method to measure coefficient of thermal expansion of aggregates,” J. Mater. Civ. Eng. 21(12), 781–788 (2009).
[Crossref]

2008 (1)

Y. Morita, K. Arakawa, and M. Todo, “Experimental analysis of thermal displacement and strain distributions in a small outline J-leaded electronic package by using wedged-glass phase-shifting moiré interferometry,” Opt. Lasers Eng. 46(1), 18–26 (2008).
[Crossref]

2007 (1)

F. Pignatiello, M. De Rosa, P. Ferraro, S. Grilli, P. De Natale, A. Arie, and S. De. Nicola, “Measurement of the thermal expansion coefficients of ferroelectric crystals by a moiré interferometer,” Opt. Commun. 277(1), 14–18 (2007).
[Crossref]

2006 (1)

C. Dudescu, J. Naumann, M. Stockmann, and S. Nebel, “Characterization of thermal expansion coefficient of anisotropic materials by electronic speckle pattern interferometry,” Strain 42(3), 197–205 (2006).
[Crossref]

1983 (1)

1973 (1)

L. O. Heflinger, R. F. Wuerker, and H. Spetzler, “Thermal expansion coefficient measurement of diffusely reflecting samples by holographic interferometry,” Rev. Sci. Instrum. 44(5), 629–633 (1973).
[Crossref]

Arakawa, K.

Y. Morita, K. Arakawa, and M. Todo, “Experimental analysis of thermal displacement and strain distributions in a small outline J-leaded electronic package by using wedged-glass phase-shifting moiré interferometry,” Opt. Lasers Eng. 46(1), 18–26 (2008).
[Crossref]

Arie, A.

F. Pignatiello, M. De Rosa, P. Ferraro, S. Grilli, P. De Natale, A. Arie, and S. De. Nicola, “Measurement of the thermal expansion coefficients of ferroelectric crystals by a moiré interferometer,” Opt. Commun. 277(1), 14–18 (2007).
[Crossref]

Arola, D.

B. Liu, Q. Wei, J. Tu, D. Arola, and D. Zhang, “Inspection of the interior surface of cylindrical vessels using optic fiber shearography,” Meas. Sci. Technol. 28(9), 095202 (2017).
[Crossref]

Boyraz, T.

U. Onen and T. Boyraz, “Microstructural characterization and thermal properties of aluminium titanate/spinel ceramic matrix composites,” Acta Phys. Pol. A 125(2), 488–490 (2014).
[Crossref]

Cheng, C. C.

C. T. Meng, C. C. Cheng, C. C. Hsu, and C. C. Wu, “Effective thermal expansion coefficient measurement of holographic material using total internal reflection heterodyne interferometry,” Opt. Eng. 54(9), 094105 (2015).
[Crossref]

De Natale, P.

F. Pignatiello, M. De Rosa, P. Ferraro, S. Grilli, P. De Natale, A. Arie, and S. De. Nicola, “Measurement of the thermal expansion coefficients of ferroelectric crystals by a moiré interferometer,” Opt. Commun. 277(1), 14–18 (2007).
[Crossref]

De Rosa, M.

F. Pignatiello, M. De Rosa, P. Ferraro, S. Grilli, P. De Natale, A. Arie, and S. De. Nicola, “Measurement of the thermal expansion coefficients of ferroelectric crystals by a moiré interferometer,” Opt. Commun. 277(1), 14–18 (2007).
[Crossref]

De. Nicola, S.

F. Pignatiello, M. De Rosa, P. Ferraro, S. Grilli, P. De Natale, A. Arie, and S. De. Nicola, “Measurement of the thermal expansion coefficients of ferroelectric crystals by a moiré interferometer,” Opt. Commun. 277(1), 14–18 (2007).
[Crossref]

Dudescu, C.

C. Dudescu, J. Naumann, M. Stockmann, and S. Nebel, “Characterization of thermal expansion coefficient of anisotropic materials by electronic speckle pattern interferometry,” Strain 42(3), 197–205 (2006).
[Crossref]

Ferraro, P.

F. Pignatiello, M. De Rosa, P. Ferraro, S. Grilli, P. De Natale, A. Arie, and S. De. Nicola, “Measurement of the thermal expansion coefficients of ferroelectric crystals by a moiré interferometer,” Opt. Commun. 277(1), 14–18 (2007).
[Crossref]

Grilli, S.

F. Pignatiello, M. De Rosa, P. Ferraro, S. Grilli, P. De Natale, A. Arie, and S. De. Nicola, “Measurement of the thermal expansion coefficients of ferroelectric crystals by a moiré interferometer,” Opt. Commun. 277(1), 14–18 (2007).
[Crossref]

Ha, S. K.

K. Hayat and S. K. Ha, “Non-contact measurement of the coefficient of thermal expansion of Al 6061-T6 with fiber Bragg grating sensors,” J. Mechanical Sci. Technol. 28(2), 621–626 (2014).
[Crossref]

Hayat, K.

K. Hayat and S. K. Ha, “Non-contact measurement of the coefficient of thermal expansion of Al 6061-T6 with fiber Bragg grating sensors,” J. Mechanical Sci. Technol. 28(2), 621–626 (2014).
[Crossref]

He, W.

K. Zhang, W. He, L. Zhang, X. Zhao, and Y. Tian, “Measuring the thermal expansion coefficient of the carbon fiber optical tube by heterodyne laser interferometry,” Proc. SPIE 10141, 10141l (2016).

Heflinger, L. O.

L. O. Heflinger, R. F. Wuerker, and H. Spetzler, “Thermal expansion coefficient measurement of diffusely reflecting samples by holographic interferometry,” Rev. Sci. Instrum. 44(5), 629–633 (1973).
[Crossref]

Hsu, C. C.

C. T. Meng, C. C. Cheng, C. C. Hsu, and C. C. Wu, “Effective thermal expansion coefficient measurement of holographic material using total internal reflection heterodyne interferometry,” Opt. Eng. 54(9), 094105 (2015).
[Crossref]

Liu, B.

B. Liu, Q. Wei, J. Tu, D. Arola, and D. Zhang, “Inspection of the interior surface of cylindrical vessels using optic fiber shearography,” Meas. Sci. Technol. 28(9), 095202 (2017).
[Crossref]

Macy, W. W.

Meng, C. T.

C. T. Meng, C. C. Cheng, C. C. Hsu, and C. C. Wu, “Effective thermal expansion coefficient measurement of holographic material using total internal reflection heterodyne interferometry,” Opt. Eng. 54(9), 094105 (2015).
[Crossref]

Morita, Y.

Y. Morita, K. Arakawa, and M. Todo, “Experimental analysis of thermal displacement and strain distributions in a small outline J-leaded electronic package by using wedged-glass phase-shifting moiré interferometry,” Opt. Lasers Eng. 46(1), 18–26 (2008).
[Crossref]

Mukhopadhyay, A. K.

A. K. Mukhopadhyay and D. G. Zollinger, “Development of dilatometer test method to measure coefficient of thermal expansion of aggregates,” J. Mater. Civ. Eng. 21(12), 781–788 (2009).
[Crossref]

Naumann, J.

C. Dudescu, J. Naumann, M. Stockmann, and S. Nebel, “Characterization of thermal expansion coefficient of anisotropic materials by electronic speckle pattern interferometry,” Strain 42(3), 197–205 (2006).
[Crossref]

Nebel, S.

C. Dudescu, J. Naumann, M. Stockmann, and S. Nebel, “Characterization of thermal expansion coefficient of anisotropic materials by electronic speckle pattern interferometry,” Strain 42(3), 197–205 (2006).
[Crossref]

Onen, U.

U. Onen and T. Boyraz, “Microstructural characterization and thermal properties of aluminium titanate/spinel ceramic matrix composites,” Acta Phys. Pol. A 125(2), 488–490 (2014).
[Crossref]

Pignatiello, F.

F. Pignatiello, M. De Rosa, P. Ferraro, S. Grilli, P. De Natale, A. Arie, and S. De. Nicola, “Measurement of the thermal expansion coefficients of ferroelectric crystals by a moiré interferometer,” Opt. Commun. 277(1), 14–18 (2007).
[Crossref]

Song, M. H.

M. H. Song, G. H. Wu, N. Wang, and G. Y. Zhang, “Coefficient of thermal expansion and compute of carbon fibre reinforced magnesium composites,” Rare Met. Mater. Eng. 38(6), 1043–1047 (2009).

Spetzler, H.

L. O. Heflinger, R. F. Wuerker, and H. Spetzler, “Thermal expansion coefficient measurement of diffusely reflecting samples by holographic interferometry,” Rev. Sci. Instrum. 44(5), 629–633 (1973).
[Crossref]

Stockmann, M.

C. Dudescu, J. Naumann, M. Stockmann, and S. Nebel, “Characterization of thermal expansion coefficient of anisotropic materials by electronic speckle pattern interferometry,” Strain 42(3), 197–205 (2006).
[Crossref]

Tian, Y.

K. Zhang, W. He, L. Zhang, X. Zhao, and Y. Tian, “Measuring the thermal expansion coefficient of the carbon fiber optical tube by heterodyne laser interferometry,” Proc. SPIE 10141, 10141l (2016).

Todo, M.

Y. Morita, K. Arakawa, and M. Todo, “Experimental analysis of thermal displacement and strain distributions in a small outline J-leaded electronic package by using wedged-glass phase-shifting moiré interferometry,” Opt. Lasers Eng. 46(1), 18–26 (2008).
[Crossref]

Tu, J.

B. Liu, Q. Wei, J. Tu, D. Arola, and D. Zhang, “Inspection of the interior surface of cylindrical vessels using optic fiber shearography,” Meas. Sci. Technol. 28(9), 095202 (2017).
[Crossref]

Wang, N.

M. H. Song, G. H. Wu, N. Wang, and G. Y. Zhang, “Coefficient of thermal expansion and compute of carbon fibre reinforced magnesium composites,” Rare Met. Mater. Eng. 38(6), 1043–1047 (2009).

Wei, Q.

B. Liu, Q. Wei, J. Tu, D. Arola, and D. Zhang, “Inspection of the interior surface of cylindrical vessels using optic fiber shearography,” Meas. Sci. Technol. 28(9), 095202 (2017).
[Crossref]

Wu, C. C.

C. T. Meng, C. C. Cheng, C. C. Hsu, and C. C. Wu, “Effective thermal expansion coefficient measurement of holographic material using total internal reflection heterodyne interferometry,” Opt. Eng. 54(9), 094105 (2015).
[Crossref]

Wu, G. H.

M. H. Song, G. H. Wu, N. Wang, and G. Y. Zhang, “Coefficient of thermal expansion and compute of carbon fibre reinforced magnesium composites,” Rare Met. Mater. Eng. 38(6), 1043–1047 (2009).

Wuerker, R. F.

L. O. Heflinger, R. F. Wuerker, and H. Spetzler, “Thermal expansion coefficient measurement of diffusely reflecting samples by holographic interferometry,” Rev. Sci. Instrum. 44(5), 629–633 (1973).
[Crossref]

Zhang, D.

B. Liu, Q. Wei, J. Tu, D. Arola, and D. Zhang, “Inspection of the interior surface of cylindrical vessels using optic fiber shearography,” Meas. Sci. Technol. 28(9), 095202 (2017).
[Crossref]

Zhang, G. Y.

M. H. Song, G. H. Wu, N. Wang, and G. Y. Zhang, “Coefficient of thermal expansion and compute of carbon fibre reinforced magnesium composites,” Rare Met. Mater. Eng. 38(6), 1043–1047 (2009).

Zhang, K.

K. Zhang, W. He, L. Zhang, X. Zhao, and Y. Tian, “Measuring the thermal expansion coefficient of the carbon fiber optical tube by heterodyne laser interferometry,” Proc. SPIE 10141, 10141l (2016).

Zhang, L.

K. Zhang, W. He, L. Zhang, X. Zhao, and Y. Tian, “Measuring the thermal expansion coefficient of the carbon fiber optical tube by heterodyne laser interferometry,” Proc. SPIE 10141, 10141l (2016).

Zhao, X.

K. Zhang, W. He, L. Zhang, X. Zhao, and Y. Tian, “Measuring the thermal expansion coefficient of the carbon fiber optical tube by heterodyne laser interferometry,” Proc. SPIE 10141, 10141l (2016).

Zollinger, D. G.

A. K. Mukhopadhyay and D. G. Zollinger, “Development of dilatometer test method to measure coefficient of thermal expansion of aggregates,” J. Mater. Civ. Eng. 21(12), 781–788 (2009).
[Crossref]

Acta Phys. Pol. A (1)

U. Onen and T. Boyraz, “Microstructural characterization and thermal properties of aluminium titanate/spinel ceramic matrix composites,” Acta Phys. Pol. A 125(2), 488–490 (2014).
[Crossref]

Appl. Opt. (1)

J. Mater. Civ. Eng. (1)

A. K. Mukhopadhyay and D. G. Zollinger, “Development of dilatometer test method to measure coefficient of thermal expansion of aggregates,” J. Mater. Civ. Eng. 21(12), 781–788 (2009).
[Crossref]

J. Mechanical Sci. Technol. (1)

K. Hayat and S. K. Ha, “Non-contact measurement of the coefficient of thermal expansion of Al 6061-T6 with fiber Bragg grating sensors,” J. Mechanical Sci. Technol. 28(2), 621–626 (2014).
[Crossref]

Meas. Sci. Technol. (1)

B. Liu, Q. Wei, J. Tu, D. Arola, and D. Zhang, “Inspection of the interior surface of cylindrical vessels using optic fiber shearography,” Meas. Sci. Technol. 28(9), 095202 (2017).
[Crossref]

Opt. Commun. (1)

F. Pignatiello, M. De Rosa, P. Ferraro, S. Grilli, P. De Natale, A. Arie, and S. De. Nicola, “Measurement of the thermal expansion coefficients of ferroelectric crystals by a moiré interferometer,” Opt. Commun. 277(1), 14–18 (2007).
[Crossref]

Opt. Eng. (1)

C. T. Meng, C. C. Cheng, C. C. Hsu, and C. C. Wu, “Effective thermal expansion coefficient measurement of holographic material using total internal reflection heterodyne interferometry,” Opt. Eng. 54(9), 094105 (2015).
[Crossref]

Opt. Lasers Eng. (1)

Y. Morita, K. Arakawa, and M. Todo, “Experimental analysis of thermal displacement and strain distributions in a small outline J-leaded electronic package by using wedged-glass phase-shifting moiré interferometry,” Opt. Lasers Eng. 46(1), 18–26 (2008).
[Crossref]

Proc. SPIE (1)

K. Zhang, W. He, L. Zhang, X. Zhao, and Y. Tian, “Measuring the thermal expansion coefficient of the carbon fiber optical tube by heterodyne laser interferometry,” Proc. SPIE 10141, 10141l (2016).

Rare Met. Mater. Eng. (1)

M. H. Song, G. H. Wu, N. Wang, and G. Y. Zhang, “Coefficient of thermal expansion and compute of carbon fibre reinforced magnesium composites,” Rare Met. Mater. Eng. 38(6), 1043–1047 (2009).

Rev. Sci. Instrum. (1)

L. O. Heflinger, R. F. Wuerker, and H. Spetzler, “Thermal expansion coefficient measurement of diffusely reflecting samples by holographic interferometry,” Rev. Sci. Instrum. 44(5), 629–633 (1973).
[Crossref]

Strain (1)

C. Dudescu, J. Naumann, M. Stockmann, and S. Nebel, “Characterization of thermal expansion coefficient of anisotropic materials by electronic speckle pattern interferometry,” Strain 42(3), 197–205 (2006).
[Crossref]

Other (2)

ASTM E289–04, “Standard Text Method for Linear Thermal Expansion of Rigid Solids With Interferometry,” http://www.astm.org .

C. M. Vest, Holographic Interferometry (Wiley, 1979).

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Figures (8)

Fig. 1
Fig. 1 Geometry of the composite specimens. All dimensions are in millimeters.
Fig. 2
Fig. 2 Optical arrangement for CTE measurement.
Fig. 3
Fig. 3 Schematic diagram of the experimental arrangement.
Fig. 4
Fig. 4 Temperature versus time for the heating cycle.
Fig. 5
Fig. 5 Relationship between wrapped phase and time.
Fig. 6
Fig. 6 Relationship between displacement and temperature readout for the Aluminum sample.
Fig. 7
Fig. 7 Variations of displacement and temperature readout during the heating and cooling process.
Fig. 8
Fig. 8 The change of CTE for the CFRP laminates with temperature.

Tables (2)

Tables Icon

Table 1 Information about the tested composites.

Tables Icon

Table 2 The CTEs for the various CFRPs

Equations (7)

Equations on this page are rendered with MathJax. Learn more.

α= ε ΔT = w l 0 ΔT
I= a 2 + b 2 +2abcos(φψ)
| I ' I|=|4absin( ΔφΔψ 2 )sin(φψ+ ΔφΔψ 2 )|
ΔφΔψ= 2π λ δ
δ=(1+cosa)Δl
Δl= λ(ΔφΔψ) 2π(1+cosa)
ε=Δl/ l 0 = λ(ΔφΔψ) 2π l 0 (1+cosa)

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