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Specimen gratings made from body art paper for in-plane moiré strain analysis
Polymer Testing 24 (2005) 535–539 www.elsevier.com/locate/polytest
Test Method
Specimen gratings made from body art paper for in-plane moire´ strain analysis Nai-Shang Liou* Department of Mechanical Engineering, Southern Taiwan University of Technology, 1 Nan-Tai St., Yuang-Kang City, Tainan Hsien 710, Taiwan, ROC Received 12 August 2004; accepted 30 September 2004
Abstract The Moire´ method is a useful tool for in-plane full-field displacement measurement and strain analysis. This paper presents a convenient method for forming a grating to be used for geometry moire´ and Fourier transform moire´ and grid method (FTMGM) on the surface of polymeric specimens. In general, polymeric materials have low modulus of elasticity and can undergo large deformation during tests. These conditions put restrictions on selection of feasible gratings for moire´ strain analysis of polymeric materials. In the current paper, a novel use of a grating made by special inkjet printer tattoo paper allows us to perform full-field strain analyses of polymeric materials by using the geometry moire´ method and FTMGM. This grating has low modulus and can be bonded to the polymeric specimen surface in a very short time and can survive large deformations. These properties make it a practical grating for full-field strain analysis of polymeric material, using moire´ methods. The grating making procedures are explained in detail. Two moire´ applications are demonstrated, including geometry moire´ and Fourier transform moire´ methods for the in-plane deformation analysis of a U shape ethylene vinyl acetate specimen under tensile load. q 2004 Elsevier Ltd. All rights reserved. Keywords: Moire´ strain analysis; Full-field strain measurement; Fourier transform moire´; Grid method
1. Introduction In-plane moire´ methods are useful full-field methods for 2D deformation and strain analysis. These methods are used extensively by researchers and engineers in different fields for different applications like electro-packaging, composite material testing and fracture mechanics. There are different implementations of the 2D moire´ method, e.g. geometry moire´, moire´ interferometry, Fourier transform moire´, etc. The information of moire´ methods is carried by the moire´ fringes that are formed. The quality of specimen gratings plays an important role in moire´ methods. Since only high quality gratings can produce accurate and low noise moire´
* Tel.: C886 6 2533131x3546; fax: C866 6 242 5092. E-mail address: [email protected] 0142-9418/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymertesting.2004.09.015
fringes for further displacement and strain analysis, different techniques have been developed to produce specimen gratings for different moire´ applications. High density diffraction specimen gratings can be made by methods described in Refs. [1–4] for moire´ interferometry and microscope moire´ applications. Gratings for geometry moire´ can be put onto specimens by methods like scribing, etching, ruling, etc. [5]. There is no standard method for making specimen gratings for moire´ methods. Electron beam lithography was used to generate moire´ grating on the specimen surface by Chen et al. [6]. Tuttle [7] used a laser printer to produce gratings on overhead transparency film for the geometry moire´ method. New methods for making specimen gratings for different moire´ applications emerge as suitable new technology become available. There are particular requirements for moire´ gratings used for testing of polymeric material. In general, polymeric material will
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N.-S. Liou / Polymer Testing 24 (2005) 535–539
Fig. 1. Procedure for producing grating on polymeric specimen.
undergo large deformation during testing and the elastic modulus of the polymer is low, so the specimen grating used for test of such material should be able to survive large deformation without severe degradation and delamination. Furthermore, the specimen grating should have very low elastic modulus so it will not reinforce the specimen during the test. The grating-making procedure developed by Liou and Huang [8] meets these requirements and can be used for in-plane geometry moire´ and Fourier transform moire´ strain analysis of polymeric material; however, this procedure is relatively cumbersome. In the current paper, a more handy method for making and applying gratings on polymeric specimens which can meet the aforementioned requirements is proposed.
2. Procedure In the current procedure, moire´ gratings were produced from special paper and an inkjet printer. The procedure to make and apply gratings onto a U shape specimen is as follows. The cross-grating pattern was designed on a computer and saved as an image file. This grating pattern was printed out by using an inkjet printer on AVERYw inkjet printable tattoo paper. The frequency of the grating can be controlled by the grating image and print setup of the printer. Photo paper and the best printing quality were selected in the printer setup dialog box for printing. After printing, the special paper was allowed to dry for 5 min and a cover film
was applied to the printed paper as shown in Fig. 1a. This film consists of a plastic sheet and a thin adhesive polymer layer. After removing any bubbles between the film and printed paper by using a pen or a ruler to squeeze the paper surface, the grating set was ready for use. The grating pattern was cut to fit the shape of specimen and to leave approximately a 1 mm edge. The film of the grating set was rubbed before peeling off the plastic sheet in order to secure the film adhesive surface onto the printed paper. Fig. 1b shows the procedure to peel off the plastic sheet of cover film from a U shape grating set tailored for a U shape specimen. The adhesive polymer layer remained on the grating pattern after the plastic sheet of the film was peeled off. Then the grating pattern, with the adhesive polymer side facing the specimen, was placed onto the specimen as shown in Fig. 1c. By wiping the specimen surface with wet rag to make the grating pattern fully wet for 10 s, the grating pattern was transferred onto the specimen after the paper layer was removed as shown in Fig. 1d.
3. Experiments For demonstration purposes, following the aforementioned procedure, a 1 line/mm cross-grating was made and applied on a U shape specimen made from Ethylene Vinyle Acetate (EVA) foam material for in-plane geometry moire´ and FTM analysis. The undeformed and deformed status of a specimen put on a loading
N.-S. Liou / Polymer Testing 24 (2005) 535–539
537
Fig. 2. (a) Undeformed specimen. (b) Specimen under tensile load.
Fig. 3. Geometry moire´ fringe patterns: left-hand side is the v field fringe pattern and right-hand side is the u field fringe pattern.
fixture is shown in Fig. 2. For geometry moire´ analysis, a reference grating with the same spatial frequency as the specimen grating was put in front of the specimen. This grating was made by printing straight lines on transparency film using a laser printer. Due to the symmetry of the specimen, the reference grating was made in such a way that the left portion of the grating consisted of horizontal lines and the right portion of the grating consisted of vertical lines so both u and v field fringe patterns could be seen simultaneously during the test. The moire´ fringe is a locus of points showing the same displacement component in the direction perpendicular to the lines of the master grating. The Moire´ fringe pattern can be visualized as a contour map of a displacement field that represents the displacement in the direction perpendicular to the lines of master grating. Once u and v displacement fields have been found by using reference grating lines perpendicular to the x and y axes of specimen respectively, the Cartesian components of the displacement derivatives can be calculated. For finite deformation and strain analysis, components of
Fig. 4. Real part of complex moire´ fringe patterns computed from Fourier transform moire´ and grid method: (a) u field, (b) v field.
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N.-S. Liou / Polymer Testing 24 (2005) 535–539
the Almansi strain tensor EA, given by 1 EA Z ½I K ðF$FT ÞK1 2
(1)
where F is the deformation gradient tensor, can be calculated from derivatives of displacements. Fig. 3 shows both u and v field geometry moire´ fringe patterns of the deformed specimen under tensile load. Fourier Transform Moire´ and Grid Method (FTMGM), developed by Morimoto et al. [9] is a fullfield non-contact method which can be used to measure in-plane displacements and strains. It is an objective method since all of the computational work and strain analysis can be done by computer once the image of a deformed specimen with grating is acquired. Human error can be minimized so the accuracy is high. This method is suitable for strain analysis of polymeric materials which may undergo large deformation. The theory of FTMGM is detailed in Refs. [5,9,10]. Fig. 4 shows the real part of complex moire´ fringe patterns formed by the FTMGM method. The full-field Almansi strain components, computed by FTMGM, of deformed specimen are shown in Fig. 5.
4. Conclusion A novel procedure for making specimen gratings for geometry moire´ and Fourier transform moire´ strain analysis was developed. Gratings made by this procedure have low elastic modulus and can survive large deformations. This makes it very suitable for full-field in-plane strain analysis of polymeric materials. The grating can be easily applied not only flat surfaces but also to curved surfaces. The grating has the potential to be applied to other types of highly deformed materials like biological soft tissues for full-field strain measurement. Acknowledgements The financial support from National Science Council of Taiwan ROC (NSC-92-2212-E-218-010) is gratefully acknowledged.
References
Fig. 5. Almansi strain components computed from complex moire´ fringe patterns shown in Fig. 4: (a) E11, (b) E12 and (c) E22.
[1] D. Post, B. Han, P. Ifju, High Sensitivity Moire-Experimental Analysis for Mechanics and Materials, Springer, New York, 1994. [2] P. Ifju, D. Post, Zero thickness specimen gratings for moire interferometry, Experimental Techniques 15 (2) (1991) 45– 47. [3] X. Niu, P. Ifju, J. Bianchi, B. Wallace, A diffraction grating for compliant and porous material, Experimental Techniques 24 (1) (2000) 27–30.
N.-S. Liou / Polymer Testing 24 (2005) 535–539 [4] Y. Guo, P. Ifju, R. Boeman, F. Dai, Formation of specimen gratings for moire interferometry applications, Experimental Techniques 23 (5) (1999) 28–32. [5] A. Kobayashi, Handbook on Experimental Mechanics, Society for Experimental Mechanics, 1993. [6] H. Chen, D. Liu, A. Lee, Moire in atomic force microscope, Experimental Techniques 24 (1) (2000) 31–32. [7] M. Tuttle, Demonstrating moire fringes using gratings produced with a laser printer, Experimental Techniques 21 (5) (1997) 19–22.
539
[8] N. Liou, C. Huang, Fourier transform moire´ strain analysis by using cross gratings produced from iron-on paper and inkjet printer, Polymer Testing 22 (5) (2003) 487–490. [9] Y. Morimoto, Y. Seguchi, T. Higashi, Application of moire analysis of strain using fourier transform, Optical Engineering 27 (1988) 650–656. [10] Y. Morimoto, Y. Seguchi, T. Higashi, Two-dimensional moire method and grid method using Fourier transform, Experimental Mechanics 29 (1989) 399–404.
Test Method
Specimen gratings made from body art paper for in-plane moire´ strain analysis Nai-Shang Liou* Department of Mechanical Engineering, Southern Taiwan University of Technology, 1 Nan-Tai St., Yuang-Kang City, Tainan Hsien 710, Taiwan, ROC Received 12 August 2004; accepted 30 September 2004
Abstract The Moire´ method is a useful tool for in-plane full-field displacement measurement and strain analysis. This paper presents a convenient method for forming a grating to be used for geometry moire´ and Fourier transform moire´ and grid method (FTMGM) on the surface of polymeric specimens. In general, polymeric materials have low modulus of elasticity and can undergo large deformation during tests. These conditions put restrictions on selection of feasible gratings for moire´ strain analysis of polymeric materials. In the current paper, a novel use of a grating made by special inkjet printer tattoo paper allows us to perform full-field strain analyses of polymeric materials by using the geometry moire´ method and FTMGM. This grating has low modulus and can be bonded to the polymeric specimen surface in a very short time and can survive large deformations. These properties make it a practical grating for full-field strain analysis of polymeric material, using moire´ methods. The grating making procedures are explained in detail. Two moire´ applications are demonstrated, including geometry moire´ and Fourier transform moire´ methods for the in-plane deformation analysis of a U shape ethylene vinyl acetate specimen under tensile load. q 2004 Elsevier Ltd. All rights reserved. Keywords: Moire´ strain analysis; Full-field strain measurement; Fourier transform moire´; Grid method
1. Introduction In-plane moire´ methods are useful full-field methods for 2D deformation and strain analysis. These methods are used extensively by researchers and engineers in different fields for different applications like electro-packaging, composite material testing and fracture mechanics. There are different implementations of the 2D moire´ method, e.g. geometry moire´, moire´ interferometry, Fourier transform moire´, etc. The information of moire´ methods is carried by the moire´ fringes that are formed. The quality of specimen gratings plays an important role in moire´ methods. Since only high quality gratings can produce accurate and low noise moire´
* Tel.: C886 6 2533131x3546; fax: C866 6 242 5092. E-mail address: [email protected] 0142-9418/$ - see front matter q 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.polymertesting.2004.09.015
fringes for further displacement and strain analysis, different techniques have been developed to produce specimen gratings for different moire´ applications. High density diffraction specimen gratings can be made by methods described in Refs. [1–4] for moire´ interferometry and microscope moire´ applications. Gratings for geometry moire´ can be put onto specimens by methods like scribing, etching, ruling, etc. [5]. There is no standard method for making specimen gratings for moire´ methods. Electron beam lithography was used to generate moire´ grating on the specimen surface by Chen et al. [6]. Tuttle [7] used a laser printer to produce gratings on overhead transparency film for the geometry moire´ method. New methods for making specimen gratings for different moire´ applications emerge as suitable new technology become available. There are particular requirements for moire´ gratings used for testing of polymeric material. In general, polymeric material will
536
N.-S. Liou / Polymer Testing 24 (2005) 535–539
Fig. 1. Procedure for producing grating on polymeric specimen.
undergo large deformation during testing and the elastic modulus of the polymer is low, so the specimen grating used for test of such material should be able to survive large deformation without severe degradation and delamination. Furthermore, the specimen grating should have very low elastic modulus so it will not reinforce the specimen during the test. The grating-making procedure developed by Liou and Huang [8] meets these requirements and can be used for in-plane geometry moire´ and Fourier transform moire´ strain analysis of polymeric material; however, this procedure is relatively cumbersome. In the current paper, a more handy method for making and applying gratings on polymeric specimens which can meet the aforementioned requirements is proposed.
2. Procedure In the current procedure, moire´ gratings were produced from special paper and an inkjet printer. The procedure to make and apply gratings onto a U shape specimen is as follows. The cross-grating pattern was designed on a computer and saved as an image file. This grating pattern was printed out by using an inkjet printer on AVERYw inkjet printable tattoo paper. The frequency of the grating can be controlled by the grating image and print setup of the printer. Photo paper and the best printing quality were selected in the printer setup dialog box for printing. After printing, the special paper was allowed to dry for 5 min and a cover film
was applied to the printed paper as shown in Fig. 1a. This film consists of a plastic sheet and a thin adhesive polymer layer. After removing any bubbles between the film and printed paper by using a pen or a ruler to squeeze the paper surface, the grating set was ready for use. The grating pattern was cut to fit the shape of specimen and to leave approximately a 1 mm edge. The film of the grating set was rubbed before peeling off the plastic sheet in order to secure the film adhesive surface onto the printed paper. Fig. 1b shows the procedure to peel off the plastic sheet of cover film from a U shape grating set tailored for a U shape specimen. The adhesive polymer layer remained on the grating pattern after the plastic sheet of the film was peeled off. Then the grating pattern, with the adhesive polymer side facing the specimen, was placed onto the specimen as shown in Fig. 1c. By wiping the specimen surface with wet rag to make the grating pattern fully wet for 10 s, the grating pattern was transferred onto the specimen after the paper layer was removed as shown in Fig. 1d.
3. Experiments For demonstration purposes, following the aforementioned procedure, a 1 line/mm cross-grating was made and applied on a U shape specimen made from Ethylene Vinyle Acetate (EVA) foam material for in-plane geometry moire´ and FTM analysis. The undeformed and deformed status of a specimen put on a loading
N.-S. Liou / Polymer Testing 24 (2005) 535–539
537
Fig. 2. (a) Undeformed specimen. (b) Specimen under tensile load.
Fig. 3. Geometry moire´ fringe patterns: left-hand side is the v field fringe pattern and right-hand side is the u field fringe pattern.
fixture is shown in Fig. 2. For geometry moire´ analysis, a reference grating with the same spatial frequency as the specimen grating was put in front of the specimen. This grating was made by printing straight lines on transparency film using a laser printer. Due to the symmetry of the specimen, the reference grating was made in such a way that the left portion of the grating consisted of horizontal lines and the right portion of the grating consisted of vertical lines so both u and v field fringe patterns could be seen simultaneously during the test. The moire´ fringe is a locus of points showing the same displacement component in the direction perpendicular to the lines of the master grating. The Moire´ fringe pattern can be visualized as a contour map of a displacement field that represents the displacement in the direction perpendicular to the lines of master grating. Once u and v displacement fields have been found by using reference grating lines perpendicular to the x and y axes of specimen respectively, the Cartesian components of the displacement derivatives can be calculated. For finite deformation and strain analysis, components of
Fig. 4. Real part of complex moire´ fringe patterns computed from Fourier transform moire´ and grid method: (a) u field, (b) v field.
538
N.-S. Liou / Polymer Testing 24 (2005) 535–539
the Almansi strain tensor EA, given by 1 EA Z ½I K ðF$FT ÞK1 2
(1)
where F is the deformation gradient tensor, can be calculated from derivatives of displacements. Fig. 3 shows both u and v field geometry moire´ fringe patterns of the deformed specimen under tensile load. Fourier Transform Moire´ and Grid Method (FTMGM), developed by Morimoto et al. [9] is a fullfield non-contact method which can be used to measure in-plane displacements and strains. It is an objective method since all of the computational work and strain analysis can be done by computer once the image of a deformed specimen with grating is acquired. Human error can be minimized so the accuracy is high. This method is suitable for strain analysis of polymeric materials which may undergo large deformation. The theory of FTMGM is detailed in Refs. [5,9,10]. Fig. 4 shows the real part of complex moire´ fringe patterns formed by the FTMGM method. The full-field Almansi strain components, computed by FTMGM, of deformed specimen are shown in Fig. 5.
4. Conclusion A novel procedure for making specimen gratings for geometry moire´ and Fourier transform moire´ strain analysis was developed. Gratings made by this procedure have low elastic modulus and can survive large deformations. This makes it very suitable for full-field in-plane strain analysis of polymeric materials. The grating can be easily applied not only flat surfaces but also to curved surfaces. The grating has the potential to be applied to other types of highly deformed materials like biological soft tissues for full-field strain measurement. Acknowledgements The financial support from National Science Council of Taiwan ROC (NSC-92-2212-E-218-010) is gratefully acknowledged.
References
Fig. 5. Almansi strain components computed from complex moire´ fringe patterns shown in Fig. 4: (a) E11, (b) E12 and (c) E22.
[1] D. Post, B. Han, P. Ifju, High Sensitivity Moire-Experimental Analysis for Mechanics and Materials, Springer, New York, 1994. [2] P. Ifju, D. Post, Zero thickness specimen gratings for moire interferometry, Experimental Techniques 15 (2) (1991) 45– 47. [3] X. Niu, P. Ifju, J. Bianchi, B. Wallace, A diffraction grating for compliant and porous material, Experimental Techniques 24 (1) (2000) 27–30.
N.-S. Liou / Polymer Testing 24 (2005) 535–539 [4] Y. Guo, P. Ifju, R. Boeman, F. Dai, Formation of specimen gratings for moire interferometry applications, Experimental Techniques 23 (5) (1999) 28–32. [5] A. Kobayashi, Handbook on Experimental Mechanics, Society for Experimental Mechanics, 1993. [6] H. Chen, D. Liu, A. Lee, Moire in atomic force microscope, Experimental Techniques 24 (1) (2000) 31–32. [7] M. Tuttle, Demonstrating moire fringes using gratings produced with a laser printer, Experimental Techniques 21 (5) (1997) 19–22.
539
[8] N. Liou, C. Huang, Fourier transform moire´ strain analysis by using cross gratings produced from iron-on paper and inkjet printer, Polymer Testing 22 (5) (2003) 487–490. [9] Y. Morimoto, Y. Seguchi, T. Higashi, Application of moire analysis of strain using fourier transform, Optical Engineering 27 (1988) 650–656. [10] Y. Morimoto, Y. Seguchi, T. Higashi, Two-dimensional moire method and grid method using Fourier transform, Experimental Mechanics 29 (1989) 399–404.