PHOTOELASTIC MATERIALS: DETERMINING MODULUS OF ELASTICITY AND

POISSON’S RATIO IN TENSILE TESTING

W. A. Soares1; L. L. da Silva; J. J. Vilela1; N. A, Rocha1; V. C. E. Almeida1; G. C.

Soares2; T. R. Mansur1

Av. Presidente Antônio Carlos, 6.627, Campus da UFMG – Pampulha, Belo

Horizonte - Minas Gerais, Brasil, soaresw@cdtn.br

1 Centro de Desenvolvimento da Tecnologia Nuclear – CDTN/CNEN

2 Departamento de Engenharia Metalúrgica e de Materiais, Escola de Engenharia,

Universidade Federal de Minas Gerais - UFMG

ABSTRACT

Photoelasticity is a method for measuring and visualizing stresses in loaded models

or structures using birefringent material. It has been used in dentistry investigations

to visualize stress distribution around loaded dental implants inserted into birefringent

polymers. Normally, these investigations are done in association with finite element

analysis, which requires elastic properties like modulus of elasticity and Poisson’s

ratio. A PSM-1 polymer was investigated through three different methods in order to

determine which would be the most appropriate: clip-on extensometer, video

extensometer and strain gages. Test specimens were machined according to ASTM

D 638–14 and analyzed in a transmission polariscope in order to visualize the

possible inclusion of residual stresses. Uniaxial tensile tests were performed in a

universal testing machine. Results pointed out that strain gages provided more

accurate and precise results than other methods employed for both investigated

material properties.

Keywords: Modulus of elasticity, Poisson's ratio, Tensile testing, Photoelasticity,

Birefringent materials.

1 INTRODUCTION

Polymers with birefringence under loading are key input in photoelasticity, a

method for measuring and visualizing stress fields in models or actual structures

under loading. Models are generally used in transmission photoelasticity while

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reflection photoelasticity is used when actual structures have to be investigated.

Such birefringence associated with polarized lens and a light source produces

patterns denominated isochromatic fringes which display interesting information on

stress concentration, an important safety reference for analyzing a loaded structure.

Photoelasticity is employed in areas ranging from engineering to dentistry. It has

been employed in dentistry investigations to visualize stress distribution around

loaded dental implants inserted into a photoelastic polymer block (Fig. 1). Normally,

these investigations are done in association with finite element analysis, which

requires material properties like modulus of elasticity and Poisson’s ratio. In order to

make this analysis, such properties for polymers have to be known in advance.

However, these properties are not easily found in the literature. In addition, before

molding this block, a polymer has to be prepared using specific proportion of a

precursor polymer and a hardener and which solidifies after curing. As a result the

elastic properties can be dependent on such proportion.

Figure 1. Isochromatic fringes in a photoelastic polymer around a loaded dental implant.(1)

In 2016, CDTN’s Stress Analysis Laboratory received a request to determine

these properties for a specific dentistry dissertation. However, no procedure was

available to attend such demand, and it was then decided to define standard

dimensions of the photoelastic specimen as well as establishing the steps to be

followed in the tensile testing of such materials. Three different techniques were

chosen for determining the elastic properties of such polymers: clip-on extensometer,

video extensometer and strain gages.

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2 MATERIALS AND METHODS

2.1 Materials and equipment

A 20 years old photoelastic sheet Type PSM-1 10”x20” and 0.25” of nominal

thickness supplied by Photoelastic Division of Measurements Group was the material

source used for extracting the test specimens. This sheet was stored in its original

packaging inside the laboratory. All main equipment used for determining the elastic

properties of the PSM-1 specimens are summarized in Table 1.

Table 1. Equipment specifications.

Equipment Supplier Type Purpose Remarks

Universal testing

machine Instron 5882 Load application 100 kN load cell

Clip-on extensometer

Instron 2630-100

Series Measuring modulus of

elasticity Gage length 50 mm

Video extensometer

Instron 2663-821 SN: 5265

Measuring modulus of elasticity and Poisson's

ratio

Minimum gage length 10 mm and minimum gage

width 8 mm

Voltmeter Agilent 34970A Measuring feed voltage

and output voltage 34401 A – 6 ½ Digit

Multimeter

Transmission polariscope

Measurements Group

Series 060

Observing probable residual stress in

machined specimens

Fixed in the Stress Analysis Laboratory

Mobile transmission polariscope

CDTN Dark field Monitoring stress field

during the tensile testing Adaptable to Instron used

A metallic matrix compatible with Type I ASTM(2) 638-14 was produced for

machining the photoelastic specimens. Loctite Bond 496, a fast curing adhesive, was

used for bonding strain gage on specimen surface. A ¼ Wheatstone bridge circuit

with a 5 Volts feed voltage was used for each strain gage. TLM strain gages type

CFLA-1-350-11 with a gage factor of 2.09±1% and gage length of 1mm and

manufactured by Tokyo Sokki Kenkyujo Company were used in the tests. For the

samples analyzed utilizing the video and clip-on extensometers, the Bluehill 2

software was used to monitor load application and calculate modulus of elasticity and

compute Poisson’s ratio.

2.2 Specimens: type, dimensions, material integrity and loading

The standard specimen was selected according to ASTM D 638-14: Standard

Test Method for Tensile Properties of Plastics(2). Three specimens were extracted

from the photoelastic sheet’s longitudinal direction, while other four were extracted

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from the transverse direction. The specimens were machined with the help of a

metallic matrix in order to obtain the specimen Type I as prescribed in the prior

mentioned standard. ASTM E132: Standard Test Method for Poisson’s Ratio at

Room Temperature(3) was also used to position strain gages in some specimens. Fig.

2 illustrates sheet and specimen reference orientations for purpose of calculations.

Fig 2 shows also specimens, location of extraction and employed methods. Fig.3

illustrates Type I specimen dimensions.

Figure 2. Sheet and specimen reference orientations and identification of specimens in terms of location and employed methods.

Figure 3. ASTM D 638-14 (2) standardized specimen dimensions.

Prior to extracting the specimens, sheet material integrity was verified to know if

the material still had its photoelastic properties, like the capability of generating

isochromatic fringes under load when observed in a polariscope. In order to

investigate if residual stresses had been introduced by machining, the photoelastic

PSM-1 sheet was observed in a transmission polariscope. All specimens extracted

from this sheet were also analyzed in this same polariscope with the purpose of

viewing possible addition of residual stress during the machining process and after

the tensile testing to monitor if the material had exceeded the elastic regime. Fig. 4

shows isochromatic fringes in one PSM-1 specimen under pure bending. It can be

seen that the selected material does still have its capacity to generate such fringes.

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Figure 4. Isochromatic fringes in a specimen in pure bending as seen in a transmission polariscope.

Once the specimens had its material integrity verified, one specimen from sheet

transverse direction (S1T) was submitted to a complete tensile testing, overcoming

its ultimate tensile strength, and consequently necking. It was an exploratory test to

define the maximum load to be applied in order to limit the strains in the elastic

region, once only the modulus of elasticity and Poisson’s ratio were the intended

properties to be investigated. Elastic behavior was observed up to 4000 N, yielding

point was reached at 5000 N and necking formation was observed during tensile

testing.

Each specimen was submitted to uniaxial tensile loading in a universal testing

machine, as specified in Table 1, using three loading cycles. At the end of each

loading cycle, the crosshead stopped and unloaded, returning to its initial condition.

Each loading cycle was performed with a test velocity of 1 mm/min.

A mobile polariscope adapted to the loading machine allowed inspecting

possible specimen misalignment when positioning it in the tensile testing machine’s

wedge grips. The polariscope was used for inspecting strain gage bonding effects on

the specimen surface and also effects from welding electrical wires on gage tabs.

The specimen with clip-on extensometer already mounted was also inspected in the

polariscope in order to verify possible bending effects.

2.3 Modulus of elasticity and Poisson’s ratio definitions

The modulus of elasticity E is defined in formula (A), where σ is the normal

tensile stress, ε is the strain and Δ is the increment. Normal stress σ is found dividing

load by the cross-sectional area and ε is the length increment divided by the initial

reference length.

E = Δσ / Δε (A)

Poisson’s ratio ν is defined by formula (B), where εL is the lateral strain and εA is

the axial strain, having as reference orientations in Fig. 2.

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ν = - εL / εA (B)

In (B) εA is equal to ΔLA / L0A, where L0A is the gauge length in the axial direction and

ΔLA is the respective elongation of LA0 under load. εL has the same definition but in the

lateral direction.

Axial tension and axial strain are input data to compute the modulus of

elasticity. Modulus of elasticity can be determined from the angular coefficient of the

linear regression applied to axial stress against axial strain data.

The modulus of elasticity and the Poisson’s ratio were calculated, respectively,

as the mean of all results from loading sequences involved in these analyses and

then computed the margin of error (95% Confidence interval for small samples).

2.4 Strain gage method

A pair of strain gages was located on opposite sides of each specimen,

according to ASTM(3), as illustrated in Fig. 5. Strain measurements were done for

each side individually, as only two voltmeters with one channel each were available.

In the employed arrangement, strain gages were spatially and electrically

independent.

Figure 5. Strain gage arrangement on side A of a specimen.

Axial and lateral strains are indirectly measured through electrical signal output

from Wheatstone bridge from which the strain gage makes part as a resistor

component of such bridge. Conversion of electrical signal to strain is done with the

following equation:

ε = ( 4∗∆V ) / ( V*K ) (C)

in which ε is the strain, ∆V is the bridge output voltage, V is the excitation voltage

and K is the gage factor. Such formula is used for computing both axial and lateral

strains.

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2.5 Clip-on extensometer method

A clip-on extensometer, as specified in Table 1, was used to determine the

modulus of elasticity of two specimens. The gage length (50 mm) for computing

strain is a parameter intrinsic to the employed clip-on extensometer. Fig. 6 illustrates

the type of clip-on extensometer used to measure axial strain during tensile testing.

Figure 6. Clip-on extensometer type utilized during tensile testing.

Figure 7. Illustration of specimen in video extensometer method

2.6 Video extensometer method

Table 1 presents specification of the video extensometer and equipment used

for determining the modulus of elasticity and Poisson’s ratio. Fig. 7 illustrates

specimen under monochromatic light of such video. Axial and lateral strains are

determined based on marks done by the user on the specimen as shown in Fig. 8.

These marks delimit the specimen’s gage length (axial direction) and gage width

(lateral direction) for the purpose of computing axial and lateral strains, respectively.

In this research, values of 50 and 10 mm where marked on axial and lateral

directions, accordingly. Once the specimen is positioned on the grips, the video

extensometer system reads the actual values of these gages and shows them on the

computer screen (50.23 x 12.18 mm for S4 T and 51.69 x 9.661 mm for S6 L).

Figure 8. Gage length (L0A) and gage width (L0L) for computing strains with video extensometer.

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3 RESULTS AND DISCUSSION

The tensile testing was performed at room temperature, in a range of

temperature of 20-25 oC, in which no noticeable influence is introduced by such

thermal load(4).

A survey on elastic properties of PSM-1 in the literature indicated values of

modulus of elasticity ranging from 2200 to 2500 MPa and Poisson’s ratio of

approximately 0.38.(4-12) It was not possible to know the methods employed for

determining these values. Table 2 shows results of this survey, displaying modulus of

elasticity and Poisson’s ratio reference values for the employed photoelastic material

Table 2. Reference values of PSM-1 modulus of elasticity and Poisson’s ratio.(4-12)

Reference Modulus of elasticity (MPa) Poisson's ratio

MISKIOGLU et al. 1981 2390 0.38

BAEK, Tae-Hyun et al. 2015 2482 -

PRAMOD, R.2015 2390 0.38

UDD, E et al. 2011 2300 0.4

FREIRE, J. L. F. et al. 2009 2200 -

DOYLE, J. F. 2004 2500 0.38

MAHINFALAH, M. 1988 2390 0.38

BABAK, R. 1987 2480 0.38

BEN AICHA, L. et al. 1986 2400 0.38

Figs. 9 and 10 present the mean values of Poisson‘s ratio and modulus of

elasticity for the investigated samples, differentiating the results based on the

direction in which specimens where extracted from the parent polymer sheet.

Figure 9. Mean Poisson's ratio and respective 95% confidence interval for specimens extracted from the transverse and longitudinal direction.

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Figure 10. Mean modulus of elasticity and respective 95% confidence interval for specimens extracted from the transverse and longitudinal direction.

Considering the margin of error of the results presented in Figs. 9 and 10, no

assertion can be inferred in relation to possible influence of specimen extraction

direction on both elastic properties investigated in this paper.

For both methods shown in Fig. 11, the mean Poisson’s values were higher

than the expected value found in the literature survey. However, strain gage

presented result closer the expected value than the video extensometer. Clip-on

extensometer was not used for this measuring as a result of no clip-on transverse

type being available.

Figure 11. Mean Poisson's ratio determined via video extensometer and strain gage for the sample tested in each method.

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Figure 12. Mean modulus of elasticity determined via video extensometer, clip-on extensometer and strain gage for the sample tested in each method.

The mean modulus of elasticity obtained through strain gage was found to be

the most precise and accurate and its margin of error is contained in the survey value

interval, which corroborates with its validity. Although it exhibited a larger margin of

error, the clip-on extensometer also revealed a mean modulus of elasticity similar to

those of the survey. Nonetheless, the video extensometer provided a mean modulus

of elasticity marginally divergent from the other methods and the survey, and also

displayed a greater margin of error, which is in accordance with what was previously

presented on the Poisson’s ratio analysis.

Because of variability inherent to photoelastic materials, properties values from

product tables given by the supplier are to be taken as nominal values, and

calibration for a particular batch of materials is always recommended.(9)

4 CONCLUSIONS

All conclusions in terms of results refer to a single 20 years old PSM-1

photoelastic sheet, manufactured by Measurements Group, in conjunction with two

tensile specimens for each method. Despite its age, the material still retained its

capacity of generating isochromatic fringes.

Results pointed out that the strain gage provided more accurate and precise

results than other two methods and with a smaller margin of error for mean modulus

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of elasticity. On the other hand, the clip-on extensometer method presented smaller

margin of error than that of the video extensometer. Mean Poisson’s ratio computed

with strain gage displayed more precise results than with video extensometer method

and presented a smaller margin of error. Mean modulus of elasticity and Poisson’s

ratio calculated through data from the video extensometer both presented divergent

values from the ones obtained via other methods and in the literature survey, and

also displayed the largest margin of error among the studied techniques. Thus, it can

be concluded that strain gage analysis is the most appropriate technique for

assessing the investigated properties.

Considering the number of specimens used and the margin of error obtained,

no assertion can be inferred in relation to possible influence of specimen extraction

direction on both elastic material properties investigated in this paper.

The use of transmission polariscope was very interesting, once some

characteristics like possible misalignment of the specimen when positioned for

testing could be detected. It was also observed that bonding strain gages did not

have a significant interference in the stress field and that the used clip-on

extensometer did not introduce relevant bending effects during the tensile testing.

This research provided a better understanding of the challenges involved in the

calculation of the elastic properties of photoelastic polymers.

More investigations are needed, using an adequate number of specimens, as

recommended by ASTM standard, in order to determine the investigated elastic

properties with a more satisfactory statistical treatment.

ACKNOWLEDGMENTS

This research work was done in the Centro de Desenvolvimento da Tecnologia

Nuclear (CDTN/CNEN) in partnership with Universidade Federal de Minas Gerais

(UFMG) and partially supported by Fundação de Amparo à Pesquisa do Estado de

Minas Gerais (FAPEMIG), and Financiadora de Estudos e Projetos (FINEP).

REFERENCES

1. MARTINS, A. V. Análise fotoelástica da união dente-implante com plataforma

switching, sistema de retenção tipo cone Morse e roscas quadradas. 2013, 116p.

Dissertação (Mestrado em Odontologia) - Faculdade de Odontologia da

Universidade Federal de Minas Gerais, UFMG-MG, Belo Horizonte.

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2. ASTM Standard D638, 2014, Standard Test Method for Tensile Properties of

Plastics, ASTM International, West Conshohocken, PA, 2006, DOI: 10.1520/D0638-

14, www.astm.org.

3. ASTM Standard E132, 2004 (2010), Standard Test Method for Poisson’s Ratio at

Room Temperature, ASTM International, West Conshohocken, PA, 2006, DOI:

10.1520/E0132-04R10 , www.astm.org.

4. MISKIOGLU, I.; GRYZAGORIDES, J.; BURGER, C. P. Material properties in

thermal-stress analysis. Experimental Mechanics, August 1981, pp. 295-301,1981.

5. BAEK, Tae-Hyun; KIM, Myung-Soo; KIM, Young-Chul. Stress Intensity Factor

Measurement by Photoelasticity. Advanced Science and Technology Letters -

Mechanical Engineering, Vol.108, p6-9, 2015.

6. PRAMOD, R. Digital Optical Measurement Techniques and Applications, 1st

Edition, Canton St. Norwood, MA, Artech House, 2015.

7. UDD, E; SPILMAN, W. B. Jr. Fiber Optic Sensors: An Introduction for Engineers

and Scientists, 2nd edition, Hoboken, New Jersey: John Wiley & Sons, Inc, 2011.

8. FREIRE, J. L. F.; VOLOSHIN, A. Photoelasticity, in Experimental Mechanics, [Ed.

FREIRE, J. L. F.], In Encyclopedia of Life Support Systems, Developed under the

Auspices of the UNESCO, Eolss Publishers, Oxford, UK, 2009.

9. DOYLE, J. F. Modern Experimental Stress Analysis: Completing the Solution of

Partially Specified Problems, March, Hoboken, Nova Jersey: John Wiley & Sons, Inc.

2004.

10. MAHINFALAH, M. Photoelastic determination of stress intensity factors for sharp

re-entrant corners in plates under extension, 1988, 124p. Dissertation (Doctor of

Philosophy in Engineering Science and Mechanics) - Iowa State University, Iowa.

11. BABAK, R. Laser dynamic photoelasticity and digital image analysis for

nondestructive evaluation of surface and near surface flaws through ultrasonic

spectroscopy. Iowa State University,1987, 228p. Dissertation (Doctor of Philosophy

in Engineering Science and Mechanics Major); Iowa State University Ames, Iowa.

12. BEN AICHA, L.; GILIBERT, Y. R. A. (1986, march). Measure and design of

stresses in adhesive bonded trusses: extensometrical and laser-elastimetrical

methods. In: Proceedings of the VIIIth International Conference on Experimental

Stress Analysis, Amsterdam, The Netherlands: Weringa.

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