Identification of the source of the thermoelastic resonse from orthotroic laminated comosites S. Sambasivam, S. Quinn and J.M. Dulieu-Barton School of Engineering Sciences, University of Southamton, Highfield, Southamton SO17 1BJ, United Kingdom sshamala@soton.ac.uk SUMMARY In revious work, a series of theoretical considerations have been made aimed at identifying the source and assessing rominent factors influencing the thermoelastic resonse from laminated comosites. In this aer four different methods of interreting the data are investigated and the theoretical thermoelastic resonse is comared to exerimental data to identify the source of the thermoelastic resonse. Keywords: hermoelastic stress analysis (SA), Glass fibre reinforced olymer (GFRP) Introduction hermoelastic stress analysis (SA) is based on infra-red thermograhy, where the small temerature changes resulting from changes in elastic stresses are obtained by measuring the change in infra-red hoton emission. he technique has advantages over other exerimental techniques through its ability to rovide full-field, non-contact stress data from structures under dynamic load in ractically real time. A full understanding of the effect of the fundamental uncertainties, such as the source of the thermoelastic signal and the influence of the alied loading conditions, on the resonse is critical if quantitative stress data is to be extracted from the thermal measurements. Previous research [1] has shown that the interretation of the thermoelastic resonse from orthotroic comosite materials requires secial consideration. he influence of the surface resin rich layer that occurs in comosite comonents as a consequence of the manufacturing rocess has been investigated and was used as a basis for calibration. he work [1] showed that for E-glass/eoxy re-reg laminates consideration of the surface resin layer as the source of the resonse does not rovide satisfactory agreement. In the current aer it is shown that the strain witness assumtion [2, 3] is only valid for comosite laminates with sufficient surface resin thickness to revent heat conduction. o interret the thermoelastic resonse from an orthotroic laminated comosite material the usual aroach [4, 5, 6], is to assume that the resonse is a function of the surface ly stresses and their associated coefficients of thermal exansion (CE). In this work a further two theoretical aroaches are exlored; (i) the thermoelastic resonse of the laminate is governed by its global mechanical and thermal roerties, and (ii) a combination of the ly by ly mechanical roerties combined with global thermal roerties. his gives four ossible means of interretation, all of which are discussed in the aer.
Influence of the surface resin rich layer on thermoelastic resonse In revious studies [2, 3] it has been assumed that the resonse is from the surface resin layer, it is said to act as a strain witness. herefore the resin must be such that it revents the temerature change that occurs in the surface ly from conducting through the resin to the material surface. o act as a strain witness the surface layer must be thin comared to the thickness of the secimen so that the laminate strains are fully transmitted from the surface ly to the surface of the resin. If the resin is acting as a strain witness then the strain in a given direction in the resin layer is equal to the strain in the same direction in the laminate so the sum of the rincial strains in a comosite laminate can be related to the stresses in the resin layer as follows: 1 r xc yc ( xr yr ) (1) Er where E is Young s modulus and is Poisson s ratio, x and y are the change in the rincial stresses and the subscrit c and r reresent comosite and resin resectively. he temerature change, in the surface resin layer is related to the measured strain by substituting the right hand term in Equation (1) to give: r E r ( x y ) ( xc yc ) C rcpr 1 r (2) where is the surface temerature, is the density and C is the secific heat at constant ressure, is the coefficient of thermal exansion (CE) in the rincial stress directions. For an orthotroic material the stresses are couled with CEs in the direction of interest as follows[4]: ( xx yy ) C It would therefore be very convenient to be able to aly the strain witness assumtion to comosite comonents so that the couling between the stresses and the CE can be neglected in the analysis. Equation (2) shows that for laminates made with the same resin with different lay-us, the thermoelastic temerature change from the surface resin layer should be the same if the sum of the direct strains is constant. Previous work by the authors [1] has shown that this is not the case. It should be noted that the stresses in the orthotroic layers of a comosite laminate vary with fibre orientation and moreover it is certain that the stress carried by the resin surface layer will be small comared to that of laminate. his means the stress induced temerature change in the resin surface layer will be different to that in the surface ly of the laminate and deending on the ly orientation may cause large temerature gradients between the surface layer and the orthotroic substrate. Heat transfer between the resin and the laminate and vice versa is therefore a distinct ossibility. he measured surface temerature changes could therefore be a result of the (3)
strain witness effect, a result of heat transfer through the resin giving a resonse from the surface ly, or a combination of both. he resonse is clearly deendent on the thickness of the surface resin and the orientation of the subsurface ly. In SA, a cyclic load is alied to achieve seudo adiabatic conditions. he question is at what frequency is heat diffusion through the resin rich surface layer revented so that it can act as a strain witness. o address this, an aluminium stri secimen of dimensions 105 x 13 x 1.2mm was reared with art of the surface coated with eoxy resin (60 m thick) and the other art coated with two asses of RS matt black aint. his secimen was devised as it is imossible to remove the eoxy layer effectively from the surface of a comosite laminate. Furthermore, it is extremely difficult to manufacture a fibre reinforced olymer comosite without a surface resin layer, articularly if a vacuum consolidation is used. herefore it was decided to add a resin layer to a simle secimen. o examine if at ractical laboratory loading frequencies adiabatic conditions could be achieved the secimen was subjected to a constant uniaxial stress range of 52.2 MPa whilst the loading frequencies was varied from 10 to 60 Hz. Under ure tension loading, the stress is uniform and therefore no heat transfer in the secimen, enabling the diffusion characteristics of the coatings to be examined in isolation. If the resonse is constant over the frequency range this is a good indication of adiabatic behaviour. he temerature changes measured from the ainted and eoxy coated arts of the secimen are shown in Figure 1. Using the material roerties for the aluminium given in able 1 it is ossible to derive a theoretical temerature change for the aluminium; this is shown in Figure 1. It is also ossible to derive the temerature change for the eoxy acting as a strain witness using the values given in able 1. It is assumed that the emissivity of the aint and the eoxy is 0.92 [7, 8]. he resonse from the ainted surface is constant over the frequency range and virtually identical to the calculated value. his is a clear indication that the resonse is adiabatic and the aint coating is sufficiently thin to allow comlete heat transfer from the surface of the aluminium to its surface. he measurements from the resin do not corresond with the calculated value for the strain witness resonse and show a monotonic decrease over the frequency range. As the frequency increases the values aroach the strain witness value. However, at lower frequencies these results indicate that there is heat transfer from the interface between the eoxy and the aluminium to the surface of the resin. As the resin layer is usually much thinner than 60 m in a olymer comosite this clearly indicates that the orthotroic surface layer has a significant role in the thermoelastic measurements. o aly the findings of the above to comosite laminate, a 2D heat transfer model was constructed to determine the thickness of the surface resin required to revent heat conduction in order for the strain witness assumtion to be alicable. he model was constructed using ANSYS with PLANE55 thermal elements. he model showed that a loading frequency above 33 Hz is required for the strain witness treatment to be alicable. his finding is somewhat suorted by the data in Figure 1 as at around 30Hz the resonse seems to become uniform. However the difference between the exerimental and calculated value could be attributed to differences in mataterial roerties and the emissivity. he same model was imlemented for a unidirectional
laminate (to consider the resin layer and comosite material interface). he initial uniform temerature in the surface layer was calculated using Equation (2) and at the interface, using Equation (3), see able 4. he FE results showing the relationshi between the resin thickness and the loading frequency for thermal equilibrium to be achieved in the surface resin layer for UD(0) and UD(90) are shown in Figure 3. his clearly shows that for a loading frequency of 10 Hz, for the given temerature gradient the resin layer thickness should be minimum of 90 m for UD(0) and 100 m for UD(90) so that the surface measurements are not affected by the heat transfer. he thickness of the resin layer for the secimens used in this work is 30 m according to Figure 3, a loading frequency of aroximately 67 Hz for UD(0) and 112 Hz for UD(90) are required to achieve adiabatic conditions for the strain witness treatment to be valid. his shows that for the material considered in this work (considering the temerature gradient between the interface and surface layer), the result of heat transfer through the resin gives a resonse from the surface ly. herefore, in the next section in the aer exlores fully the interretation of the fibre orientation on the thermoelastic resonse. able 1: Mechanical and hysical roerties of unidirectional E-glass/eoxy reimregnated comosite, eoxy and aluminium Secimen Young s Modulus (GPa) Poisson s ratio E 1 E 2 12 21 Density, ρ (kg/m 3 ) CE, (x 10-6 / o C) α 1 α 2 Secific heat caacity, C (J/(kg o C)) hermal Conductivity k (W/m o C) UD 34.2 10.0 0.325 0.100 1230 9 31 843 - Eoxy 4.2 n/a 0.413 n/a 1207 52 n/a 1230 0.175 Aluminium 68 n/a 0.330 n/a 2700 21 n/a 900 -. Figure 1: Change in the surface temerature of aluminium coated with an eoxy layer and aint coating
Figure 2: he relation between the thickness of the resin rich and the required loading frequency to achieve adiabatic conditions (from 2D FE analysis) hermoelastic resonse of a comosite lamina In most studies of comosite materials using SA [4, 6] it has been the case that the materials examined and the loading are such that the material axes (1, 2) (i.e. axis system referenced to the fibre direction) coincide with the rincial stress axes (x, y) in the lamina, see Figure 3(a). However, when a lamina is subjected to general stress at an angle in relation to the rincial material direction, the rincial stress axes will not coincide with the material axes (see Figure 3(b)). he temerature change measured in SA is a scalar hysical quantity that is indeendent of the system axis. herefore an exression of the in one axis system (e.g. the 1, 2 axes) in terms of another axis system (i.e. the x, y axes) should be equal. he only tensor quantities in Equation (2) are the coefficient of thermal exansion and the stresses. herefore, the roduct of these terms in any two arbitrary axes (e.g. i, j) should be equal: (4) i, j i, j x,y x,y 1,2 1,2 o rove that the equation is valid, it is necessary to erform the transformation of the CE and the stress: i, j i, j x,y x,y (5) where is the transformation matrix he coefficients of thermal exansions are second-order tensors and therefore they transform like the strain comonents, (i.e. s = 2 xy ). In which, xy is the shear CE on
the x axis along the y direction and yx is the y axis along the x direction (i.e. yx = xy ) and s is the total measure of the CE in the x-y lane (also known as the engineering shear coefficient of thermal exansion). y x 2, y j 2 1, x i 1 (a) (b) Figure 3: Schematic diagram of the coordinate system and nomenclature (a) on axis laminate (b) off-axis laminate herefore, the transformation relation is given as: cos sin cossin x y s i, j x sin y cos s cos sin 2x sin cos 2y sin cos s(cos sin ) (6) he transformation of stress is given as: cos sin 2 sin cos x y s i, j x sin y cos 2 s sin cos x cos sin y sin cos s(sin cos ) (7) By multilying Equations (6) and (7) it can be shown that: (8) i, j i, j x x y y s s herefore the general term can be concluded to be an invariant. However, in i, j i, j the lamina rincial material directions 6 = 0 and in the rincial stress directions s is zero so for these two cases equation (8) reduces to:
(9) i, j i, j 1 2 x x y y o comare the measured value with a measured strain value for validation uroses, it is necessary to reformulate Equation (8) in terms of alied strain in the laminate: Q C 1,2 1,2 x,y (10) where [Q] 1,2 is the material stiffness matrix. Equation (10) can be exanded as: [ Q Q ( cos sin cos sin ) Q Q C x y s 1 11 2 12 x y s 1 1 22 sin cos cos sin ] (11) When a uniaxial tensile stress is alied to a balanced orthotroic laminate the shear strain in the laminate ( sl ) is zero, x = xl and y = yl so Equation (11) can be simlified as: [ Q Q ( cos sin ) Q Q C x sin cos ] y 1 11 2 12 x y 1 1 22 (12) For a balanced orthotroic laminate constructed from ±45 o angle ly Equation (12) can be further simlified to: x y 1 Q11 Q12 2 Q12 Q22 C 2 (13) he introduction of stress invariant concet, in order formulate the temerature change from the orthotroic substrate clears any confusion relating to the use of reference axes for the system [9]. It is clear that a consistant use of any axes system is accetable. hermoelastic resonse from a multidirectional comosite laminate When assessing the behaviour of a general multidirectional comosite laminate (consisting of lamina with arbitrary orientations) classical laminate late theory (CLP) is used so that the material can be treated as a homogeneous orthotroic late. Here the mechanical and thermoelastic roerties are considered ly by ly and then brought together relative to (say) the laminate axis to rovide a global stiffness and CE. For quasi-isotroic laminates (i.e. (0, 90) s and (0, ±45, 90) s ) it is evident that the global CE
is equal in the longitudinal and transverse directions (i.e. = xl = yl ) because of the stacking sequence. herefore, it may be ertinent to exress the thermoelastic temerature change in the following manner: A A A A C xl 11 12 xl yl 12 yl where A ij is the global stiffness of the laminate. (14) Equation (14) simly assumes that the material resonse is that of a homogeneous orthotroic material. A further and as yet unexlored idea is that the CE is couled in the stack (i.e. the thermal strain is constant in the through thickness direction) with the surrounding layers and this also may have an effect on the resonse. o exlore this, the orthotroic nature of the surface ly is retained in the treatment but the CE is treated as a global roerty as the lies are bonded together and are not free to deform indeendently, which gives the following equation: Q Q Q Q C xl 11 12 xl yl 12 yl he different scale of idealisation in each treatment, aims to rovide an insight into the thermoelastic behaviour of comosite materials. his is achieved by comuting the thermoelastic temerature change based on each treatment and comaring it with the measured temerature change from an orthotroic laminate. hermoelastic work he material used for manufacturing the test secimens was a unidirectional glass/eoxy re-imregnated material. he mechanical roerties and hysical roerties such as density, secific heat caacity and CE were determined according to resective ASM standards from unidirectional comosite test couons as rovided in able 1. he global mechanical and hysical roerties are given in able 2. o validate the theoretical treatments, Unidirectional (UD), Angle ly (AP), off-axis unidirectional (OA), cross-ly (CP) and quasi-isotroic (QI) anels were manufactured with different stacking sequences and consolidated in an autoclave. Four different sets of CP laminates were manufactured; one with a 0 o surface ly (CP0) and another with a 90 o surface ly (CP90) and also with 0 and 90 ly grous (i.e. [0 3,90 3 ] s and [90 3,0 3 ] s ) to evaluate the effect of surface ly on the thermoelastic signal. wo different sets of QI laminate with similar surface layer (i.e. 0 o ) and similar mechanical roerties (i.e.[0,±45,90] s and [0,90,±45] s ) were manufactured to evaluate influence of sub-surface lies on deth of the thermoelastic resonse. he test secimens were mounted in an Instron servohydraulic test machine and a cyclic tensile load was alied at a loading frequency of 10 Hz. A strain gauge rosette was attached to the secimens to measure the strain in the laminate rincial directions. he thermoelastic temerature change (averaged over a uniform area) were collected from each secimen. (15)
able 2: Global mechanical and hysical roerties of the laminates Secimen Young s Modulus (GPa), E L Poisson s ratio, L CE, α (x 10-6 / o C) CP 20.0 0.15 10.59 AP 9.5 0.55 16.20 QI 19.7 0.29 9.25 able 3: Details of alied load, strains and thermoelastic data from the test Secimen Load (kn) Alied strain Strain sum, Mean Amlitude ε xl ε (ε xl +ε xl ) yl Surface temerature, (K) CP(0) 0.7 0.55 0.001949-0.000296 0.001653 291.55 CP(0)3 1.7 1.55 0.001750-0.000209 0.001541 294.90 CP(90) 0.7 0.55 0.001993-0.000312 0.001681 290.57 CP(90)3 1.7 1.55 0.001750-0.000209 0.001541 295.26 OA 0.7 0.60 0.002119-0.000803 0.001316 293.45 AP 0.5 0.41 0.003371-0.001640 0.001731 294.91 AP3 1.7 1.60 0.004425-0.002725 0.001700 295.2 QI (45) 0.9 0.88 0.002281-0.000694 0.001587 292.03 QI(90) 0.9 0.85 0.003210-0.001021 0.002189 296.09 Eoxy 1.4 1.30 0.002690-0.00109 0.001600 291.35 RESULS AND DISCUSSION Figure 4 show the thermoelastic data collected from each seciment. It is aarent from the thermoelastic images that there are significant differences in the obtained from the different secimens, with the surface ly orientation and lay-u evident in the images. his indicates that the resonse is most likely to be from the orthotroic layer as the fibre orientation in the surface layer is clearly visible; however this can only be established using accurate material roerty data. A further observation from the image data is that there are significant differences in the thermoelastic temerature change obtained from the CP(0) and CP(90) secimens due to the differences in the surface ly orientations, and the data becomes much more uniform when the laminate is thicker. A similar trend is also observed for AP and AP3 lies indicating the ossible influence from subsurface lies. his statement is further suorted by the observed difference between the two different QI laminates, which have similar surface lies and mechanical roerties yet there are clear differences in the thermoelastic data. he measured (with standard deviation) and calculated temerature change are summarised in able 4. In most cases the values redicted by the four methods are very close. By accounting for the scatter in the data, it is difficult to establish if one rediction is
roviding better results than another. It is clear that equation (14) generally rovides values outside of the scatter bands. For laminates with stacked ly grou surface layers there is a good agreement between the measured data and Equation (3). It is clear that for some laminates the stress induced temerature change is less in the surface ly than in the resin and for these cases the heat transfer will be from the surface resin to surface ly. able 4: hermoelastic resonse from the comosite secimens Secimen, measured Resin (Eq. 2), Surface ly (Eq. 12), Global (Eq. 14), Mixed (Eq. 15) UD(0) 0.147 (±0.0090) 0.129 0.141 0.141 0.141 UD(90) 0.104 (±0.0135) 0.124 0.104 0.104 0.104 CP(0) 0.147 (±0.0089) 0.127 0.135 0.175 0.141 CP(90) 0.129 (±0.0214) 0.130 0.106 0.171 0.104 CP(0)3 0.119 (±0.0069) 0.118 0.125 0.174 0.143 CP(90)3 0.101 (±0.0107) 0.118 0.097 0.173 0.106 AP 0.121 (±0.0152) 0.133 0.125 0.132 0.127 AP3 0.127 (±0.0111) 0.130 0.125 0.135 0.131 QI(45) 0.138 (±0.0012) 0.123 0.136 0.144 0.136 QI(90) 0.112 (±0.0090) 0.120 0.133 0.143 0.129 (a) (b) (c) (d) (e) (f) (g) (h) Figure 4: hermoelastic images obtained from secimens at loading frequencies of 10Hz a) CP(0), b) CP(90), c) CP(0)3, d) CP(90)3, e) AP, f) AP3, g) QI(45) and h) QI (90)
CONCLUSIONS his study has shown that for the material considered, E-glass/eoxy re-reg laminates, of the two standard aroaches the orthotroic surface layer interretation rovides the best agreement to measured data. he benefit of considering other aroaches is demonstrated and this work highlights the imortance of careful consideration of the source of the thermoelastic signal while working with comosite materials. References 1. Sambasivam, S., Quinn, S., and Dulieu-Barton, J.M., Proc. SEM XI International Congress on Exerimental and Alied Mechanics, 10, 2008 2. Emery,.R., Dulieu-Barton, J.M., Earl, J.S., and Cunningham P.R., Comosites Science and echnology,. 743-752, 2008 3. Pitarresi, G., Found, M.S., and Patterson, E.A., Comosites Science and echnology, Vol. 65,. 269-280, 2005 4. Stanley, P., and Chan, W.K., Journal of Strain Analysis, Vol. 23,.137-143, 1988 5. Feng, Z., Zhang, D., Rowlands, R. E., and Sandor, B. I., Exerimental Mechanics, Vol. 32,. 89-95, 1992 6. Pitarresi, G., Conti, A., and Galietti, U., Alied Mechanics and Materials, Vols. 3-4,. 167-172, 2005 7. Oliver, D. E. and Webber, J. M. B., Proc. Vth International Congress on Exerimental Mechanics, Montreal,. 539 546,1984 8. DL003U-I Altair LI User Manual, Cedi Infrared Systems, 2006 9. Potter, R.., Proc. 2 nd Int. Conf. on Stress Analysis by hermoelastic echniques., London, Int Soc. Photo Otical Instr. Eng., SPIE (Vol.731),. 110-120, 1987