ADVANCED MOISTURE MODELING OF POLYMER COMPOSITES

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1 Proceedings of the 6th Annual ISC Graduate Research Symposium ISC-GRS 22 April 3, 22, Rolla, Missouri ADVANCED MOISTURE MODELING OF POLYMER COMPOSITES ABSTRACT Long term moisture exposure has been shown to affect the mechanical performance of polymeric composite structures. This reduction in mechanical performance must be accommodated for during product design in order to ensure long term structure survival. In order to determine the longterm moisture effects on composite components, representative parts are commonly tested after having been exposed to designed moisture conditioning environment. This moisture conditions are established in order to rapidly drive moisture into test specimens simulating worst-case long term exposure scenarios. Currently accepted methodologies for analyzing the time required to condition specimens are limited, allowing only simple geometry and an assumption that diffusivity rates are independent of the flow path or direction. Therefore, a more advanced finite element method is desired. In the current work, a three dimensional model is developed and implemented in commercial finite element code. The parametric study has been conducted for complex shapes, moisture diffusion pathways, and varying moisture and temperature conditions. Finite element results are validated with a one-dimensional analytical model and experimental results.. INTRODUCTION Composite materials due to the combination of multiphase materials, usually carbon or glass pre-impregnated with a resin system, have increasingly become the preferred building material over other materials such as aluminum by industries desiring high strength/stiffness to weight ratios and the high temperature tolerance []. The makeup of composites allows moisture to be absorbed from the environment, which can affect the structural integrity of composite structures [2-5]. Diffusion of this absorbed moisture is extremely slow so thin parts may reach moisture equilibrium while thick parts will never become fully soaked within their service life [6]. Industry determine the long-term moisture effects on the mechanical performance of components made from composite materials by placing representative parts in an accelerated moisture-conditioning chamber to simulate the worst-case real world exposure conditions or Design Moisture Content (DMC). Knowledge of the proper duration of time that a part remains in the chamber is crucial since a sample that is not soaked long enough to meet real world conditions will show overly optimistic test results, but a part that is over-soaked not only lengthens testing time but could produce overly conservative design values which can increase component weight. A predefined soak period based on one-dimensional calculations is currently used to derive the post-conditioning weight of the sample. When the sample reaches the targeted weight gain, the specimen is removed from conditioning and proceeds to test. Reaching the desired moisture content is achieved through the use of the weight equation when moisture equilibrium content is dependent upon the RH but not affected by temperature. Traditionally, the W8GAIN code which was developed by Springer [7] is used in industry for analysis in testing composite parts, but complex shaped composites require more in-depth analysis. The aim of the current research is the determination of the desired time soak period through exact analyses of thick composite using the finite element analysis software ABAQUS to accurately evaluate moisture diffusion in polymer composites. 2. MATHEMATICAL BACKGROUND A comprehensive 3D model was developed and implemented in ABAQUS to simulate moisture diffusion from any surface and varying moisture/temperature conditions in complex shapes. The varying moisture/temperature conditions for this research will be defined as such: accelerated conditions will typically refer to 6 F (7. C), 95 % relative humidity (RH) while service conditions will refer to 8 F (26.7 C), 82 % RH. Parts placed in accelerated conditions were commonly soaked for 2 days while the service conditions were calculated to be soaked for years to reach the DMC. Parts in both of these conditions were analyzed using Fick s Equation. The analyses in this research were performed with the equation derived in Fick s second law, simply known as Fick s equation [8]. Fick s equation predicts how the concentrate will change with time based of the rate of diffusion. Fick s equation is written as: c c = D t z () z where c is the moisture concentration, D z is the moisture coefficient, z is the distance through the thickness, and t is the

2 time. The required soaking duration is determined by calculating the weight of the moisture that is absorbed into a sample. The use of the weight equation, shown below, allows for the calculation of the final weight of the sample, signifying it has reached the desired moisture content. M = W W W X (2) where W is the weight of moist material and Wd is the weight of dry material. Diffusivity coefficients for a glass epoxy have been provided for D x, D y, and D z, which are the diffusion coefficients parallel to the fiber direction, perpendicular to the fiber, and through the thickness of the laminate respectively. For the Fickian model to be implemented, the diffusion must be dependent only on temperature, thus the three diffusivities have values provided at two different temperatures shown in both standard and metric units in Table. As this research included analyzing the moisture diffusion at temperatures not shown in the tables, the values of the diffusivity coefficients at those temperatures were either interpolated or extrapolated using Equation 3. where c D T = d exp ( ) (3) T d = D e (. ) (4) c = ln( )(T )(T ) (5) (T ) (T ) where D TL is diffusivity at lower temperature, D TH is diffusivity at higher temperature, D T is diffusivity at desired temperature, T L is lower temperature [ F], T H is higher temperature [ F], T d is temperature at which diffusivity is needed. Moisture equilibrium of the glass epoxy at the desired RH is provided in Table 2. Given moisture equilibriums at two relative humidity, the moisture equilibrium can be interpolated or extrapolated using Equation 4. Meq = a RC RH b (6) where a = M RC RH (7) b = log ( ) ( M M ) (8) where M eq is moisture equilibrium, M eq_l is moisture equilibrium at the lower temperature, M eq_h is moisture equilibrium at the higher temperature, RC is the resin content, RH is the desired relative humidity. The capabilities of the W8GAIN code are limited to the D Fick s equation. The W8GAIN code is limited to a flat plate that is either considered infinite by being sufficiently large in length to width versus thickness dimensions or the edges are insulated. However, to overcome this limitation, a modified diffusivity coefficient can be obtained using the equations for edge effect properties, Equation 5 for a homogeneous material and Equation 6 for an orthotropic material. This research includes a comparison using a modified diffusivity coefficient and a true 3D analysis. D m = D z ( + h l + h w )2 (9) D m = D z ( + h l D D + h 2 w D ) D () where D m is the modified diffusivity coefficient through the thickness; D X, D Y, D Z are the diffusivity coefficients through the thickness and in the directions of exposed edges; h is the thickness of the part; and l and w are the part dimensions for length and width. Five varied sets of analyses were run in this research, the first three determined accuracy of the ABAQUS models. The three accuracy sets included a series of convergence analyses; a 2D model in ABAQUS using diffusion moving in only a single direction was compared to the output of the W8GAIN. And the other two further analysis use experimental data to compare ABAQUS results to laboratory tests with thin unidirectional laminate and thick unidirectional laminate, respectively. 3. FINITE ELEMENT MODELING The finite element formulation using Galerkin s Weighted Residual Method is as follows [9]: [K]{c} + [M]{c } = {F} () [M] = [N] T [N] dv (2) [K] = [B] T [D] [B]dV (3) {F} = q[n] T dγ (4) where [K] is moisture diffusivity matrix, [M] is moisture velocity matrix, [N] is shape functions, {F} is moisture flow vector, {c} is nodal moisture content and {c } is rate of change of nodal moisture content. The diffusivity matrix [D] is given by: D [D] = [ D 22 ] D 33 [B] is the matrix containing derivatives of shape functions: [N] x [N] [B] = y [N] [ z ] 4. ANALYSIS AND RESULTS 4. SAMPLE PARAMETERS The moisture models used for comparison between W8GAIN and ABAQUS, for comparison of edge effects, and for designing an accelerated conditioning cycle were given the 2

3 Moisture Content (ppm) Moisture Content (ppm) dimensional parameters of 3.5 in. x.5 in. x.5 in. (88.9 mm x 6.35 mm x 6.35 mm). These measurements are representative of a laboratory test sample. The diffusivity coefficients for the three primary axes are given for two temperatures in SI and Standard units and are shown in Table. Table Diffusivity coefficients for two temperatures in the primary axes Elements 5 Elements Elements 33 Elements Temperature 8 F (26.7 C) 6 F (7. C) Dx mm 2 /hr (in. 2 /sec) 7.9 x -5 (3.4 x - ).9 x -3 (8.2 x - ) Dy mm 2 /hr (in. 2 /sec) 7.43 x -5 (3.2 x - ).77 x -3 (7.6 x - ) Dz mm 2 /hr (in. 2 /sec) 5.34 x -5 (2.3 x - ).5 x -3 (4.95 x - ) The second set of parameters required for the analyses moisture equilibrium at the RH that the composite experienced are given in Table 2 for two different relative humidity. Table 2 Moisture equilibrium constants for two relative humidities Relative Humidity Moisture equilibrium ppm (%).8,8 (.8).95 7, (.7) 4.2 CONVERGENCE STUDY A mesh convergence using a 2D model.5 in. (38. mm) in X-direction and 3 in. (76.2 mm) in Y-direction was run in ABAQUS. The diffusion was only considered in the X- direction therefore symmetry could be used resulting in a model half the width of the lab sample, and moisture boundary conditions were only applied to the left side of the model. The different runs used 3, 5,, 7, and 33 elements in the X- direction and only element in the Y-direction. Deviations were evident in the case of two elements, which had a higher concentration, and the case of five elements, which had a lower concentration nearer to the left edge. The remaining cases showed the results converging upon each other. Although the case of 33 elements converged producing an element width of.545 mm, the number of elements was increased to 6 to give a more standardized width of.635 mm, which was used throughout the remaining analyses Depth (mm) Figure Element convergence 4.3 COMPARISON OF ABAQUS WITH W8GAIN Output from the ABAQUS model for 2 days using the accelerated conditions and the parameters relating to that using the D x diffusivity with a half model thickness of.5 in. (38. mm) were compared to the W8GAIN output with the same conditions. The diffusivity coefficients and moisture equilibrium were obtained from Tables and Depth (mm) Figure 2 Comparison with Dx diffusivity (W8GAIN vs. ABAQUS) W8GAIN ABAQUS ABAQUS output for years with service conditions and the parameters relating to that using the D z diffusivity and a half model thickness of.5 in (2.7 mm) were compared to the W8GAIN output with the same conditions. When the moisture equilibrium was interpolated for the service conditions that have an 82 % RH the result was.24 % or 2,4 ppm. The diffusivity coefficients and moisture equilibrium were obtained from Tables and 2. The outputs from the W8GAIN code versus the ABAQUS model for accelerated and service conditions are shown in Figures 2 and 3, respectively. Both of these graphs show how the output from the ABAQUS model matched to the output of the W8GAIN verifying that the model was producing accurate results. 3

4 Moisture Content (%) Moisture content (%) Moisture Content (%) Moisture content (%) Two other convergence studies are also conducted under constant environmental and varying environmental conditions, respectively. All the parameters need are listed in Table 3 []. Table 3 coefficients for test coupons Properties Material Name Diffusivity Moisture Equilibrium Half thickness Length Width Diffusivity after Edge Correction Factor Initial Moisture Content Specifications Glass fiber/epoxy Tape.4726E-9 in 2 F (.976E-3 mm 2 7. C) % RH.25 in (6.35mm) 3.5 in (88.9 mm).5 in (2.7 mm) 2.7E-9 in 2 6 F (5.4E-4 mm 2 7. C). % ( ppm) Edge Correction Factor Figure 3 shows good convergence when the element size decreases. In this case, the glass/epoxy laminate with.5 inch thickness is exposed to 6 and 95% relative humidity for 68 days, which refers to constant environmental condition. Figure 4 shows the results of ABAQUS 2D matches well with W8GAIN under this constant environment. In the varying environmental condition, in which the specimen with same dimension is exposed to 6 and 95% relative humidity for 68 days, and then 82% relative humidity for 68 days, the good convergence is also shown as in Figure 5. Also, the results of ABAQUS 2D matches well with W8GAIN program results elements 4 elements elements 3 elements elements elements 4 elements elements 3 elements elements Depth position (in) Figure 5 Convergence study under varying environment.4.2 W8GAIN PROGRAM ABAQUS Depth position (in.) Figure 3 Convergence study under constant environment W8GAIN PROGRAM ABAQUS Depth position (in.) Figure 4 ABAQUS 2D comparison with W8GAIN under constant environment Depth position (in) Figure 6 ABAQUS 2D comparison with W8GAIN under varying environment 4.4 COMPARISON WITH EXPERIMENTAL DATA Laboratory tests were conducted in which glass/epoxy thin composite coupons (thin laminate), measuring.5 in. x.5 in. x 3.5 in. (2.7 mm x 2.7 mm x 88.9 mm), were exposed to 6 F (7. C), at 95 % relative humidity for 75 days. The test results presented in are compared with a 2D ABAQUS model. 4

5 Total Moisture Absorption (%) TOTAL MOISTURE ABSORPTION (%) Properties used are given in Table 3. Figure 7 shows the close agreement of simulation results and the experimental findings..3 ABAQUS 3D RESULT EXPERIMENTAL DATA.9.8 ABAQUS Results Experimental Data EXPOSURE TIME (days) Figure 8 Thick Laminate experimental data vs. ABAQUS 3D Exposure Time (days) Figure 7 Thin Laminate experimental data vs. ABAQUS 2D Another test is conducted in which glass/epoxy thick composite coupons, measuring.75 in. x.75 in. x 2.25 in. (44.45 mm x mm x 3.5 mm), were exposed to 6 F (7. C), at 95 % relative humidity for 75 days. The test results presented are compared with 3D ABAQUS model. Properties used are given in Table 3. In this case, equations (5)-(9) are used to calculate the diffusivities since those parameters are not available in the technical documents. Firstly, use the modified diffusivity along z-direction divides the edge correction factor to get the transverse diffusivity D 22, then use the known fiber volume fraction and equations (5-6) to get D. And then use the transformation equations (7-8) and transformation angles α, β, γ (α = ; β = 9, γ = 9 in unidirectional laminates) to get the diffusivities along three directions. The final diffusivities we get is as follows: D Y = D Z = D 22 =.4954 E-9 in 2 /s, D X = D = E-9 in 2 /s. D = ( 2v f )D r (5) D 22 = ( 2 v f π ) D r (6) D x = D cos 2 α + D 22 sin 2 α (7) D y = D cos 2 β + D 22 sin 2 β (8) D z = D cos 2 γ + D 22 sin 2 γ (9) where D is longitudinal diffusivity, D 22 is transverse diffusivity, D r diffusivity in resin matrix, D X, D Y, D Z are diffusivities along X, Y, Z axis, respectively. α, β, γ are angles of the fiber direction with respect to X, Y, Z axis. After applying these parameters into the modeling, the 3D result is presented in Figure 8, in which the 3D result matches well with the experimental findings. The moisture concentration distribution along orthogonal sections is show in Figure 9. Figure 9 Moisture content distribution after 75 days exposure 5. CONCLUSIONS A comprehensive 3D model was developed and implemented in ABAQUS to simulate the moisture absorption in composite materials during service conditions. A convergence study was performed to ensure the accuracy of the model. Results from D and 2D models were compared to the analytical and experimental findings. 3D analysis exhibited lower average moisture content in comparison with the prediction from the existing models. Furthermore, the traditional method did not give a true profile of the moisture content at different locations in the part. Conventional D moisture model has been reliable for moisture diffusion only in one direction. The present model can implement the Fick's equation in all directions resulting in accurate distribution of moisture in the composite part. Also, for thin composite laminate, the 2D results already match very well with experimental results since the moisture diffusion through thin laminate s edges is not significant. However, for thick composite laminate, the moisture diffusion through thickness area is significant thus we have to take it into account. In such case, the edge correction factor is not suitable 5

6 anymore; the diffusivities along all the directions should be defined. 6. ACKNOWLEDGMENTS Partial support from Intelligent Systems Center is gratefully acknowledged. The authors would like to thank Aaron Buchok from Bell Helicopter Textron Inc. for his helpful suggestions. 7. REFERENCES [] Agarwal, B. D., Broutman, L. J. and Chandrashekhara, K., 26, Analysis and Performance of Fiber Composites, Third Edition, John Wiley & Sons, Inc. Hoboken, New Jersey, Chap.. [2] Li, M., 2, Temperature and Moisture Effects on Composite Materials for Wind Turbine Blades, Master thesis, Montana State University, Bozeman, Montana. [3] Browning, C. E., 977, The Mechanism of Elevated Temperature Property Losses in High Performance Structural Epoxy Resin Matrix Material after Exposure to High Humidity Environments, Ph. D. thesis, University of Dayton, Dayton, Ohio. [4] Loos, A. C. and Springer, G. S., 98, Moisture Absorption of Graphite-Epoxy Composition Immersed in Liquids and in Humid Air, Environmental Effects on Composite Materials, Vol. 9, pp [5] Shen, C. H. and Springer, G. S., 98, Effects of Moisture and Temperature on the Tensile Strength of Composite Materials, J. Composite Materials, Vol. 2, pp [6] Pierron F., Poireet, Y. and Vautrin, A., 22, A Novel Procedure for Identification of 3D Moisture Diffusion Parameters on Thick Composites: Theory, Validation and Experimental Results, J. Composite Materials, Vol. 36, pp [7] Shen, C. H. and Springer, G. S., 976, Moisture Absorption and Desorption of Composite Materials, J. Composite Materials, Vol., pp [8] Crank, J., 975, The Mathematics of Diffusion, Second Edition, Oxford University Press, Ely House, London, Chap.. [9] Wondwose Ali, B. S. C. E., 2, Finite Element Temperature Development and Moisture Diffusion Prediction Models for Concrete at Early Ages using Matlab, Master thesis, Texas Tech University, Texas. [] Bell Helicopter, 997, Prediction of Moisture Absorption in Composite Materials, Report NO