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The effects of hygric pressure, salt concentration and temperature on the hygric expansion of composite material
Composites Science and Technology 62 (2002) 799–803 www.elsevier.com/locate/compscitech
The effects of hygric pressure, salt concentration and temperature on the hygric expansion of composite material Cho-Liang Tsaia,*, Yi-Shiun Tsaib, Chih-Hung Chiangc a
Department of Construction Engineering, National Yunlin University of Science and Technology, 123, Sec. III University Road, Touliu, Yunlin 640, Taiwan b General Education Center, Hsiuping Institute of Technology, Taichung 412, Taiwan c Department of Construction Engineering, Chaoyang University of Technology, Taichung 413, Taiwan Received 8 May 2001; received in revised form 14 January 2002; accepted 20 February 2002
Abstract Moisture absorption causes the expansion of composite material. Such expansion is physically reversible and dominated by the characteristic property of the composite material. However, many environmental factors can alter this hygric behavior. This work addresses the effects of external hygric pressure, salt concentration and environmental temperature, upon the hygric expansion of composite material submerged in water. Embedded strain gages were used to monitor hygric expansion. The final hygric strains of glass/epoxy submerged in water under different environmental conditions were measured and the corresponding diffusivities were calculated. The results confirm that hygric pressure, salt concentration, and temperature importantly affect the hygric behavior of composite materials. The process and results of this work are critical to designing composite structures—especially those serving in marine environment. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Hygric expansion
1. Introduction Expansion of polymeric matrix composite induced by moisture absorption is one of the hygric behaviors which can be characterized in terms of the longitudinal and transverse moisture expansion coefficients (CMEs), b1 and b2 [1,2]. This hygric expansion can be measured with a micrometer, caliper, or strain gage, or by the hunch-up or curvature technique [3–9]. Micrometers and calipers are conventional tools, reliable and accurate enough to measure the transverse hygric expansion of a composite lamina. However, the hygric expansion of a composite lamina in the longitudinal direction is usually much less than that in the transverse direction. The hygric expansion of the fiber is usually very small and tends to constrain the expansion of the matrix. Some fibers such as carbon fiber exhibit a small negative hygric expansion [10], which compensates for part of the hygric expansion of the epoxy matrix, making the total longitudinal hygric expansion
* Corresponding author. Tel.: +886-5-534-2601x4719. E-mail address: [email protected] (C.-L. Tsai).
of the carbon/epoxy lamina too small to be measured by conventional tools [1]. Tsai and Wooh [8,9] developed the curvature technique to characterize the hygric behavior of composite materials according to the relationship between the curvature change of a strip shape cross-ply laminate [0n/90n] and the hygric expansions in both of its layers. The curvature technique can be employed to quantify the small b1 and the b2 of a unidirectional composite lamina. Tsai and Wooh [7] also developed the hunch-up technique to characterize the hygric behavior of composite materials such as woven fiber composites, with small coefficients of moisture expansion in both principle directions. In the process of this technique, a strip shape unidirectional composite laminate or woven fiber composite laminate with all the layers stacked in the same direction is squeezed into a slightly shorter space in a rigid frame, hunching up like an arch. The hunch-up height is sensitive to the expansion of the specimen due to temperature or moisture absorption. The coefficient of moisture expansion of the laminate can be calculated accurately from the change in hunch-up height. The strain gage is another convenient tool for characterizing the hygric behavior of composite lamina [4].
0266-3538/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(02)00048-9
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C.-L. Tsai et al. / Composites Science and Technology 62 (2002) 799–803
In this study, creep resistant encapsulated strain gages [11] were embedded in woven glass/epoxy laminates to monitor their hygric expansions while they were submerged in different depths of water at different temperatures and salt concentrations. Fick’s diffusion law was adapted to describe the moisture diffusion [7–9]. The diffusivity can be calculated from the hygric strain since the strain is proportional to the moisture concentration [1]. Experimental results indicate that the final hygric strain and diffusivity are sensitive to the environmental conditions considered.
2. Theoretical background Once a dry composite laminate is submerged into water it begins to absorb water and expand. If the diffusion in the thickness direction occurs only through the surface of the specimen and follows Fick’s diffusion law, the moisture concentration in the laminate can be written as, " # ðn1Þ 1 4 X ð1Þ 2 ðn=hÞ2 Dt nz cðt; zÞ ¼ C 1 e cos n¼1;3;5... h n ð1Þ where c(t, z) is the moisture concentration as a function of immersion time t and thickness coordinate z, C is the saturated moisture concentration, h is the thickness of the laminate, and D is the diffusivity in thickness direction of the laminate. The origin of the thickness coordinate z is at the center of the laminate. Assume that the hygric expansion is proportional to the moisture concentration with a coefficient b. Assuming no constraints, the hygric strain in the laminate will be, "ðt; zÞ ¼ "
1 4 X ð1Þ bC 1 n¼1;3;5... n
ðn1Þ 2
eðn=hÞ
2
nz Dðt Þ cos h
# ð2Þ
Under plane remains plane assumption, the hygric strain of the whole laminate e(t) can be involved in zero loading condition. ð h=2 0¼
½eðtÞ "ðt; zÞ Qdz
ð3Þ
where S is the saturated hygric strain of the laminate and S=bC. The result shows that the hygric strain of a composite laminate submerged in water increases monotonically, asymptotically approaching S. The diffusivity D controls the diffusion rate. Both S and D are material constant. However, their values depend on several environmental factors such as hygric pressure, temperature and salt concentration.
3. Experimental procedure Embedded strain gages were used to measure the hygric strains of the composite laminates to determine their hygric diffusivity in the thickness direction. The strain gages were embedded in the first principle direction to monitor the hygric expansion in this direction. The hygric behavior in the second principle direction of the chosen material is similar to that in the first principle direction and can be similarly characterized. The specimens used in this study were [016] woven E-glass/epoxy (Style 109 Woven E-Glass Fabric/FR-4 Epoxy Novolac System, IBM). Table 1 lists the properties of the material. Each specimen was 5 5 cm and 0.078 cm thick. All the edges were sealed with 5 mm thick silicon glue to prevent moisture diffusion through the edges. WK strain gages, which are very stable in long-term measurement, were used. The gages’ grids are made of nickel–chromium and fully encapsulated in glass-fiber-reinforced epoxy-phenolic resin. The measuring error of the WK gage is less than 40 106 for 2.5 years’ continuous measurement under 75 C [11]. The gages were embedded at the center of each laminate. Each specimen was completely dried by post-curing under 80 C in a thermal chamber until its weight became stable, and then being left inside the chamber to cool off prior to the experiment. This step usually took 4 days. Three groups of experiments were conducted. The first group was to investigate the effect of hygric pressure on the hygric expansion of composite laminate. An 8 m high PVC pipe was constructed with its lower end sealed. It was filled with pure water. A thermostat and circulation system maintained the temperature of the water inside Table 1 The properties of woven E-glass/epoxy lamina
h=2
where Q is the stiffness of the material. Q=Q11=E1/(1– 1221) for 0 laminates and Q=Q22=E2/(11221) for 90 laminates [1]. The hygric strain of the laminate can be derived as "
1 8 X 1 ðn=hÞ2 Dt eðtÞ ¼ S 1 2 e n¼1;3;5... n2
# ð4Þ
E1 E2 12 G12 a1 (below 108 C) a2 (below 108 C) b1 (w.r.t. volume gain ratio) b2 (w.r.t. volume gain ratio) Thickness of lamina
15.2 GPa 13.1 GPa 0.18 2.7 GPa 1.58 g/cm3 20 106/ C 25 106/ C 0.08 0.09 0.004875 cm
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C.-L. Tsai et al. / Composites Science and Technology 62 (2002) 799–803
the pipe at 25 1 C. The specimens were submerged to the desired depth and the embedded strain gage was hooked to a data acquisition system. Five depths were tested —5, 100, 300, 500 and 700 cm. Different depth of water represented different hygric pressures. The second group was to investigate the effect of the concentration of salt in the water. All the specimens were submerged at a depth of 5 cm. The container was enclosed in a thermal chamber and the temperature inside was maintained at 25 1 C. Three salt (NaCl) concentrations were tested —0, 5 and 10% by weight. Data were recorded as in the first group of experiments. The third group was to study the effect of the temperature of the water. All specimens were submerged to a depth of 5 cm in fresh water. The container was enclosed in a thermal chamber or refrigerator and the temperature inside was maintained at 4 1, 25 1 or 60 1 C throughout the experiment. Data were recorded as in the first group of experiments.
0¼
( m X i¼1
"
1 X
"
1 8 X 1 ðn=hÞ2 Dti ei S 1 2 e n¼1;3;5... n2 #
ti eðn=hÞ
2
#) ð8Þ
Dti
n¼1;3;5...
Rearrange Eqs. (7) and (8), to obtain " # 1 m P 8 X 1 ðn=hÞ2 Dti ei 1 2 e n¼1;3;5... n2 i¼1 S¼ " #2 1 m P 8 X 1 ðn=hÞ2 Dti 1 2 e n¼1;3;5... n2 i¼1 m P
S¼
4. Experimental results and analysis
i¼1
" ei
1 P
ð9Þ
# ti eðn=hÞ
2
Dti
n¼1;3;5...
#9 8" 1 > 8 X 1 ðn=hÞ2 Dti > > > > > 1 2 e > > 2 = < m n P n¼1;3;5... " # 1 > P i¼1> 2 > > > > > > ti eðn=hÞ Dti ; :
ð10Þ
n¼1;3;5...
Three specimens were tested under each environmental condition and hygric strain vs. immersion time data were recorded. The error of each measured hygric strain ei at immersion time ti with respect to the theoretical value e(ti) calculated by Eq. (4) is, " # 1 8 X 1 ðn=hÞ2 Dti e ei eðti Þ ¼ ei S 1 2 ð5Þ n¼1;3;5... n2 The summation of the squared error is, s¼
m X ½ei eðti Þ 2 i¼1
¼
( m X
" ei S 1
i¼1
Let Eq. (9) equal to Eq. (10) to obtain the equation for solving D. # 1 8 X 1 ðn=hÞ2 Dti ei 1 2 e n¼1;3;5... n2 i¼1 " #2 ¼ 1 m P 8 X 1 ðn=hÞ2 Dti 1 2 e n¼1;3;5... n2 i¼1 " # m 1 P P 2 ei ti eðn=hÞ Dti m P
"
i¼1
1 8 X 1 ðn=hÞ2 Dti e 2 n¼1;3;5... n2
#) 2 ð6Þ
ð11Þ
n¼1;3;5...
8" #9 1 X > > 2 8 1 > > > > > 1 2 eðn=hÞ Dti > > > 2 = < n m P n¼1;3;5... " # > 1 i¼1> > > P 2 > > > > ti eðn=hÞ Dti > > ; : n¼1;3;5...
where m is the number of data points of each experiment. Based on least square curve fitting theory, the s in Eq. (6) should be minimized. In order to find the solutions of S and D for obtaining minimum s, let the derivatives of s with respect to S and D equal zero. Two equations are obtained.
0¼
( m X i¼1
"
"
1 8 X 1 ðn=hÞ2 Dti ei S 1 2 e n¼1;3;5... n2
1 8 X 1 ðn=hÞ2 Dti 1 2 e n¼1;3;5... n2
#
#)
ð7Þ
The Newton iteration method can be employed to solve D from Eq. (11) numerically. S can then be calculated from either Eq. (9) or (10). Figs. 1 and 2 show the hygric strains, and S and D respectively, of the specimens at different depths of pure water at 25 C. Figs. 3 and 4 show those values for specimens in 5 cm of salty water with different salt concentrations at 25 C. Figs. 5 and 6 show those values for specimens in 5 cm of pure water at different temperatures. Three specimens were tested under each environmental condition. The standard deviations of the calculated S and D values are 5 105 and 7 106 day/cm2, respectively.
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C.-L. Tsai et al. / Composites Science and Technology 62 (2002) 799–803
Fig. 1. Hygric strains of [016] woven glass/epoxy composite vs. emersion time under the conditions of temperature=25 C, salt concentration=0%; and immersion depths of (a) 5cm; (b) 100 cm; (c) 300 cm; (d) 500 cm; (e) 700 cm. Fig. 4. Saturated hygric strain and diffusivity of [016] woven glass/ epoxy composite vs. salt concentration.
Fig. 2. Saturated hygric strain and diffusivity of [016] woven glass/ epoxy composite vs. immersion depth.
Fig. 5. Hygric strains of [016] woven glass/epoxy composite vs. immersion time under the conditions of immersion depth=5 cm, salt concentration=0% and temperatures of (a) 4 C; (b) 25 C; (c) 60 C.
Fig. 3. Hygric strains of [016] woven glass/epoxy composite vs. immersion time under the conditions of immersion depth=5 cm, temperature=25 C and salt concentrations of (a) 0%; (b) 5%; (c) 0%.
Fig. 6. Saturated hygric strain and diffusivity of [016] woven glass/ epoxy composite vs. temperature.
C.-L. Tsai et al. / Composites Science and Technology 62 (2002) 799–803
5. Discussion and conclusions Composite structures serving in a marine environment frequently experiences complicated conditions. Hygric expansion must be considered in their design. The expansion mismatch between layers causes extra stress in the laminate. Hygric expansion is sensitive to many environmental factors, including hygric pressure, salt concentration and surrounding temperature. Experimental results indicated that both saturated hygric strain S and diffusivity D are sensitive to these three factors. The pressure of each meter deep pure water can increase the values of S and D by approximately 1.4 105 and 2.1 106 day/cm2. Each percentage of salt concentration in water can increase the values of S and D by approximately 2.0 105 and 2.5 106 day/ cm2; 1 C may increase the values of S and D by approximately 1.7 106 and 2.5 107 day/cm2. In reality, the maximum static plus dynamic water pressure experienced by a composite structure like a ship or submarine could be as high as 1 MPa. The salt concentration of sea water varies from 3 to 20%. Of course, other solutes in water may also affect the hygric behavior of composite material. The temperature of water in an ocean normally varies between 10 and 30 C. If the structure carries equipment such as an engine, that generates heat, the material may have to withstand temperature exceeding 100 C. All the factors may interact with others. Discussions of the interactions are not in the scope of this work. Assuming they exist simultaneously and act independently, the S and D may increase by roughly 2.0 103 and 140 106 day/cm2. In such cases, the hygric behavior of the composite material is very different from the original behavior. Under such harsh conditions, the material must withstand huge extra stress caused by hygric behavior especially around the edges of the laminate [12–15]. Neglecting these considerations in the design stage may result in unexpected failure. This work presents the quantified sensitivities of hygric properties of the chosen material to environmental factors. The process for measuring hygric strain and calculating the diffusivity of composite material under specific environmental conditions is described. The
803
interactions between all the environmental factors are important research topics in the future. References [1] Daniel IM, Ishai O. Engineering mechanics of composite materials. New York: Oxford University Press Inc.; 1994. [2] Hahn HT, Kim RY. Swelling of composite laminates. In: Vinson JR, editor. Environmental effects on composite materials, ASTM STP 658. Philadelphia: American Society for Testing and Materials; 1978. p. 98–120. [3] Whitney JM, Daniel IM, Byron Pipes R. Experimental mechanics of fiber reinforced composite materials, monograph No. 4. Rev Ed. Englewood Cliffs, NJ: Society for Experimental Mechanics, Bethel, CT, Prentice-Hall; 1985. [4] Yaniv G, Peimanidis G, Daniel IM. Method for hygrothermal characterization of graphite/epoxy composite. J Composite Technol Res 1987;9:21–5. [5] Lee J-W. Damage development, property degradation and fatigue life prediction in composite laminates. Ph.D dissertation, Northwestern University, Evanston, IL, August 1988. [6] Daniel IM, Wang TM, Gotro JT. Thermomechanical behavior of multilayer structures in microelectronics, Proceeding of winter annual meeting of ASME, San Francisco, CA, 10–15 December 1989, 89-WA/EEP-43. [7] Tsai C-L, Wooh S-C. Hygric characterization of woven glass/ epoxy composites. Experimental Mechanics 2001;41(1):70–6. [8] Tsai C-L, Wooh S-C. A novel method to determine the moisture concentration in composite laminates. International Journal of Materials and Products Technology 2002;17(1/2):143–55. [9] Tsai C-L, Wooh S-C, Hwang S-F, Du Y. Hygric characterization of composites using an antisymmetric crossply specimen. Experimental Mechanics 2001;41(3):270–6. [10] Tsai C-L, Chiang C-H. Characterization of hygric behavior of single fiber. Composite Science and Technology 2000;60(14):2725–9. [11] Freynik Jr., HS, Dittbenner GR. Strain-gage stability measurements for years at 70 C in air, Proceeding of 1975 SESA Spring Meeting, Chicago, IL, 12–16 May, 1975. [12] Wang ASD, Crossman FW. Some new results on edge effect in symmetric composite laminates. J Composite Materials 1977;11: 92–106. [13] Wang ASD, Crossman FW. Edge effects on thermally induced stresses in composite laminates. J Composite Materials 1977;11: 300–12. [14] Wang ASD, Crossman FW. Calculation of edge stresses in multilayer laminates by sub-structuring. J Composite Materials 1978; 12:76–83. [15] Crossman FW, Wang ASD. Stress field induced by transient moisture sorption in finite-width composite laminates. J Composite Materials 1978;12:2–18.
The effects of hygric pressure, salt concentration and temperature on the hygric expansion of composite material Cho-Liang Tsaia,*, Yi-Shiun Tsaib, Chih-Hung Chiangc a
Department of Construction Engineering, National Yunlin University of Science and Technology, 123, Sec. III University Road, Touliu, Yunlin 640, Taiwan b General Education Center, Hsiuping Institute of Technology, Taichung 412, Taiwan c Department of Construction Engineering, Chaoyang University of Technology, Taichung 413, Taiwan Received 8 May 2001; received in revised form 14 January 2002; accepted 20 February 2002
Abstract Moisture absorption causes the expansion of composite material. Such expansion is physically reversible and dominated by the characteristic property of the composite material. However, many environmental factors can alter this hygric behavior. This work addresses the effects of external hygric pressure, salt concentration and environmental temperature, upon the hygric expansion of composite material submerged in water. Embedded strain gages were used to monitor hygric expansion. The final hygric strains of glass/epoxy submerged in water under different environmental conditions were measured and the corresponding diffusivities were calculated. The results confirm that hygric pressure, salt concentration, and temperature importantly affect the hygric behavior of composite materials. The process and results of this work are critical to designing composite structures—especially those serving in marine environment. # 2002 Elsevier Science Ltd. All rights reserved. Keywords: Hygric expansion
1. Introduction Expansion of polymeric matrix composite induced by moisture absorption is one of the hygric behaviors which can be characterized in terms of the longitudinal and transverse moisture expansion coefficients (CMEs), b1 and b2 [1,2]. This hygric expansion can be measured with a micrometer, caliper, or strain gage, or by the hunch-up or curvature technique [3–9]. Micrometers and calipers are conventional tools, reliable and accurate enough to measure the transverse hygric expansion of a composite lamina. However, the hygric expansion of a composite lamina in the longitudinal direction is usually much less than that in the transverse direction. The hygric expansion of the fiber is usually very small and tends to constrain the expansion of the matrix. Some fibers such as carbon fiber exhibit a small negative hygric expansion [10], which compensates for part of the hygric expansion of the epoxy matrix, making the total longitudinal hygric expansion
* Corresponding author. Tel.: +886-5-534-2601x4719. E-mail address: [email protected] (C.-L. Tsai).
of the carbon/epoxy lamina too small to be measured by conventional tools [1]. Tsai and Wooh [8,9] developed the curvature technique to characterize the hygric behavior of composite materials according to the relationship between the curvature change of a strip shape cross-ply laminate [0n/90n] and the hygric expansions in both of its layers. The curvature technique can be employed to quantify the small b1 and the b2 of a unidirectional composite lamina. Tsai and Wooh [7] also developed the hunch-up technique to characterize the hygric behavior of composite materials such as woven fiber composites, with small coefficients of moisture expansion in both principle directions. In the process of this technique, a strip shape unidirectional composite laminate or woven fiber composite laminate with all the layers stacked in the same direction is squeezed into a slightly shorter space in a rigid frame, hunching up like an arch. The hunch-up height is sensitive to the expansion of the specimen due to temperature or moisture absorption. The coefficient of moisture expansion of the laminate can be calculated accurately from the change in hunch-up height. The strain gage is another convenient tool for characterizing the hygric behavior of composite lamina [4].
0266-3538/02/$ - see front matter # 2002 Elsevier Science Ltd. All rights reserved. PII: S0266-3538(02)00048-9
800
C.-L. Tsai et al. / Composites Science and Technology 62 (2002) 799–803
In this study, creep resistant encapsulated strain gages [11] were embedded in woven glass/epoxy laminates to monitor their hygric expansions while they were submerged in different depths of water at different temperatures and salt concentrations. Fick’s diffusion law was adapted to describe the moisture diffusion [7–9]. The diffusivity can be calculated from the hygric strain since the strain is proportional to the moisture concentration [1]. Experimental results indicate that the final hygric strain and diffusivity are sensitive to the environmental conditions considered.
2. Theoretical background Once a dry composite laminate is submerged into water it begins to absorb water and expand. If the diffusion in the thickness direction occurs only through the surface of the specimen and follows Fick’s diffusion law, the moisture concentration in the laminate can be written as, " # ðn1Þ 1 4 X ð1Þ 2 ðn=hÞ2 Dt nz cðt; zÞ ¼ C 1 e cos n¼1;3;5... h n ð1Þ where c(t, z) is the moisture concentration as a function of immersion time t and thickness coordinate z, C is the saturated moisture concentration, h is the thickness of the laminate, and D is the diffusivity in thickness direction of the laminate. The origin of the thickness coordinate z is at the center of the laminate. Assume that the hygric expansion is proportional to the moisture concentration with a coefficient b. Assuming no constraints, the hygric strain in the laminate will be, "ðt; zÞ ¼ "
1 4 X ð1Þ bC 1 n¼1;3;5... n
ðn1Þ 2
eðn=hÞ
2
nz Dðt Þ cos h
# ð2Þ
Under plane remains plane assumption, the hygric strain of the whole laminate e(t) can be involved in zero loading condition. ð h=2 0¼
½eðtÞ "ðt; zÞ Qdz
ð3Þ
where S is the saturated hygric strain of the laminate and S=bC. The result shows that the hygric strain of a composite laminate submerged in water increases monotonically, asymptotically approaching S. The diffusivity D controls the diffusion rate. Both S and D are material constant. However, their values depend on several environmental factors such as hygric pressure, temperature and salt concentration.
3. Experimental procedure Embedded strain gages were used to measure the hygric strains of the composite laminates to determine their hygric diffusivity in the thickness direction. The strain gages were embedded in the first principle direction to monitor the hygric expansion in this direction. The hygric behavior in the second principle direction of the chosen material is similar to that in the first principle direction and can be similarly characterized. The specimens used in this study were [016] woven E-glass/epoxy (Style 109 Woven E-Glass Fabric/FR-4 Epoxy Novolac System, IBM). Table 1 lists the properties of the material. Each specimen was 5 5 cm and 0.078 cm thick. All the edges were sealed with 5 mm thick silicon glue to prevent moisture diffusion through the edges. WK strain gages, which are very stable in long-term measurement, were used. The gages’ grids are made of nickel–chromium and fully encapsulated in glass-fiber-reinforced epoxy-phenolic resin. The measuring error of the WK gage is less than 40 106 for 2.5 years’ continuous measurement under 75 C [11]. The gages were embedded at the center of each laminate. Each specimen was completely dried by post-curing under 80 C in a thermal chamber until its weight became stable, and then being left inside the chamber to cool off prior to the experiment. This step usually took 4 days. Three groups of experiments were conducted. The first group was to investigate the effect of hygric pressure on the hygric expansion of composite laminate. An 8 m high PVC pipe was constructed with its lower end sealed. It was filled with pure water. A thermostat and circulation system maintained the temperature of the water inside Table 1 The properties of woven E-glass/epoxy lamina
h=2
where Q is the stiffness of the material. Q=Q11=E1/(1– 1221) for 0 laminates and Q=Q22=E2/(11221) for 90 laminates [1]. The hygric strain of the laminate can be derived as "
1 8 X 1 ðn=hÞ2 Dt eðtÞ ¼ S 1 2 e n¼1;3;5... n2
# ð4Þ
E1 E2 12 G12 a1 (below 108 C) a2 (below 108 C) b1 (w.r.t. volume gain ratio) b2 (w.r.t. volume gain ratio) Thickness of lamina
15.2 GPa 13.1 GPa 0.18 2.7 GPa 1.58 g/cm3 20 106/ C 25 106/ C 0.08 0.09 0.004875 cm
801
C.-L. Tsai et al. / Composites Science and Technology 62 (2002) 799–803
the pipe at 25 1 C. The specimens were submerged to the desired depth and the embedded strain gage was hooked to a data acquisition system. Five depths were tested —5, 100, 300, 500 and 700 cm. Different depth of water represented different hygric pressures. The second group was to investigate the effect of the concentration of salt in the water. All the specimens were submerged at a depth of 5 cm. The container was enclosed in a thermal chamber and the temperature inside was maintained at 25 1 C. Three salt (NaCl) concentrations were tested —0, 5 and 10% by weight. Data were recorded as in the first group of experiments. The third group was to study the effect of the temperature of the water. All specimens were submerged to a depth of 5 cm in fresh water. The container was enclosed in a thermal chamber or refrigerator and the temperature inside was maintained at 4 1, 25 1 or 60 1 C throughout the experiment. Data were recorded as in the first group of experiments.
0¼
( m X i¼1
"
1 X
"
1 8 X 1 ðn=hÞ2 Dti ei S 1 2 e n¼1;3;5... n2 #
ti eðn=hÞ
2
#) ð8Þ
Dti
n¼1;3;5...
Rearrange Eqs. (7) and (8), to obtain " # 1 m P 8 X 1 ðn=hÞ2 Dti ei 1 2 e n¼1;3;5... n2 i¼1 S¼ " #2 1 m P 8 X 1 ðn=hÞ2 Dti 1 2 e n¼1;3;5... n2 i¼1 m P
S¼
4. Experimental results and analysis
i¼1
" ei
1 P
ð9Þ
# ti eðn=hÞ
2
Dti
n¼1;3;5...
#9 8" 1 > 8 X 1 ðn=hÞ2 Dti > > > > > 1 2 e > > 2 = < m n P n¼1;3;5... " # 1 > P i¼1> 2 > > > > > > ti eðn=hÞ Dti ; :
ð10Þ
n¼1;3;5...
Three specimens were tested under each environmental condition and hygric strain vs. immersion time data were recorded. The error of each measured hygric strain ei at immersion time ti with respect to the theoretical value e(ti) calculated by Eq. (4) is, " # 1 8 X 1 ðn=hÞ2 Dti e ei eðti Þ ¼ ei S 1 2 ð5Þ n¼1;3;5... n2 The summation of the squared error is, s¼
m X ½ei eðti Þ 2 i¼1
¼
( m X
" ei S 1
i¼1
Let Eq. (9) equal to Eq. (10) to obtain the equation for solving D. # 1 8 X 1 ðn=hÞ2 Dti ei 1 2 e n¼1;3;5... n2 i¼1 " #2 ¼ 1 m P 8 X 1 ðn=hÞ2 Dti 1 2 e n¼1;3;5... n2 i¼1 " # m 1 P P 2 ei ti eðn=hÞ Dti m P
"
i¼1
1 8 X 1 ðn=hÞ2 Dti e 2 n¼1;3;5... n2
#) 2 ð6Þ
ð11Þ
n¼1;3;5...
8" #9 1 X > > 2 8 1 > > > > > 1 2 eðn=hÞ Dti > > > 2 = < n m P n¼1;3;5... " # > 1 i¼1> > > P 2 > > > > ti eðn=hÞ Dti > > ; : n¼1;3;5...
where m is the number of data points of each experiment. Based on least square curve fitting theory, the s in Eq. (6) should be minimized. In order to find the solutions of S and D for obtaining minimum s, let the derivatives of s with respect to S and D equal zero. Two equations are obtained.
0¼
( m X i¼1
"
"
1 8 X 1 ðn=hÞ2 Dti ei S 1 2 e n¼1;3;5... n2
1 8 X 1 ðn=hÞ2 Dti 1 2 e n¼1;3;5... n2
#
#)
ð7Þ
The Newton iteration method can be employed to solve D from Eq. (11) numerically. S can then be calculated from either Eq. (9) or (10). Figs. 1 and 2 show the hygric strains, and S and D respectively, of the specimens at different depths of pure water at 25 C. Figs. 3 and 4 show those values for specimens in 5 cm of salty water with different salt concentrations at 25 C. Figs. 5 and 6 show those values for specimens in 5 cm of pure water at different temperatures. Three specimens were tested under each environmental condition. The standard deviations of the calculated S and D values are 5 105 and 7 106 day/cm2, respectively.
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Fig. 1. Hygric strains of [016] woven glass/epoxy composite vs. emersion time under the conditions of temperature=25 C, salt concentration=0%; and immersion depths of (a) 5cm; (b) 100 cm; (c) 300 cm; (d) 500 cm; (e) 700 cm. Fig. 4. Saturated hygric strain and diffusivity of [016] woven glass/ epoxy composite vs. salt concentration.
Fig. 2. Saturated hygric strain and diffusivity of [016] woven glass/ epoxy composite vs. immersion depth.
Fig. 5. Hygric strains of [016] woven glass/epoxy composite vs. immersion time under the conditions of immersion depth=5 cm, salt concentration=0% and temperatures of (a) 4 C; (b) 25 C; (c) 60 C.
Fig. 3. Hygric strains of [016] woven glass/epoxy composite vs. immersion time under the conditions of immersion depth=5 cm, temperature=25 C and salt concentrations of (a) 0%; (b) 5%; (c) 0%.
Fig. 6. Saturated hygric strain and diffusivity of [016] woven glass/ epoxy composite vs. temperature.
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5. Discussion and conclusions Composite structures serving in a marine environment frequently experiences complicated conditions. Hygric expansion must be considered in their design. The expansion mismatch between layers causes extra stress in the laminate. Hygric expansion is sensitive to many environmental factors, including hygric pressure, salt concentration and surrounding temperature. Experimental results indicated that both saturated hygric strain S and diffusivity D are sensitive to these three factors. The pressure of each meter deep pure water can increase the values of S and D by approximately 1.4 105 and 2.1 106 day/cm2. Each percentage of salt concentration in water can increase the values of S and D by approximately 2.0 105 and 2.5 106 day/ cm2; 1 C may increase the values of S and D by approximately 1.7 106 and 2.5 107 day/cm2. In reality, the maximum static plus dynamic water pressure experienced by a composite structure like a ship or submarine could be as high as 1 MPa. The salt concentration of sea water varies from 3 to 20%. Of course, other solutes in water may also affect the hygric behavior of composite material. The temperature of water in an ocean normally varies between 10 and 30 C. If the structure carries equipment such as an engine, that generates heat, the material may have to withstand temperature exceeding 100 C. All the factors may interact with others. Discussions of the interactions are not in the scope of this work. Assuming they exist simultaneously and act independently, the S and D may increase by roughly 2.0 103 and 140 106 day/cm2. In such cases, the hygric behavior of the composite material is very different from the original behavior. Under such harsh conditions, the material must withstand huge extra stress caused by hygric behavior especially around the edges of the laminate [12–15]. Neglecting these considerations in the design stage may result in unexpected failure. This work presents the quantified sensitivities of hygric properties of the chosen material to environmental factors. The process for measuring hygric strain and calculating the diffusivity of composite material under specific environmental conditions is described. The
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interactions between all the environmental factors are important research topics in the future. References [1] Daniel IM, Ishai O. Engineering mechanics of composite materials. New York: Oxford University Press Inc.; 1994. [2] Hahn HT, Kim RY. Swelling of composite laminates. In: Vinson JR, editor. Environmental effects on composite materials, ASTM STP 658. Philadelphia: American Society for Testing and Materials; 1978. p. 98–120. [3] Whitney JM, Daniel IM, Byron Pipes R. Experimental mechanics of fiber reinforced composite materials, monograph No. 4. Rev Ed. Englewood Cliffs, NJ: Society for Experimental Mechanics, Bethel, CT, Prentice-Hall; 1985. [4] Yaniv G, Peimanidis G, Daniel IM. Method for hygrothermal characterization of graphite/epoxy composite. J Composite Technol Res 1987;9:21–5. [5] Lee J-W. Damage development, property degradation and fatigue life prediction in composite laminates. Ph.D dissertation, Northwestern University, Evanston, IL, August 1988. [6] Daniel IM, Wang TM, Gotro JT. Thermomechanical behavior of multilayer structures in microelectronics, Proceeding of winter annual meeting of ASME, San Francisco, CA, 10–15 December 1989, 89-WA/EEP-43. [7] Tsai C-L, Wooh S-C. Hygric characterization of woven glass/ epoxy composites. Experimental Mechanics 2001;41(1):70–6. [8] Tsai C-L, Wooh S-C. A novel method to determine the moisture concentration in composite laminates. International Journal of Materials and Products Technology 2002;17(1/2):143–55. [9] Tsai C-L, Wooh S-C, Hwang S-F, Du Y. Hygric characterization of composites using an antisymmetric crossply specimen. Experimental Mechanics 2001;41(3):270–6. [10] Tsai C-L, Chiang C-H. Characterization of hygric behavior of single fiber. Composite Science and Technology 2000;60(14):2725–9. [11] Freynik Jr., HS, Dittbenner GR. Strain-gage stability measurements for years at 70 C in air, Proceeding of 1975 SESA Spring Meeting, Chicago, IL, 12–16 May, 1975. [12] Wang ASD, Crossman FW. Some new results on edge effect in symmetric composite laminates. J Composite Materials 1977;11: 92–106. [13] Wang ASD, Crossman FW. Edge effects on thermally induced stresses in composite laminates. J Composite Materials 1977;11: 300–12. [14] Wang ASD, Crossman FW. Calculation of edge stresses in multilayer laminates by sub-structuring. J Composite Materials 1978; 12:76–83. [15] Crossman FW, Wang ASD. Stress field induced by transient moisture sorption in finite-width composite laminates. J Composite Materials 1978;12:2–18.