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Cure monitoring and residual stress sensing of single-carbon fiber reinforced epoxy composites using electrical resistivity measurement
COMPOSITES SCIENCE AND TECHNOLOGY Composites Science and Technology 65 (2005) 571–580 www.elsevier.com/locate/compscitech
Cure monitoring and residual stress sensing of single-carbon fiber reinforced epoxy composites using electrical resistivity measurement Joung-Man Park
a,*
, Sang-Il Lee a, Jin-Ho Choi
b
a
b
Department of Polymer Science and Engineering, Research Center for Aircraft Parts Technology, Gyeongsang National University, Chinju 660-701, Republic of Korea School of Transport Vehicle Engineering, Research Center for Aircraft Parts Technology, Gyeongsang National University, Chinju 660-701, Republic of Korea Received 25 July 2003; received in revised form 12 February 2004; accepted 1 September 2004 Available online 19 November 2004
Abstract Temperature sensing and cure monitoring of the single-carbon fiber/epoxy composites were studied by the measurement of electrical resistivity as a new approach. IFSS and the difference in electrical resistivity (DR) between before and after curing were highest for the smallest gauge length of the specimen. As curing temperature increased, logarithmic electrical resistivity of steel fiber increased due to the increased the mean path of the free electron. On the other hand, those of semi-conductive carbon and SiC fibers decreased due to the intrinsic electrical properties based on the band theory. Residual stress built in the fiber was highest at the fiber axis direction, whereas residual stress of built in the matrix was relatively higher for the fiber circumference and radius direction. Residual stresses by the calculating method were consistent well with those from the finite element analysis (FEA). The behavior of electrical resistivity was responded well quantitatively with the change of curing temperature and epoxy matrix modulus. Electrical resistance measurement of conductive fiber composites can be applicable for the useful technique to evaluate cure monitoring and residual stress sensing. 2004 Elsevier Ltd. All rights reserved. Keywords: B. Interfacial strength; C. Residual stress; D. Acoustic emission; Electrical resistivity; Cure monitoring
1. Introduction Recently a new evaluation technique of interfacial properties as well as curing characteristics and the residual stress were investigated by the measurement of electrical resistivity using various conductive fiber reinforced composites. The conductive fiber reinforced composites were studied as new self-strain and/or selfdamage health monitoring sensors under temperature change and under applied load [1–3]. *
Corresponding author. Tel.: +82 55 751 5300/591 751 5300; fax: +82 55 752 0075/591 752 0075. E-mail address: [email protected] (J.-M. Park). 0266-3538/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2004.09.019
Temperature sensing and cure monitoring have been studied as an economical new evaluation for the monitoring of curing characteristics, interfacial properties and nondestructive behavior because conductive fiber can act as a sensor in itself as well as a reinforcing fiber [4,5]. The electrical resistance difference and residual stress were investigated for single carbon fiber composite, and residual stress affected on the interfacial adhesion between fiber and matrix in composite materials [4]. For carbon fiber/polymer composites, the endothermic peak at the annealing temperature and frictional change in electrical resistance were studied by differential scanning calorimetry (DSC) and DC electrical resistance measurement. During cyclic heating/cooling
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processes, thermal interlaminar damages were also evaluated by the measurement of contact resistivity of carbon fiber laminates [5]. Cure monitoring and their characterization including residual stress were studied by means of the common methods such as thermal and dielectric analysis. To minimize residual stress in the thermosetting epoxy, the optimum cure cycle was evaluated using dilatometer and DSC. The volume change depending on the elapsed time and temperature was measured during various curing cycles. In DSC the differential heat flow between the sample and the reference was measured with linearly programmed temperature rise [6]. Dielectric sensor was used to measure the cure degree of carbon fiber/epoxy composite. Dielectric analysis or dielectrometry can be used to investigate the processing characteristics and chemical structure of polymers and other organic materials by measuring their dielectric properties. Under electrical field, the change of electrical dipole alignment and the charged ion mobility can be used to infer the information concerning on the bulk material properties, such as its viscosity, rigidity, reaction rate, and cure state, etc. During cure monitoring, dipoles and charged ions in dielectric materials could be rearranged under AC electrical filed. The alignment of dipoles and ions might be allowed during curing. However, the alignment could be difficult as the curing progressed [7–9]. Residual stress in the fiber-reinforced composite occurred usually due to thermal contraction of the matrix or the difference of thermal expansion coefficient (TEC) between fiber and matrix. This stress may affect on the interface between fiber and matrix, and may have a great influence on the mechanical performance of microcomposites. Residual stress can affect actually on the fiber stress or the interfacial shear strength (IFSS) [10,11]. The measurement of residual stress/strain on the fiber can be measured by Raman scattering method [12,13] and other optical technique [14]. These techniques are difficult to measure directly residual stress because the fiber strain is anisotropy and the fiber is embedded in the matrix. Genidy et al. [11,15] and Madhukar et al. [16– 18] attempted to measure directly residual compressive stress to obtain optimized curing cycle with free stress. Inhomogeneous structure of polymeric composites causes to develop internal stresses due to matrix volume change during curing. Volume change occurs during curing and cooling down processes. Most of the previous studies [11–18] on residual stress were concentrated on the stress development during cooling down. A new testing method in this work was used to monitor the fiber stress that developed around single fiber composites (SFC) during heating or cooling. A relationship between cure cycle and residual stress was studied and it was
shown that cure-induced stress and residual stress vary with different resin types. The residual stress in SFC was experimentally evaluated by the technique based on the continuous monitoring during fragmentation testing [19]. The difference between the strain at the break of a single fiber in air and the strain embedded in a polymer matrix could be measured as a function of temperature. By considering the compressive fiber modulus, the strain difference might be converted into fiber compressive stress related to the matrix thermal shrinkage after curing the specimen [19]. Residual stress in bismaleimide/carbon fiber composite model depending on the curing cycle was studied using finite element analysis (FEA) [20]. The comparison of theoretical prediction, numerical simulation, and the experimental result shows a generally good agreement. In this work, during curing process, the electrical resistance of carbon fiber composite was measured to evaluate curing characteristics and residual stress change depending on the gauge length, curing temperature and matrix modulus with differing curing agent ratios. Residual stress was measured by the von Mises criterion and then the equivalent stress was evaluated by FEA. The relationship between the electrical resistivity, residual stress and IFSS was investigated for single carbon fiber/epoxy composites. Ultimately the temperature sensing and cure monitoring were correlated by the electrical resistance measurement.
2. Experimental 2.1. Materials Carbon fiber of 8 lm (Taekwang Industrial Co., Korea) and of 18 lm (Mitsubishi Chemical Co., Japan) in average diameter was used as conductive reinforcing materials. SiC fiber (Textron Co.) of 138 lm and steel fiber (No. 1 guitar string of Segovia Instruments Co., Korea) of 280 lm were used for comparison. Testing specimens were prepared with epoxy resin (YD-128, Kukdo Chemical Co., Korea). Epoxy resin is based on diglycidyl ether of bisphenol-A (DGEBA). Polyoxypropylene diamines (Jeffamine D-400 and D-2000, Huntzman Petrochemical Co.) were used as curing agents. The flexibility of specimens was controlled by mixing ratio of D-400 versus D-2000. 2.2. Methodologies 2.2.1. Preparation of testing specimens Two type specimens were prepared for electro-micromechanical test and curing monitoring. Fig. 1(a) exhibits a dogbone-shaped specimen to measure electrical resistivity change during curing, and then to evaluate IFSS
J.-M. Park et al. / Composites Science and Technology 65 (2005) 571–580 Silver Paste A
2 mm
th
Cu rre nt Co V ol nt ta ac ge t Co s nt ac ts
B
G
au
ge
Le
ng
5 mm
D
C
Carbon fiber
(a)
Current Contacts Voltage Contacts 10 mm AB 1.2 mm
C D
Carbon Fiber Silver Paste
Epoxy
(b)
Teflon Release Film
Fig. 1. Schematic illustration of two-type testing composites for: (a) electro-micromechanical test; (b) cure monitoring.
of the microcomposite was monitored during curing process. Electrical resistivity was obtained from the measured electrical resistance, cross-sectional area of the conductive fiber, A, and electrical contact length, Lec of the testing fiber connecting to copper wires. The relationship between electrical resistivity, q and resistance, R is as follows: A q¼ R: ð1Þ Lec Electrical resistance was measured by four-point probe method as shown in Fig. 1(b). Silver paste was used as electrically connecting glue at junctions A, B, C and D to maintain electrical contact between the fiber and leading wires. The voltage was measured between junctions B and C, and the current was measured between junctions A and D. Total electrical resistance, RTot between B and C may include Rc based on the contact resistance by silver paste beside Rf due to the electrical resistance by the fiber as follows: RTot ¼ Rc þ Rf :
as a function of measuring gauge length, such as 2, 5, 32, 60, 100 mm. Fig. 1(b) shows single carbon fiber/epoxy composites to measure the electrical resistivity during curing process. To make dogbone-type specimen for measuring the electrical resistance and evaluating the IFSS, single carbon fiber was fixed with the axial direction in a silicone mold. After carbon fiber and lead wires were electrically connected using silver paste, epoxy resin was poured into the silicone mold, and then epoxy was cured as scheduled curing steps. For the specimen for measuring electrical resistance, two pairs of narrow copper wires were fixed transversely on a mold-releasing teflon film with attaching guide tapes, and then single fiber was laid down with the longitudinal direction. The guide tapes can prevent the overflow of resin and specimens dimension was measured after curing. A silver paste was used to connect electrically at the intersecting point between carbon fiber and copper wires. After the suitable amount of epoxy resin was poured into the silicone mold, single carbon fiber/epoxy composite was cured. 2.2.2. Electrical resistance measurement During the curing process, the electrical resistance was measured using a digital multimeter (HP34401A). For the curing monitoring, curing cycle was set up as three steps that were composed of the precuring step at 80 C for 1 h, the postcuring step at 120 C for 1 h and finally slow cooling step at room temperature for 6 h. Curing process of all microcomposites was performed in a drying oven. After a testing specimen was placed in the oven, the composite and the multimeter were connected electrically using very thin copper wires. Electrical resistance
573
ð2Þ
Since the value of Rc is negligibly small due to very high conductivity of silver paste comparing to Rf, it can be considered that the voltage developed between junctions B and C becomes nearly fibers resistance RTot ffi Rf :
ð3Þ
2.2.3. IFSS measurement To measure IFSS depending on the gauge length, curing temperature and surface treatment, a specially designed mini-tensile testing machine was used with a polarized-light microscope. After the testing specimen was fixed in the mini-tensile testing machine, the composite was incrementally strained and the fiber was broken into small fragments. Load was applied until no longer fiber breaks occurred, and then the critical fiber fragment length, lc was measured under an optical microscope equipped with a calibrated eyes piece lens. IFSS was determined by Drzals equation [21] that was modified from Kelly–Tysons equation. By introducing Weibull distribution for aspect ratio, the IFSS was exhibited in the form as follows: rf 1 s¼ C 1 ; ð4Þ b 2a where a and b are scale and shape parameters of Weibull distribution for aspect ratio (lc/d), and C is gamma function. Since the fiber tensile strength is very difficult to measure directly at the critical fragment length (usually less than 1 mm), fiber strength at such a very short length can be resulted from calculating method. After fiber strength was usually determined at the measurable gauge length with 2 mm, it was subjected to subsequent extrapolation to smaller gauge length using Weibull
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weakest link rule [22]. Tensile strength at a critical fragment length can be obtained as follows: rf ¼ r0
1=q lc ; l0
ð5Þ
where r0 is the fiber tensile strength at measurable gauge length, and q is the shape parameter of Weibull distribution for fiber tensile strength. 2.2.4. Residual stress from typical criterions and FEA It is commonly known that residual stress occurred by the different TEC between fiber and matrix during curing and subsequent cooling process. If interfacial adhesion is perfect and the strain of matrix and fiber is the same value, the relationship among residual stress, TEC and elastic modulus could be designated as follows: rRf rRm þ af DT ¼ þ am DT ; Ef Em
ð6Þ
where rRf is the longitudinal residual stress built up in the fiber, rRm is the residual stress built up in the matrix, Ef is the modulus of fiber, Em is the modulus of matrix, af is TEC of fiber, am is TEC of matrix, and DT is the temperature change. A following equation is usually satisfied since there is no external force on the microspecimen: rf V f þ rm V m ¼ 0;
tion of matrix is too high in the SFC, the residual stress of matrix can generally be estimated by the following equation: rRm ¼ ðam af Þ DT EðeÞ;
ð9Þ
where E(e) is the modulus which obtained from the measured stress–strain curve of the specimen. TEC of the fiber is smaller than that of the matrix, and may be neglected in the calculating Eq. (9). The residual stress, resulted from the experimentally calculating method, has been correlated with the value estimated from FEA using commercial ANSYS 5.5. Fig. 2 shows FEA model and the element mesh. The quarter section of the microspecimen was only modeled because geometrical symmetry was considered in the specimen structure. The total number of nodes and element were 22,649 and 19,600, respectively. Nonlinear approach in FEA was used under the multi-linear curve resulted from true stress–strain curve. The each stress components, acted on the fiber and matrix, were converted into von Mises equivalent stress. The relationship between stress components and equivalent residual stress was designated by von Mises criterion
ð7Þ
where Vf and Vm are the volume fraction of fiber and matrix, respectively. Combining Eqs. (6) and (7), the following equation was designated for calculating the residual stress in the fiber: rRf ¼
Ef Em V m ðam af Þ DT : ðV m Em þ V f Ef Þ
Carbon Fiber
ð8Þ
The shrinkage of the epoxy is higher than that of the carbon fiber. The residual stress of matrix in SFC was calculated simply from TEC of each components and the modulus of SFC specimen. Because the volume frac-
Epoxy Matrix
Fig. 2. Quarter model for FEA simulation of residual stress.
Table 1 Interfacial properties and electrical resistivity before and after curing process Gauge length (mm)
Electrical resistivity Before cure
2 5 32 60 100 a b c
1.96 1.84 1.95 1.85 1.97
(0.2)c (0.2) (0.1) (0.1) (0.1)
Average fragment length (mm)
After cure
D Resistivity (103 X cm)
2.42 2.03 2.02 1.90 2.02
0.47 0.19 0.08 0.05 0.05
(0.2) (0.3) (0.1) (0.1) (0.1)
Drzal equation: sd = (rf/2a) Æ C [1 (1/b)]. Kelly–Tyson: sk = (rf Æ d)/(2 Æ lc). Standard deviation, 5 specimens were used.
(0.13) (0.07) (0.02) (0.01) (0.00)
358.8 489.9 592.0 595.5 598.5
IFSS (MPa) Drzala
Kellyb
64.2 42.1 33.6 33.2 33.6
56.0 38.7 31.0 30.7 30.6
J.-M. Park et al. / Composites Science and Technology 65 (2005) 571–580 80
1.0
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h iffi 2 2 2 1 2 2 2 req ¼ 2 ðrr rh Þ þ ðrh rz Þ þ ðrz rr Þ þ 6srh þ 6shz þ 6szr ;
0.8
ð10Þ
∆ (Resistivity) IFSS
0.6 40 0.4
∆ (Resistivity)
60
IFSS (MPa)
575
where r is the normal stress, s is the shear, subscript r, h, z are the fiber radius direction, the fiber circumference direction, and the fiber axis direction.
3. Results and discussion
20 0.2
3.1. Electrical resistivity and IFSS
0.0
0
2
5
32
60
100
Gauge Length (mm) Fig. 3. Comparison of difference in electrical resistivity before and after curing and IFSS depending on the gauge length.
σf τ 0
(a) 5mm
σf τ
0
(b) 32 mm
σf τ
0
Table 1 and Fig. 3 show interfacial properties and the electrical resistivity of the single carbon fiber composites depending on the gauge length using fragmentation test and during cure monitoring. As gauge length increased, average fragment length increased whereas IFSS decreased. It might be considered that fiber strength increased at critical fragment length by weakest link rule and average IFSS in longitudinal direction decreased as shown in Fig. 4. Fig. 4 exhibits a schematic illustration of fiber strength and IFSS as a function of gauge length in SFC specimen. As gauge length increased, average IFSS decreased although fiber strength was not remarkably changed. The difference in electrical resistivity before and after curing was highest at the gauge length with 2 mm. The difference in electrical resistivity decreased exponentially until 60 mm, and then they did not show significant change at higher gauge length. The difference in electrical resistivity could be expected to occur from the thermal residual stress due to the mismatch of TEC between fiber and matrix during curing process. This phenomenon might be because average residual stress diminished with increasing gauge length. 3.2. Electrical resistivity during curing process
(c) 60mm Fig. 4. Schematic illustrations of fiber strength and average IFSS depending on the gauge length in SFC.
Table 2 shows the electrical and mechanical properties of four-type conductive fibers. Electrical resistance was measured at the distance between two voltage contacts with 32 mm, whereas mechanical properties were
Table 2 Intrinsically electrical and mechanical properties of various conductive fibers Fiber
Diameter (lm) a
Carbon Carbonb SiCc Steeld a b c d e
8 18 138 280
Electrical resistance (X) 4
1.19 · 10 (570) 1.57 · 103 (120) 0.34 · 103 (10) 0.57 (0.07)
Electrical resistivity (104 X cm)
Tensile strength (MPa)
Elastic modulus (GPa)
18.6 (0.9)e 12.5 (1.0) 156.8 (5.3) 1.09 (0.14)
2828 1772 3613 1461
245 212 162 193
PAN based (Taekwang Industrial Co., Korea). Pitch coal tar based (Mitsubishi Chemical Co., Japan). Made in Textron Co. No. 1 string of guitar (Segovia Instruments Co., Korea). Standard deviation.
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measured at 20 mm in gauge length, respectively. Electrical resistance was very different among four conductive fibers due to differing intrinsic ingredients and materials unique characteristics. Fig. 5 shows the comparison of electrical resistivity change in bare fiber without matrix and single-fiber embedded epoxy composite during curing process. As curing temperature increased, logarithmic electrical resistivity of steel fiber increased, whereas that of carbon fiber was trended to decrease. Electrical resistivity of SiC fiber exhibits nearly same behavior like carbon fiber. This might be due to the difference of inherent electrical properties between steel and carbon fibers based on the band theory [23–25]. Logarithmic electrical resistivity of three bare fibers before curing is equal to the value after curing. On the other hands, electrical resistivity of their composites after curing was higher than that of the before curing. It might be explained that residual stress occurred during curing due to the different TEC between fiber and matrix. Fig. 6 shows schematic models based on the band theory for three different type materials. Electron cannot jump from the filled level to the empty level because the energy gap is too wide in insulator. In semiconductor, e.g., carbon and SiC fiber, the electron jumping between the filled and the empty level occur partially above 0 K. Electrons are free to jump without activation energy because no energy gap exists in conductor such as steel fiber. Fig. 7(a) exhibits the comparison of schematic models for the fine structure of metallic steel fiber in order to explain electrical behavior. As the curing temperature increases, the activated mobility increases; stereo-regularity of metal lattice decreases; the mean path of
Empty level
Empty level
Empty level
Energy gap
Filled level
Filled level
Filled level
Conductor (Metal) Semiconductor
Insulator Fig. 6. Comparison of energy gap for three materials based on the band theory.
Elevated Temperature e-
Disorder structure
Increasing T
Room Temperature e-
(a)
-1.81
SiC fiber/epoxy
-1.82
Bare SiC fiber
Conduction electron
-1.83
140
-1.84
120
-1.85 -2.74
Carbon fiber/epoxy
-2.75
Bare carbon fiber
-2.76
100 80 60
-4.55 -4.60 Temperature
-4.65
Steel fiber/epoxy
-4.70 -4.75
Stereo-regular bcc structure
40
Conduction band (Empty level)
Temperature (oC)
Log [Electrical Resistivity (Ω ·cm)]
-1.80
Energy gap
20
Electron hole
Bare steel fiber
0
100
200
300
400
0 500
Time (min) Fig. 5. Comparison of logarithmic electrical resistivity as a function of curing temperature in three bare fibers and their composites during curing process.
Valence band (Filled level)
(b) Fig. 7. Schematic illustration of: (a) fine molecular structure in the steel fiber; (b) conduction and valence bands in the carbon or SiC fibers.
J.-M. Park et al. / Composites Science and Technology 65 (2005) 571–580
free electron increases; and then electrical conductivity decreases. The energy gap is known to be existed for semi-conductive SiC and carbon fibers. As the temperature increases, the mobility, the number and density of jumping free electron increases as designated in Fig. 7(b). It means that electrical conductivity increases and thus electrical resistivity decreases.
50
(e)
Stress (MPa)
40
3.3. Residual stress by typical criterion and FEA
577
D400 : D2000 (Temp.) (a) 2.7 : 0.3 (100 oC) (b) 2.7 : 0.3 (120 oC) (c) 2.7 : 0.3 (140 oC) (d) 2.5 : 0.5 (120 oC) (e) 3.0 : 0.0 (120 oC)
(b)
30 (c)
(a)
20 (d)
Fig. 8(a) shows the behavior of the electrical resistivity for single carbon fiber/epoxy composites with curing temperature during curing process. As curing temperature increased, the difference in electrical resistivity before and after curing increased. This might be considered that relatively higher residual stress occurred for both the fiber and matrix at higher temperature. In Fig. 8(b), the difference in electrical resistivity before
10
0
5
10
20 40 60 80 100
Strain (%) Fig. 9. Comparison of stress–strain curves of neat epoxy resin as a function of curing conditions.
400
2.14 140oC
0
∆R
2.10 120oC
Stress (MPa)
Electrical Resistivity (x 10-3Ω ·cm)
0
2.06 100oC 2.02
-400
σr σθ σz τrθ τθz τzr
-800
-1200 1.98
σz
-1600
-2000
1.94 0
100
(a)
200
300
400
500
0
Time (min)
10
2.14
20
30
40
50
60
Z-Direction (mm)
(a) 2000
(2)
2.10
1800
(3)
∆R
2.06
2.02
1.98
(1) D400 : D2000 = 3.0 : 0 (2) D400 : D2000 = 2.5 : 0.5 (3) D400 : D2000 = 2.7 : 0.3
Equivalent Stress (MPa)
Electrical Resistivity ( x 10-3 Ω ·cm)
(1)
1600
1400
1200
1.94 0
(b)
100
200
300
400
500
1000 0
Time (min) (b)
Fig. 8. Comparison of electrical resistivity change depending on the curing conditions: (a) curing temperature; (b) curing agent composition.
10
20
30
40
50
60
Z-Direction (mm)
Fig. 10. Comparison of: (a) stress components of all directions; (b) equivalent residual stress built in the fiber by FEA.
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J.-M. Park et al. / Composites Science and Technology 65 (2005) 571–580
and after curing in the condition (3) with the optimum composition was largest under same curing temperature, whereas those of the condition (1) and (2) were smaller. Fig. 9 exhibits the stress–strain curve of neat epoxy resin as a function of curing condition. These curves are actually used for nonlinear analysis of residual stress by FEA. As curing temperature and the content of D400 curing agent with short chain length increased, matrix modulus increased whereas the elongation decreased. Fig. 10 shows the comparison of (a) all stress component and (b) equivalent stress of von Mises criterion built in the fiber by FEA. Residual stress on the fiber axial direction is highest, whereas the other stress is near zero and overlapped as shown in Fig. 10(a). Residual stress of the fiber axial direction, rz is trended to be similar to an equivalent stress of z-direction. This might be considered that the stress of the fiber axial direction has the significant effect on the total residual stress built on
the fiber. Fig. 11 exhibits (a) all stress component and (b) equivalent stress of built on the matrix. The stress of fiber axial direction is very small, whereas that of fiber circumference, rh and radial direction, rr is relatively higher. Total sum of the matrix stress in circumference and radial directions is similar to an equivalent stress of von Mises criterion. Minus and plus values are to indicate compressive and tensile stresses, respectively. It might be explained that two stress components with the circumference and radius direction have the effect on the total residual stress built in the matrix. Fig. 12 shows the equivalent stress of (a) the fiber and (b) the matrix by FEA. The equivalent stress of the fiber is small at the edge ends of model specimen and is larger at the center region, whereas that of matrix is high at the edge ends of specimen and is smaller at the center region. Both residual stresses built in the fiber and matrix increased with increasing curing temperature.
2000
10
σθ
6 σr τrθ
4
Stress (MPa)
Equivalent Stress of Fiber (MPa)
8
σθ τz
σz τzr
2 0 σz
-2 -4
σr
-6 -8
10
20
30
40
50
2.7g:0.3g (120oC)
1400 2.7g:0.3g (100oC)
1200 3.0g:0g (120oC)
0
10
(a)
Z-Direction (mm)
20
30
40
50
Z-Direction (mm) 18
Equivalent Stress of Matrix (MPa)
16
Equivalent Stress (MPa)
2.7g:0.3g (140oC)
60
18
14
12
10
(b)
2.5g:0.5g (120oC)
1600
1000
0
(a)
8
1800
0
01
20
30
40
50
Fig. 11. Comparison of: (a) stress components of all directions; (b) equivalent residual stress built in the matrix by FEA.
14 2.7g:0.3g (140oC)
12
2.7g:0.3g (120oC) 3.0g:0g (120oC)
10 2.7g:0.3g (100oC) 2.5g:0.5g (120oC)
8
60
Z-Direction (mm)
16
0
(b)
10
20
30
40
50
Z-Direction (mm)
Fig. 12. Equivalent residual stress by von Mises criterion depending on the curing conditions: (a) fiber; (b) matrix.
J.-M. Park et al. / Composites Science and Technology 65 (2005) 571–580
579
Table 3 Residual stress and IFSS of carbon fiber composites depending on the curing conditions No.
1 2 3 4 5 a b
Composition of curing agent D400
D2000
2.7 2.7 2.7 2.5 3.0
0.3 0.3 0.3 0.5 0
Curing temperature (C)
100 120 140 120 120
TEC (106/C)
77.4 69.1 64.3 81.8 53.6
Matrix modulus (GPa)
1.73 1.85 1.92 1.05 2.19
Residual stress by calculation
Residual stress by FEM
Chunga
Godab
Fiber
Matrix
1191 1347 1517 1595 1045
10.0 12.1 14.2 8.4 11.1
1375 1534 1713 1819 1189
13.0 15.3 16.8 13.1 14.7
IFSS (MPa)
DR (X)
25.1 31.5 35.3 28.0 26.3
157.5 260.0 365.3 239.4 194.0
Ref. [5]. Ref. [22].
Table 3 shows the comparison of residual stress, IFSS, and other parameters depending on the curing temperature and curing agent composition for SFC specimen. As curing temperature increased, IFSS increased and residual stresses increased. Residual stress of fiber and matrix by calculating method appeared nearly same trend as the value by the FEA. Both residual stresses resulted from the calculation and the simulation methods increased with increasing curing temperature. IFSS and the difference in electrical resistance showed the similar behavior like residual stress. For curing agent compositions, the maximum optimized residual stresses and IFSS showed for the ratio of D400 versus D2000 with 2.7:0.3, which have the moderate modulus of matrix.
atively higher at the fiber circumference and radial directions. The equivalent stress of the fiber is small at the edge ends of model specimen and is higher at the center region, whereas that of matrix is high in the edge ends of model specimen and is smaller in the center region. Ultimately, both residual stresses built in the fiber and matrix increased with increasing curing temperature. As curing temperature increased, both residual stresses between the fiber and matrix resulted from the criterion and FEA increased. During curing process, the measurement of electrical resistance can be a useful method to estimate temperature sensing and cure monitoring for conductive carbon fiber reinforced composites.
Acknowledgement 4. Conclusions Interfacial evaluation on temperature sensing and cure monitoring for the single-carbon fiber/epoxy composites were investigated by the measurement of electrical resistivity. IFSS and the difference in electrical resistivity before and after curing were highest at the smallest gauge length. In the medium gauge length, they changed exponentially, and then they did not show significant change at higher gauge length. As curing temperature was elevated, logarithmic electrical resistivity of steel fiber increased, whereas those of carbon and SiC fibers were trended to decrease due to the band theory. With increasing curing temperature, the difference in electrical resistivity before and after increased curing for carbon fiber composites. This might be considered that higher residual stress occurred in the fiber and matrix at higher curing temperature. With increasing contents of D400 curing agent with short chain length, elastic modulus increases, whereas other parameters such as IFSS and residual stress increased, and then decreased. This might be due to the optimum matrix modulus condition for the maximum performance of composites. Residual stress built in the fiber was highest at the fiber axial direction, whereas that of built in the matrix was rel-
This study was supported financially by the Korea Science and Engineering Foundation (KoSEF) through the Research Center for Aircraft Parts Technology (ReCAPT) and BK21 program, Gyeongsang National University, Korea. References [1] Bontea DM, Chung DDL, Lee GC. Damage in carbon fiberreinforced concrete, monitored by electrical resistance measurement. Cem Conc Res 2000;30:651–9. [2] Yuse K, Bathias C. Smart NDT using electrical resistance method for delamination monitoring in CFRP. In: Proceedings ICCM-12, Paris, France; 1999. p. 767–76. [3] Frakhanel B, Muller E, Frakhanel T, Siegel W. Conductive SiCfibre reinforced composites as a model of smart composnents. J Euro Ceram Soc 1998;18:1821–5. [4] Wang X, Chung DDL. Residual stress in carbon fiber embedded in epoxy, studied by simultaneous measurement of applied stress and electrical resistance. Compos Interf 1998;5:277–81. [5] Chung DDL. Thermal analysis of carbon fiber polymer–matrix composites by electrical resistance measurement. Thermoc Acta 2000;364:121–32. [6] Hodges J, Yates B, Darby MI, Wostenholm GH, Clemmet JF, Keates TF. Residual stresses and the optimum cure cycle for an epoxy resin. J Mater Sci 1989;24:1984–90. [7] Kim JS, Lee DG. On-line cure monitoring and viscosity measurement of carbon fiber epoxy composite materials. J Mater Process Technol 1993;37:405–16.
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[8] Twombly B, Shepard DD. Simultaneous dynamic-mechanical analysis and dielectric analysis of polymers (DMA–DEA). Intrum Sci Technol 1994;22:259–71. [9] Kim JS, Lee DG. Measurement of the degree of cure of carbon fiber epoxy composite materials. J Compos Mater 1996;30:1436–57. [10] Lee S, Springer GS. Effects of cure on the mechanical properties of composites. J Compos Mater 1988;22:15–29. [11] Genidy MS, Madhukar MS, Russell JD. Optimized cure cycle to minimize fiber stresses in polymer matrix composites. In: Proceedings ICCM-11 Gold Coast Australia IV. p. 171–80. [12] Hu X, Stanford JL, Young RJ. Strain measurement and deformation analysis in a diacetylene-containing urethane copolymer using Raman spectroscopy. Polymer 1994;35:80–5. [13] Landro LD, Palonca A, Sala G. Residual stresses in bismaleimide/carbon fiber composites laminate. Polym Compos 1995;16:176–283. [14] ODwyer MJ, Maistros GM, James SW, Tatam RP, Partridge IK. Relating the state of cure to the real-time internal strain development in a curing composite using in-fibre Bragg gratings and dielectrical sensors. Meas Sci Technol 9:1153–8. [15] Genidy MS, Madhukar MS, Russell JD. A feedback system to obtain an optimum cure cycle for thermoset matrix composite. In: 29th inter SAMPE techno conference. p. 302–16. [16] Madhukar MS, Genidy MS, Russell JD. A new method to reduce cure-induced stress in thermoset polymer composites, Part I: Test method. J Compos Mater 2000;34:1883–904. [17] Madhukar MS, Genidy MS, Russell JD. A new method to reduce cure-induced stress in thermoset polymer composites, Part II:
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closed loop feedback control system. J Compos Mater 2000;34:1905–25. Madhukar MS, Genidy MS, Russell JD. A new method to reduce cure-induced stress in thermoset polymer composites, Part III: correlating stress, history to viscosity, degree of cure, and cure shrinkage closed loop feedback control system. J Compos Mater 2000;34:1926–47. Detassis M, Pegoretti A, Migliaresi C, Wagner HD. Experimental evaluation of residual stress in single fibre composites by means of the fragmentation test. J Mater Sci 1996;31:2385–92. Landro LD, Palonca A, Sala A. Residual thermal stresses in bismaleimide/carbon fiber composite laminates. Polym Compos 1995;16:276–83. Drzal LT, Rich MJ, Koeing MF, Lloyd PF. Adhesion of graphite fibers to epoxy matrices: II. The effect of fiber finish. J Adhes 1983;16:133–52. Goda K, Park JM, Netravali AN. New theory to obtain Weibull fibre strength parameters from a single-fibre composite test. J Mater Sci 1995;30:2722–8. Van Vlack LH. Conductive material. Korea edition.. Elements of materials science and engineering, vol. 11. Reading (MA): Addison-Wesley; 1991. p. 318–434. Wnek GE. Electrically conductive polymer composites. In: Skothein TA, editor. Handbook of conducting polymers, vol. 1. New York: Marcel Dekker; 1986. p. 205–12. Epstein AJ. AC conductivity of polyacethylene: distinguishing mechanisms of charge transport. In: Skothein TA, editor. Handbook of conducting polymers, vol. 2. New York: Marcel Dekker; 1986. p. 1041–91.
Cure monitoring and residual stress sensing of single-carbon fiber reinforced epoxy composites using electrical resistivity measurement Joung-Man Park
a,*
, Sang-Il Lee a, Jin-Ho Choi
b
a
b
Department of Polymer Science and Engineering, Research Center for Aircraft Parts Technology, Gyeongsang National University, Chinju 660-701, Republic of Korea School of Transport Vehicle Engineering, Research Center for Aircraft Parts Technology, Gyeongsang National University, Chinju 660-701, Republic of Korea Received 25 July 2003; received in revised form 12 February 2004; accepted 1 September 2004 Available online 19 November 2004
Abstract Temperature sensing and cure monitoring of the single-carbon fiber/epoxy composites were studied by the measurement of electrical resistivity as a new approach. IFSS and the difference in electrical resistivity (DR) between before and after curing were highest for the smallest gauge length of the specimen. As curing temperature increased, logarithmic electrical resistivity of steel fiber increased due to the increased the mean path of the free electron. On the other hand, those of semi-conductive carbon and SiC fibers decreased due to the intrinsic electrical properties based on the band theory. Residual stress built in the fiber was highest at the fiber axis direction, whereas residual stress of built in the matrix was relatively higher for the fiber circumference and radius direction. Residual stresses by the calculating method were consistent well with those from the finite element analysis (FEA). The behavior of electrical resistivity was responded well quantitatively with the change of curing temperature and epoxy matrix modulus. Electrical resistance measurement of conductive fiber composites can be applicable for the useful technique to evaluate cure monitoring and residual stress sensing. 2004 Elsevier Ltd. All rights reserved. Keywords: B. Interfacial strength; C. Residual stress; D. Acoustic emission; Electrical resistivity; Cure monitoring
1. Introduction Recently a new evaluation technique of interfacial properties as well as curing characteristics and the residual stress were investigated by the measurement of electrical resistivity using various conductive fiber reinforced composites. The conductive fiber reinforced composites were studied as new self-strain and/or selfdamage health monitoring sensors under temperature change and under applied load [1–3]. *
Corresponding author. Tel.: +82 55 751 5300/591 751 5300; fax: +82 55 752 0075/591 752 0075. E-mail address: [email protected] (J.-M. Park). 0266-3538/$ - see front matter 2004 Elsevier Ltd. All rights reserved. doi:10.1016/j.compscitech.2004.09.019
Temperature sensing and cure monitoring have been studied as an economical new evaluation for the monitoring of curing characteristics, interfacial properties and nondestructive behavior because conductive fiber can act as a sensor in itself as well as a reinforcing fiber [4,5]. The electrical resistance difference and residual stress were investigated for single carbon fiber composite, and residual stress affected on the interfacial adhesion between fiber and matrix in composite materials [4]. For carbon fiber/polymer composites, the endothermic peak at the annealing temperature and frictional change in electrical resistance were studied by differential scanning calorimetry (DSC) and DC electrical resistance measurement. During cyclic heating/cooling
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processes, thermal interlaminar damages were also evaluated by the measurement of contact resistivity of carbon fiber laminates [5]. Cure monitoring and their characterization including residual stress were studied by means of the common methods such as thermal and dielectric analysis. To minimize residual stress in the thermosetting epoxy, the optimum cure cycle was evaluated using dilatometer and DSC. The volume change depending on the elapsed time and temperature was measured during various curing cycles. In DSC the differential heat flow between the sample and the reference was measured with linearly programmed temperature rise [6]. Dielectric sensor was used to measure the cure degree of carbon fiber/epoxy composite. Dielectric analysis or dielectrometry can be used to investigate the processing characteristics and chemical structure of polymers and other organic materials by measuring their dielectric properties. Under electrical field, the change of electrical dipole alignment and the charged ion mobility can be used to infer the information concerning on the bulk material properties, such as its viscosity, rigidity, reaction rate, and cure state, etc. During cure monitoring, dipoles and charged ions in dielectric materials could be rearranged under AC electrical filed. The alignment of dipoles and ions might be allowed during curing. However, the alignment could be difficult as the curing progressed [7–9]. Residual stress in the fiber-reinforced composite occurred usually due to thermal contraction of the matrix or the difference of thermal expansion coefficient (TEC) between fiber and matrix. This stress may affect on the interface between fiber and matrix, and may have a great influence on the mechanical performance of microcomposites. Residual stress can affect actually on the fiber stress or the interfacial shear strength (IFSS) [10,11]. The measurement of residual stress/strain on the fiber can be measured by Raman scattering method [12,13] and other optical technique [14]. These techniques are difficult to measure directly residual stress because the fiber strain is anisotropy and the fiber is embedded in the matrix. Genidy et al. [11,15] and Madhukar et al. [16– 18] attempted to measure directly residual compressive stress to obtain optimized curing cycle with free stress. Inhomogeneous structure of polymeric composites causes to develop internal stresses due to matrix volume change during curing. Volume change occurs during curing and cooling down processes. Most of the previous studies [11–18] on residual stress were concentrated on the stress development during cooling down. A new testing method in this work was used to monitor the fiber stress that developed around single fiber composites (SFC) during heating or cooling. A relationship between cure cycle and residual stress was studied and it was
shown that cure-induced stress and residual stress vary with different resin types. The residual stress in SFC was experimentally evaluated by the technique based on the continuous monitoring during fragmentation testing [19]. The difference between the strain at the break of a single fiber in air and the strain embedded in a polymer matrix could be measured as a function of temperature. By considering the compressive fiber modulus, the strain difference might be converted into fiber compressive stress related to the matrix thermal shrinkage after curing the specimen [19]. Residual stress in bismaleimide/carbon fiber composite model depending on the curing cycle was studied using finite element analysis (FEA) [20]. The comparison of theoretical prediction, numerical simulation, and the experimental result shows a generally good agreement. In this work, during curing process, the electrical resistance of carbon fiber composite was measured to evaluate curing characteristics and residual stress change depending on the gauge length, curing temperature and matrix modulus with differing curing agent ratios. Residual stress was measured by the von Mises criterion and then the equivalent stress was evaluated by FEA. The relationship between the electrical resistivity, residual stress and IFSS was investigated for single carbon fiber/epoxy composites. Ultimately the temperature sensing and cure monitoring were correlated by the electrical resistance measurement.
2. Experimental 2.1. Materials Carbon fiber of 8 lm (Taekwang Industrial Co., Korea) and of 18 lm (Mitsubishi Chemical Co., Japan) in average diameter was used as conductive reinforcing materials. SiC fiber (Textron Co.) of 138 lm and steel fiber (No. 1 guitar string of Segovia Instruments Co., Korea) of 280 lm were used for comparison. Testing specimens were prepared with epoxy resin (YD-128, Kukdo Chemical Co., Korea). Epoxy resin is based on diglycidyl ether of bisphenol-A (DGEBA). Polyoxypropylene diamines (Jeffamine D-400 and D-2000, Huntzman Petrochemical Co.) were used as curing agents. The flexibility of specimens was controlled by mixing ratio of D-400 versus D-2000. 2.2. Methodologies 2.2.1. Preparation of testing specimens Two type specimens were prepared for electro-micromechanical test and curing monitoring. Fig. 1(a) exhibits a dogbone-shaped specimen to measure electrical resistivity change during curing, and then to evaluate IFSS
J.-M. Park et al. / Composites Science and Technology 65 (2005) 571–580 Silver Paste A
2 mm
th
Cu rre nt Co V ol nt ta ac ge t Co s nt ac ts
B
G
au
ge
Le
ng
5 mm
D
C
Carbon fiber
(a)
Current Contacts Voltage Contacts 10 mm AB 1.2 mm
C D
Carbon Fiber Silver Paste
Epoxy
(b)
Teflon Release Film
Fig. 1. Schematic illustration of two-type testing composites for: (a) electro-micromechanical test; (b) cure monitoring.
of the microcomposite was monitored during curing process. Electrical resistivity was obtained from the measured electrical resistance, cross-sectional area of the conductive fiber, A, and electrical contact length, Lec of the testing fiber connecting to copper wires. The relationship between electrical resistivity, q and resistance, R is as follows: A q¼ R: ð1Þ Lec Electrical resistance was measured by four-point probe method as shown in Fig. 1(b). Silver paste was used as electrically connecting glue at junctions A, B, C and D to maintain electrical contact between the fiber and leading wires. The voltage was measured between junctions B and C, and the current was measured between junctions A and D. Total electrical resistance, RTot between B and C may include Rc based on the contact resistance by silver paste beside Rf due to the electrical resistance by the fiber as follows: RTot ¼ Rc þ Rf :
as a function of measuring gauge length, such as 2, 5, 32, 60, 100 mm. Fig. 1(b) shows single carbon fiber/epoxy composites to measure the electrical resistivity during curing process. To make dogbone-type specimen for measuring the electrical resistance and evaluating the IFSS, single carbon fiber was fixed with the axial direction in a silicone mold. After carbon fiber and lead wires were electrically connected using silver paste, epoxy resin was poured into the silicone mold, and then epoxy was cured as scheduled curing steps. For the specimen for measuring electrical resistance, two pairs of narrow copper wires were fixed transversely on a mold-releasing teflon film with attaching guide tapes, and then single fiber was laid down with the longitudinal direction. The guide tapes can prevent the overflow of resin and specimens dimension was measured after curing. A silver paste was used to connect electrically at the intersecting point between carbon fiber and copper wires. After the suitable amount of epoxy resin was poured into the silicone mold, single carbon fiber/epoxy composite was cured. 2.2.2. Electrical resistance measurement During the curing process, the electrical resistance was measured using a digital multimeter (HP34401A). For the curing monitoring, curing cycle was set up as three steps that were composed of the precuring step at 80 C for 1 h, the postcuring step at 120 C for 1 h and finally slow cooling step at room temperature for 6 h. Curing process of all microcomposites was performed in a drying oven. After a testing specimen was placed in the oven, the composite and the multimeter were connected electrically using very thin copper wires. Electrical resistance
573
ð2Þ
Since the value of Rc is negligibly small due to very high conductivity of silver paste comparing to Rf, it can be considered that the voltage developed between junctions B and C becomes nearly fibers resistance RTot ffi Rf :
ð3Þ
2.2.3. IFSS measurement To measure IFSS depending on the gauge length, curing temperature and surface treatment, a specially designed mini-tensile testing machine was used with a polarized-light microscope. After the testing specimen was fixed in the mini-tensile testing machine, the composite was incrementally strained and the fiber was broken into small fragments. Load was applied until no longer fiber breaks occurred, and then the critical fiber fragment length, lc was measured under an optical microscope equipped with a calibrated eyes piece lens. IFSS was determined by Drzals equation [21] that was modified from Kelly–Tysons equation. By introducing Weibull distribution for aspect ratio, the IFSS was exhibited in the form as follows: rf 1 s¼ C 1 ; ð4Þ b 2a where a and b are scale and shape parameters of Weibull distribution for aspect ratio (lc/d), and C is gamma function. Since the fiber tensile strength is very difficult to measure directly at the critical fragment length (usually less than 1 mm), fiber strength at such a very short length can be resulted from calculating method. After fiber strength was usually determined at the measurable gauge length with 2 mm, it was subjected to subsequent extrapolation to smaller gauge length using Weibull
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weakest link rule [22]. Tensile strength at a critical fragment length can be obtained as follows: rf ¼ r0
1=q lc ; l0
ð5Þ
where r0 is the fiber tensile strength at measurable gauge length, and q is the shape parameter of Weibull distribution for fiber tensile strength. 2.2.4. Residual stress from typical criterions and FEA It is commonly known that residual stress occurred by the different TEC between fiber and matrix during curing and subsequent cooling process. If interfacial adhesion is perfect and the strain of matrix and fiber is the same value, the relationship among residual stress, TEC and elastic modulus could be designated as follows: rRf rRm þ af DT ¼ þ am DT ; Ef Em
ð6Þ
where rRf is the longitudinal residual stress built up in the fiber, rRm is the residual stress built up in the matrix, Ef is the modulus of fiber, Em is the modulus of matrix, af is TEC of fiber, am is TEC of matrix, and DT is the temperature change. A following equation is usually satisfied since there is no external force on the microspecimen: rf V f þ rm V m ¼ 0;
tion of matrix is too high in the SFC, the residual stress of matrix can generally be estimated by the following equation: rRm ¼ ðam af Þ DT EðeÞ;
ð9Þ
where E(e) is the modulus which obtained from the measured stress–strain curve of the specimen. TEC of the fiber is smaller than that of the matrix, and may be neglected in the calculating Eq. (9). The residual stress, resulted from the experimentally calculating method, has been correlated with the value estimated from FEA using commercial ANSYS 5.5. Fig. 2 shows FEA model and the element mesh. The quarter section of the microspecimen was only modeled because geometrical symmetry was considered in the specimen structure. The total number of nodes and element were 22,649 and 19,600, respectively. Nonlinear approach in FEA was used under the multi-linear curve resulted from true stress–strain curve. The each stress components, acted on the fiber and matrix, were converted into von Mises equivalent stress. The relationship between stress components and equivalent residual stress was designated by von Mises criterion
ð7Þ
where Vf and Vm are the volume fraction of fiber and matrix, respectively. Combining Eqs. (6) and (7), the following equation was designated for calculating the residual stress in the fiber: rRf ¼
Ef Em V m ðam af Þ DT : ðV m Em þ V f Ef Þ
Carbon Fiber
ð8Þ
The shrinkage of the epoxy is higher than that of the carbon fiber. The residual stress of matrix in SFC was calculated simply from TEC of each components and the modulus of SFC specimen. Because the volume frac-
Epoxy Matrix
Fig. 2. Quarter model for FEA simulation of residual stress.
Table 1 Interfacial properties and electrical resistivity before and after curing process Gauge length (mm)
Electrical resistivity Before cure
2 5 32 60 100 a b c
1.96 1.84 1.95 1.85 1.97
(0.2)c (0.2) (0.1) (0.1) (0.1)
Average fragment length (mm)
After cure
D Resistivity (103 X cm)
2.42 2.03 2.02 1.90 2.02
0.47 0.19 0.08 0.05 0.05
(0.2) (0.3) (0.1) (0.1) (0.1)
Drzal equation: sd = (rf/2a) Æ C [1 (1/b)]. Kelly–Tyson: sk = (rf Æ d)/(2 Æ lc). Standard deviation, 5 specimens were used.
(0.13) (0.07) (0.02) (0.01) (0.00)
358.8 489.9 592.0 595.5 598.5
IFSS (MPa) Drzala
Kellyb
64.2 42.1 33.6 33.2 33.6
56.0 38.7 31.0 30.7 30.6
J.-M. Park et al. / Composites Science and Technology 65 (2005) 571–580 80
1.0
rffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi h iffi 2 2 2 1 2 2 2 req ¼ 2 ðrr rh Þ þ ðrh rz Þ þ ðrz rr Þ þ 6srh þ 6shz þ 6szr ;
0.8
ð10Þ
∆ (Resistivity) IFSS
0.6 40 0.4
∆ (Resistivity)
60
IFSS (MPa)
575
where r is the normal stress, s is the shear, subscript r, h, z are the fiber radius direction, the fiber circumference direction, and the fiber axis direction.
3. Results and discussion
20 0.2
3.1. Electrical resistivity and IFSS
0.0
0
2
5
32
60
100
Gauge Length (mm) Fig. 3. Comparison of difference in electrical resistivity before and after curing and IFSS depending on the gauge length.
σf τ 0
(a) 5mm
σf τ
0
(b) 32 mm
σf τ
0
Table 1 and Fig. 3 show interfacial properties and the electrical resistivity of the single carbon fiber composites depending on the gauge length using fragmentation test and during cure monitoring. As gauge length increased, average fragment length increased whereas IFSS decreased. It might be considered that fiber strength increased at critical fragment length by weakest link rule and average IFSS in longitudinal direction decreased as shown in Fig. 4. Fig. 4 exhibits a schematic illustration of fiber strength and IFSS as a function of gauge length in SFC specimen. As gauge length increased, average IFSS decreased although fiber strength was not remarkably changed. The difference in electrical resistivity before and after curing was highest at the gauge length with 2 mm. The difference in electrical resistivity decreased exponentially until 60 mm, and then they did not show significant change at higher gauge length. The difference in electrical resistivity could be expected to occur from the thermal residual stress due to the mismatch of TEC between fiber and matrix during curing process. This phenomenon might be because average residual stress diminished with increasing gauge length. 3.2. Electrical resistivity during curing process
(c) 60mm Fig. 4. Schematic illustrations of fiber strength and average IFSS depending on the gauge length in SFC.
Table 2 shows the electrical and mechanical properties of four-type conductive fibers. Electrical resistance was measured at the distance between two voltage contacts with 32 mm, whereas mechanical properties were
Table 2 Intrinsically electrical and mechanical properties of various conductive fibers Fiber
Diameter (lm) a
Carbon Carbonb SiCc Steeld a b c d e
8 18 138 280
Electrical resistance (X) 4
1.19 · 10 (570) 1.57 · 103 (120) 0.34 · 103 (10) 0.57 (0.07)
Electrical resistivity (104 X cm)
Tensile strength (MPa)
Elastic modulus (GPa)
18.6 (0.9)e 12.5 (1.0) 156.8 (5.3) 1.09 (0.14)
2828 1772 3613 1461
245 212 162 193
PAN based (Taekwang Industrial Co., Korea). Pitch coal tar based (Mitsubishi Chemical Co., Japan). Made in Textron Co. No. 1 string of guitar (Segovia Instruments Co., Korea). Standard deviation.
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measured at 20 mm in gauge length, respectively. Electrical resistance was very different among four conductive fibers due to differing intrinsic ingredients and materials unique characteristics. Fig. 5 shows the comparison of electrical resistivity change in bare fiber without matrix and single-fiber embedded epoxy composite during curing process. As curing temperature increased, logarithmic electrical resistivity of steel fiber increased, whereas that of carbon fiber was trended to decrease. Electrical resistivity of SiC fiber exhibits nearly same behavior like carbon fiber. This might be due to the difference of inherent electrical properties between steel and carbon fibers based on the band theory [23–25]. Logarithmic electrical resistivity of three bare fibers before curing is equal to the value after curing. On the other hands, electrical resistivity of their composites after curing was higher than that of the before curing. It might be explained that residual stress occurred during curing due to the different TEC between fiber and matrix. Fig. 6 shows schematic models based on the band theory for three different type materials. Electron cannot jump from the filled level to the empty level because the energy gap is too wide in insulator. In semiconductor, e.g., carbon and SiC fiber, the electron jumping between the filled and the empty level occur partially above 0 K. Electrons are free to jump without activation energy because no energy gap exists in conductor such as steel fiber. Fig. 7(a) exhibits the comparison of schematic models for the fine structure of metallic steel fiber in order to explain electrical behavior. As the curing temperature increases, the activated mobility increases; stereo-regularity of metal lattice decreases; the mean path of
Empty level
Empty level
Empty level
Energy gap
Filled level
Filled level
Filled level
Conductor (Metal) Semiconductor
Insulator Fig. 6. Comparison of energy gap for three materials based on the band theory.
Elevated Temperature e-
Disorder structure
Increasing T
Room Temperature e-
(a)
-1.81
SiC fiber/epoxy
-1.82
Bare SiC fiber
Conduction electron
-1.83
140
-1.84
120
-1.85 -2.74
Carbon fiber/epoxy
-2.75
Bare carbon fiber
-2.76
100 80 60
-4.55 -4.60 Temperature
-4.65
Steel fiber/epoxy
-4.70 -4.75
Stereo-regular bcc structure
40
Conduction band (Empty level)
Temperature (oC)
Log [Electrical Resistivity (Ω ·cm)]
-1.80
Energy gap
20
Electron hole
Bare steel fiber
0
100
200
300
400
0 500
Time (min) Fig. 5. Comparison of logarithmic electrical resistivity as a function of curing temperature in three bare fibers and their composites during curing process.
Valence band (Filled level)
(b) Fig. 7. Schematic illustration of: (a) fine molecular structure in the steel fiber; (b) conduction and valence bands in the carbon or SiC fibers.
J.-M. Park et al. / Composites Science and Technology 65 (2005) 571–580
free electron increases; and then electrical conductivity decreases. The energy gap is known to be existed for semi-conductive SiC and carbon fibers. As the temperature increases, the mobility, the number and density of jumping free electron increases as designated in Fig. 7(b). It means that electrical conductivity increases and thus electrical resistivity decreases.
50
(e)
Stress (MPa)
40
3.3. Residual stress by typical criterion and FEA
577
D400 : D2000 (Temp.) (a) 2.7 : 0.3 (100 oC) (b) 2.7 : 0.3 (120 oC) (c) 2.7 : 0.3 (140 oC) (d) 2.5 : 0.5 (120 oC) (e) 3.0 : 0.0 (120 oC)
(b)
30 (c)
(a)
20 (d)
Fig. 8(a) shows the behavior of the electrical resistivity for single carbon fiber/epoxy composites with curing temperature during curing process. As curing temperature increased, the difference in electrical resistivity before and after curing increased. This might be considered that relatively higher residual stress occurred for both the fiber and matrix at higher temperature. In Fig. 8(b), the difference in electrical resistivity before
10
0
5
10
20 40 60 80 100
Strain (%) Fig. 9. Comparison of stress–strain curves of neat epoxy resin as a function of curing conditions.
400
2.14 140oC
0
∆R
2.10 120oC
Stress (MPa)
Electrical Resistivity (x 10-3Ω ·cm)
0
2.06 100oC 2.02
-400
σr σθ σz τrθ τθz τzr
-800
-1200 1.98
σz
-1600
-2000
1.94 0
100
(a)
200
300
400
500
0
Time (min)
10
2.14
20
30
40
50
60
Z-Direction (mm)
(a) 2000
(2)
2.10
1800
(3)
∆R
2.06
2.02
1.98
(1) D400 : D2000 = 3.0 : 0 (2) D400 : D2000 = 2.5 : 0.5 (3) D400 : D2000 = 2.7 : 0.3
Equivalent Stress (MPa)
Electrical Resistivity ( x 10-3 Ω ·cm)
(1)
1600
1400
1200
1.94 0
(b)
100
200
300
400
500
1000 0
Time (min) (b)
Fig. 8. Comparison of electrical resistivity change depending on the curing conditions: (a) curing temperature; (b) curing agent composition.
10
20
30
40
50
60
Z-Direction (mm)
Fig. 10. Comparison of: (a) stress components of all directions; (b) equivalent residual stress built in the fiber by FEA.
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and after curing in the condition (3) with the optimum composition was largest under same curing temperature, whereas those of the condition (1) and (2) were smaller. Fig. 9 exhibits the stress–strain curve of neat epoxy resin as a function of curing condition. These curves are actually used for nonlinear analysis of residual stress by FEA. As curing temperature and the content of D400 curing agent with short chain length increased, matrix modulus increased whereas the elongation decreased. Fig. 10 shows the comparison of (a) all stress component and (b) equivalent stress of von Mises criterion built in the fiber by FEA. Residual stress on the fiber axial direction is highest, whereas the other stress is near zero and overlapped as shown in Fig. 10(a). Residual stress of the fiber axial direction, rz is trended to be similar to an equivalent stress of z-direction. This might be considered that the stress of the fiber axial direction has the significant effect on the total residual stress built on
the fiber. Fig. 11 exhibits (a) all stress component and (b) equivalent stress of built on the matrix. The stress of fiber axial direction is very small, whereas that of fiber circumference, rh and radial direction, rr is relatively higher. Total sum of the matrix stress in circumference and radial directions is similar to an equivalent stress of von Mises criterion. Minus and plus values are to indicate compressive and tensile stresses, respectively. It might be explained that two stress components with the circumference and radius direction have the effect on the total residual stress built in the matrix. Fig. 12 shows the equivalent stress of (a) the fiber and (b) the matrix by FEA. The equivalent stress of the fiber is small at the edge ends of model specimen and is larger at the center region, whereas that of matrix is high at the edge ends of specimen and is smaller at the center region. Both residual stresses built in the fiber and matrix increased with increasing curing temperature.
2000
10
σθ
6 σr τrθ
4
Stress (MPa)
Equivalent Stress of Fiber (MPa)
8
σθ τz
σz τzr
2 0 σz
-2 -4
σr
-6 -8
10
20
30
40
50
2.7g:0.3g (120oC)
1400 2.7g:0.3g (100oC)
1200 3.0g:0g (120oC)
0
10
(a)
Z-Direction (mm)
20
30
40
50
Z-Direction (mm) 18
Equivalent Stress of Matrix (MPa)
16
Equivalent Stress (MPa)
2.7g:0.3g (140oC)
60
18
14
12
10
(b)
2.5g:0.5g (120oC)
1600
1000
0
(a)
8
1800
0
01
20
30
40
50
Fig. 11. Comparison of: (a) stress components of all directions; (b) equivalent residual stress built in the matrix by FEA.
14 2.7g:0.3g (140oC)
12
2.7g:0.3g (120oC) 3.0g:0g (120oC)
10 2.7g:0.3g (100oC) 2.5g:0.5g (120oC)
8
60
Z-Direction (mm)
16
0
(b)
10
20
30
40
50
Z-Direction (mm)
Fig. 12. Equivalent residual stress by von Mises criterion depending on the curing conditions: (a) fiber; (b) matrix.
J.-M. Park et al. / Composites Science and Technology 65 (2005) 571–580
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Table 3 Residual stress and IFSS of carbon fiber composites depending on the curing conditions No.
1 2 3 4 5 a b
Composition of curing agent D400
D2000
2.7 2.7 2.7 2.5 3.0
0.3 0.3 0.3 0.5 0
Curing temperature (C)
100 120 140 120 120
TEC (106/C)
77.4 69.1 64.3 81.8 53.6
Matrix modulus (GPa)
1.73 1.85 1.92 1.05 2.19
Residual stress by calculation
Residual stress by FEM
Chunga
Godab
Fiber
Matrix
1191 1347 1517 1595 1045
10.0 12.1 14.2 8.4 11.1
1375 1534 1713 1819 1189
13.0 15.3 16.8 13.1 14.7
IFSS (MPa)
DR (X)
25.1 31.5 35.3 28.0 26.3
157.5 260.0 365.3 239.4 194.0
Ref. [5]. Ref. [22].
Table 3 shows the comparison of residual stress, IFSS, and other parameters depending on the curing temperature and curing agent composition for SFC specimen. As curing temperature increased, IFSS increased and residual stresses increased. Residual stress of fiber and matrix by calculating method appeared nearly same trend as the value by the FEA. Both residual stresses resulted from the calculation and the simulation methods increased with increasing curing temperature. IFSS and the difference in electrical resistance showed the similar behavior like residual stress. For curing agent compositions, the maximum optimized residual stresses and IFSS showed for the ratio of D400 versus D2000 with 2.7:0.3, which have the moderate modulus of matrix.
atively higher at the fiber circumference and radial directions. The equivalent stress of the fiber is small at the edge ends of model specimen and is higher at the center region, whereas that of matrix is high in the edge ends of model specimen and is smaller in the center region. Ultimately, both residual stresses built in the fiber and matrix increased with increasing curing temperature. As curing temperature increased, both residual stresses between the fiber and matrix resulted from the criterion and FEA increased. During curing process, the measurement of electrical resistance can be a useful method to estimate temperature sensing and cure monitoring for conductive carbon fiber reinforced composites.
Acknowledgement 4. Conclusions Interfacial evaluation on temperature sensing and cure monitoring for the single-carbon fiber/epoxy composites were investigated by the measurement of electrical resistivity. IFSS and the difference in electrical resistivity before and after curing were highest at the smallest gauge length. In the medium gauge length, they changed exponentially, and then they did not show significant change at higher gauge length. As curing temperature was elevated, logarithmic electrical resistivity of steel fiber increased, whereas those of carbon and SiC fibers were trended to decrease due to the band theory. With increasing curing temperature, the difference in electrical resistivity before and after increased curing for carbon fiber composites. This might be considered that higher residual stress occurred in the fiber and matrix at higher curing temperature. With increasing contents of D400 curing agent with short chain length, elastic modulus increases, whereas other parameters such as IFSS and residual stress increased, and then decreased. This might be due to the optimum matrix modulus condition for the maximum performance of composites. Residual stress built in the fiber was highest at the fiber axial direction, whereas that of built in the matrix was rel-
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