INFLUENCE OF THE TESTING GAGE LENGTH IN THE STRENGTH, YOUNG S MODULUS AND WEIBULL MODULUS OF CARBON FIBRES ABSTRACT

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1 INFLUENCE OF THE TESTING GAGE LENGTH IN THE STRENGTH, YOUNG S MODULUS AND WEIBULL MODULUS OF CARBON FIBRES Saulo Santesso Garrido (*), Luiz Claudio Pardini (**) (*) Universidade Estadual Paulista Instituto de Química Araraquara SP (**) Centro Técnico Aeroespacial Instituto de Aeronáutica e Espaço Divisão de Materiais AMR São José dos Campos SP ABSTRACT Carbon Fibres are the most used reinforcement for advanced composites. due to their superior electrical and mechanical properties and light weight, which in turn is translated into a high strength/density ratio composite. Their usefulness is intrisically related to their microstructure, i.e., amount of functional groups, degree of heat treatment and porosity. The amount of functional groups has a strong influence on the composite properties while heat treatment and porosity are responsible for carbon fibre s strength and modulus. During processing a number of cracks, voids and fibrillar misalignments, are created either during the PAN precursor processing and during heat treatment to final convertion to carbon. Such inhomogeneities give rise to an appreciable scatter in carbon fibres strength. Their brittle failure behaviour and scatter in strength are characteristic features of any other ceramics material. The most used statistical tool that deals with this characteristic variability in properties is the Weibull statistics, either as a statistical process control tool or during qualification programs. Thus, the present work investigated the influence of the testing gage length in the strength, Young s modulus and Weibull modulus of carbon fibres in order to stablish a guideline tool for a qualification procedure for these materials. Filaments of gage length of 25 mm, 5 mm, 75 mm and 1 mm were tested. The increase in the gage length leads to a decrease in carbon fibre s strength due to an increase in flaw population. The Young s modulus was calculated by two methods: (i) interaction between testing equipment/specimen and (ii) ASTM D3379M. The first method proved to be more accurate considering manufacture s data for Young s Modulus (28 GPa). The Weibull modulus calculated from the tensile tests for gage lengths tested varied from 5, to 5,5 indicating a good homogeneity in terms of properties and a good control of processing parameters. Key-words : Carbon Fibres, Young s modulus, Tensile Strength, Weibull modulus. CONGRESSO BRASILEIRO DE ENGENHARIA E CIÊNCIA DOS MATERIAIS, 14., 2, São Pedro - SP. Anais 2411

2 INTRODUCTION A considerable progress over the past three decades has been made in the carbon fibre technology, but as many other things, they are not created equal. Many factors contribute to this variability in properties, and the first of all is the raw material. Carbon fibres are mainly manufactured by spinning termoplastic fibres, predominantly polyacrilonitrile and pitch, which under controlled drawing and pyrolysis are converted to stiff oriented carbon. As a consequence their mechanical properties vary according to the characteristics of the precursor fibre and the processing itself. During precursor manufacturing and further heat treatment a lot of defects are created, such as, fibrilar misalignments and many ultramicropores, and one can expect a scatter in carbon fibre s strength. Thus, it is necessary to implement a statistical process control or qualification programs in order to reduce variability of carbon fiber key characteristics, because properties of structural composites are a function of both fibre distribution strength at short gauge lengths and fibre elastic modulus. On the other hand, composite properties are highly influenced by fibre/matrix bonding. As mentioned before, statistical process control or qualification programs applied to carbon fibres are based on evaluation of mechanical properties. Tensile strength is very easy to measure on carbon fibres. Although carbon fibre filaments are very thin ( 7,5 µm diameter) they can be easily fitted in paper tab and tensile tests can be easily performed. On the other hand, their inherent brittleness cause dificulties to measure deformation by standard strain-sensing devices, such as strain-gages, extensometers, etc, or by other more sophisticated and expensive techniques such as optical methods. So, the purpose of this work is to use two alternative methologies, the first one based on the system compliance, as stated in the ASTMD3379, and the second into account the rigidity of the equipment where carbon fibres are tested. In the latter method the result of the tensile test, plot of force as function of elongation, reflect the interaction between the testing equipment and specimen under test (Guimaraes 1978). Both methods used the same set of data for calculations. Unlike physical parameters such as elastic modulus, density, etc, filament strength is a statistical parameter which can not be fully described by a single value. The most used statistical tool to describe the variability in strength for materials which exhibit brittle catastrophic failure, such as carbon fibres, is the Weibull distribution, which in turn gives the Weibull modulus by properly treating the strength data. The Weibull modulus is not a material constant but gives a good indication of how homogeneous is the material. CONGRESSO BRASILEIRO DE ENGENHARIA E CIÊNCIA DOS MATERIAIS, 14., 2, São Pedro - SP. Anais 2412

3 MATERIALS AND EXPERIMENTAL In the present work the carbon fibre studied was a PAN-based high strength type manufactured by Hexcel Carbon Fibres, under the trade name of AS4-GP. The carbon fibres were tested according to ASTM D3379M Standard. The fibres were cut in dissimilar positions from the fibre tow assuring a random selection of single filaments. Gage lengths of 25 mm, 5 mm, 75 mm and 1 mm were prepared by moulting in a paper support tab, as shown in Figure 1. The testing speed was 2,5 mm/min and graphic paper speed was 2 mm/min, giving a ratio of,125 mm. The testing machine used during the work was an Instron 1131, and a load cell of 5 gf. filament test speciment length Figura 1 Support tab for testing fibre filaments according to ASTM D3379M. The tensile test give us a load as a function of extension curve up to failure. Tensile strength was calculated as follows: σ = F/A (2) Where F = force to failure (N), A = average filament area (4, m 2 ). The carbon fibre modulus was calculated following two procedures. The first is described in ASTM D3379M Standard. The procedure suggests that indicated compliance is first calculated as follows: Ca = (I/P).(H/S) (3) Where I = total extension for straight line section of load/time curve extrapolated across full chart scale (mm), H = crosshead speed (mm/s), P = full scale force (N), S = chart speed (mm/s). The true compliance is then calculated as: C = C a C s (4) Where C = true compliance (mm/n), Cs = system compliance (mm/n). The Young s Modulus is calculated as a corrected value by the equation : Ym = L/(C.A) (5) Where Ym = Young s modulus (GPa), L = specimen gage length (mm), C = True compliance (mm/n), and A = average filament area (m 2 ). CONGRESSO BRASILEIRO DE ENGENHARIA E CIÊNCIA DOS MATERIAIS, 14., 2, São Pedro - SP. Anais 2413

4 Fiorce (gf) full scale θ extension (mm) I Figure 2 Graphic representation of a tensile test of a carbon fibre single filament. The second method to correct the Young s modulus value followed a procedure which takes into account the interaction equipment/specimen described by Guimarães (1978). According to this method the equipment and the specimen are considered as two springs in series, as shown in Figure 3, one representing the testing machine, having a rigidity Km, and the other the specimen, having a rigidity proporcional to the Young s modulus, as follows (Guimarães 1978) : 1/Ks = 1/Km + (1/E).L/A (6) where Ks is the rigidity of the system, L is the specimen lenght, E = Young s modulus, A = cross section area of the specimen. In the early beginning of the test, the specimen is in the elastic regime and the slope of the load/extension curve can be used to calculate Ks, as follows: Ks = (tg θ o ) -1 (7) The angle θ o is measured, as indicated in Figure 2, and Young s modulus can be calculate by the equation 8: Km = [tg θ o -1 ((Lo/Ao)/E)] -1 (tg θ o ) -1 = 1/Km + 1/E (Lo/Ao) (8) where Lo and Ao are the initial lengtht and cross section area of the specimen. CONGRESSO BRASILEIRO DE ENGENHARIA E CIÊNCIA DOS MATERIAIS, 14., 2, São Pedro - SP. Anais 2414

5 P = K. δ Xm e testing machine L σ = E.ε o e specimen Figure 3 - system testing equipment/specimen in the elastic regime. If θo is known, and tg θo is plotted as a function of Lo/Ao, values for Km and E can be obtained. The Weibull modulus was also determined for each carbon fibre filament gage length tested. This is accomplished by the equation (9) and considering the assumption of a constant volume for the samples which results in a straight line: lnln (1/1-P) = m.ln σ - m.ln σ o (9) The Weibull modulus is obtained by plotting ln[ln(1/(1-p))] as function of ln σ. The probability from medium position corresponding to the i-th observation is given by P=1/N+1, where N is number of samples. The Weibull parameter (m) is obtained by linear regression. RESULTS AND DISCUSSIONS Table 1 shows results for extension and strain obtained for each gage length tested. Table 1 - Properties of AS4-GP-6K carbon fibre at various specimen length Specimen Length (mm) Tensile strength (GPa) Extension at break (mm) calculated strain (%) (*) Young s modulus (*) 25 2,9,325 1,318 22, 5 2,7,5631 1,126 24, 75 2,66,8351 1,113 24, 1 2,54 1,882 1,88 233, (*) assuming ideal Hookean behaviour for carbon fibres CONGRESSO BRASILEIRO DE ENGENHARIA E CIÊNCIA DOS MATERIAIS, 14., 2, São Pedro - SP. Anais 2415

6 Table 1 shows a trend where the higher gage length of the fibre filament tested the lower is the tensile strength. This trend has been shown also by other researcherd, and it is related to the increase in flaw population when higher gage length is used for testing ( Hitchon 1979). Hookean behaviour is assumed in the calculation of Young s modulus, and as a consequence the figures need a correction that are explained next. METHOD ASTM 3329M The corrected Young s modulus is calculated by equation 5. The true compliance (C) is obtained by subtracting the system compliance (Cs), taking it at zero gage length in Figure 4, from the indicated compliance (Ca) for each gage length, equation 3. Table 2 shows the results for the corrected Young s modulus. Ca (mm/kg),8,7,6,5,4,3,2,1 y =,64x +,42 R 2 =, Gage length (mm) Figure 4 - Graphical plot for the system (testing equipment) compliance Table 2 - Corrected Young s modulus according to ASTM D3329M Specimen gage length (mm) Extension (I) (mm) Corrected E (GPa) 25,325 27, 5, , 75, ,3 1 1, , Average 35 ± 24 CONGRESSO BRASILEIRO DE ENGENHARIA E CIÊNCIA DOS MATERIAIS, 14., 2, São Pedro - SP. Anais 2416

7 The average result for the corrected Young s modulus, using the ASTM D3329M is within the range of Young s modulus specified by the manufacturer, for intermediate Young s modulus carbon fibres ( GPa). Although no information is available from the testing conditions used by the manufacturer, a good agreement in the results was found by following procedure stated in ASTM3329M indicates good agreement in the results. METHOD TESTING EQUIPMENT/SPECIMEN INTERACTION (RIGIDITY METHOD) This method needs initiallly the value of the angle θ from the load/extension curve, Figure 2, for each specimen tested, and also the gage length/filament cross section (Lo/Ao) ratio. Table 3 shows results for these parameters, and graphical plot from these results is shown in Figure 5. Table 3 Results for (tg θ o ) -1 and gage length/cross section area (Lo/Ao) for each gage length tested. Specimen Gage length (Lo) (mm) (tg θ o ) -1 Lo/Ao (mm -1 ) 25 3, , , , (Tg Θo) -1 (mm/n) 1,2 1,8,6,4 y = 4E-7x +,65 R 2 =,9964, L o /A o (mm -1 ) Figure 5 Graphical plot of equation 8 taken from experimental data from Table 3. CONGRESSO BRASILEIRO DE ENGENHARIA E CIÊNCIA DOS MATERIAIS, 14., 2, São Pedro - SP. Anais 2417

8 The angular coefficient taken from the graph of Figure 5 is equal to According to method which takes into account the interaction between the testing equipment and the specimen gage length (rigidy method), the corrected Young s modulus is given by the inverse of the angular coefficient. Thus, the value of the corrected Young s modulus obtained by rigidity method is equal to 25 GPa. This value is in the lower range of the value for Young s modulus reported by the manufacture s data sheet, for an intermediate modulus carbon fibres ( GPa), and therefore this method is quite good for the determination of Young s modulus of carbon fibres in the range of gage length studied. The value of Km taken from the inverse of the linear coefficient is 154 kn/m. WEIBULL MODULUS The Weibull modulus of carbon fibres were calculated for the gage length tested according to equation 9. The plots for each gage length are shown in Figure 6. The equation of the line draw through the points have the form y = ax + b, where a represents the Weibull modulus (Pina 1997). The Weibull parameter m can be regarded as a flaw frequency distribution factor (Weibull 1951). High values of m indicates that flaws are evenly distributed throughout the material, whatever they are plentiful or not, and hence strength is nearly independent of length. Low values of m flaws are fewer and less evenly distributed, causing greater scatter in strength. All graphical plots of Weibull distribution for ASG4-GP carbon fibres shows that m falls in a narrow range (m = 3, 3,6), indicating that the latter assumption, fewer flaws less evenly distributed, is the case for this fibre. Flaws in carbon fibres are mainly represented by pores. The carbon fibre of the type used in this work is characterized by a mean pore diameter of about 5,5 nm, and a broad ultramicropore distribution in the range of 2 nm to 4 nm, and a pore volume of,2% (Lee 1997). This figures indicates that strength statitics of ASG4-GP is controlled by small flaw population. The Weibull theory also states that for a material of homogeneous quality having a unimodal distribution of flaw size the value of m should be the same at all sample length, and the mean value of strength at the different lengths should increase with decrease in length. The ASG4-GP carbon fibre follows this trend, which indicates that it has an unimodal distribution of flaw size. Despite the high scatter in the tensile strength values for ASG4-GP carbon fibre ( 3%), commonly found for this kind of material, the narrow range of m parameter indicates that it has an homogeneous quality. CONGRESSO BRASILEIRO DE ENGENHARIA E CIÊNCIA DOS MATERIAIS, 14., 2, São Pedro - SP. Anais 2418

9 2 1 (A) 25 mm (B) 5 mm 2 1 Ln[Ln(1/(1-P))] y = 3,248x - 26,262 R 2 =,9336 Ln[Ln(1/(1-P))] y = 3,5581x - 28,486 R 2 =, ,25 7,5 7,75 8 8,25 8,5 8,75 Ln σ (MPa) ,25 7,5 7,75 8 8,25 8,5 8,75 Ln σ (GPa) 2 1 (C) 75 mm (C) 1 mm 2 1 Ln[Ln(1/(1-P))] y = 3,1389x - 25,19 R 2 =,9715 Ln(Ln(1/(1-P)) y = 3,959x - 24,637 R 2 =, ,25 7,5 7,75 8 8,25 8,5 Ln σ (MPa) ,25 7,5 7,75 8 8,25 8,5 Ln σ (MPa) Figure 6 - Weibull plots for carbon fibres ASG4K of length 25 mm, 5 mm, 75 mm and 1 mm. CONGRESSO BRASILEIRO DE ENGENHARIA E CIÊNCIA DOS MATERIAIS, 14., 2, São Pedro - SP. Anais 2419

10 (A) CONGRESSO BRASILEIRO DE ENGENHARIA E CIÊNCIA DOS MATERIAIS, 14., 2, São Pedro - SP. Anais 2411

11 CONCLUSION Tensile strength, Young s modulus and Weibull were evaluated for an intermediate modulus carbon fibre. Because carbon fibres are thiny it is not possible to use conventional strain-gages in order to measure deformation and calculate the Young s modulus. This can be done by using two approaches. The first is the one following procedure stated in ASTM D3379 Standard and the second a procedure which takes into account the interaction between testing equipment and specimen under test. As any other material, carbon fibres has defects created during processing. In general this defects are mainly ultramicropores and fibril misalignments. These defects cause scatter in strength. Tensile strength for the fibre studied varied from 2,54 GPa, at a gage length of 1 mm, to 2,9 GPa, at gage length of 25 mm. The scatter in strength was greater than 3% leading to a low value of Weibull modulus at all gage lengths tested. This in turn indicates that the carbon fibre used in the this work has an homogeneous quality and the idea of fewer flaws evenly distributed throughout the length of the filament is strongly accepted. REFERENCES ASTM D3379 Tensile Strength and Young s Modulus for High-Modulus Single-Filament Materials Guimarães, J. R. C., Chawla, K. K., Características de Rigidez de Máquina Universal para Ensaios de Tração, Metalurgia, Vol. 34, no 249, p , Ago/1978 Lee, J. S. ; T. J. Kang, Changes in Physico-Chemical and Morphological Properties of Carbon Fiber by surface Treatment, Carbon, Vol. 35, n. 2, pág , Pina, S. R. O., Piorino-Neto, F., Pardini, L. C., Weibull Modulus of Bi-directional Carbon Fibre Reinforced Carbon Composites, 23th Biennial Conference on Carbon, 1997, Newcastle-upon-Tyne-UK. Weibull, W.. A Statistical Distribution Function of wide Applicability, J. Appl. Mechanics, Vol. 18, p , CONGRESSO BRASILEIRO DE ENGENHARIA E CIÊNCIA DOS MATERIAIS, 14., 2, São Pedro - SP. Anais 24111