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New test approach to determine the transverse tensile strength of CFRP with regard to the size effect
Composites Communications 1 (2016) 54–59
Contents lists available at ScienceDirect
Composites Communications journal homepage: www.elsevier.com/locate/coco
New test approach to determine the transverse tensile strength of CFRP with regard to the size effect Wilfried V. Liebig a,n, Christian Leopold a, Thomas Hobbiebrunken b, Bodo Fiedler a a b
Technische Universität Hamburg-Harburg, Institute of Polymer Composites, Denickestrasse 15, D-21073 Hamburg, Germany Airbus Operations GmbH, Kreetslag 10, D-21129 Hamburg, Germany
art ic l e i nf o
a b s t r a c t
Article history: Received 8 August 2016 Received in revised form 5 September 2016 Accepted 6 September 2016
The subject of this work is the investigation of the size effect on transverse strength of CFRP. A new test approach uses the remaining parts of already tested specimens for a second transverse tensile test. With this method it is analysed, whether first failure is dominated by the most critical flaw inside the material or at a load that is equivalent to the maximum tensile strength of the matrix. Thickness of the specimens is varied to study the influence of specimen volume on transverse tensile strength. Test results show that strength follows the trend of defect distribution with increasing strength for decreasing volume. Second failure strength is higher than first failure strength, showing that first failure occurs at the most critical defect and gives no evidence of the maximum transverse tensile strength of the material. Stress at second failure showed less scatter, proving good applicability of the proposed test method. & 2016 Elsevier Ltd. All rights reserved.
Keywords: A. Carbon fibres B. Mechanical properties C. Statistical properties/methods D. Mechanical testing
1. Introduction A very important aspect of variability in mechanical properties of large composite structures, which should be considered in design, is the size effect. It is assumed that mean strength of flawsensitive materials decreases with increasing material volume [1,2]. In addition, inter-fibre failure (IFF) occurs at lower strains than fibre failure (FF) in unidirectional (UD) fibre-reinforced plastics (FRP). Hence, the transverse strength of composites is often a limiting design factor. It is influenced by matrix strength (cohesion failure) and fibre–matrix interface strength (adhesion failure) [3]. Cracks meander between both characteristics whereat no clear differentiation is possible. First failure is dominated by the weakest link, which is the most critical defect within the material. These defects are distributed according to Weibull's theory [4]. On a micro-scale level, fibres show a higher stiffness than the matrix leading to stress concentrations in the matrix. These stress concentrations cause premature failure, although the strength of the matrix increases by decreasing volume [2]. First investigations about the size effect concerning the transverse strength of composites were performed by Adams et al. [5]. In this study, a comparison was made between flexural and tensile n
Corresponding author. E-mail addresses: [email protected] (W.V. Liebig), [email protected] (C. Leopold), [email protected] (T. Hobbiebrunken), fi[email protected] (B. Fiedler). http://dx.doi.org/10.1016/j.coco.2016.09.003 2452-2139/& 2016 Elsevier Ltd. All rights reserved.
strengths in which flexural tests always gave higher values. Further investigations on the size effect were made by O'Brien and Salpekar [6] who tested specimens of different widths and different thicknesses in transverse fibre direction. Their test results indicated that matrix dominated strength properties varied with the volume of the material to be stressed, with strength decreasing as volume increased [6]. Both Adams et al. [5] and O'Brien and Salpekar [6] used CFRP in their studies, whereas Wisnom and Jones [7] and Wisnom [8] also reported results for GFRP. They compared curved unidirectional beams with the shape of a hump backed bridge with the in-plane transverse tensile strength. It was concluded that the lower in-plane strength matched closely the value expected for the much larger volume of material based on the Weibull parameters from the interlaminar tests [7]. Mespoulet [9] compared transverse tensile strengths of carbon/epoxy with different volumes at straight sided and doubly waisted specimens. It could be shown that higher strength of doubly waisted specimens (smaller volume than straight sided specimens) is due to smaller volume. However, it could not be clearly carved out whether a better surface finish on smaller specimens or the size effect led to these results. O'Brien et al. reported that the trend of decreasing strength with increasing specimen width, and hence increasing volume, which would be anticipated from Weibull scaling law, was not clearly apparent in three and four point bending tests [10]. Nevertheless, for increasing span length, and hence increasing volume, it could be observed that strengths decreased. But also in this study, due to a significant panel-to-panel variability, it could not clearly figured out whether the expected scaling was due to the size effect.
W.V. Liebig et al. / Composites Communications 1 (2016) 54–59
These uncertainties lead to the subject of this work, which is the investigation of the size effect on the transverse strength of CFRP. In order to understand whether first failure strength corresponds to the true failure strength of the material, a second transverse tensile test is performed by using a part of the specimen out of the already tested volume. This approach allows us to determine the strength of the second failure and to investigate whether weakest link theory could be applied or not and a size effect within a single specimen volume exists.
2. Experimental study
55
l0 = 150 mm between the tabs. As already investigated by O'Brien [6], a complex stress field is located close to the end tabs. Due to the fact, that this stress concentration promotes premature failure, the measured values of transverse strength are more conservative. In addition, the effect of stress concentration in the vicinity of load application fades away after a distance from the load application equal to approximately specimen thickness [12]. In all cases, just specimens that failed in a distance of at least twice the respective specimen thickness from the end tabs are used to determine the transverse strength. Before the transverse tensile tests, the specimens are dried according to DIN EN 3615 [13] for avoiding moisture influence on the test results.
2.1. Materials and sample preparation
2.2. Tensile test
Unidirectional prepreg material HexPly-M21/34%/UD194/ T800S from Hexcel is used for producing specimens for transverse tensile tests. The lay-up is ⎡⎣ 90°⎤⎦ , where n is varied with
Quasi static transverse tensile tests are carried out (DIN EN ISO 527-5 [11]) using a Zwick/Roell Z010 universal test machine. The load is continuously measured with a load cell with a maximum load of 10 kN. The displacement is recorded via the traverse of the machine. If first failure is in the middle region of the free test length, the longer half of this specimen is prepared with end tabs, as described in Section 2.1, and tested again until specimens fail for the second time. The stress at this failure will be referred to as second failure strength. This is to determine the remaining strength and to evaluate, whether first failure occurs at the most critical defect or at a load that is equivalent to the maximum tensile strength of the matrix in the respective configurations. In addition, the effect of further damage can be evaluated. If the specimen is damaged in other locations than the one of the first failure during the first test, the second failure strength would be below the first failure strength. Otherwise the weakest link dominates failure behaviour. This approach is shown schematically in Fig. 1. It has to be mentioned, that the material failure representing the second weakest link in the chain model, may not be within the free test length of this second specimen but could also be positioned under the new applied end tab with which volume of the original specimen half is lost. In cross-ply specimens, crack density in the 90°-layer depends on its thickness [14,15]. If first damage led not to ultimate failure of the specimen, the further damage would be distributed with a certain density that would be higher for the thinner specimens. With the reported crack densities for cross-ply laminates e.g. by Parvizi et al. [14,15] however, further damage should occur in the free test length of the second test specimens as well, if present. The strain rate is kept always constant by adjusting the crosshead speed of the machine according to the specimen length, starting with a cross-head speed of 1 mm/min for free test length of l0 = 150 mm [11]. After failure, the fracture surfaces of representative specimens are observed by scanning electron microscopy (SEM) (Leo Gemini 1530). The SE2 detector with a working distance between 7 mm and 9 mm at 10 keV is used without any sputtering of the surface.
n
n = 3, 5, 10, 16, in order to investigate the influence of the specimen thickness. Cured ply thickness is approximately 190 μm. The specimen geometry is according to DIN EN ISO 527-5 [11] with length l = 250 mm and width w = 25 mm ± 0.1 mm (refer to Fig. 1). As the thickness is varied, specimens with thickness t higher or lower than 2 mm deviate from the normative reference, whereas the dimensions of the specimens with n ¼ 10 fulfil these requirements [11]. Laminate plates of 300 300 mm with varying thicknesses are laid-up by hand and cured in an autoclave for 120 min at 180 °C and 7 bar pressure as recommended by the manufacturer. Specimens are cut out using a diamond saw. Due to the difficult handling of the thin specimens and to avoid an additional influence on the test results as reported in [9] polishing of the edges is omitted. Surface condition of the edges influences the failure process with rougher surfaces leading to crack initiation at lower strains. But as failure is assumed for this type of specimens to initiate at the edges anyway and all specimens are cut under the same conditions, edge roughness should be the same, making the results well comparable. In addition, surface quality with regard to roughness was quite high after the sawing due the use of a diamond saw with well-chosen cutting parameters (comparable to polishing with abrasive paper with a grain size of 800). Three plates of each configuration are produced in order to regard statistical variations of the manufacturing process within the test results. Fibre reinforced elastomer end tabs are glued on the specimens by using a thermoset adhesive, leaving a distance of
3. Results and discussion
Fig. 1. Schematical sketch of (a) specimen for transverse tensile test, (b) specimen after first failure and (c) specimen after second failure.
The first and second failure strength are compared for several number of plies, so that the transverse strength in dependency of the volume as well as the influence of pre-existing damage in case of the second failure strength can be evaluated. Fig. 2 shows the t transverse tensile strength R22 for all tested specimens versus their volume, which varies according to different thicknesses (number of plies n) of the four configurations regarded. First failure of a specimen is indicated with open white symbols. Second failure strength (refer to Section 2.2) is represented with filled black symbols. The values of first and second failure strength of the
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W.V. Liebig et al. / Composites Communications 1 (2016) 54–59
t Fig. 2. Transverse tensile strength R22 of M21/T800S versus specimen volume V.
Table 1 Transverse tensile strength of M21/T800S specimens in dependency of their volume. 1st failure No.
2nd failure
Strength / MPa
Volume
Strength / MPa
Volume
/ mm3
/ mm3
Length /mm
2–3 2–5 2–9 3–1 3–6 3–8 4–2 4–5 4–7
77.9 78.2 72.9 63.6a 65.5 73.0 70.5 79.3 64.7
11,322 11,335 11,333 11,164 11,407 11,397 11,250 11,444 11,435
79.2 84.4 75.7 68.7 67.7 77.7 75.5 71.8 79.3
8033 8339 8143 6154 4449 6870 7582 3879 6191
106.4 110.4 107.8 82.7 58.5 90.4 101.1 50.8 81.2
10 plies
1–2 1–4 1–7 2–3 2–5 2–8 4–2 4–4 4–8
74.1 69.5 74.1 64.7a 65.2 72.0 72.0 71.1 65.9
7034 7101 7089 7106 7141 7127 6993 7147 7095
72.2 74.4 84.5 84.0 81.1 80.9 76.6 74.0 74.4
4512 4728 4738 4535 4560 4626 2307 3364 5122
96.2 99.9 100.3 95.7 95.8 97.4 49.5 70.6 108.3
5 plies
1–3 1–6 1–9 3–3 3–6 3–8 4–2 4–6 4–8
78.1 79.1 82.4 83.9 78.3 70.7 75.8 73.6 64.2
3585 3587 3542 3552 3664 3546 3513 3626 3581
80.9 77.3 83.0 79.5 84.9 76.2 81.2 82.3 76.6
2474 2046 1837 1069 1197 2551 2229 2489 2307
103.5 85.6 77.8 45.1 49.0 107.9 95.2 103.0 96.6
3 plies
1–2 1–5 1–7 2–2 2–3 2–5 4–5 4–6 4–8
77.0 71.4 77.1 74.6 70.3a 72.4 73.9 81.2 78.3
2079 2167 2192 2156 2154 2124 2170 2189 2179
85.9 81.5 76.7 73.5a 72.6a 74.8 82.6a 81.2a 82.1
1357 1397 1347 1409 1537 1373 640 672 1024
97.9 96.7 92.2 98.0 107.0 97.0 44.2 46.1 70.5
16 plies
a
second failure strength are in the same range of 7 4 MPa. Only for two specimens, number 4–5 and 3–3, the second failure strength is lower than the first failure strength. In total, the values for first and second transverse failure clearly indicate that the strength is higher with decreasing volume of the specimen. This implies that first failure occurs at the most critical defect in the range of the tested volume [1] and strength at first failure is not the ultimate transverse tensile strength of the material. Second failure occurs for most specimens at higher loads and thus results from a less critical defect than the one responsible for first failure. When considering possible damage in the optically undamaged regions of the specimen after the first test, which cannot be excluded, the influence of a critical defect is even more highlighted, because second failure occurs at higher loads despite a possible pre-existing damage in the specimens at the same strain rate. Concerning defects in a brittle material, the principle of the weakest link that determines the strength of a chain is applicable. With increasing number of links in a chain, the probability to have a weak link in the chain increases as well, therefore the strength tends to decrease with increasing number of links. For a volume, the strength under uniform stress is dominated by the largest defect. Defects are randomly distributed with larger volumes having a higher probability of containing larger defects and thus lower strength. This size effect can be described by a statistical distribution proposed by Weibull in 1951 [1] that is widely used to represent the strength of brittle materials [16]. The size effect in solids with probability Pi(σ ) and critical stress sc as a function of the stress s is described with the following equation [1]: m
Pi(σ ) = 1 − e−( σc ) σ
(1)
where m is the Weibull-module. The double logarithmic representation for the first and the second failure is shown in Fig. 3. Values of m1 = 16.14 and σ0,1 = 75.66 MPa for first failure respectively m2 = 20.50 and σ0,2 = 80.25 MPa for second failure are determined. The Weibull-modulus from first to second failure increases by 21.27%, indicating that strength scattering decreases, which is in contrast to Weibull's theory [4] and previous investigations on a size effect in epoxy resin [2]. This can be explained with the weakest link being eliminated after the first test in this study. Hence, with the largest flaw excluded, higher strengths with less scattering can be obtained. The minimum failure strengths (excluding the values marked with a rectangle in Fig. 5) are plotted against volume on a log-log scale. This is shown in the Weibull weak link scaling diagram in Fig. 4. The curve through these values to determine the Weibullmodulus m for minimum transverse tensile strength should be a straight line with a slope of −1/m.
Values regarded for Weibull weak link scaling diagram (Fig. 4).
specimens are given in Table 1 for the different number of plies. The length of the secondly tested specimen is also given. For most specimens, the second failure strength is higher than the first failure strength. For specimens 1–2, 1–6, 1–7, 2–2 and 4–6, first and
Fig. 3. 1st failure (Weibull modulus m¼ 16.14 and σ0 = 75.66 MPa ); 2nd failure (Weibull modulus m¼ 20.50 and σ0 = 80.25 MPa ).
W.V. Liebig et al. / Composites Communications 1 (2016) 54–59
In order to compare two different volumes V1 and V2 with their strengths σult,1 and σult,2, Eq. (2) is used. 1
σult,1 σult,2
⎛ V ⎞− m = ⎜ 1⎟ ⎝ V2 ⎠
(2)
Fig. 4. Weibull weak link scaling diagram. All values are out of Table 1.
t Fig. 5. Transverse tensile strength R22 of M21/T800S in dependency of specimen volume V with Weibull plot. (□: outlier not regarded for Weibull weak link scaling diagram in Fig. 4).
57
The comparison of the median values for transverse tensile strength of the different configurations shows also a slight trend of increasing strength with decreasing number of plies and thus decreasing volume, but standard deviations are quite high, as shown in Fig. 5. In this diagram, the values for first failure strength of the specimen are presented as a box plot and second failure is indicated with symbols. A spline through the minimum values of each volume as well as the Weibull plot show the volume effect resulting from a statistical distribution of defects that is according to Weibull's theory of defect distribution [1]. The Weibull plot (dotted line in Fig. 5) shows good agreement with the data. One value, marked with a open white square, is regarded as an outlier and thus omitted for the fit. The horizontal line at 86 MPa indicates the ultimate transverse tensile strength of the material for the tested volumes, which results from the maximum interfacial strength of fibre and matrix. Except the one value already mentioned, all values for transverse tensile strength lie in the range or within the ultimate value and that one dominated by the statistical distribution of defects as a Weibull envelope curve. Photos of the representative fracture surface after first failure of the thinnest (n ¼3 plies) and the thickest (n ¼ 16 plies) configurations are shown in Fig. 6. As can be seen in the pictures, both specimens failed with a single crack through the width transverse to the loading direction. All other specimens showed the same brittle fracture behaviour at final failure, as expected. This is important, because Weibull theory is only valid while the failure mode is the same for all specimens [16]. Despite the general failure mode remaining the same with increasing volume, differences in the roughness of the crack surface can be observed like fibre bridging occurring in thicker configurations. Single fibres are also observed to split into the fracture surface of the thinnest configuration, but the amount is smaller. One reason may be the broader crack surface, presupposed by the higher thickness, which may account for more fibres to bridge during crack propagation in the matrix between the fibres and thus results in a slightly rougher fracture surface. This is further investigated in SEM. SEM images of a representative fracture surface of the thinnest (n ¼3 plies) and the thickest (n ¼16 plies) configurations are shown in Fig. 7. Smooth fibre surfaces are visible in both configurations (refer to Figs. 7(c) and (a)), indicating fibre–matrix interface failure. In some areas residual matrix still sticks on the fibres that hints at good fibre–matrix bonding and thus cohesive matrix failure in these locations (refer to Fig. 7(d)). In addition, cusps that results from a local shear failure of the matrix [17,18] occur. They are shown in SEM images with higher magnification in
Fig. 6. Characteristics of 1st failure of (a) n¼ 3 and (b) n¼ 16 plies.
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W.V. Liebig et al. / Composites Communications 1 (2016) 54–59
Fig. 7. SEM images of representative fracture surfaces of specimens of the thickest and thinnest configuration with n¼ 16 and n¼ 3 layers. (a) Fracture surface of a specimen with 16 layers. (b) Detail of (a) showing interfacial failure and residual matrix on the fibres resulting from cohesive matrix failure. (c) Fracture surface of a specimen with 3 layers. (d) Detail of (c) showing matrix cusps between the fibres.
Fig. 7(d) for n ¼3 layers and 7(b) for n ¼16 layers respectively. Crack propagation at final failure is therefore assumed to be mostly adhesive but partly cohesive, depending on the local interfacial strength. Since there are no significant differences in the fracture surfaces of specimens with different thicknesses, the failure mode is confirmed to be the same for all specimens and Weibull theory is fully applicable.
4. Conclusion The subject of this work is the investigation of the size effect on transverse tensile strength of CFRP. As values for this strength of FRP obtained by respective tests depend on the statistical defect distribution. The new test approach allows us to analyse the influence of statistical defect distribution leads to more accurate values for the transverse tensile strength of FRP. The results of the study show that first transverse failure occurs at the most critical defect (weakest link) and second failure strength is higher than first failure strength. Even when considering pre-existing damage, the second failure of the smaller volumes occurs at higher strengths, so that still conservative values for the smaller volumes are given. With decreasing of testing volume Weibull distribution becomes smaller (Weibull module m increases) i.e. reliability becomes more accurate, which highlights the applicability of the new test approach. With decreasing specimen volume, the transverse strength increases significantly. Transverse strength is dominated by IFF, which depends on interfacial strength of the fibre–matrix bond and defect distribution within specimen volume. It could be concluded, that the new method provides a more accurate measure of transverse tensile strength, which may be used along with Weibull scaling to predict transverse strength of smaller volumes e.g. 90° layers in cross-ply laminates during fatigue loading or micromechanical modelling.
Acknowledgements The authors gratefully acknowledge the financial support of the German Research Foundation (DFG) within the project FI 688/5-1.
References [1] W. Weibull, A statistical distribution function of wide applicability, J. Appl. Mech. 18 (1951) 293–297. [2] T. Hobbiebrunken, B. Fiedler, M. Hojo, M. Tanaka, Experimental determination of the true epoxy resin strength using micro-scaled specimens, Compos.: Part A 38 (2007) 814–818. [3] T. Hobbiebrunken, M. Hojo, T. Adachi, C. De Jong, B. Fiedler, Evaluation of interfacial strength in CF/epoxies using FEM and in-situ experiments, Compos.: Part A 37 (2006) 2248–2256. [4] W. Weibull, A statistical theory of the strength of materials, R. Swed. Inst. Eng. Res. 151 (1939) 1–45. [5] D.F. Adams, T.R. King, D.M. Blackketter, Evaluation of the transverse flexure test method for composite materials, Compos. Sci. Technol. 39 (1990) 341–353. [6] T.K. O'Brien, S.A. Salpekar, Scale Effects on the Transverse Tensile Strength of Graphite Epoxy Composites, NASA Technical Memorandum 107637, AVSCOM Technical Report 92-B-009, 1992. [7] M.R. Wisnom, M.I. Jones, Size effects in interlaminar tensile and shear strength of unidirectional glass fibre/epoxy, J. Reinf. Plast. Compos. 15 (1996) 2–15. [8] M.R. Wisnom, Size effects in tensile, compressive and interlaminar failure of unidirectional composites, in: Proceedings of the ASME Aerospace Division, AD-vol. 55, 1997, pp. 67–77. [9] S. Mespoulet, Through thickness test methods for laminated composite materials (Ph.D. thesis), Imperial College, London, 1998. [10] T.K. O'Brien, A.D. Chawan, K. DeMarco, I. Paris, Influence of Specimen Preparation and Specimen Size on Composite Transverse Tensile Strength and Scatter, NASA TM-2001-211030, ARL-TR-2540, 2001. [11] DIN EN ISO 527-5, Plastics—Determination of Tensile Properties—Part 5: Test Conditions for Unidirectional Fibre-Reinforced Plastic Composites, 1997. [12] M. De Saint-Venant, De la torsion des prismes avec des considérations sur leur flexion ainsi que sur l'équlibre des solides élastiques en général, Paris, Imprimerie Impériale, 1855. [13] DIN EN 3615, Aerospace Series—Fibre Reinforced Plastics—Determination of the Conditions of Exposure to Humid Atmosphere and of Moisture Absorption, 1999. [14] A. Parvizi, K.W. Garrett, J.E. Bailey, Constrained cracking in glass fibre-reinforced epoxy cross-ply laminates, J. Mater. Sci. 13 (1) (1978) 195–201. [15] A. Parvizi, J.E. Bailey, On multiple transverse cracking in glass fibre epoxy
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cross-ply laminates, J. Mater. Sci. 13 (10) (1978) 2131–2136. [16] M.R. Wisnom, Size effects in the testing of fibre-composite materials, Compos. Sci. Technol. 59 (1999) 1937–1957. [17] B. Fiedler, M. Hojo, S. Ochiai, K. Schulte, M. Ando, Failure behavior of an epoxy matrix under different kinds of static loading, Compos. Sci. Technol. 61 (2001)
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1615–1624. [18] E.S. Greenhalgh, C. Rogers, P. Robinson, Fractographic observations on delamination growth and the subsequent migration through the laminate, Compos. Sci. Technol. 69 (2009) 2345–2351.
Contents lists available at ScienceDirect
Composites Communications journal homepage: www.elsevier.com/locate/coco
New test approach to determine the transverse tensile strength of CFRP with regard to the size effect Wilfried V. Liebig a,n, Christian Leopold a, Thomas Hobbiebrunken b, Bodo Fiedler a a b
Technische Universität Hamburg-Harburg, Institute of Polymer Composites, Denickestrasse 15, D-21073 Hamburg, Germany Airbus Operations GmbH, Kreetslag 10, D-21129 Hamburg, Germany
art ic l e i nf o
a b s t r a c t
Article history: Received 8 August 2016 Received in revised form 5 September 2016 Accepted 6 September 2016
The subject of this work is the investigation of the size effect on transverse strength of CFRP. A new test approach uses the remaining parts of already tested specimens for a second transverse tensile test. With this method it is analysed, whether first failure is dominated by the most critical flaw inside the material or at a load that is equivalent to the maximum tensile strength of the matrix. Thickness of the specimens is varied to study the influence of specimen volume on transverse tensile strength. Test results show that strength follows the trend of defect distribution with increasing strength for decreasing volume. Second failure strength is higher than first failure strength, showing that first failure occurs at the most critical defect and gives no evidence of the maximum transverse tensile strength of the material. Stress at second failure showed less scatter, proving good applicability of the proposed test method. & 2016 Elsevier Ltd. All rights reserved.
Keywords: A. Carbon fibres B. Mechanical properties C. Statistical properties/methods D. Mechanical testing
1. Introduction A very important aspect of variability in mechanical properties of large composite structures, which should be considered in design, is the size effect. It is assumed that mean strength of flawsensitive materials decreases with increasing material volume [1,2]. In addition, inter-fibre failure (IFF) occurs at lower strains than fibre failure (FF) in unidirectional (UD) fibre-reinforced plastics (FRP). Hence, the transverse strength of composites is often a limiting design factor. It is influenced by matrix strength (cohesion failure) and fibre–matrix interface strength (adhesion failure) [3]. Cracks meander between both characteristics whereat no clear differentiation is possible. First failure is dominated by the weakest link, which is the most critical defect within the material. These defects are distributed according to Weibull's theory [4]. On a micro-scale level, fibres show a higher stiffness than the matrix leading to stress concentrations in the matrix. These stress concentrations cause premature failure, although the strength of the matrix increases by decreasing volume [2]. First investigations about the size effect concerning the transverse strength of composites were performed by Adams et al. [5]. In this study, a comparison was made between flexural and tensile n
Corresponding author. E-mail addresses: [email protected] (W.V. Liebig), [email protected] (C. Leopold), [email protected] (T. Hobbiebrunken), fi[email protected] (B. Fiedler). http://dx.doi.org/10.1016/j.coco.2016.09.003 2452-2139/& 2016 Elsevier Ltd. All rights reserved.
strengths in which flexural tests always gave higher values. Further investigations on the size effect were made by O'Brien and Salpekar [6] who tested specimens of different widths and different thicknesses in transverse fibre direction. Their test results indicated that matrix dominated strength properties varied with the volume of the material to be stressed, with strength decreasing as volume increased [6]. Both Adams et al. [5] and O'Brien and Salpekar [6] used CFRP in their studies, whereas Wisnom and Jones [7] and Wisnom [8] also reported results for GFRP. They compared curved unidirectional beams with the shape of a hump backed bridge with the in-plane transverse tensile strength. It was concluded that the lower in-plane strength matched closely the value expected for the much larger volume of material based on the Weibull parameters from the interlaminar tests [7]. Mespoulet [9] compared transverse tensile strengths of carbon/epoxy with different volumes at straight sided and doubly waisted specimens. It could be shown that higher strength of doubly waisted specimens (smaller volume than straight sided specimens) is due to smaller volume. However, it could not be clearly carved out whether a better surface finish on smaller specimens or the size effect led to these results. O'Brien et al. reported that the trend of decreasing strength with increasing specimen width, and hence increasing volume, which would be anticipated from Weibull scaling law, was not clearly apparent in three and four point bending tests [10]. Nevertheless, for increasing span length, and hence increasing volume, it could be observed that strengths decreased. But also in this study, due to a significant panel-to-panel variability, it could not clearly figured out whether the expected scaling was due to the size effect.
W.V. Liebig et al. / Composites Communications 1 (2016) 54–59
These uncertainties lead to the subject of this work, which is the investigation of the size effect on the transverse strength of CFRP. In order to understand whether first failure strength corresponds to the true failure strength of the material, a second transverse tensile test is performed by using a part of the specimen out of the already tested volume. This approach allows us to determine the strength of the second failure and to investigate whether weakest link theory could be applied or not and a size effect within a single specimen volume exists.
2. Experimental study
55
l0 = 150 mm between the tabs. As already investigated by O'Brien [6], a complex stress field is located close to the end tabs. Due to the fact, that this stress concentration promotes premature failure, the measured values of transverse strength are more conservative. In addition, the effect of stress concentration in the vicinity of load application fades away after a distance from the load application equal to approximately specimen thickness [12]. In all cases, just specimens that failed in a distance of at least twice the respective specimen thickness from the end tabs are used to determine the transverse strength. Before the transverse tensile tests, the specimens are dried according to DIN EN 3615 [13] for avoiding moisture influence on the test results.
2.1. Materials and sample preparation
2.2. Tensile test
Unidirectional prepreg material HexPly-M21/34%/UD194/ T800S from Hexcel is used for producing specimens for transverse tensile tests. The lay-up is ⎡⎣ 90°⎤⎦ , where n is varied with
Quasi static transverse tensile tests are carried out (DIN EN ISO 527-5 [11]) using a Zwick/Roell Z010 universal test machine. The load is continuously measured with a load cell with a maximum load of 10 kN. The displacement is recorded via the traverse of the machine. If first failure is in the middle region of the free test length, the longer half of this specimen is prepared with end tabs, as described in Section 2.1, and tested again until specimens fail for the second time. The stress at this failure will be referred to as second failure strength. This is to determine the remaining strength and to evaluate, whether first failure occurs at the most critical defect or at a load that is equivalent to the maximum tensile strength of the matrix in the respective configurations. In addition, the effect of further damage can be evaluated. If the specimen is damaged in other locations than the one of the first failure during the first test, the second failure strength would be below the first failure strength. Otherwise the weakest link dominates failure behaviour. This approach is shown schematically in Fig. 1. It has to be mentioned, that the material failure representing the second weakest link in the chain model, may not be within the free test length of this second specimen but could also be positioned under the new applied end tab with which volume of the original specimen half is lost. In cross-ply specimens, crack density in the 90°-layer depends on its thickness [14,15]. If first damage led not to ultimate failure of the specimen, the further damage would be distributed with a certain density that would be higher for the thinner specimens. With the reported crack densities for cross-ply laminates e.g. by Parvizi et al. [14,15] however, further damage should occur in the free test length of the second test specimens as well, if present. The strain rate is kept always constant by adjusting the crosshead speed of the machine according to the specimen length, starting with a cross-head speed of 1 mm/min for free test length of l0 = 150 mm [11]. After failure, the fracture surfaces of representative specimens are observed by scanning electron microscopy (SEM) (Leo Gemini 1530). The SE2 detector with a working distance between 7 mm and 9 mm at 10 keV is used without any sputtering of the surface.
n
n = 3, 5, 10, 16, in order to investigate the influence of the specimen thickness. Cured ply thickness is approximately 190 μm. The specimen geometry is according to DIN EN ISO 527-5 [11] with length l = 250 mm and width w = 25 mm ± 0.1 mm (refer to Fig. 1). As the thickness is varied, specimens with thickness t higher or lower than 2 mm deviate from the normative reference, whereas the dimensions of the specimens with n ¼ 10 fulfil these requirements [11]. Laminate plates of 300 300 mm with varying thicknesses are laid-up by hand and cured in an autoclave for 120 min at 180 °C and 7 bar pressure as recommended by the manufacturer. Specimens are cut out using a diamond saw. Due to the difficult handling of the thin specimens and to avoid an additional influence on the test results as reported in [9] polishing of the edges is omitted. Surface condition of the edges influences the failure process with rougher surfaces leading to crack initiation at lower strains. But as failure is assumed for this type of specimens to initiate at the edges anyway and all specimens are cut under the same conditions, edge roughness should be the same, making the results well comparable. In addition, surface quality with regard to roughness was quite high after the sawing due the use of a diamond saw with well-chosen cutting parameters (comparable to polishing with abrasive paper with a grain size of 800). Three plates of each configuration are produced in order to regard statistical variations of the manufacturing process within the test results. Fibre reinforced elastomer end tabs are glued on the specimens by using a thermoset adhesive, leaving a distance of
3. Results and discussion
Fig. 1. Schematical sketch of (a) specimen for transverse tensile test, (b) specimen after first failure and (c) specimen after second failure.
The first and second failure strength are compared for several number of plies, so that the transverse strength in dependency of the volume as well as the influence of pre-existing damage in case of the second failure strength can be evaluated. Fig. 2 shows the t transverse tensile strength R22 for all tested specimens versus their volume, which varies according to different thicknesses (number of plies n) of the four configurations regarded. First failure of a specimen is indicated with open white symbols. Second failure strength (refer to Section 2.2) is represented with filled black symbols. The values of first and second failure strength of the
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t Fig. 2. Transverse tensile strength R22 of M21/T800S versus specimen volume V.
Table 1 Transverse tensile strength of M21/T800S specimens in dependency of their volume. 1st failure No.
2nd failure
Strength / MPa
Volume
Strength / MPa
Volume
/ mm3
/ mm3
Length /mm
2–3 2–5 2–9 3–1 3–6 3–8 4–2 4–5 4–7
77.9 78.2 72.9 63.6a 65.5 73.0 70.5 79.3 64.7
11,322 11,335 11,333 11,164 11,407 11,397 11,250 11,444 11,435
79.2 84.4 75.7 68.7 67.7 77.7 75.5 71.8 79.3
8033 8339 8143 6154 4449 6870 7582 3879 6191
106.4 110.4 107.8 82.7 58.5 90.4 101.1 50.8 81.2
10 plies
1–2 1–4 1–7 2–3 2–5 2–8 4–2 4–4 4–8
74.1 69.5 74.1 64.7a 65.2 72.0 72.0 71.1 65.9
7034 7101 7089 7106 7141 7127 6993 7147 7095
72.2 74.4 84.5 84.0 81.1 80.9 76.6 74.0 74.4
4512 4728 4738 4535 4560 4626 2307 3364 5122
96.2 99.9 100.3 95.7 95.8 97.4 49.5 70.6 108.3
5 plies
1–3 1–6 1–9 3–3 3–6 3–8 4–2 4–6 4–8
78.1 79.1 82.4 83.9 78.3 70.7 75.8 73.6 64.2
3585 3587 3542 3552 3664 3546 3513 3626 3581
80.9 77.3 83.0 79.5 84.9 76.2 81.2 82.3 76.6
2474 2046 1837 1069 1197 2551 2229 2489 2307
103.5 85.6 77.8 45.1 49.0 107.9 95.2 103.0 96.6
3 plies
1–2 1–5 1–7 2–2 2–3 2–5 4–5 4–6 4–8
77.0 71.4 77.1 74.6 70.3a 72.4 73.9 81.2 78.3
2079 2167 2192 2156 2154 2124 2170 2189 2179
85.9 81.5 76.7 73.5a 72.6a 74.8 82.6a 81.2a 82.1
1357 1397 1347 1409 1537 1373 640 672 1024
97.9 96.7 92.2 98.0 107.0 97.0 44.2 46.1 70.5
16 plies
a
second failure strength are in the same range of 7 4 MPa. Only for two specimens, number 4–5 and 3–3, the second failure strength is lower than the first failure strength. In total, the values for first and second transverse failure clearly indicate that the strength is higher with decreasing volume of the specimen. This implies that first failure occurs at the most critical defect in the range of the tested volume [1] and strength at first failure is not the ultimate transverse tensile strength of the material. Second failure occurs for most specimens at higher loads and thus results from a less critical defect than the one responsible for first failure. When considering possible damage in the optically undamaged regions of the specimen after the first test, which cannot be excluded, the influence of a critical defect is even more highlighted, because second failure occurs at higher loads despite a possible pre-existing damage in the specimens at the same strain rate. Concerning defects in a brittle material, the principle of the weakest link that determines the strength of a chain is applicable. With increasing number of links in a chain, the probability to have a weak link in the chain increases as well, therefore the strength tends to decrease with increasing number of links. For a volume, the strength under uniform stress is dominated by the largest defect. Defects are randomly distributed with larger volumes having a higher probability of containing larger defects and thus lower strength. This size effect can be described by a statistical distribution proposed by Weibull in 1951 [1] that is widely used to represent the strength of brittle materials [16]. The size effect in solids with probability Pi(σ ) and critical stress sc as a function of the stress s is described with the following equation [1]: m
Pi(σ ) = 1 − e−( σc ) σ
(1)
where m is the Weibull-module. The double logarithmic representation for the first and the second failure is shown in Fig. 3. Values of m1 = 16.14 and σ0,1 = 75.66 MPa for first failure respectively m2 = 20.50 and σ0,2 = 80.25 MPa for second failure are determined. The Weibull-modulus from first to second failure increases by 21.27%, indicating that strength scattering decreases, which is in contrast to Weibull's theory [4] and previous investigations on a size effect in epoxy resin [2]. This can be explained with the weakest link being eliminated after the first test in this study. Hence, with the largest flaw excluded, higher strengths with less scattering can be obtained. The minimum failure strengths (excluding the values marked with a rectangle in Fig. 5) are plotted against volume on a log-log scale. This is shown in the Weibull weak link scaling diagram in Fig. 4. The curve through these values to determine the Weibullmodulus m for minimum transverse tensile strength should be a straight line with a slope of −1/m.
Values regarded for Weibull weak link scaling diagram (Fig. 4).
specimens are given in Table 1 for the different number of plies. The length of the secondly tested specimen is also given. For most specimens, the second failure strength is higher than the first failure strength. For specimens 1–2, 1–6, 1–7, 2–2 and 4–6, first and
Fig. 3. 1st failure (Weibull modulus m¼ 16.14 and σ0 = 75.66 MPa ); 2nd failure (Weibull modulus m¼ 20.50 and σ0 = 80.25 MPa ).
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In order to compare two different volumes V1 and V2 with their strengths σult,1 and σult,2, Eq. (2) is used. 1
σult,1 σult,2
⎛ V ⎞− m = ⎜ 1⎟ ⎝ V2 ⎠
(2)
Fig. 4. Weibull weak link scaling diagram. All values are out of Table 1.
t Fig. 5. Transverse tensile strength R22 of M21/T800S in dependency of specimen volume V with Weibull plot. (□: outlier not regarded for Weibull weak link scaling diagram in Fig. 4).
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The comparison of the median values for transverse tensile strength of the different configurations shows also a slight trend of increasing strength with decreasing number of plies and thus decreasing volume, but standard deviations are quite high, as shown in Fig. 5. In this diagram, the values for first failure strength of the specimen are presented as a box plot and second failure is indicated with symbols. A spline through the minimum values of each volume as well as the Weibull plot show the volume effect resulting from a statistical distribution of defects that is according to Weibull's theory of defect distribution [1]. The Weibull plot (dotted line in Fig. 5) shows good agreement with the data. One value, marked with a open white square, is regarded as an outlier and thus omitted for the fit. The horizontal line at 86 MPa indicates the ultimate transverse tensile strength of the material for the tested volumes, which results from the maximum interfacial strength of fibre and matrix. Except the one value already mentioned, all values for transverse tensile strength lie in the range or within the ultimate value and that one dominated by the statistical distribution of defects as a Weibull envelope curve. Photos of the representative fracture surface after first failure of the thinnest (n ¼3 plies) and the thickest (n ¼ 16 plies) configurations are shown in Fig. 6. As can be seen in the pictures, both specimens failed with a single crack through the width transverse to the loading direction. All other specimens showed the same brittle fracture behaviour at final failure, as expected. This is important, because Weibull theory is only valid while the failure mode is the same for all specimens [16]. Despite the general failure mode remaining the same with increasing volume, differences in the roughness of the crack surface can be observed like fibre bridging occurring in thicker configurations. Single fibres are also observed to split into the fracture surface of the thinnest configuration, but the amount is smaller. One reason may be the broader crack surface, presupposed by the higher thickness, which may account for more fibres to bridge during crack propagation in the matrix between the fibres and thus results in a slightly rougher fracture surface. This is further investigated in SEM. SEM images of a representative fracture surface of the thinnest (n ¼3 plies) and the thickest (n ¼16 plies) configurations are shown in Fig. 7. Smooth fibre surfaces are visible in both configurations (refer to Figs. 7(c) and (a)), indicating fibre–matrix interface failure. In some areas residual matrix still sticks on the fibres that hints at good fibre–matrix bonding and thus cohesive matrix failure in these locations (refer to Fig. 7(d)). In addition, cusps that results from a local shear failure of the matrix [17,18] occur. They are shown in SEM images with higher magnification in
Fig. 6. Characteristics of 1st failure of (a) n¼ 3 and (b) n¼ 16 plies.
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Fig. 7. SEM images of representative fracture surfaces of specimens of the thickest and thinnest configuration with n¼ 16 and n¼ 3 layers. (a) Fracture surface of a specimen with 16 layers. (b) Detail of (a) showing interfacial failure and residual matrix on the fibres resulting from cohesive matrix failure. (c) Fracture surface of a specimen with 3 layers. (d) Detail of (c) showing matrix cusps between the fibres.
Fig. 7(d) for n ¼3 layers and 7(b) for n ¼16 layers respectively. Crack propagation at final failure is therefore assumed to be mostly adhesive but partly cohesive, depending on the local interfacial strength. Since there are no significant differences in the fracture surfaces of specimens with different thicknesses, the failure mode is confirmed to be the same for all specimens and Weibull theory is fully applicable.
4. Conclusion The subject of this work is the investigation of the size effect on transverse tensile strength of CFRP. As values for this strength of FRP obtained by respective tests depend on the statistical defect distribution. The new test approach allows us to analyse the influence of statistical defect distribution leads to more accurate values for the transverse tensile strength of FRP. The results of the study show that first transverse failure occurs at the most critical defect (weakest link) and second failure strength is higher than first failure strength. Even when considering pre-existing damage, the second failure of the smaller volumes occurs at higher strengths, so that still conservative values for the smaller volumes are given. With decreasing of testing volume Weibull distribution becomes smaller (Weibull module m increases) i.e. reliability becomes more accurate, which highlights the applicability of the new test approach. With decreasing specimen volume, the transverse strength increases significantly. Transverse strength is dominated by IFF, which depends on interfacial strength of the fibre–matrix bond and defect distribution within specimen volume. It could be concluded, that the new method provides a more accurate measure of transverse tensile strength, which may be used along with Weibull scaling to predict transverse strength of smaller volumes e.g. 90° layers in cross-ply laminates during fatigue loading or micromechanical modelling.
Acknowledgements The authors gratefully acknowledge the financial support of the German Research Foundation (DFG) within the project FI 688/5-1.
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