Modelling of Strength and Stiffness Behaviour of Natural Fibre Reinforced Polypropylene Composites

Transcription

1 Modelling of Strength and Stiffness Behaviour of Natural Fibre Reinforced Polypropylene Composites Modelling of Strength and Stiffness Behaviour of Natural Fibre Reinforced Polypropylene Composites Taha I.*, El-Sabbagh A.** and Ziegmann G.*** Institute for Polymer Materials and Plastics Processing, Agricolastrasse 6, Clausthal-Zellerfeld, Germany Received: 24 December 2007, Accepted: 30 January 2008 SUMMARY The mechanical behaviour (strength and stiffness) of natural fibre reinforced thermoplastics is investigated on the example of an injection moulded sisal-polypropylene system. An analytical model based on the rule of mixtures is developed to predict the mechanical behaviour of such composites. Considering interfacial characteristics this model accounts for the different modes of load transfer between matrix and fibre and their changeover. Close agreement between model and experimental results was achieved at low fibre contents (below 20 wt.%) as well as at higher contents (exceeding 40 wt.%). The model was finally verified against the experimental data and against available literature results. INTRODUCTION The use of natural fibres for polymer reinforcement is gaining increased attention, not only on the research but also on the industrial scale. The diversity of economical and ecological advantages, in addition to their low density and good specific properties makes natural fibres not only interesting as filler but also as a competitive reinforcement material 1,2. However, next to low thermal stability, high moisture absorption and the polar characteristics, which make natural fibres incompatible with many thermoplastic polymers 3, the mechanical behaviour of the composites is often difficult to predict. Experimental work and literature survey evidence that the mechanical behaviour, especially the strength does not follow the rule of mixtures. At low fibre contents (below 10 vol.%) natural fibre composites witness a drop in tensile strength properties, which is recovered up to around 40 % fibre volume content beyond which property deterioration again takes over as can be depicted from 4-7. Mathematical modelling of natural fibre composite behaviour allows mechanical engineers and designers to predict the mechanical properties of this new material group and to accordingly determine necessary processing parameters and filling grades to attain desired product requirements. EXPERIMENTAL Materials Sisal fibre bundles were supplied by the Liros-Rosenberger Tauwerk AG. The average fibre diameter is 68 μm with an overall density of 1.3 g/cm³. Single fibre tensile tests are carried out according to DIN for 100 single Figure 1. Strength and stiffness of sisal-pp composite system at different fibre weight fractions *iman.taha@tu-clausthal.de, **ahmed.sabbagh@tu-clausthal.de, ***Ziegmann@puk.tu-clausthal.de Smithers Rapra Technology, 2008 Polymers & Polymer Composites, Vol. 16, No. 5,

2 Taha I., El-Sabbagh A. and Ziegmann G. fibres at a crosshead speed of 1 mm/ min using a 2.5 kn load cell. Tensile strength and stiffness is found to be 1500 MPa and 38 GPa, respectively. The applied DOW H734-52RNA Polypropylene (PP) is a homopolymer developed for thin wall, high speed injection moulding with good flow and physical properties. Tensile strength and stiffness are measured according to DIN EN ISO 527-2/1BB/2 and are found to average 34 MPa and 1.99 GPa, respectively. Composite Manufacturing Compounds are developed by means of a PolyLab system kneader from Thermo Haake (Rheomix 600P), where the polymer is first melted and homogenized at 50 rpm for 5 min, then further kneaded after the addition of the short cut fibres (5-10 mm in length) for another 10 min up to constant torque, to ensure homogeneous fibre dispersion in the matrix. The compound is then shredded and injection moulded at C, 800 bar and 22 cm³/s. Mechanical Testing Tensile tests are conducted on a Zwick Universal Testing Machine at a crosshead speed of 2 mm/ min according to DIN EN ISO 527-2/1BB/2. Further, Interfacial Shear Strength (IFSS) is determined by means of single fibre pull-out tests, which is described in more detail in 8. The IFSS of sisal- PP composites is found to average 6.1 MPa. Modelling Most of the applied models are based on elementary mechanics and evolve from the common Rule Of Mixtures (ROM) 5,6,9,10. In these models it is primarily to be noted that they assume a linear relationship between the fibre volume fraction and the property under consideration. Further assuming full utilisation of fibre reinforcing potential based on perfect fibrematrix bonding, it is to be noted that the ROM predicts fibre properties at 100% fibre content as can be depicted in Figure 2, which is only valid for continuous fibres. Taking short fibres into consideration, the lack of adhering material would result in the measurement of zero tensile properties at 100 % fibre content, as there is no adhesion between the individual fibres. In attempt to modify the ROM to satisfy the experimental data, a number of different factors have been introduced leading to the general model skeleton presented in Equation (1), where c, m and f denote composite, matrix and fibre respectively; P is the property under consideration, the volume fraction, and η 1 η 2 are correction factors. P c = P m (1 )+ ( )P f (1) The above equation, although it might account for short/discontinuous fibres or even random fibre orientation it still does not account for the deterioration in mechanical properties in the range below and above 10 and 40 wt.% respectively. Composite Stiffness Behaviour Alvarez [11] investigates four methods of stiffness calculation namely; series mode as shown in Equation 1, parallel mode, modified rule of mixture by introducing an empirical factor on the fibre strengthening term, and finally a combination of the components of the series and parallel strengthening as presented in Equation (2). E c = x.[e m.(1 v f )+ E f.v f ] E +(1 x). m.e f E f.(1 v f )+ E m.v f (2) Figure 2. Mechanical behaviour of natural fibre composites against volume fraction for continuous fibres The numerical approach of Halpin- Tsai equations 12,13 often shows good compromise with the experimental stiffness values. Tsai-Pagano model similarly applies a combination of the expected longitudinal stiffness to the transversal one in ratio of to ,15. Cox-Krenchel model 16 used again Equation (1) and defines the length efficiency factor (Equation (3)) as Cox 17 and introduces the orientation factor (Equation (4)) as illustrated by Rosenthal 18. This model is accepted and applied by many researchers 5,7,9,10. tanh(l /2) le = 1 l /2 where = 1 2G m r f E f ln(r / r f ) (3) where r f is the fibre diameter and R is the inter-fibral distance based on homogeneous geometrical packing. Assuming a square packing factor R/ /4 r f is to be taken as. oe = n a n cos 4 n (4) where a n represents the fibre fraction in the direction of φ n neglecting the transverse deformations 18. For in-plane random distribution η o is and 0.2 for 3-d distribution. Figure 3 shows different modelling approaches in comparison with the 296 Polymers & Polymer Composites, Vol. 16, No. 5, 2008

3 Modelling of Strength and Stiffness Behaviour of Natural Fibre Reinforced Polypropylene Composites Figure 3. Stiffness experimental results against different modelling approaches Figure 4 shows different strength modelling methods against experimental results. The Kelly- Tysson model is found to lie closest in agreement. Therefore, the Kelly- Tysson model is applied in this work as a basis for further modification. experimental results obtained. The Cox-Krenchel model is found to show closest agreement to the experimental results. Therefore, the Cox-Krenchel model is found suitable to be used for stiffness modelling and for further modifications to be implemented. Composite Strength Behaviour Similar to the prediction of composite stiffness behaviour, strength properties are also often modelled applying the rule of mixtures and its modified form as given by Equation (1). Glasser et al. 6 used this form to estimate composite tensile strength, where he defined the modification factors to be 0.5 through curve fitting. Sarkar 19 and Cao 20 introduced defect factors d f, d m in fibre and matrix strengthening terms in addition to an empirical factor k as shown in Equation 5, which are however complicated to determine. c = m.e kd m.(1 v f )+ f.e kd f. (5) Similar to the proposed Cox-Krenchel model for the prediction of composite stiffness, Kelley 17 and Tyson consider both fibre length and orientation efficiency factors. The orientation factor η oσ is to be determined according to Equation (4) (as for the stiffness orientation factor), whereas the length efficiency factor η lσ is given by Equation (6). 1 l c 2l nl l c l = l l <l c 2l c (6) The effect of fibre length distribution was investigated applying Weibull distribution concepts 9. Accordingly, strength and stiffness values are integrated over the range of fibre length variation. Further models explain composite failure in terms of four aspects namely; fibre-pull-out, debonding, tensile and shear modes 15,21, which again requires complex measurement of various properties. Development of New Models for the Estimation of Composite Strength and Stiffness Behaviour Summarising observations concerning available models for the prediction of tensile strength and stiffness behaviour of natural fibre reinforced composites, following statements can be made: - In many models a linear relationship between fibre volume fraction and mechanical stiffness or strength is assumed. This implies an increase in strength and stiffness up to a maximum value of mere fibre properties at =1. As mentioned above, this assumption is to a certain extent acceptable if continuous fibres are taken into consideration (practically ultimate fibre properties cannot be attained since a 100 % filling can hardly be achieved). For short fibres however, 100 % fibre content implies the lack of adhering matrix between individual fibres, leading to the measurement of zero tensile properties. - Few researchers 6,15, describe a nonlinear composite behaviour against increased fibre volume fraction. Matrix properties are thought to dominate up to a critical volume fraction, after which the fibre starts to share in overall composite strengthening. Such behaviour assumes both elastic fibre and matrix, where matrix failure strain exceeds fibre failure strain (ε f < ε m ). - Efficiency factors are introduced to the rule of mixtures to fit models to the experimental results. Such factors are primarily introduced to the fibre strengthening term of the ROM, and are deduced Polymers & Polymer Composites, Vol. 16, No. 5,

4 Taha I., El-Sabbagh A. and Ziegmann G. Figure 4. Strength experimental results against fibre volume fraction for different modelling approaches In the modified model η oe is assumed to have a value approximate to unity, since stiffness is measured at preliminary stage of loading, which implies that the surface stiffness dominates the measurable composite stiffness. This assumption lies in agreement with the experimentations discussed by Neves et al. 22. High values of η oe approaching unity are accordingly reported near composite surface opposed to low values at the core. either by direct empirical fitting approaches (such as Glasser 6 ), or by mathematical calculations (η l η o ). - Most models assume fibre s surface area to be totally surrounded by matrix. Moreover, perfect adhesion is considered to take place between the total fibre surface area and the matrix and hence maximum load transfer is assumed. - Available applicable models neglect the obvious decrease in strength at low fibre contents and attribute it to the versatility of the natural fibres mechanical properties or they are interested in the results at higher composites. - The available applicable models neglect the obvious decrease in strength at very high (above 0.4). Taking the above mentioned facts into consideration following models are suggested for the prediction of short in plane randomly oriented natural fibre polymer composite stiffness (Equation (7)) and strength (Equation (8)) behaviours. E c = E m (1 )+ oe le a E f (7) c = k m. m (1 ) +k f. o l a f + k p. p (8) where η oe and η oσ are the fibre orientation factors for strength and stiffness, respectively; η le and η lσ are the respective fibre length efficiency factors as defined by Krenchel 14 and Kelly-Tyson 17 and given by Equation (3), Equation (4) and Equation (6). E, σ and stand for stiffness, strength and fibre volume fraction respectively, whereas c, f and m respectively denote the composite, fibre and matrix. The factors k m, k f and k p are factors denoting matrix, fibre, and interface shares in composite load bearing efficiency, as will be discussed in detail in the following section. Last, a further agglomeration factor η a is introduced to the modified Cox-Krenchel and Kelly-Davies models. A further consideration implemented to the general Cox-Krenchel equations is the divergence between experimental and estimated stiffness values at higher fibre contents, taking into account the non-linear behaviour of the composites opposed to the linear Cox-Krenchel description. Assuming that the fibres agglomerate at higher contents the matrix will not be able to perfectly surround every single fibre and will herewith not be able to successfully transfer loads. Such behaviour is simulated by the introduction of an agglomeration factor η a as a function of the volume fraction and the packing geometry 7. Figure 2 illustrates the tensile behaviour of continuous fibre composites according to the rule of mixtures. Applying a volume fraction of 100% would lead to the estimation of the tensile properties of the mere fibres P f (practically a 100% fibre integration is not possible, and hence only around 70% of fibre ultimate properties can be reached at highest filling grades). However, the case is different when introducing short fibres into the matrix material (Figure 5). The lack of adhering material would theoretically result in the measurement of zero tensile properties at 100% fibre content, due to the absence of force transmitting material. When considering a square packing factor (π/4), it becomes apparent that the maximum possible volume fraction lies at 78%, after which only 298 Polymers & Polymer Composites, Vol. 16, No. 5, 2008

5 Modelling of Strength and Stiffness Behaviour of Natural Fibre Reinforced Polypropylene Composites reduced load can be carried by the composite system, due to lacking adhesion between the individual fibres. Consequently, this drop is assumed to gradually occur as a function of fibreto-fibre contact - or in other words fibre agglomeration. This in turn depends on the fibre content in terms of and the processing conditions. Poor mixing conditions during compounding would enhance fibre agglomeration, whereas proper mixing would ideally lead to well dispersed fibres in the matrix. Accordingly, the agglomeration factor ηa is a function of, the packing conditions (c=1/packing factor), and a pattern exponent n accounting for mixing conditions, as proposed by Equation (9). According to the experimental work of compounding and mixing a value of n=2 is found to be appropriate. At a fibre content of 100% the agglomeration factor yields zero value, i.e. 100 % short randomly oriented fibres are not able to transfer loads, which lies in agreement with the first assumptions made in this study. Figure 5. Mechanical behaviour of natural fibre composites against volume fraction for discontinuous fibres and the effect of fibre packing Figure 6. 3-dimensional fibre array a = 1 ( c ) n (9) At low fibre contents both fibre and matrix contribute to the overall tensile behaviour and load is transferred either by the fibre (limited by the fibre tensile strength) and/or through the fibre-matrix interface (limited by the interfacial shear strength IFSS). The extent of each parameter s share in load bearing is governed by two corresponding factors k f and k p : At low fibre contents fibres are free to move such that weak interfaces can easily act out, herewith reducing the fibre s share in load bearing. Composite behaviour is here governed by pull-out failure according to its occurrence probability k p. The higher the probability, the lower the load transfer to the fibre and the weaker the composite. Within this scope, the fibre content controls the movement behaviour of the fibres in terms of available distance between two adjacent fibres 2R. At high fibre volume fraction, the spaces in between are limited, and the fibres get entangled upon movement, resulting in interlocking conditions. The limiting factor to fibre movement is reached when the inter-fibre distance reduces to that of a fibre diameter d. At this stage interlocking prevents the fibres from movement. Consequently, the determining factor in fibre pull-out is the ratio 2R/d. When 2R/d reaches 1, interlocking prevents pull-out to take place and the probability lies at k p =0. The factor k p is a pure geometrical factor and is suggested to be area sensitive rather than linear space dependant, according to Equation (10), where 2R is the inter-fibre distance and d the average fibre diameter as illustrated in Figure 6. k p = 1 d 1 d 2R d 2 2 (10) Where, d 1 and d 2 are the fibre diameters in two orthogonal directions and d 1 > d 2 where d 1 /d 2 is a correction factor to Polymers & Polymer Composites, Vol. 16, No. 5,

6 Taha I., El-Sabbagh A. and Ziegmann G. account for the oval geometry of the fibre cross section. By increasing fibre volume fraction interlocking conditions force the fibre to carry all transmitted loads. As a consequence k p =1 leads to k f =0 and vice versa. This implies that failure is expected to take place either by pullout or by fibre failure. The probability for one of the two failure modes to take place is dependant on the other. Hence, the second factor k f describing the probability of pull-out occurrence can be evaluated in relation to k p as in Equation (11). k f = 1 k p (11) Assuming that the matrix yield strain is lower than the fibre failure strain, full utilisation of both fibre and matrix ultimate tensile properties can be made use of, as illustrated in Figure 7. Accordingly the factor k m (matrix share) is assumed to be maximum, i.e. equal to unity. Validation of Developed Model Against Experimental and Literature Results The application of the new stiffness model with c=1.273 (the packing factor is π/4 assuming a square packing arrangement) and n=2 for sisal-pp is illustrated in Figure 8. The new model shows a very conforming description with the experimental results. The nonlinear elastic behaviour against fibre volume fraction, especially at higher fibre contents becomes obvious, and is Figure 7. Representative stress-strain curve for the case that ε m >ε f Figure 8. Proposed model and effect of agglomeration factor on sisal-pp composite stiffness behaviour also very well described by the newly introduced model. Applying the new governing model for tensile strength in short fibre reinforced composites as given by Equation (8), it can be seen that the tensile strength of the composite is composed of the sum of the individual performance of the matrix and fibre bearing strengths, and the interface in between up to fibre pullout. The effect of these load bearing components is illustrated in Figure 9 to result in a sum closely describing the experimentally obtained data. It becomes apparent that the contribution of each element varies with respect to the fibre content in the composite. Whereas the matrix can carry fewer loads, due to its reduced volume fraction, the fibre takes over, and increases the overall composite strength through its higher tensile properties. Last but not least at a threshold volume fraction t, due to fibre interlocking, the probability of pull-out to occur reduces to zero and the load is primarily carried by the fibre cross-section. In the following the new strength model is applied to a case from literature data, where a flax-pp composite is examined by Sparnins [Spa-06, And-06]. In this study flax- PP composites were produced from compounds obtained by co-extrusion of granulated polypropylene and flax fibres. Anderson considered in his prediction calculations a simple critical-zone model by Fukuda and Chou and modified it according to the suggestions of Jayaraman and Kortschot. The fibre strength as a function of its length is evaluated according to the modified Weibull distribution. Hence, for the strength in case of three-dimensional fibre orientation assumed for extruded fibre composites, the strength the model is given by Equation (12). 300 Polymers & Polymer Composites, Vol. 16, No. 5, 2008

7 Modelling of Strength and Stiffness Behaviour of Natural Fibre Reinforced Polypropylene Composites Figure 9. Proposed model against experimental data of sisal-pp, showing the contribution of matrix, fibre and their interface in the total composite tensile strength behaviour trend with the variation of the fibre content. CONCLUSIONS Reinforcement of thermoplastic matrices with almost 35% fibre volume fraction sisal shows almost 300% stiffness improvement on one side and slight strength improvement on the other side. Figure 10. Proposed model showing improved prediction of the strength of extruded flax-pp composites. The model is based on σ = 27 and 1170 MPa for matrix and fibre, respectively; IFSS = 8 MPa; l = 0.42 mm; d = mm The rule of mixtures is modified to include the effect of fibre pullout in reducing composite strength at low volume fractions (<10%). Furthermore, the reduced composite strength behaviour at higher fibre contents (>30%) is successfully modelled by the introduction of an agglomeration factor. This describes the situation of matrix-starved areas and uncovered fibres at high fibre contents. The fibre dispersion, as a factor depending on composite fabrication conditions, is also involved to account for the influence of different processing techniques. Moreover, the assumption of higher orientation factor (equal to unity) in stiffness modelling at the composite surface is validated and is found to yield good agreement with experimental results. The suggested modification factors in the strength model explains the handover of the strengthening sources in the composite system. REFERENCES c = 5 f (l)l 1 l 5 crit l l l crit 1 l crit h(l)dl + (1 ) m(12) 2l Andersons et al. observed that the experimental and predicted strength values are to a certain extent reasonably well correlated, although the strength is consistently overestimated. Therefore, an empirical fibre efficiency factor η s of 0.63 was introduced to the fibre contribution term to yield an improved curve fitting. Figure 10 shows that the new developed model as given by Equation (8) does not only yield good accuracy of strength value prediction, but additionally well describes the strength Bogoeva-Gaceva, G., Avella, M., Malinconico, M., Buzarovska, A., Grozdanov, A. Gentile, G. and Errico, M., Natural fiber ecocomposites, Polym. Compos., DOI /pc, Van de Velde, K., and Kiekens, P., Influence of fiber surface characteristics on the flax/ polypropylene interface, J. Thermoplast. Compos. Mater., 14, May 2001, Saheb, D. and Jog, J. Natural fiber polymer composites: A review, Adv. Polym. Tech., 18(4) (1999) Polymers & Polymer Composites, Vol. 16, No. 5,

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