(a) assessment of the current (2010) and expected future (2020) of the global market;

(b) identification of the key growth segments for these composites, with an emphasis on the ecological and environmental benefits;

(c) identification of the suppliers contributing at all levels to preserve the value chain from fibre suppliers to composite product manufacturers.

(a) instantaneous time-independent elastic deformation;

(b) linear viscoelastic region (compliance is independent of stress);

(c) equilibrium region/nonlinear viscoelastic region (compliance is dependent on stress);

(d) recovery region.

11.2.1 Linear and nonlinear viscoelasticity

For a given constant load σ₁, the measurement of time dependent strain ε₁ is shown in Fig. 11.3. The specimen is allowed to recover and a greater stress σ₂ is applied. The time dependence of the strain ε₂ is also shown in Fig. 11.3.

At a given time t₁ and t₂ after stretching, if ε₁ and ε₂ are linear with the representing stresses, σ₁ and σ₂, the stress strain relationship can be given by:

Thus, for any arbitrary time t, the strains at the two stresses can be expressed as:

The strains in the above experiments are proportional to the applied stresses. In general, for a given applied stress σ, creep compliance D(t) is a ratio of strain to stress at a given time t.

This property is described as linear viscoelasticity. In the linear range, the compliance is independent of the stresses employed in the creep test (σ₁, σ₂ or any other stress values). The strain limits in which a specimen is linear viscoelastic can be ascertained by a simple creep test. A transition from the linear to the nonlinear viscoelastic region is shown in Fig. 11.4.

Most polymers usually demonstrate a linear viscoelastic property at low stresses (maximum strain corresponding to ~0.005 or less). At higher stress levels, the material establishes nonlinear viscoelastic behaviour and does not keep the same linear relation between stress and strain. Nunez et al. carried out short term and long-term creep tests on polypropylene/wood flour composites. The creep deformation for strain-time plots was linear up to 10 MPa.⁷ This signified that the maximum applied stress that works in the linear viscoelastic range is 10 MPa.

11.2.2 Superposition principles

The two superposition principles are significant in anticipating the creep behaviour of plastic materials when they are in the linear viscoelastic range. First, the Boltzmann superposition principle (BSP), depicts the response of a material to various loading histories. The second is the time–temperature-superposition principle, also known as the Williams–Landel–Ferry (WLF) equation, that identifies the equivalence of time and temperature. This will be discussed in the next section.

The Boltzmann superposition principle is applied and limited to the linear viscoelastic region of the polymers.^8–10 It states that the response of a polymer to a given loading is independent of the responses to any other loadings already present in it. Thus, each loading step forms an independent contribution to the final strain, so that the cumulative strain is obtained through the addition of all the contributions.

At time τ₁ stress σ₁ is applied and the strain induced is given by:

According to linear viscoelasticity, the compliance D(t) is independent of stress, i.e. D(t) is the same for all stresses at a particular time. If the stress increment σ₂ − σ₁ is applied at time τ₂ and the strain increases due to the stress increment, σ₂ − σ₁ is:

Likewise, the strain increase attributed to σ₃ − σ₂ can be given by:

For creep, the total strain may be expressed by:

or

where D(t) = 1/E(t) is the compliance, a characteristic of the polymer at a given temperature and initial stress. In other words, the BSP shows that the effect of a compound cause is the sum of the effects of the individual causes.¹¹ Another outcome of the BSP is that the recovery is a mirror image of the preceding creep. i.e. creep and recovery are similar in magnitude.¹²

(a) Experimental characterization of creep properties of the composites.

(b) Modelling the measured creep data.

(c) Prediction of the long-term creep behaviour of the composites through short term test measurements.

11.3.1 Factors affecting creep of natural fibre composites

A combination of elastic deformation and viscous flow (i.e. viscoelastic deformation) generally causes creep in polymers. Creep in thermoplastic materials can be ascribed to various material properties, such as crystallinity, molecular orientation¹³, and environmental and external factors such as applied stress, temperature and humidity.

The creep behaviour of the composite is governed by either the polymer matrix or the reinforcing fibres, depending upon the amount of fibres and fillers and the orientation of the reinforcing fibres within the polymer matrix. For example, the creep deformation of composites which rely upon the reinforcement of long unidirectional fibres is influenced by the creep of the fibres when they are aligned in the direction of loading. On the other hand, it is determined by the matrix creep if the fibres are discontinuous or randomly oriented. The creep mechanism is also greatly affected by the kind of interaction that occurs between the matrix and the fibre. The better the adhesion between the matrix and the fibre, the more effective will be the stress transfer and hence the creep deformation is less.

11.3.2 Effect of filler loading, stress and temperature

Wood fibres are generally preferred to inorganic fibres for noncritical applications because they have certain advantages such as lightweight fibres, ease of processing and high-volume low-cost composite production. A creep study becomes a necessity if the wood fibre reinforced thermoplastics need to be considered for long-term loading applications. Nunez et al. observed the effect of the following variables on the creep behaviour of polypropylene/wood flour composites: filler content (which varied from 0 to 60%), compatibilizing agent polypropylene maleic anhydride copolymer (PPMAN), and temperature.⁷ Creep deformation reduced with: increasing wood flour content (except at much higher filler concentrations where wetting and filler dispersion problems start), the addition of PPMAN, and low temperatures. They modelled the creep compliance using Burger’s model and the power law equation and ascertained that Burger’s model provides a good description of the linear viscoelastic behaviour of the composite. The effect of the concentration of untreated wood flour on PP composites is displayed in Fig. 11.5. With an increased woodflour content, as expected, deformation decreases owing to the enhanced rigidity of the composites. However 60 wt% woodflour composite is an exception to this as the matrix cannot wet the filler completely rendering the filler-filler interaction weaker and therefore allowing it to be broken easily during deformation.

Cellulosic fibres, being predominantly polar, easily absorb moisture. Thus, studies have focused more on enhancing the interfacial adhesion between chemically and physically incompatible phases.¹⁴ The interfacial adhesion can be modified in several ways:

A sizing agent, used mainly in the papermaking industry, was indicated to be an appealing method of surface modification for natural fibres.^15,16 Researchers have also pointed out that, lignin, a constituent of natural fibres, can be employed as a coupling agent.^17,18 Lignin carries polar (hydroxyl) groups, nonpolar hydrocarbon, and benzene rings and can be used to achieve compatibility between natural fibres and the thermoplastic matrix.

The effect of variation in the interfacial interaction between the matrix and the fibre on the creep behaviour of the composite also has been studied (see Fig. 11.6).⁷ When 5% PPMAN is introduced into the composite system, the deformation is reduced in comparison with untreated composites. With increasing PPMAN content, the extent of creep deformation reduced further owing to the better dispersion of the woodflour and the improved interfacial adhesion. With 10% PPMAN, a reduction of 45% creep deformation compared with neat PP was observed.

As PP is partially crystalline, the crystalline phase hinders the mobility of the amorphous phase. With increasing temperature, the movement of the amorphous part increases, sidelining the reinforcing effect of the crystalline phase, and increasing the extent of creep deformation, as shown in Fig. 11.7. The strains measured at the end of the test, at 50 and 80 ^oC, are 2.15 and 3.93 times the strain recorded at 20 ^oC. At 80 ^oC, the creep curve enters the third zone (Fig. 11.2), where the strain rate increases with time.

Wood and thermoplastics are viscoelastic materials and both respond differently to creep behaviour.^19–21 The water/moisture uptake of wood–plastics composites is probably the only limiting factor to exploring their applicability in the construction of outdoor facilities. Wood fibre reinforced composites can take up a large amount of water because wood, which consists mainly of cellulose fibres, contains numerous hydroxyl groups that are strongly hydrophilic. The rate of moisture absorption in natural fibre–thermoplastic composites depends on the type of fibre and matrix, temperature, and the variation in water distribution within the composite.^22–24

The effect of water absorption on the creep behaviour of wood plastic composites has been studied by Kazemi Najafi et al.²⁵ Employing up to 80% of medium density fibreboard flour as a natural fibre into recycled HDPE, it was observed that the creep strain decreased with increasing lignocellulosic flour, whereas water absorption enhanced the creep deformation of the composite. It was shown that the creep strain increased with immersion time owing to the additive effect of the absorbed water on fibre–matrix debonding, making the relaxation of the molecules easier at a higher moisture content. Bledzki and Faruk conducted a short term flexural creep test to study the creep behaviour of wood fibre PP composites.²⁶ Creep resistance was found to be increased by the addition of an MAH-PP compatibilizer, with decreasing temperature and also with increasing wood fibre content. Pooler and Smith²⁷ have proposed wood plastic composites as an alternative to treated timber for waterfront structures because of their ability to resist water absorption and degradation without chemical treatment. With increasing wood fibre concentration, the moisture content in the composites increases.²⁷ Fibre length and geometry play a significant role in deciding the equilibrium moisture content (volume expansion). Bledzki and Faruk²⁶ have also noted that long wood fibre-reinforced composites are more hygroscopic (nearly twice) than the hardwood composites at higher concentrations of fibre (Fig. 11.8). The use of compatibilizer MAH-PP reduced the hygroscopicity and significantly affected the impact properties. With increasing wood fibre content, the damping index was observed to increase, and this correspondingly lowered the impact strength of the composite. Long wood fibre reinforced PP composites displayed higher impact resistance than their hardwood fibre reinforced counterparts. The compatibilizer MAH-PP improves fibre dispersion in the matrix and facilitates the interfacial adhesion between the phases. It was observed that the MAH-PP treated composites exhibited an enhanced modulus and decreased creep in the composite.

Wood can be used as a substitute filler to reinforce traditional thermoplastics and biopolymers.^28–30 However, environmental problems such as deforestation, forest degradation and the impact on global warming and biodiversity has prompted studies on how to utilize other lingo-cellulosic materials in the form of agro residues from annual crops.³¹ These field crop residues and/or agricultural byproducts, such as cereal straw, rice husk, corn stalk, corn cob, soy stalk and bagasse, are very cheap, voluminous and easily available as raw materials.³² Xu and coworkers investigated the creep behaviour of bagasse/PVC (recycled and virgin) and bagasse/HDPE (recycled and virgin) composites.^33,34 Bagasse is a byproduct obtained from sugarcane processing. Acha et al. studied the creep and dynamic mechanical behaviour of bidirectional jute fabric/PP composites.³⁵ The interfacial adhesion between the polar fibres and the nonpolar matrix was improved by two different methods:

It was observed that the creep deformation decreased with increasing jute content in PP (see Fig. 11.9). The Burger model fitted well to compositions of varying jute concentration in the creep part of the curve. The equation used for theoretical calculations of creep deformation is:

where, σ₀ is applied stress, t is time, E₀, and η₀ are the modulus of the spring and the viscosity of the dashpot for the Maxwell element, respectively, whereas E₁ and η₁ are the same for Voigt element. A drop in the immediate deformation and the slope of the steady-state creep zone was also observed.

Figure 11.10 displays the creep–recovery graphs for various fibre/matrix treated composites. Surprisingly, the esterified fabrics reinforced and lignin modified PP matrix composites showed the highest creep deformation, whereas both the samples prepared with PPMAN as a compatibilizer displayed the lowest values. Figure 11.11 is the attestation of these results: Fig. 11.11a shows the smoother surface of the esterified fabrics compared with the untreated one (Fig. 11.11c), but even after that the creep deformation is still higher. Figure 11.11c displays no adherence of the PP matrix to the untreated fibres, confirming poor interfacial adhesion between the phases.

on the contrary, it can be seen that the PP has distributed evenly onto the fibre surface (as there is no gap present at the interface) as shown in Fig. 11.11d and 11.11e, which shows the better wettability of the fibres to the matrix. Better interfacial interaction is reflected in the better creep resistance of the composite material.³⁶ It was observed that both the coupling agents G3003 and E-43 wax worked well: G3003 induced better creep performance, possibly because it has a higher molecular mass than E-43 wax, molecular weight (MW) ~ 52,000 and 9,100, respectively. A mass coupling agent with higher MW can form better and tighter entanglements with the PP matrix. Where the coupling agent has a lower MW, the creep deformation is expected to be higher as it acts as a lubricant. Another point to note is that the maleic anhydride content of G3003 is lower than that of E-43 wax. This leads to the conclusion that a higher concentration of maleation is not really required to saturate the fibre surface –OH groups. Acha et al.³⁵ have further analyzed the effect of the amount of the coupling agent applied on the interfacial adhesion and hence on the creep performance of the composite (Fig. 11.10). The creep deformation for 3 and 5 wt% is nearly the same, making it clear that 5 wt% of G3003 coupling agent is sufficient to saturate the fibre surface. However, further increase in the compatibilizing agent (7 and 9 wt% respectively) demonstrated an increase in the creep deformation as shown in Fig. 11.12. The maleated PP is less regular than the virgin PP. With an increasing concentration of maleated PP, the degree of grafting increases, which correspondingly reduces its ability to crystallize.³⁷ In semicrystalline polymers such as PP, creep resistance increases with the increasing percentage of crystallinity,^38–40 which effectively reduces with excessive compatibilizing agent. It was expected that the anhydride chains attached to the fibres were either too short or else the polarity of fibres was still much higher than that of the PP matrix. At the same time, the increased smoothness of the fibres reduced mechanical interlocking, causing a reduction in the interfacial strength of the composite. Lignin modified PP composites also showed a higher creep deformation, suggesting that lignin is a poor compatibilizer for the PP–jute system.

11.4.1 Four-element Burgers model

The easiest way to model the combined viscous and elastic behaviour of a polymer is to employ the mechanical analogs: dashpots (viscous behaviour) and springs (elastic behaviour). The four-element Burgers model is more often used for modelling the creep behaviour of natural fibre reinforced polymer composites.^7,35

The various combinations of the spring (elastic deformation) and dashpot (viscous flow) can be correlated with the creep–recovery graph of polymers. The Maxwell model with the spring and dashpot attached in a series, does not work well for creep. It deforms continuously with time as the dashpot responds for loading. The Kelvin–Voigt model with the spring and dashpot in parallel is another simple representation of creep. It displays the time-dependent response of the strain as the viscous flow in the dashpot is opposed by the spring flow. It does not represent instantaneous elastic deformation as well as continued flow under equilibrium. To resolve the problems of the Maxwell and Kelvin–Voigt models, the four-element model developed combines the spring and dashpot in a series and parallel combination as shown in Fig. 11.13. This model exhibited reasonable success in simulating the linear viscoelastic behaviour of polymers. It displays all the regions that are generally observed in real polymers including time-independent elastic deformation, a levelled-off equilibrium region and a recovery region too. For the analysis of the creep–recovery graph, stress and strain curves are generally plotted against time and the data is fitted into the four-element model as shown in Fig. 11.14. It can alternatively be quantitatively analyzed for properties such as modulus, viscosity, irrecoverable creep and retardation time.

One can see that the elastic, viscous, and viscoelastic behaviour of the polymer sample can be easily differentiated. The creep experiment starts when the stress σ₀ is applied to the polymer at time t = 0. With the application of stress (σ₀), the polymer shows some instantaneous deformation that corresponds to σ₀/E_x (OP), where E_x is the independent spring constant of the model as shown in Fig. 11.13. The spring elongates immediately and locks itself after a certain degree of extension. After the time-independent deformation, the separate dashpot (η_x) and the complete Voigt element (E_y and η_y) start responding. At the end, when the stress is relieved completely, the independent spring recoils immediately to the same extent (p = p). The share of the independent dashpot of the total deformation can be correlated with the slope of the strain–time graph when it reaches the equilibrium flow region. The gradient of the line (QR) will be equal to σ₀/η_x. Using that gradient, one can determine the permanent set of the sample by extending the time to t_f, where the creep test ends. The permanent set in the sample = σ₀t_f/η_x (r = r′). This independent dashpot does not recover as there is no restraining force acting on it. The permanent set shows the permanent deformation left in the material and that which can be correlated with this independent dashpot. This dashpot represents the molecules slipping past each other. The middle graph corresponding to the linear viscoelastic region (PQ) can be represented by the voigt element of the four-element model. The equations for compliance and strain measurement, respectively, take the form:

where D(t) is the creep compliance.

where _{1; 2} and ₃ are the elastic, viscoelastic and viscous behaviour contributions, respectively.

Wong and Shanks (2008) have quantitatively resolved the creep–recovery behaviour of a natural fibre–biopolymer composite system into elastic deformation, viscoelastic deformation and viscous flow (see Fig. 11.15).⁴¹ It was observed that the total creep strain of the unmodified PLA-flax and PHB–flax composite displayed a significant amount of creep. With the use of plasticizers such as tributyl citrate, triethyl citrate and glyceryl triacetate and the interfacial modifier, thiodiphenol, the total creep is effectively reduced in comparison with the unmodified composite system. After quantification of the various deformations, they found that the decrease in the total creep of the modified composites employing either plasticizers or modifiers is accompanied by a decrease in the permanent strain and an increase in the recoverable strain. on the contrary, the addition of a toughening agent, hyperbranched polyester, increased the permanent strain and reduced the recoverable strain, enhancing the overall creep strain of the composites.

With increasing stress levels from 5 to 15 MPa, it was observed that the total creep strain of the flax–PLLA and flax–PHB unmodified composites increased substantially (Fig. 11.16). Compared with the unmodified system, the use of plasticizers and thiodiphenol reduced the total creep much more. Plasticized composites have the ability to sustain higher loads without suffering a significant increase in the creep strain of the composites.⁴¹ The incorporation of toughness modifier, hyperbranched polyester (HBP), increased the creep behaviour. Thiodiphenol was the best additive in terms of reducing the total creep strain, decreasing 83% of the creep with just 5% of it in the composite system. The suppression of the creep was explained by the reduction in the viscous flow contribution of the total creep and the significant increase in the elastic and viscoelastic deformation.

11.4.2 Time–temperature superposition

The determination of the long-term performance of reinforced composites has often been hindered by the expensive and time-consuming experimentation necessary to obtain reliable results. The time–temperature superposition (TTS) principle, the most useful extrapolation technique applied to almost all types of plastics, was originally developed in the mid-1950s.^42,43 In the late 1970s this method was expanded for use with fibre-reinforced composites.^4244-45 Time–temperature superposition is based on the assumption that the effect of temperature on the time-dependent behaviour of a material is equivalent to a stretching or shrinking of the real time for temperatures above or below the reference temperature. Thus when plotted on graphs where the abscissa is defined as log time, the individual creep/stress relaxation graphs obtained at different temperatures can be shifted to the left or right to obtain a continuous master graph which spans a much longer time period than was actually employed in testing. The master graph is then used to predict the long-term behaviour of the composites.

Long-term experiments are replaced by short-term tests at higher temperatures. The shifting distance is generally termed the shift factor. The polymers that follow TTS extrapolation are thermorheologically simple and the rest of them are thermorheologically complex. It is evident that the superposition theory is based on the molecular behaviour of polymers and hence uses the term activation energy (E_α) to formulate the equations, such as the Arrhenius equation:⁴⁶

where, α_T is the horizontal shift factor, R is the universal gas constant, T⁰ is the reference temperature (K), and T is the temperature at which the test is performed (K). Regression analysis is generally carried out employing this equation to evaluate the activation energy for different materials from the experimental data.

One more empirical equation is generally used for TTS: the William–Landel–Ferry (WLF) equation. This equation gives a correlation of temperature with time. For example, if the information at higher temperatures is available, then we can interpolate/extrapolate this data to longer times to correspond with the lower temperature data. The WLF equation takes the following form

where T is the temperature at which the test is carried out. Even though the TTS theory was developed earlier and mainly for amorphous polymers, Neilsen and Landel mentioned that it could also be applied to semicrystalline polymers.⁴⁷ The changes in the degree of crystallinity with temperature and hence the changes in the modulus of elasticity with temperature in semicrystalline polymers correspond to a part of the vertical shift factor. Neilsen and Landel concluded that the vertical shift factors are mostly empirical with hardly any theoretical validation. Ward argued that the TTS theory cannot be applied to crystalline polymers as their thermal behaviour is rather complex.⁸ Faucher modified the statements and stated that the theory could be applicable to crystalline polymers provided the polymer structure was maintained in the testing condition, and that it was possible with sufficiently low strain.⁴⁸

There have been many studies on the applicability of the Arrhenius equation or WLF equation to apply TTS to the creep data.^49–53 Pooler et al.²⁷ applied TTS to wood fibre/HDPE composites and emphasized that only a single horizontal shifting is enough to superimpose the creep data. With the use of DMA experiments, storage modulus graphs were only used to ascertain the shift factors, marginalizing other viscoelastic parameters. The TTS theory was also applied by Tajvidi et al.⁵⁴ to the kenaf fibre/HDPE composite. They observed that the frequency sweep data could be superimposed well with the two-dimensional minimization method to satisfy the TTS requirements. Shift factors conformed to an Arrhenius equation for temperature dependence.

11.4.3 Findley’s power law model

Various researchers have suggested empirical relations to describe the viscoelastic behaviour of fibre-reinforced composites. The Findley power law model is one of the most widely employed analytical models for elaborating the viscoelastic behaviour of fibre-reinforced polymer composites.⁵⁵ It has the form:

where _o is the instantaneous (elastic) strain, (t) is time dependent creep strain at time t, a is the amplitude of transient creep strain and b is the time exponent.

The Findley power law model, one of the simple empirical mathematical models, was used to simulate the creep behaviour of reinforced wood–plastic deck boards.⁵⁶ The power law model formulated by Findley has become a more popular analytical model for describing the viscoelastic behaviour of fibre-reinforced polymer composites under a constant stress. This model has been used in many studies^33,57–59 and documented for predicting the time-dependent behaviour of fibre-reinforced polymer composites. The model has also been recommended by the American Society of Civil Engineers (ASCE) Structural plastic design manual for the analysis of fibre reinforced plastic composites (FRPC).⁶⁰

11.4.4 Two-parameter power law model

In general, creep strain is presented as relative creep (_r); a percentage of elastic strain in the material. The equation becomes

where A₀ is the slope of the power law model. Taking logarithms to both sides to obtain a linear relationship between A₀ and n,

The two-parameter power law model is also used for the creep modelling of kenaf fibre/HDPE composites.⁵⁴

11.4.5 Prediction of long-term creep behaviour of the composites

During the short-term testing of the polymer, we generally do not take physical ageing into consideration owing to the short length of time involved. Compliance makes the value lower than expected, when ageing of the material occurs.^61–64 So, it is really important to validate the data obtained from the short term test. Thus, the master graph generated from the short-term creep test may not depict the actual creep behaviour of the composite in the long term. Sometimes, to cross-check the data obtained from the master graph, long-term experiments are also conducted.

Xu et al. employed several creep models (like Findley’s Power Law Model, Burger’s Model, two-parameter power law model) for bagasse/PVC composites.³⁴ All of these models were capable of fitting the creep data but the Burger’s model and two-parameter power law model yielded the most consistent parameters. The time–temperature superposition model predicted the creep behaviour better from the short term tests for PVC composites than from those for the HDPE composites. The three-day creep test (as displayed in Fig. 11.17) for the composites showed a similar trend of the creep curves to those in the 30 min tests (not shown here). It was found that the Burger’s model fitted well for all composites over the entire long-run test. But the parameters for the 30 min test were very different from those for the long-duration creep test. Based on the sum of the squares, Findley’s power law model was also found to fit well over the entire range but the parameters were different and sensitive to different graph shapes and did not maintain consistency. A comparative study was made of creep prediction with the short-term (30 min.) test employing TTS and the long-run experimental results. It was observed that the TTS theory predicted well the creep data for the bagasse/PVC composites and overestimated it in the case of the HDPE composites. This inconsistency in the results for various composites indicated a need for further study and modification of the TTS theory before applying it to natural fibre reinforced polymer composites.

11.8.1 Internal/material variables

In general, the fatigue properties of composites depend on the polymer type (brittle or soft matrix)/structure, MW, crosslinking, type of filler, and its content. For polymer composites with a brittle matrix such as epoxy, it is the interfacial strength parameter that plays an important role in the fatigue behaviour of composites. The interfacial strength controls the crack propagation (crack bridging, debonding) phenomenon. With poor interfacial bonding between the phases, debonding and fictional sliding occur readily upon crack extension, allowing the long fibres to remain intact and bridge the crack. Contrarily, a stronger interface suppresses sliding and contributes to fibre fracture instead of bridging the crack.^113,114 Microcracking in toughened epoxy/polyester as well as in thermoplastic matrices is also a dominant energy dissipation mechanism precluding plastic deformation (which readily occurs in bulk matrix).¹¹⁶

11.8.2 External variables

External variables include the effects of stress amplitude, stress intensity factor, mean stress, temperature, frequency and environment. A systematic study of these variables on the fatigue mechanism of natural fibre reinforced polymer composites is needed to exploit these composites in wide-ranging external surroundings. Some work related to S–N plots and constant life line graphs provide some basic information regarding the effect of these variables on the fatigue behaviour of composites.

11.12.1 Abbreviations

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