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Gelatin yarns inspired by tendons — Structural and mechanical perspectives
Materials Science and Engineering C 47 (2015) 1–7
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Materials Science and Engineering C journal homepage: www.elsevier.com/locate/msec
Gelatin yarns inspired by tendons — Structural and mechanical perspectives Hila Klein Selle a,b, Benny Bar-On c, Gad Marom a,⁎, H. Daniel Wagner b,⁎ a b c
Casali Center of Applied Chemistry, The Institute of Chemistry, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
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Article history: Received 21 July 2014 Received in revised form 26 October 2014 Accepted 1 November 2014 Available online 5 November 2014 Keywords: Tendon structure Gelatin Extrusion Single filaments Parallel yarns Twisted yarns Mechanical properties
a b s t r a c t Tendons are among the most robust structures in nature. Using the structural properties of natural tendon as a foundation for the development of micro-yarns may lead to innovative composite materials. Gelatin monofilaments were prepared by casting and spinning and small yarns—with up to ten filaments—were assembled into either parallel or 15° twisted yarns. The latter were intended as an attempt to generate mechanical effects similar to those arising from the crimp pattern in tendon. The mechanical properties of parallel and 15° twisted gelatin yarns were compared. The effect of an increasing number of filaments per yarn was also examined. The mechanical properties were mostly affected by the increasing number of filaments, and no benefit arose from twisting small yarns by 15°. However, since gelatin filaments are elasto-plastic rather than fully elastic, much increased toughness (by up to a factor of five for a ten filament yarn) can be achieved with yarns made of elasto-plastic filaments, as demonstrated by experiments and numerical simulations. The resulting effect shows some resemblance to the effect of crimp in tendons. Finally, we developed a dependable procedure to measure the toughness of single filaments based on the test of a yarn rather than on a large number of individual filament tests. © 2014 Elsevier B.V. All rights reserved.
1. Introduction In the course of the last decades efforts have been made to develop grafts of soft connective tissues (e.g. blood vessels, tendons, ligaments) by means of a biologically-inspired strategy [1–3]. Thorough understanding of these soft tissues in conjunction with the progress achieved in biomedical synthetic components, indicates that synthetic collagen fibers offer significant advantages over traditional polymers for soft tissue repair and replacement [4]. A tendon is a soft connective tissue that generally experiences forces that are purely longitudinal and tensile as it transmits the contraction of muscle to bone [5]. It is one of the toughest structures found in nature. Emulating the tendon's unique characteristics may bring about the use of wires or ropes that may function as active components to generate, transmit, and convert power and motion. Such a bio-inspired approach may stimulate innovative thinking in the structural design of future engineering composite materials. The main goal of the present paper, which rests on the observed mechanical toughness of natural tendon, is to develop a bio-inspired and bio-compatible implantable yarn material based on porcine skin gelatin.
⁎ Corresponding authors. E-mail addresses: [email protected] (G. Marom), [email protected] (H. Daniel Wagner).
http://dx.doi.org/10.1016/j.msec.2014.11.001 0928-4931/© 2014 Elsevier B.V. All rights reserved.
The tendon presents a unique hierarchical structure in which all levels of organization from the molecular through the macroscopic are oriented to optimize the reversible and irreversible tensile properties along the length of the tendon without fracture. Its most fundamental levels consist of tropocollagen helix molecules. The multi-level organization imparts toughness to the tendon [6–8]. The hierarchical structure of tendon includes collagen fibrils that have a wavy appearance, characterized as a planar zigzag. This crimp waveform is gradually straightened when the tendon is stretched along its length, and its magnitude determines the reversible elastic properties of the tendon [6]. The crimp could also have a toughening effect as the tendon strain progressively increases with uncrimping. The primary constituents of tendon are water and type I collagen [5]. Collagen's main role is to provide structural integrity to the tissue. Collagen, as a fibrous, structural protein is composed of a right-handed bundle of three parallel, left handed helixes of polyproline type II. The resulting triple helical structure is called tropocollagen [6,9–11]. Generally, the mechanical properties of biological materials (such as collagen) and structures are of great significance to virtually all physiological properties at each and every scale [12]. Among biomaterials, collagen-derived gelatin is particularly interesting. In a dehydrated state, gelatin is a partially crystalline polymer with a relatively low melting point in the range of 40 °C–150 °C, depending on the amount of plasticizer used [13,14]. Gelatin is a very important polymer, primarily used as a gelling agent forming transparent, elastic, thermo-reversible
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gels at room temperature. Currently, it is mainly used by industries in the food and pharmaceutical sectors (with analog photography industries being important historical users), but it has several other technical applications [9]. Gelatin is a high molecular weight and water-soluble protein produced through thermal denaturation of collagen. Although it has lower strength and stiffness than collagen, it is easier to extract and prepare than collagen and thus more practical and economical to use [15–17]. Through the thermal denaturation of collagen (collagen– gelatin transition process), the highly organized, water insoluble collagen fiber transforms from an infinite, asymmetric network of linked tropocollagen units to a system of independent, water-soluble molecules with far less internal order [18]. Depending on the treatment of collagen, either gelatin type A or gelatin type B can be obtained, where the former is extracted from collagen by acid treatment, while the latter is extracted by alkaline treatment [19]. Two main sources for the preparation of gelatin are bovine and porcine collagens, which have been implanted clinically for decades and whose hydrolysis products, i.e. bovine and porcine skin gelatins, are widely utilized in food industries. However, porcine skin gelatin (of type A) is stiffer than bovine skin gelatin due to its high degree of cross-linking as well as the significant amounts of glycine and proline contained in it [15,20]. In addition, the hydrogen bonds in porcine skin gelatin between water molecules and free hydroxyl groups of amino acids positively influence gelatin strength [21]. For these reasons, porcine skin gelatin was selected for this research. The mechanical and thermal properties of gelatin are related to its denaturation level, i.e. the triple helix content of the protein. These properties are substantially influenced by parameters such as molecular weight, polydispersity, thermal history, water content, and the time and mode of drying[9,22–24]. Gelatin based materials are hygroscopic materials that are very sensitive to environmental conditions, such as temperature and relative humidity [25]. The gelatin structure forms a three-dimensional network containing zones of inter-molecular microcrystalline junctions. When this system is dehydrated, it may result in brittle structures. This can be prevented by the addition of plasticizers to reduce interchain interactions and improve film flexibility [26]. A widely used plasticizer is Glycerol, which is non-volatile and has constant mass during aging of the films [14]. Gelatin based materials with plasticizer have sufficient stability, strength and flexibility to be useful for making films, monofilaments and fibers that can serve as reinforcements for composites [13], or used for yarns. Yarns are typically interlocked fibrous bundles constituting a basic building block for complex fibrous architectures [27]. Usually, the fibers within the yarn are twisted, mainly to achieve a coherent structure that cannot easily be split by lateral actions. This configuration provides continuous yarn integrity and forces the array of multiple fibers to behave as a single unit. However, twisting results in lower yarn strength due to fiber obliquity; moreover, fiber damage may appear when a high degree of twist is applied, with potential yarn strength reduction [28–30]. Although the effects of yarn twist remain debatable, its application does result in a more intimate interaction between fibers than in a loose yarn made of parallel fibers. This, of course (as well as the filament length which is not considered here) influences the strength and modulus of a yarn, as well as the strength variability [31–33]. Various theoretical models of Young's modulus and strength of twisted yarns have recently been reviewed by Sui et al. [30]. Twisted yarns composed of (twisted) fibers have a unique strengthgenerating mechanism, in which the force that is breaking the structure is strengthening it at the same time [28]. In other words, on the one hand there are variables such as inter-fiber friction and lateral contractions due to fiber twisting that reduce the tensile strength of the yarn, while on the other hand there are rope unwinding mechanisms that, similar to waviness release in natural tendon, amplify ductility [4,30, 32,33]. Such a mechanism is bound to give rise to complications, with the yarn strength predicted to be smaller than the constituent fiber
strength. This insight confirms that yarn strength is not strictly an intrinsic property of its constituent materials. Rather, it is also dependent on the yarn structure as well as on loading conditions [28]. Here we investigate the tensile mechanical behavior of micro-scale yarn specimens made of a small number of gelatin micro-filaments. The main parameter is the number of filaments (in resemblance to the hierarchical structure of a tendon composed of different layers), in both parallel and twisted configurations. 2. Materials and methods 2.1. Preparation and drying of gelatin film For the purpose of producing gelatin fibers, gelatin films were prepared with an initial composition of 0.005 wt.% sodium azide (RiedeldeHaën, India), 67.5 wt.% three distilled water (TDW), 5.4 wt.% glycerol (Gadot, IL) and 27 wt.% gelatin (pigskin gelatin, 300 Bloom, Sigma Aldrich, IL). Sodium azide (used as a preservative) was dissolved in TDW. Subsequently, glycerol (used as a lubricant) was added, followed by gelatin which was added and mixed gradually. The resulting solution was immersed in an oil bath at 85 °C for 3 h. Afterwards, it was poured into a Teflon mold and transferred to an incubator (at a constant temperature of 25 °C) which contained silica for stabilization overnight. After stabilizing, the resulting film was cut into strips and dried in an incubator for 4 additional days, until its water content got down to 20% [13]. The water functioned as the main plasticizer. Hence, it was very important to control the drying process to reach a 20% water content prior to extrusion. For this purpose, Thermo Gravimetric Analysis (TGA) measurements (Mettler Toledo, TGA/DSC 1 STARe system) were performed repeatedly to measure the amount of water in the specimens. The thermal method consisted of heating from 20 °C until 200 °C at a heating rate of 10 °C/min, in a nitrogen atmosphere [34]. Eventually, the chosen composition of the film right before extrusion was 0.005 wt.% of sodium azide, 20 wt.% of TDW, 10 wt.% of glycerol, and 70 wt.% of gelatin. 2.2. Filament preparation and storage To prepare a filament, the film strips were cut into square pellets that were then fed via a hopper into a twin-screw micro-compounder/ extruder (DSM, Xplore, 15 cc, Geleen, Netherlands) used for hot-melt extrusion. The micro-compounder barrel was subjected to a nitrogen atmosphere and was gradually heated to 105 °C, which was the extrusion (die) temperature. The resulting filaments were stored in a closed container to which Magnesium–Hexa-Hydrate (MgCl2*6H2O) was added (to preserve humidity of around 35% by balancing the salt vapor pressure and that of the air). This was done to guarantee a constant level of water in the filaments. 2.3. Sample preparation Filaments prepared by a hot-melt extrusion method were cut into 12 cm long specimens. These filaments were photographed with an optical microscope (Wild Heerbrugg, model 4680) connected to a camera (Moticom 1000, 1.3 M pixel, USB 2.0) using a computer program that enabled high-resolution images. Their diameters were typically about 400 μm, as measured with ImageJ software. To prepare yarn specimens with a parallel configuration, the filaments were simply attached to each other and glued at the edges. Twisted yarn specimens were prepared with a manual device in which parallel filaments were gripped between a fixed and a swivel clamp. The latter was turned around by a crank shaft and the degree of twist was measured with ImageJ. The twist angle is defined as the angle between a filament direction and the central axis.
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2.4. Yarn morphology A Scanning Electron Microscope (SEM) (FEI HRSEM Sirion) was used to observe the filaments in the different yarn specimens, before and after tensile tests. A standard specimen preparation procedure was used, namely, the specimens were placed on a SEM stub covered with carbon tape and were subsequently coated with a thin layer of Au–Pd using a SC7640 Sputter. Afterwards, the specimens were cleaned by blowing nitrogen on their surface. 2.5. Mechanical properties Mechanical tensile tests were performed on a universal testing machine (INSTRON 3345, 500 kN load cell). The specimen gauge length was 12 cm in all cases (monofilaments and yarns), and the crosshead displacement rate was 50 mm/min. Force–elongation curves of single filaments and yarns, and the corresponding stress–strain behavior, were obtained, from which the mechanical properties were evaluated. The effect of the number of gelatin filaments per yarn on the mechanical properties was examined for both parallel and twisted yarn configurations, and a comparison between these configurations for a constant number of filaments was also performed. Several groups of gelatin filamentary samples were prepared for tensile testing. The first group included monofilament specimens; the other groups consisted of (i) three sets of yarn specimens with a varying number of parallel filaments per yarn (2, 4 and 10), and (ii) three sets of yarn specimens with a varying number of twisted filaments per yarn (2, 4 and 10). The angle in all twisted yarns was 15°. A twist angle of 15° was selected since it is known that both the modulus and the strength of yarns are maximized at small angles (b 30°) [29]. The mechanical properties of all specimens were normalized to a standard moisture content of 6.5%. At least 9 specimens were tested for each set. Optical microscope images of the parallel and twisted samples containing 10 filaments per yarn are presented in Fig. 1 for illustration. 3. Results and discussion 3.1. Stress–strain behavior 3.1.1. Monofilaments A typical stress–strain curve of a gelatin monofilament is presented in Fig. 2. A yield point appears (at stress σy) followed by a drop and a plateau (starting at strain εp), indicating that the gelatin fibers are elasto-plastic, similar to other polymers such as polycarbonate or polypropylene [35–37]. The yield point and ensuing growth in strain without change in stress most likely arise from molecular flow (possibly accompanied by necking, although this was not clear). Subsequently, the filament remains perfectly plastic until a maximum strain (εmax), where failure occurs. Contrasting with this, a purely elastic monofilament (carbon for example) would simply fail at the maximum stress
Fig. 2. Typical elasto-plastic stress–strain curve of a gelatin monofilament in tension. Young's modulus is the slope at the origin of axes and the yield strength, strain at onset of plasticity and strain at failure are indicated (see text for details).
(σy) with no plastic deformation. Four parameters thus describe the behavior of a gelatin filament (Fig. 2): Young's modulus E (thus, the slope at the origin of the stress–strain curve), the yield stress σy, the onset of plasticity at strain εp, and the failure strain εmax. The maximum stress (or strain) of most fiber types usually exhibits significant variability, classically analyzed by fitting the data to a Weibull distribution. Physical justification for the use of this distribution has been discussed in the literature [38–41]. Gelatin monofilaments indeed follow the Weibull model, as shown in Fig. 3a–b and Table 1, with an adequate fit (R2 N 0.92). The Weibull scale (α) and shape (β) parameters are indicators of the average value and variability of the population, respectively. In particular, the shape parameter of the failure strain is very low, which indicates very high variability of this material parameter. 3.1.2. Multi-filament yarns The stress–strain curves of gelatin yarns made of elasto-plastic filaments exhibit progressive, stepwise failures of the individual monofilaments, from the filament with the lowest failure strain to that with the largest failure strain. A yield point appears each time a monofilament fails, as seen in Fig. 4 for a typical parallel yarn. Whether parallel or twisted, the yarns do not fail at one site only, as a compact material, likely because the interaction (bonding) between the filaments is weak. 3.1.3. Simulated stress–strain behavior of yarns Based on the experimental evidence that the 15° twist used here has only a minor effect on the yarn mechanical properties, an approximate loose-bundle simulation with equal load sharing among the filaments and no interaction was developed here for the yarn mechanical behavior. Equal-strain conditions were considered for all filaments in the yarn.
Fig. 1. Optical microscope images of two representative gelatin yarns, with ten parallel (a) and ten twisted (b) filaments.
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Fig. 4. Typical stress–strain curve of a gelatin yarn containing ten parallel filaments. The failure of each individual filament in the yarn is clearly visible.
each simulation, deterministic values for E, σy, εp and εmax were sampled from the corresponding Weibull distributions for each filament in the yarn. The yarn was then progressively stretched, and the resultant stress–strain curve was calculated via the above loose-bundle model. The strength and toughness of the yarn were calculated from the stress–strain curve, and the procedure was repeated a large number of times, from which the strength and toughness statistics of a large ensemble of yarns were extracted. Results of the simulations indicate that the average strength of elasto-plastic bundles, 33.8 ± 0.1 MPa, is slightly higher than the strength of elastic bundles, 28.3 ± 0.1 MPa. The toughness of elasto-plastic bundles, 5.5 ± 0.4 MJ/m3, on the other hand, is significantly higher than that of elastic bundles, 0.7 ± 0.02 MJ/m3.
3.2. Increasing the yarn size Fig. 3. Fitting gelatin monofilament data to a Weibull distribution: (a) yield strength and (b) failure strain. Values of the scale (α) and shape (β) parameters are indicated in each case.
The stress of each individual filament was extracted from the monofilament stress–strain behavior (Fig. 2), and the overall stress of the yarn was then obtained by summing the contributions from the individual monofilaments. Fig. 5 presents the resulting theoretical stress–strain curves for three elastic yarns (red) and three elasto-plastic yarns (blue), each with 10 filaments, using statistically distributed values for E, σy, εp and εmax of the yarn fibers. As seen, the simulated behavior of elasto-plastic yarns is in good agreement with the experiment, except for differences in the strain scale which could originate from fiber interaction effects not accounted for in our model. Fig. 5 also shows that elastic and elasto-plastic yarns exhibit similar elastic behavior, with some differences in strength. However, significant differences in toughness (viewed simply as the area under the curve) are obtained. To further examine these similarities and differences, Monte-Carlo simulations were also performed using large sets (1000 repetitions) to evaluate the statistical strength and toughness of elastic and elasto-plastic yarns containing 10 filaments. At the beginning of
The mechanical properties of gelatin yarns (yield stress and strain, Young's modulus and toughness) were investigated as the yarn size (number of filaments) was increased. Both parallel and twisted configurations were considered. Graphs depicting the mechanical properties as a function of yarn size are presented in Fig. 6.
Table 1 Weibull scale (α) and shape (β) parameters for E, σy, σp, and εmax of single gelatin filaments. Parameter
Scale parameter (α)
Shape parameter (β)
E (GPa) σy (MPa) σp (MPa) εmax (%)
1.4 43.4 29.6 23.3
6.6 9.3 6.7 1.5
Fig. 5. Simulated stress–strain curves for three elastic yarns (red) and three elasto-plastic yarns (blue), each with 10 filaments, using statistically distributed values for E, σy, εp and εmax of the yarn fibers. Elastic and elasto-plastic yarns exhibit similar elastic behavior, with some differences in strength, but with significant differences in toughness (the area under the curve). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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The yield strength of each yarn was calculated based on the initial cross-sectional area, taken as the sum of the initial (before tensile testing) cross-sectional areas of all filaments in the yarn. The crosssectional areas of parallel and twisted specimens were calculated in the same way. Fig. 6a shows that the yield strength of yarns decreases exponentially as the number of filaments increases, for both yarn configurations (parallel or twisted). A t-test shows that this decreasing trend has statistical significance. It corresponds to theoretical predictions from classical bundle theory, namely that (i) the mean strength of a bundle is always lower than the mean strength of a single fiber, and (ii) as the number of fibers in the yarn increases, the mean strength of the bundle decreases (the bundle weakens as the number of fibers increases). Semi-empirical models [28–31] as well as stochastic arguments [32,33] have been presented in the past to justify this behavior. Note also from Fig. 6a that (i) the decrease in yield strength weakens gradually as the number of fibers increases, and (ii) a 15° twist has no effect on the yield strength. Fig. 6b shows that the yield strain of yarns increases exponentially as the number of filaments increases. Here again, twisting the yarn to 15° has no significant effect. The strain increase in a yarn is thought to occur due to friction forces between the filaments that prevent immediate failure of the yarn following the first (and subsequent) filament break. In Fig. 6c the Young's modulus of the yarns is shown to decrease exponentially as the number of filaments increases, for the two yarn configurations. This statistically significant trend appears to be more difficult to justify theoretically since existing semi-empirical models [28–31] for the yarn over filament modulus ratio do not include a direct dependence on the yarn size (mainly the effect of twist on modulus is
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analyzed in the literature, and no experimental data for the role of yarn size seem to exist). Toughness, calculated as the area under the stress–strain curve (thus the energy that the yarn is able to absorb until final rupture), is the most significantly affected mechanical property, with a strong, linear increase as a function of the number of filaments in the yarn, see Fig. 6d. The toughness ratio for a 10-fiber yarn over a single fiber is particularly high, namely a 6-fold increase, and is observed for both yarn configurations, with statistically significant t-test results. This implies that yarns of many filaments absorb much higher energy levels than yarns containing just a few, likely due to the stepped breakage pattern—namely, the elastic-plastic behavior—of the filaments in the multi-filament yarn. As the yarn is strained the filaments in the yarn break individually, with each filament dissipating energy comprising fracture/tear energy and inter-filament frictional work, until final yarn failure. A yarn twist of 15° did not appear to significantly affect any of the mechanical parameters compared to parallel yarns, regardless of the yarn size. It is however likely that twist-related effects could exist at other angles, as observed for example for the strength and the modulus of various polymer fibers [28–33]. This will be studied in future work. 3.3. Further discussion of the strength and toughness of individual filaments in an elasto-plastic yarn Tensile tests of relatively large sets (typically 25 specimens or more) of single fibers are routinely performed to measure their mechanical strength. Such tests are time-consuming and moderately difficult to perform. A number of authors (for example, Calard and Lamond [42]) have proposed to infer the strength of individual filaments from the
Fig. 6. Yield strength (a), strain (b), Young's modulus (c) and toughness (d) of parallel and twisted yarns, as a function of yarn size (number of filaments). The error bars designate the standard deviation.
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testing of yarns, which seems to be advantageous since a single test provides the properties of all the fibers in the yarn, as well as the properties of the yarn itself. Models exist [29–33,42], and can be verified, for the relationships between the tensile strengths of the yarn and of the single filaments, as well as between the degrees of scatter of the yarn and the filaments. 3.3.1. Strengths of filaments from progressive fracture of a yarn Filament fracture strengths were calculated from the evolving individual fracture events, appearing as steps in the force-elongation curves (for example, see Fig. 4). When the filament strengths were calculated using the initial yarn cross-sectional area (the sum of the crosssectional areas of all the filaments in the yarn), a decrease in filament strength was observed, as expected; however, when the calculation was based on the true cross-sectional area (thus, accounting for the areas of yet unbroken filaments), the fracture strength of each progressively breaking filament in the yarn remained constant on average. The fracture strengths of the filaments in the parallel yarns were only very slightly higher than those in the twisted yarn. 3.3.2. Toughness of an isolated monofilament from the progressive fracture of a yarn Of interest now is the toughness of a yarn and its correlation with the toughness of single elasto-plastic filaments constituting the yarn. We are unaware of any previous work, experimental or theoretical, that addresses this issue, yet it seems to us that it is as interesting as the classical consideration between yarn strength and single filament strength. The basic question is the following: assuming that the stress–strain curve of an elasto-plastic yarn is given, can we devise a method to back-calculate the toughness of each individual filament constituting the yarn? To answer this, the following procedure is proposed, noting that in general, accurate estimations are difficult to make due to the inherent statistical variability of the filament parameters (E, σy, σp, εmax, and the filament diameter d). The toughness is an integral quantity and most of it arise in the present case (gelatin filaments) from the plastic region. As a consequence, an analysis that pertains to a purely elastic behavior, wherein the toughness per individual filament is calculated by separate integration of consecutive wedge segments of the stress–strain curve, is not applicable. Thus, it is not feasible to infer the toughness of individual filaments from that of the yarn (in analogy to the discussion of the strength); instead, the toughness can be estimated by means of the values of εmax of each filament. For the sake of simplicity, we demonstrate the procedure using the stress–strain curve of a two-filament bundle (Fig. 7). The curve includes an initial elastic region followed by a drop, usually considered to reflect a yielding behavior (ε b εp). This is followed by a perfectly-plastic region (ε N εp), characterized by progressive filament breakage with maximal strains εmax(1), εmax(2), etc. The (approximate) toughness of an isolated filament, extracted from the stress–strain curve of a yarn, can then be evaluated as follows. 1. Calculate the area U0 under the stress–strain curve for ε b εp. This is the toughness of the yarn (all filaments) up to the plasticity plateau, and the contribution in this region of an individual filament to the yarn toughness is simply U0/Nfilaments, where Nfilaments is the number of filaments in the yarn, and we have assumed that all have identical diameters. 2. The area under the stress–strain curve for ε N εp represents the plastic contribution of all filaments to the yarn toughness. In this region, the breaking points of the filaments can be easily identified (e.g. εmax(1), εmax(2)) and horizontal lines from each of these can be drawn back to εp. The resultant area of each rectangular sub-region (e.g. Up1 and Up2) represents the plastic toughness contribution of the individual filaments to the yarn toughness. 3. The contribution Ui of the ith filament to the overall toughness of the yarn is therefore Ui = U0/Nfilaments + Upi.
Fig. 7. Graphical demonstration of the procedure developed to measure the toughness of single filaments based on the test of a yarn rather than on a large number of individual filament tests. This is illustrated here using the stress–strain curve of a typical two-filament gelatin yarn. The plastic onset εp and maximal strain points εmax(1) and εmax(2), are easily identified. The toughness of the yarn originates from the elastic–inelastic and perfectlyplastic contributions. Up1 and Up2 represent the toughness of the individual filaments in the plastic region. The error bars designate the standard deviation.
4. The toughness of an isolated filament, Γi, is obtained by dividing Ui by the relative cross section area of the filament in the yarn (1/Nfilaments), namely Γi = Ui Nfilaments. The results for twisted specimens presented in Fig. 8 show that as the filaments in the yarn progressively fail, their toughness significantly increases so that the toughness of the filaments that break last is—generally—the highest (similar to strength, where the strongest filaments in a yarn generally break last). However, the variability in the results also increases significantly, likely due to a number of reasons, including the filament–filament interactions and the high sensitivity to temperature variability as friction increases. Here too it was impossible to observe a consistent effect of the 15° yarn twist. We have occasionally observed that much higher toughness results are obtained for the progressively failing filaments but at this stage we cannot pinpoint the exact cause of this variability. Finally, the average toughness of single filaments can be reliably calculated from a yarn test, as in Fig. 9 and the results compare favorably with single filament testing for which Γ(N = 1) = 6.1 J/m3.
Fig. 8. Single filament toughness as the yarn failure proceeds. The toughness of the filament that break last is the highest. Note also the increasing filament toughness variability as the yarn failure progresses. The error bars designate the standard deviation.
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be independent of the twist. Note that the intention here was not to replicate the mechanical effects of tendon crimp, but only to possibly account for similar effects via twist. The origin of the significant toughness in gelatin is its inherent elasto-plastic behavior. A major difference between tendon and gelatin in terms of toughness, however, is the fact that tendon crimp is reversible whereas gelatin plasticity is not.
Acknowledgments We acknowledge the support from the Israel Science Foundation (Grant No. 1509/10) and from the G. M. J. Schmidt Minerva Centre of Supramolecular Architectures. This research was made possible in part by the generosity of the Harold Perlman family. H.D. Wagner is the recipient of the Livio Norzi Professorial Chair. It is a pleasure to thank Mrs Rawan Khatib, Hannah Harel and Erica Wiesel for their assistance and helpful advices with the technical procedures.
Fig. 9. Average toughness of single filaments calculated from a yarn test. As seen, results compare favorably with single filament testing (indicated by the gray area). The error bars designate the standard deviation.
4. Summary and conclusions This study aimed to expand and enrich the existing knowledge of tensile mechanical behaviors of yarn structures inspired by tendons and made of gelatin micro-filaments, from a structural and mechanical perspective. It was based on the use of gelatin micro-filaments prepared by the mix-melt-extrusion method that is of potential commercial feasibility. The main factors that control the mechanical properties of the gelatin yarn structure are the relevant property of the individual filament, the number of filaments per yarn and the inter-filament pressure and friction. The effect of the yarn configuration (15° twisted or parallel) seems to be negligible, although a study using a wider spectrum of twist angles is required to confirm this. The rules by which these factors determine the yarn's property depend on the specific property as follows. The static properties of the yarn, namely the yield strength and the stiffness (modulus of elasticity) decrease as the number of filaments per yarn is increased, likely due to the effect of inter-filament contact pressure that generates stress concentrations at contact points along the yarn. Conversely to the yield stress and stiffness, the yield strain of the yarn increases as the number of filaments per yarn is increased. This effect is produced under tensile loading as the twisted structure is straightened out and the inter-filament angle decreases. Considering the toughness, it is evident from the observation that it increases drastically with the number of filaments, a result that goes hand in hand with the increased strain to failure, so that the toughness of the yarn is not merely the sum of the toughness contributions of the filaments, but in addition a major component is attributed to the high strain work of deformation. Finally, we developed a dependable procedure to measure the toughness of single filaments based on the test of a yarn rather than on a large number of individual filament tests. Based on this study it is possible to conclude that a yarn property is the product of the corresponding properties of the constituents and of their number (a hierarchical consideration) plus a structural factor contribution (twist and crimp) that sets the inter-filament interactions. The toughness effects of a twisted gelatin yarn configuration, originally assumed to be reminiscent of those of the crimped waveform orientation of collagen fibers in tendons, have limited similarities only. Indeed, although toughness of gelatin yarns increases with yarn size, it seems to
References [1] H.H. Lu, S.D. Subramony, M.K. Boushell, X. Zhang, Ann. Biomed. Eng. 38 (2010) 2142–2154. [2] D.H. Kim, D.R. Wilson, A.T. Hecker, T.M. Jung, C.H. Brown, Am. J. sports Med. 31 (2003) 861–867. [3] U. Izhar, H. Schwalb, J.B. Borman, G.R. Hellener, A. Hotoveli-Salomon, G. Marom, T. Stern, D. Cohn, J. Surg. Res. 95 (2001) 152–160. [4] R.A. Gross, B. Kalra, Science 297 (2002) 803–807. [5] K.G. Vogel, J. Musculoskelet. Nueronal Interact. 3 (2003) 323–325. [6] E. Baer, J. Cassidy, A. Hiltner, Pure Appl. Chem. 63 (1991) 961–973. [7] P. Fratzl, Curr. Opin. Colloid Interface Sci. 8 (2003) 32–39. [8] K.A. Hansen, J.A. Weiss, J.K. Barton, J. Biomech. Eng. 124 (2002) 72. [9] A. Bigi, S. Panzavolta, K. Rubini, Biomaterials 25 (2004) 5675–5680. [10] M. Shoulders, R. Raines, Annu. Rev. Biochem. 78 (2009) 929–930. [11] A.K Harvey, M.S. Thompson, M. Brady, Proc. Conf on Medical Image Understanding and Analysis (MIUA) 2010, 1-5, University of Warwick, UK, 2009. [12] M. Buehler, Acta Mech. Solida Sin. 23 (2010) 471–483. [13] J.W. Park, W. Scott Whiteside, S.Y. Cho, LWT Food Sci. Technol. 41 (2008) 692–700. [14] M. Coppola, M. Djabourov, M. Ferrand, Macromol. Symp. 273 (2008) 56–65. [15] R. Hafidz, C. Yaakob, Int. Food Res. J. 18 (2011) 787–789. [16] C.N. Grover, R.E. Cameron, S.M. Best, J. Mech. Behav. Biomed. Mater. 10 (2012) 62–74. [17] E. Rosellini, C. Cristallini, N. Barbani, G. Vozzi, P. Giusti, J. Biomed. Mater. Res. A 91 (2009) 447–453. [18] A. Veis, The macromolecular chemistry of gelatin, 1964. [19] M. Aviv-Gavriel, N. Garti, H. Füredi-Milhofer, Langmuir 29 (2013) 683–689. [20] K. Lynn, I.V. Yannas, W. Bonfield, J. Biomed. Mater. Res. B Appl. Biomater. 71 (2004) 343–354. [21] J.A. Arnesen, A. Gildberg, Bioresour. Technol. 82 (2002) 191–194. [22] C. Joly-Duhamel, D. Hellio, M. Djabourov, Langmuir 18 (2002) 7208–7217. [23] C. Dai, Y. Chen, M. Liu, J. Appl. Polym. Sci. 99 (2006) 1795–1801. [24] I. Yakimets, N. Wellner, A.C. Smith, R.H. Wilson, I. Farhat, J. Mitchell, Polymer 46 (2005) 12577–12585. [25] P. Bergo, P.J. Sobral, Food Hydrocoll. 21 (2007) 1285–1289. [26] F.M. Vanin, P.J. Sobral, F.C. Menegalli, R. Carvalho, A.M.Q.B. Habitante, Food Hydrocoll. 19 (2005) 899–907. [27] Y. Zhou, J. Fang, X. Wang, T. Lin, J. Mater. Res. 27 (2011) 537–544. [28] N. Pan, J. Mater. Sci. 28 (1993) 6107. [29] J.W.S. Hearle, P. Grosberg, S. Backer, Structural Mechanics of Fibers, Yarns and Fabrics, Wiley-Interscience, New York-London-Sydney-Toronto, 1969. [30] Y. Rao, R. Farris, J. Appl. Polym. Sci. 77 (2000) 1938–1949. [31] X. Sui, E. Wiesel, H.D. Wagner, Polymer 53 (2012) 5037–5044. [32] S.L. Phoenix, Statistical theory for the strength of twisted fiber bundles with applications to yarns and cables, Text. Res. J. 49 (July 1979) 407–423. [33] N. Pan, D. Brookstein, J. Appl. Polym. Sci. 83 (2002) 610–630. [34] S. Omeroglu, Fibers Text. East. Eur. 14 (2006) 53–57. [35] N. Brown, I.M. Ward, J. Polym. Sci. A-2 (6) (1968) 607–620. [36] S. Bahadur, Polym. Eng. Sci. 13 (4) (1973) 266–272. [37] J. Lu, K. Ravi-Chandar, Int. J. Solids Struct. 36 (1999) 391–425. [38] P. Ray, B.K. Chakrabarti, J. Phys. C Solid State Phys. 18 (1985) L185. [39] P. Ray, B.K. Chakrabarti, Solid State Commun. 53 (1985) 477. [40] S.B. Batdorf, Nucl. Eng. Des. 35 (1975) 349–360. [41] H.D. Wagner, J. Polym. Sci. B Polym. Phys. 27 (1989) 115–149. [42] V. Calard, J. Lamon, Compos. Sci. Technol. 64 (2004) 701–710.
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Materials Science and Engineering C journal homepage: www.elsevier.com/locate/msec
Gelatin yarns inspired by tendons — Structural and mechanical perspectives Hila Klein Selle a,b, Benny Bar-On c, Gad Marom a,⁎, H. Daniel Wagner b,⁎ a b c
Casali Center of Applied Chemistry, The Institute of Chemistry, The Hebrew University of Jerusalem, Edmond J. Safra Campus, Givat Ram, Jerusalem 91904, Israel Department of Materials and Interfaces, Weizmann Institute of Science, Rehovot 76100, Israel Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva 84105, Israel
a r t i c l e
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Article history: Received 21 July 2014 Received in revised form 26 October 2014 Accepted 1 November 2014 Available online 5 November 2014 Keywords: Tendon structure Gelatin Extrusion Single filaments Parallel yarns Twisted yarns Mechanical properties
a b s t r a c t Tendons are among the most robust structures in nature. Using the structural properties of natural tendon as a foundation for the development of micro-yarns may lead to innovative composite materials. Gelatin monofilaments were prepared by casting and spinning and small yarns—with up to ten filaments—were assembled into either parallel or 15° twisted yarns. The latter were intended as an attempt to generate mechanical effects similar to those arising from the crimp pattern in tendon. The mechanical properties of parallel and 15° twisted gelatin yarns were compared. The effect of an increasing number of filaments per yarn was also examined. The mechanical properties were mostly affected by the increasing number of filaments, and no benefit arose from twisting small yarns by 15°. However, since gelatin filaments are elasto-plastic rather than fully elastic, much increased toughness (by up to a factor of five for a ten filament yarn) can be achieved with yarns made of elasto-plastic filaments, as demonstrated by experiments and numerical simulations. The resulting effect shows some resemblance to the effect of crimp in tendons. Finally, we developed a dependable procedure to measure the toughness of single filaments based on the test of a yarn rather than on a large number of individual filament tests. © 2014 Elsevier B.V. All rights reserved.
1. Introduction In the course of the last decades efforts have been made to develop grafts of soft connective tissues (e.g. blood vessels, tendons, ligaments) by means of a biologically-inspired strategy [1–3]. Thorough understanding of these soft tissues in conjunction with the progress achieved in biomedical synthetic components, indicates that synthetic collagen fibers offer significant advantages over traditional polymers for soft tissue repair and replacement [4]. A tendon is a soft connective tissue that generally experiences forces that are purely longitudinal and tensile as it transmits the contraction of muscle to bone [5]. It is one of the toughest structures found in nature. Emulating the tendon's unique characteristics may bring about the use of wires or ropes that may function as active components to generate, transmit, and convert power and motion. Such a bio-inspired approach may stimulate innovative thinking in the structural design of future engineering composite materials. The main goal of the present paper, which rests on the observed mechanical toughness of natural tendon, is to develop a bio-inspired and bio-compatible implantable yarn material based on porcine skin gelatin.
⁎ Corresponding authors. E-mail addresses: [email protected] (G. Marom), [email protected] (H. Daniel Wagner).
http://dx.doi.org/10.1016/j.msec.2014.11.001 0928-4931/© 2014 Elsevier B.V. All rights reserved.
The tendon presents a unique hierarchical structure in which all levels of organization from the molecular through the macroscopic are oriented to optimize the reversible and irreversible tensile properties along the length of the tendon without fracture. Its most fundamental levels consist of tropocollagen helix molecules. The multi-level organization imparts toughness to the tendon [6–8]. The hierarchical structure of tendon includes collagen fibrils that have a wavy appearance, characterized as a planar zigzag. This crimp waveform is gradually straightened when the tendon is stretched along its length, and its magnitude determines the reversible elastic properties of the tendon [6]. The crimp could also have a toughening effect as the tendon strain progressively increases with uncrimping. The primary constituents of tendon are water and type I collagen [5]. Collagen's main role is to provide structural integrity to the tissue. Collagen, as a fibrous, structural protein is composed of a right-handed bundle of three parallel, left handed helixes of polyproline type II. The resulting triple helical structure is called tropocollagen [6,9–11]. Generally, the mechanical properties of biological materials (such as collagen) and structures are of great significance to virtually all physiological properties at each and every scale [12]. Among biomaterials, collagen-derived gelatin is particularly interesting. In a dehydrated state, gelatin is a partially crystalline polymer with a relatively low melting point in the range of 40 °C–150 °C, depending on the amount of plasticizer used [13,14]. Gelatin is a very important polymer, primarily used as a gelling agent forming transparent, elastic, thermo-reversible
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gels at room temperature. Currently, it is mainly used by industries in the food and pharmaceutical sectors (with analog photography industries being important historical users), but it has several other technical applications [9]. Gelatin is a high molecular weight and water-soluble protein produced through thermal denaturation of collagen. Although it has lower strength and stiffness than collagen, it is easier to extract and prepare than collagen and thus more practical and economical to use [15–17]. Through the thermal denaturation of collagen (collagen– gelatin transition process), the highly organized, water insoluble collagen fiber transforms from an infinite, asymmetric network of linked tropocollagen units to a system of independent, water-soluble molecules with far less internal order [18]. Depending on the treatment of collagen, either gelatin type A or gelatin type B can be obtained, where the former is extracted from collagen by acid treatment, while the latter is extracted by alkaline treatment [19]. Two main sources for the preparation of gelatin are bovine and porcine collagens, which have been implanted clinically for decades and whose hydrolysis products, i.e. bovine and porcine skin gelatins, are widely utilized in food industries. However, porcine skin gelatin (of type A) is stiffer than bovine skin gelatin due to its high degree of cross-linking as well as the significant amounts of glycine and proline contained in it [15,20]. In addition, the hydrogen bonds in porcine skin gelatin between water molecules and free hydroxyl groups of amino acids positively influence gelatin strength [21]. For these reasons, porcine skin gelatin was selected for this research. The mechanical and thermal properties of gelatin are related to its denaturation level, i.e. the triple helix content of the protein. These properties are substantially influenced by parameters such as molecular weight, polydispersity, thermal history, water content, and the time and mode of drying[9,22–24]. Gelatin based materials are hygroscopic materials that are very sensitive to environmental conditions, such as temperature and relative humidity [25]. The gelatin structure forms a three-dimensional network containing zones of inter-molecular microcrystalline junctions. When this system is dehydrated, it may result in brittle structures. This can be prevented by the addition of plasticizers to reduce interchain interactions and improve film flexibility [26]. A widely used plasticizer is Glycerol, which is non-volatile and has constant mass during aging of the films [14]. Gelatin based materials with plasticizer have sufficient stability, strength and flexibility to be useful for making films, monofilaments and fibers that can serve as reinforcements for composites [13], or used for yarns. Yarns are typically interlocked fibrous bundles constituting a basic building block for complex fibrous architectures [27]. Usually, the fibers within the yarn are twisted, mainly to achieve a coherent structure that cannot easily be split by lateral actions. This configuration provides continuous yarn integrity and forces the array of multiple fibers to behave as a single unit. However, twisting results in lower yarn strength due to fiber obliquity; moreover, fiber damage may appear when a high degree of twist is applied, with potential yarn strength reduction [28–30]. Although the effects of yarn twist remain debatable, its application does result in a more intimate interaction between fibers than in a loose yarn made of parallel fibers. This, of course (as well as the filament length which is not considered here) influences the strength and modulus of a yarn, as well as the strength variability [31–33]. Various theoretical models of Young's modulus and strength of twisted yarns have recently been reviewed by Sui et al. [30]. Twisted yarns composed of (twisted) fibers have a unique strengthgenerating mechanism, in which the force that is breaking the structure is strengthening it at the same time [28]. In other words, on the one hand there are variables such as inter-fiber friction and lateral contractions due to fiber twisting that reduce the tensile strength of the yarn, while on the other hand there are rope unwinding mechanisms that, similar to waviness release in natural tendon, amplify ductility [4,30, 32,33]. Such a mechanism is bound to give rise to complications, with the yarn strength predicted to be smaller than the constituent fiber
strength. This insight confirms that yarn strength is not strictly an intrinsic property of its constituent materials. Rather, it is also dependent on the yarn structure as well as on loading conditions [28]. Here we investigate the tensile mechanical behavior of micro-scale yarn specimens made of a small number of gelatin micro-filaments. The main parameter is the number of filaments (in resemblance to the hierarchical structure of a tendon composed of different layers), in both parallel and twisted configurations. 2. Materials and methods 2.1. Preparation and drying of gelatin film For the purpose of producing gelatin fibers, gelatin films were prepared with an initial composition of 0.005 wt.% sodium azide (RiedeldeHaën, India), 67.5 wt.% three distilled water (TDW), 5.4 wt.% glycerol (Gadot, IL) and 27 wt.% gelatin (pigskin gelatin, 300 Bloom, Sigma Aldrich, IL). Sodium azide (used as a preservative) was dissolved in TDW. Subsequently, glycerol (used as a lubricant) was added, followed by gelatin which was added and mixed gradually. The resulting solution was immersed in an oil bath at 85 °C for 3 h. Afterwards, it was poured into a Teflon mold and transferred to an incubator (at a constant temperature of 25 °C) which contained silica for stabilization overnight. After stabilizing, the resulting film was cut into strips and dried in an incubator for 4 additional days, until its water content got down to 20% [13]. The water functioned as the main plasticizer. Hence, it was very important to control the drying process to reach a 20% water content prior to extrusion. For this purpose, Thermo Gravimetric Analysis (TGA) measurements (Mettler Toledo, TGA/DSC 1 STARe system) were performed repeatedly to measure the amount of water in the specimens. The thermal method consisted of heating from 20 °C until 200 °C at a heating rate of 10 °C/min, in a nitrogen atmosphere [34]. Eventually, the chosen composition of the film right before extrusion was 0.005 wt.% of sodium azide, 20 wt.% of TDW, 10 wt.% of glycerol, and 70 wt.% of gelatin. 2.2. Filament preparation and storage To prepare a filament, the film strips were cut into square pellets that were then fed via a hopper into a twin-screw micro-compounder/ extruder (DSM, Xplore, 15 cc, Geleen, Netherlands) used for hot-melt extrusion. The micro-compounder barrel was subjected to a nitrogen atmosphere and was gradually heated to 105 °C, which was the extrusion (die) temperature. The resulting filaments were stored in a closed container to which Magnesium–Hexa-Hydrate (MgCl2*6H2O) was added (to preserve humidity of around 35% by balancing the salt vapor pressure and that of the air). This was done to guarantee a constant level of water in the filaments. 2.3. Sample preparation Filaments prepared by a hot-melt extrusion method were cut into 12 cm long specimens. These filaments were photographed with an optical microscope (Wild Heerbrugg, model 4680) connected to a camera (Moticom 1000, 1.3 M pixel, USB 2.0) using a computer program that enabled high-resolution images. Their diameters were typically about 400 μm, as measured with ImageJ software. To prepare yarn specimens with a parallel configuration, the filaments were simply attached to each other and glued at the edges. Twisted yarn specimens were prepared with a manual device in which parallel filaments were gripped between a fixed and a swivel clamp. The latter was turned around by a crank shaft and the degree of twist was measured with ImageJ. The twist angle is defined as the angle between a filament direction and the central axis.
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2.4. Yarn morphology A Scanning Electron Microscope (SEM) (FEI HRSEM Sirion) was used to observe the filaments in the different yarn specimens, before and after tensile tests. A standard specimen preparation procedure was used, namely, the specimens were placed on a SEM stub covered with carbon tape and were subsequently coated with a thin layer of Au–Pd using a SC7640 Sputter. Afterwards, the specimens were cleaned by blowing nitrogen on their surface. 2.5. Mechanical properties Mechanical tensile tests were performed on a universal testing machine (INSTRON 3345, 500 kN load cell). The specimen gauge length was 12 cm in all cases (monofilaments and yarns), and the crosshead displacement rate was 50 mm/min. Force–elongation curves of single filaments and yarns, and the corresponding stress–strain behavior, were obtained, from which the mechanical properties were evaluated. The effect of the number of gelatin filaments per yarn on the mechanical properties was examined for both parallel and twisted yarn configurations, and a comparison between these configurations for a constant number of filaments was also performed. Several groups of gelatin filamentary samples were prepared for tensile testing. The first group included monofilament specimens; the other groups consisted of (i) three sets of yarn specimens with a varying number of parallel filaments per yarn (2, 4 and 10), and (ii) three sets of yarn specimens with a varying number of twisted filaments per yarn (2, 4 and 10). The angle in all twisted yarns was 15°. A twist angle of 15° was selected since it is known that both the modulus and the strength of yarns are maximized at small angles (b 30°) [29]. The mechanical properties of all specimens were normalized to a standard moisture content of 6.5%. At least 9 specimens were tested for each set. Optical microscope images of the parallel and twisted samples containing 10 filaments per yarn are presented in Fig. 1 for illustration. 3. Results and discussion 3.1. Stress–strain behavior 3.1.1. Monofilaments A typical stress–strain curve of a gelatin monofilament is presented in Fig. 2. A yield point appears (at stress σy) followed by a drop and a plateau (starting at strain εp), indicating that the gelatin fibers are elasto-plastic, similar to other polymers such as polycarbonate or polypropylene [35–37]. The yield point and ensuing growth in strain without change in stress most likely arise from molecular flow (possibly accompanied by necking, although this was not clear). Subsequently, the filament remains perfectly plastic until a maximum strain (εmax), where failure occurs. Contrasting with this, a purely elastic monofilament (carbon for example) would simply fail at the maximum stress
Fig. 2. Typical elasto-plastic stress–strain curve of a gelatin monofilament in tension. Young's modulus is the slope at the origin of axes and the yield strength, strain at onset of plasticity and strain at failure are indicated (see text for details).
(σy) with no plastic deformation. Four parameters thus describe the behavior of a gelatin filament (Fig. 2): Young's modulus E (thus, the slope at the origin of the stress–strain curve), the yield stress σy, the onset of plasticity at strain εp, and the failure strain εmax. The maximum stress (or strain) of most fiber types usually exhibits significant variability, classically analyzed by fitting the data to a Weibull distribution. Physical justification for the use of this distribution has been discussed in the literature [38–41]. Gelatin monofilaments indeed follow the Weibull model, as shown in Fig. 3a–b and Table 1, with an adequate fit (R2 N 0.92). The Weibull scale (α) and shape (β) parameters are indicators of the average value and variability of the population, respectively. In particular, the shape parameter of the failure strain is very low, which indicates very high variability of this material parameter. 3.1.2. Multi-filament yarns The stress–strain curves of gelatin yarns made of elasto-plastic filaments exhibit progressive, stepwise failures of the individual monofilaments, from the filament with the lowest failure strain to that with the largest failure strain. A yield point appears each time a monofilament fails, as seen in Fig. 4 for a typical parallel yarn. Whether parallel or twisted, the yarns do not fail at one site only, as a compact material, likely because the interaction (bonding) between the filaments is weak. 3.1.3. Simulated stress–strain behavior of yarns Based on the experimental evidence that the 15° twist used here has only a minor effect on the yarn mechanical properties, an approximate loose-bundle simulation with equal load sharing among the filaments and no interaction was developed here for the yarn mechanical behavior. Equal-strain conditions were considered for all filaments in the yarn.
Fig. 1. Optical microscope images of two representative gelatin yarns, with ten parallel (a) and ten twisted (b) filaments.
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Fig. 4. Typical stress–strain curve of a gelatin yarn containing ten parallel filaments. The failure of each individual filament in the yarn is clearly visible.
each simulation, deterministic values for E, σy, εp and εmax were sampled from the corresponding Weibull distributions for each filament in the yarn. The yarn was then progressively stretched, and the resultant stress–strain curve was calculated via the above loose-bundle model. The strength and toughness of the yarn were calculated from the stress–strain curve, and the procedure was repeated a large number of times, from which the strength and toughness statistics of a large ensemble of yarns were extracted. Results of the simulations indicate that the average strength of elasto-plastic bundles, 33.8 ± 0.1 MPa, is slightly higher than the strength of elastic bundles, 28.3 ± 0.1 MPa. The toughness of elasto-plastic bundles, 5.5 ± 0.4 MJ/m3, on the other hand, is significantly higher than that of elastic bundles, 0.7 ± 0.02 MJ/m3.
3.2. Increasing the yarn size Fig. 3. Fitting gelatin monofilament data to a Weibull distribution: (a) yield strength and (b) failure strain. Values of the scale (α) and shape (β) parameters are indicated in each case.
The stress of each individual filament was extracted from the monofilament stress–strain behavior (Fig. 2), and the overall stress of the yarn was then obtained by summing the contributions from the individual monofilaments. Fig. 5 presents the resulting theoretical stress–strain curves for three elastic yarns (red) and three elasto-plastic yarns (blue), each with 10 filaments, using statistically distributed values for E, σy, εp and εmax of the yarn fibers. As seen, the simulated behavior of elasto-plastic yarns is in good agreement with the experiment, except for differences in the strain scale which could originate from fiber interaction effects not accounted for in our model. Fig. 5 also shows that elastic and elasto-plastic yarns exhibit similar elastic behavior, with some differences in strength. However, significant differences in toughness (viewed simply as the area under the curve) are obtained. To further examine these similarities and differences, Monte-Carlo simulations were also performed using large sets (1000 repetitions) to evaluate the statistical strength and toughness of elastic and elasto-plastic yarns containing 10 filaments. At the beginning of
The mechanical properties of gelatin yarns (yield stress and strain, Young's modulus and toughness) were investigated as the yarn size (number of filaments) was increased. Both parallel and twisted configurations were considered. Graphs depicting the mechanical properties as a function of yarn size are presented in Fig. 6.
Table 1 Weibull scale (α) and shape (β) parameters for E, σy, σp, and εmax of single gelatin filaments. Parameter
Scale parameter (α)
Shape parameter (β)
E (GPa) σy (MPa) σp (MPa) εmax (%)
1.4 43.4 29.6 23.3
6.6 9.3 6.7 1.5
Fig. 5. Simulated stress–strain curves for three elastic yarns (red) and three elasto-plastic yarns (blue), each with 10 filaments, using statistically distributed values for E, σy, εp and εmax of the yarn fibers. Elastic and elasto-plastic yarns exhibit similar elastic behavior, with some differences in strength, but with significant differences in toughness (the area under the curve). (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
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The yield strength of each yarn was calculated based on the initial cross-sectional area, taken as the sum of the initial (before tensile testing) cross-sectional areas of all filaments in the yarn. The crosssectional areas of parallel and twisted specimens were calculated in the same way. Fig. 6a shows that the yield strength of yarns decreases exponentially as the number of filaments increases, for both yarn configurations (parallel or twisted). A t-test shows that this decreasing trend has statistical significance. It corresponds to theoretical predictions from classical bundle theory, namely that (i) the mean strength of a bundle is always lower than the mean strength of a single fiber, and (ii) as the number of fibers in the yarn increases, the mean strength of the bundle decreases (the bundle weakens as the number of fibers increases). Semi-empirical models [28–31] as well as stochastic arguments [32,33] have been presented in the past to justify this behavior. Note also from Fig. 6a that (i) the decrease in yield strength weakens gradually as the number of fibers increases, and (ii) a 15° twist has no effect on the yield strength. Fig. 6b shows that the yield strain of yarns increases exponentially as the number of filaments increases. Here again, twisting the yarn to 15° has no significant effect. The strain increase in a yarn is thought to occur due to friction forces between the filaments that prevent immediate failure of the yarn following the first (and subsequent) filament break. In Fig. 6c the Young's modulus of the yarns is shown to decrease exponentially as the number of filaments increases, for the two yarn configurations. This statistically significant trend appears to be more difficult to justify theoretically since existing semi-empirical models [28–31] for the yarn over filament modulus ratio do not include a direct dependence on the yarn size (mainly the effect of twist on modulus is
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analyzed in the literature, and no experimental data for the role of yarn size seem to exist). Toughness, calculated as the area under the stress–strain curve (thus the energy that the yarn is able to absorb until final rupture), is the most significantly affected mechanical property, with a strong, linear increase as a function of the number of filaments in the yarn, see Fig. 6d. The toughness ratio for a 10-fiber yarn over a single fiber is particularly high, namely a 6-fold increase, and is observed for both yarn configurations, with statistically significant t-test results. This implies that yarns of many filaments absorb much higher energy levels than yarns containing just a few, likely due to the stepped breakage pattern—namely, the elastic-plastic behavior—of the filaments in the multi-filament yarn. As the yarn is strained the filaments in the yarn break individually, with each filament dissipating energy comprising fracture/tear energy and inter-filament frictional work, until final yarn failure. A yarn twist of 15° did not appear to significantly affect any of the mechanical parameters compared to parallel yarns, regardless of the yarn size. It is however likely that twist-related effects could exist at other angles, as observed for example for the strength and the modulus of various polymer fibers [28–33]. This will be studied in future work. 3.3. Further discussion of the strength and toughness of individual filaments in an elasto-plastic yarn Tensile tests of relatively large sets (typically 25 specimens or more) of single fibers are routinely performed to measure their mechanical strength. Such tests are time-consuming and moderately difficult to perform. A number of authors (for example, Calard and Lamond [42]) have proposed to infer the strength of individual filaments from the
Fig. 6. Yield strength (a), strain (b), Young's modulus (c) and toughness (d) of parallel and twisted yarns, as a function of yarn size (number of filaments). The error bars designate the standard deviation.
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testing of yarns, which seems to be advantageous since a single test provides the properties of all the fibers in the yarn, as well as the properties of the yarn itself. Models exist [29–33,42], and can be verified, for the relationships between the tensile strengths of the yarn and of the single filaments, as well as between the degrees of scatter of the yarn and the filaments. 3.3.1. Strengths of filaments from progressive fracture of a yarn Filament fracture strengths were calculated from the evolving individual fracture events, appearing as steps in the force-elongation curves (for example, see Fig. 4). When the filament strengths were calculated using the initial yarn cross-sectional area (the sum of the crosssectional areas of all the filaments in the yarn), a decrease in filament strength was observed, as expected; however, when the calculation was based on the true cross-sectional area (thus, accounting for the areas of yet unbroken filaments), the fracture strength of each progressively breaking filament in the yarn remained constant on average. The fracture strengths of the filaments in the parallel yarns were only very slightly higher than those in the twisted yarn. 3.3.2. Toughness of an isolated monofilament from the progressive fracture of a yarn Of interest now is the toughness of a yarn and its correlation with the toughness of single elasto-plastic filaments constituting the yarn. We are unaware of any previous work, experimental or theoretical, that addresses this issue, yet it seems to us that it is as interesting as the classical consideration between yarn strength and single filament strength. The basic question is the following: assuming that the stress–strain curve of an elasto-plastic yarn is given, can we devise a method to back-calculate the toughness of each individual filament constituting the yarn? To answer this, the following procedure is proposed, noting that in general, accurate estimations are difficult to make due to the inherent statistical variability of the filament parameters (E, σy, σp, εmax, and the filament diameter d). The toughness is an integral quantity and most of it arise in the present case (gelatin filaments) from the plastic region. As a consequence, an analysis that pertains to a purely elastic behavior, wherein the toughness per individual filament is calculated by separate integration of consecutive wedge segments of the stress–strain curve, is not applicable. Thus, it is not feasible to infer the toughness of individual filaments from that of the yarn (in analogy to the discussion of the strength); instead, the toughness can be estimated by means of the values of εmax of each filament. For the sake of simplicity, we demonstrate the procedure using the stress–strain curve of a two-filament bundle (Fig. 7). The curve includes an initial elastic region followed by a drop, usually considered to reflect a yielding behavior (ε b εp). This is followed by a perfectly-plastic region (ε N εp), characterized by progressive filament breakage with maximal strains εmax(1), εmax(2), etc. The (approximate) toughness of an isolated filament, extracted from the stress–strain curve of a yarn, can then be evaluated as follows. 1. Calculate the area U0 under the stress–strain curve for ε b εp. This is the toughness of the yarn (all filaments) up to the plasticity plateau, and the contribution in this region of an individual filament to the yarn toughness is simply U0/Nfilaments, where Nfilaments is the number of filaments in the yarn, and we have assumed that all have identical diameters. 2. The area under the stress–strain curve for ε N εp represents the plastic contribution of all filaments to the yarn toughness. In this region, the breaking points of the filaments can be easily identified (e.g. εmax(1), εmax(2)) and horizontal lines from each of these can be drawn back to εp. The resultant area of each rectangular sub-region (e.g. Up1 and Up2) represents the plastic toughness contribution of the individual filaments to the yarn toughness. 3. The contribution Ui of the ith filament to the overall toughness of the yarn is therefore Ui = U0/Nfilaments + Upi.
Fig. 7. Graphical demonstration of the procedure developed to measure the toughness of single filaments based on the test of a yarn rather than on a large number of individual filament tests. This is illustrated here using the stress–strain curve of a typical two-filament gelatin yarn. The plastic onset εp and maximal strain points εmax(1) and εmax(2), are easily identified. The toughness of the yarn originates from the elastic–inelastic and perfectlyplastic contributions. Up1 and Up2 represent the toughness of the individual filaments in the plastic region. The error bars designate the standard deviation.
4. The toughness of an isolated filament, Γi, is obtained by dividing Ui by the relative cross section area of the filament in the yarn (1/Nfilaments), namely Γi = Ui Nfilaments. The results for twisted specimens presented in Fig. 8 show that as the filaments in the yarn progressively fail, their toughness significantly increases so that the toughness of the filaments that break last is—generally—the highest (similar to strength, where the strongest filaments in a yarn generally break last). However, the variability in the results also increases significantly, likely due to a number of reasons, including the filament–filament interactions and the high sensitivity to temperature variability as friction increases. Here too it was impossible to observe a consistent effect of the 15° yarn twist. We have occasionally observed that much higher toughness results are obtained for the progressively failing filaments but at this stage we cannot pinpoint the exact cause of this variability. Finally, the average toughness of single filaments can be reliably calculated from a yarn test, as in Fig. 9 and the results compare favorably with single filament testing for which Γ(N = 1) = 6.1 J/m3.
Fig. 8. Single filament toughness as the yarn failure proceeds. The toughness of the filament that break last is the highest. Note also the increasing filament toughness variability as the yarn failure progresses. The error bars designate the standard deviation.
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be independent of the twist. Note that the intention here was not to replicate the mechanical effects of tendon crimp, but only to possibly account for similar effects via twist. The origin of the significant toughness in gelatin is its inherent elasto-plastic behavior. A major difference between tendon and gelatin in terms of toughness, however, is the fact that tendon crimp is reversible whereas gelatin plasticity is not.
Acknowledgments We acknowledge the support from the Israel Science Foundation (Grant No. 1509/10) and from the G. M. J. Schmidt Minerva Centre of Supramolecular Architectures. This research was made possible in part by the generosity of the Harold Perlman family. H.D. Wagner is the recipient of the Livio Norzi Professorial Chair. It is a pleasure to thank Mrs Rawan Khatib, Hannah Harel and Erica Wiesel for their assistance and helpful advices with the technical procedures.
Fig. 9. Average toughness of single filaments calculated from a yarn test. As seen, results compare favorably with single filament testing (indicated by the gray area). The error bars designate the standard deviation.
4. Summary and conclusions This study aimed to expand and enrich the existing knowledge of tensile mechanical behaviors of yarn structures inspired by tendons and made of gelatin micro-filaments, from a structural and mechanical perspective. It was based on the use of gelatin micro-filaments prepared by the mix-melt-extrusion method that is of potential commercial feasibility. The main factors that control the mechanical properties of the gelatin yarn structure are the relevant property of the individual filament, the number of filaments per yarn and the inter-filament pressure and friction. The effect of the yarn configuration (15° twisted or parallel) seems to be negligible, although a study using a wider spectrum of twist angles is required to confirm this. The rules by which these factors determine the yarn's property depend on the specific property as follows. The static properties of the yarn, namely the yield strength and the stiffness (modulus of elasticity) decrease as the number of filaments per yarn is increased, likely due to the effect of inter-filament contact pressure that generates stress concentrations at contact points along the yarn. Conversely to the yield stress and stiffness, the yield strain of the yarn increases as the number of filaments per yarn is increased. This effect is produced under tensile loading as the twisted structure is straightened out and the inter-filament angle decreases. Considering the toughness, it is evident from the observation that it increases drastically with the number of filaments, a result that goes hand in hand with the increased strain to failure, so that the toughness of the yarn is not merely the sum of the toughness contributions of the filaments, but in addition a major component is attributed to the high strain work of deformation. Finally, we developed a dependable procedure to measure the toughness of single filaments based on the test of a yarn rather than on a large number of individual filament tests. Based on this study it is possible to conclude that a yarn property is the product of the corresponding properties of the constituents and of their number (a hierarchical consideration) plus a structural factor contribution (twist and crimp) that sets the inter-filament interactions. The toughness effects of a twisted gelatin yarn configuration, originally assumed to be reminiscent of those of the crimped waveform orientation of collagen fibers in tendons, have limited similarities only. Indeed, although toughness of gelatin yarns increases with yarn size, it seems to
References [1] H.H. Lu, S.D. Subramony, M.K. Boushell, X. Zhang, Ann. Biomed. Eng. 38 (2010) 2142–2154. [2] D.H. Kim, D.R. Wilson, A.T. Hecker, T.M. Jung, C.H. Brown, Am. J. sports Med. 31 (2003) 861–867. [3] U. Izhar, H. Schwalb, J.B. Borman, G.R. Hellener, A. Hotoveli-Salomon, G. Marom, T. Stern, D. Cohn, J. Surg. Res. 95 (2001) 152–160. [4] R.A. Gross, B. Kalra, Science 297 (2002) 803–807. [5] K.G. Vogel, J. Musculoskelet. Nueronal Interact. 3 (2003) 323–325. [6] E. Baer, J. Cassidy, A. Hiltner, Pure Appl. Chem. 63 (1991) 961–973. [7] P. Fratzl, Curr. Opin. Colloid Interface Sci. 8 (2003) 32–39. [8] K.A. Hansen, J.A. Weiss, J.K. Barton, J. Biomech. Eng. 124 (2002) 72. [9] A. Bigi, S. Panzavolta, K. Rubini, Biomaterials 25 (2004) 5675–5680. [10] M. Shoulders, R. Raines, Annu. Rev. Biochem. 78 (2009) 929–930. [11] A.K Harvey, M.S. Thompson, M. Brady, Proc. Conf on Medical Image Understanding and Analysis (MIUA) 2010, 1-5, University of Warwick, UK, 2009. [12] M. Buehler, Acta Mech. Solida Sin. 23 (2010) 471–483. [13] J.W. Park, W. Scott Whiteside, S.Y. Cho, LWT Food Sci. Technol. 41 (2008) 692–700. [14] M. Coppola, M. Djabourov, M. Ferrand, Macromol. Symp. 273 (2008) 56–65. [15] R. Hafidz, C. Yaakob, Int. Food Res. J. 18 (2011) 787–789. [16] C.N. Grover, R.E. Cameron, S.M. Best, J. Mech. Behav. Biomed. Mater. 10 (2012) 62–74. [17] E. Rosellini, C. Cristallini, N. Barbani, G. Vozzi, P. Giusti, J. Biomed. Mater. Res. A 91 (2009) 447–453. [18] A. Veis, The macromolecular chemistry of gelatin, 1964. [19] M. Aviv-Gavriel, N. Garti, H. Füredi-Milhofer, Langmuir 29 (2013) 683–689. [20] K. Lynn, I.V. Yannas, W. Bonfield, J. Biomed. Mater. Res. B Appl. Biomater. 71 (2004) 343–354. [21] J.A. Arnesen, A. Gildberg, Bioresour. Technol. 82 (2002) 191–194. [22] C. Joly-Duhamel, D. Hellio, M. Djabourov, Langmuir 18 (2002) 7208–7217. [23] C. Dai, Y. Chen, M. Liu, J. Appl. Polym. Sci. 99 (2006) 1795–1801. [24] I. Yakimets, N. Wellner, A.C. Smith, R.H. Wilson, I. Farhat, J. Mitchell, Polymer 46 (2005) 12577–12585. [25] P. Bergo, P.J. Sobral, Food Hydrocoll. 21 (2007) 1285–1289. [26] F.M. Vanin, P.J. Sobral, F.C. Menegalli, R. Carvalho, A.M.Q.B. Habitante, Food Hydrocoll. 19 (2005) 899–907. [27] Y. Zhou, J. Fang, X. Wang, T. Lin, J. Mater. Res. 27 (2011) 537–544. [28] N. Pan, J. Mater. Sci. 28 (1993) 6107. [29] J.W.S. Hearle, P. Grosberg, S. Backer, Structural Mechanics of Fibers, Yarns and Fabrics, Wiley-Interscience, New York-London-Sydney-Toronto, 1969. [30] Y. Rao, R. Farris, J. Appl. Polym. Sci. 77 (2000) 1938–1949. [31] X. Sui, E. Wiesel, H.D. Wagner, Polymer 53 (2012) 5037–5044. [32] S.L. Phoenix, Statistical theory for the strength of twisted fiber bundles with applications to yarns and cables, Text. Res. J. 49 (July 1979) 407–423. [33] N. Pan, D. Brookstein, J. Appl. Polym. Sci. 83 (2002) 610–630. [34] S. Omeroglu, Fibers Text. East. Eur. 14 (2006) 53–57. [35] N. Brown, I.M. Ward, J. Polym. Sci. A-2 (6) (1968) 607–620. [36] S. Bahadur, Polym. Eng. Sci. 13 (4) (1973) 266–272. [37] J. Lu, K. Ravi-Chandar, Int. J. Solids Struct. 36 (1999) 391–425. [38] P. Ray, B.K. Chakrabarti, J. Phys. C Solid State Phys. 18 (1985) L185. [39] P. Ray, B.K. Chakrabarti, Solid State Commun. 53 (1985) 477. [40] S.B. Batdorf, Nucl. Eng. Des. 35 (1975) 349–360. [41] H.D. Wagner, J. Polym. Sci. B Polym. Phys. 27 (1989) 115–149. [42] V. Calard, J. Lamon, Compos. Sci. Technol. 64 (2004) 701–710.