Introduction

Cellulose is the most abundant natural polymer. It is a semicrystalline polymer where crystal and amorphous phases coexist, with the crystalline phase stabilized by strong hydrogen bonds. On heating, cellulose does not exhibit crystal melting—rather, the polymer undergoes degradation. Solvents that can disrupt intra-molecular hydrogen bonding can dissolve cellulose, offering a route to process it into useful products. To convert cellulose into continuous fiber form for use in textile applications, it has to be regenerated. In this process, the native cellulose is dissolved and regenerated fibers are produced by spinning the solution into a non-solvent coagulation bath. The details of the fiber regeneration process play a critical role in determining the microstructure of the regenerated fiber, and therefore in determining its properties.

The steps of cellulose fiber regeneration are schematically depicted in Scheme 1. Wood pulp is dissolved in a solvent and the solution is extruded through spinneret holes into a coagulation bath that contains a non-solvent. The non-solvent extracts the solvent, regenerating the cellulose in fiber form. Several processes based on this general scheme have been developed for dissolution of native cellulose and its regeneration as fibers (Woodings 2001; Zhang et al. 2018). The two main industrially practiced processes are the lyocell and viscose processes, that we now describe briefly.

Scheme 1
scheme 1

Regeneration process for the production of cellulose fibers

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The viscose process was developed over a century ago, in 1891. Here, cellulose pulp is reactively dissolved in sodium hydroxide base to form sodium cellulosate (Woodings 2001). This solution is aged at 40–60 °C such that the degree of polymerization (DP) of cellulose is reduced from 750–850 to 270–350. This results in a decrease in solution viscosity to processable values. Sodium cellulosate is then treated with carbon disulphide to form sodium cellulose xanthate, which is dissolved in dilute sodium hydroxide to form viscose dope. Subsequently, the solution is extruded through spinnerets into a coagulation bath containing sulphuric acid and salts, ZnSO4 and Na2SO4. The xanthate reacts vigorously with the acid solution and is neutralized to cellulose. The fiber thus obtained is washed and dried. Cellulose undergoes recrystallization during the spinning and coagulation steps. The lyocell process is more recent, and was first commercialized in 1984 (Woodings 2001). Here, cellulose pulp is dissolved in an aqueous solution of N-Methylmorpholine N-oxide (NMMO). The cellulose in solution has a DP of 500–600 (Zhang et al. 2018). The solution (called dope) is then extruded using spinnerets, across an air gap, into a coagulation bath containing water. In the coagulation bath, water acts as a non-solvent for the cellulose and extracts NMMO to regenerate the cellulose fiber.

In this paper, we examine similarities and differences in the structure and properties of fibers from viscose and lyocell processes. We begin by summarizing aspects that have been previously reported in the literature (Schuster et al. 2003; Rous et al. 2004; Abu-Rous et al. 2006) and, that are consistent with data on fibers investigated here. When examined using a scanning electron microscope (SEM), there are significant differences in the shapes of the fiber cross-section for viscose and lyocell fibers (Fig. 1a, b). Viscose fibers exhibit a highly irregular cross section (Fig. 1a). lyocell fibers do not show a perfectly circular cross-section either—however, they are significantly more regular than the viscose fibers (Fig. 1b). The shape of the cross-section is a consequence of the regeneration process and the difference between viscose and lyocell fibers has been previously reported (Woodings 2001).

Fig. 1
figure 1

SEM images of the fiber cross sections for a viscose and b lyocell fibers. Representative optical microscopy images of dyed and microtomed cross section of c viscose and d lyocell fibers

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Further, in experiments where the fibers are dyed and examined in cross-section under an optical microscope, we observe that the viscose fibers possess a radial skin layer that exhibits higher dye uptake than the core (Fig. 1c). In contrast, we observe uniform dye uptake throughout the cross-section of lyocell fibers (Fig. 1d). Thus, not only are the lyocell fibers more uniformly shaped in cross-section, there are also no radial gradients that are reflected in the dye uptake. Reports in the literature suggest that the regeneration process of viscose fibers results in the formation of a skin layer with a lower crystallinity than the core, resulting in the observed radial differences (Morehead and Sisson 1945; Kato 1959).

There are several reports that investigate the effect of regeneration processes on the structure and properties of cellulose fibers (Fink et al. 1987, 2001; Lenz et al. 1993; Kim 2005; Adusumalli et al. 2006; Gindl et al. 2006a; Cai et al. 2007; Jiang et al. 2012a). Jiang et al. compared regenerated cellulose fibers made from viscose, lyocell and modifications of these processes (Jiang et al. 2012a, b). They demonstrated that lyocell fibers have higher specific modulus (viz. elastic modulus/specific gravity) and tenacity (viz. breaking load/linear density) in both dry and wet state, when compared with viscose fibers. However, the strain at break is lower for lyocell fibers relative to viscose. They used wide-angle X ray diffraction (WAXD) to demonstrate that lyocell fibers have a higher crystallinity relative to viscose fibers and suggested that the higher modulus of the lyocell fibers arises from their higher crystallinity. Reports have related the elongation at break to the crystallinity and crystalline orientation in cellulose fibers. Detailed analyses of the effects of processing parameters such as draw ratio, spinning speed etc. on properties and structure have been reported in the literature (Bryant and Walter 1959; Kong and Eichhorn 2005; Kong et al. 2007; Jiang et al. 2012a, b). It has been shown that on increasing the spinning speed and draw ratio, the crystalline orientation increases. Fibers characterized by higher orientation fail at lower elongation relative to those with lower orientation, viz. spun at lower draw ratios (Kong et al. 2008). On stretching, there is an increase in the orientation exhibited by fibers with a low initial orientation (Kong et al. 2007; Jiang et al. 2012a, b). Previous studies have also reported the influence of wetting lyocell and viscose cellulose fibers with water on their mechanical properties (Kreze et al. 2001; Jiang et al. 2012a, b; Ganser et al. 2015). These reports indicate that the water uptake of viscose fibers is higher relative to lyocell. This results in a significant decrease in the tenacity of viscose fibers on wetting. Since lyocell fibers show a lower water uptake, the decrease in their wet state tenacity is lower.

The mechanical response of various cellulosic fibers have been described using phenomenological models as well as molecular mechanics (Eichhorn et al. 2005; Kong et al. 2007; Zhang et al. 2013). These models typically capture the effect of molecular deformation and crystal domain orientation on the stress–strain behavior of these fibers. However, given the microstructural complexity of cellulose fibers, these models are inadequate to capture the behavior of cellulose fibers subjected to different mechanical histories. Recently, we reported (Sharma et al. 2018) the development of a phenomenological model that accurately captures the mechanical response of semicrystalline fibers in the linear response regime. We demonstrated the use of this model to fit stress–strain, stress relaxation and recovery data for a wide variety of fibers, including natural fibers such as silk and regenerated cellulose as well as synthetic PET and PAN fibers. Notably, we demonstrated that for semicrystalline fibers with a glassy amorphous phase, the fit parameters could be directly related to microstructural features. Thus, this model provides important insights into the microstructural underpinnings of the mechanical response of glassy semicrystalline polymer fibers.

Here, we contrast the mechanical response of regenerated cellulose fibers prepared using viscose and lyocell processes. We subject viscose and lyocell fibers to mechanical deformation, and fit this data to our phenomenological model. The microstructural parameters obtained from this fit characterize the two fibers. At elongational strains of a few percent, regenerated cellulose fibers show a decrease in the slope of the stress–strain curve. This has been identified as the yield point in the literature (Meredith 1945a, b; Gindl et al. 2006a, b). We demonstrate that this does not represent a true yield point for either viscose or lyocell fibers. On wetting the fibers, there is a change in the apparent yield strain. The nature of this change is qualitatively different for viscose and lyocell fibers, indicative of structural differences between these fibers.

Materials and methods

We perform experiments on commercial regenerated cellulose fibers manufactured using lyocell and viscose processes. These fibers were provided by Aditya Birla Science and Technology Company Pvt. Ltd. The linear mass density of lyocell fibers is 1.15 ± 0.29 den and that of viscose fibers is 1.2 ± 0.13 den. Viscose and lyocell fibers are characterized by a crystallinity index of 0.27-0.3 and 0.36-0.4, respectively (from a ratio of intensity under crystalline peaks to total intensity in WAXD, the range represents sample to sample variations). Lyocell fibers show higher crystal orientation with a Herman orientation parameter of 0.7, relative to 0.66 for viscose. Experiments were performed on “dry” fibers, conditioned at 25 °C and 55% RH for over a day, as well as on fibers soaked in water for at least 30 min. During measurements on wet fibers, the fiber is kept in contact with a pool of water so that it does not dry out during the experiment.

Mechanical measurements

Fibers were subjected to different mechanical histories using the ARES G2 rheometer (TA Instruments). Specifically, we perform stress strain, cyclic loading/unloading, stress relaxation and stress recovery experiments. For each test, a single fiber is clamped in the torsion fixture of the rheometer using a paper frame set up as described by Gindl and co-workers (Adusumalli et al. 2006) with gauge length between 10 and 11 mm. Each measurement is repeated at least 10 times and representative data are presented. We obtain the stress by dividing the force obtained from the rheometer by the average cross sectional area of the fiber.

Stress strain measurements are performed on single fibers stretched at a constant strain rate of 4 × 10−3 s−1 until failure. Cyclic loading/unloading experiments are performed by stretching a single fiber to a predetermined strain at a fixed rate (4 × 10−3 s−1) after which the strain is decreased at the same rate to zero strain. These measurements are performed for different values of strains chosen below and above the apparent yield point. For stress relaxation measurements, fibers are stretched at a strain rate of 4 × 10−3 s−1 to a specified final strain. The strain is then held constant to monitor the evolution of stress. In stress recovery experiments, fibers are stretched to a final strain and are maintained at that strain for 1 h. After 1 h, strain on the fiber is decreased at 4 × 10−3 s−1 until the stress becomes zero. Subsequently, the fiber is held at that strain and the evolution of stress is monitored.

Wide angle X-ray diffraction (WAXD)

WAXD measurements are made on fibers in dry state. The diameter of the X-ray spot is greater than the average fiber diameter—hence, WAXD measurements are made on a bundle of fibers. These fibers are combed to straighten them and are then clamped in the WAXD. All measurements are made using Rigaku R Axis IV ++ equipped with a microfocus source (Cu Kα radiation, λ = 0.154 nm, 1.2 kW rotating anode generator).

We mount a stretching device (Linkam Tensile Stress Testing System - TST350) on the WAXD instrument to perform in situ diffraction measurements during stretching. WAXD measurement is performed on combed, straightened fibers in the unstretched state at first; then the fibers are stretched at a strain rate of 4 × 10−3 s−1 to a specific value of final strain and are held at this strain for 2 days to allow the stress to relax to a plateau. Once the stress plateaus, WAXD is performed again on these stretched fibers (Fig. 2).

Fig. 2
figure 2

a 2D wide-angle x ray pattern showing highly anisotropic scattering from regenerated cellulose fibers. b 1D data for lyocell and viscose fibers indexed based on the literature (Chen et al. 2006; Jiang et al. 2012a, b)

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2D air background is subtracted from the WAXD data obtained for each sample after normalizing for scattering time. 2D data is converted to 1D data using RIGAKU 2DP software.

Model

In our previous report (Sharma et al. 2018), we described a phenomenological model to fit the linear mechanical response data for semicrystalline fibers with a glassy amorphous phase. As shown schematically in Fig. 3, the model comprises of parallel connected units having a spring in series with a Kelvin-Voigt element. To describe the slow relaxation of the amorphous phase, we assume a variation in dashpot relaxation times (τ) across the units while the spring moduli (Ec and Ea) are constant. Phenomenological spring dashpot models have been used extensively in the literature to model different polymer fibers (Wilding and Ward 1984; Manich et al. 2000; Krasnov et al. 2008). However, while previous models were typically able to capture the fiber response to only specific modes of mechanical deformation, the model in Fig. 3 has been demonstrated to capture stress–strain, stress relaxation and stress recovery for several natural and synthetic polymer fibers.

Fig. 3
figure 3

Representation of the phenomenological model employed to capture mechanical response of fibers

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This model yields the following equations for stress strain (σs–s) and stress relaxation (σr) experiments as:

$$\sigma_{{\text{s - s}}} = \mathop \int \limits_{ - \infty }^{\infty } \text{P}(\uptau) \frac{{{E_{\text{c}}}}}{{{E_{\text{c}}} + {E_{\text{a}}}}}\left[ {{E_{\text{a}}\varepsilon } + {E_{\text{c}}\tau \dot{\varepsilon }}\left( {1 - {\text{e}}^{{ - \frac{{\text{t}}}{\uptau}}} } \right)} \right]d\uptau$$
(1)
$$\sigma_{\text{r}} = \mathop \int \limits_{ - \infty }^{\infty } \text{P}(\tau) \left\{ {\left[ {\sigma_{\text{o}} - \frac{{{E_{\text{c}}E_{\text{a}}\varepsilon }}}{{{E_{\text{c}} + E_{\text{a}}}}} } \right]{\text{e}}^{{ - \frac{\text{t}}{\uptau}}} + \frac{{{E_{\text{c}}E_{\text{a}}\varepsilon }}}{{{E_{\text{c}} + E_{\text{a}}}}}} \right\}d\uptau$$
(2)

where P(τ) is relaxation time distribution, σo is stress at t = 0 in stress relaxation experiments, ε is strain and \({\dot{\varepsilon }}\) is the strain rate (= 4 × 10−3 s−1 in our case). Stress–strain and stress relaxation experimental data are fitted using this model using regularization, to obtain the fit parameters, Ec, Ea and P(τ), that characterize the fibers. We have shown that for semicrystalline fibers with a glassy amorphous phase, Ec corresponds to the crystalline phase while Ea and P(τ) characterize the response of the amorphous regions of the fiber. Ec from the model fit matches that obtained from independent WAXD experiments, while the activation energy from relaxation time spectra correspond to that reported for sub Tg β-relaxations.

Results and discussions

Mechanical response and model fit

The stress required to elongate cellulose fibers is linear in the extensional strain at low strains. We stretch both viscose and lyocell fibers at a strain rate of 4 × 10−3 s−1 to a strain of 0.4% and 0.6% respectively, in the linear response region, and then hold for 3600 s and finally decrease the strain until the stress becomes zero (as indicated in the schematic in Fig. 4a). The experimental data and the fit to the phenomenological model (depicted in Fig. 3) is shown in Fig. 4b. The model parameters from the fit, Ec and Ea are shown in Table 1 and P(τ) are shown in Fig. 5. Previously (Sharma et al. 2018), we have shown that the moduli Ec and Ea can be associated with the crystalline and amorphous phases, respectively, and P(τ) represents the relaxation time spectrum in the glassy amorphous phase.

Fig. 4
figure 4

a Schematic of the extensional strain imposed on the fibers in stress–strain (light orange), stress relaxation (green) and stress recovery (lavender) experiments. b Experimental data for stress strain, stress relaxation and stress recovery experiments. (Color figure online)

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Table 1 Crystalline and amorphous moduli from model fitting and WAXD
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Fig. 5
figure 5

Relaxation time spectra for lyocell and viscose fibers obtained from the model fitting

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The mechanical response of lyocell and viscose fibers exhibit qualitative similarities—however, there are quantitative differences. The slope of the stress–strain data is higher for lyocell fibers relative to viscose. Consequently, the crystalline modulus (Ec) for lyocell fibers (15 GPa) is higher than that for viscose fibers (12.5 GPa) by about 20%. Here, Ec does not represent the modulus of the unit cell of a cellulose crystal (Mann and Roldan-Gonzales 1962; Sakurada et al. 1966; Nishino et al. 1995)—rather, it corresponds to lumped parameter description of the crystalline regions that averages over the details of the semicrystalline microstructure. For both viscose and lyocell, Ec is about an order of magnitude higher than the amorphous phase modulus, Ea. On holding the fibers at constant strain, the stress shows a slow logarithmic relaxation and then plateaus on holding for 3600 s (Fig. 4b, middle). Subsequently, the strain is decreased at 4 × 10−3 s−1 until the stress goes to zero (at a strain of approximately 0.34% for lyocell and 0.26% for viscose). On holding at this strain, the stress is observed to recover (Fig. 4b, right). A broad relaxation time spectrum, P(τ), is required to capture the slow stress decay and stress recovery. We observe that the data for both viscose and lyocell are fitted well by a bimodal P(τ) (Fig. 5). We note that P(τ) is broader for lyocell (relative to viscose) and extends from over an order of magnitude smaller in time scales to over an order of magnitude higher.

Wide-angle X ray measurements

The moduli of the crystalline and the amorphous phases can be independently determined using WAXD. Cellulose fibers show uniaxial symmetry with the crystal c-axis along the fiber direction. Therefore, fiber stretching results in an increase in the c-axis unit cell dimension (and a corresponding decrease along the a and b axes). We calculate the strain on cellulose crystals from the change in the c lattice parameter of the fibers, as \(\upvarepsilon_{{\text{c} }} ( = \frac{{\Delta \text{c}}}{{\text{c}_{\text{o}} }})\). When a semicrystalline fiber is stretched, it has been shown that crystal and amorphous phases experience the same stress (Young 1995; Yeh and Young 1998; Sirichaisit et al. 2003). Therefore, the crystalline modulus can be calculated as a ratio of the experimentally imposed stress to the WAXD crystalline strain, \(\upvarepsilon_{\text{c}}\). To estimate the amorphous modulus, we perform WAXD on stretched fibers, after the stress has relaxed to a plateau value. In these experiments, we stretch cellulose fibers to a strain of 1% and then hold the fibers at that strain for over 2 days to ensure that stress relaxation is complete before we perform WAXD. After stress relaxation, the crystal and amorphous regions can be modeled as springs in series (Dulmage and Contois 1958; Sakurada et al. 1962, 1964; Sharma et al. 2018). Therefore, the strain on amorphous phase is calculated as \(\upvarepsilon_{\text{a}} { = \varepsilon } -\upvarepsilon_{\text{c}}\) and moduli of crystalline and amorphous phase are calculated as:

$$\text{E}_{\text{c}} = \frac{\upsigma}{{\upvarepsilon_{\text{c}} }}\quad \text{E}_{\text{a}} = \frac{\upsigma}{{\upvarepsilon_{\text{a}} }}$$
(3)

Ec and Ea obtained from WAXD for both fibers are shown in Table 1. We observe that these values are in reasonable agreement with those obtained from model fits to the mechanical data. This supports our assertion that the model parameters, Ec and Ea, characterize the crystal and amorphous regions, respectively, of the semicrystalline fiber. We note that our model represents a minimal description of the semicrystalline state, and does not explicitly account for the degree of crystallinity, crystal orientation, spatial variations in microstructure, etc. Therefore, Ec and Ea, represent effective moduli that present a lumped description of the complex semicrystalline microstructure of the fibers. Therefore, we attribute the higher value of Ec for lyocell to the higher degree of crystallinity and crystal orientation that one associates with this process (relative to viscose). Similarly, we speculate that the higher value of Ea might correspond to greater coupling between the crystal and amorphous states in the more crystalline lyocell fiber that results in greater constraints on mobility of the glassy amorphous phase.

The glassy amorphous phase in regenerated cellulose fibers is known to be characterized by significant structural heterogeneity. Manabe et al. (1986) have demonstrated that regenerated cellulose fibers obtained from different processes exhibit several distinct dynamical mechanical absorptions. They suggest that the amorphous phase in regenerated cellulose can be characterized by five different dynamical environments that differ in the extent of intra- and intermolecular hydrogen bonding, and by the presence of absorbed water. Further, it has been reported in the literature that polysaccharides (including regenerated cellulose fibers) exhibit different modes (β, βwet, σ, γ) in dielectric relaxation spectra below the glass transition temperature (Sakurada et al. 1964; Manabe et al. 1986; Einfeldt et al. 2003). Specifically, the βwet relaxation is attributed to the presence of water in cellulose at room temperature, and is present in addition to the β relaxation. It has been shown that even vacuum dried samples contain a small amount of moisture that is associated with the cellulose, resulting in βwet relaxation (Einfeldt et al. 2003). We note that our measurements on “dry” fibers correspond to fibers conditioned at a relative humidity of 55% at room temperature. Therefore, we anticipate that the amorphous phase is characterized by structural heterogeneity in hydrogen bonding and absorbed water. The breadth observed for P(τ) is consistent with this heterogeneity and it is also not particularly surprising that P(τ) is not monomodal. However, given the structural complexity in regenerated cellulose, it is not possible to associate P(τ) with any specific structural motif.

Temperature dependent mechanical response

Temperature dependent measurements were performed on single fibers, using the ARES-G2 rheometer equipped with a forced convection oven. The forced convection oven controls the temperature of dry air that is allowed to flow over the sample, so that the required temperature is attained. Fibers are allowed to equilibrate in the oven atmosphere, characterized by dry air at the set temperature for at least 2 h before measurements.

Stress–strain and stress relaxation experiments are performed at different temperatures and the data is fitted to the model (Fig. 3) to obtain fit parameters, Ec, Ea and P(τ). Temperature dependent P(τ) for lyocell and viscose are shown in Fig. 6a, b respectively. Temperature dependent moduli, Ec and Ea are shown in Fig. 6c. On heating, we observe a progressive narrowing of P(τ) for both lyocell and viscose. The mode at higher τ moves to shorter times on heating and appears to merge with the lower τ peak, such that eventually P(τ) becomes monomodal. The transition to faster monomodal relaxation happens at lower temperature for the viscose fibers and P(τ) is monomodal already at 393 K. For lyocell, P(τ) becomes monomodal at a temperature between 393 and 473 K. We note that the transition from bimodal P(τ) at low temperatures to monomodal on heating is reversible, suggesting that heating does not result in chemical degradation of the cellulose fibers. In the literature, it has been demonstrated that the βwet mode disappears above 423 K due to drying of the fibers. Thus, a temperature dependent transition occurs from multimodal low temperature relaxation spectra to monomodal at high temperature (Einfeldt et al. 2000, 2003; Meißner et al. 2000) Our results are broadly consistent with these reports. Our data also suggests that higher temperatures are required for the higher crystallinity lyocell fibers to transition to faster monomodal relaxations.

Fig. 6
figure 6

Relaxation time spectra for a lyocell and b viscose at increasing temperatures. c Variation in the values of Ec and Ea obtained from the model with temperature

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There is a monotonic decrease in both Ec and Ea for lyocell and viscose on heating (Fig. 6c). There is a 3–4 fold reduction in the value of crystalline modulus on heating from 333 to 473 K, for both lyocell and viscose. At all temperatures, Ec > Ea. The values of Ec and Ea for lyocell are higher than the corresponding values for viscose. A decrease in the solid modulus of regenerated cellulose fibers on heating has been previously reported (Zhou et al. 2001). Molecular dynamics simulations (Bergenstråhle et al. 2007) of the temperature dependent modulus of crystalline unit cells in native cellulose indicate conformational changes in cellulosic chains present in the unit cell. There is thermal expansion in the unit cell on heating and a decrease in the hydrogen bonding, resulting in a decrease in the crystalline modulus. We anticipate that similar processes take place in regenerated cellulose on heating. A decrease in the crystalline modulus and conformational changes in the cellulose chains result in the observed decrease in Ec, the effective modulus that characterizes the crystalline phase. The decrease in Ea is consistent with the increased motional freedom in the glassy amorphous phase indicated by the temperature dependent P(τ).

Apparent yield of fibers on stretching

On stretching, there is a decrease in the slope of the stress–strain curve for lyocell fibers above a strain of 1.2% and for viscose fibers above a strain of 1.3% (Fig. 7a). Stress increases linearly above the critical strain until the fiber fails. Lyocell and viscose show qualitatively similar response—however, as in the linear response region, there are quantitative differences above the critical strain as well. This critical strain has been previously reported and it has been suggested that this is a consequence of plastic yielding of the fiber (Meredith 1945a, b; Gindl and Keckes 2006; Gindl et al. 2006a, b) Therefore, it is referred to as the fiber yield point in the literature. The critical strain is very reproducible across different fibers produced using one particular process, and the values that we obtain are comparable to those reported in the literature (Kong and Eichhorn 2005; Gindl and Keckes 2006; Gindl et al. 2006a, b). Therefore, the critical strain appears to be a function of the fiber microstructure that develops during the regeneration process.

Fig. 7
figure 7

a Stress vs strain data for dry fibers. Cyclic loading/unloading performed on b lyocell and c viscose fibers immediately after the first cycle and 24 h later. d Creep compliance for lyocell and viscose fibers unloaded to 6 MPa after loading beyond critical strain

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When lyocell or viscose fibers are stretched to a strain (= 4%, rate = 4 × 10−3 s−1) higher than the critical value, we observe a decrease in slope of the stress–strain curve at the critical strain, followed by a subsequent monotonic increase (Fig. 7b, c). On unloading the fiber at the same rate, we observe that the stress does not trace the same path. Rather, it decays to zero at a strain of about 2%. Thus, there is residual strain in the fiber on unloading. When the same fiber is stretched in a second loading cycle, the stress does not increase immediately since the residual strain results in slack in the fiber. Once the strain exceeds the slack in the fiber, stress increases with strain, at a slope comparable to the low strain elastic modulus of the original fiber (Fig. 7b, c). At a nominal strain of 4% (relative to the original fiber length), the fiber shows the same value of stress in the second loading cycle as in the first. On unloading the fiber after the second cycle of stretching, the stress decreases along the same path as for the first unloading cycle (Fig. 7b, c). Thus, there appears to be a qualitative change in the stress–strain response of the fibers once it is stretched beyond the critical strain. This behavior is qualitatively similar for lyocell and viscose fibers. We now perform stress–strain measurements on a fiber that was stretched to 4% strain, viz. above the critical strain, and was then unloaded and kept in the unloaded state for a long time (1 day in our experiments). We observe that the stress–strain curve for this sample is unchanged from the original sample (Fig. 7b, c). Therefore, the change in both lyocell and viscose fibers due to “yielding” when they are strained to above the critical strain is not a permanent plastic deformation. Rather, the fiber is able to recover to its original state over an extended period of time. This observation suggests that, in contrast to what has been suggested in the literature (Meredith 1945a, b; Gindl and Keckes 2006; Gindl et al. 2006a, b), it is not appropriate to term the critical strain as the yield point for the fiber. Therefore, we refer to this strain as the apparent yield point.

Since the kinetics of structural recovery in fibers stretched above the critical strain are very slow, we use creep measurements to quantify the time-dependent changes. Here, a fiber is stretched to a strain greater than the critical strain and is then unloaded to zero stress. Subsequently, we impose a small probe stress on the fiber (σ = 6 MPa in our experiments) and observe the change in fiber strain with time. We maintain the fiber at constant stress and observe that the strain decreases with time as can be seen from the creep compliance (\(\text{J} = \frac{{|\upvarepsilon(\text{t})|}}{\upsigma}\)) (Fig. 7d). We observe a slow, logarithmic increase in creep compliance with time suggesting that the structural recovery of the fiber after apparent yield is slow and is characterized by a wide distribution of time scales. We notice that the strain recovers faster in case of viscose fibers than for lyocell fibers. However, for both viscose and lyocell, there is no permanent set and the fibers recover over a long time. The nature of the structural change in the fiber at the apparent yield point and of the slow recovery are not known at this time and require further investigation.

Cyclic loading/unloading measurements to investigate the apparent yield point

When we stretch either lyocell or viscose fibers to a strain (= 0.4%) below the critical strain, we observe that the stress during unloading traces the same path as during loading (Fig. 8a). Both elongation and unloading are performed at a strain rate of 4 × 10−3 s−1. Thus, fibers elongated to strains lower than the critical strain recover elastically. On stretching the fibers to strains (= 4%) exceeding the critical strain, we observe apparent yield on loading and a residual strain on unloading (Fig. 8b). When the fiber is immediately subjected to a second loading–unloading cycle, we no longer observe yielding during the loading step. We observe that during loading the fiber during the second cycle, the slack in the fiber, viz. the strain at which the stress increases above zero is lower than the residual stress during unloading in the first cycle. This is consistent with the literature (Meredith 1945a, b). Over subsequent cycles of loading and unloading the same fiber, we observe that the slack in the fiber during loading (relative to the first cycle) becomes equal to the residual strain on unloading. Thus, the stress–strain curve for loading–unloading cycles forms a loop, and there is hysteresis between loading and unloading (Fig. 8b). In all the cycles, the maximum stress observed on stretching to 4% strain remains the same as in the first loading experiment.

Fig. 8
figure 8

Cyclic loading/unloading experiments performed a below the critical strain (at 0.4%) and b above critical strain (at 4%) (Unfilled circles—loading, filled circles—unloading). c Variation of the residual strain with the maximum loading strain. Black line is the extrapolation of data points

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We perform cyclic loading/unloading experiments at different value of imposed strain (εm) and plot the experimentally observed residual strain (εr) versus the imposed strain (Fig. 8c). A fresh fiber is used for each experiment at a different value of εm. At low imposed strains, we see elastic fiber response and the residual strain is zero. Extrapolating the residual strain to zero linearly allows us to determine the critical point for apparent yield for the fibers. We confirm that this value of strain is the same as that obtained from the kink in the stress–strain plot (= 1.2% and 1.3% for lyocell and viscose, respectively), viz. the apparent yield point for the fiber. In all these experiments, both viscose and lyocell fibers show the same qualitative behavior.

We now repeatedly stretch a single fiber and cycle it to progressively increasing strains above the apparent yield (Fig. 9). We reiterate that the apparent yield strain is very reproducible and is a characteristic of the regeneration process. The values of the apparent yield obtained in our experiments are consistent with the values reported in the literature (Kong and Eichhorn 2005; Gindl and Keckes 2006; Gindl et al. 2006a, b). In our experiment, we first stretch lyocell and viscose fibers to a strain of 4% (above the apparent yield ≈ 1%), corresponding to a maximum stress, σ1 (= 125 MPa for viscose and = 230 MPa for lyocell fibers, Fig. 9a). We then unload the fiber and then stretch it out so that the slack in the fiber is removed. The fiber is then subjected to a second stretching cycle to a strain of 5% (higher than in the first cycle). We observe that the stress increases smoothly (and approximately linearly) until σ1 and then exhibits a kink beyond which the slope of the stress–strain curve decreases (Fig. 9b). Thus, the apparent yield point is now defined by the memory of the maximum stress experienced by the fiber in the previous loading cycle. We repeat this process by stretching the fiber through two more cycles, to strains of 6.2% for lyocell and 6.8% for viscose (Fig. 9c) and 7% for lyocell and 8% for viscose (Fig. 9d). As in the second cycle, we observe that the position of the apparent yield strain keeps shifting with each cycle and is defined by the maximum stress experienced in the previous cycle. Further, the slopes of the initial (before kink) and post apparent yield stress–strain data is approximately preserved for each cycle. Therefore, the “low strain” fiber modulus remains the same for all cycles, independent of the apparent yield point. Thus, our data suggests that the apparent yield strain is characteristic of the fiber structure. The fiber structure set by regeneration and the spinning process determines the apparent yield of the as spun fiber. On stretching the fiber beyond the apparent yield, there is a change in fiber structure that encodes the memory of the maximum stress experienced by the fiber. In subsequent stretching cycles, the apparent yield moves to higher strains determined by the maximum stress in the previous cycle. This memory decays slowly, logarithmically in time, eventually recovering the apparent yield determined by the regeneration and spinning processes.

Fig. 9
figure 9

Single fibers loaded to different increasing strains in different cycles. Black dashed arrows show shift in the position of kink

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It is remarkable that the mechanical response of lyocell and viscose fibers are qualitatively similar, despite the differences in cellulose molecular weight, process differences and structural differences (manifested in the cross-sectional shape of the fibers and the radial variations in their semicrystalline microstructure). In the final section, we investigate the effect of wetting cellulose fibers with water, and show that this reveals qualitative differences between lyocell and viscose fibers.

Mechanical response of wet fibers

On wetting with water, there is a dramatic decrease in the modulus of both viscose and lyocell fibers. The modulus of viscose fibers decreases by about an order of magnitude from the dry state, while there is a 3.6-fold decrease for lyocell fibers (Fig. 10a). Further, there is a qualitative change in the shape of the stress strain curve for fibers soaked in water. Unlike the dry fibers, we no longer observe a well-defined apparent yield strain. Therefore, it is not clear from the stress–strain data if wet fibers experience apparent yielding.

Fig. 10
figure 10

a Stress vs strain data for water soaked fibers. Wet fibers cyclic loading b at low strains and c at high strains. (Unfilled circles—loading, filled circles—unloading) d extrapolation of residual strain data for fibers in wet state

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We now perform repeated cycles of loading/unloading experiments on the wet fibers. For low values of strain (for example, 1%, Fig. 10b), we observe that the decrease in stress on unloading a fiber follows the same path as during loading. Thus, similar to the case of dry fibers, there is an elastic region at low strain. When fibers are subjected to higher strains (for example, 8%, Fig. 10c), we observe that the decrease of stress on unloading no longer follows the same path as the increase on stretching. Similar to the case of the dry fibers, the stress decreases to zero at a non-zero residual strain. When wet fibers subjected to high strains are unloaded and held in the unloaded state, we observe slow logarithmic recovery. However, the rate of recovery is so slow that we never observe full recovery in case of wet fibers.

To determine the critical apparent yield strain in wet fibers, we obtain the residual strain (εr) during unloading when the fiber is subjected to the first loading/unloading cycle. When εr is plotted as a function of the imposed strain on the fibers, εm, we obtain the apparent yield by extrapolating εr to zero (Fig. 10d). Thus, even when there is no abrupt change in the slope of the stress–strain curve, we can obtain the apparent yield strain from the extrapolation of εr to zero. Using this, we observe that the apparent yield strain for lyocell fibers is estimated as 1.2%, similar to the value for the dry fiber. In contrast, there is a large increase in the apparent yield strain for the viscose fibers, with wet fibers showing an apparent yield of 4.8%, as compared to 1.3% for dry fibers.

What are the structural underpinnings of the differences in behavior of the apparent yield strain on wetting for lyocell and viscose fibers? It is not possible to directly address this question based on the existing data. However, we note that the higher decrease in the wet state modulus relative to dry for the viscose fibers, and the increase in apparent yield strain on wetting are consistent with the picture of viscose fibers having a lower crystallinity and less constrained glassy amorphous phase. Additionally, when we compared the humidity uptake of both fibers (by conditioning them at 95% humidity at 30 °C), we observed that viscose fibers absorb 28–29% moisture by weight (relative to oven dried samples). In contrast, lyocell fibers absorb 22–24% moisture, clearly lower than viscose. Thus, it appears that the amorphous phase is more readily accessible in the viscose fibers. Absorption of higher amounts of moisture by the viscose probably results in significant changes in the hydrogen bonded structure in the glassy amorphous phase and consequently, in a greater enhancement in mobility. It is possible that the change in the apparent yield strain on wetting is another manifestation of such structural differences in the organization of semicrystalline microstructure in viscose and lyocell fibers.

Conclusions

Structural differences between regenerated cellulose fibers prepared using the lyocell and viscose processes do not result in qualitative differences in the stress–strain, stress relaxation and stress recovery behavior. This is remarkable since, even at a gross macroscopic level, there are remarkable differences between lyocell and viscose fibers: lyocell fibers are characterized by a smooth, approximately circular cross-section and are radially uniform, while viscose fibers have a highly irregular cross-section and have a high crystallinity core surrounded by a lower crystallinity shell. Our results suggest that the mechanical response of semicrystalline fibers in the linear response region can be adequately described by a minimal model that invokes only crystal-amorphous coexistence. Fitting the mechanical data on the fibers to a model reveals quantitative differences between the fibers. Lyocell fibers have a higher crystalline and amorphous moduli and a broader relaxation spectrum relative to viscose. We attribute these differences to a higher degree of crystallinity that is more intimately associated with the glassy amorphous phase in lyocell. This is consistent with higher water absorption in viscose fibers and with a dramatic wetting-induced change in apparent yielding. Indeed, the change in the apparent yield strain on wetting viscose is the only qualitative difference relative to lyocell (where wetting does not significantly influence the apparent yield strain). We also explore the apparent yield observed on subjecting cellulose fibers to large strains. In the literature, the critical strain above which there is a decrease in the stress–strain slope of cellulose fibers has been identified as the yield point. However, we demonstrate for the first time that this does not represent a true plastic yield process. Fibers stretched above this apparent yield exhibit slow, logarithmic recovery over about a day, to recover their original as-spun state. The structural implications of the apparent yield strain are unclear at this time. When lyocell or viscose fibers are stretched above the apparent yield point, the fibers retain the memory of this mechanical history. This memory is not permanent but decays logarithmically as the fiber regains its original structure.