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Temperature-humidity-time equivalence and relaxation in dynamic viscoelastic response of Chinese fir wood
Construction and Building Materials 227 (2019) 116637
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Temperature-humidity-time equivalence and relaxation in dynamic viscoelastic response of Chinese fir wood Tianyi Zhan a, Jiali Jiang b, Jianxiong Lu c,⇑, Yaoli Zhang a, Jianmin Chang d a
College of Materials Science and Engineering, Nanjing Forestry University, Nanjing 210037, PR China Research Institute of Wood Industry of Chinese Academy of Forestry, Beijing 100091, PR China c College of Material Science and Engineering, Central South University of Forestry and Technology, Hunan Collaborative Innovation Center for Effective Utilizing of Wood and Bamboo Resources, Changsha 410004, PR China d College of Materials Science and Technology, Beijing Forestry University, Beijing 100083, PR China b
h i g h l i g h t s The (temperature-)humidity-time equivalence principle was applicable for describing evolution of wood stiffness. The humidity-time equivalence principle failed to predict wood damping properties, regardless of hygrothermal condition. The unstable configuration of wood cell wall induced by the varying moisture content accelerated the relaxation transition.
a r t i c l e
i n f o
Article history: Received 27 April 2019 Received in revised form 25 July 2019 Accepted 2 August 2019
Keywords: Viscoelasticity Hygrothermal Temperature-humidity-time equivalence Relaxation Moisture state
a b s t r a c t Design, application and service life of modern engineered wood and its products are closely related to environmental temperature and relative humidity (RH). In this study, the frequency-dependent viscoelastic properties of Chinese fir wood were investigated under different hygrothermal conditions (temperature: 30–80 °C, RH: 0–85%), to verify the applicability of humidity-time and temperature-humiditytime equivalence principles to wood viscoelasticity (i.e., the equal effects of elevating temperature, increasing RH, or prolonging testing time on the changes of stiffness and damping). The relaxation of wood cell wall was compared under moisture equilibrium and non-equilibrium states. It was demonstrated that both the humidity-time equivalence and temperature-humidity-time equivalence principles were applicable for describing the evolution of wood stiffness. Master curves constructed by humiditytime equivalence and temperature-time equivalence principles were basically overlapped at a shorttime region (frequency >0.01 Hz) when reference condition was 30 °C/0% RH. However, the humiditytime equivalence principle failed to predict wood damping properties, regardless of hygrothermal condition. The testing frequency (fc, assigned to the transition of different relaxation processes) corresponded to the local minimum value of tan d was ranged from 8 to 30 Hz and moved to the high frequency direction with increasing RH level. The fc value at moisture equilibrium state was lower than non-equilibrium state (no matter moisture adsorption or desorption). It was attributed the higher fc value at moisture nonequilibrium state to the unstable configuration structure of wood cell wall. These findings not only help understanding the wood-water relations, but also be relevant for the utilization and production processes of engineered wood and its products in the construction and building fields. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Wood, as one of the most common nature materials, has traditionally been used as construction structure components [1,2]. Due to its light-weight and high-strength properties, engineered wood and its products (EWPs) can be used in large-scale constructions, ⇑ Corresponding author. E-mail address: [email protected] (J. Lu). https://doi.org/10.1016/j.conbuildmat.2019.08.018 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
such as multi-story residential buildings, bridges, industrial halls, concert halls, etc. [3–6]. During the using processes, EWPs exchange water with surroundings by adsorption or desorption of moisture. In hence, the dimension design, application and service life of EWPs are closely related with environmental conditions [7,8]. Temperature and (or) relative humidity (RH) of ambient environment fluctuate continuously, and thus elastic and viscoelastic responses of EWPs change all the time [9].
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Commonly, the room temperature modulus is often the only value given to describe the mechanical property of EWPs [10,11]. While, the temperature dependence of the viscoelasticity of wood is complex because it is a multi-component polymeric material. The temperature-time equivalence principle is widely used to describe the creep, relaxation and dynamic viscoelasticity of EWPs under a wide temperature range [12–17]. The temperature-time equivalence principle means elevating temperature or prolonging testing time has equal effect on changing mechanical properties of EWPs. By the temperature-time equivalence principle, viscoelastic behaviors of EWPs over many decades were predicted from short-time testing by relating the response to functions of time and temperature [18]. As an important issue, the applicability of the temperature-time equivalence principle to EWPs is still controversial [19,20], because different components in wood cell wall have different temperature-dependent performances [16]. Analogous to temperature-time equivalence principle, humidity-time equivalence and temperature-humidity-time equivalence principles are also applied to investigate the rheological properties of polymers [21–25]. Humidity-time equivalence principle is verified by a stepwise increase of RH levels at a constant temperature. Considering wood is a humidity-sensitive material, the application of (temperature-)humidity-time equivalence principle on predicting viscoelastic properties of EWPs is useful to elucidate the evolution of moisture-induced stresses during wood drying or daily utilization [4,26], and optimize the thermal-hygro-mechanical (THM) treatment technique (such as densification and welding) [27,28]. In addition to prediction of long-term viscoelastic behaviors, the in situ structure and organization of components in wood cell wall can also be analyzed by the temperature-time equivalence principle [29,30]. The characteristics of molecular motions and the glass transition temperature of components in wood cell wall could be described by this equivalence [12,19,30]. Among components in wood cell wall, the in situ lignin glass transition was quite sensitive to moisture content (MC) of wood [31]. When wood MC increased as a consequence of increment of ambient RH, the glass transition temperature of lignin moved to low-temperature regions [20]. Wood possesses low stiffness and high damping no matter temperature or RH level increase. In other words, both the increasing temperature and RH level have similar effects on changing viscoelastic properties of wood. Similar to the temperature-time equivalence principle, the humidity-time equivalence principle is also rationalized for describing motions of polymers [32,33]. At a series of given RH levels, the hydration activates the molecular motion over short and long distances in a similar way as thermal energy [21]. When water penetrates wood cell walls, the movement pace of amorphous polymers is speeded up. The relaxation times of amorphous polymers are shortened with the increasing wood MC [34]. The relaxation is reflected as temperature- or frequency-dependent damping peak during the dynamic viscoelastic test [35]. When temperature changes, wood MC is influenced and the viscoelasticity varies consequently. Contemporary rheological device – dynamic viscoelastic analyzer (DMA) equips with humidity accessory which can control RH level precisely even temperature up to 90 °C. Using this kind of device, the evolution of viscoelastic properties of wood at certain hygrothermal condition could be evaluated. In this study, the frequency-dependent viscoelastic properties of Chinese fir (Cunninghamia lanceolata) were tested under different hygrothermal conditions (temperature: 30–80 °C, RH: 0–85%). In these hygrothermal conditions, the wood specimens held a series of constant MCs, i.e., under moisture equilibrium states. The applicability of humidity-time and temperature-humidity-time equivalence principles to viscoelastic properties of wood under moisture equilibrium states were investigated. In addition, the relaxation
of Chinese fir was compared under moisture equilibrium and non-equilibrium states.
2. Materials and methods 2.1. Materials Chinese fir specimens with a dimension of 60 12 2.5 mm3 (L R T) were successively obtained from similar portions of heartwood with a straight grain. Before the testing, all specimens were conditioned in sealed containers over P2O5, or saturated solutions of LiCl2, MgCl2, NaBr, NaCl or KCl, which provided RH of 0, 11, 33, 58, 75 or 85%, respectively. All the conditionings were conducted at room temperature (25 °C). The corresponding MC of conditioned specimens was 0.6, 3.2, 7.4, 13.1, 17.9 or 22.2%, respectively.
2.2. Viscoelasticity measurements After conditioning, the specimens were placed into DMA Q800 (TA Instruments, New Castle, DE, USA) for tests at moisture equilibrium and non-equilibrium states. The schematic illustration of the whole test is displayed in Fig. 1. During the DMA test, a dualcantilever bending mode (15 lm amplitude) was selected at a series of scanning frequencies from 100 to 1 Hz. DMA equipped with a humidity accessory which controlled the RH by modulating the mixture of dry nitrogen and saturated moisture. All tests were carried out within the linear viscoelastic region. The frequency-dependent viscoelastic properties are commonly evaluated as storage modulus (E0 ), loss modulus (E00 ) and loss factor (tand = E00 /E0 ). E0 and E00 represent the elastic and viscous response of the specimens under the action of loading. Tand represents the ratio of dissipated energy to stored energy. In this study, E0 and tand were used to characterize the frequency-dependent properties and the relaxation processes.
2.2.1. Humidity-time equivalence and relaxation tests Frequency-dependent E0 and tan d were measured as follows: (1) Mounted the specimens with different MCs (0.6, 3.2, 7.4, 13.1, 17.9 or 22.2%) into the testing chamber, (2) Adjusted chamber humidity to the corresponding conditioning RH (0, 11, 33, 58, 75 or 85%), (3) Ramped temperature to target one (30–80 °C, 10 °C/step), (4) Equilibrated the specimens at constant temperature and humidity conditions for 30 min, (5) Examined by the iso-hygrothermal frequency-sweep (100–1 Hz). The results of frequency-sweep measurement at 0% RH with a series of temperatures were also used as the temperature-time equivalence test and is displayed in Section 3.2. Three measurements were performed for each condition.
2.2.2. Relaxation test during moisture adsorption (1) Mounted the specimens with 0.6% MC (conditioned at 0% RH) into the testing chamber of DMA Q800, (2) Adjusted chamber humidity to 0% RH, (3) Ramped temperature to target level (30–80 °C, 10 °C/step), (4) Equilibrated the specimens at constant temperature and humidity conditions for 30 min, (5) Ramped humidity from 0 to 30, 60 or 90% RH with 2% RH/min ramping rate, (6) Isothermal frequency-sweep (100–1 Hz) at five time-points (experimental initiation, termination of RHramp, 60 min under RHisohume, 120 min under RHisohume, and 240 min under RHisohume). Three measurements were performed for each condition. Detailed method was referenced from Zhan et al [16].
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Fig. 1. Schematic illustration of the sample preparation and viscoelastic test.
2.2.3. Relaxation test during moisture desorption (1) Mounted the specimens with 22.2% MC (conditioned at 85% RH) into the testing chamber of DMA Q800, (2) Adjusted chamber humidity to 85% RH, (3) Ramped temperature to target level (30– 80 °C, 10 °C/step), (4) Equilibrated the specimens at constant temperature and humidity conditions for 30 min, (5) Ramped humidity from 85 to 60, 30 or 0% RH with 2% RH/min ramping rate, (6) Isothermal frequency-sweep (100–1 Hz) at five time-points (experimental initiation, termination of RHramp-down, 60 min under RHisohume-down, 120 min under RHisohume-down, and 240 min under RHisohume-down). Three measurements were performed for each condition. Detailed method was referenced from Zhan et al [17].
3. Results 3.1. Frequency-dependent viscoelasticity The changes of E0 as a function of frequency are displayed in Fig. 2. Most standard deviations of E0 were smaller than 280 Mpa2. With the increasing frequency, an increase in storage modulus E0 was observed, regardless of hygrothermal conditions. Commonly, less interior friction of wood polymers could be obtained at higher frequencies, attributing to the less segmental motion [36]. At a given testing, frequency E0 decreased with the
increasing humidity level, while 11% RH at 30 °C was an exception. When the testing frequency was 1 Hz, typical changes of RHdependent E0 at 30 and 80 °C are exhibited in Fig. 3. According to Fig. 3, compared to the 30 °C/0% RH condition, a slightly increment of E0 at 30 °C/11% RH could be observed more obviously. The similar phenomenon was reported in other studies [37–39]. Oven-dry wood did not form an ordered cohesion state, and some adsorption points remained vacant [38]. A slight MC increment from the ovendry state would induce a bridge effect involving hydrogen bonds between molecular chains. In hence, E0 value at 30 °C/11% RH condition was higher than that at 30 °C/0% RH. Fig. 4 shows the changes of frequency-dependent tan d at a series of hygrothermal conditions. Most standard deviations of tan d were smaller than 0.003. With the increasing frequency, tan d decreased firstly, and then increased (Fig. 4). The local minimum values of tan d occurred at the frequency ranging from 8 to 30 Hz, regardless of hygrothermal condition. The frequency corresponded to the local minimum value of tan d was named as ‘‘characteristic frequency (fc)” hereinafter. The decreased damping followed by an increase was also reported by previous studies [36,40]. Chakravartula and Komvopoulos [40] stated that the increase of damping with the increasing frequency was associated with the localized softening of the amorphous phase due to the large amount of energy dissipated. Jiang et al. [36] supposed that the minimum value of damping was assigned to a change in relax-
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3.2. Temperature-humidity-time equivalence
Storage modulus E' (MPa)
7000
Prior to the investigation of temperature-humidity-time equivalence, the application of humidity-time equivalence to wood stiffness and damping was examined. Based on Eqs. (1) and (2), the equivalent relations for E0 and tan d of Chinese fir were calculated:
6000
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Relative humidity (%) Fig. 3. Changes in the storage modulus E0 as a function of humidity level measured at 1 Hz.
ation behavior of wood cell wall. Menard [35] pointed out that, if the viscoelasticity could be tested over a wide enough frequency range, the plot of viscoelastic parameter vs. frequency appeared a reverse-like temperature scan. Hence, the relaxation process (during the temperature scan) could be reasonably observed during the frequency scan. Zhang et al. [41] investigated the viscoelastic properties of wood cell wall by means of nanoindentation test and found that a flat peak around 30 Hz was related to the glass transition of hemicellulose. It was assumed that, in this study, when testing frequency was lower than fc, the relaxation process was probably associated with the glass transition of hemicellulose with low molecular weight [41]. When the testing frequency was higher than fc, the relaxation process may be assigned to the motions of both methylol groups in the amorphous region of wood cell wall and adsorbed water molecules in wood [20]. For easy further description, the former and the later relaxation processes were labelled as a and b relaxation processes, respectively.
E0 ðRH; logf Þ ¼ E0 ðRHr ; logaRH=RHr þ logf Þ
ð1Þ
tandðRH; logf Þ ¼ tandðRHr ; logaRH=RHr þ logf Þ
ð2Þ
where f is the testing frequency, RHr is the reference RH, and log aRH/RHr is the horizontal shift factor. By shifting a series of RH dependency E0 and tan d to the results at the reference RH (0%), the master curves were constructed as shown in Figs. 5 and 6. In Fig. 5, the smooth master curves of E0 could be found at all the hygrothermal temperatures, while the master curves of tan d displayed as scattered distributions regardless of temperature (Fig. 6). For some amorphous polymers, their master curves of damping could be successfully constructed [22,42], because the free volume within polymers increased linearly with an increase in MC [42]. Cramer et al. [21] carried out the humidity-time equivalence on conductivity of polyelectrolyte complexes and considered that the hydration activated polymer motions in a similar way by thermal energy. However, since wood was a multi-phase system [43], chemical components in wood cell walls held different relaxation behaviors and different hygroscopicities. At a given humidity level, the amounts of free volume that induced by water varied within different components. To verify the temperature-humidity-time equivalence principle on wood stiffness, the secondary master curve at a reference temperature (Tr) of 30 °C was developed by Eq. (4) based on the results shown in Fig. 5.
E0 ðT; logf Þ ¼ E0 ðT r ; logaT=T r þ logf Þ
ð3Þ 0
The secondary master curve of E is presented in Fig. 7. To exhibit it more clearly, some plots were deleted, while the remained plots still shown the smooth secondary master curve of E0 (Fig. 7). This result implied that the temperature-humidity-time
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Frequency (Hz) Fig. 5. Master curve of storage modulus E0 as a function of frequency from 30 to 80 °C.
equivalence principle was applicable for constructing a master curve of wood stiffness. Additionally, the master curves developed by the temperature-time equivalence principle and the humiditytime equivalence principle at a reference condition (temperature: 30 °C, RH: 0%) were compared, being shown as the inset in Fig. 7. For the identical reference temperature and humidity condition, the master curves obtained by temperature-time equivalence principle were basically overlapped when frequency was more than 0.01 Hz. The similar overlap was also reported for other polymers [32,44]. Although master curves were overlapped for a
short-term region, a slightly difference could be found for a longterm region, i.e. at low frequency region (inset in Fig. 7). Such a difference was caused by the structural change during the moisture adsorption [23]. Fig. 7 The master curve of storage modulus E0 constructed by the temperature-humidity-time equivalence principle. The inset shows a comparison of master curves constructed by the temperature-time equivalence principle and the humidity-time equivalence principle at an identical temperature (30 °C) and RH (0%) condition
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by temperature-time equivalence by humidity-time equivalence 1E-10
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Fig. 7. The master curve of storage modulus E constructed by the temperature-humidity-time equivalence principle. The inset shows a comparison of master curves constructed by the temperature-time equivalence principle and the humidity-time equivalence principle at an identical temperature (30 °C) and RH (0%) condition.
3.3. Mechanical relaxation According to the statistical analysis, fc moved to the high frequency direction with the increasing RH level irrespective of temperature (Fig. 4). The relationships between fc and MC are presented in Fig. 8. When temperature was 30 °C, fc increased from 8 to 34 when MC ramped from 0.6 to 22.2%. The moved fc illustrated the acceleration of the transition of a and b relaxation processes (i.e., the relaxation time durations of molecular motions were shortened). When moisture molecules exist within the cell walls, the cell walls swelled and released some free spaces for molecular motions. In addition, water played a role of plasticizer and formed hydrogen bonds to hemicellulose and paracrystalline cellulose [45]. The plasticization effect of moisture lowered the energy required to initiate the chain mobility, resulting in the shortening in the polymer’s relaxation time. To clarify the influence of moisture states (equilibrium or non-equilibrium) on relaxation, relaxation test of wood samples at moisture non-equilibrium states (adsorption and desorption) were tested and the results of fc are displayed in Fig. 8. At all the hygrothermal temperatures, fc at
moisture non-equilibrium state increased with transient MC, and was higher than equilibrium state (no matter adsorption or desorption). 4. Discussion Chinese fir was a common species planted in the south of China. Due to the relative simple structure (more than 90% was consisted of tracheid cells), Chinese fir was appropriate to be a ‘‘model species” in wood science field. The investigation of its viscoelasticity at different hygrothermal conditions was helpful for designing dimensions for structure-used wood and optimizing THM techniques. At higher MCs, plasticization effect of water behaved discrepancy in different layers [middle lamella (ML), primary cell wall (P), and secondary wall (S1, S2 and S3)]. In ML and P, relative contents of lignin were much higher than in secondary wall, which was less hygroscopic than carbohydrates [45]. Distinct extents of swelling induced localized strain between the different layers and caused fiber splitting [28,46]. Moreover, when temperature
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Moisture equilibrium
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Moisture content (%) Fig. 8. Influence of moisture content on characteristic frequency of wood in moisture equilibrium and non-equilibrium (adsorption and desorption) states.
Fig. 9. Three molecular motions types in wood cell wall: (a) the relaxation process of polar groups; (b) the reorientation of adsorbed water; and (c) the relaxation process of compound groups.
rose the heating energy caused segmental motions for wood polymer, resulting in decreased stiffness [47,48]. In hence, more obvious decrement of stiffness with the increasing RH could be found at high temperature (Fig. 3). According to Figs. 5 and 7, both the humidity-time equivalence and temperature-humidity-time equivalence principles were applicable for describing the evolution of wood stiffness. The application of (temperature-)humidity-time equivalence in predicting wood stiffness would be benefit to calculate moisture-induced stresses in wood drying or daily service process [49], and optimize wood densification performance in different THM conditions [50,51]. Master curves of E0 spanned about 12 orders of magnitude from 30 to 80 °C. In other word, the accelerated viscoelastic was charac-
terized of approximately 3 centenaries beyond the test duration. Strategically, the comparison of predicted and real-tested stiffness after a long duration was doable, which was helpful to provide reference basis in the utilization of EWPs. While, the absent real-test is a limitation of this study, and will be conducted in the future. The molecular motions in wood cell wall were divided into three types [52]: (1) the relaxation process based on polar groups (especially methylol groups in the amorphous region) (Fig. 9a); (2) the reorientation of adsorbed water or (and) water cluster (Fig. 9b); and the relaxation process based on the compound group of ‘‘polar group and adsorbed water” (Fig. 9c). The unstable configuration of wood cell wall induced by the varying MC provided additional spaces for the motions of polar groups and the compound of ‘‘polar group and adsorbed water”. More free spaces for
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molecular motions shortened the relaxation times, and the transition of a and b relaxation processes was accelerated. For further elucidate the configurations of polymers in wood cell wall, the molecular motions in different moisture states (equilibrium, adsorption or desorption) could be in-depth explored by dynamic Fourier-transform infrared spectroscopy. 5. Conclusions (1) Increased E0 could be found at low temperature or RH condition, or with the increasing test frequency. Both the humidity-time equivalence and temperature-humiditytime equivalence principles were applicable for describing evolution of wood stiffness. At a reference condition (30 °C, 0% RH), master curves constructed by humidity-time equivalence and temperature-time equivalence principles were compared, which were basically overlapped at short-time region (frequency was higher than 0.01 Hz). The application of (temperature-)humidity-time equivalence could be used to predict wood stiffness in the utilization and production processes of EWPs in the construction and building fields. (2) The humidity-time equivalence principle failed to predict wood damping properties, regardless of hygrothermal condition. With the increasing frequency, tan d decreased firstly, and then increased. The characteristic frequency (fc) corresponded to the local minimum value of tan d ranging from 8 to 30 Hz, and moved to the high frequency direction with the increasing RH level. (3) At all the hygrothermal temperatures, fc at moisture equilibrium state was lower than non-equilibrium state. The variation of fc at different moisture states confirmed that the unstable configuration of wood cell wall induced by the varying MC provided additional spaces for the molecular motions and accelerated the relaxation transition.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was financially supported by the National Key Research and Development Program of China (2017YFD0600202), the National Natural Science Foundation of China (No. 31700487), the Natural Science Foundation of Jiangsu Province (CN) (No. BK20170926). Tianyi Zhan would like to gratefully acknowledge the financial support from the Jiangsu provincial government scholarship program. References [1] M.K. Kuzman, P. Groselj, Wood as a construction material: comparison of different construction types for residential building using the analytic hierarchy process, Wood Res. 57 (4) (2012) 591–600. [2] J.H. Park, Y. Kang, J. Lee, S.J. Chang, S. Wi, S. Kim, Development of wood-lime boards as building materials improving thermal and moisture performance based on hygrothermal behavior evaluation, Constr. Build. Mater. 204 (2019) 576–585. [3] A.K. Bin Marsono, A.T. Balasbaneh, Combinations of building construction material for residential building for the global warming mitigation for Malaysia, Constr. Build. Mater. 85 (2015) 100–108. [4] S. Fortino, P. Hradil, A. Genoese, A. Genoese, A. Pousette, Numerical hygrothermal analysis of coated wooden bridge members exposed to Northern European climates, Constr. Build. Mater. 208 (2019) 492–505.
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T. Zhan et al. / Construction and Building Materials 227 (2019) 116637 [34] S. Hucˇ, T. Hozjan, S. Svensson, Rheological behavior of wood in stress relaxation under compression, Wood Sci. Technol. 52 (3) (2018) 793–808. [35] K. Menrad, Dynamic Mechanical Analysis: A Practical Introduction, CRC Press, Boca Raton, Fla, USA, 2008. [36] J. Jiang, J. Lu, Y. Zhao, Y. Wu, Influence of frequency on wood viscoelasticity under two types of heating conditions, Dry Technol. 28 (6) (2010) 823–829. [37] E. Obataya, M. Norimoto, J. Gril, The effects of adsorbed water on dynamic mechanical properties of wood, Polymer 39 (14) (1998) 3059–3064. [38] C. Takahashi, N. Nakazawa, K. Ishibashi, I. Iida, Y. Furuta, Y. Ishimaru, Influence of variation in modulus of elasticity on creep of wood during changing process of moisture, Holzforschung 60 (4) (2006) 445–449. [39] J. Lu, J. Jiang, Y. Wu, X. Li, Z. Cai, Effect of moisture sorption state on vibrational properties of wood, Forest Prod. J. 62 (3) (2012) 171–176. [40] A. Chakravartula, K. Komvopoulos, Viscoelastic properties of polymer surfaces investigated by nanoscale dynamic mechanical analysis, Appl. Phys. Lett. 88 (13) (2006) 131901. [41] T. Zhang, S.L. Bai, Y.F. Zhang, B. Thibaut, Viscoelastic properties of wood materials characterized by nanoindentation experiments, Wood Sci. Technol. 46 (5) (2012) 1003–1016. [42] H. Fujita, A. Kishimoto, Diffusion-controlled stress relaxation in polymers. II. Stress relaxation in swollen polymers, J. Polym. Sci. 28 (118) (1958) 547–567. [43] T. Nakano, Applicability condition of time–temperature superposition principle (TTSP) to a multi-phase system, Mech. Time-depend. Mater. 17 (3) (2013) 439–447.
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Construction and Building Materials journal homepage: www.elsevier.com/locate/conbuildmat
Temperature-humidity-time equivalence and relaxation in dynamic viscoelastic response of Chinese fir wood Tianyi Zhan a, Jiali Jiang b, Jianxiong Lu c,⇑, Yaoli Zhang a, Jianmin Chang d a
College of Materials Science and Engineering, Nanjing Forestry University, Nanjing 210037, PR China Research Institute of Wood Industry of Chinese Academy of Forestry, Beijing 100091, PR China c College of Material Science and Engineering, Central South University of Forestry and Technology, Hunan Collaborative Innovation Center for Effective Utilizing of Wood and Bamboo Resources, Changsha 410004, PR China d College of Materials Science and Technology, Beijing Forestry University, Beijing 100083, PR China b
h i g h l i g h t s The (temperature-)humidity-time equivalence principle was applicable for describing evolution of wood stiffness. The humidity-time equivalence principle failed to predict wood damping properties, regardless of hygrothermal condition. The unstable configuration of wood cell wall induced by the varying moisture content accelerated the relaxation transition.
a r t i c l e
i n f o
Article history: Received 27 April 2019 Received in revised form 25 July 2019 Accepted 2 August 2019
Keywords: Viscoelasticity Hygrothermal Temperature-humidity-time equivalence Relaxation Moisture state
a b s t r a c t Design, application and service life of modern engineered wood and its products are closely related to environmental temperature and relative humidity (RH). In this study, the frequency-dependent viscoelastic properties of Chinese fir wood were investigated under different hygrothermal conditions (temperature: 30–80 °C, RH: 0–85%), to verify the applicability of humidity-time and temperature-humiditytime equivalence principles to wood viscoelasticity (i.e., the equal effects of elevating temperature, increasing RH, or prolonging testing time on the changes of stiffness and damping). The relaxation of wood cell wall was compared under moisture equilibrium and non-equilibrium states. It was demonstrated that both the humidity-time equivalence and temperature-humidity-time equivalence principles were applicable for describing the evolution of wood stiffness. Master curves constructed by humiditytime equivalence and temperature-time equivalence principles were basically overlapped at a shorttime region (frequency >0.01 Hz) when reference condition was 30 °C/0% RH. However, the humiditytime equivalence principle failed to predict wood damping properties, regardless of hygrothermal condition. The testing frequency (fc, assigned to the transition of different relaxation processes) corresponded to the local minimum value of tan d was ranged from 8 to 30 Hz and moved to the high frequency direction with increasing RH level. The fc value at moisture equilibrium state was lower than non-equilibrium state (no matter moisture adsorption or desorption). It was attributed the higher fc value at moisture nonequilibrium state to the unstable configuration structure of wood cell wall. These findings not only help understanding the wood-water relations, but also be relevant for the utilization and production processes of engineered wood and its products in the construction and building fields. Ó 2019 Elsevier Ltd. All rights reserved.
1. Introduction Wood, as one of the most common nature materials, has traditionally been used as construction structure components [1,2]. Due to its light-weight and high-strength properties, engineered wood and its products (EWPs) can be used in large-scale constructions, ⇑ Corresponding author. E-mail address: [email protected] (J. Lu). https://doi.org/10.1016/j.conbuildmat.2019.08.018 0950-0618/Ó 2019 Elsevier Ltd. All rights reserved.
such as multi-story residential buildings, bridges, industrial halls, concert halls, etc. [3–6]. During the using processes, EWPs exchange water with surroundings by adsorption or desorption of moisture. In hence, the dimension design, application and service life of EWPs are closely related with environmental conditions [7,8]. Temperature and (or) relative humidity (RH) of ambient environment fluctuate continuously, and thus elastic and viscoelastic responses of EWPs change all the time [9].
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Commonly, the room temperature modulus is often the only value given to describe the mechanical property of EWPs [10,11]. While, the temperature dependence of the viscoelasticity of wood is complex because it is a multi-component polymeric material. The temperature-time equivalence principle is widely used to describe the creep, relaxation and dynamic viscoelasticity of EWPs under a wide temperature range [12–17]. The temperature-time equivalence principle means elevating temperature or prolonging testing time has equal effect on changing mechanical properties of EWPs. By the temperature-time equivalence principle, viscoelastic behaviors of EWPs over many decades were predicted from short-time testing by relating the response to functions of time and temperature [18]. As an important issue, the applicability of the temperature-time equivalence principle to EWPs is still controversial [19,20], because different components in wood cell wall have different temperature-dependent performances [16]. Analogous to temperature-time equivalence principle, humidity-time equivalence and temperature-humidity-time equivalence principles are also applied to investigate the rheological properties of polymers [21–25]. Humidity-time equivalence principle is verified by a stepwise increase of RH levels at a constant temperature. Considering wood is a humidity-sensitive material, the application of (temperature-)humidity-time equivalence principle on predicting viscoelastic properties of EWPs is useful to elucidate the evolution of moisture-induced stresses during wood drying or daily utilization [4,26], and optimize the thermal-hygro-mechanical (THM) treatment technique (such as densification and welding) [27,28]. In addition to prediction of long-term viscoelastic behaviors, the in situ structure and organization of components in wood cell wall can also be analyzed by the temperature-time equivalence principle [29,30]. The characteristics of molecular motions and the glass transition temperature of components in wood cell wall could be described by this equivalence [12,19,30]. Among components in wood cell wall, the in situ lignin glass transition was quite sensitive to moisture content (MC) of wood [31]. When wood MC increased as a consequence of increment of ambient RH, the glass transition temperature of lignin moved to low-temperature regions [20]. Wood possesses low stiffness and high damping no matter temperature or RH level increase. In other words, both the increasing temperature and RH level have similar effects on changing viscoelastic properties of wood. Similar to the temperature-time equivalence principle, the humidity-time equivalence principle is also rationalized for describing motions of polymers [32,33]. At a series of given RH levels, the hydration activates the molecular motion over short and long distances in a similar way as thermal energy [21]. When water penetrates wood cell walls, the movement pace of amorphous polymers is speeded up. The relaxation times of amorphous polymers are shortened with the increasing wood MC [34]. The relaxation is reflected as temperature- or frequency-dependent damping peak during the dynamic viscoelastic test [35]. When temperature changes, wood MC is influenced and the viscoelasticity varies consequently. Contemporary rheological device – dynamic viscoelastic analyzer (DMA) equips with humidity accessory which can control RH level precisely even temperature up to 90 °C. Using this kind of device, the evolution of viscoelastic properties of wood at certain hygrothermal condition could be evaluated. In this study, the frequency-dependent viscoelastic properties of Chinese fir (Cunninghamia lanceolata) were tested under different hygrothermal conditions (temperature: 30–80 °C, RH: 0–85%). In these hygrothermal conditions, the wood specimens held a series of constant MCs, i.e., under moisture equilibrium states. The applicability of humidity-time and temperature-humidity-time equivalence principles to viscoelastic properties of wood under moisture equilibrium states were investigated. In addition, the relaxation
of Chinese fir was compared under moisture equilibrium and non-equilibrium states.
2. Materials and methods 2.1. Materials Chinese fir specimens with a dimension of 60 12 2.5 mm3 (L R T) were successively obtained from similar portions of heartwood with a straight grain. Before the testing, all specimens were conditioned in sealed containers over P2O5, or saturated solutions of LiCl2, MgCl2, NaBr, NaCl or KCl, which provided RH of 0, 11, 33, 58, 75 or 85%, respectively. All the conditionings were conducted at room temperature (25 °C). The corresponding MC of conditioned specimens was 0.6, 3.2, 7.4, 13.1, 17.9 or 22.2%, respectively.
2.2. Viscoelasticity measurements After conditioning, the specimens were placed into DMA Q800 (TA Instruments, New Castle, DE, USA) for tests at moisture equilibrium and non-equilibrium states. The schematic illustration of the whole test is displayed in Fig. 1. During the DMA test, a dualcantilever bending mode (15 lm amplitude) was selected at a series of scanning frequencies from 100 to 1 Hz. DMA equipped with a humidity accessory which controlled the RH by modulating the mixture of dry nitrogen and saturated moisture. All tests were carried out within the linear viscoelastic region. The frequency-dependent viscoelastic properties are commonly evaluated as storage modulus (E0 ), loss modulus (E00 ) and loss factor (tand = E00 /E0 ). E0 and E00 represent the elastic and viscous response of the specimens under the action of loading. Tand represents the ratio of dissipated energy to stored energy. In this study, E0 and tand were used to characterize the frequency-dependent properties and the relaxation processes.
2.2.1. Humidity-time equivalence and relaxation tests Frequency-dependent E0 and tan d were measured as follows: (1) Mounted the specimens with different MCs (0.6, 3.2, 7.4, 13.1, 17.9 or 22.2%) into the testing chamber, (2) Adjusted chamber humidity to the corresponding conditioning RH (0, 11, 33, 58, 75 or 85%), (3) Ramped temperature to target one (30–80 °C, 10 °C/step), (4) Equilibrated the specimens at constant temperature and humidity conditions for 30 min, (5) Examined by the iso-hygrothermal frequency-sweep (100–1 Hz). The results of frequency-sweep measurement at 0% RH with a series of temperatures were also used as the temperature-time equivalence test and is displayed in Section 3.2. Three measurements were performed for each condition.
2.2.2. Relaxation test during moisture adsorption (1) Mounted the specimens with 0.6% MC (conditioned at 0% RH) into the testing chamber of DMA Q800, (2) Adjusted chamber humidity to 0% RH, (3) Ramped temperature to target level (30–80 °C, 10 °C/step), (4) Equilibrated the specimens at constant temperature and humidity conditions for 30 min, (5) Ramped humidity from 0 to 30, 60 or 90% RH with 2% RH/min ramping rate, (6) Isothermal frequency-sweep (100–1 Hz) at five time-points (experimental initiation, termination of RHramp, 60 min under RHisohume, 120 min under RHisohume, and 240 min under RHisohume). Three measurements were performed for each condition. Detailed method was referenced from Zhan et al [16].
T. Zhan et al. / Construction and Building Materials 227 (2019) 116637
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Fig. 1. Schematic illustration of the sample preparation and viscoelastic test.
2.2.3. Relaxation test during moisture desorption (1) Mounted the specimens with 22.2% MC (conditioned at 85% RH) into the testing chamber of DMA Q800, (2) Adjusted chamber humidity to 85% RH, (3) Ramped temperature to target level (30– 80 °C, 10 °C/step), (4) Equilibrated the specimens at constant temperature and humidity conditions for 30 min, (5) Ramped humidity from 85 to 60, 30 or 0% RH with 2% RH/min ramping rate, (6) Isothermal frequency-sweep (100–1 Hz) at five time-points (experimental initiation, termination of RHramp-down, 60 min under RHisohume-down, 120 min under RHisohume-down, and 240 min under RHisohume-down). Three measurements were performed for each condition. Detailed method was referenced from Zhan et al [17].
3. Results 3.1. Frequency-dependent viscoelasticity The changes of E0 as a function of frequency are displayed in Fig. 2. Most standard deviations of E0 were smaller than 280 Mpa2. With the increasing frequency, an increase in storage modulus E0 was observed, regardless of hygrothermal conditions. Commonly, less interior friction of wood polymers could be obtained at higher frequencies, attributing to the less segmental motion [36]. At a given testing, frequency E0 decreased with the
increasing humidity level, while 11% RH at 30 °C was an exception. When the testing frequency was 1 Hz, typical changes of RHdependent E0 at 30 and 80 °C are exhibited in Fig. 3. According to Fig. 3, compared to the 30 °C/0% RH condition, a slightly increment of E0 at 30 °C/11% RH could be observed more obviously. The similar phenomenon was reported in other studies [37–39]. Oven-dry wood did not form an ordered cohesion state, and some adsorption points remained vacant [38]. A slight MC increment from the ovendry state would induce a bridge effect involving hydrogen bonds between molecular chains. In hence, E0 value at 30 °C/11% RH condition was higher than that at 30 °C/0% RH. Fig. 4 shows the changes of frequency-dependent tan d at a series of hygrothermal conditions. Most standard deviations of tan d were smaller than 0.003. With the increasing frequency, tan d decreased firstly, and then increased (Fig. 4). The local minimum values of tan d occurred at the frequency ranging from 8 to 30 Hz, regardless of hygrothermal condition. The frequency corresponded to the local minimum value of tan d was named as ‘‘characteristic frequency (fc)” hereinafter. The decreased damping followed by an increase was also reported by previous studies [36,40]. Chakravartula and Komvopoulos [40] stated that the increase of damping with the increasing frequency was associated with the localized softening of the amorphous phase due to the large amount of energy dissipated. Jiang et al. [36] supposed that the minimum value of damping was assigned to a change in relax-
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3.2. Temperature-humidity-time equivalence
Storage modulus E' (MPa)
7000
Prior to the investigation of temperature-humidity-time equivalence, the application of humidity-time equivalence to wood stiffness and damping was examined. Based on Eqs. (1) and (2), the equivalent relations for E0 and tan d of Chinese fir were calculated:
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ation behavior of wood cell wall. Menard [35] pointed out that, if the viscoelasticity could be tested over a wide enough frequency range, the plot of viscoelastic parameter vs. frequency appeared a reverse-like temperature scan. Hence, the relaxation process (during the temperature scan) could be reasonably observed during the frequency scan. Zhang et al. [41] investigated the viscoelastic properties of wood cell wall by means of nanoindentation test and found that a flat peak around 30 Hz was related to the glass transition of hemicellulose. It was assumed that, in this study, when testing frequency was lower than fc, the relaxation process was probably associated with the glass transition of hemicellulose with low molecular weight [41]. When the testing frequency was higher than fc, the relaxation process may be assigned to the motions of both methylol groups in the amorphous region of wood cell wall and adsorbed water molecules in wood [20]. For easy further description, the former and the later relaxation processes were labelled as a and b relaxation processes, respectively.
E0 ðRH; logf Þ ¼ E0 ðRHr ; logaRH=RHr þ logf Þ
ð1Þ
tandðRH; logf Þ ¼ tandðRHr ; logaRH=RHr þ logf Þ
ð2Þ
where f is the testing frequency, RHr is the reference RH, and log aRH/RHr is the horizontal shift factor. By shifting a series of RH dependency E0 and tan d to the results at the reference RH (0%), the master curves were constructed as shown in Figs. 5 and 6. In Fig. 5, the smooth master curves of E0 could be found at all the hygrothermal temperatures, while the master curves of tan d displayed as scattered distributions regardless of temperature (Fig. 6). For some amorphous polymers, their master curves of damping could be successfully constructed [22,42], because the free volume within polymers increased linearly with an increase in MC [42]. Cramer et al. [21] carried out the humidity-time equivalence on conductivity of polyelectrolyte complexes and considered that the hydration activated polymer motions in a similar way by thermal energy. However, since wood was a multi-phase system [43], chemical components in wood cell walls held different relaxation behaviors and different hygroscopicities. At a given humidity level, the amounts of free volume that induced by water varied within different components. To verify the temperature-humidity-time equivalence principle on wood stiffness, the secondary master curve at a reference temperature (Tr) of 30 °C was developed by Eq. (4) based on the results shown in Fig. 5.
E0 ðT; logf Þ ¼ E0 ðT r ; logaT=T r þ logf Þ
ð3Þ 0
The secondary master curve of E is presented in Fig. 7. To exhibit it more clearly, some plots were deleted, while the remained plots still shown the smooth secondary master curve of E0 (Fig. 7). This result implied that the temperature-humidity-time
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Frequency (Hz) Fig. 5. Master curve of storage modulus E0 as a function of frequency from 30 to 80 °C.
equivalence principle was applicable for constructing a master curve of wood stiffness. Additionally, the master curves developed by the temperature-time equivalence principle and the humiditytime equivalence principle at a reference condition (temperature: 30 °C, RH: 0%) were compared, being shown as the inset in Fig. 7. For the identical reference temperature and humidity condition, the master curves obtained by temperature-time equivalence principle were basically overlapped when frequency was more than 0.01 Hz. The similar overlap was also reported for other polymers [32,44]. Although master curves were overlapped for a
short-term region, a slightly difference could be found for a longterm region, i.e. at low frequency region (inset in Fig. 7). Such a difference was caused by the structural change during the moisture adsorption [23]. Fig. 7 The master curve of storage modulus E0 constructed by the temperature-humidity-time equivalence principle. The inset shows a comparison of master curves constructed by the temperature-time equivalence principle and the humidity-time equivalence principle at an identical temperature (30 °C) and RH (0%) condition
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0% RH
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Frequency (Hz) Fig. 6. Master curve of loss factor tan d as a function of frequency from 30 to 80 °C.
Storage modulus E' (MPa)
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Tr=30°C RHr=0%
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by temperature-time equivalence by humidity-time equivalence 1E-10
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Frequency (Hz) 0
Fig. 7. The master curve of storage modulus E constructed by the temperature-humidity-time equivalence principle. The inset shows a comparison of master curves constructed by the temperature-time equivalence principle and the humidity-time equivalence principle at an identical temperature (30 °C) and RH (0%) condition.
3.3. Mechanical relaxation According to the statistical analysis, fc moved to the high frequency direction with the increasing RH level irrespective of temperature (Fig. 4). The relationships between fc and MC are presented in Fig. 8. When temperature was 30 °C, fc increased from 8 to 34 when MC ramped from 0.6 to 22.2%. The moved fc illustrated the acceleration of the transition of a and b relaxation processes (i.e., the relaxation time durations of molecular motions were shortened). When moisture molecules exist within the cell walls, the cell walls swelled and released some free spaces for molecular motions. In addition, water played a role of plasticizer and formed hydrogen bonds to hemicellulose and paracrystalline cellulose [45]. The plasticization effect of moisture lowered the energy required to initiate the chain mobility, resulting in the shortening in the polymer’s relaxation time. To clarify the influence of moisture states (equilibrium or non-equilibrium) on relaxation, relaxation test of wood samples at moisture non-equilibrium states (adsorption and desorption) were tested and the results of fc are displayed in Fig. 8. At all the hygrothermal temperatures, fc at
moisture non-equilibrium state increased with transient MC, and was higher than equilibrium state (no matter adsorption or desorption). 4. Discussion Chinese fir was a common species planted in the south of China. Due to the relative simple structure (more than 90% was consisted of tracheid cells), Chinese fir was appropriate to be a ‘‘model species” in wood science field. The investigation of its viscoelasticity at different hygrothermal conditions was helpful for designing dimensions for structure-used wood and optimizing THM techniques. At higher MCs, plasticization effect of water behaved discrepancy in different layers [middle lamella (ML), primary cell wall (P), and secondary wall (S1, S2 and S3)]. In ML and P, relative contents of lignin were much higher than in secondary wall, which was less hygroscopic than carbohydrates [45]. Distinct extents of swelling induced localized strain between the different layers and caused fiber splitting [28,46]. Moreover, when temperature
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Moisture equilibrium
Characteristic frequency (fc)
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Desorption 40
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Moisture content (%) Fig. 8. Influence of moisture content on characteristic frequency of wood in moisture equilibrium and non-equilibrium (adsorption and desorption) states.
Fig. 9. Three molecular motions types in wood cell wall: (a) the relaxation process of polar groups; (b) the reorientation of adsorbed water; and (c) the relaxation process of compound groups.
rose the heating energy caused segmental motions for wood polymer, resulting in decreased stiffness [47,48]. In hence, more obvious decrement of stiffness with the increasing RH could be found at high temperature (Fig. 3). According to Figs. 5 and 7, both the humidity-time equivalence and temperature-humidity-time equivalence principles were applicable for describing the evolution of wood stiffness. The application of (temperature-)humidity-time equivalence in predicting wood stiffness would be benefit to calculate moisture-induced stresses in wood drying or daily service process [49], and optimize wood densification performance in different THM conditions [50,51]. Master curves of E0 spanned about 12 orders of magnitude from 30 to 80 °C. In other word, the accelerated viscoelastic was charac-
terized of approximately 3 centenaries beyond the test duration. Strategically, the comparison of predicted and real-tested stiffness after a long duration was doable, which was helpful to provide reference basis in the utilization of EWPs. While, the absent real-test is a limitation of this study, and will be conducted in the future. The molecular motions in wood cell wall were divided into three types [52]: (1) the relaxation process based on polar groups (especially methylol groups in the amorphous region) (Fig. 9a); (2) the reorientation of adsorbed water or (and) water cluster (Fig. 9b); and the relaxation process based on the compound group of ‘‘polar group and adsorbed water” (Fig. 9c). The unstable configuration of wood cell wall induced by the varying MC provided additional spaces for the motions of polar groups and the compound of ‘‘polar group and adsorbed water”. More free spaces for
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molecular motions shortened the relaxation times, and the transition of a and b relaxation processes was accelerated. For further elucidate the configurations of polymers in wood cell wall, the molecular motions in different moisture states (equilibrium, adsorption or desorption) could be in-depth explored by dynamic Fourier-transform infrared spectroscopy. 5. Conclusions (1) Increased E0 could be found at low temperature or RH condition, or with the increasing test frequency. Both the humidity-time equivalence and temperature-humiditytime equivalence principles were applicable for describing evolution of wood stiffness. At a reference condition (30 °C, 0% RH), master curves constructed by humidity-time equivalence and temperature-time equivalence principles were compared, which were basically overlapped at short-time region (frequency was higher than 0.01 Hz). The application of (temperature-)humidity-time equivalence could be used to predict wood stiffness in the utilization and production processes of EWPs in the construction and building fields. (2) The humidity-time equivalence principle failed to predict wood damping properties, regardless of hygrothermal condition. With the increasing frequency, tan d decreased firstly, and then increased. The characteristic frequency (fc) corresponded to the local minimum value of tan d ranging from 8 to 30 Hz, and moved to the high frequency direction with the increasing RH level. (3) At all the hygrothermal temperatures, fc at moisture equilibrium state was lower than non-equilibrium state. The variation of fc at different moisture states confirmed that the unstable configuration of wood cell wall induced by the varying MC provided additional spaces for the molecular motions and accelerated the relaxation transition.
Declaration of Competing Interest The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper. Acknowledgments This work was financially supported by the National Key Research and Development Program of China (2017YFD0600202), the National Natural Science Foundation of China (No. 31700487), the Natural Science Foundation of Jiangsu Province (CN) (No. BK20170926). Tianyi Zhan would like to gratefully acknowledge the financial support from the Jiangsu provincial government scholarship program. References [1] M.K. Kuzman, P. Groselj, Wood as a construction material: comparison of different construction types for residential building using the analytic hierarchy process, Wood Res. 57 (4) (2012) 591–600. [2] J.H. Park, Y. Kang, J. Lee, S.J. Chang, S. Wi, S. Kim, Development of wood-lime boards as building materials improving thermal and moisture performance based on hygrothermal behavior evaluation, Constr. Build. Mater. 204 (2019) 576–585. [3] A.K. Bin Marsono, A.T. Balasbaneh, Combinations of building construction material for residential building for the global warming mitigation for Malaysia, Constr. Build. Mater. 85 (2015) 100–108. [4] S. Fortino, P. Hradil, A. Genoese, A. Genoese, A. Pousette, Numerical hygrothermal analysis of coated wooden bridge members exposed to Northern European climates, Constr. Build. Mater. 208 (2019) 492–505.
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