Tensile strength estimation of paper sheets made from recycled wood and non-wood fibers using machine learning

Abstract

The deterioration of fiber properties during recycling processes, especially the loss of tensile strength, raises concerns that paper products made from recycled fibers might not satisfy quality requirements. The purpose of this paper is to estimate the deterioration of tensile strength and the damage in paper sheets made of recycled fibers using the theory of damage mechanics and machine learning methods. Experiments were carried out to recycle wood fibers and non-wood fibers four times, and the physicochemical properties of the handsheets made from these fibers were measured after each recycling. Water retention value and relative bonded area were selected as the features to estimate and predict tensile strength during recycling because they had strong correlations with tensile strength. This paper proposed a damage index to quantitatively express the severity of the damage in paper sheets based on the experimental investigation and the theory of damage mechanics. Thus, the deterioration of tensile strength could be estimated and predicted. To determine the damage index, a curve fitting model based on the hyperbolic theory of pulp properties was developed. The proposed quantitative expression of the damage index is: $\mathit{D}=\frac{{\left(D_s-\mathit{h}\right)}^2}{a^2}-\frac{{\left(D_h-\mathit{k}\right)}^2}{b^2}$, where the coefficients were determined through the curve fitting model. This paper also developed a long short-term memory recurrent neural network model to determine the damage index according to the sequence of recycling. Both models were trained with the experimental data of water retention value and relative bonded area. The estimation and prediction by the curve fitting model were more accurate than those of the neural network model. The root mean square errors by the curve fitting model were 0.0278 for estimation, 0.1667 for prediction; and by the neural network model were 0.2445 for estimation, 0.2206 for prediction, respectively. After the damage index was determined, the deterioration of tensile strength then could be calculated as T = T₀ (1–D).

Keywords:

• recycled fibers
• tensile strength
• damage estimation
• damage index
• curve fitting
• long short term memory
• recurrent neural network

1. Introduction

Recycling is a key solution to the challenge of environmental pollution and resource shortages (Al-Hasan et al., 2020). With innovations in technologies, materials recovered from waste have found applications in various areas (Haque et al., 2021). Recycled fibers from waste paper have been widely utilized as manufacturing and construction materials all over the world (Solahuddin & Yahaya, 2022). The quality requirements of recycled fibers include mechanical properties, physical properties, optical properties, printability, appearance properties, and so on (Campano et al., 2018). However, successive recycling processes cause damage in paper, which includes macro and micro changes in fibers. During papermaking and recycling processes, fibers have to endure shearing, pressing, and drying, which results in significant changes in properties (Hubbe et al., 2003; Nazhad, 2005). After each recycling process, the volume and shape of lumens and the volume of pores in fiber walls may change considerably (Chen et al., 2010; Hubbe et al., 2007). The decrease of the water retention value (WRV) and the loss of fiber flexibility leads to the decrease in tensile strength, tear resistance, and folding endurance of paper sheets (Hubbe et al., 2007). These changes have been attributed to the loss of bonding potential, which is mainly determined by physical property changes during recycling processes, since no significant chemical property change occurs during recycling (Bouchard & Douek, 1994).

One of the major problems with paper recycling is the gradual loss in fiber strength during successive recycling processes (Hamzeh et al., 2013; M Zhang et al., 2002). Though it was observed that the tensile strength and density of recycled mechanical pulp did not decrease but slightly increased because the fibers became flattening and flexible to increase bonding potential (Howard & Bichard, 1992). Researchers have long been developing technologies to reduce tensile loss in order to improve the quality of recycled fibers (Nordström & Hermansson, 2017; Seo et al., 2002). Inter-fiber bonding enhancement, ultrasonic treatment, and other methods have been utilized to improve the mechanical properties of recycled fibers (Bajpai, 2010; Manfredi et al., 2013; Tatsumi et al., 2000).

Studies of the impact of fiber morphology on paper sheets have been carried out using various theories and equipment (Belle & Odermatt, 2016; Moral et al., 2010). Based on the theory of damage mechanics, damage will cause the ultra-structural disfigurement of fibers, which results in structure and property deterioration (Neagu et al., 2006). On the other hand, damage can be used to estimate the material property deterioration caused by changes in loading, ambient temperature, and so on. Since damage will unavoidably cause the deterioration of microstructures and macro properties during recycling, it is important to identify a damage index in the process where the damage is introduced. Thus, the changes in mechanical properties can be analyzed and described using the theory of damage mechanics of solid materials. The damage index should be a variable of interior states, which describes the irreversible changes in the structure of paper sheets (Keränen & Retulainen, 2016; Retulainen & Keränen, 2017). Hence, the damage index should be determined by some macro variables or micro parameters of paper sheets. It must also be measurable or obtainable easily.

The Page equation (Page, 1993, 1969) describing the relationship between fiber configurations and the tensile strength of wet and dry sheets was proposed in 1969, and it has been widely used ever since (Duker & Lindström, 2008; Lindström et al., 2016). However, the Page equation is a simplified approach, and it cannot be utilized to evaluate shear strength in once-dried fibers because of limited assumptions (Seth & Page, 1996). There is no targeted theory that quantitatively relates the deterioration of fiber configurations and paper properties to the tensile strength of paper sheets during recycling processes. A quantitative expression of the mechanical damage in paper sheets after recycling processes would be important and highly desirable. Gurunagul et al. examined the contribution of the loss of fiber–fiber bond strength on the deterioration of tensile strength of once-dried paper sheets, but they eliminated the impact of fines by using long and straight fibers only (Gurnagul et al., 2001). Jin et al. explored the relationship between the tensile strength of recycled paper sheets and the wettability of a single fiber as well as the inter-fiber bond strength. They used the factor of fiber–fiber bond weakness to indicate the fiber–fiber bond strength and found that during recycling processes, the factor of fiber–fiber bond weakness tended to increase and the fiber–fiber bond strength became weaker which led to the loss of tensile strength of paper sheets (Jin et al., 2022). However, this factor focused on the inter-fiber bond strength only, though it was the main factor affecting the tensile strength of paper sheets. The recycling effect has been examined mainly on mechanical and chemical wood pulps, while recycled non-wood fibers have been seldom studied. This is because wood fibers account for a significant share of the global pulp and paper industry. Non-wood fibers are not favorable compared with wood fibers, because they are only available seasonally and regionally; they have various physical and chemical properties; they have lower production yields, and so on (El-Sayed et al., 2020). However, non-wood fibers are valuable resources for the pulp and paper industry, especially for regions that have limited forest resources. In some developing countries, e.g., China and India, 70% of the raw materials used in the paper and pulp industry come from non-wood plants (Liu et al., 2018). As technological innovations are shaping the future of the pulp and paper industry, non-wood fibers will play an indispensable role as a raw material resource (Salehi et al., 2017; Tschirner et al., 2007). This paper examines the property deterioration of reed fibers during recycling.

The aim of this study is to estimate and predict the deterioration of tensile strength as well as other properties of paper sheets made from both wood and non-wood fibers such as bleached and unbleached softwood pulp, reed pulp, etc., in recycling processes. The theory and assumptions of damage mechanics for solid materials can be introduced to understand, analyze, and model the damage behavior of paper sheets during fiber recycling processes. Thus, the recycled fibers can be classified based on their damage severity and utilized in the manufacturing of different paper products.

The experiments simulating recycling processes were conducted four times to examine the changes in fiber configurations and paper sheet properties. The decrease in the area carrying the load of tensile force was evaluated to estimate the damage developed in paper sheets made of recycled wood and non-wood fibers. The relationship between the loss of hydrogen bonding capacity and the deterioration of properties of paper sheets was evaluated. Based on the theory of damage mechanics, a mathematical model was proposed to quantify the loss of tensile strength during recycling processes. The proposed damage index D was derived from a hyperbolic model: $\mathit{D}=\frac{{\left(D_s-\mathit{h}\right)}^2}{a^2}-\frac{{\left(D_h-\mathit{k}\right)}^2}{b^2}$, where D_h and D_s represented the deterioration of the water retention value (WRV) and the relative bonded area (RBA), respectively. The coefficients a, b, h, k were determined with the aid of curve fitting. The deterioration of tensile strength then could be calculated as T = T₀ (1–D). The proposed method explored the possibility to quantitatively express the damage during recycling using a damage index and directly determine the tensile strength of paper products after recycling.

Machine learning is a family of algorithms that enable machines to make decisions by learning from usually limited datasets presented to them, where information is not available thoroughly. Machine learning methods have been widely utilized in estimating and predicting properties of pulp and paper; since pulp and paper manufacturing is a complicated process where different events occur simultaneously (Almonti et al., 2021; Li et al., 2021; Y Zhang et al., 2021). Almonti et al. implemented a neural network to predict the length of outgoing fibers from a refining process based on the main process parameters. Their study aimed at optimizing the refining process and their neural network model excellently predicted the length of refined fibers (Almonti et al., 2019). Tofani et al. developed a multiple linear regression model to determine in advance if recovered waste paper mixtures could achieve the desired brightness (Tofani et al., 2022). Their model correlated the resulting brightness to the different fiber compositions of the waste paper after bleaching processes. Despite some limitations, the model could predict the brightness of recovered paper under specific bleaching conditions. In this paper, a neural network model was trained to estimate the damage index as compared with the proposed curve fitting method. Recurrent neural networks (RNNs) are a class of neural networks that are suitable to process sequence data exhibiting temporal dynamic behavior. Long Short-Term Memory (LSTM) networks are a variant of RNNs. LSTM networks can solve the problem of long-time dependencies, when desired outputs depend on input presented a long time ago (Yu et al., 2019).

The proposed curve fitting model and neural network model utilized regression analysis to identify the inherent relationship between the physicochemical properties and tensile strength of recycled fibers. The proposed damage index was determined by approximating the sequence data, i.e., properties measured after each consecutive recycling, with characteristic expressions. The proposed models could estimate the current and predict the next damage index and the deterioration of tensile strength during the successive recycling. The proposed approach employed the advancement of machine learning and utilized data-driven-based models to analyze the complicated recycling processes alternatively. As far as we know, using a LSTM model to estimate the physicochemical properties and predict the damage index of tensile strength during recycling processes is not reported in the literature.

2. Materials and methods

2.1. Materials

Softwood fibers and reed fibers were investigated in the experiments. The unbleached and the bleached kraft softwood pulps used in this study were commercial pulps of northern softwood (Spruce) from Canada. The fiber morphology is shown in Figure 1 (Liang & Chen, 2015). The pulps with the beating degrees at 34 SR and 60 SR were examined. The alkaline peroxide mechanical pulp (APMP) was Triploid Aspen prepared in the lab. The reed pulp was a common reed (Phragmites australis) pulp obtained from a pulp and paper mill in China, i.e., Tianjin Paper Mill Co., Ltd.

Figure 1. Fiber morphology of bleached kraft softwood pulp.

2.2. Experimental methods

The experiments were carried out based on the Technical Association of the Pulp and Paper Industry (TAPPI) standards. The TAPPI standard of “Forming Handsheets for Physical Tests of Pulp” describes the method of forming test handsheets to determine the properties of pulp. It includes a complete description of the standard apparatus, e.g., disintegrator, sheet machine, used in forming handsheets (Technical Association of the Pulp and Paper Industry, 2018). It also specifies the procedure to obtain a representative test specimen, including disintegration, sheetmaking, couching, pressing, drying, and testing (Technical Association of the Pulp and Paper Industry, 2018). The TAPPI standard of “Physical Testing of Pulp Handsheets” describes the procedure to test pulp handsheets. It defines the measurements of handsheet properties such as tensile strength, grammage, scattering coefficient, etc. (Technical Association of the Pulp and Paper Industry, 2021).

The bleached and unbleached softwood pulps and the reed pulp were refined by a PFI mill made by Paper and Fibre Research Institute, Norwegian, for laboratory beating of pulp. Handsheets were formed using the various aforementioned pulp samples. A hydraulic pulper made by the Shaanxi University of Science & Technology Machinery Plant, China, was utilized to recycle the pulp fibers. A Kajaani Fiber Analyzer manufactured by Kajaani Electronics Ltd., Finland, was used to measure the fiber morphology. The light scattering coefficient of paper sheets was measured using a brightness tester manufactured by Hangzhou Pnshar Technology Co., Ltd., China. The degree of polymerization of celluloses was measured according to the Chinese National Standards (GB1548-89). The zero-span tensile strength of the pulp fibers was measured with a zero-span tensile strength apparatus manufactured by China National Pulp and Paper Research Institute Ltd. Thus, handsheets were formed, tested, defibrated, and formed again to evaluate the deterioration of fiber properties during recycling processes.

The infrared spectra were acquired by an infrared (IR) spectrometer manufactured by Bruker Corporation, USA, using the transmission mode. A mixture of 100 mg pulp and dried potassium bromide (KBr) powder (1:100, w:w) was pressed into a transparent disc for IR analysis. The infrared crystal index was calculated as follows (Jiang et al., 2019):

C.I. = I₁₃₇₂/I₂₉₀₀ (1)

where C.I. is the crystal index, and I₁₃₇₃ and I₂₉₀₀ are the spectral intensity at the indicated wave numbers. The 1372 cm⁻¹ and the 2900 cm⁻¹ peaks are the stretching vibrations of CH and CH₂, respectively.

The X-ray diffraction analysis was carried out using a spectrograph made by Philip Co. The degree of crystallinity from X-ray diffraction was calculated as follows:

The relative crystallinity index (%; He et al., 2008):

(2) $\mathit{RCI}=\frac{{\mathit{I}}_{002}-I_{\mathit{am}}}{I_{002}}\times 100$(2)

The degree of crystallinity (%; Wan et al., 2010):

(3) $\mathit{\alpha }=\frac{{\mathit{I}}_{002}}{I_{002}+I_{\mathit{am}}}\times 100$(3)

where, I₀₀₂ is the peak intensity at 2θ ≈ 22.5°, which expresses the diffraction intensity of crystalline fields. I_am is the signal intensity at 2θ ≈ 18°, which expresses the diffraction intensity of amorphous regions. The samples were glued on the sample holder, and the spectra were taken using a Cu Kα source at an output power of 40 KV/100 mA. The spectra were recorded at double diffraction angles with the 2θ ranging from 5° to 40°.

The WRV of the pulp samples was measured using a high-speed centrifuge. A quantity of wet pulp (equivalent to 1.5 g oven-dried pulp) was centrifuged at 3000 rpm for 15 minutes, and the WRV was calculated by (Jiang et al., 2019):

(4) $\mathit{WRV}=\frac{\mathit{Wc}.\mathit{f}.-\mathit{Wo}.\mathit{d}.}{\mathit{Wo}.\mathit{d}.}$(4)

where W_c.f. and W_o.d. are the centrifuged wet weight and the oven-dried weight, respectively.

The RBA was calculated as follows (Tao & Liu, 2011):

(5) $\mathit{RBA}=1-\frac{S}{S_0}$(5)

where, S is the measured light scattering coefficient of paper sheets. S indicates the actual area providing effective hydrogen bonds. S_o is the light scattering coefficient of the sheet with no fiber hydrogen bond. The S_o can be substituted by the S value when the tensile strength is equal to zero, i.e., the S value at the intersection of the extended curve of tensile strength vs. the light scattering coefficient and the axis along which the tensile strength is equal to zero. Using the light scattering method to determine the RBA is one of the most common techniques, though it has limitations (Tao & Liu, 2011).

The physicochemical properties of recycled fibers were measured during the successive recycling processes, from the original fibers until after having been recycled four times. The properties measured were zero-span tensile strength, zero-span tensile index, grammage, degree of polymerization (DP), fiber length, crystalline indices, degree of crystallinity, WRV, RBA, tensile strength, etc.

2.3. Long short-term memory recurrent neural networks

Neural networks are a series of computational algorithms utilized for machine learning, and they have been widely applied to analyze the properties of pulps and fibers (Adamopoulos et al., 2016). In this study, a model of long short-term memory recurrent neural network was developed to estimate and predict the deterioration and damage that occurred during recycling. Recurrent neural networks allow information likely having an influence on others to persist so that they can model data along a temporal sequence. RNNs can form a much deeper understanding of a data sequence and its temporal dynamics because they have internal memory and past outputs can be presented as inputs for the next time step. However, they have difficulties learning long-term dependencies, i.e., the dependencies between inputs and outputs span long temporal intervals (Pascanu et al., 2013). Long short-term memory networks are designed to solve this problem by introducing gates and cell states to regulate information.

Figure 2 shows the structure of an LSTM cell which comprises three gates (Smagulova & James, 2019):

Figure 2. Cell of LSTM RNN.

Forget gate: The left part is the forget gate. It determines if the information from the previous cell state (C) should be forgotten or not. Equation 6(6) $f_t=\mathit{\sigma }\left(W_f\cdot \left[h_{\mathit{t}-1},x_t\right]+b_f\right)$(6) calculates the forget gate’s activation vector based on the input (x) and the hidden state (h), where b and W are biases and weights.

Input gate: The middle part is the input gate which quantifies the importance of the input and decides what new information should be stored in the cell state. The input gate’s activation vector (i) and the cell input activation vector ($\tilde{C}$) are obtained by Equations 7(7) $i_t=\mathit{\sigma }\left(W_i\cdot \left[h_{\mathit{t}-1},x_t\right]+b_i\right)$(7) and 8(8) ${\tilde{C}}_{\mathit{t}}=\mathit{tanh}\left(W_C\cdot \left[h_{\mathit{t}-1},x_t\right]+b_C\right)$(8) , respectively. Equation 9(9) $C_t=f_t\cdot C_{\mathit{t}-1}+i_t\cdot {\tilde{C}}_{\mathit{t}}$(9) updates the current cell state.

Output gate: The right part is the output gate. It regulates the output prediction which is also the hidden state for the next time step. Equations 10(10) $o_t=\mathit{\sigma }\left(W_o\cdot \left[h_{\mathit{t}-1},x_t\right]+b_o\right)$(10) and 11(11) $h_t=o_t\cdot \mathit{tanh}\left(C_t\right)$(11) decide the output gate’s activation vector and the output/hidden state vector.

(6) $f_t=\mathit{\sigma }\left(W_f\cdot \left[h_{\mathit{t}-1},x_t\right]+b_f\right)$(6)

(7) $i_t=\mathit{\sigma }\left(W_i\cdot \left[h_{\mathit{t}-1},x_t\right]+b_i\right)$(7)

(8) ${\tilde{C}}_{\mathit{t}}=\mathit{tanh}\left(W_C\cdot \left[h_{\mathit{t}-1},x_t\right]+b_C\right)$(8)

(9) $C_t=f_t\cdot C_{\mathit{t}-1}+i_t\cdot {\tilde{C}}_{\mathit{t}}$(9)

(10) $o_t=\mathit{\sigma }\left(W_o\cdot \left[h_{\mathit{t}-1},x_t\right]+b_o\right)$(10)

(11) $h_t=o_t\cdot \mathit{tanh}\left(C_t\right)$(11)

The LSTM RNN model was developed using MATLAB toolbox. It was designed to have two features and one response, i.e., Ds and Dh were imported as input data and the damage index was considered as target data. Four groups of sequence data were input for training, and one group was utilized for testing and prediction. The hidden units were chosen as 200 and the maximum epochs were 250. The Adam optimization algorithm was adopted for gradient descent optimization because of its convenience and efficiency.

2.4. Methodology flowchart

The methodology flowchart of this research is presented in Figure 3. The various virgin fibers were utilized to form handsheets first, then the handsheets were defibrated to produce recycled fibers. Afterwards, handsheets were formed by the recycled fibers and then were defibrated and reformed again. The recycling process would repeat for four times, and the handsheets were tested to determine the fiber properties during the process. The hyperbolic curve fitting model and the LSTM neural network model were developed based on the experimental data. Finally, the estimation and prediction of tensile strength from the two models were determined and compared.

Figure 3. Methodology flowchart.

3. Results

3.1. Effect of recycling on properties of recycled fibers

The experimental results show that the properties responded to recycling negatively. In most of the cases, the deterioration of the properties after the first recycling was much worse than that of any other recycling (Hubbe, 2014). This is because hornification, the collapsing of internal pore structures of fibers during drying processes, is irreversible or partially reversible (Kumar et al., 2020). Usually, after four or five recycling processes, the properties of fibers did not change much. Among these properties, some deteriorated much more during recycling, while others were not affected significantly, e.g., fiber length (Yamauchi, 2018). As Table 1 shows, fiber length did not reduce dramatically because during recycling fibers were not further shortened by pulping, and handsheets were not calendered (Howard & Bichard, 1992).

Table 1. Fiber length during recycling processes (mm)

Recycling times		0	1	3	5
Reed Pulp	Arithmetic mean	0.30	0.31	0.31	0.30
	Weighted average	0.59	0.55	0.55	0.56
	Weighted Weighted average	0.91	0.84	0.80	0.85
Wood Pulp	Arithmetic mean	1.52	1.49	1.48	1.50
	Weighted average	2.28	2.25	2.20	2.26
	Weighted Weighted average	0.71	0.68	0.71	0.71

Table 2 lists the change of properties of reed fibers during successive recycling processes. The zero-span tensile strength was used to indicate the single fiber strength in this study. The results illustrate that after each time of the recycling, the fiber strength of the reed pulp decreased slightly. Because fibers were subjected to various hydraulic and mechanical shear forces during a recycling process, the scission of the macromolecules of celluloses took place. The decrease in DP of fibers after recycling processes also supports this conclusion. However, the effect of recycling on the single fiber strength was far less than that on the tensile strength of paper sheets. It was as expected that fiber recycling would have a negative effect on the single fiber strength. But the loss of the single fiber strength after one recycle was only 2% for the reed pulp. Interestingly, the loss of single fiber strength was only about 6% after as many as three recycles. The increase in the degree of crystallinity within fibers would compensate for the single fiber strength loss caused by the scission of cellulose chains during recycling. However, the effect was little, compared with other factors, including the change in the swelling capacity of fibers. The degree of crystallinity of fibers increased as they were subjected to each successive recycling. It is obvious that the area of the crystalline region in the fibers expanded and the crystalline indices increased gradually. Such changes led to a decrease in the swelling capacity and the hydrogen bonding capacity of fibers, which in turn caused the loss of the strength of paper sheets.

Table 2. Properties of reed fibers during recycling

Recycle Number
	0	1	2	3	4
Properties
Zero-span tensile strength (kg/15 mm)	7.95	7.63	7.80	7.69	7.58
Zero-span tensile index (Nm/g)	808.7	793.0	775.1	760.2	748.6
Basis weight (g/m^2)	73.57	64.33	65.61	64.65	63.69
Degree of polymerization	644	549	545	542	536
Fiber length (mm)	0.91	0.84	0.81	0.80	0.82
Degree of crystallinity (%)	77.34	77.89	79.91	80.62	81.33
Crystalline indices (%)	70.71	71.62	74.86	75.97	77.08
WRV (g/g)	2.02	1.80	1.65	1.60	1.56
RBA	0.23	0.20	0.18	0.18	0.16
Tensile index (Nm/g)	28.14	25.35	23.12	21.95	20.22

Tensile strength is one of the most important properties of paper products. It is a concern of using recycled fibers since the deterioration of tensile strength during recycling lower the quality of paper products. In order to ensure paper products have acceptable quality, it is imperative to estimate and predict the deterioration of tensile strength during recycling processes. Figure 4 shows the impact of recycling on the tensile strength of paper sheets made from recycled wood pulps and reed pulps. The results indicate that the tensile strength of paper sheets made of both wood pulps and non-wood pulps responded to recycling negatively. The tensile strength of paper sheets dropped 15% to 35% after four recycling processes, and the highest loss of tensile strength occurred after the first recycling. Additionally, the decrease in the tensile strength of unrefined pulps was less than that of refined pulps, and the decrease in the tensile strength of high yield pulps was less than that of chemical pulps.

Figure 4. Effect of recycling on tensile strength of different pulps.

Figure 5 shows the effect of fiber recycling on the WRV of different pulps. The decrease of the WRV typically fell in the range from 20% to 40% after having been recycled five times, depending on different pulps. For all pulp samples, the magnitude of the change in WRV after the first recycling was greater than that of the subsequent recycling processes. Experiments showed that the WRV of pulps reflected the wet flexibility and contributed directly to the hydrogen bonding capacity (Hubbe et al., 2007). In order to further investigate the relationship between fiber recycling and tensile strength, the effect of recycling on the RBA of paper sheets was also examined. As shown in Figure 6, after having been recycled four times, the RBA of paper sheets made from different pulps was reduced from 10% to 40%. The maximum change occurred within the sheets made from reed pulp. During recycling, the fiber hornification took place, which resulted in the loss of fiber swelling capacity and wet flexibility (Somwang et al., 2002). These changes in turn led to the reduction of the hydrogen bonding capacity of fibers. Hydrogen bonding is generally considered as the bonding mechanism between fibers, though it was observed to be less important than expected (Hirn & Schennach, 2015).

Figure 5. Effect of recycling on WRV.

Figure 6. Effect of recycling on RBA.

3.2. Correlation coefficients of physicochemical properties with tensile strength

The proposed approach utilized data-driven-based models, so it is important to select representative features by removing irrelevant, redundant, or noisy data. Among the various physicochemical properties measured during recycling processes, not all of them were associated with tensile strength deterioration. In order to determine the properties that can be utilized to estimate and predict the damage of fibers during recycling, the correlation coefficients of the measured physicochemical properties with tensile strength were calculated using MATLAB. The correlation coefficient is a statistical measure reflecting the interdependence of variables, and its value is between −1 and 1. The correlation coefficients of −1 and 1 represent the perfect negative and positive correlation, and 0 indicates no relationship between the variables. Figure 7 shows the absolute linear correlation coefficients of the measured properties with the tensile strength of reed fibers. From the results, the WRV and RBA had correlation coefficients as high as 0.983 and 0.997, respectively. The high correlation coefficients indicate the high association between the two properties with tensile strength. Therefore, they were chosen as the features to determine the deterioration of tensile strength. During the successive recycling processes, the degree of crystallinity and the crystalline indices increased while the tensile strength decreased. The degree of crystallinity and crystalline indices were negatively associated with the tensile strength, though the absolute values of the correlation coefficients were also high, 0.974 and 0.975, respectively. They were not chosen as features, because they needed either an IR spectrometer or an X-ray spectrograph to measure, and they were also highly related to WRV.

Figure 7. Correlation coefficients of properties and tensile strength.

4. Discussion

4.1. Damage of paper sheets made of recycled fibers

The tensile force acting on a sheet is applied to the glycosidic bonds within celluloses and the hydrogen bonds between fibers. The Van der Waals force also exists between fibers, and it turned out to be the most prominent bonding mechanism according to Hirn’s model (Hirn & Schennach, 2015). The quantity and the distribution of glycosidic bonds and hydrogen bonds in paper sheets are not uniform; there are many micro disfigurements (Hughes, 2012). So, paper is typically a congenitally damaged material from the aspect of damage mechanics.

Page equation describes the comprehensive account of tensile strength depending on the fiber properties and the bonding among fibers (Page, 1969):

(12) $\frac{1}{T}=\frac{9}{8\mathit{Z}}+\frac{12\mathit{c}}{\mathit{bPL}\left(\mathit{RBA}\right)}$(12)

where Z is zero span tensile index, c is fiber coarseness, b is fiber–fiber bond strength, P is the perimeter of fiber cross section, and L is fiber length. The fiber–fiber bond strength can be determined through plotting of the following equation, which is obtained from rearranging Equation 12(12) $\frac{1}{T}=\frac{9}{8\mathit{Z}}+\frac{12\mathit{c}}{\mathit{bPL}\left(\mathit{RBA}\right)}$(12) and substituting RBA with Equation 5 (Gurnagul et al., 2001):

(13) ${\left[\left(\frac{1}{T}\right)-\left(\frac{9}{8\mathit{Z}}\right)\right]}^{-1}=\mathit{b}\left[\frac{1}{k}-\frac{S}{k{S}_0}\right]$(13)

where $\mathit{k}=\frac{12\mathit{c}}{\mathit{PL}}$. It was speculated that the fiber–fiber bond strength of recycled fibers decreased because of the loss of surface molecules’ mobility which was resulted from the loss of swelling capacity upon drying (Gurnagul et al., 2001). However, Page equation did not consider kinks or curls, and the impact of fines was eliminated by using long and straight fibers in some experiments (Gurnagul et al., 2001).

The rupture of a paper sheet is a dynamic process, and it depends on the variation of strain and stress caused by the applied tensile force (Borodulina et al., 2012). Bearing the tensile force continuously, the hydrogen bonds between fibers and fine fibers will rupture first, which leads to stress concentration because of asymmetric stress in the local area. As such, the tensile force applied to the rest of the area will increase, and ruinous rupture will eventually take place.

4.2. Damage index and the effective tensile strength of paper sheets

From Page equation, it was presumed that the tensile strength decreased during recycling processes mainly because of the decrease in the fiber–fiber bond strength, and the relationship of tensile strength and the fiber–fiber bond strength could be written as (Jin et al., 2022):

(14) $\frac{1}{T}=\frac{1}{F}+\frac{1}{B}$(14)

where F = 8Z/9 is the fiber strength index, B is the bond strength index and 1/B is the factor of fiber–fiber bond weakness. Jin et al. examined the factor of fiber–fiber bond weakness during recycling processes, and found that for all the softwood pulp fibers, the factor of fiber–fiber bond weakness tended to increase and the fiber–fiber bond became weaker as the recycling number increased (Jin et al., 2022). In their recycling experiment of the softwood pulp fibers, Jin et al. also evaluated the correlation between the tensile strength and the factor of fiber–fiber bond weakness and found the correlation was as high as R² = 0.98 (Jin et al., 2022). The proposed factor of fiber–fiber bond weakness focused on the change of fiber–fiber bond strength during recycling and explained that the deterioration of tensile strength of paper sheets was mainly because of the decrease of fiber–fiber bond strength, which was resulted from the loss of the wettability of paper fibers (Jin et al., 2022).

Among paper sheet properties, the factors determining the tensile strength include not only the fiber–fiber bonds but also the fiber length, the fiber strength, etc. Theoretically, there are some factors that can be chosen to express the damage severity of paper sheets. However, it is hard to identify a factor that not only can express the damage severity but also can quantitatively relate to mechanical properties of paper sheets. To address this issue, a damage index was proposed. If such a damage index can be identified with the aid of damage mechanics, then the damage and property deterioration of paper sheets due to recycling can be estimated quantitatively. Ideally, the damage index should be experimentally obtainable and can indicate the macro-mechanical properties of the sheets.

In Figure 8, (a) is an ideal sheet with no interior damage at all, and (b) is a real sheet with some interior damage. As illustrated in Figure 8, the stress on a paper sheet subjected to a tensile force is the ratio of the tensile force to the area that bears the force:

Figure 8. Different stresses on paper with different damage states.

(15) ${\sigma }_0=\frac{F}{A_0}$(15)

Considering a sheet formed with recycled fibers, the cross-sectional area subjected to the tensile force decreases from A₀ to A due to the deterioration of sheet properties and the change of fiber configurations during recycling processes. Based on the hypothesis of stress-strain equivalence, it is reasonable to propose a damage index as follows:

(16) $\mathit{D}=\frac{A_0-\mathit{A}}{A_0}=1-\mathit{\hspace{0.17em}}\frac{A}{A_0}$(16)

If a sheet is made from virgin pulps, it is not an ideal sheet because of fiber defects and damage during processing (Hughes, 2012). However, the damage in the pulp before refining is relatively little, then it may be assumed that A= A₀, and D= 0. The sheet can bear the maximum rupture tensile force. If the sheet is made from recycled pulps with damaged fibers, then A= A₀ (1-D), A< A₀, and D> 0. The maximum rupture tensile force that the sheet can bear will be reduced according to the damage index after each recycling process. The more severe the damage developed during fiber recycling, the less the tensile force that the sheet can bear. If a sheet is damaged to the maximum extent possible, i.e., A= 0, the sheet will lose its strength completely.

4.3. Quantitative expression of damage index

Although the deterioration of the fiber properties, including single fiber strength, degree of crystallinity, degree of polymerization of celluloses, and so on, causes sheet damage; the losses of hydrogen bonding capacity are a main component. Hence, the damage index should reflect the change of hydrogen bonding capacity. From the calculation of correlation coefficients, WRV and RBA were chosen as features, and they were both related to hydrogen bonding capacity. Since hyperbolic models relate variables with a constant of physical significance, they can be utilized to simplify the concept of paper structure and represent the relationship of tensile strength, the light scattering coefficient, and so on (Ring, 2011). For example, the following equation describes the inverse relationship between the tensile strength and the light scattering coefficient (Ring, 2011):

(17) $\left(\mathit{T}-T_{\mathit{disp}}\right)\left(\mathit{s}-s_{\mathit{disp}}\right)=\left(\mathit{\gamma }{T}_{\mathit{disp}}{s}_{\mathit{disp}}\right)->\mathrm{constant}$(17)

Based on the hyperbolic models, Equation 18(18) $\mathit{D}=\frac{{\left(D_s-\mathit{h}\right)}^2}{a^2}-\frac{{\left(D_h-\mathit{k}\right)}^2}{b^2}$(18) is proposed to describe the paper sheet damage index:

(18) $\mathit{D}=\frac{{\left(D_s-\mathit{h}\right)}^2}{a^2}-\frac{{\left(D_h-\mathit{k}\right)}^2}{b^2}$(18)

where a, b, h, and k are coefficients related to fiber properties during recycling processes. They vary with respect to pulp properties, such as the fiber coarseness, and the average fiber cross-sectional area, etc. They also vary with respect to bleaching conditions, degrees of refining, and so on. The hyperbolic center is (h, k), which indicates the shift from the origin. The coefficients were determined through the curve fitting toolbox in MATLAB. Ds and Dh are sub-indices (sub-variables) composing the damage index of paper sheets. The physical meaning of Ds is the damage variable related to the no-bond area of recycled sheets:

(19) $D_s=1-\frac{\mathit{RBA}}{RB{A}_0}$(19)

where RBA and RBA₀ are the relative bonded areas before and after recycling. Dh is a variable indicating the severity of paper damage related to hornification:

(20) $D_h=1-\frac{\mathit{WRV}}{WR{V}_0}$(20)

where WRV and WRV₀ are the water retention values before and after recycling. Based on the theory of damage mechanics and tensile strength hyperbolas (Ring, 2011), an equation expressing the relationship between the damage index and the tensile strength can be written as follows:

$\mathit{T}=T_0\left(1-\mathit{D}\right)$(21)

where T and T₀ represent the tensile strength of the sheet before and after recycling. Figure 9 shows the linear relationship between the damage index and the loss of tensile strength of paper sheets made of various pulps during recycling processes. The damage indexes were derived from Equation 21 based on the experimental data. The graph shows the damage index changed the most after the first recycling, in accordance with the worst deterioration of the properties of fibers endured the irreversible recycling process. The damage index proposed in this paper could quantitatively express the deterioration in tensile strength during recycling. Thus, if the damage index could be estimated and predicted, then it can be used to estimate and predict the tensile strength of paper sheets.

Figure 9. Damage index and tensile strength after each recycling.

In this paper, a curve fitting model based on Equation 18(18) $\mathit{D}=\frac{{\left(D_s-\mathit{h}\right)}^2}{a^2}-\frac{{\left(D_h-\mathit{k}\right)}^2}{b^2}$(18) as well as an LSTM RNN model considering the recycling processes as a dynamic event sequence was utilized to estimate and predict the damage index, and Figure 10 shows the results. For both methods, the training data, which were Ds and Dh after each recycling, were utilized to train the models first. After the models had been set up, the training data were input into the models to estimate the damage index as compared with the experimental results. The testing data which had not been presented to the models were used for predictions. The accuracy of the estimation and prediction of curve fitting was better than that of the LSTM RNN. The LSTM RNN model had memory to store previous time step information, as more training data accumulated during the successive four recycling processes, the accuracy improved. For the estimation of the training data, the RMSE (root mean square error) of the curve fitting estimation was 0.0278, while the RMSE of the LSTM RNN estimation was 0.2445. For the testing data or prediction, the RMSE of the curve fitting estimation was 0.1667, while the RMSE of the LSTM RNN estimation was 0.2206. In order to improve the accuracy of the estimation of the LSTM RNN, more experimental data would be needed for training.

Figure 10. Damage index estimation based on curve fitting and neural network.

From the results, the proposed damage index could be used to estimate and predict the tensile strength of handsheets made of recycled fibers. The curve fitting model was developed based on Equation 18(18) $\mathit{D}=\frac{{\left(D_s-\mathit{h}\right)}^2}{a^2}-\frac{{\left(D_h-\mathit{k}\right)}^2}{b^2}$(18) and it simplified the calculation from a hyperbolic model. In this paper, an LSTM neural network model was developed to determine the damage index during recycling. An LSTM model can also be utilized to analyze and determine other properties which cannot be expressed directly with a mathematical model since the successive recycling process can be considered as a dynamic sequence. The LSTM model can store information from previous recycles, so it is suitable to analyze recycled fibers which have endured multiple recycles.

5. Conclusions

The properties of fibers deteriorate during recycling processes, which raises concerns about the quality of paper products made of recycled fibers. This paper aims to estimate the deterioration of tensile strength and the damage in paper sheets made of recycled wood and non-wood fibers by means of the theory of non-continuum damage mechanics and machine learning methods. To investigate the deterioration of fiber properties due to recycling, experiments were carried out to simulate recycling processes for four times. Various physicochemical properties were measured after each recycling process. Due to the fact that water retention value and relative bonding area were strongly correlated with tensile strength, they were chosen to estimate and predict the loss of tensile strength and the damage developed during recycling processes.

Based on the experimental results and damage mechanics, a damage index was proposed according to the hyperbolic model: $\mathit{D}=\frac{{\left({\mathit{D}}_{\mathit{s}}-\mathit{h}\right)}^2}{{\mathit{a}}^2}-\frac{{\left({\mathit{D}}_{\mathit{h}}-\mathit{k}\right)}^2}{{\mathit{b}}^2}$. The curve fitting method was utilized to identify the coefficients in the equation. Then, T = T₀ (1—D) was proposed to estimate and predict the tensile strength deterioration during recycling. The proposed approach to estimate and predict the damage index and the tensile strength can be utilized to determine in advance the quality of paper products made from recycled fibers; thus, the applications of the recycled fibers can be selected. A recurrent neural network with long short-term memory was designed and trained to estimate and predict the damage index as compared with the curve fitting method. The accuracy of the estimations of the neural network was less than that of the curve fitting estimations. For the curve fitting method, the RMSE of estimation for training data was 0.0278, for testing or prediction was 0.1667. For LSTM RNN estimation, the RMSE for training was 0.2445, for testing or prediction was 0.2206. From the results, the proposed method could be utilized to estimate and predict the tensile strength of paper products made of recycled fibers. The proposed method using an LSTM RNN model to analyze tensile strength and paper damage during recycling processes is novel. The memory of LSTM RNN models can store information of previous recycling, so it is suitable to analyze other variables during multiple recycling processes. In the future, further analysis will be conducted to determine the coefficients in the damage index equation through experimental data so that a better understanding of the physical significances of the coefficients can be achieved. The other limitation of this study is that different compositions of fibers have not been considered; while in real life, recovered fibers are combinations of various types of fibers. Experiments on recycled fibers obtained from different waste paper streams will be carried out to study the impact of different fiber compositions on tensile strength.

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