properties of paper - materials · pdf filetu/e mechanical engineering section mechanics of...

TU/e Mechanical Engineering Section Mechanics of Materials

Eindhoven, July 2009

Properties of paper The mechanical behavior of single paper fibers

Author: R.W. Koppelaar MT 09.10

Bachelor final project Supervisors: ir. L.A.A. Beex

dr. ir. R.H.J. Peerlings

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Contents 1. Introduction 2 2. Literature study

1. Composition of paper 3 2. Structure of single fibers 4

3. Measurement methodology

1. Sample preparation 6 2. Data acquisition 8 3. Measurement reliability 9

4. Results

1. Basic properties 13 2. Stiffness 13 3. Failure 17

5. Conclusions and recommendations 19 Appendix A References 20

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Chapter 1 Introduction The worldwide production of paper and paperboard exceeds 300 million tons per year. This class of materials has a wide range of applications, which each require specific properties. The macroscopic properties of paper are mostly determined by the micro structural fiber network which it consists of. Studying this interplay between the micro structure and macroscopic properties of paper may ultimately result in more appropriate paper properties for certain applications. Each fiber in the network is unique because it may originate from another tree or from another annual ring and may have been differently bashed out of a tree. Another important issue for the behavior of paper is the manufacturing process. During manufacturing fiber pulp is dropped onto a wire at a significant speed causing a preferred orientation of the fibers. This makes paper an anisotropic material. The bonding and writing performances of paper are improved by multiple additives altering the total behavior of the paper. A way to study the impact of the properties of single fibers and the network which they form on the overall properties of a sheet of paper is to model the microstructure of paper as an infinite number of X-braced unit cells as shown in figure 1.1. For implementing this model, however, geometrical and mechanical properties of the individual fibers are required.

Necessary properties are the geometry properties of a single fiber, i.e. fiber length, as well as the area and shape of cross section. Mechanical properties like stiffness and strength need to be determined by a tensile test. Difficulty may arise in gripping single fibers for such a test without damaging them and in determining the cross section. This report starts with examining the existing literature on the subject. A summary of this is presented in chapter 2. In chapter 3 the experimental methods are described. In chapter 4 the results are presented and finally the conclusions are drawn in chapter 5.

Figure 1.1: X-braced unit cell [16]

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Chapter 2 Literature study 2.1 Composition of paper Paper can consist of nonwood fibers as well as wood fibers. Nonwood fibers originate from natural sources such as food crop residues and cotton. The fibers tested in this project are wood fibers. Therefore the focus will be on the properties of those fibers. Fillers have an important role in paper and are used because of their brightness and fine particles, improving different properties of the paper sheet. The opacity is improved by titanium dioxide, while clay, calcium carbonate and talc provide gloss. Amorphous silica, silicates, calcium carbonates and clay improve the ink holdout. Calcium carbonate is known for its use in cigarette paper, where it controls the porosity and burning rate of the paper [5]. Under a microscope paper seems a randomly oriented network of fibers. Very few fibers have their axes aligned in directions other than parallel to the plane op the sheet. A majority of the fibers have their axes oriented in the machine direction [1].

Figure 2.1: Layers within the fiber; middle lamella (ML), primary layer (P), secondary layers (S1-S3) and lumen (L) [9]

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2.2 Structure of single fibers Internally, fibers consist of smaller fibers called fibrils. The fibrillar structure of paper fibers consist of multiple layers. The outer layer is called the middle lamella (ML); it is followed by the primary wall (P). The most important layers of the fiber are the secondary layers (S1-S3) which are dominant in most mechanical properties of single fibers. The center of the unbeaten fiber is a hollow lumen (L) [4,9,11] as shown in figure 2.1. Mechanical processing of wood to single fibers may cause the lumen to collapse and thereby reduce the visible dimensions of the fiber. The layers of the fiber are built from fibrils. The structure in layers is caused by differences in orientation of fibrils. The presence of the lumen explains that fibers have their highest strength in the longitudinal direction of the fiber [3]. Electron-microscopic and WAXS (wide-angle X-ray scattering) data indicate that the diameter of elementary fibrils is about 3.5 nm. Elementary fibrils, form microfibrils with a diameter of 10-30 nanometer, which in turn form macrofibrils. In a tree the middle lamella is the first layer to be formed and it serves a cementing purpose. The second layer that is formed is the primary wall, which is a loose random structure of macrofibrils. The secondary walls are in most cases subdivided into three stiff layers. The S2 layer contributes most to the bulk of cell wall material, as well as to its physical and mechanical properties. The main difference between the three secondary layers is the fibril orientation angle which varies from 50° to 70° for the S1, 10° to 30° for the S2 and 60° to 90° for the S3 layer. These varying fibril orientations produce a mechanical locking effect, leading to a very high stiffness of the overall fiber [2].

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Many references present the dimensions of various types of paper fibers. An extensive set

Table 2.1: Distribution of fiber length in two paper samples [12]

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of properties, like contour length, projected length and curl, is given in [3]. The values that have been found in references [1,6-14] are of a wide range. The average fiber length ranges from 0.9 to 7.0mm while the fiber width ranges from 10 to 50μm. The shortest fibers are in the interval 0.0-0.1mm according to [12]. An example of the distribution of fiber length in two paper samples is shown in table 2.1. Reports on the mechanical properties of paper fibers are limited to indirect measurements. The mechanical behavior of wood however provides a rough estimate for the properties of single paper fibers that are bashed out of a tree. Tensile tests with the elongation subjected in the direction of the fibers give such an estimate. The Young’s modulus of wood is typically in the range of 6-20GPa [17].

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Chapter 3 Measurement methodology This chapter describes chronologically the steps taken towards an accurate measurement. It starts with obtaining single paper fibers. The fibers need to be restrained, forming a sample that can be pulled by a tensile stage. The way in which these tests are executed is described in detail. The data acquisition and data processing is detailed. The errors that occur during the experiments are described separate. Finally the conclusions from this chapter are drawn. 3.1 Sample preparation The easiest way to obtain separate fibers is to pull them directly from a paper sample. However, fibers often break when pulled out of normal paper and board. Pulling fibers from a pulp plate solely containing virgin fibers is much easier since these fibers have not been processed for optimum adhesion. The tensile stage, as shown in figure 3.1, allows observation of tensile testing experiments at extremely low forces, yet very high load resolution, according to specifications down to 1×10-5 N with a speed range of 0,1 to 20 µm/s. In testing the lower speed limit could not be reached. The load is measured by the principle of frequency variations on a spring-loaded metal wire. The displacement is taken by a linear variable differential transformer (LVDT). One side is attached to a parallel sled, driven by a combination of DC-tacho-motor/angular encoder for precise recognition of the displacement.

Figure 3.1: Fiber tensile stage

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The easiest way to pull on fibers would be by directly clamping the fiber in the clamps of a tensile stage. Ordinary clamps however provide not enough grip to actually grip the fiber. Efforts to improve the grip of the clamps using small pieces of sand paper or rubber were unsuccessful. Fibers therefore have first been glued at both ends to paper strips, which can be clamped in a tensile stage more reliable. This provides the opportunity to prepare a large number of samples without using the tensile stage. A problem which may occur is that the fibers are torn from the glue in a brittle fashion as shown in figure 3.2. This effect can be related to the spherical shape of the droplet of glue. The fiber is not evenly held by the glue, since the fiber is better supported in the direction of the underlying paper than in the direction of the surrounding air. A solution could be to sandwich the fiber between two pieces of paper, thereby removing the difference between top and bottom of the sample. This solution however is not very practical because the fibers are too small to precisely put a piece of paper on top of the first piece without displacing the fiber. Other types of glue stay too fluid and fibers are easily pulled out. The best results were obtained using fast drying glues.

During preparation of the samples, a paper clamp was used to hold the two pieces of paper fixed. Once the sample was clamped between the two clamps of the tensile stage, the paper clamp could easily be removed, thereby leaving the fiber as the only connection between the two clamps. In this manner the samples can be produced in large numbers without occupying the tensile stage. Other advantages are that they are quite reproducible and can easily be clamped without tearing the fiber. The final experimental setup is shown in figure 3.3.

Figure 3.2: Three images showing brittle fracture of glue on the right side of the sample

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3.2 Data acquisition The fibers that are used for tensile testing are characterized by three images from a stereo microscope. The first image contains the entire sample, the second gives a good idea of the gauge length of the fiber and the third image is used to determine the cross section of the fiber. The difference between the length of the fiber and its gauge length should be noted. The actual length of the fiber may be up to twice the gauge length, as parts of the fiber are embedded in the glue droplets. This is illustrated in figure 3.4, in which the fiber is indicated as the dashed line, while the gauge length is marked by dots.

Figure 3.4: Sample with the indicated length and gauge length

Figure 3.3: The final experimental setup, two separate T-shaped pieces of paper to clamp

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Determining the strain optically, using microscopy, is a direct and reliable way of measuring strain. It allows one to avoid using the elongation measured by the tensile stage, which includes deformation of the glue and the pieces of paper used to clamp the fiber. The tensile test has to take place under the stereomicroscope with a camera mounted on top. By monitoring the entire fiber, the displacement of two points at a relatively large distance from another can be measured. The automatic tracking option of the microscope’s software can not be used for paper fibers because their appearance changes under influence of the strain. The fibers tend to straighten under a load, thereby altering the reflection of the light. Light spots become darker and dark spots start to reflect light, making it impossible to automatically track these points. Less advanced but more accurate is the option to track the points manually. The points need to be selected with the cursor from the first image to the last. Using the relative displacement of two points, a strain is determined. The time at which the pictures were taken is used to obtain the corresponding force from the force-time data of the tensile stage. Images with a high resolution are better to obtain a highly reliable relative displacement but have the disadvantage that they take some time before they are saved on the computer. The engineering strain is defined as the increase in length of the fiber divided by the initial length. This definition of strain does not require conversion from pixels to meters and is therefore straightforward. It is important to state that the engineering strain is obtained over an interval which not includes the entire strain trajectory. The engineering strain from zero load to failure is higher. The relative displacement from which the engineering strain is derived is obtained by subtracting the initial and final coordinates of two points on the fiber. This method is not only valid for the total interval from initial conditions to failure but on every arbitrary interval between. The Young’s modulus relates stress linearly to the strain. Since this relationship differs for every material, the Young’s modulus is material dependent.

r0

0

A

lFE

(1)

The Young’s modulus is hard to obtain for the fibers tested. The main problem is that measuring the cross sectional area of each fiber is very inaccurate. A property that can be obtained from the measurements is a constant which is the Young’s modulus multiplied by the cross section calculated by dividing the force difference by the strain difference thereby avoiding the unreliable A0.

0EAF

c

(2)

3.3 Measurement reliability The tensile tests take place in a changing environment. For this reason the temperature and humidity are being measured. The fact that the fibers are biological cells gives reason to believe that small variations in the temperature and humidity could result in different values for force and strain. The relation between humidity, temperature and test results have not yet been studied, and would make an interesting subject for future experiments.

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Measuring of force with the tensile stage is done by analyzing the frequency of a string between a fixed point and one of the clamps of the tensile stage. The resolution of this measurement is 1mN. The force is not always returned to zero when a fiber breaks. This is caused by the design of the tensile stage. The right clamp rests on two leaf springs, allowing it to rest in several equilibrium positions. The translation from one to another equilibrium position happens during the tensile test or perhaps after the breaking of the fiber. The error in the force has a maximum of 20mN. The force-displacement data recorded gives no reason to believe that the transfer happens suddenly during the tensile test. Therefore this error is not taken into account when analyzing the force-displacement curve. Another error caused by the tensile stage is the drift of the displacement in time. This phenomenon can be characterized by measuring without a sample and without a prescribed displacement. This test shows a value of -1.9μm per minute. Since a tensile test takes a maximum of two minutes, drift alters the mean velocity only by 0.07%, which is an insignificant amount. The tensile stage has a controller to regulate the velocity of the stage. However, the selected velocity is not always the velocity that is obtained. Especially small desired velocities do not correspond with the actual velocity. The lowest steady state velocity obtained is 0.75 mm/s. In practice the velocity of the clamps is measured during the tensile test to obtain the true speed of the clamps. The clamps have a height difference of 450μm, which is large compared to the 1-2mm length of the samples. This height difference is causing a difference between the measured force and the actual axial force acting in the fiber. In the tensile tests the pieces of paper form a part of the samples were bent, leaving a height difference of less than 10μm. This height difference is small compared to the gauge length. Therefore it is not necessary to take this error into account in further calculations. The microscope and camera also have their limitations with respect to the resolution of the images they create. The effect of limited resolution can be characterized by calculating the error in strain, computed with an estimated maximum error of two pixels in the manual tracking. The effects can be estimated by the simple calculations done below with:

rll 01 (3)

Where l1 is the length in the deformed state, l0 the initial gauge length and δr is the elongation as shown is figure 3.5.

rr

l

0

(4)

With l0 the initial gauge length and εr the engineering strain.

2r

E2

(5)

With E2 the error when the manual tracking has a supposed error of two pixels.

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The main conclusion from table 3.1 is that the resolution is of great importance. The initial gauge length is about 60% of the total width of the image. The relation between the length, relative elongation and error is then given by;

r0l

2a

(6)

With a being the maximum allowed error at a 2 pixel offset in the manual tracking analysis. Therefore the error can be decreased linearly with the resolution. The largest error introduced in the experiments is the measurement of the cross section of a fiber. The cross section is determined from an image at a high magnification. The fibers are similar to a strip of paper as shown in figure 3.5. The strip is twisted but also somewhat curled. When determining the cross section of this paper strip from figure 3.5 the largest and smallest width of the strip are relevant dimensions. The smallest width can be taken as an indication for the thickness of the strip while the largest width is an indication of the actual width of the strip. The actual width of the strip used is 3.0cm, the thickness of the strip is unknown but is on the order of 0.1mm. From this image the estimated width and height would result in a cross section that is an order of magnitude larger than the actual cross section.

l0 (in pixels) 1500-2500 δr (in pixels) 35-140 εr (in %) 2-6% E2 (in %) 1.4-5.7%

Figure 3.5: Deformation of a fiber with initial length l0 and deformed length l1

Table 3.1: Error in optical tracking

Figure 3.5: Twisted piece of paper

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A better estimate would be obtained when assuming the fibers to be of constant cross sectional area or of constant aspect ratio between height and width. The constant width of the fiber is estimated from measurements to be 35μm and from the aspect ratio height-width we assume a height of 7μm. The resulting cross sectional area is 245μm2 this will be the constant cross sectional area used for further calculations. The maximum error is this assumption is estimated to be 100μm. The camera software saves the time in seconds accurately, thereby allowing one to link the images and force-time data with an accuracy of 1 second. Dependent on the velocity of the tensile stage the total error in the force is therefore 1.0-2.0mN.

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Chapter 4 Results 4.1 Basic properties From sample measurements the values in table 4.1 for length gauge length and width, according to figure 3.3, are obtained. Maximum length (in mm) 5.9 Gauge length (in μm) 580-2600 Width (in μm) 5.0-50

4.2 Stiffness The stiffness is determined for three tensile tests with reliable data. In this paragraph the data of these three experiments, named sample 1-3, are stated. Sample 1

Table 4.1 General geometric properties

Figure 4.1: Sample 1 in initial undeformed state

Figure 4.2: Force-displacement curve of sample 1 from the tensile stage

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Tracking point 1 Tracking point 2 F1::Frame F3::X F4::Y F1::Frame F3::X F4::Y Pixels Pixels Pixels Pixels

6 168 845 6 1714 9627 171 845 7 1723 9598 172 845 8 1730 9589 173 845 9 1737 955

10 175 844 10 1745 95311 177 844 11 1754 95112 180 843 12 1759 95013 186 844 13 1767 949

Sample 2

Table 4.2 Tracking data of sample 1



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11 496 251 11 2934 19213 491 252 13 2946 19315 488 253 15 2956 19317 484 254 17 2964 19319 484 254 19 2975 19321 479 254 21 2981 19323 477 254 23 2993 19325 474 254 25 3002 19327 471 255 27 3011 19329 469 256 29 3021 19331 469 256 31 3031 19333 466 257 33 3041 193

Sample 3

Table 4.3: Tracking data of sample 2



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10 541 170 10 2951 27312 539 171 12 2966 27214 537 173 14 2981 27216 536 175 16 2998 27118 538 175 18 3013 27020 538 177 20 3025 26622 538 177 22 3035 26624 541 178 24 3050 267

For sample 2 the calculations are stated below. - From the displacement-time curve during the measurement of the force-elongation curve a steady velocity is obtained on an interval of 150.93s and 118.8μm, which yields a mean velocity of 0.7871μm/s. - The time between the first and the last image in the tracking analysis is 90 seconds. - The linear part of the force-elongation curve is 180mN with an elongation of 88μm, which yields 2.046mN/μm. From previous numbers the conclusion can be drawn that the difference in force between the first and last image is 144.9mN. The tracking analysis is necessary to obtain the correct elongation of the fiber over the interval. - The elongation of the sample is 137 pixels; the magnification and resolution correspond to 0.767μm/pixel. Combining the two yields an elongation of 104μm. - The engineering strain on the interval between the first and last image is calculated with the initial gauge length of 2439 pixels and the elongation of 137 pixels, which yields an engineering strain of 5.62%. - Using (2) a constant EA of 2578mN is derived. Under the assumption, made in paragraph 3.3 that the cross section is constant at 245μm2, a Young’s modulus of 10.5GPa is obtained. In table 4.5 the summary of the measured and calculated values is given.

Table 4.4: Tracking data of sample 3

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Sample 1 Sample 2 Sample 3Velocity tensile stage (μm/s) 1.0549 0.7871 1.0185 Time between the images (s) 66 90 41 Coefficient force-elongation (mN/μm) 0.9821 2.0455 1.988 ∆F (mN) 68.377 144.9 83.01 δ (pixel) 34 137 98 l0 (pixel) 1550 2439 2412 ε (%) 2.19 5.62 4.08 EA (mN) 3122 2578 2035 E (GPa) 12.7 10.5 8.3

The engineering strain of the tested fibers is between 2% and 6%. This is the largest engineering strain that could be obtained from the measurement data as discussed in paragraph 3.2. The force-elongations curves of the fiber give reason to believe that the fibers have a linear stress-strain curve with according modulus. The Young’s modulus of the three most reliable measurements is determined to be between 8 and 13GPa. To obtain a more realistic value the common used Young’s modulus multiplied by the initial cross section is used, eliminating the unreliable cross sectional area. The value of this parameter is between 2.0 and 3.0N. 4.3 Failure The paper fibers seem to break in a brittle way in the test, although this is not certain since they break in the zones that are affected by glue. Due to the fact that failure is brittle, the actual breaking process cannot be caught in detail by the microscope and camera. The force-elongation curve of the tensile stage confirms the observation that brittle failure occurs since the force decreases abruptly from the maximum value to zero. From literature we know that paper fibers are built from micro fibrils that form a spiral around the fiber axis. The S2-layer dominates the mechanical behavior in axial direction for single paper fibers. The fibrils are related to the elastic modulus and tensile strength of a fiber.

Table 4.5: Summary of data and calculated values for three samples

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The failure occurs in the dominating S2-layer. For extended study on breaking behavior of paper fibers it is necessary to look on even smaller scale. The breaking or tearing of micro fibrils is the cause for failure on sub-micro scale. From the experiments some observations about the breaking strength can be made. The first is that the breaking strength is strongly dependent on the fiber. This is expected based on the variety of fibers and their mechanical history as mentioned in the introduction. Many fibers break in the region where the glue affects the behavior of the fiber. This means that, in these tests, the zones which are affected by the glue have a lower critical force than the unaffected zones. These measurements thus give a lower bound for the breaking strength. In figure 4.2 the breaking force of fifteen samples is displayed. The samples numbered 20-24 had the failure in the region unaffected by the glue. The last four samples, numbered 26-29, were torn out of the glue but had a significant value of the force before doing so. Interesting is to see that most fibers break at a value between 100 and 200mN.

Figure 4.2: Breaking force for each sample

0

50

100

150

200

250

300

0 5 10 15 20 25 30

Sample number

For

ce (

mN

)

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Chapter 5 Conclusions and recommendations The measurements described in this report are greatly influenced by two errors: the error in the tracking analysis by incorrectly identifying points in the initial and deformed state and, more importantly, determining the cross section of the fiber. The tracking error and the error in the cross section are both inserted directly in the formula for the Young’s modulus. Reducing these errors is a direct improvement in accuracy of the final result, the Young’s modulus. The final value of the Young’s modulus is, with its limitations in mind, a good indication. The value is realistic for wood fibers according to literature. The engineering strain that has been calculated is a lower bound for the strain at which failure occurs. For a better understanding of the breaking behavior of single fibers a study on the breaking behavior of micro fibrils is necessary. Another interesting subject for further study is the influence of environmental conditions on the properties of single fibers. An important conclusion that can be drawn is that even though the clamping of the fibers comes with many problems, the accuracy of the results largely depends on the limitations of the microscope and camera. Further improvement of measurements is necessary to obtain reproductive measurements in large numbers. A promising option is using computer controlled micro grippers, ensuring a controlled way of sample preparation. The dimensions of paper fibers are well described in literature. The values from measurements correspond to those values, although they were less quantitative. Mechanical properties of single paper fibers are hardly presented in literature. In determining the properties many problems arise. To obtain better measurement data the tensile stage needs to be adjusted to guarantee steady and axial elongation.

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Appendix

A References [1] William E. Scott and James C. Abbott, Properties of paper: an introduction (1989) second edition, revised, 58. [2] Herbert Sixta, Gerald Koch, Handbook of pulp (2006 Weinhein), Volume 1, 41-44. [3] Herbert Sixta, Handbook of pulp (2006 Weinheim), Volume 2, 1269-1278. [4] Kaarlo Niskanen, Papermaking science and technology; book 16 Paper Physics, (Helsinki 1998), [5] Robert Hagemeyer and Dan Manson, Pulp and paper manufacture; volume 6 Stock Preparation (1992), 19-37. [6] Robert Higham, A handbook of papermaking, Oxford (1963), 14. [7] Kenneth Britt, Handbook of pulp and paper technology, New York (1964), 19. [8] Christopher Biermann, Handbook of puling and papermaking; second edition, Oregon (1996), 42-44. [9] Gary Smook, Handbook for pulp & paper technologists; second edition, (1992), 4-11. [10] United Nations, Pulp and paper prospects in Latin Amerika, New York (1955),256 and 295. [11] Ronald Macdonald, Pulp and paper manufacture; volume 1 the pulping of wood, (1950),1-31. [12] Institute of paper chemistry, Characterization of pulps for papermaking; A comparison of some fiber measurement techniques, Project 2406 report four, Appleton (1966), 20-44. [13] Carl Jentzen, The effect of stress applied during drying on some of the properties of individual pulp fibers, Appleton (1964), 11-85. [14] Richard Ellis and Alan Rudie, Ideal fibers for pulp and paper products, Atlanta (1991), 2. [15] Qingzheng Cheng and Siqun Wang, A method for testing the elastic modulus of single cellulose fibrils via atomic force microscopy. Composites Part A 39 (2008), 1838-1843. [16] J. van Beeck, Paper: A closer study; On the relation between micro structure and mechanical properties of paper, Eindhoven (2008), 16 [17] S.I. Wiselius, Hout vademecum, Almere (1994),68-85.

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