Tensile Stress-strain Properties and Fracture Resistance of Paper

Document Sample
Tensile Stress-strain Properties and Fracture Resistance of Paper Powered By Docstoc
					             Tensile Stress-Strain Properties and Fracture Resistance of
                                Paper and Paperboard



                                        T. Yokoyama and K. Nakai
             Department of Mechanical Engineering, Okayama University of Science
                           1-1 Ridai-cho, Okayama 700-0005, Japan




ABSTRACT

  The tensile stress-strain properties and fracture resistance of two kinds of commercial paper and paperboard
were determined in a tensile testing machine equipped with a non-contacting optical extensometer. PPC (or
copy) paper, UKP-sack paper and paperboard were tested at about 25 °C. and 25% ~ 55% relative humidity. A
dumbbell-type or necked-down specimen specified in the JIS Z 2201 for sheet materials was used in the
tension tests, instead of a constant-width strip specimen specified in the JIS P 8113 (ASTM D828). Tension
specimens were cut in three directions from each type of paper and paperboard on a paper cutter, following a
steel template. The thickness of paper was carefully measured with a high-precision digital micrometer under a
constant pressure. The effects of specimen shape and size, test direction, moisture content and strain rate on
the tensile properties and fracture resistance were examined in detail.


1. INTRODUCTION

  The increasing diversity of end-use applications of paper and paperboard requires accurate assessment of
their mechanical properties in various aspects. Tensile properties and fracture resistance are the most
important characteristics to be determined in the fabrication process and in the physical characterization of
paper and paperboard. A test method for determining the tensile properties of paper and paperboard has been
specified in the JIS P 8113 (ASTM D828) [1]. In the test method, the paper tensile strength (S) is defined as the
maximum load per unit width on a constant-width strip specimen, because of difficulties associated with
measurement of the real thickness of paper. However, the paper tensile strength (S) is not a true tensile
strength, which makes it impossible to make a direct comparison with tensile properties of other engineering
materials.
  In the present work, we attempted to characterize the tensile stress-strain behavior and fracture resistance
of two types of commercial paper and paperboard. They were tested at room temperature and two different
relative humidity. The stress-stain curves were accurately determined in a tensile testing machine equipped
with a non-contacting optical extensometer on dumbbell-type (necked-down) specimens. The influences of
specimen shape and size, test direction, moisture content and strain rate on the tensile properties and fracture
resistance were investigated.



2. MATERIALS AND SPECIMEN PREPARATION
   Machine-made papers were selected for test: copy paper, sack paper made from unbleached kraft pulp (or
UKP-sack paper), and paperboard. They are manufactured in such a way that the axes of the fibers tend to be
aligned parallel to the flow of the paper through the paper machine (see Fig.1a). Dumbbell-type (or necked-
down) specimens were cut from each type of paper and paperboard in the three directions (see Fig.1b). on a
paper cutter, following 1-mm thickness steel templates of JIS Z 2201 specimens 5 and 6 [2] as shown in Fig. 2.
The specimen’s ends were over-wrapped with chip board doublers to prevent localized end failure. Their basic
properties in the machine and cross-machine directions are given in Table 1. Note that paper whose basis
                            2
weight larger than 200g/m is classified as paperboard in the paper industry. It is very difficult to determine the
real thickness of paper because of its roughness surface texture. In this study, the thickness of paper was
carefully measured with a digital micrometer Mitutoyo: GMA-25 DM under a constant pressure of 31kPa with
an accuracy of ±4µm. Furthermore, the surface roughness Ra (center-lined average roughness) was measured
in both MD and CD with a surface roughness tester (Mitutoyo: MST-301). The paper tensile strength (S) given
in Table 1 was determined on constant-width strip specimens of 25mm in width by 250mm in length adopted as
an ASTM D828 Standard for paper testing. Obviously, the paper tensile strength (S) is not a true tensile
strength.




                                Z

                                                  MD
                                                 (machine direction)



                                                 CD
                                            (cross-machine direction)
             direction of paper flow through
             paper machine

                                    (a)                                                     (b)

    Fig. 1 (a) Principal material directions in paper; (b) three directions in which tension specimens are cut.
               The longitudinal direction in paper ordinarily corresponds to the machine direction.



                 Table 1 Basic properties of two kinds of commercial paper and paperboard tested

                                                                              Roughness      Tensile strength
                           Basis weight     Thickness Apparent density         Ra (µm)          S (kN/m)
                               (g/m2)         t (µm)    ρ (kg/m3)
                                                                              MD       CD         MD     CD

            Copy paper              (64)*       85 (90)        753           2.5      2.7         3.9    2.2

       UKP-sack paper               (85)       125             680           4.0      3.8         6.6    3.4
            Paperboard              (390)      750             520           5.3      5.5         23.2   9.2

                     *Note: values in parentheses are taken from catalogues by paper manufacturers
                                                      200




                         SPECIMEN 5                    50

                                                       60             (DIMENSIONS IN MM)
                                                       130




                                      SPECIMEN 6       25
                                                       40


              Fig. 2 Geometry of JIS Z 2201 sheet specimens 5 and 6 (dumbbell-type specimens)


3. TESTING APPARATUS WITH NON-CONTACTING OPTICAL DEVICE
  It is virtually impossible to mechanically measure the deformation of paper specimen in a conventional
universal testing machine with a strain-gaged extensometer, and hence we used a tensile testing machine       JT
Tohsi Inc.: Little Senstar LSC-1/30    equipped with a non-contacting optical extensometer using a CCD camera
(see Fig.3). The applied load was measured with a load cell of 1kN capacity and the elongation over a 50 mm
gage length marked on a reduced section of paper specimen was determined with the optical extensometer.
The resulting tensile load-elongation relation was then converted to the nominal tensile stress-strain curve. The
crosshead velocity was set at 3mm/min and 30mm/min. The data processing was performed on a personal
computer (Dell: Optiplex GX280). Tension tests were conducted at about 25 °C and 25% ~ 55% relative
humidity.

                             CCD                                TESTING MACHINE
                            CAMERA




                                                                 PERSONAL COMPUTER




      Fig. 3 Picture of tensile testing machine equipped with optical extensometer and personal computer


4. RESULTS AND DISCUSSION

4.1 Effect of Specimen Shape and Size
  In an effort to examine the effect of specimen shape on paper properties, the stress-strain curves for copy
paper in MD from dumbbell-type specimen 5 and the constant-width strip specimen were measured and shown
in Fig.4. Before testing, a small pretension load of 1 N was applied to straighten the specimen. The dotted-solid
line indicates the stress-strain curve from the constant-width strip specimen whose strain was determined from
the crosshead movement. Comparison indicates that the constant-width strip specimen does not provide the
accurate stress-strain data when the deformation over the gage length is not measured using a non-contacting
extensometer. Typical stress-strain curves for copy paper in both MD and CD from dumbbell-type specimens 5
and 6 are given in Fig. 5. The size effect [3] is clearly observed, that is, the tensile strength of copy paper
greatly decreases, and the strain-to-fracture increases in CD with increasing specimen size. This is because of
the increased statistical probability of the occurrence of a failure-induced flaw in the specimen. Therefore, it is
required to evaluate fracture toughness of paper and paperboard from a fracture mechanics point of view.
Taking account of the actual size of paper and paperboard used, all the tensile stress-strain data shown in
Figures given below were obtained from the larger size of dumbbell-type specimen 5 of a 50 mm gage length.



  100                                                                      100
            COPY PAPER                         DUMBBELL (JIS SP.5)                   COPY PAPER                                         0
            t = 85µm                                 (GAGE MARK)                                                                       90   (CD)
   80                                          STRIP                       80        JIS Z 2201 SPECIMEN
               .
            55%. RH                                  (CLAMP DISP.)                   t = 85µm
                                                                                                                       : FRACTURE
                                                                                     55% RH
                                                                                                 No. 6             .       -3

   60
                                  : FRACTURE
                                                                           60
                                                                                                                   ε=10         /s
                                VCH= 3mm/min
                                                                                             No. 5
                                                         MD                                                        w = 15mm
                                                                                                                   GL = 25mm
   40                                                                      40                              No. 6

                                                                                                                            No. 5

   20                                                                                                                                w = 25mm
                                                                           20                                                        GL = 50mm



    0                                                                       0
        0              2        4         6              8           10          0           2          4              6                8          10
                           TENSILE STRAIN ε (%)                                                   TENSILE STRAIN       ε (%)
  Fig.4 Comparison of tensile stress-strain curves for                    Fig.5 Effect of specimen size on tensile stress-strain
 copy paper in MD from dumbbell type-specimen and                                 curves for copy paper in MD and CD
                    strip specimen


4.2 Effect of Test Direction
  Typical tensile stress-strain curves for paper and paperboard in three different test directions are shown in
Figs. 6 to 8. It is observed that Young’s modulus and tensile strength decrease, and the strain-to-fracture and
absorbed energy increase with increasing angle from MD. A large difference in paper tensile properties in
different test directions is due to the fact that machine-made paper and paperboard have more fibers aligned in
MD. The paperboard with the highest thickness has the lowest strength properties in each test direction. This is
because the fiber strength of paperboard is different from that of other two papers. The tensile data are
summarized in Table 2, where each value indicates the average and standard deviation of the five tests. The
tensile properties of UKP- sack paper in both MD and CD are consistent with those given in [4]. Figure 9 shows
fracture appearance of paper and paperboard specimens, indicating that fractures occurred inside the
extensometer gage length. Note that fractures in the 45 degree paper and paperboard specimens took place at
planes at around 15 deg to 40 deg to the loading axis, which do not suggest shear failure. The fracture direction
corresponds nearly to the CD direction in which less fibers are aligned.
100                                                                                            100
          COPY PAPER                                             0       (MD)                                  UKP-SACK PAPER                                          0        (MD)
          JIS Z 2201 SPECIMEN 5                                 45                                             JIS Z 2201 SPECIMEN 5                                   45
 80                                                                                              80
          t = 85µm                                                                                             t = 125µm
                                                                90       (CD)                                                                                          90       (CD)
          55% RH                                                                                               55% RH

                                          : FRACTURE                                                                                              : FRACTURE
 60                                   .                                                          60                                           .      -3
                                      ε=10   -3
                                                  /s (VCH= 3mm/min)                                                                           ε=10        /s (VCH= 3mm/min)


 40                                                                                              40



 20                                                                                              20



 0                                                                                                    0
      0            2              4                  6               8              10                    0                2              4                6                8          10

                          TENSILE STRAIN                ε (%)                                                                         TENSILE STRAIN           ε (%)
Fig. 6 Effect of test direction on tensile stress-strain                                              Fig. 7 Effect of test direction on tensile stress-
                curves for copy paper                                                                        strain curves for UKP-sack paper

                                           100
                                                          PAPERBOARD                                                   0       (MD)

                                                         JIS Z 2201 SPECIMEN 5                                        45
                                             80
                                                         t = 750µm                                                    90       (CD)
                                                         55% RH

                                                                                              : FRACTURE
                                             60                                           .      -3
                                                                                         ε=10         /s (VCH= 3mm/min)


                                             40



                                             20



                                              0
                                                    0                2              4                     6                8             10
                                                                            TENSILE STRAIN                    ε (%)
                                                           Fig. 8 Effect of test direction on tensile
                                                            stress-strain curves for paperboard



                                                                                                                                                                                -3
      Table 2 Summary of tensile properties of paper and paperboard tested at a strain rate of nearly 10 /s
                                                 in MD and CD

                                                         Young's modulus                                  Tensile strength        Strain-to   Tensile energy
                                                                                Proof strength                                    -fracture     absorption
                                                              (GPa)              σ 0.2 (MPa)                 σ (MPa)                ε f (%)              3
                                                                                                                                                  f (MJ/m )

                                          MD              6.54 0.64             34.8 3.8                  49.3 2.4               1.7 0.2      0.56 0.08
                       Copy paper
                                          CD              3.13 0.54             10.2 2.0                  25.3 1.6               6.3 0.7      1.18 0.18

                                          MD              7.74 0.75             35.2 3.4                  54.7 2.0               1.7 0.2      0.61 0.07
                   UKP-sack paper
                                          CD              2.71 0.13             13.0 2.7                  28.2 0.8               4.3 0.3      0.83 0.09

                                          MD              4.96 0.52             16.2 1.6                  30.3 0.6               1.9 0.2      0.38 0.05
                       Paperboard
                                          CD              1.44 0.16              6.8 1.3                  12.7 0.1               4.9 0.2      0.50 0.03
                                     COPY PAPER                               UKP-SACK PAPER                        PAPERBOARD

                                 MD      45             CD                  MD        45         CD               MD        45      CD




                    Fig. 9 Fracture appearance of dumbbell-type specimens of paper and paperboard



4.3 Effect of Moisture Content
The effect of moisture content [5] on the tensile stress-strain curves for the two types of paper in the three
different test directions is shown in Figs.10 and 11, respectively. It is found that the tensile strength greatly
increases and the strain-to-fracture decreases with decreasing moisture content from 55 % to 25% relative
humidity in each test direction. The decrease in moisture content has the same effect on paper tensile
properties as the increase in strain rate does.

  100                                                                                      100
           COPY PAPER
                                                                   0   (MD)
                                                                                                    UKP-SACK PAPER
                                                                                                    UKP-SACK PAPER                                      0    (MD)
           JIS Z 2201 SPECIMEN 5                                  45                                 JIS Z 2201 SPECIMEN 5                             45
  80                                                                                       80          JIS Z 2201 SPECIMEN 5
           t = 85µm                                               90   (CD)                          t = 125µm                                         90    (CD)
                                                                                                       t = 125µm
                        25% RH                                                                                 25% RH
                                                 : FRACTURE                                                                           : FRACTURE
  60                                                                                       60
                    55% RH
                         25% RH
                                               ε.=10   -3
                                                            /s (Vch = 3mm/min)                                    55% RH            ε.=10   -3
                                                                                                                                                 /s (Vch = 3mm/min)

                            55% RH                                                                                25% RH
                                      25% RH
  40                                                                                       40                              55% RH
                                                                                                                                    55% RH
                                                                                                                       25 25% RH
                                               55% RH
  20                                                                                       20


   0                                                                                        0
       0            2           4       6                          8             10             0             2          4        6                      8            10
                           TENSILE STRAIN          ε (%)                                                               TENSILE STRAIN            ε (%)
      Fig.10 Effect of moisture content on tensile                                                  Fig.11 Effect of moisture content on tensile
   stress-strain curves for copy paper in three test                                                stress- strain curves for UKP-sack paper in
                       directions                                                                                three test directions

4.4 Effect of Strain Rate
  In order to study the effect of strain rate on paper properties, the tensile stress-strain relations for copy paper
are determined at two different strain rates and shown in Fig. 12. Clearly, the deformation stress increases
slightly with increasing strain rate in both MD and CD, whereas the strain-to-fracture hardly varies with strain
rate. The similar strain rate dependence of the
                                                            100
deformation stress is reported in [3]. From Figs. 6 to 8,              COPY PAPER
                                                                                                                                                       0
it is conceivable that machine-made paper and                         JIS Z 2201 SPECIMEN 5                                                           90       (CD)
                                                             80
                                                                      t = 85µm
paperboard are sheet materials with orthotropic                       55% RH                                             : FRACTURE

anisotropy as well as viscoelasticity [6].                   60                   .      -2
                                                                                  ε=10        /s
                                                                                  .      -3
                                                                                  ε=10        /s
4.5 Fracture Resistance of Paper                             40
                                                                                                                                   .
   The resistance of paper to crack propagation in the                                                                         ε=10             -2
                                                                                                                                                     /s
                                                                                                                               .
tensile mode is an important sheet property, because         20                                                                ε=10        -3
                                                                                                                                                /s

of the presence of flaws or defects in the sheet.
 A
device for measuring fracture resistance is shown in         0
                                                                  0               2                   4                  6                                8            10
Fig.13. Two alignment rods are firmly attached to the                                            ε (%)
                                                                                         TENSILE STRAIN

lower clamp. The upper clamp moves on the                         Fig. 12 Effect of strain rate on tensile stress-strain
                                                                         curves for copy paper in MD and CD
alignment rods. These maintain parallelism between
the clamp faces during loading. Fracture resistance of

                                                            200
                                                                      COPY PAPER
                                                                                                                                                 0         (MD)
                                                                      t = 85µm                                                                  90         (CD)
                                                            150
                                                                                                                 VCH= 1mm/min

                                                                                                                     SEN SPECIMEN
                                                            100
                                                                                                                                                          a 0 = 33mm
                                                                                                                 l        a0
                                                                                      Δa= 12.4mm                                   b                      b = 100mm
                                                                                                                                                          l = 50mm
                                                            50
                                                                                                          Δa= 12.6mm


                                                              0
                                                                  0           0.5        1       1.5                                                                   2
                                                                           CROSSHEAD DISPLACEMENT δ (mm)

                                                                  Fig. 14 Typical tensile load-elongation curves for
                                                                  quasi-static crack propagation for copy paper in
                                                                                     MD and CD

                                                            200
                                                                      UKP-SACK PAPER
    Fig. 13 Picture of device for measuring fracture                                                                                             0            (MD)
                                                                      t = 125µm                                                                 90            (CD)
     resistance using single-edged specimen with
                                                            150
                  constant wide width                                                                            VCH= 1mm/min

                                                                                                   Δa= 20.7mm

     Table 3 Typical values of fracture resistance for      100                                               Δa= 19.5mm
     copy paper and UKP-sack paper in MD and CD                                                                          SEN SPECIMEN

                                                                                                                                                          a 0 = 33mm
                        Fracture resistance G c (kJ/m2)      50
                                                                                                                     l       a0                           b = 100mm
                                                                                                                                       b
                             MD              CD                                                                                                           l = 50mm

        Copy paper            9.1 (5)        14.2 (5)
                                                              0
                                                                  0                   0.5                    1                              1.5                        2
     UKP-sack paper          13.0 (5)        11.5 (5)
                                                                           CROSSHEAD DISPLACEMENT δ (mm)
    Note: figure in (   ) indicates the number of tests
                                                                      Fig. 15 Typical tensile load-elongation curves
                                                                        for quasi-static crack propagation for UKP-
                                                                               sack paper in MD and CD
copy paper and UKP-sack paper was evaluated on a single-edged notched (SEN) specimen with a100mm-
wide width, under the assumption of small scale yielding. It is accepted that fracture resistance depends on the
strip specimen geometry and the initial crack length to specimen width ratio ao/b. Following Seth’s article [7],
the crack length ratio ao/b was set to be 0.33. The initial crack was inserted into wide-width strip specimens on
the paper cutter. Typical tensile load-elongation relations from the SEN specimens of copy paper and UKP-
sack paper in both MD and CD are presented in Figs.14 and 15. The crack extension length ∆a was accurately
measured with an Image Sensor (Keyence: CV-3000). Fracture resistance is calculated by dividing the area
∆W under the tensile load-elongation curve by generated crack area. Typical values of fracture resistance for
the two papers are listed in Table 3. Note that Gc of copy paper is lower than that of UKP-sack paper in MD,
whereas Gc of copy paper is higher than that of UKP-sack paper in CD.


5. CONCLUSIONS

  The in-plane tensile stress-strain behavior and fracture resistance for copy paper, UKP-sack paper and
paperboard have been characterized in the testing machine equipped with the optical extensometer on the
dumbbell-type specimens and the SEN specimens. Tension tests and fracture resistance tests were performed
in both MD and CD. From the experimental results, we can draw the following conclusions:
   1.   The stress-strain characteristics are very sensitive to the specimen geometry and size.
   2.   The stress-strain characteristics are significantly affected by the strain rate and moisture content.
   3.   Machine-made paper and paperboard show orthotropic, anisotropic and viscoelastic behavior. The
        degree of anisotropy for them can be ranked as:
                              paperboard > UKP-sack paper > copy paper
   4.   Fracture resistance varies, depending on the type of paper as well as the test direction.


Acknowledgements

  This research program has been supported in part by a FY 2004 fund for Improvement of Private School
Facilities provided by the Ministry of Education, Culture, Sports, Science and Technology of Japan. We wish to
thank T. Odamura, Y. Yoshida and M. Terada for their technical assistance with the experimental work.


References

[1] JIS P 8113: JIS Handbook-32, Paper and Pulp, Japanese Standards Association, p. 218 (2003).
[2] JIS Z 2201: JIS Handbook-1, Steels, Japanese Standards Association, p. 121 (1994).
[3] Setterholm, V.C. and Kuenzi, E.W.: Method for determining tensile properties of paper, Tappi J., Vol. 40, No.
  6, 197A-204A (1957).
[4] Tanaka, A. and Yamauchi, T.: Crack propagation of paper under fracture toughness testing, J. Pack. Sci.
  Technol., Vol. 6, No. 6, 324-332 (1997).
[5] Benson, R.E.: Effects of relative humidity and temperature on tensile stress-strain properties of kraft
  linerboard, Tappi J., Vol. 54, No. 5, 699-703 (1971).
[6] Mark, R.E. (Editor): Handbook of Physical and Mechanical Testing of Paper and Paperboard, Vol. 1, Marcel
   Dekker Inc., New York, p. 255 (1983).
[7] Seth, R.S.: Measurement of fracture resistance of paper, Tappi J., Vol. 62, No. 7, 92-95 (1979).

				
DOCUMENT INFO