TENSILE STRENGTH, BREAKING LENGTH, TENSILE INDEX, STRETCH, TENSILE ENERGY ABSORPTION, AND TENSILE STIFFNESS

IntroductionTensile strength: The tensile strength of paper is measured by

applying a tensile force parallel to the plane of the paper and great enough to induce failure or rupture. In the case of paper or other thin webs, tensile strength is then defined as the breaking force (load) per standard width of the specimen; in the present experiment, for example, the tensile strength of paper is determined in units of kN/m. This practice differs from that adopted in other engineering fields and material science where one defines the tensile strength as breaking force per unit cross-sectional area.

The tensile strength of paper and paperboard, being defined as the breaking force per standard width, will still depend on basis weight. All else being the same, the tensile strength will be greater for paper of higher basis weight. Tensile strength is, therefore, not a material property and tells us nothing about the inherent strength of a particular paper grade. A simple measure of inherent strength is obtained by dividing tensile strength by basis weight. In this way we get the tensile strength per unit basis weight. Different paper grades can be compared on this basis as to their inherent strength.

Breaking length: It turns out that this quantity, the tensile strength per unit basis weight, has the significance of "breaking length". The notion of breaking length is as follows. Imagine a paper strip so long that its weight equals its tensile strength. Such a strip, if vertically suspended from one end, would break of its own weight. The length of this strip is called the breaking length of the paper.

Breaking length is generally used in the paper trade to characterize the inherent strength of paper. It affords an excellent basis for comparing the strength of papers made from different furnishes and having different

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basis weight.The tensile tester used in this course, the "Alwetron TH-1" of

Lorentzen and Wettre (Sweden), automatically calculates the breaking length and prints it out in units of km.

Tensile index: The tensile index is also a measure of inherent strength of paper and is similar to the notion of breaking length. Although it does not have quite the graphic significance that breaking length has, the tensile index has been increasingly used in the literature following the conversion to SI units. The tensile index is calculated according to

The tensile index is neither calculated nor printed out by the tensile instrument. One easily obtains the tensile index, however, by multiplying the breaking length, given in km, by 9.81 (Nm/gf)/km.

Stretch: The percentage elongation of a paper at the instant of failure is called stretch. Stretch is measured in this experiment at the same time the tensile strength is determined. A paper specimen of initial span l0 will increase in length when a tensile force acts on it. Suppose that, at the instant the specimen breaks, its length has increased to l0 + ΔlB. Then the percent elongation at failure, or stretch, will be ( ΔlB / l0 ) 100. Papers differ greatly in the amount of stretch they will undergo when stressed to failure. Rather rigid papers such as glassine and bond paper have low stretch, typically 2%. Compliant papers such as creped paper have relatively high stretch, often more than 10%.

Tensile energy absorption (TEA): In a tensile test, the tensile force applied to the specimen is steadily increased. At the same time, the specimen elongates under the influence of this tensile force. It is clear that work is being done on the specimen. The work done up to the instant of tensile failure is called the "work to rupture". Let the tensile specimen have

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initial span l0 and width b. One then defines the tensile energy absorption (TEA) as

Thus, TEA is the work to rupture per unit lateral area of the specimen.The TEA is automatically computed and printed out by the instrument,

in units of Joule/m2. The printout uses the term "work" instead of TEA.Tensile stiffness: The instrument also determines the tensile stiffness,

D. With reference to Figure 1, this can be defined as follows. Shown in Figure 1 is a typical curve of tension T (tensile force divided by specimen width) versus strain ε (relative elongation, Δl/l0). Notice the initial straight-line part of the curve. The tensile stiffness, D, is the slope, tan α, of this initial straight-line part. In mathematical language we have D = tan α, or

The tensile stiffness is printed out by the instrument in units of kN/m. Tensile stiffness is related to Young’s modulus, E, which we encountered above in our discussion of bending stiffness (see page 5 - 12):

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where t is the caliper. As t can be defined and measured only in an arbitrary way, paper technologists prefer to state Young’s modulus in length units, LE:

The ratio D/W can be obtained unequivocally.

SignificanceThe breaking length is greatly influenced by the kind and quality of

the fiber constituents, by their pulping, bleaching, and refining pretreatment, and by the way the sheet is formed on the paper machine. Various additives to the furnish can affect breaking length dramatically.

Weak spots and defects such as slime spots, hair cuts, and calender cuts in the sample may initiate failure, but it is the lack of inherent strength in the structure that permits the crack to continue.

The tensile test is far superior to the bursting test in every way. The bursting strength is a complicated function of both tensile strength and stretch, lumping these different aspects of tensile behavior together in a confusing way. The tensile test, in addition to giving tensile strength and stretch separately, has the great advantage that it detects differences in the

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machine and cross direction of paper. Finally, modern tensile test equipment such as the Alwetron TH-1 is at least as easy and convenient to use as a burst tester.

Tensile strength correlates well with the durability and serviceability of many papers, such as bag, wrapping, gummed tape, and others subjected to direct tensile stresses in converting or in use. In printing papers, tensile strength indicates the potential resistance to breaking when the web is subjected to tensile forces during travel from the roll through the press mechanism in the web-fed printing systems.

High elongation to break together with low bending stiffness is indicative of the ability of paper to conform to a desired contour and therefore is important for creped papers, towels, and bagging.

High TEA is particularly important in shippping sack papers. The greater the TEA, the more likely a sack filled with cement or the like will survive intact when dropped from a certain height.

Young’s modulus, and therefore tensile stiffness, have an effect on bending stiffness, see equation (1) on page 5 - 12. In bond paper, the desirable “rattle” is largely due to high tensile stiffness. Tensile stiffness is also important because it is related to the performance of paper and board in many converting operations.

Outline of the Test ProceduresGiven below are two different test procedures, and both have been

stored in computer memory as programs that can readily be called up and used.

The first, program # 55, is used for testing machine-made paper and board and incorporates all the recommendations of TAPPI standard T-494 (“Tensile breaking properties of paper and paperboard, using constant rate

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of elongation apparatus”): The width of the sample strip must be 1 inch; the span, i.e. the initial length of the specimen between clamps, must be 180 mm; the clamp speed has been programed for 25 mm/min.

The second, program # 100, is used for testing handsheets. Accordingly, the recommendations of TAPPI standard T-220 (“Physical testing of pulp handsheets”) have been included in this program: The width of the sample strip must be 15 mm; the span must be 100 mm; and the clamp speed is 25 mm/min.

Clearly, these two programs should not be confused with one another.The general test procedure is quite similar in both programs,

consisting of a preliminary test to be done on one sample strip, and the actual test series to be done on n sample strips. The purpose of the preliminary test is to obtain a good estimate of the breaking force of the sample. Based on this result, optimal test parameters can then be determined for the actual test series.

TAPPI standard T-494 for machine-made paper and board stipulates that in the actual test series, n=10 strips be tested in either principal direction. In this course, however, only five strips should be tested in either direction so as to conserve sample. This means that you should cut six strips in MD (one for the preliminary test and 5 for the actual test series) and six strips in CD. The strip width should be 1 inch, the length at least 230 mm.

TAPPI standard T-220 for handsheets requires that 5 n 10. Using six strips for tensile testing, you have one strip for the preliminary test and five strips for the actual test series. As noted above, the strip width is 15 mm.

Reject readings from individual strips if the strip slips in the jaws or breaks within the clamping area.

Turn on the power to the Alwetron TH-1 by pushing the toggle switch

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on the rear panel from "0" (off-position) to "1" (on-position). Allow 30 minutes for warm up. Notice that this instrument has a load limit of 1 kN and a basis weight limit of 500 gf/m 2 . The clamp pressure of the instrument can be adjusted. Normally, use 0.5 M Pa as indicated on the outer black scale of the pressure gage located under the printer on the left-hand side of the instrument’s front panel. As you begin testing, the window display initially shows "Program rev. 6.5". To proceed, the operator must press the key "YES" on the keyboard. The entire measurement procedure consists of a dialog between instrument and operator. The instrument poses questions that are displayed in the window, and the operator responds by pressing appropriate keys and by inserting specimens at certain stages of the procedure.

Test Procedure for Machine-Made Paper and Board, Program #55

Preliminary test with one sample in either direction:

STEP WINDOW DISPLAY PRESSKEY

COMMENT

1 Program rev. 6.5_ YES

2 PAPER IN PRINTER?_ YES The clamp moves; wait until it stops.

3 CHOOSE PROGRAM_ PF2

4 SPEC No ?_ 55

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5 SPEC No ? 55_ YES

6 No OF TEST PIECES?_ 1

7 No OF TEST PIECES? 1_ YES

8 trig F % ?_ 0 Set 0 for preliminary test only.

9 trig F %? 0_ YES

10 delta F %?_ 0 Set 0 for preliminary test only.

11 delta F %? 0_ YES

12 RESOLUTION micro meter?_ 10

13 RESOLUTION micro meter? 10_ YES

14 GAIN 1?_ YES

15 STIFFNESS EVALUATION?_ NO In the preliminary test NO.

16 GRAMMAGE g/m2 ?_ W Enter the grammage W of your sample.

17 GRAMMAGE g/m2 ? W_ YES

18 SAMPLE No ?_ nnn Assign an identifying number to your sample and enter it here.

19 SAMPLE No ? nnn YES

20 * MACHINE DIRECTION?_ YES

21 TEST PIECE No 1 ?_ YES Insert your sample between the clamps before you press “YES”. Upon pressing “YES”, the tensile test starts.

22 F=6.018k I=1.69 W=60.49 t=7.5 OK?_ YES/NO After the sample has broken, the window dis-plays data such as those shown at the left.F is papermaker’s tensile strength in kN/m.I is the stretch in %.W is the tensile energy absorption in J/m2.t is the time to rupture in seconds.On pressing YES (accept) or NO (reject), the MD data are printed out.

23 * CROSS DIRECTION ?_ YES

24 TEST PIECE No 1 ?_ YES Insert your sample between the clamps before you press “YES”. Upon pressing “YES”, the tensile test starts.

25 F=5.703 k I=1.67 W=57.15 t=7.4 OK ?_

YES/NO On pressing YES (accept) or NO (reject), the CD data are printed out. This completes the preliminary test.

26 No OF TEST PIECES ?_ The instrument has returned to step 6 and is ready for the actual test.

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This concludes the preliminary test. A comment on steps 22 and 25 is in order. Notice that the window displays, in addition to certain test data, the question “OK?”. The meaning of this question is this: Do you, the operator, accept this test as valid or not? If the sample slipped or broke in the clamp, reject the test as invalid and press the NO key; otherwise, press YES. The data of a rejected test are printed out but not used in the calculation of average values for tensile strength, stretch, etc.

Before continuing, you should now calculate the parameter values to be entered in the course of the actual test.

First, on the printout obtained during the preliminary test, find the breaking force for both the machine direction and the cross direction. On the printout, the breaking force is designated Fmax and given in Newtons (N). Choose the greater of the two forces. Determine a gain factor (GF) for the actual test according to the following rule:

Fmax, N Gain Factor250 to 1000 1125 to 250 40 to 125 8

Next, calculate the parameters P1 and P2 as follows:

P1 = Fmax / 500 (5)P2 = 0.018 Fmax (6)

You are now ready to continue with the actual test, outlined below.

Actual test with n samples in each direction:

STEP WINDOW DISPLAY PRESSKEY

COMMENT

26 No OF TEST PIECES?_ n Enter the number of samples, n, to be tested in either direction.

27 No OF TEST PIECES? n_ YES

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28 trig F % ?_ P1 Enter the value calculated according to equation (5).

29 trig F %? P1_ YES

30 delta F %?_ P2 Enter the value calculated according toequation (6).

31 delta F %? P2_ YES

32 RESOLUTION micro meter?_ 10

33 RESOLUTION micro meter? 10_ YES

34 GAIN 1?_ YES/NO When the gain factor determined above appears in the window, press “YES”.Otherwise, press “NO”.35 GAIN 4?_ YES/NO

36 GAIN 8?_ YES/NO

37 STIFFNESS EVALUATION?_ YES/NO Decide whether or not you wish to obtain the tensile stiffness. If you decide against it and press “NO”, then statements # 38 to 41 will not appear in the display window.

38 dF/dL LOWER END % ?_ 2

39 dF/dL LOWER END % ? 2 _ YES

40 STIFFNESS POINTS ?_ 18 The value 18 is predicated on a resolution of10 μ. In general, enter 180/(resolution in μ).

41 STIFFNESS POINTS ? 18_ YES

42 GRAMMAGE g/m2 ?_ W Enter the grammage W of your sample.

43 GRAMMAGE g/m2 ? W_ YES

44 SAMPLE No ?_ nnn Assign an identifying number to your sample and enter it here.

45 SAMPLE No ? nnn YES

46 * MACHINE DIRECTION?_ YES

47 TEST PIECE No 1 ?_ YES Insert your sample between the clamps before you press “YES”. Upon pressing “YES”, the tensile test starts.

48 F=6.018k I=1.69 W=60.49 t=7.5 OK?_ YES/NO After the sample has broken, decide whether you accept (“YES”) or reject (“NO”) the test. The window displays data such as those shown at the left, whereF is papermaker’s tensile strength in kN/m;I is the stretch in %;W is the tensile energy absorption in J/m2;t is the time to rupture in seconds.

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On pressing YES/NO, these data and others are immediately printed out.

49 TEST PIECE No 2 ?_ YES Insert your sample between the clamps before you press “YES”. Upon pressing “YES”, the tensile test starts.

50 F=5.98k I=1.73 W=63.71 t=7.4 OK?_ YES/NO

Continue until n samples have been tested in the machine direction.

51 * CROSS DIRECTION ?_ YES

52 TEST PIECE No 1 ?_ YES Insert your sample between the clamps before you press “YES”.

53 F=5.703 k I=1.67 W=57.15 t=7.4 OK ?_

YES/NO

Continue until n samples have been tested in the cross direction.

Upon completion of all tests, the means, coefficients of variation, values of the set of parameters chosen for the test, sample number, and program number are printed out.

54 No OF TEST PIECES ?_ The instrument has returned to step 6 of the program. You can run a new sample, first the preliminary test, then the actual test.

This completes the test procedure for machine-made paper.If at any stage of testing the instrument functions in unexpected ways,

see the last section on “Contingencies”.

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Test Procedure for Handsheets, Program #100

Preliminary test with one sample:

STEP WINDOW DISPLAY PRESSKEY

COMMENT

1 Program rev. 6.5_ YES

2 PAPER IN PRINTER?_ YES The clamp moves; wait until it stops.

3 CHOOSE PROGRAM_ PF2

4 SPEC No ?_ 100

5 SPEC No ? 100_ YES

6 No OF TEST PIECES?_ 1

7 No OF TEST PIECES? 1_ YES

8 trig F % ?_ 0 Set 0 for preliminary test only.

9 trig F %? 0_ YES

10 delta F %?_ 0 Set 0 for preliminary test only.

11 delta F %? 0_ YES

12 RESOLUTION micro meter?_ 10

13 RESOLUTION micro meter? 10_ YES

14 GAIN 1?_ YES

15 STIFFNESS EVALUATION?_ NO In the preliminary test NO.

16 GRAMMAGE g/m2 ?_ W Enter the grammage W of your sample.

17 GRAMMAGE g/m2 ? W_ YES

18 SAMPLE No ?_ nnn Assign an identifying number to your sample and enter it here.

19 SAMPLE No ? nnn YES

20 TEST PIECE No 1 ?_ YES Insert your sample between the clamps before you press “YES”. Upon pressing “YES”, the tensile test starts.

21 F=6.018k I=1.69 W=60.49 t=7.5 OK?_ YES/NO After the sample has broken, the window dis-plays data such as those shown at the left.F is papermaker’s tensile strength in kN/m.I is the stretch in %.W is the tensile energy absorption in J/m2.t is the time to rupture in seconds.On pressing YES (accept) or NO (reject), the data are printed out.

22 No OF TEST PIECES ?_ The instrument has returned to step 6 and is ready for the actual test.

This concludes the preliminary test. Before continuing, you should now calculate the parameter values to be entered in the course of the actual test.

First, on the printout obtained during the preliminary test, find the breaking force, which is designated Fmax and given in Newtons (N). Determine a gain factor (GF) for the actual test according to the following rule:

Fmax, N Gain Factor250 to 1000 1125 to 250 40 to 125 8

Next, calculate the parameters P1 and P2 according to equations (5) and (6), which are repeated here for convenience:

P1 = Fmax / 500 (5)P2 = 0.018 Fmax (6)

You are now ready to continue with the actual test, outlined below.

Actual test with n samples:

STEP WINDOW DISPLAY PRESSKEY

COMMENT

24 No OF TEST PIECES?_ n Enter the number of samples, n, to be tested.

25 No OF TEST PIECES? n_ YES

26 trig F % ?_ P1 Enter the value calculated according toequation (5).

27 trig F %? P1_ YES

28 delta F %?_ P2 Enter the value calculated according toequation (6).

29 delta F %? P2_ YES

30 RESOLUTION micro meter?_ 10

31 RESOLUTION micro meter? 10_ YES

32 GAIN 1?_ YES/NO When the gain factor determined above appears in the window, press “YES”.Otherwise, press “NO”.33 GAIN 4?_ YES/NO

34 GAIN 8?_ YES/NO

35 STIFFNESS EVALUATION?_ YES/NO Decide whether or not you wish to obtain the tensile stiffness. If you decide against it and press “NO”, then statements # 36 to 39 will not appear in the display window.

36 dF/dL LOWER END % ?_ 2

37 dF/dL LOWER END % ? 2 _ YES

38 STIFFNESS POINTS ?_ 10 The value 10 is predicated on a resolution of10 μ. In general, enter 100/(resolution in μ).

39 STIFFNESS POINTS ? 10_ YES

40 GRAMMAGE g/m2 ?_ W Enter the grammage W of your sample.

41 GRAMMAGE g/m2 ? W_ YES

42 SAMPLE No ?_ nnn Assign an identifying number to your sample and enter it here.

43 SAMPLE No ? nnn YES

44 TEST PIECE No 1 ?_ YES Insert your sample between the clamps before you press “YES”. Upon pressing “YES”, the tensile

test starts.

45 F=6.018k I=1.69 W=60.49 t=7.5 OK?_ YES/NO After the sample has broken, decide whether you accept (“YES”) or reject (“NO”) the test. The window displays data such as those shown at the left, whereF is papermaker’s tensile strength in kN/m;I is the stretch in %;W is the tensile energy absorption in J/m2;t is the time to rupture in seconds.On pressing YES/NO, these data and others are immediately printed out.

46 TEST PIECE No 2 ?_ YES Insert your sample between the clamps before you press “YES”. Upon pressing “YES”, the tensile test starts.

47 F=5.98k I=1.73 W=63.71 t=7.4 OK?_ YES/NO

Continue until n samples have been tested.

Upon completion of all tests, the means, coefficients of variation, values of the set of parameters chosen for the test, sample number, and program number are printed out.

48 No OF TEST PIECES ?_ The instrument has returned to step 6 of the program. You can run a new sample, first the preliminary test, then the actual test.

This completes the test procedure for handsheets.If at any stage of testing the instrument functions in unexpected ways,

see the section on “Contingencies” below.

ContingenciesWindow displays “OVERLOAD! RETURN?”

If you have chosen a gain factor of 1, this message means that your sample exceeds the load cell capacity of 1000 N. Such a sample cannot be tested on this instrument.

If you have chosen a gain factor of 4 or 8, the message means that your gain factor is too high and should be reduced: from 4 to 1, or from 8 to 4. In this case it is best to discontinue the present test series and start over. To do so, proceed as follows:

Window display Press key CommentOVERLOAD! RETURN? YES Data are printed out. Ignore these.TEST PIECE No x? CTRL + 9 Press both keys simultaneously.TEST PIECE No x? EXIT? YESSAVE AS SPEC No? NOPRINT SPECIFICATION? NOCHOOSE PROGRAM

As the last window display indicates, the instrument has returned to step 3 of either program # 55 or program # 100. You need not repeat the preliminary test. Instead, start over with the actual test, keeping the previous parameter estimates but using a lower gain factor.

You run out of sample before completing all n testsSuppose you had entered n=5 at the beginning of the actual test;

therefore, the instrument expects 5 accepted tests. Further suppose that in

the course of testing, the third sample broke in the clamp, so you rejected that test. If you don’t have enough paper or board left to cut another sample, you will have to exit after only four accepted tests. Here is how to accomplish this and obtain the average values on only four tests. The display window asks for TEST PIECE No 6, and you respond as follows:

Window display Press keyTEST PIECE No 6?_ NONo OF TEST PIECES?_

After you press NO, you immediately get all means and coefficients of variation printed out. With the display “No OF TEST PIECES?”, the instrument has returned to the beginning of the actual test and is ready for a new test series.

Error message: “WARNING: SOME POINTS NOT RECORDED”The condition indicated by this error message can occur if either your

sample has unusually high stretch or you have entered too small a “resolution”. The resolution of 10 suggested in the above programs should be adequate in most cases. If the error message does occur, then the remedy is to choose a greater resolution, perhaps 20.

Error message: “INTERNAL COMMUNICATION ERROR Z8 - 80"If this error message occurs, simply press the small red reset button

on the back panel. The instrument returns to the very beginning of the program, and you can start over.

ReportReport the average value of tensile strength in kN/m (kilonewtons per

meter) and in kgf/15 mm for both principal directions. Similarly, report the breaking length in km, the tensile index, the stretch in %, the tensile energy

absorption in J/m2 and lb/in, the tensile stiffness in kN/m, and LE in km. Also, give a 95% confidence interval for each mean. The 95% confidence interval for the breaking length, LB, and the other quantities that are indirectly determined should be obtained by the method of error propagation.

ReferencesTAPPI T 220TAPPI T 494