The Effect of the Difference between the Tensile and Compressive Properties on the Bending Behaviour of Nylon Mono-filaments1

Transcription

1 Bulletin of the Japanese Society of Scientific Fisheries 48(7), (1982) The Effect of the Difference between the Tensile and Compressive Properties on the Bending Behaviour of Nylon Mono-filaments1 Katsutaro YAMAMOTO *2 (Received November 11, 1981) The tensile and compressive tests were performed with the nylon mono-filament, and the different stress-strain curves in tension and compression were obtained from the tests. To estimate the effect of the difference between the tensile and compressive properties on the bending behaviour, the stress-strain curve was approximated with two type broken lines, and then the extents of the shift of the neutral axis and the bending moments were calculated to various bending curvature, respectively. The calculated results of the bending moment agreed closely with the results of the bending tests of the same material. Fishing gears receive various types of external forces during the time of hanging, operating or setting them. And then the twine, which com poses the large part of a fishing gear, is deformed by the force. This force-deformation behaviour of the twine is related deeply to the strength and the catching ability of the fishing gear. Here, as a fundamental study to clarify these relations, mechanical properties of twines shall be investi gated in connection with stress-strain properties of filament materials. In the theory of elasticity, it is usually defined that a linear relationship is established between the stress and strain in certain limited extents, and the many problems of the elastic matter are analyzed under this definition. However, be cause the external force acting on the filament as a structural element of the twine usually exceeds such a limit, the linear relationship between the stress and the strain may no longer exist. And further, it is expected that the tensile and com pressive moduli in the stress-strain curve are not equal. In such a non-linear relationship, formulae in the theory of elasticity cannot be used without alteration. In this paper, in order to investigate the effect of the difference between the tensile and compres sive properties of the bending behaviour, the tensile and compressive tests were performed with the nylon monofilament and the stress-strain curves were obtained from the tests. Especially, the stress-strain curve in compression, which is con sidered to be equal in tension, is obtained from the direct testing method. And the results of bending tests of the same material are explained using the stress-strain curve. Materials and Methods Both tensile and compressive tests were made on one thick nylon mono-filament, which was a commercial type about 2.01mm in diameter, at 60-65% r.h. and Ž. The nylon mono filament before testing was wound up in a coil about 20cm in diameter and stored in the dark. It was used for tests without special treatments. Tensile Tests The tensile tester used was an Instron type Shimadzu Auto-graph 2000 with the load cell. Nylon mono-filament was cut in suitable length as samples. The one end of the sample was directly held in a upper flat chuck of the tester, the other end was applied with a load of 895g to prevent loosing, and the middle of the sample was held in a lower flat chuck. Because the effect of chucks on the elongation of samples is unknown, the change of chuck dis tance is not equal to the true elongation of the sample. To avoid this difficulty, the initial dis tance between the chucks were set to be 100mm, 200mm and 300mm. The difference between the elongation of samples due to the chuck dis tances, therefore, was equal to the elongation of a sample of length =100 mm, = 100mm or =200mm. The tensile

2 888 YAMAMOTO speeds were selected to obtain a same strain speed (0.83% per sec), i.e., 50mm/min at the chuck distance 100mm, 100mm/min at 200mm and 150mm/min at 300mm, respectively. Tensile tests were made on 5 samples every three chuck distances, i.e., total number was 15 samples. Compressive Tests The compressive test of textile fiber is a small in number in comparison with the tensile test, and there are a few compressive stress-strain curves obtained from the direct measurement of fiber axial compression. These circumstances arise from the following three main reasons: 1) it is a most difficult to exclude buckling the sample with a sufficiently large height/diameter ratio, 2) an accuracy of measuring the small elongations or loads, therefore, is not satisfactory, 3) the end effect of bearing surfaces on the sample deforma tions cannot be estimated exactly. For the above reasons, the compressive property is considered to be equal to the tensile one and the stress-strain curve is assumed to behave identically in tension and compression. BACKER1) obtained the compressive stressstrain curves of the nylon and polyethylene mono filaments by direct measurements, and he derived the initial compressive moduli from the curves. The values appeared to be stringly influenced by the height/diameter ratio of samples. And the values were generally below that of the tensile modulus but approaching it as the ratio was increased. MILES2) has taken the compression measurements of the nylon mono-filament and reported a difference between the stress-strain curves in tension and in compression. ELDER3) investigated the initial tensile and compressive moduli of the nylon, polyethylene, polypropylene, polyvinylidence choride and polyester mono filaments. The values showed very little varia tion for the same material. In this sudy, according to MILES,2) the samples were made in the following manner. Namely, holes were drilled in three plastic plates (about 3.3, 2.1, 1.3mm thickness) with a diameter allow ing a tight fit when the filament was inserted in it. The samples were inserted in several holes and roughly cut off at the surface of the plate by a sharp blade knife, and then the two surface of the plate and sample were carefully ground by a whetstone. The small cylindrical samples were then pushed out from the plate. The sample length, depending on the amount of grinding, Fig. 1. Compressive testing device. Fig. 2. Bending form of the mono-filament and the measured lengths of a and 2b. F is the bending load and P is the maximum bending point. lied in the range from 3.25 to 3.29mm (height/ diameter was about 1.6), 2.05 to 2.09mm (1.0) and 1.42 to 1.49mm (0.7), respectively. Tests were done by the simple device of a flat vice and a load cell as shown in Fig. 1. The sample was sandwiched in between; two iron plates of the vice and the load cell, without a treatment of lubrication, and was the load applied by steps. The shrinkages of the sample were measured by a travelling micro-scope. Bending Tests Tests were done by the same device used in compressive tests. The filament was cut off at a length of 30 mm to 120 mm, as were the samples. The sample was held between two iron plates and a load was applied in order to create a bending situation as shown in Fig. 2, and the lengths of a and 2b were measured by the travelling micro scope. Results Tensile Behaviour and Discussions Tensile stress-strain curve derived from the

3 Bending Behaviour of Nylon Mono-filaments 889 sive curve is parallel to the strain axis and the stress cannot exceed 6.7kg/mm2. These striking differences between the tensile and compressive behaviour of the nylon mono filament indicate that the theory of elasticity will not apply to the mechanical properties of nylon twines. Bending Behaviour Bending monent M was calculated by the following equation, M=F ~a, (1) the radius of curvature p at bending maximum point P, because the bending form is approximated to be a semi-ellipse, was determined by ĕ b2 ^ Fig. 3. Tensile stress-strain curve of the nylon mono filament used. tensile load-elongation curves is shown in Fig. 3. Each circle point is an average of 15 samples and a cross mark shows a breaking point. Compressive Behaviour Compressive stress-strain curve is shown in Fig. 4 with the tensile curve for comparison. In the curve, the marks present the difference of height/diameter ratio of the samples, but although they differ from BACKER'S results, there is no remarkable difference between them. The present compressive stress-strain curve is in the similar form as MILES' results; namely, until about a 1% strain the compressive curve overlaps the tensile curve but above a 1% strain the curves are clearly different. At about a 16 strain, without a precise yield point, the compres a (2) where F is the bending load, a the length of major axis and b the length of minor axis; these values being measured in bending tests. Substituting M and p obtained from the above Eqs. (1) and (2) into the formulae in the simple bending theory of elastic isotropic matters, the bending stress and strain were calculated. The results are shown in Fig. 5 as a bending stress strain curve, in which the tensile curve is also drawn. Simple bending is considered to be a pheno menon of the tension and compression along the filament axis.therefore, if the tensile property is equal to the compressive one and the tensile stress-strain curve is expressed as a straight line as an elastic isotropic matter, the bending stress strain curve must be equal to the tensile curve. Surely, FREESTON and PLATT,4) in the study of filament bending recovery, assumed that the Fig. 4. Comparison of the tensile and compressive stress-strain curves of the nylon mono-filamen t used.

4 Pn= 890 YAMAMOTO filament behaved in the same manner in compres sion as in tension. However, the stressstrain curve of visco-elastis matter as nylon does not only give a straight line but also the moduli in tension and compression are not equal. It is natural that the bending stress-strain curve ac cording to the simple bending theory of elasticity, as in Fig. 5, does not agree with the tensile stress strain curve. BACKER,1) MILES,2) CHAPMAN5) and LAMB et al.8) suggested that, if the compres sive modulus differs from the tensile modulus, a neutral axis will no longer lie at the center of the bending cross-section. Especially, LAMB et al. have calculated the extent of the shift of neutral axis in the works of bending recovery of single filaments. Here, according to the method of LAMS et al., the above results of bending tests will be explained theoretically by the shift of neutral axis, and the extent of the shift will be calculated from the stress. strain curve to be approximated with straight lines of two difference types. 1. a-type approximation If the stress-strait curve is lineally approximated as shown in Fig 6(a), called a-type approximation, the stress dis. tribution in the circular cross-section may be presented as in Fig. 6(b). For convenience, let p R=y and ƒå R= ƒï, and let the positions of neutral axis be yn and the broken point of two straight'lines y* and also let the coressponding position ratios be pn and p* respectively. Then the force equilibrium in this cross-section can be written as the following equation 2ER2/ƒÅ+p{ ç1p* ( p-pn)(1-p2)1/2dp +a çp*-1 (P-P*)(1-p2)1/2dp +(P*-Pn) çp*-1(1-p2)1/2dp}=0, (3) where ƒ is a gradient ratio of two straight lines (=ratio of compressive modulus to tensile modulus) and E is a gradient of straight line in tension (=YOUNG'S modulus). When the integrations are carried out, this becomes 2/ƒÎ(1-ƒ )[ƒî/p*+1/3(1-p*2)3/2 +1/2P*{P*(1-P*2)1/2+sin-1p*}]. (4) Eq. (4), if p* is considered as a constant, is a linear equation for ƒ. Fig. 7 is the pn -ƒ curves Fig. 5. Comparison of the tensile and bending stress strain curves of the nylon mono-filament used. The stresses were determined by the simple bending theory of elastic isotropic matters. obtained by inserting the difference values of P* from -1 to 1 into Eq. (4). And, the strain ƒã* at the broken point is related to pn, p* and ƒå by the following equation Fig. 6. a-type approximation. Linear model of stress-strain behaviour (a) and stress distribution in the bending cross-section of a mono-filament (b).

5 Bending Behaviour of Nylon Mono-filaments b-type approximation Next, in the same manner as LAMB et al., if the stress-strain curve is lineally approximated with three straight lines connecting at two broken points as shown in Fig. 8 (a), this is called b-type approximation, the stress distribution in the circular cross-section may be presented as in Fig. 8(b), in which y* is the posi tion of the yield strain ƒã* and the stresses at range of y from -R to y* are constant. Fig. 7. Relations between p,n and a with various P* in the case of a-type approximation. ƒã*= P*-Pn/ƒÅ+Pn (5) Therefore, after solving the force equilibrium equation in much the same way as a-type approxi mation, the gradient ratio ƒ (=intial modulus ratio of compression to tension) is given by the following equation Since the values of ƒ, P* and ƒã* are able to be known from the stress-strain curve of a given material, the relation between the magnitude of where (8) bending curvature rj and the corresponding posi tion ratio of neutral axis pn, after deciding the value of pn by Eq. (4), is obtained from Eq. (5). On the other hand, the bending moment M in this section is given by (9) This equation is identical to LAMB'S equation (8)6) except the sign of p*. Fig. 9 shows pn -ƒ curves calculated from Eq. (8) by inserting the values ofp*. Since the relation among ƒã*, P*, ƒå and Pn is also presented by Eq. (5) in this case, the relation between ƒå and pn can be seen. The bending moment M is given by the follow Solving, this becomes ing equation (10) where Fig. 8. b-type approximation. Linear model of the stress-strain behaviour (a) and stress distribu tion in the bending cross-section of a mono-filament (b).

6 892 YAMAMOTO (11) Now, the results of the present bending tests for the nylon monofilament will be considered in relation to the shift of neutral axis. In Table 1, the values of E, a and a*, under the stress-strain curve of the nylon mono-filament was made by approximating the above two type broken lines, which are presented respectively. Using the Fig. 11. Relations between the bending moment M and the magnitude of bending curvature ƒå in the present bending tests of the nylon mono-filament. values in Table 1, the position ratio of neutral axis pn. to the various bending curvature ƒå was calculated for a- and b-type approximations. Fig. 9. Relations between pn and ƒ with various p* in the case of b-type approximation. Table 1. The values of E, a and ƒã* in a- and b-type approximations for the nylon mono-filament used The results are shown as pn-ƒå) curves in Fig. 10. And, using this relation between pn and ƒå, the bending moment M was calculated by Eqs. (7) and (10). The results are shown as M-ƒÅ cuvres in Fig. 11. But the values of the moment were already corrected by the initial curvature of sample about ƒï= 100mm, i.e., the correct moment values were 1.74 kg Emm for a-type and 1.36kg Emm for b-type approximation. In Fig. 11, both M-ƒÅ curves are almost in agreement with the experimented points,' but in a small range of ƒå the approximation of b-type is in good agreement with the points and in a large part of ƒå the approximation of a-type is good. The question of which type selection shall be de cided from the magnitude of bending curvature From the above evidences, it is clear that the difference between the tensile and compressive properties of materials have direct effects upon the simple bending behaviour, and the striking feature due to the difference is represented as a shift of neutral axis. In the present bending tests of the nylon mono-filament, the bending moments which were calculated with the con sideration of the shift of neutral axis are in good. Fig. 10. Relations between p. and ƒå in a- and b-type approximations for the nylon mono-filament used. agreement with the experimental values. And also it is suggested that the stress-strain curve in compression of materials, which is rarely ever

7 Bending Behaviour of Nylon Mono-filaments 893 presented, is as essential as the stress-strain curve in tension to clarify the mechanical properties of twines. Acknowledgements The author is grateful to Dr. 0. SATO and Dr. K. NASHIMOTO (Faculty of Fisheries, Hokkaido University) for their suggestions and reviewing the manuscript. References 1) S. BACKER: Text. Res. J., 30, (1960). 2) J. B. MiLEs: Text. Res. J., 30, (1960). 3) H. M. ELDER: J. Text. Inst., 57, T8-T14 (1966). 4) W. D. FREESToN ad M. M. PLATT: Text. Res. J., 34, (1964). 5) B. M. CHARMAN: J. Text. Inst., 64, (1973). 6) G. E. R. LAMB, R. H. BUTLER, and D. C. PREVORSEK: Text. Res. J., 45, (1975).