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Reply to comments on “Frictional properties of branched polyethylene I: The true area of contact”
383
another value of m being obtained, the new value is inadmissible as being outside the range 2 - 3 or being affected by experimental errors in replotting the data. The mode of polymer deformation for a normal load of 0.91 kgf is considered to be different from that for a load ten times greater (9.08 kgf). However, contrary findings were assumed in ref. 1.
1 P. J. Aird and B. W. Cherry, Frictional properties of branched polyethylene I: The true area of contact, Wear, 47 (1978) 231. 2 M. C. Shaw, A. Ber and P. A. Marvin, J. Basic Eng., 82 (1960) 342. 3 T. Wanheim, Wear, 25 (1973) 225. 4 F. P. Bowden and D. Tabor, Friction and Lubrication of Solids, Oxford Univ. Press: Clarendon Press, Oxford, 1950. 5 M. E. Merchant, interdisciplinary Approach to Friction and Wear, Proc. NASA Sponsored Symp., San Antonio, Texas, November 1967, p. 181. 6 I. Finnie and M. C. Shaw, Trans. ASME, 78 (1956) 1649. 7 S. Kobayashi and E. G. Thomsen, J. Eng. Znd., 82 (1960) 324. 8 J. F. Archard, Nature (London), 172 (1951) 918. 9 J. A. Greenwood and J. P. B. Williamson, Proc. R. Sot. London, Ser. A, 19 (1966) 295. 10 F. P. Bowden and D. Tabor, Br. J. Appl. Phys., I7 (1966) 1521. 11 S. C. Cohen and D. Tabor, Proc. R. Sot. London, Ser. A, 291 (1966) 186. 12 A. S. Lodge and H. G. Howell, Proc. Phys. Sot., London, Ser. B, 67 (1954) 89. 13 A. I. Bailey and J. S. Courtney-Pratt, F’roc. R. Sot. London, Ser. A, 277 (1955) 500. 14 N. Adams, J. Appl. Polym. Sci., 7 (1963) 2075. 15 F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Vol. 2, Oxford Univ. Press: Clarendon Press, Oxford, 1964. 16 P. J. Aird, M. Eng. Sci. Thesis, Monash Univ., Australia, 1976. 17 C. Rubenstein, Proc. Phys. Sot., London, Ser. B, 69 (1956) 921. (Received October 10, 1979)
M. ES. ABDEL MONEIM 5 Abdel Aziz Fahmy Street, Villa Abdel Moneim, Heliopolis, Cairo, Egypt
Reply to comments on “Frictional properties of branched polyethylene I: The true area of contact” We are very grateful to Abdel Moneim for his kind comments on the design of the apparatus for simultaneously determining the frictional force, the normal force and the apparent area of contact of a polymeric hemisphere and a glass substrate which we described in ref. 1. We must also thank him for giving us the opportunity to acknowledge, as we failed adequately to do in our original paper, that a collaborator in the original design of the apparatus was Dr. C. M. Pooley in the days when she was still Miss C. M. Holmes. Abdel Moneim expresses concern that we apparently treat the deformation of the polymer as viscoelastic and have second thoughts towards the end of the paper. Here we must apologize for having failed to make clear that one objective of our paper was to test whether the “working relation” (as it
384
was described
by Cohen and Tabor
[ 21)
d = fQW/~)llmJpm
(1)
adequately describes the relation between load and area of contact for a soft spherical indenter in contact with a rigid surface. It is for this reason that we adopted Cohen and Tabor’s definition (not our own) of hi and E as a dimensionless constant and an elastic modulus respectively. Our results are shown in Fig. 5 of ref. 1 and, as Abdel Moneim correctly points out, these points are just replotted in Fig. 6. It is of course unfortunate that the values of m deduced from the two plots differ and even lie outside the allowable range of 2 < m < 3. However, we believe that if we have to choose between our experimental results being wrong and eqn. (1) being wrong then our choice is the latter. We would point out that Cohen and Tabor considered it no more than a working relation and that it is one which assumes linear behaviour in the polymer, an assumption which cannot be justified under the circumstances of the deformation. A major cause of Abdel Moneim’s concern as to the correctness of our interpretation appears to stem from the fact that we assume that, even though P is less than 0.3, yield takes place away from the line of interfacial contact and that the apparent area of contact can be substituted for the true area of contact. Whilst we would venture to suggest that a later paper of ours [3] might add weight to the hypothesis that we have advanced, we would also like to make the point that it is possibly less than entirely obvious that one can argue by analogy with the behaviour of metals as Abdel Moneim has done that a coefficient of friction of 0.3 vitiates the possibility of yield away from the interface. Unlike such high surface energy solids as metals, polyethylene (yc = 30 mN mm-‘) may well not be contaminated by the surface layers which are necessary to explain the limitation to junction growth which prevents complete seizure in metals [4]. Consequently we find no conceptual problem in assuming that adhesion adequate to prevent interfacial shear can obtain in the experimental situation with which we are concerned. We conclude by thanking Abdel Moneim for his comments and apologize again for failing adequately to make clear that our object was not to use eqn. (1) but to find out whether there is evidence on which we could abuse it. 1 2 3 4
P. J. Aird and B. W. Cherry, Wear, 47 (1978) 231 - 241. S. C. Cohen and D. Tabor, Proc. R. Sot. London, Ser. A, 291 (1966) P. J. Aird and B. W. Cherry, Wear, 51 (1978) 147 - 155. F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Univ. Press: Clarendon Press, Oxford, 1964, p. 74.
(Received
December
14, 1979)
P. J. AIRD
186
- 207.
Vol. 2, Oxford
and B. W. CHERRY
Department of Materials Engineering, Monash University, Clay ton, Victoria, Australia
another value of m being obtained, the new value is inadmissible as being outside the range 2 - 3 or being affected by experimental errors in replotting the data. The mode of polymer deformation for a normal load of 0.91 kgf is considered to be different from that for a load ten times greater (9.08 kgf). However, contrary findings were assumed in ref. 1.
1 P. J. Aird and B. W. Cherry, Frictional properties of branched polyethylene I: The true area of contact, Wear, 47 (1978) 231. 2 M. C. Shaw, A. Ber and P. A. Marvin, J. Basic Eng., 82 (1960) 342. 3 T. Wanheim, Wear, 25 (1973) 225. 4 F. P. Bowden and D. Tabor, Friction and Lubrication of Solids, Oxford Univ. Press: Clarendon Press, Oxford, 1950. 5 M. E. Merchant, interdisciplinary Approach to Friction and Wear, Proc. NASA Sponsored Symp., San Antonio, Texas, November 1967, p. 181. 6 I. Finnie and M. C. Shaw, Trans. ASME, 78 (1956) 1649. 7 S. Kobayashi and E. G. Thomsen, J. Eng. Znd., 82 (1960) 324. 8 J. F. Archard, Nature (London), 172 (1951) 918. 9 J. A. Greenwood and J. P. B. Williamson, Proc. R. Sot. London, Ser. A, 19 (1966) 295. 10 F. P. Bowden and D. Tabor, Br. J. Appl. Phys., I7 (1966) 1521. 11 S. C. Cohen and D. Tabor, Proc. R. Sot. London, Ser. A, 291 (1966) 186. 12 A. S. Lodge and H. G. Howell, Proc. Phys. Sot., London, Ser. B, 67 (1954) 89. 13 A. I. Bailey and J. S. Courtney-Pratt, F’roc. R. Sot. London, Ser. A, 277 (1955) 500. 14 N. Adams, J. Appl. Polym. Sci., 7 (1963) 2075. 15 F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Vol. 2, Oxford Univ. Press: Clarendon Press, Oxford, 1964. 16 P. J. Aird, M. Eng. Sci. Thesis, Monash Univ., Australia, 1976. 17 C. Rubenstein, Proc. Phys. Sot., London, Ser. B, 69 (1956) 921. (Received October 10, 1979)
M. ES. ABDEL MONEIM 5 Abdel Aziz Fahmy Street, Villa Abdel Moneim, Heliopolis, Cairo, Egypt
Reply to comments on “Frictional properties of branched polyethylene I: The true area of contact” We are very grateful to Abdel Moneim for his kind comments on the design of the apparatus for simultaneously determining the frictional force, the normal force and the apparent area of contact of a polymeric hemisphere and a glass substrate which we described in ref. 1. We must also thank him for giving us the opportunity to acknowledge, as we failed adequately to do in our original paper, that a collaborator in the original design of the apparatus was Dr. C. M. Pooley in the days when she was still Miss C. M. Holmes. Abdel Moneim expresses concern that we apparently treat the deformation of the polymer as viscoelastic and have second thoughts towards the end of the paper. Here we must apologize for having failed to make clear that one objective of our paper was to test whether the “working relation” (as it
384
was described
by Cohen and Tabor
[ 21)
d = fQW/~)llmJpm
(1)
adequately describes the relation between load and area of contact for a soft spherical indenter in contact with a rigid surface. It is for this reason that we adopted Cohen and Tabor’s definition (not our own) of hi and E as a dimensionless constant and an elastic modulus respectively. Our results are shown in Fig. 5 of ref. 1 and, as Abdel Moneim correctly points out, these points are just replotted in Fig. 6. It is of course unfortunate that the values of m deduced from the two plots differ and even lie outside the allowable range of 2 < m < 3. However, we believe that if we have to choose between our experimental results being wrong and eqn. (1) being wrong then our choice is the latter. We would point out that Cohen and Tabor considered it no more than a working relation and that it is one which assumes linear behaviour in the polymer, an assumption which cannot be justified under the circumstances of the deformation. A major cause of Abdel Moneim’s concern as to the correctness of our interpretation appears to stem from the fact that we assume that, even though P is less than 0.3, yield takes place away from the line of interfacial contact and that the apparent area of contact can be substituted for the true area of contact. Whilst we would venture to suggest that a later paper of ours [3] might add weight to the hypothesis that we have advanced, we would also like to make the point that it is possibly less than entirely obvious that one can argue by analogy with the behaviour of metals as Abdel Moneim has done that a coefficient of friction of 0.3 vitiates the possibility of yield away from the interface. Unlike such high surface energy solids as metals, polyethylene (yc = 30 mN mm-‘) may well not be contaminated by the surface layers which are necessary to explain the limitation to junction growth which prevents complete seizure in metals [4]. Consequently we find no conceptual problem in assuming that adhesion adequate to prevent interfacial shear can obtain in the experimental situation with which we are concerned. We conclude by thanking Abdel Moneim for his comments and apologize again for failing adequately to make clear that our object was not to use eqn. (1) but to find out whether there is evidence on which we could abuse it. 1 2 3 4
P. J. Aird and B. W. Cherry, Wear, 47 (1978) 231 - 241. S. C. Cohen and D. Tabor, Proc. R. Sot. London, Ser. A, 291 (1966) P. J. Aird and B. W. Cherry, Wear, 51 (1978) 147 - 155. F. P. Bowden and D. Tabor, The Friction and Lubrication of Solids, Univ. Press: Clarendon Press, Oxford, 1964, p. 74.
(Received
December
14, 1979)
P. J. AIRD
186
- 207.
Vol. 2, Oxford
and B. W. CHERRY
Department of Materials Engineering, Monash University, Clay ton, Victoria, Australia