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Glassy polymers (plastics)
MEETINGS
ture has a direct bearing on the size effect so frequently observed in notch brittle tests. In large specimens the requisite strain may be accommodated in a local plastic zone, so that the specimen will fracture before general yield.
6. Crack propagation A crack probably requires less plastic flow, and hence a smaller tensile stress, for propagation than nucleation. The strain rate at the tip of a running crack must be very high, and at least in ferrous metals the yield stress is, as gtated abo~ze, sensitive to strain rate. Moreover, ahead of a crack there exist triaxial stresses, so that the material cannot flow as freely as in a plain tensile specimen under the same tensile stress. Thus higher tensile stresses --perhaps three times higher--can be supported without plastic flow and may be high enough to cause fracture. That triaxial stresses are sometime important is suggested by the fact that the fracture often becomes ductile where it intersects a free surface, at which the transverse stresses are zero and hence triaxiality disappears. REFERENCES J. R. Low, JR., The Fracture of Metals, Progress in Materials Science, Vol. 10, Pergamon, London. J. F. KNOTT A~D A. H. COTTRELL, Notch brittleness in mild steel, J. Iron Steel Inst., 201 (1963) 249.
IV. Glassy Polymers (Plastics) J. P. Berry
1. Structure and mechanical properties Polymers are characterised by a long-chain molecular structure in which identical repeating units are linked by covalent (usually carbon-carbon) bonds, i.e. they are organic compounds. The main variations in chemical structure, and hence properties, arise by changing the substituent in the vinyl monomer. The substituent then occurs on alternate carbon atoms in the polymer molecule. In the solid (glassy) state there are three types of molecular interaction : (i) directed covalent bonds between the chain atoms; (ii) non-directed forces--such as Van der Waals interaction, dipole association, hydrogen bonding, etc. ; (iii) molecular entanglements. The second and third types of interaction have
309
lower energies than the first, and at sufficiently high temperature (80°-150°C) the materials melt, but retain their long chain character in the fluid state. In the solid glassy state the molecules are randomly disposed and the mechanical properties are isotropic. The stress-strain curve is essentially linear to the fracture point, but because of the relatively low transition (softening) temperature, the properties are time and temperature dependent.
2. Application of the Griffith theory to glassy polymers The Griffith theory assumes that tensile strength is determined by the presence of flaws and that the ultimate stress is inversely proportional to the square root of flaw size. This conclusion has been checked for the glassy polymers poly(methylmethacrylate) and polystyrene by determining the tensile strength of samples containing inserted defects of known size. The proportionality constant yields a value for the energy for the formation of unit area of fracture surface (y) (2 × 105 ergs/cmZ), which is insensitive to changes in sample geometry, and (within limits) to testing rate. The same value of the parameter can be obtained by a cleavage experiment which involves an entirely different sample geometry and stress system, and hence it may be regarded as a material constant. The value of the constant increases by a factor of 5 over the temperature range + 50 to -200°C, and it is sensitive to changes in molecular characteristics. On introducing chemical cross links [into poly(methyl methacrylate)] the fracture surface energy is reduced by a factor of 4, and it shows a linear, (but not very strong) dependence on the reciprocal of molecular weight, in common with other mechanical properties. In experiments performed on pre-oriented samples the fracture surface energy is increased when the fracture is propagated normal to the direction of molecular orientation (× 5), and reduced when propagated in the direction of orientation, (× 0.1) compared with the results on conventional (unoriented) samples. In the experiments described the fracture surface energy is always much greater (× 10 3) than calculated from the molecular structure. The discrepancy is attributed to inelastic processes occurring at the tip of the flaw due to the local stress concentration, which results in the formation of a surface layer of structure different from the substrate. Deviation from the theoretical (Griffith] behaviour occurs at small inserted flaw sizes when the Mater. Sci. Eng., 1 (1966/67)296-311
310
MEETINGS
natural, adventitious flaws are of comparable size to those introduced artificially. In glassy polymers the natural flaw which initiates fracture in conventional samples arises from a craze. It is possible to define an inherent flaw size (Co) and this appears related to a material property, its tendency to develop crazes. Thus Co for poly(methyl methacrylate) is only about 1/20 of the value for polystyrene, a finding consistent with the difference in crazing propensity. On varying the temperature from + 50 to -200°C, the inherent flaw size [for poly(methyl methacrylate)] first decreases by a factor of 2 to its value at room temperature and then increases ( x 4) to its value at - 200°C. Crosslinking reduces Coby a factor of 3, and it is essentially independent of molecular weight. When a fracturing stress is applied to an oriented sample along the direction of orientation, the inherent flaw size is increased by a factor of 3. It appears therefore that the inherent flaw size varies in much the same way as the fracture surface energy as the experimental conditions are changed. This is due to the fact that the tensile strength is less sensitive to the experimental variables than the two parameters (~ and Co) which control it, according to the Griffith theory. Unfortunately there is no satisfactory independent method of characterizing Co in any quantitative sense.
3. Significance of v and Co (mechanism of fracture) Crazes are flat reflecting entities developed by imposed tensile stress, which persist after the removal of the stress. They are sharply bounded regions consisting of oriented molecules interspersed with about 50 ~ by volume of voids. As the imposed stress is increased they grow in size, presumably change in structure, and eventually lead to fracture. Examination of the initiation site on fracture surfaces (of polystyrene) gives direct evidence of the open structure of the craze from which that surface was generated. The layer of material on the fracture surface [of poly(methyl methacrylate)] gives rise to interference colours, and its refractive index (and presumably structure) is the same as that of a craze in the same material. Thus the mechanism of brittle fracture in glassy polymers seems to involve the formation and rupture of craze material. The fracture surface energy (V) is related to the energy dissipated in forming the craze material, by molecular orientation and void formation, and the inherent flaw size (Co)is related to the critical size of the craze
immediately prior to rupture. It is therefore not surprising that the two parameters show the same variations in value with changing experimental conditions and that the tensile strengths of the materials are likewise insensitive to those changes. The basic problems in the brittle fracture of polymers are concerned with the initiation, growth and changing structure of crazes, and in particular with defining the critical factors of size and structure that determine the onset of the mechanical instability that can be treated in terms of the Griffith theory. REFERENCES J. P. BERRY,Brittle behaviour of polymeric solids. Chapter IIB in B. ROSEN(ed.), Fracture Processes in Polymeric Solids, Interscience/Wiley, New York, 1964. R. P. KAMBOUR,Polymer, 4 (1963) 143. R. P. KAMBOtm, J. Polymer Sci., 3 (1965) 1713.
11". Format of the Meeting It is, of course, impossible to assess the success of the meeting in quantitative terms, or indeed to define precisely what constitutes "success". It appears, however, that the primary objective, which was to promote inter-disciplinary interaction, was achieved, to judge by the scope and vigour of the discussion. It is probable, though less certain, that the extent of the interaction was greater than it would have been had the meeting been organized on more conventional lines. On the other hand, no basically new ideas were proposed resulting from the synthesis of alternative points of view, although it is possible that such new ideas will be formulated subsequently. Although it is difficult to estimate the value of the meeting, it is still possible to make some comments on the arrangements, and on the principles underlying them. Background information was provided prior to the meeting, but it appeared that the extent of the preparation was inadequate. This was not entirely due to lack of effort on the part of the participants, but rather to the complexity of the subject matter. Brittle fracture is a complicated phenomenon, and even the definition of basic terms and concepts provided considerable scope for discussion and difference of opinion. The materials considered represent a wide range of structural and chemical types, which has determined, in large part, the Mater. Sci. Eng., 1 (1966/67) 296-311
ture has a direct bearing on the size effect so frequently observed in notch brittle tests. In large specimens the requisite strain may be accommodated in a local plastic zone, so that the specimen will fracture before general yield.
6. Crack propagation A crack probably requires less plastic flow, and hence a smaller tensile stress, for propagation than nucleation. The strain rate at the tip of a running crack must be very high, and at least in ferrous metals the yield stress is, as gtated abo~ze, sensitive to strain rate. Moreover, ahead of a crack there exist triaxial stresses, so that the material cannot flow as freely as in a plain tensile specimen under the same tensile stress. Thus higher tensile stresses --perhaps three times higher--can be supported without plastic flow and may be high enough to cause fracture. That triaxial stresses are sometime important is suggested by the fact that the fracture often becomes ductile where it intersects a free surface, at which the transverse stresses are zero and hence triaxiality disappears. REFERENCES J. R. Low, JR., The Fracture of Metals, Progress in Materials Science, Vol. 10, Pergamon, London. J. F. KNOTT A~D A. H. COTTRELL, Notch brittleness in mild steel, J. Iron Steel Inst., 201 (1963) 249.
IV. Glassy Polymers (Plastics) J. P. Berry
1. Structure and mechanical properties Polymers are characterised by a long-chain molecular structure in which identical repeating units are linked by covalent (usually carbon-carbon) bonds, i.e. they are organic compounds. The main variations in chemical structure, and hence properties, arise by changing the substituent in the vinyl monomer. The substituent then occurs on alternate carbon atoms in the polymer molecule. In the solid (glassy) state there are three types of molecular interaction : (i) directed covalent bonds between the chain atoms; (ii) non-directed forces--such as Van der Waals interaction, dipole association, hydrogen bonding, etc. ; (iii) molecular entanglements. The second and third types of interaction have
309
lower energies than the first, and at sufficiently high temperature (80°-150°C) the materials melt, but retain their long chain character in the fluid state. In the solid glassy state the molecules are randomly disposed and the mechanical properties are isotropic. The stress-strain curve is essentially linear to the fracture point, but because of the relatively low transition (softening) temperature, the properties are time and temperature dependent.
2. Application of the Griffith theory to glassy polymers The Griffith theory assumes that tensile strength is determined by the presence of flaws and that the ultimate stress is inversely proportional to the square root of flaw size. This conclusion has been checked for the glassy polymers poly(methylmethacrylate) and polystyrene by determining the tensile strength of samples containing inserted defects of known size. The proportionality constant yields a value for the energy for the formation of unit area of fracture surface (y) (2 × 105 ergs/cmZ), which is insensitive to changes in sample geometry, and (within limits) to testing rate. The same value of the parameter can be obtained by a cleavage experiment which involves an entirely different sample geometry and stress system, and hence it may be regarded as a material constant. The value of the constant increases by a factor of 5 over the temperature range + 50 to -200°C, and it is sensitive to changes in molecular characteristics. On introducing chemical cross links [into poly(methyl methacrylate)] the fracture surface energy is reduced by a factor of 4, and it shows a linear, (but not very strong) dependence on the reciprocal of molecular weight, in common with other mechanical properties. In experiments performed on pre-oriented samples the fracture surface energy is increased when the fracture is propagated normal to the direction of molecular orientation (× 5), and reduced when propagated in the direction of orientation, (× 0.1) compared with the results on conventional (unoriented) samples. In the experiments described the fracture surface energy is always much greater (× 10 3) than calculated from the molecular structure. The discrepancy is attributed to inelastic processes occurring at the tip of the flaw due to the local stress concentration, which results in the formation of a surface layer of structure different from the substrate. Deviation from the theoretical (Griffith] behaviour occurs at small inserted flaw sizes when the Mater. Sci. Eng., 1 (1966/67)296-311
310
MEETINGS
natural, adventitious flaws are of comparable size to those introduced artificially. In glassy polymers the natural flaw which initiates fracture in conventional samples arises from a craze. It is possible to define an inherent flaw size (Co) and this appears related to a material property, its tendency to develop crazes. Thus Co for poly(methyl methacrylate) is only about 1/20 of the value for polystyrene, a finding consistent with the difference in crazing propensity. On varying the temperature from + 50 to -200°C, the inherent flaw size [for poly(methyl methacrylate)] first decreases by a factor of 2 to its value at room temperature and then increases ( x 4) to its value at - 200°C. Crosslinking reduces Coby a factor of 3, and it is essentially independent of molecular weight. When a fracturing stress is applied to an oriented sample along the direction of orientation, the inherent flaw size is increased by a factor of 3. It appears therefore that the inherent flaw size varies in much the same way as the fracture surface energy as the experimental conditions are changed. This is due to the fact that the tensile strength is less sensitive to the experimental variables than the two parameters (~ and Co) which control it, according to the Griffith theory. Unfortunately there is no satisfactory independent method of characterizing Co in any quantitative sense.
3. Significance of v and Co (mechanism of fracture) Crazes are flat reflecting entities developed by imposed tensile stress, which persist after the removal of the stress. They are sharply bounded regions consisting of oriented molecules interspersed with about 50 ~ by volume of voids. As the imposed stress is increased they grow in size, presumably change in structure, and eventually lead to fracture. Examination of the initiation site on fracture surfaces (of polystyrene) gives direct evidence of the open structure of the craze from which that surface was generated. The layer of material on the fracture surface [of poly(methyl methacrylate)] gives rise to interference colours, and its refractive index (and presumably structure) is the same as that of a craze in the same material. Thus the mechanism of brittle fracture in glassy polymers seems to involve the formation and rupture of craze material. The fracture surface energy (V) is related to the energy dissipated in forming the craze material, by molecular orientation and void formation, and the inherent flaw size (Co)is related to the critical size of the craze
immediately prior to rupture. It is therefore not surprising that the two parameters show the same variations in value with changing experimental conditions and that the tensile strengths of the materials are likewise insensitive to those changes. The basic problems in the brittle fracture of polymers are concerned with the initiation, growth and changing structure of crazes, and in particular with defining the critical factors of size and structure that determine the onset of the mechanical instability that can be treated in terms of the Griffith theory. REFERENCES J. P. BERRY,Brittle behaviour of polymeric solids. Chapter IIB in B. ROSEN(ed.), Fracture Processes in Polymeric Solids, Interscience/Wiley, New York, 1964. R. P. KAMBOUR,Polymer, 4 (1963) 143. R. P. KAMBOtm, J. Polymer Sci., 3 (1965) 1713.
11". Format of the Meeting It is, of course, impossible to assess the success of the meeting in quantitative terms, or indeed to define precisely what constitutes "success". It appears, however, that the primary objective, which was to promote inter-disciplinary interaction, was achieved, to judge by the scope and vigour of the discussion. It is probable, though less certain, that the extent of the interaction was greater than it would have been had the meeting been organized on more conventional lines. On the other hand, no basically new ideas were proposed resulting from the synthesis of alternative points of view, although it is possible that such new ideas will be formulated subsequently. Although it is difficult to estimate the value of the meeting, it is still possible to make some comments on the arrangements, and on the principles underlying them. Background information was provided prior to the meeting, but it appeared that the extent of the preparation was inadequate. This was not entirely due to lack of effort on the part of the participants, but rather to the complexity of the subject matter. Brittle fracture is a complicated phenomenon, and even the definition of basic terms and concepts provided considerable scope for discussion and difference of opinion. The materials considered represent a wide range of structural and chemical types, which has determined, in large part, the Mater. Sci. Eng., 1 (1966/67) 296-311