Failure modes of elastomers

En,qinmriny

Fnrrrure

Mcchania,

1973, Vol. 5, pp. 555-562.

FAILURE

Pergamon

Press.

MODES

Printed

in Great

Britain

OF ELASTOMERS?

FREDERICK R. EIRICH Polytechnic Institute of Brooklyn 333 Jay Street Brooklyn, New York 11201, U.S.A. Abstract-The mechanical response of elastomeric materials is known to depend greatly on their ability to crystallize under strain, on the difference between the glass transition and the usage temperature, on the density of permanent and transient crosslinks, and on the filler. Strength properties and failure incidences of high modulus polymers follow the same statistics that are observed during the fracture of brittle materials. The same is practically true for elastomers also but, in addition, their ultimate properties are well described by a failure envelope which approximates time-temperature superposability. A detailed understanding, integrating all of these observations so as to present a uniform mechanism of large elastomeric deformations and elastomeric failure has not been achieved. A qualitative scheme will be proposed that accounts for the observed behavior by pointing out how rigid domains tend to create in the rubber matrix those conditions that permit it to come close to the largest stretchability of a given network.

INTRODUCTION THE MECHANICAL response of elastomeric materials is known to depend greatly on their ability to crystallize under strain, on the difference between the glass transition and the usage temperature, on the density of permanent and transient crosslinks, and on the filler. Strength properties and failure incidences of high modulus polymers follow the same statistics that are observed during the fracture of brittle materials. The same is practically true for elastomers also but, in addition, their ultimate properties are well described by a failure envelope which approximates time-temperature superposability. A detailed understanding, integrating all of these observations so as to present a uniform mechanism of large elastomeric deformations and elastomeric failure has not been achieved [ 11. In the following, a qualitative scheme will be proposed that should account for the observed behavior more satisfactorily. The main points of this discussion will be based on the fact that amorphous elastomefs are undercooled liquids which would flow indefinitely if the molecular chains were not constrained by an irregular network formed by chemical intermolecular linkages. In many cases, strains induce chain alignment, crystallization, and/or sufficient entanglement so as to amount to a time dependent, physical, network[2]. In any case, the initial resistance to deformation is largely entropic and the equilibrium moduli are therefore low. The effective instantaneous moduli during (and even a short time after) realistic straining rates may rise substantially when the direct stress transmission through the chemical or physical network is augmented by molecular friction. At high extensions, network sequences of shorter chains carry a disproportionate load. particularly at stress equilibrium. The liability to successive rupture of a relatively small number of load bearing chains without frictional support at points of stress concentrations, such as cracks or network irregularities, leads to flaw acceleration. This explains the observation that, at temperatures far above the glass transition, but below rapid chemical decomposition, the equilibrium strength of fully amorphous, crosslinked, elastomers is only a few percent of the best possible, or calculated, values[3]. Increasing crosslink uniformity, by introduction interchangeable, thermally or stress tPresented at the Symposium on Fracture and Fatigue at the School of Engineering and Applied Science, George Washington University, Washington, D.F. May 3-5, 1972.

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labile, links increases the elastomeric strength appreciably[4], but not nearly as much as the self-reinforcement described below. Elastomeric moduli and strength rise dramatically if[5,6, 151, during straining, the rubber chain molecules are capable of extensive alignment or crystallization, so that locally the number of load bearing chains per cross section, as well as the uniformity of the load distribution, is increased[31 (see Figs. 1 and 2). The rise in elastomeric moduli at large deformations and the high strength then observed represent a form of work hardening dubbed, in this context, ‘self-reinforcement’[7]. This term has been chosen because of the similarity of this phenomenon with the well-known reinforcement effect (increase in modulus and ultimate properties) by filler particles. Filler reinforcement is assumed[8] to be caused by additional crosslinks by elastomeric surface attachement, FRACTION

0.2 (1

-

OF MAXIMAL

0.4

EXTENSION

0.6

0.8

1.0

Tension OS Function of Extension

600-

INCREASE

IN DENSITY

(“lo)

Fig. 1. Stress f’ (tension) as a function of strain, experimental Curve a, theoretical Curve (Langevin) b. Curves c and d show the increase in modulus with increasing density. The density increase paralleling the fractional extension is proportional to the percentage increase of crystallinity. Curve c, crystal formation in tension, Curve d, crystal melting during strain return. Natural rubber.

E ( kg/cm2)

Fig. 2. Relation between rupture stress and Young’s modulus, E, (a function of P,r,,, for various vulcanizates (From Gent, 1966).

Failure modes of elastomers

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and increased frictional energy dissipation due to non-affine filler particle motion, to arise further from a miniaturization of the matrix which, by preventing the development of large fissures, permits flaw or filler induced microcavitation to occur harmlessly while converting large amounts of elastic energy into heat and surface energy. Domains of higher modulus, such as formed in the elastomer as a result of the straining process, must have similar effects on elastomeric properties. The similarity of action of strain induced, and of added, harder domains during large deformation and during rupture processes are the specific topic of this discussion. RUPTURE MECHANISM AND SELF-REINFORCEMENT Ruptures of molecular chains (which can be considered as stress activated bond dissociations) represent microcavitations, the coalescence of which leads to small voids, increasing the number of flaws always accidentally present. The well known stress concentrations around flaws may reach critical levels at comparatively low macro stresses and cause crack growth, often assisted by the triaxially dilative nature of the local stress fields[9]. The rate of growth depends on flaw geometry and on Griffith-type energy imbalances such that, when the increment of energy stored elastically in the walls near, e.g. the tip of a crack exceeds that of the energy stored and dissipated as the crack is lengthened and fresh surface is exposed, crack propagation capable of catastrophic acceleration will ensue. Dissipation of stored energy, by flow at the tip of the crack, by chain alignment, chain rupture, and free, chain retraction, alters the energy balance greatly[lO]. Energy storage is further diminished, and dissipation enhanced, by crack branching. The dissipative processes during crack propagation may outweigh the elastically stored energy by factors of lo6 or higher[ 111, and are the basis for the observation that stress-strain hysteresis and strength increase together [ 121. Since any factors that increase dissipative processes will help to avoid accumulation of excessive strain energy, the development of many small, non-catastrophic, microfailures (crazes) is a powerful factor for the survival of harder plastics [ 131; to a lesser extent the same is true for elastomers. However, as they become capable of bearing high stresses at higher rates of shear, at large elongations, or in highly filled states, crazing is a factor again. Recently, one has recognized yet another significant reduction of energy storage, i.e. by the viscoelastic deformation of the hard domains seen in ‘block elastomers’ [ 141, presumably made possible by domain plasticization by intruding elastomeric chains. Similar plastic dissipative deformation should occur within para-crystalline, or crystalline, domains formed in strained elastomers. The unfolding and folding of chains during strain induced domain formations also constitute deformation processes that dissipate energy and permit stress and strain relaxation by recrystallization. The double action of self-reinforcement, by chain alignment that raises local moduli, and by energy dissipation, increasingly receives support from many specific observations: while elastomeric strength increases parallel with strain birefringence and crystallization [I 51, amorphous rubbers at constant strain lose rapidly (by relaxation) whatever chain alignment may have been created by the straining process, so that they may fail with timell61. There may be strain recovery of uncrosslinked (raw), and extensive stress relaxation of crosslinked, rubbers after fast deformation[l5]. One finds (Fig. 3) a decrease in strength with crosslinking of rubbers because this interferes with chain alignment and raises the stress concentrations [ 171. The strength increases as the temperature approaches the glass transition range where the formation of glassy

558 STABLE

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AND

CRACK

UNSTABLE

GROWTH

Fig. 3. Some likely stress distributions near the tips of cracks; a,, low crosslink density, stationary crack; a*, low crosslink density, incipient motion; b,, high crosslink density, stationary crack: b,, high crosslink density, incipient motion; c ,, moving crack, slow velocity; c2, moving crack high velocity; d,, moving crack with plastic flow, low velocity; & moving crack with plastic flow, high velocity, (the scale along r for cases d is about 2 x that of cases a-c); 6, affected zone: d, domain size.

domains is enhanced [ 181. There is substantial similarity between the failure envelopes of crystallizing and filled elastomers [ 161. The strength of block-copolymer elastomers which contain glassy islands is greater than that of the simple elastomersI 191. Conversely, any factors that decrease the elastomeric ability to crystallize, such as structure variations or increasing temperatures, are paralleled by decreasing strength. We found recently, e.g. that even during very fast stretching the tensile stress rises in line with the crystallizability of a particular elastomer. Natural rubber (NR), which crystallizes much better than synthetic cis-polyisoprene (Natsyn) rubber, shows a correspondingly greater increase in modulus and strength with strain. However, NR crystallization and modulus are reduced to that of Natsyn, if the external temperature is raised above the melting temperature, of about 9O”C, for the crystallites of strained NR [20]. THE MOLECULAR MECHANISM OF ELASTOMERIC FAILURE Specifically, we propose the following sequence of changes as underlying most of the elastomeric extension and fracture processes. Any given sample of an elastomer defined by n, the average number has a characteristic limiting stretch ratio: Xk,, = &n112, of the independent statistical links between crosslink points of the network[l81, i.e. by the crosslink density. During a typical tensile test of an elastomer, about the first one third of the stress-strain curve to rupture follows the neo-Hookean law. Subsequently, the curve rises increasingly steeply above it, approximately following an inverse Langevin function[ 151, indicative of the fewer conformations available to

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the network chains upon stretching. Ultimately, when many of the chains are fully stretched, the moduli (and strength values) becomes quite high (Fig. 1) of the order of log dyne/cm2. The load bearing and retracting forces are now a function of the bonds of the stress activated chain backbone rather than the result of the randomizing thermal motions of the segments though, like all materials, because of their imperfections, elastomers never exhibit the full potential either of modulus, strength, or extensibility. How much of it can be attained is directly related to the mechanically induced degree of morphological changes. They range from near fluidity at low rates, or temperatures far above the glass transition, to rigid domains at high strain rates and/or low temperatures. Depending, thus, on induced morphology, elastomers exhibit property differences of orders of magnitude. The most important factors are that at low strains or equilibrium conditions the stress is not equally borne by all of the network chains and that with extension, the network becomes increasingly supported by strain induced formation of stronger domains, and by molecular friction during deformation [2 11. Since the same morphology changes are liable to occur in the domains ahead of a growing, or potentially growing, crack, it follows that, depending not only on elastomeric structure, but equally much on the prevailing conditions, a piece of rubber may vary from being highly notch sensitive, to becoming extremely tough. In the former case, the elastomer will fail in brittle fashion at low stresses, long before reaching the ultimate extensibility defined by the crosslink density; in the latter, it is likely to come much closer to the potential stretch. However, since in that case the sample work hardens until few relaxation mechanisms are left, ductile-brittle transition failures begin to play a part at high stress levels. A contributing factor to failure prior to hi,, is also that n is not only an average, but itself subject to great variations, as many chains are trapped by entanglements or in hard domains in ways that will reduce their extensibility. The whole situation is depicted in Fig. 4 which shows[20] as a function of increasing formation of hard domains, the rise of the stress-strain curves from P to S (O-R, drop by chain alignment.)

1

1

I

1

0.2

0.4

0.6

I

1 0.8

I/X Fig. 4. Mooney Rivlin plot for natural rubber; strain rate 3,6%/set; 25°C; h?, = 8950; crosslink density 1.04 X 10e4 mole cm; 2C, = 2.5 X lo3 g/cm; 2C, = 1.67x IO3g/cm2.

Summarizing, elastomers in uniaxial stretch never reach their full elongation, but fail prematurely, the earlier the more high mobility of the chains leads to direct load bearing of the unaided network. Figure 5 shows schematically a set of elastomeric stressstrain curves as a function of temperature and strain rate. Curve e is the extrapolated experimental equilibrium and stress-strain curve, A the observable failure envelope, and i, the failure locus at A:,,, anticipated if there are no premature failures due to local Griffith type overloads on the network.

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F--A

A--F decreasing rote increasing temp

Fig. 5. Schematic set of stress-strain curves, A-F, of an elastomer as affected by temperature and strain rate. Curve e is for perfect equilibrium: Curve f, the observable failure envelope: the line i connects the postulated rupture points, if the samples were free from flaw induced premature rupture.

Apart from their early failure which is not unlike that of all other materials, elastomers exhibit further peculiar features which also bear discussion. The three most characteristic ones have been pointed out already: (a) the extremely high energies for rupture or tearing and for crack propagation; the latter may be 10” x, or more, in excess of the normal surface energies; (b) the very large differences in strength properties shown by crystallizable and non-crystallizable, as well as filled and non-filled elastomers; and (c) the unusually large influence of the rate of strain. There is general agreement, as outlined above, how (b) and (c) can be rationalized. Of particular importance for elastomeric behavior, but generally not taken into account, is the fact that under suitable Conditions more cracks will be inhibited from growing by workhardening and attending dissipating mechanisms than in other materials. Thus, a large part of any highly extended rubber is affected not only by the few growing, but a!so by the many abortive flaws, with a corresponding large dissipation of energy throughout the whole specimen. If an individual crack eventually propagates, extensive local stress and strain rate magnifications contribute further to the magnitude of the rupture energy and affect all morphology changes in several important ways. While the material immediately ahead. of the crack front is, by definition, strained to the reversible limit, the material further away in the line of advance must be brought to this state on a time scale dictated by the rate of crack growth. For a rate of, E. and a depth, 6, to which the material is affected in advance, the strain rate c athwart the moving crack is: d = y

(A,,,--

l), in per

cent/set. If e = 10-l cmlsec, X,,, = 11, and 6 = 1O-3cm., one finds: c = lo5 per cent set-l. These are plausible values but, even for slower crack velocities and larger zones of prestrain, the strain rates across the crack tip are high enough to allow for maximal extension and workhardening. Since c grows with ?, this alone tends to counteract crack propagation. Moreover, fast stretching at the apex means a fast increase in crack radius, and very highly increased energy dissipation: ri/ -- r) (i‘)‘, even if q remains constant. More likely[22], though, r) will first decrease, then increase with c. The

Failure

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dissipational heating also will assist plastic flow of strain hardened domains even for moderate temperature increases. By retarding crack growth, strain rate magnification, local workhardening, stress and strain relaxation, and dissipation permit the elastomeric sample as a whole reach Amax and explain the very high tear, or crack propagation, energies. The interplay of these processes certainly underlies several other observations. Firstly, since the eventual giving way of the material may happen anywhere within the extensively stretched domain ahead of the tip, rupture processes will occur in appreciable depth to either side of the original crack plane, especially along the 45” line of the maximum shear stress. Secondly, after the crack has been slowed down or stopped, the stress will build up further in the crack walls as the specimen as a whole is stretched further. The now hardened material will be less able to repeat the self-reinforcing processes (a form of fatigue), will rupture after a few cycles, and the crack will start moving again. After several repeats the crack will acquire a length for which the stress concentrations are sufficient to rupture even the strongest domain and, at this critical dimension, the crack will begin to move fast and far[23]. Thirdly, the inherent periodic stop and go character of flaw propagation will occur in steady stress applications as well as during periodic stressing where it is well known[ 111; it is also likely to be the basis of the often observed knotty tearing of elastomers. CONCLUSIONS The central argument here proposed is, then, that the already uncommon features of elastomeric deformation are magnified viscoelastic by flaw distortion and the strain induced processes at the tips of cracks. They are yet raised to a third level of effectiveness by composite morphologies that exist by virtue of indigenous, or strain induced, crystalline domains or filler particles away from cracks. Besides acting as non-rupturing blocks in the path of the cracks, harder domains, by undergoing smaller strains at any given macroscopic deformation, cause substantial strain and strain rate magnification in the matrix, and even more extreme strain conditions and energy expenditure ahead of advancing cracks.t Elastomers, which through fillers or by self-reinforcement reach a high percentage of their theoretical extensibility, may be placed among the toughest materials known. Weakness, or premature rupture, may be attributed to weak zones of the network which, in their limited critical elongation, are not supported by the remainder of the matrix. High strength fracture occurs close to maximum extensions when the very small remaining deformation reduces energy dissipation and enhances the transition from ductile to brittle behavior. If this outline of the rupture processes on the molecular level is accepted, it follows that the failure envelope of elastomers entails three very different rupture regimes. The lower rising branch is that of a weak gel, in which premature ruptures of the enmeshing network are triggered by accidental, micron sized, flaws, which grow and cause failure at low overall stresses in accordance with low moduli and surface energies. The steeply, and eventually vertically, rising branch of the failure envelope is that of increasingly fibrous specimens in which energy investiture is balanced by viscoelastic dissipation and rising moduli that cause most cracks to stop except for a few which cause brittleplastic failure. The last portion of the failure envelope, at high rupture stresses and decreasing elongations, represents the brittle failure of the workhardened and/or glassy tThis

will be discussed

KI’.MVdS.NaLD

in more detail in a parallel

publication[24].

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material. Except for this last branch, the elastomeric failure pattern is that of a basically weak material that is capable of unusual workhardening and of dissipating amounts of energy by orders of magnitude larger than those of other materials, all H-phenomena which are based on extensibilities orders of magnitude larger than other materials may undergo. REFERENCES 111 R. F. Landel and R. Fedors, In, Fracture Processes in Polymeric Solids (Ed. B. Rosen), p. 36 1. Wiley Interscience, New York (1964); E. H. Andrews,J. Me& Phys. Solids 11, 231 (1961); Proceedings of the Conference on Yield and Fracture. Oxford (1966), p. 176. Institute of Physics and Physics Society, London. Ul R. S. Porter and J. F. Johnson, Chem. Reo. 66,1(1966). [31 F. Bueche and J. C. Halpin, J. appl. Phys. 35,36 (1964). [41 A. V. Tobolsky and P. F. Lyons, ONR Tech. Rept. RLT-99 (1967). [51 M. Leitner, Trans. Faraday Sot. 51, 1015-1021 (1955). 161 D. J. Dunning and P. J. Pennels (1967) Rubber Chem. Technol. 40,138 1. [71 F. R. Eirich On the two-phase nature of the mechanical response of pure andjlled elastomers, Transactions of the International Conference on Mechanical Behavior of Materials, Vol. HI, p. 407. Kvoto. (1971). of Elastomers (Ed. G. Kraus), p. 69. Wiley Interscience, New York: @I A. R. Payne, In, Reinforcement SeealsoCompositeMaterials,Vol. III.p.407. Kyoto(l971). 191 M. L. Williams, In, Fracture of Solids: (Eds. Dl C. Drucker and J. J. Gilman), p. 157. Wiley (Interscience), New York (1963). 1101 M. L. Williams and K. L. DeVries, In, Proceedings ofthe 5th International Congress on Rheology, (Kyoto Ed. S. Onogi), p. 139. Univ. Park Press, Baltimore, Maryland. [l l] G.-J. Lake and P. BLindelyJ. appl. PolymerSci.10, 343-351 (i966). [I21 G. A. Grosch. J. A. C. Harwood and A. R. Payne, In, Proceedings of the Conference on Yield und Fracture Oxford, 1966 p. 144. Institute of Physics & Physics Society, London (1967). [ 131 L. C. Cessna, Jr. and S. S. Stemstein, In, Fundamental Phenomena in the Materials Sciences, Vol. 4. p. 45. Plenum Press, New York (1967). [ 14[ R. A. Dickie and T. L. Smith,J. Polymer Sci. AZ, 687 (1969). [ 151 L. R. G. Treloar, The Physics of Rubber Elasticity, 2d Ed. Clarendon Press, Oxford (1958). [ 161 T. L. Smith, In, Rheology (Ed. F. R. Eirich), Vol. 5, p. 127. Academic Press, New York (1969). [ 171 F. R. Eirich and T. L. Smith, Molecular mechanical aspects of the isothermal rupture of elastomers, In, Fracture, VII, p. 352, (Ed. H. Liebowitz), Academic Press, New York (1972). [18] W. E. Wolstenholme,Appl. PotymerSymp. 6, 16 (1967). [19] T. L. Smith and R. A. Dickie,J. Polymer Sci. A2,635 (1968b). [20] Z. Glaser and F. R. Eirich, Thermomechanics and Structure of Elastomers, Polytechnic Inst. of Brooklyn, Aerospace Labs., Rept. 69-38 (1969). [21] F. Bueche, Physical Properties ofPolymers, Wiley, Interscience, New York (1962). [22] A. N. Gent,J. appl. Polymer Sci. 6,433 (1962). Reprinted in Rubber Chem. Technol. 36,697 (I 963). [23] J. C. Halpin and H. W. Polley, J. Comp. Mater. 1,64 (1967). [24] F. R. Eirich, Transactions qfRubbercon, Brit. Inst. of Rubber Ind., Brighton, In press ( 1973). (Received

3 July 1972)