Rupture Of Rubber Research Articles

Puncture of elastomer membranes by medical needles. Part II: Mechanics

Resistance to puncture by medical needles is becoming one of the most critical mechanical properties of rubber membranes, which are heavily used in protective gloves. Yet the intrinsic material parameters controlling the process of puncture by medical needles are still unknown. In a first paper presenting this two-part study, it has been shown that puncture by medical needles proceeds gradually as the needle cuts through the rubber membrane. The phenomenon of puncture by medical needles was revealed to involve contributions both from friction and fracture energy, in a similar way as for cutting. The use of a lubricant was not successful for removing the friction contribution for the determination of the material fracture energy corresponding to puncture by medical needles. This paper describes an alternative approach based on the application of a prestrain to the sample in a similar way as the work of Lake and Yeoh on cutting. A theoretical formulation for the tearing energy is derived from the theory of Rivlin and Thomas on the rupture of rubber. It is validated with a model extending expressions provided by the linear elastic fracture mechanics (LEFM) to include the non-linear stress–strain behavior displayed by rubber. For low values of the tearing energy, the total fracture energy, i.e. the sum of the puncture and tearing energies, is constant; the material fracture energy is obtained by extrapolation at zero tearing energy. This prestrain method allowed a complete removal of the friction contribution. The value obtained for the fracture energy corresponding to puncture by medical needles is found to be larger than the energy associated to cutting and smaller than that obtained for tearing. This can be related to the value of the crack tip diameter, which is, in that case, given by the needle cutting edge diameter.

Fatigue initiation and propagation in natural and synthetic rubbers

Elastomeric matrix composites are usually reinforced by mineral particles such as carbon black and sometimes by long metallic or organic fibers. In the absence of fiber, rubbers can be considered as nanocomposites. In service conditions, the fatigue damage of rubbers is a combination of: (a) mechanical damage; (b) chemical damage; (c) thermal damage. Experience shows that, in cyclic loading, rubbers are damaged to the point of formation of one or several cracks which then propagate. As for metal, it is recommended to study separately initiation of cracks and then their propagation. Generally speaking, the fatigue resistance is affected by chemical transformation such as crystallisation. It means that compression loading is an important factor. To show this effect, an axisymetric hour-glass shape specimen ( D=25 mm) is proposed to test rubbers. A large effect has been found of the mean stress on the fatigue strength depending on the chemical composition of the materials and of crystallisation transformation if it appears. The crack growth rate is studied using linear fracture mechanics as proposed earlier (Rivlin RS, Thomas AG. Rupture of rubber: I. Characteristic energy for tearing. J Polymer Sci 1953;10(3):291). In this case, the strain energy release rate G is substituted for the concept of tearing energy T. The application of fracture mechanics to elastomers generates some difficulties because of the important deformability. In order to apply a tension–compression loading a thick edge notched specimen is recommended with two lateral grooves ( W=150 mm, B=25 mm). For low values of Δ T, a threshold can de defined depending on the R ratio. It is shown that for a high R ratio the fatigue crack would not propagate if the crystallisation transformation is high. In contrast, if R=−1, the threshold disappears. A finite element simulation of stresses and strains is presented in order to get a better explanation of the experimental results.

Effect of chemical and physical crosslinks on strength of rubber and plastics—a theoretical approach

AbstractFor rupture of rubber and plastics, three types are proposed: (a) elastic, (b) plastic, and (c) brittle. For (a) the rupture takes place at the ultimate elongation of chains between crosslinks. Strength f is proportional to the number of crosslinks and also the fraction of effective chains giving the optimum degree of vulcanization ν. Both ν and f at the maximum strength decrease with increasing the bond energy D of crosslinks. The rupture in (b) occurs for filled rubbers. The maximum reinforcement with filler is expected to be attained at 20% volume fraction of filler from the pseudo‐link model in which the number of links are proportional to the specific surface area, the fraction, and the adsorption ability of the filler particles. For (c) the craze occurs due to the breakdown of pseudo‐crosslinks of the smallest size b, and b is 2 at the glass transition temperature. Impact strength is improved by the dispersion of rubber particles at the optimum fraction of 13% and under the small distance of neighboring particles, which is 0.4 μm and is corresponding to the relaxation distance. © 1994 Wiley & Sons, Inc.

Path-Independent integral for rupture of perfectly elastic materials

The path-independent integral of Rice and Sanders is generalized to the case of perfectly elastic materials so that the rupture of rubber can be included. As a simple application to the tearing of rubber, the integral is used to relate the tearing energy and the strain concentration which confirms the strain concentration theory of Thomas.

Rupture of rubber. XI. Tensile rupture and crack growth in a noncrystallizing rubber

A theory of tensile rupture in a noncrystallizing rubber, a particular instance of a more general theory of rupture in simple extension, is outlined. The theory assumes that failure takes place by growth of a crack from some imperfection in the material where the stress is high locally. The imperfections are considered as being equivalent, in terms of stress concentration effects, to small cracks initially present in the material, and the conditions for crack growth to occur are then treated on the basis of the tearing energy criterion of Part I. It is assumed, by analogy with tearing on a macroscopic scale, that the crack grows continuously with time at a rate, dc/dt, given by: dc/dt = ATn, where A and n are constants and T is the energy expended per unit increase in crack length, per unit thickness of specimen. The predicted relationships of the breaking time to the stored energy density and initial crack length for specimens tested by stretching at uniform rates and by holding at fixed extensions are first compared with the results of model experiments on test pieces containing small tears and cuts. Values of A and n derived from tear test data are used in the theoretical relationships, and it is shown that there is fair agreement with experiment. Results of tests on tensile test pieces containing no deliberately introduced tears or cuts are then shown to be consistent with a failure mechanism of the above type. It appears, however, that the tearing energies in tensile rupture are lower than those observed in tear tests, and reasons for this difference are discussed.

Rupture of rubber. X. The change in stored energy on making a small cut in a test piece held in simple extension

AbstractApplication of the tearing energy criterion (Part I of this work) to the problem of the tearing of a rubber strip that contains a small cut or tear of length c in one edge and is stretched in simple extension is based on the relation Wi – W = K(λ)c2hE, where Wi and W are the total stored energies of the strip in the absence and presence of the cut, respectively, h is the thickness λ0 of the strip, E is the stored‐energy density in the central region of simple extension, and K(λ) is a numerical factor that varies with the extension ratio λ in this region. An experimental method is described for measuring (Wi – W), which enables the factor K(λ) to be evaluated. The results indicate that K(λ) decreases from a value of about 3 at low extensions to a value somewhat below 2 at λ = 3. The experiments also provide a more stringent test of the accuracy of the above relation than has been possible hitherto.

Rupture of rubber

The theory of the tearing of rubber has been further confirmed by experiments on three test pieces of widely different shapes, for each of which the ‘tearing energy’ can be calculated. This rupture concept has been used to interpret measurements of out growth under conditions of both static and dynamic loading.

Rupture of Rubber. VII. Effect of Rate of Extension in Tensile Tests

Abstract There are few published measurements on the effect of rate of extension in tensile rupture tests on rubber vulcanizates. The most extensive data on a single vulcanizate are those of Dogadkin and Sandomirskii˘ and of Smith. These measurements were made on GR-S gum vulcanizates and covered a similar range of rates of extension, from about 0.02 to 20%/sec. Ring specimens were used in both cases, and tensile strength and breaking extension were measured over a wide temperature range. Villars has made tensile strength and breaking extension measurements on double dumbbell specimens of several gum and filled vulcanizates extended at various rates in the range 10,000 to 100,000%/sec. Kainradl and Handler have reported tensile strength measurements for several filled vulcanizates, obtained with dumbbell specimens extended at four different rates of extension covering a range from about 1 to 100,000%/sec. All these results indicate that tensile strength and breaking extension can vary appreciably with the rate of extension of the specimen. Complete load-extension curves are not given in any of these papers. In the present paper an autographic method is described for obtaining the load-extension curves of ring specimens extended at various rates from about 0.1 to 2000%/sec. Results showing the effect of the rate of extension on the tensile strength and breaking extension and on the load-extension curve are given for GR-S vulcanizates. The data were obtained primarily for the comparisons of tear and tensile rupture measurements given in a subsequent paper (Part VIII).

Rupture of Rubber

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Rupture of rubber. VII. Effect of rate of extension in tensile tests

An autographic method is described for obtaining loadextension curves of ring specimens extended at various rates from about 0.1 to 2000% per second. Results showing the effect of the rate of extension on the tensile strength and breaking extension and on the load-extension curve are given for a GR-S gum vulcanizate and for two GR-S vulcanizates containing carbon black. The tensile strength of the gum vulcanizate, at the temperatures at which the tests were carried out, increases uniformly with the rate of extension, but the tensile strength of the filled vulcanizates passes through a maximum. The effect of the rate of extension on the load-extension curve of the gum vulcanizate is that to be expected from the viscoelastic properties of the material; the effect in the case of the filled vulcanizates is more complex. These results are briefly discussed.

Rupture of rubber. VI. Further experiments on the tear criterion

A criterion for the tearing of rubber based on an energy balance approach, proposed previously, has been critically examined experimentally. This criterion implies that the energy required to form unit area of surface by tearing should be a constant of the material, and it can be tested by finding if tearing results from test pieces of different shapes are selfconsistent. Previous work has indicated that the criterion is approximately correct for natural rubber, and the present paper gives a much more rigorous check for a noncrystallizing and therefore more convenient material (GR-S). The results from three test pieces of widely different shapes show excellent agreement. The material used exhibited an abrupt change in the mode of tearing as the tearing energy increased through 3 × 106 ergs/cm.2, the rate of tearing suddenly increasing from about 10−2 to 10 cm./sec. This correlated with a change in the appearance of the torn surfaces from rough to smooth.

Rupture of rubber. VIII. Comparisons of tear and tensile rupture measurements

The energy to initiate tearing at an incision with a tip of semicircular form was shown in a previous paper to be approximately equal to Ed, E being the work to break/unit volume as measured in a tensile rupture test and d the diameter of the tip of the incision. In the present paper this relation is used to compare the effects of the speed of test on tear and tensile rupture measurements. It is shown that the variation of the work to break/unit volume with the speed of test adequately accounts for the effect of the speed of test on the energy to initiate tearing at incisions with tips of semi-circular form. It is assumed that the relation applies also in continuous tearing, d being in this case the effective diameter of the tip of the tear, and it is shown that the variation of the tearing energy with the rate of tear propagation, at low and moderate rates of propagation, may be plausibly accounted for in terms of the variation of the work to break/unit volume with the speed of test and variation of the effective diameter of the tip of the tear, d. Values of d of a few tenths of a millimeter were generally required to fit the tear and tensile rupture measurements, the values being, as expected, comparable in magnitude with the irregularities in the torn surfaces. It is shown that in certain instances the values assumed for d may be confirmed by direct measurement of the diameter of the tip of the tear.

Rupture of Rubber. V. Cut Growth in Natural Rubber Vulcanizates

Abstract It has been noted in Part I of this series (referred to hereafter as I), that if a nicked specimen of a natural rubber vulcanizate is slowly stretched, tearing occurs at the tip for quite small applied forces. In the initial stages, this tearing continues only as long as the deformation of the specimen is being increased, and virtually ceases if the deformation is held constant. This tearing is essentially time independent, and is termed “static” cut growth. If, however, the deformation is continued until the cut has grown by a few hundredths of a millimeter the growth becomes time dependent and catastrophic tearing takes place, the cut suddenly increasing in length by perhaps a millimeter or so. If a nicked specimen is alternately stretched and relaxed to the unstrained state, the cut gradually grows even though the applied force is less than that required to produce catastrophic tearing. This phenomenon is termed “dynamic” cut growth. This behavior can be compared to that of gum GR-S vulcanizates described in Part III, where static cut growth of the above type does not occur, a dead load on a test piece producing a more or less steady rate of cut growth. In the present paper, measurements on natural rubber gum vulcanizates only are described, and the numerical results expressed in terms of the theory developed in previous papers (Parts I, II and III). It has been shown in I and II that the tear behavior of differently shaped test pieces cut from thin sheets of thickness t may be correlated by means of the concept of the energy for tearing. This is defined as the value of T[=(1/t)(∂W/∂c)l] at the instant of tear, and is denoted by Tc. In the definition of T, is the total elastic energy stored in the test piece, c the length of the cut, and the subscript l indicates that the differentiation is to be carried out at constant displacement of those parts of the boundary that are not force-free. It was also shown that a convenient and direct method of obtaining Tc is by the use of the “simple extension” tear test piece described in I and shown in Figure 1, and this has been used for most of the experiments. Under most conditions, T for this test piece is nearly independent of the cut length, width of the test piece, and modulus of the rubber; T is very nearly equal to 2F/twhere F is the force applied to the arms. In the cases where the use of the above approximate relation between T and F introduces an appreciable error, the exact theory given in I was used.

Rupture of rubber. V. Cut growth in natural rubber vulcanizates

AbstractCut growth in natural rubber gum vulcanizates has been studied using both steady and repeated loading. The results have been expressed in terms of the concept of the energy for tearing that has been put forward previously. With cut growth under repeated loading the tip, initially smooth, becomes rough and the rate of growth simultaneously decreases markedly to a final steady value. Some consequences of this roughening have been discussed. Measurements of cut growth under repeated loading have also been made using two different types of test piece. A rupture criterion, which has been previously proposed, predicts a definite relationship between the behavior of the two test pieces, and this has been confirmed experimentally.

Rupture of rubber. II. The strain concentration at an incision

AbstractThe strain distribution around the tip of an incision in a thin test‐piece of highly elastic material is considered. Using the results of a previous paper, relations between this strain distribution and the over‐all forces or strains are derived for two particular types of test‐piece. Experiments designed to check the theory are described, and agreement is found to be satisfactory. The theory is extended qualitatively to the case where the test‐piece is taken to the point of rupture, and experiments are described which confirm the approximate relation derived. The relevance to tearing and to the previously proposed tear criterion is discussed.

Rupture of rubber. I. Characteristic energy for tearing

AbstractA criterion for tearing of test‐pieces cut from thin sheets of a natural rubber vulcanizate, similar in form to the Griffith criterion for spreading of a crack, is formulated. This criterion involves a characteristic energy for tearing which is independent of the shape of the test‐piece and of the disposition of the cut. It is shown how this characteristic energy can be found experimentally for a particular vulcanizate and used to predict the force required to tear test‐pieces of the vulcanizate.

The Heat of Swelling of Rubber and Its Relation to the Previous History of the Rubber and to the Nature of the Swelling Agent

Abstract The swelling method developed by Hock and Bostroem for determining calorimetrically changes in the state of energy of raw rubber (the Joule heat effect on stretching, the fiber structure of Hock, and the filler effect of Wiegand) has been developed further, especially by Hock and Hartner, with the object of obtaining information about the boundary surface energy between rubber and these fillers by means of the heat of swelling first of all of unvulcanized rubber mixtures containing active fillers such as carbon black and zinc oxide. The “activity” of fillers of this kind evidently depends upon the effect of boundary surface forces, which increase the mechanical work of rupture of rubber, A=∫p.dl, after their admixture in the rubber. To ascertain to what extent and in what quantitative way this mechanical “reënforcement” of rubber is related to the boundary surface energy, where there is mutual wetting, is a problem which is attractive both from a theoretical and technological point of view, and to the solution of which the works mentioned offer the first contributions. In continuing the experiments along the same general direction, on the one hand from the point of view of a critical examination of methods and on the other hand with the object of increasing the precision of the measurements, it was soon realized that it would be necessary to carry out special preliminary experiments. In fact, when it was once decided to replace benzine, which had been particularly suitable in experiments on the swelling of rubber mixtures because of certain unique properties, by benzene and other liquids, it became necessary to determine the heat of rubber as an objective in itself, whereas in the earlier experiments this had been only a means to an end.