R. Schirrer

Elastic recovery of a scratch in a polymeric surface: experiments and analysis

A scratch may be regarded as a tangential indentation. Hence standard indentation laws can be used to analyse the geometry of the scratches left by a moving tip on the surface of a viscoelastic viscoplastic body such as a commercial grade of cast polymethylmethacrylate (PMMA). This paper presents experimental results and an analysis of the elastic recovery of a scratch after contact with a tip. The experimental data were obtained with a new scratch apparatus fitted with a built-in microscope, which allows in situ analysis of the contact area and the groove left on the surface. The elastic plastic total penetration depth hep is split into its plastic part hp and elastic part he. In the case of full plasticity around the tip during scratching, which for an elastic plastic material implies a sufficiently high value of the contact strain, the elastic law describes the depth relaxation and experimental data agree with the analysis. In the case of a purely elastic response of the material, corresponding to low values of the contact strain, the rear contact radius is equal to the front contact radius. At intermediate levels of strain, an analysis of the elastic recovery must take into account the contribution of the plastic term to the elastic plastic response of the material.  2001 Elsevier Science Ltd. All rights reserved.

Time and temperature dependence of the scratch properties of poly(methylmethacrylate) surfaces

Most existing models describing the scratch properties of materials take into account forces acting at the interface between the material and a grooving tip, but do not consider the stress and strain properties of the material far beneath or ahead of the tip. In the case of polymer scratches, there are no models at all which take into account the viscoelastic viscoplastic behaviour of the material. In standard indentation tests with a non moving tip, the elastic plastic boundary and the limits of the region subjected to hydrostatic pressure beneath the tip are known. These models were used to analyse the geometry of the grooves left on the surface of a viscoelastic viscoplastic body by a moving cone-shaped diamond tip having a radius of about 40 μm. A new apparatus was built to control the velocity of the tip over the range 1 to 104 μm/s, at several different temperatures from −10°C to 100°C. The material was a commercial grade of cast poly(methylmethacrylate) (PMMA). The normal and tangential loads and groove size were used to evaluate the dynamic hardness, which behaved like a stress and temperature activated process. Values of the activation energy and volume of the dynamic hardness and of the interfacial shear stress were in good agreement with those usually attributed to the mechanical properties of PMMA.

Polymers toughened with rubber microspheres: an analytical solution for stresses and strains in the rubber particles at equilibrium and rupture

Large strains in rubber toughened polymers cause void formation and growth in the rubber particles and yielding in the matrix. Void formation usually precedes plasticity in the matrix around the particle and previous papers have proposed models for the relationship between rubber surface energy, volume strain energy and void growth. In this paper, it is shown that another volume criterion must also be satisfied arising from the fact that in all these models, no decohesion is allowed at the particle-matrix interface. A fracture mechanics approach, where linear and nonlinear elasticity are assumed for the matrix and the rubber particle, respectively, is used to define a void formation criterion depending on the rubber fracture surface energy. After formation, the stability of the void is examined, taking into account the volume conservation between matrix and particle and the stress due to surface tension when the void size is very small. A size effect is observed, indicating that voids cannot grow in small particles. The required value of fracture energy in a particle on a microscopic scale is discussed.

Volume change and light scattering during mechanical damage in polymethylmethacrylate toughened with core-shell rubber particles

Mechanical damage was investigated in polymethylmethacrylate toughened with core-shell (hard core) rubber particles. During a tensile experiment, volume changes, light absorption, light scattering and a small strain elastic modulus were recorded. Light scattering was quantitatively related to the number of damaged particles and a fast partial unloading technique allowed determination of the non-elastic part of these changes in material properties. Experiments performed between 10−5 and 10−1s−1 and between 20 and 70 °C showed time-temperature transitions. These appeared to be different for each property, and measurement of the activation energy for each parameter enabled microscopic damage mechanisms to be inferred. Three types of microstructural damage were observed: pure matrix plasticity at very low strain rates or high temperatures, rubber cavitation at correlated locations at medium strain rates and temperatures, and disordered cavitation, rubber tearing and matrix plasticity at high strain rates or low temperatures. The experimental mean stress triggering rubber cavitation was compared with the predicted value.

Adhesion of latex films. Part III. Surfactant effects at various peel rates

In order to study the effect of surfactants on the adhesion of latex films, peel energy versus surfactant concentration curves were established at various peel rates. The main latex polymer was a methyl methacrylate (MMA)/ethyl acrylate (EA) copolymer synthesized in the presence of a hydrophilic polyester. Another polymer, less extensively studied, a styrene/butyl acrylate/methacrylic acid terpolymer, was also used for comparison purposes. The surfactants were either sodium dodecyl sulfate (SDS) or ethoxylated nonyl phenol containing 30 segments of ethylene oxide (NP30). The substrates were glass plates or poly(ethylene terephthalate) films. It was found that with SDS-containing films, whatever the substrate or the polymer, the curves went through a maximum, whereas with NP30 they went through a minimum, at medium or high peel rates. When the peel rate was decreased, the curves flattened out and at zero peel rate (extrapolated values), they became horizontal. The peel energies at zero peel rate were three...

Mechanical interaction between spherical inhomogeneities : An assessment of a method based on the equivalent inclusion

This paper assesses the ability of the Equivalent Inclusion Method (EIM) with third order truncated Taylor series (Moschovidis and Mura, 1975) to describe the stress distributions of interacting inhomogeneities. The cases considered are two identical spherical voids and glass or rubber inhomogeneities in an infinite elastic matrix. Results are compared with those obtained using spherical dipolar coordinates, which are assumed to be exact, and by a Finite Element Analysis. The EIM gives better results for voids than for inhomogeneities stiffer than the matrix. In the case of rubber inhomogeneities, while the EIM gives accurate values of the hydrostatic pressure inside the rubber, the stress concentrations are inaccurate at very small neighbouring distances for all stiffnesses. A parameter based on the residual stress discontinuity at the interface is proposed to evaluate the quality of the solution given by the EIM. Finally, for inhomogeneities stiffer than the matrix, the method is found to diverge for expansions in Taylor series truncated at the third order.

Multiple light scattering and cavitation in two phase tough polymers

In glassy polymers toughened by inclusion of nanometric rubber particles, the high impact strength is due to cavitation of the rubber particles followed by the appearance of microshear bands in the glassy matrix. These materials are mostly opalescent or even opaque, which renders difficult any optical investigation of the damage process. Simple light scattering techniques were employed in earlier work to study the onset of damage in transparent toughened polymers. As demonstrated in one previous paper, multiple light scattering can be employed to further investigate opaque materials and hence highly damaged polymers. Coherent light backscattering in strongly opaque materials arises from the fact that an incident light beam, if not absorbed, is scattered successively by several scatterers before emerging again at the front surface of the body. The so-called coherent backscattering cone may be analyzed in terms of the size, shape, and density of the scatterers. In the present work, this technique was applied to a semicrystalline polymer and to rubber toughened PMMA containing core-shell (hard core) particles, an initially transparent material which becomes progressively opaque in the course of mechanical damage under stress. During the damage process, both the number of cavitated particles and their individual void fraction may increase, and a cavitated particle acts as a light scatterer of cross-section proportional to its void content. The weakness of such scattering techniques resides in the fact that the light scattering pattern is determined by the product of the density of the scatterers and their scattering cross-section. Consequently, the number of damaged particles cannot be separated from the particle void content. This study describes a new method based on the superposition of small elastic unloadings on the main tensile strain. During these unloadings, the number of damaged particles remains constant but their optical cross-section changes, thus leading to a supplementary equation describing the scattering properties of the body. Hence, the number of cavitated particles and their individual void fraction may be calculated separately from the experimental data. Since the use of coherent light backscattering to investigate damage mechanisms in polymers is relatively new, the paper also recalls the basic principles of multiple light scattering.

Influence of water on crack propagation in poly methyl methacrylate: craze stress and craze fibril lifetime

Polymethylmethacrylate (PMMA) is often used as a material in submarine applications. Therefore, the fracture properties of dry and wet PMMA in water and/or under hydrostatic pressure are of great importance. Previous work has shown that water strongly increases fracture toughness, and leads to a complicated figure of K1 versus crack speed, and stable-unstable crack and craze propagation, depending on external loading rate. In this study, compact tension specimens immersed in water have been tested on a tensile machine and crack tips have been observed during propagation by means of optical interferometry. Fracture stress intensity factors, and craze-zone shapes and sizes have been measured as a function of loading time and crack speed in water. The results have been rationalized in terms of craze fibril stress versus fibril extraction velocity and craze fibril lifetime versus fibril stress. Both may be expressed in terms of a stress-activated process governing fracture. It is found that, when expressed in these terms, the complicated influence of the external loading rate becomes irrelevant for describing local intrinsic material properties and K1 values. It is shown that there is no contradiction between the fact that water increases the fracture toughness, and the fact that the microscopic craze stress and craze fibril lifetime decrease at the crack tip.

Interferometrical measurement of the craze stiffness and structure of the craze fibrils in PMMA

The stiffness of a single craze produced in polymethylmethacrylate (PMMA) at several temperatures at the tip of a running crack has been measured at −25° C and 11 Hz. It has been shown that the craze stiffness increases by a factor of five when the craze is left unloaded during 400 sec at 20° C. A craze produced at 70° C is ten times stiffer than that produced at −25° C. The analogy between the craze structure and an open-cell foam or a crosslinked rubber suggests that the density of “knots” between craze fibrils is a relevant stiffness parameter, and it has been inferred that re-entanglement (welding) occurs between the craze fibrils during the relaxation process and in high-temperature crazes.

Effects of mechanical interactions on the hydrostatic stress in randomly distributed rubber particles in an amorphous polymer matrix

The equivalent inclusion method (EIM) assuming linear elasticity is used to calculate the mechanical interactions between spherical rubber particles in an amorphous matrix, as in a rubber toughened polymer. The influences of the various calculation parameters are examined and it is shown that the method can provide reliable results with regard to the level of hydrostatic stress in the particles. Damage of the material is simulated by replacing the most stressed particles by voids. Numerical simulations for several hundreds of interacting particles give information on the kinetics and spatial organisation of the damage. It appears that, as the volume fraction of particles increases from 10 to 20%, the spatial configuration of the damage evolves from a localised to a diffuse mode. These results are discussed in relation to the efficiency of rubber toughening.