György Vörös

Micromechanical deformations in particulate filled thermoplastics: volume strain measurements

Volume strain measurements were carried out on PP composites containing different CaCO3 fillers. During deformation, a volume increase was detected which could be divided into two linear sections as a function of elongation. Comparison of data with existing theories has shown that in the first part, mostly elastic deformation takes place and the slope can be related to the Poissons ratio of the composite. Scanning electron microscopy revealed that in the second stage, the dominating micromechanical deformation process is debonding. Void formation is initiated at a certain stress which approximately corresponds to the yield stress of the composites, but data in the literature and model calculations indicate that separation of the matrix/filler interface may start at lower stresses. Initiation stress depends on the particle size of the filler and on interfacial interactions. The rate of volume increase has non-linear dependence on the volume fraction of the filler. Volume strain measurements reflect micromechanical deformations well, but further study is needed to explain contradictions between experimental results and theoretical predictions.

Mechanism of interfacial interactions in particulate filled composites

A stress analysis was carried out in order to determine the local stress distribution around spherical particles in particulate filled composites. The results were introduced into the criteria for micromechanical deformations and the conditions for the initiation of each mechanism were calculated. Results of the calculations have shown that shear yielding, and possibly crazing, do not depend on thermal stresses and adhesion, but debonding does. The results of the analysis were in accordance with literature and experimental data. The calculated debonding stresses correspond to the observed values, but both debonding and yield stress depend strongly on composition, a phenomenon the analysis does not account for. The discrepancy can be explained with matrix/filler interaction and the role of the interphase. The results indicate that although stress analysis helps to predict deformation and failure in particulate filled composites, it must be further refined to find more exact solutions and the effect of inte...

An interphase with changing properties and the mechanism of deformation in particulate-filled polymers

Abstract The comparison of the results of calculations based on experimental data with those derived from a simple, two phase, elastic model proved the existence of a hard interphase in particulate-filled composites. Moreover, beside elastic properties, also other mechanical characteristics of the interphase, including yield stress, are different from those of the components. An energy analysis showed that the relationship between the yield stress of the matrix and the debonding stress determines the mechanism of deformation. Strong adhesion leads to matrix yielding, while decreased interaction leads to debonding, with a corresponding dependence of composite yield stress on filler content. Particle size, interaction and interphase properties determine the stress necessary to separate the matrix/filler interface. The thickness of the interphase depends on the strength of the interaction; a linear correlation was found between the size of the interlayer and the reversible work of adhesion.

Determination of the hardness and elastic modulus from continuous Vickers indentation testing

Continuous Vickers (Hv) indentation tests were performed on different materials (ion crystals, metals, ceramics, silica glass and plastic). Load-indentation depth curves were taken during the loading as well as during the unloading period by a computer controlled hydraulic mechanical testing machine (MTS 810). The indentation work measured both the loading and the unloading periods, and these were used for the evaluation of parameters characterizing the materials. It was found empirically that there were linear connections between the maximum load to the power 3/2 and the indentation work. These connections were used to relate the conventional hardness number, Hv, and Youngs modulus, E, with the work performed during loading and unloading. This work can be determined with great accuracy from the measurements. The values of the Youngs modulus and the Vickers hardness determined this way agree well with those obtained by conventional methods. On the basis of continuous indentation tests, materials can be easily classified into the isomechanical groups introduced by Ashby. For this classification the Hv/E ratio is generally used. As a substitute for Hv/E another parameter is recommended which can be determined easily from a single measurement.

Stress distribution in particulate filled composites and its effect on micromechanical deformation

A model was developed which assumes the spontaneous formation of an interphase around the inclusions in particulate filled composites. Elastic properties of the interphase change continuously from the surface of the particle to a matrix value far from it. Using first-order perturbation calculations an approximate analytical solution was given for the distribution of displacements and stresses around the inclusions. Fitting the model to experimental data has shown that an appropriate choice for the function and the parameters describing property changes around the inclusions makes possible the reliable prediction of composite properties. Using a simple averaging procedure, composition dependence of tensile yield stress was described; in accordance with experimental observations the model could predict composite yield stresses exceeding the matrix value and explain the effect of interfacial interactions. Comparison of the theoretical model with a previously developed semiempirical one indicates that the main factor determining yield stress is the relative load bearing capacity of the second component. Interacting stress fields compensate each other, decreasing local stress maxima; thus justifying the averaging procedure applied. Contradictions of the models are analysed and areas for further research are also indicated in the paper.

Effect of a soft interlayer with changing properties on the stress distribution around inclusions and yielding of composites

A model is presented that takes into account the presence of a soft interlayer with changing properties around an inclusion embedded into an infinite matrix. Property change in the interphase is expressed by a power law function of the form of f(r)=J(R/r)p. The equilibrium equation is satisfied by a spherical and a dipole like solution. The continuity of stresses and displacements at all interfaces are used as boundary condition. Calculations are carried out for a matrix/elastomer/filler system to predict the effect of the soft interlayer on stress distribution. According to the model the deformation of this interlayer is very large compared to that of the matrix. Very soft interlayers lead almost exclusively to compressive deformations in the entire deformed volume. Radial stress decreases considerably and the stress maximum shifts to the surface of the inclusion. Although in a somewhat lesser extent than radial stress, shear stress also decreases in the presence of the soft interlayer and stress maxima become less localized. In such a case yielding is initiated at the equator of the inclusion. Particles covered with a very soft interphase behave like cavities. A soft interphase is advantageous because it changes stress distribution and decreases stress concentration, but particles loose their reinforcing effect already at a relatively thin layer thickness.

Localized deformation bands in Portevin–LeChâtelier plastic instabilities at a constant stress rate

Abstract Portevin–Le Châtelier (PLC) plastic instabilities were examined in constant loading rate tensile tests. Irregular instability steps were observed in an intermediate stress rate region on the stress versus strain curves. The irregular steps are caused by the repeated activation of localized high deformation bands. The activation of the localized bands shows some regularity. The origin of the irregular instability steps goes back to the initialization of the first band at the onset point of the instabilities. It is argued that the appearance of irregular instability steps at low strain rates is related to the decrease of the depth of the dynamic strain aging toward small strains.

Prediction of the yield stress of composites containing particles with an interlayer of changing properties

A model is presented for the prediction of the yield stress of particulate filled composites. The model assumes the development of a hard interlayer around the particles with properties continuously changing from the surface of the filler towards a homogeneous matrix. Composite properties are derived by a simple averaging technique, which uses the stresses developing around a single particle in the calculations. The predictions of the model are compared to experimental results obtained for particulate filled LDPE, PP, and PVC composites containing fillers with different particle sizes. The results show that the development of a hard interlayer increases the local yield stress around the particles. The probability of debonding decreases as a result, and yielding does not occur close to the particle surface, but further away in the matrix. Small particles carry significant load; they may reinforce the polymer. Interacting stress fields and the presence of the hard interlayer lead to decreasing stress concentration.

On the mathematical description of the tensile stress-strain curves of polycrystalline face centered cubic metals

The stress-strain curves of polycrystalline face centered cubic metals (aluminium, copper, gold, silver and nickel) were measured by an Instron tensile test machine controlled by a computer registering 20 points per second along the load-elongation curve. The large number of measured points makes it possible to perform a detailed analysis of the mathematical structure of the stress-strain curves. General conditions are introduced which must be fulfilled by the functions which approximately describe the whole stress-strain curves. It is shown that the limiting value of a special set of suitable functions in practice describes the stress-strain curves exactly.

Effect of the Molecular Structure of the Polymer and Nucleation on the Optical Properties of Polypropylene Homo- and Copolymers

Two soluble nucleating agents were used to modify the optical properties of nine PP homo- and random copolymers. The ethylene content of the polymers changed between 0 and 5.3 wt %. Chain regularity was characterized by the stepwise isothermal segregation technique (SIST), while optical properties by the measurement of the haze of injection molded samples. Crystallization and melting characteristics were determined by differential scanning calorimetry (DSC). The analysis of the results proved that lamella thickness and change in crystallinity influence haze only slightly. A model was introduced which describes quantitatively the dependence of nucleation efficiency and haze on the concentration of the nucleating agent. The model assumes that the same factors influence the peak temperature of crystallization and optical properties. The analysis of the results proved that the assumption is valid under the same crystallization conditions. The parameters of the model depend on the molecular architecture of the polymer. Chain regularity determines supermolecular structure and thus the dependence of optical properties on nucleation.