Fuzzy variable linear programming with fuzzy technical coefficients

Fuzzy linear programming is an application of fuzzy set theory in linear decision making problems and most of these problems are related to linear programming with fuzzy variables. In this paper an approximate but convenient method for solving these problems with fuzzy non-negative technical coefficient and without using the ranking functions, is proposed. With the help of numerical examples, the method is illustrated

Volumetric strain measurement of polymeric materials subjected to uniaxial tension

A novel method for measuring and calculating volumetric strain in circular cylindrical uniaxial tension samples made from polymeric materials is proposed. It is shown that special considerations must be taken when calculating volumetric strain when a sample is in a postnecking state. Solely based on surface data, the key feature of the proposed correction is that it allows for an inhomogeneous distribution of longitudinal strain through the diameter of the sample, where a more traditional approach would be to assume a homogeneous distribution. These two approaches are evaluated by applying them to data from a close‐to‐incompressible steel sample. Whereas the proposed method indicates only a small positive increase in volume, the assumption of a homogeneous distribution results in substantial negative volumetric strains. Applying the two methods to tension samples made from HDPE and PVC, where plastic dilatation is nonlinear, again shows an initial negative volumetric strain for HDPE with the assumption of a homogeneous longitudinal strain. The proposed method predicts close‐to‐zero early‐stage volumetric strain for the same test. The differences are more subtle for samples of PVC. Micrographs obtained with scanning electron microscope show that the dilatation of PVC is related to voiding of the material around filler particles, while the underlying mechanism for HDPE is less clear. The results indicate that earlier reports of negative volumetric strain in polymers subjected to uniaxial tension might be artefacts of the implicit assumption made when calculating the volumetric strain.acceptedVersio

Influence of strain rate and temperature on the mechanical behaviour of rubber-modified polypropylene and cross-linked polyethylene

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An experimental and numerical study on the volume change of particle-filled elastomers in various loading modes

Laboratory tests show that there is a pronounced difference in the volumetric response between uniaxial tension and confined axial compression loading for commercial particle-filled hydrogenated nitrile butadiene rubber (HNBR) and fluoroelastomer (FKM) compounds. In uniaxial tension (UT), a volume increase of 5% and 20% for the HNBR and FKM respectively was present for a hydrostatic stress of less than 6 MPa, in addition, both compounds showed a clear hysteresis loop in the hydrostatic stress - volume ratio space. For confined axial compression (CAC) tests, on the other hand, the materials reached a 6–7% volume change for a hydrostatic stress of 140 MPa, and an elastic behavior was seen. This loading mode dependence of the volumetric response has severe implications for the constitutive representation of the materials. It is demonstrated that existing elastomer models, whereof many assume incompressible volumetric response, are unable to capture the behavior in both loading modes. To gain an increased understanding of the macroscopically obtained results, a tension in situ scanning electron microscopy study was performed. Matrix–particle debonding was observed to occur at the external surface of the materials, rendering a possible explanation for the loading mode dependent volumetric behavior. Finite element simulations of a single-particle model, incorporating a cylinder of matrix material with a spherical particle in its center, showed that the observed debonding can explain the experimental response of the materials in a qualitative manner

Volume growth during uniaxial tension of particle-filled elastomers at various temperatures–Experiments and modelling

A common presumption for elastomeric material behaviour is incompressibility, however, the inclusion of filler particles might give rise to matrix-particle decohesion and subsequent volume growth. In this article, the volumetric deformation accompanying uniaxial tension of particle-filled elastomeric materials at low temperatures is studied. An experimental set-up enabling full-field deformation measurements is outlined and novel data are reported on the significant volume growth accompanying uniaxial tension of two HNBR and one FKM compounds at temperatures of −18, 0, and 23 °C. The volumetric deformation was found to increase with reduced temperature for all compounds. To explain the observed dilatation, in situ scanning electron microscopy was used to inspect matrix-particle debonding occurring at the surface of the materials. A new constitutive model, combining the Bergström–Boyce visco-hyperelastic formulation with a Gurson flow potential function is outlined to account for the observed debonding effects in a numerical framework. The proposed model is shown to provide a good correspondence to the experimental data, including the volumetric response, for the tested FKM compound at all temperature levels

Volumetric strain measurement of polymeric materials subjected to uniaxial tension

A novel method for measuring and calculating volumetric strain in circular cylindrical uniaxial tension samples made from polymeric materials is proposed. It is shown that special considerations must be taken when calculating volumetric strain when a sample is in a postnecking state. Solely based on surface data, the key feature of the proposed correction is that it allows for an inhomogeneous distribution of longitudinal strain through the diameter of the sample, where a more traditional approach would be to assume a homogeneous distribution. These two approaches are evaluated by applying them to data from a close‐to‐incompressible steel sample. Whereas the proposed method indicates only a small positive increase in volume, the assumption of a homogeneous distribution results in substantial negative volumetric strains. Applying the two methods to tension samples made from HDPE and PVC, where plastic dilatation is nonlinear, again shows an initial negative volumetric strain for HDPE with the assumption of a homogeneous longitudinal strain. The proposed method predicts close‐to‐zero early‐stage volumetric strain for the same test. The differences are more subtle for samples of PVC. Micrographs obtained with scanning electron microscope show that the dilatation of PVC is related to voiding of the material around filler particles, while the underlying mechanism for HDPE is less clear. The results indicate that earlier reports of negative volumetric strain in polymers subjected to uniaxial tension might be artefacts of the implicit assumption made when calculating the volumetric strain

Volumetric strain measurement of polymeric materials subjected to uniaxial tension

A novel method for measuring and calculating volumetric strain in circular cylindrical uniaxial tension samples made from polymeric materials is proposed. It is shown that special considerations must be taken when calculating volumetric strain when a sample is in a postnecking state. Solely based on surface data, the key feature of the proposed correction is that it allows for an inhomogeneous distribution of longitudinal strain through the diameter of the sample, where a more traditional approach would be to assume a homogeneous distribution. These two approaches are evaluated by applying them to data from a close‐to‐incompressible steel sample. Whereas the proposed method indicates only a small positive increase in volume, the assumption of a homogeneous distribution results in substantial negative volumetric strains. Applying the two methods to tension samples made from HDPE and PVC, where plastic dilatation is nonlinear, again shows an initial negative volumetric strain for HDPE with the assumption of a homogeneous longitudinal strain. The proposed method predicts close‐to‐zero early‐stage volumetric strain for the same test. The differences are more subtle for samples of PVC. Micrographs obtained with scanning electron microscope show that the dilatation of PVC is related to voiding of the material around filler particles, while the underlying mechanism for HDPE is less clear. The results indicate that earlier reports of negative volumetric strain in polymers subjected to uniaxial tension might be artefacts of the implicit assumption made when calculating the volumetric strain

Anisotropic tensile behaviour of short glass-fibre reinforced polyamide-6

This paper presents an experimental investigation of injection-moulded short glass-fibre reinforced polyamide-6 reinforced with 0 wt.%, 15 wt.% and 30 wt.% fibres. The fibre orientation distributions are characterized by use of X-ray computed tomography. A shell-core-shell structure is found through the thickness of the materials, where the predominant fibre orientation is along the mould flow direction (MFD) in the shell layers and perpendicular to the MFD in the core layer. To study the mechanical behaviour, uniaxial tensile tests are conducted in seven directions relative to the MFD. The tests are instrumented with two cameras, which allows for accurate measurement of all strain components. The fibre-reinforced materials show moderate to high degree of anisotropy, increasing with the fibre content. Young’s modulus, in-plane and out-of-plane Poisson’s ratio, stress at maximum force and fracture strain vary smoothly with the in-plane specimen angle. It is demonstrated that orthotropic elasticity is an excellent approximation for the anisotropic elastic behaviour of the fibre-reinforced materials

Influence of stress triaxiality and strain rate on stress-strain behaviour and dilation of mineral-filled PVC

The influence of stress triaxiality and strain rate on the tensile behaviour of mineral-filled polyvinyl chloride (PVC) is investigated in this paper. Axisymmetric notched tensile specimens with notch radius equal to 20 mm, 5 mm and 2 mm were tested at three nominal strain rates of 0.0001s−1, 0.001s−1 and 0.01s−1. Surface deformations were measured by digital image correlation and contour tracking, employing two orthogonal cameras, whereas infrared thermography was used to measure self-heating. The yield strength of the material was found to be strain rate and pressure dependent. The volume change was estimated from the stretch field in the notch region of the specimens and found to depend on both stress triaxiality and strain rate. A marked increase of temperature was measured at the highest strain rate