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Notes: Summary The spectral decomposition of the compliance, stiffness, and failure tensors for transversely isotropic materials was studied and their characteristic values were calculated using the components of these fourth-rank tensors in a Cartesian frame defining the principal material directions. The spectrally decomposed compliance and stiffness or failure tensors for a transversely isotropic body (fiber-reinforced composite), and the eigenvalues derived from them define in a simple and efficient way the respective elastic eigenstates of the loading of the material. It has been shown that, for the general orthotropic or transversely isotropic body, these eigenstates consist of two double components, σ1 and σ2 which are shears (σ2 being a simple shear and σ1, a superposition of simple and pure shears), and that they are associated with distortional components of energy. The remaining two eigenstates, with stress components σ3, and σ4, are the orthogonal supplements to the shear subspace of σ1 and σ2 and consist of an equilateral stress in the plane of isotropy, on which is superimposed a prescribed tension or compression along the symmetry axis of the material. The relationship between these superimposed loading modes is governed by another eigenquantity, the eigenangle ω. The spectral type of decomposition of the elastic stiffness or compliance tensors in elementary fourth-rank tensors thus serves as a means for the energy-orthogonal decomposition of the energy function. The advantage of this type of decomposition is that the elementary idempotent tensors to which the fourth-rank tensors are decomposed have the interesting property of defining energy-orthogonal stress states. That is, the stress-idempotent tensors are mutually orthogonal and at the same time collinear with their respective strain tensors, and therefore correspond to energy-orthogonal stress states, which are therefore independent of each other. Since the failure tensor is the limiting case for the respective σx, which are eigenstates of the compliance tensor S, this tensor also possesses the same remarkable property. An interesting geometric interpretation arises for the energy-orthogonal stress states if we consider the “projections” of σx in the principal3D stress space. Then, the characteristic state σ2 vanishes, whereas stress states σ1, σ3 and σ4 are represented by three mutually orthogonal vectors, oriented as follows: The ε3 and ε4 lie on the principal diagonal plane (σ3δ12) with subtending angles equaling (ω−π/2) and (π-ω), respectively. On the positive principal σ3-axis, ω is the eigenangle of the orthotropic material, whereas the ε1-vector is normal to the (σ3δ12)-plane and lies on the deviatoric π-plane. Vector ε2 is equal to zero. It was additionally conclusively proved that the four eigenvalues of the compliance, stiffness, and failure tensors for a transversely isotropic body, together with value of the eigenangle ω, constitute the five necessary and simplest parameters with which invariantly to describe either the elastic or the failure behavior of the body. The expressions for the σx-vector thus established represent an ellipsoid centered at the origin of the Cartesian frame, whose principal axes are the directions of the ε1-, ε3- and ε4-vectors. This ellipsoid is a generalization of the Beltrami ellipsoid for isotropic materials. Furthermore, in combination with extensive experimental evidence, this theory indicates that the eigenangle ω alone monoparametrically characterizes the degree of anisotropy for each transversely isotropic material. Thus, while the angle ω for isotropic materials is always equal to ωi = 125.26° and constitutes a minimum, the angle |ω| progressively increases within the interval 90–180° as the anisotropy of the material is increased. The anisotropy of the various materials, exemplified by their ratiosE L/2GL of the longitudinal elastic modulus to the double of the longitudinal shear modulus, increases rapidly tending asymptotically to very high values as the angle ω approaches its limits of 90 or 180°.

Notes: Summary  The spectral decomposition of the compliance, stiffness, and failure tensors for transversely isotropic materials was studied and their characteristic values were calculated using the components of these fourth-rank tensors in a Cartesian frame defining the principal material directions. The spectrally decomposed compliance and stiffness or failure tensors for a transversely isotropic body (fiber-reinf orced composite), and the eigenvalues derived from them define in a simple and efficient way the respective elastic eigenstates of the loading of the material. It has been shown that, for the general orthotropic or transversely isotropic body, these eigenstates consist of two double components, σ 1 and σ 2, which are shears (σ 2 being a simple shear and σ 1, a superposition of simple and pure shears), and that they are associated with distortional components of energy. The remaining two eigenstates, with stress components σ 3 and σ 4, are the orthogonal supplements to the shear subspace of σ 1 and σ 2 and consist of an equilateral stress in the plane of isotropy, on which is superimposed a prescribed tension or compression along the symmetry axis of the material. The relationship between these superimposed loading modes is governed by another eigenquantity, the eigenangle ω. The spectral type of decomposition of the elastic stiffness or compliance tensors in elementary fourth-rank tensors thus serves as a means for the energy-orthogonal decomposition of the energy function. The advantage of this type of decomposition is that the elementary idempotent tensors to which the fourth-rank tensors are decomposed have the interesting property of defining energy-orthogonal stress states. That is, the stress-idempotent tensors are mutually orthogonal and at the same time collinear with their respective strain tensors, and therefore correspond to energy-orthogonal stress states, which are therefore independent of each other. Since the failure tensor is the limiting case for the respective σ x-tensors, which are eigenstates of the compliance tensor S, this tensor also possesses the same remarkable property. An interesting geometric interpretation arises for the energy-orthogonal stress states if we consider the “projections” of σ x in the principal 3D stress space. Then, the characteristic state σ 2 vanishes, whereas stress states σ 1, σ 3 and σ 4 are represented by three mutually orthogonal vectors, oriented as follows: The ε 3- and ε 4-vectors lie on the principal diagonal plane (σ3∂12) with subtending angles equaling (ω−π/2) and (π− ; ω), respectively. On the positive principal σ3-axis, ω is the eigenangle of the orthotropic material, whereas the ε 1-vector is normal to the (σ3∂12)-plane and lies on the deviatoric π-plane. Vector ε 2 is equal to zero. It was additionally conclusively proved that the four eigenvalues of the compliance, stiffness, and failure tensors for a transversely isotropic body, together with value of the eigenangle ω, constitute the five necessary and simplest parameters with which invariantly to describe either the elastic or the failure behavior of the body. The expressions for the σ x-vector thus established represent an ellipsoid centered at the origin of the Cartesian frame, whose principal axes are the directions of the ε 1, ε 3- and ε 4-vectors. This ellipsoid is a generalization of the Beltrami ellipsoid for isotropic materials. Furthermore, in combination with extensive experimental evidence, this theory indicates that the eigenangle ω alone monoparametrically characterizes the degree of anisotropy for each transversely isotropic material. Thus, while the angle ω for isotropic materials is always equal to ω i =125.26° and constitutes a minimum, the angle |ω| progressively increases within the interval 90–180° as the anisotropy of the material is increased. The anisotropy of the various materials, exemplified by their ratios E L /2G L of the longitudinal elastic modulus to the double of the longitudinal shear modulus, increases rapidly tending asymptotically to very high values as the angle ω approaches its limits of 90 or 180°.

Notes: The influence of the hard or soft inclusions and the mesophase layers in either a soft-hard-soft or hard-soft-hard combination of biphase plates submitted to dynamic tensile loads on the fracture mode and bifurcation process in both phases was investigated in this paper. It was assumed that the soft or hard matrix is infolding the hard or soft inclusion of the plate, so that the plate constitutes a meridional section of the representative volume element of a unidirectional fiber composite, or a principal section of a particulate. The influence of the mechanical properties of either phase on the crack propagation velocity and the initiation of crack bifurcation was studied by using high-speed photography and dynamic caustics. The results showed that the propagating crack tended to bifurcate either in the brittle or in the mesophase layer under certain conditions of propagation velocity. It was shown that bifurcation of a propagating crack depends on the elastic moduli and Poisson's ratios of the phases, as well as on the extent of the mesophase layer, which depended on the adhesion quality of phases.

Notes: The thermomechanical behavior of particle composites was investigated in their transition region. In particular, the value of the glass-transition temperature Tg, which constitutes an upper limit for the structurally important glassy region, was examined. According to experimental evidence existing in the literature the introduction of a reinforcing filler in a polymeric matrix causes Tg of the latter to increase, unless mechanical imperfections counterbalance the reinforcing effect or even produce a Tg for the composite which is lower than that of the matrix. Based on mechanical theories, valid for the mechanical moduli of viscoelastic particle composites, a model was introduced that explains why the glass transition of composite materials may be reduced in some cases, whereas it may be increased in others. The concept of interphase between inclusions and matrix was used for the development of the model. Interphase is assumed to be a region, which is created between the matrix material and the filler particles, both considered as homogeneous and isotropic, whose thermomechanical properties and volume fraction may be determined from the overall thermomechanical behavior of the composite.

Notes: Retardation spectra, derived from dynamic measurements of extension compliances along three decades on the logarithmic scale of frequencies in standard specimens prepared from a fiber-reinforced composite with their fibers parallel to the longitudinal axis of the specimens, have revealed the structure of the matrix material of the composite. The experimental results were used to prove that the physicochemical rearrangements in the vicinity of the inclusions, consisting of restrained development of the macromolecules and especially their side chains due to the presence of the other phase, concentration of voids and dirt, shrinkage stresses developed during curing and creating microcracks (radial as well as along the interface), are activated by the existence of high stress gradients and eventually stress singularities due to the strong adhesion developed between phases.

Notes: The adhesion between matrix and inclusions (fibers or particulates) in a composite material is one of principal factors characterizing the mechanical and physical behavior of the modern composite materials. All theoretical models describing these substances neglect to consider the influence of the boundary layer developed between phases during the preparation of the composite. In this paper, two versions of a theoretical model were introduced for the evaluation of this mesophase layer. It had been shown that this thin layer influences considerably the physical properties of the composite. It was assumed that the physical properties of the mesophase unfold from those of the hard-core fibers to those of the softer matrix. Thus, a multicylinder model was assumed, improving the classical two-cylinder model introduced by Hashin and Rosen for the representative volume element of the composite. Based on thermodynamic phenomena appearing at the glass transition temperatures of the composite and concerning the positions and the sizes of the heat-capacity jumps there, as well as on the experimental values of the longitudinal elastic modulus of the composite, the extent of the mesophase and the mechanical properties of the composite may be accurately evaluated. These versions of model are based on a previous one concerning a multilayer model, but they are considerably improved, in order to take into consideration, in a realistic manner, the physical phenomena developed in fiber-reinforced composites.

Notes: Structural changes which take place in many amorphous polymers, when they are annealed at temperatures near the glass transition temperature, have important theoretical, physical, and mechanical consequences. In this paper the possible existence of some local ordering in highlycrosslinked epoxy resins is studied. Three kinds of tests - TMA, DSC, and dynamic experiments - are used for a type of epoxy resin, cured with six different amounts of curing agent. In order to study the effect of the thermal history on the behavior of the polymer at its transition region, as well as the morphology of the materials tested, three different thermal treatments have been followed. Interesting results were derived concerning the influence of these parameters to these parameters to the mechanical characterization of the polymer.

Notes: Four polystyrene-polyurethane mechanical blends were prepared with 5, 10, 20, and 40% thermoplastic polyurethane, respectively. Their impact properties were compared with pure polystyrene and commerical types of impact polystyrene. The rheological properties of the blends were studied with DSC and dynamic mechanical spectroscopy. It was found that addition of softer polyurethane conglomerates embedded inside the polystyrene matrix, although increasing the toughness of the blend as expected from addition of the softer particulate, also increased the glassy region of the blends by shifting their Tgs to higher temperatures. A theory based on the interaction of phases was propounded explaining this phenomenon.

Notes: A class of amine-cured epoxy resins containing various amounts of polysulfide plasticizer were subjected to dynamic testing during curing at high temperature. Both E modulus and loss factor were determined simultaneously. It was proved that the method allowed for rapid determination of the general pattern of the crosslinking procedure and the necessary curing time and, in general, that dynamic methods are most suitable for the mechanical characterization of polymers under curing at each stage of the curing cycle.

Notes: The influence of moisture absorption on the extent of the boundary interphase in particulate composites is thoroughly studied. It was found that, during the process of moisture absorption there is a variation of the extent of the boundary interphase, closely related to the degradation of the mechanical behavior of the composite, as well as to the percentage amount of moisture absorbed. An explanation of the observed relationship was advanced, based on a theoretical mechanism of absorption. This study complements a previous one, where the observed degradation of the thermomechanical properties of particulate composites due to moisture absorption was shown to be intimately interrelated with the state and extent of the interphase between fillers and matrix.