Flexural and compressive strength of the landfast sea ice in the Prydz Bay, East Antarctic

A total of 25 flexural and 55 uniaxial compressive strength tests were conducted using landfast sea ice samples collected in the Prydz Bay. Three-point bending tests were performed at ice temperatures of −12 to −3 °C with force applied vertically to original ice surface, and compressive tests were performed at −3 °C with a strain-rate level of 10−6–10−2 s−1 in the directions vertical and horizontal to ice surface. Judging from crystal structure, the ice samples were divided into congelation ice, snow ice, and a mixture of the these two. The results of congelation ice showed that the flexural strength had a decreasing trend depending on porosity rather than brine volume, based on which a mathematical equation was established to estimate flexural strength. Both flexural strength and effective modulus increased with increasing platelet spacing. The uniaxial compressive strength increased and decreased with strain rate below and above the critical regime, respectively, which is 8.0 × 10−4–1.5 × 10−3 s−1 for vertically loaded samples and 2.0 × 10−3–3.0 × 10−3 s−1 for horizontally loaded samples. A drop off in compressive strength was shown with increasing sea ice porosity. Consequently, a model was developed to depict the combined effects of porosity and strain rate on compressive strength in both ductile and brittle regimes. The mechanical strength of mixed ice was lower than congelation ice, and that of snow ice was much weaker. To provide a safe guide for the transportation of goods on landfast sea ice in the Prydz Bay, the bearing capacity of the ice cover is estimated with the lower and upper envelopes of flexural strength and effective modulus, respectively, which turned out to be a function of sea ice porosity.

Effective moduli of rocks predicted by the Kuster–Toksöz and Mori–Tanaka models

Natural rocks are polymineral composites with complex microstructures. Such strong heterogeneities significantly affect the estimation of effective moduli by some theoretical models. First, we have compared the effective moduli of isotropic rocks predicted by the Kuster–Toksöz (KT) model and the Mori–Tanaka (MT) model. The widely used KT model only has finite precision in many cases because of its assumption that is restricted to the first-order scattering approximation. However, the MT model based on the Eshelby tensor in mesomechanics has the advantage of predicting effective moduli of rocks, especially when the volume fraction of embedded inclusions is sufficiently large. In addition, the MT model can be used to predict the effective modulus of anisotropic rocks, but the KT model cannot. For a certain kind of shale or tight sandstones, which are viewed as isotropic composites, both the models work well. For the medium containing spherical pores, both the models produce the same results, whereas for ellipsoidal pores the MT model is more accurate than the KT model, validated by the finite element simulations. In what follows, the applicable ranges of simplified formulas for pores with needle, coin and disk shapes, widely used in engineering, are quantitatively given based on the comparison with the results according to the reduced ellipsoidal formulas of the MT and KT models. These findings provide a comprehensive understanding of the two models in calculating the effective modulus of rocks, which are beneficial to such areas as petroleum exploration and exploitation, civil engineering, and geophysics.

Storage Moduli of in situ Polymerised and Melt Extruded PA6 Graphite (G) Composites

Four PA6/graphite (G) composites systems were made. Two in situ polymerisation equivalent in mixing strain and two melt extrusion of equivalent processing strain. The effective modulus of the carbons, room temperature storage modulus and storage modulus at 80 ⁰C were evaluated using Dynamic Mechanical and thermal Analysis (DMTA). Melt processing, was employed to make PA6/carbon composite systems over a range of loadings of Graphite (G) and Graphite Nano Platelets (GNP) fillers. Melt extrusion was carried out using 100/6 processing condition, which indicates an extrusion screw rotation frequency of 100 rpm applied for 6 minutes (min) and 200/3 processing conditions, of 200 rpm for 3 min. For in situ polymerised systems G and GNP dispersion was made using two similar conditions designated as 40/10 and 20/20. Here, 40/10 indicates that sonication amplitude of 40% was applied for 10 min, whereas in the 20/20 conditions, amplitude of 20% was applied for 20 min. For in situ Nano P INP 40/10 systems weak interaction between PA6 and GNP is indicated by the very low modulus enhancement above glass transition temperature (Tg). The modulus behaviour shows that the reinforcement provided by GNP is not significant relative to unfilled PA6, despite the low loading levels. A similar, but less pronounced, behaviour is observed for INP 20/20 system. Effective modulus for the in situ polymerised systems INP 40/10, was 4.8 GPa. Due to the low loading level of GNP used and the better reaction rates, an extrapolated modulus of 22.4 GPa is obtained in the INP 20/20 system. For G200/3 and G100/6 the trend of increasing modulus with GNP loading is not followed exactly. On all levels of loading, the relative modulus values of the INP 20/20 system are higher than those of the 40/10 system, a reflection of retention or improvement in the aspect ratio of the GNP due to less intensive sonication.

Substrate adhesion evolves non-monotonically with processing time in millimeter-scale aligned carbon nanotube arrays

Aligned carbon nanotube (CNT) array adhesion strength evolves with CNT process time, decreasing and then increasing during growth and annealing, as captured by models relating CNT diameter, array effective modulus, and CNT–substrate work of adhesion.

Time-dependent behaviour of concrete

<p>This chapter provides an introduction to the constitutive models commonly specified in design guidelines to describe the time-dependent behaviour of concrete and that can be used for the time-dependent analysis of composite structures. These formulations range from the simplest algebraic methods, such as the Effective Modulus Method that is widely recommended in design guidelines, to more sophisticated approaches that can account for creep and shrinkage effects in advanced modelling. The last part of the chapter provides a brief overview of multi-physics modelling that could be useful in predicting the concrete time-dependent response for composite construction.</p>

Introduction

<p>This chapter provides an introduction to the constitutive models commonly specified in design guidelines to describe the time-dependent behaviour of concrete and that can be used for the time-dependent analysis of composite structures. These formulations range from the simplest algebraic methods, such as the Effective Modulus Method that is widely recommended in design guidelines, to more sophisticated approaches that can account for creep and shrinkage effects in advanced modelling. The last part of the chapter provides a brief overview of multi-physics modelling that could be useful in predicting the concrete time-dependent response for composite construction.</p>

Multitudes of Voigt - Reuss forks and Voigt - Christensen - Reuss tridents

In the literature, there are many studies of the representative volume of a composite material, in particular, those calculated using the formulas of Christensen, Voigt and Reiss. The aim of this work is to study the features of evaluating the set of forks of effective modules. Methods. On the basis of solving the Lame problem (for a thick-walled sphere), a spherical model of a representative volume (cell) of a composite material with a granular (spherical) filler is compiled and the value of the effective modulus of elasticity of a two-phase composite is determined. The study of the obtained formula for the effective modulus, expressed in dimensionless quantities, for the cell material revealed its identity with the R.M. Christensens formula, expressed in dimensional values, for the bulk modulus of composites with a spherical filler. In this case, Christensens solution was previously obtained by a different method when he considered the polydisperse model of the composite. The dimensionless form of the function (effective module) of three dimensionless parameters made it possible in flat spaces (two coordinate planes) to construct graphical images of the function of the named modules according to Christensen, which are compared and combined in one figure with similar images of the functions of estimating the values of the modules (real composites) according to Voigt and Reiss. Graphical studies in relation to the spherical representative volume model show that in the flat space of the set of Voigt - Reuss forks, these forks are not narrowed, but they are partially filled by the flat space of the set of Christensen - Reiss forks. The graphs of the functions of the modules, at the same time, form, simultaneously with the sets of two-toothed forks, a set of Voigt - Christensen - Reiss trident forks (tridents), which, depending on the size of the intervals of the numbers of the studied parameters, have forks of different sizes. Results. Graphic illustrations of numerical examples have been obtained showing that for given values of the module of the matrix and filler and the volume fraction of the latter, it is possible to determine the effective volumetric module and shear module of two-phase composites, and to perform a comparison with the conclusions of the applied plan. The dimensionless form of the obtained expressions makes it possible to solve the inverse problems of the mechanics of polydisperse composites, for example, to determine the volume module of the composite components by the effective modulus obtained by mechanical testing of standard samples.