Nonlinear Mechanical Response of Polymer Matrix Composites: A Review

Abstract

The present article provides a review on the nonlinear mechanical behavior of polymer matrix composites (PMCs). Initially, essential mechanisms driving the nonlinear response of PMCs under different loading conditions are discussed. Rate-dependence, tension-compression asymmetry, viscous behavior, unloading characteristics, interaction between stress components and effects of environmental factors on mechanical properties are briefly reviewed. This is followed by a review of major approaches and constitutive models for predicting stress–strain behavior of PMCs. Following an increasing degree of complexity, models are categorized into four major classes: nonlinear elasticity models, elastic-plastic models, elastic-plastic-viscous models and Damage-Plasticity models. The vast number of existing models is mainly due to the anisotropy and inhomogeneity of PMCs. In brief, this review focuses on informing the reader of major frameworks, rather than addressing all the models in detail.     

Effect of persistence on the significance of Kendall’s tau as a measure of correlation between natural time series

Although persistence in natural data is generally admitted, its effect on the significance of various statistical tests has not been extensively studied and is sometimes overlooked or simply ignored in practice. In particular, modified tests that are robust in the presence of persistence are still lacking. In many situations, need may arise to test the significance of correlation between two observed natural time series. Although the estimation of the classical product-moment correlation coefficient is a straightforward task, classical significance testing depends on two major assumptions. The first assumption is that the data are Gaussian, which is violated by many natural time series. In this case, a distribution-free measure of correlation, such as Kendall’s tau should be used. The second, and often overlooked assumption, is that the observations in each time series are not autocorrelated, which is also violated by most natural time series. Similar to the case of trend testing (e.g. Mann-Kendall trend test), which has received some attention recently, the existence of persistence increases the chance of falsely detecting significant correlation when the two series are actually uncorrelated. In this paper, the effect of both short- and long-term persistence (STP and LTP) on the distribution of Kendall’s tau as a distribution-free measure of correlation between two time series is investigated, and an exact expression for its variance under persistence is derived. The implications of these results for the analysis of natural data are illustrated through the study of spurious correlation between a 133-year Nile flow time series from A.D. 1871 to A.D. 2003 and independent segments of a reconstruction of the North Hemisphere temperature time series from A.D. 1000 to A.D. 1980, both of which exhibit LTP. It is shown that spurious significant correlation between completely unrelated segments of the two time series is on average three times as common as in random series of the same length at the 10% significance level, which is consistent with the theoretical results. It is also shown that accounting for LTP by using the correct variance of the test statistic effectively reduces the probability of false identification to near its expected nominal value of 10%. Similar results were obtained at other significance levels.     

Aero-thermo-mechanical characteristics of imperfect shape memory alloy hybrid composite panels

A nonlinear finite element model is provided to predict the static aero-thermal deflection and the vibration behavior of geometrically imperfect shape memory alloy hybrid composite panels under the combined effect of thermal and aerodynamic loads. The nonlinear governing equations are obtained using Marguerre curved plate theory and the principle of virtual work taking into account the temperature-dependence of material properties. The effect of large deflection is included in the formulation through the von Karman nonlinear strain-displacement relations. The thermal load is assumed to be a steady-state constant-temperature distribution, whereas the aerodynamic pressure is modeled using the quasi-steady first-order piston theory. The Newton-Raphson iteration method is employed to obtain the nonlinear aero-thermal deflections, while an eigenvalue problem is solved at each temperature step and static aerodynamic load to predict the free vibration frequencies about the deflected equilibrium position. Finally, the nonlinear deflection and free vibration characteristics of a composite panel are presented, illustrating the effects of geometric imperfection, temperature rise, aerodynamic pressure, boundary conditions and shape memory alloy fiber embeddings on the panel response.     

Separation and preconcentration in a batch mode of Cd(II), Cr(III, VI), Cu(II), Mn(II, VII) and Pb(II) by solid-phase extraction by using of silica modified with N-propylsalicylaldimine

The complexes formed between IE11 and Cd(II), Cr(III), Cu(II), Mn(II) and Pb(II) were identified and confirmed by IR, UV and pH-metric titration. The uptake behavior of porous silica modified with N-propylsalicylaldimine (IE11) and these metal ions were studied. Log k(d) was found to be within the range 2.19-5.16 depending on pH and time of stirring. IE11 was used in the separation and preconcentration of Cd(II), Cr(III, VI), Cu(II), Mn(II, VII) and Pb(II) from some natural water samples. Data were compared with those obtained by the solvent extraction method APDC/MIBK. The proposed methodology allows to verify an improvement in the water quality of Nile River probably attributed to high to moderate floods in the last few years. The method was found to be accurate and not subject to random error, i.e. precise.     

The pattern of freezing of grapevine shoots during early bud growth

The pattern of freezing of two varieties of grapevine during spring bud burst was characterised using infrared thermography. All plants studied showed endogenous freezing of the stems and subsequent rapid ice spread (0.47 cm/s) analogous to ice spread in bulk water suggesting ice travel in the xylem. Barriers to ice spread were observed between stembranches and more importantly between the stem and buds. Buds froze after the stem and freezing appeared to be initiated from the stem. The lack of a fully functional xylem system is proposed as the barrier to ice spread. All buds which froze suffered complete frost kill whilst frozen stem recovered unharmed. Only 58% of the buds froze and those that did not freeze survived completely.     

Spectroscopic studies on some phenylethylamine drugs: Molecular orbital calculations

The electronic absorption spectra of some phenylethylamine drugs, namely, d-pseudoepherine, l-pseudoephedrine, l-ephedrine, dl-ephedrine dl-norephedrine, phenylethylamine, methoxyphenamine, and l-noradrenaline were investigated in polar and nonpolar solvents. The observed transitions were interpreted, and the role of σ-π interaction was explored. Molecular orbital calculations were performed on representatives of the above group of compounds, namely, d-pseudoephedrine, l-ephedrine, and l-noradrenaline using the INDO procedures and adopting the best conformer of the molecule. The transition energy, band intensity, and dipole moments were calculated and corresponded satisfactorily with the experimental values.     

Object-motion measurements using pulse-echo acoustical speckle and two-dimensional correlation

A basic theory of acoustical speckle and cross-correlation is described which utilizes the ubiquitous wave characteristics in ultrasonics. A computer-based pulse-echo system has been developed. It is interfaced to a VAX11/780 computer which operates the system and performs the data analysis. Data from three tests using specimens of steel, aluminum and Plexiglas are discussed. On each specimen, a pulse-echo scan of a scattering surface is made over some area which represents reference configuration. After the surface is displaced, a pulse-echo scan is made over the same area. A small region of the displaced configuration is correlated with the reference as a measure of object motion.     

Kinetics of hydrolysis of some new heterocyclic azomethines

Kinetics of base hydrolysis of new heterocyclic azomethines derived from active methyl quaternary salts and aromatic nitroso compounds were investigated in the presence of 70% (wt/wt) water-methanol. The base hydrolysis of these compounds is strictly first-order with respect to OH^– and azomethine. The rate determining step is suggested to be the attack of the hydroxide ion on the free base. Effects of water content and nature of organic hydroxylic solvent have been studied. It is concluded that specific solute-solvent interactions through dispersion forces play a major role in the base hydrolysis rate of the azomethines investigated. The effect of pH (2.98 – 12.24) on hydrolysis rates of compounds having a diethylamino substituent in the presence of 30% methanol has been studied. In acidic media, the rate determining step is probably the water attack on the protonated substrate.