Hugoniot States and Mie–Grüneisen Equation of State of Iron Estimated Using Molecular Dynamics

The objective of this study was to develop a micromechanical approach for determining the Mie–Grüneisen EOS parameters of iron under the Hugoniot states. The multiscale shock technique (MSST) coupled with molecular dynamics (MD) simulations was employed to describe the shocked Hugoniot relation of single-crystal (SC) and nanocrystalline (NC) iron under high pressures. The Mie–Grüneisen equation of state (EOS) parameters, the cold pressure (Pc), the cold energy (Ec), the Grüneisen coefficient (γ), and the melting temperature (Tm) are discussed. The error between SC and NC iron results was found to be less than 1.5%. Interestingly, the differences in Hugoniot state (PH) and the internal energy between SC and NC iron were insignificant, which shows that the effect of grain size (GS) under high pressures was not significant. The Pc and Ec of SC and NC iron calculated based on the Morse potential were almost the same with those calculated based on the Born–Mayer potential; however, those calculated based on the Born–Mayer potential were a little larger at high pressures. In addition, several empirical and theoretical models were compared for the calculation of γ and Tm. The Mie–Grüneisen EOSs were shown on the 3D contour space; the pressure obtained with the Hugoniot curves as the reference was larger than that obtained with the cold curves as the reference.

Investigation of creep and fatigue in high temperature polymer matrix composites using a micromechanical approach

Polymer matrix composites (PMC’s) are widely used in critical aerospace structures due to their numerous advantageous mechanical properties. Recently, PMC’s have been considered for high temperature applications where viscoelasticity arising from the time dependent nature of the polymer matrix becomes an important consideration. This inherent viscoelasticity can significantly influence deformation, strength and failure response of these materials under different loading modes and environmental factors. With a potentially large number of plies of different fiber directions and perhaps material properties, determining a fatigue failure criterion of any degree of generality through experiments only, may seem to be an unrealistic task. This difficult situation may be mitigated through the development of suitable theoretical micro or macro mechanical models that are founded on considering the fatigue failure of the constituting laminas. The micro‐approach provides a detailed examination of the individual failure modes in each of the constituent materials i.e. fiber, matrix. In this work, a micromechanical approach is used to study the role of viscoelasticity on the fatigue behavior of polymer matrix composites. In particular, the study examines the interaction of fatigue and creep in polymer matrix composites. The matrix phase is modeled as a vicoelastic material using Schapery’s single integral constitutive equation. Taking viscoelsticity into account allows the study of creep strain evolution during the fatigue loading. The fatigue failure criterion is expressed in terms of the fatigue failure functions of the constituent materials. The micromechanical model is also used to calculate these fatigue failure functions from the knowledge of the S‐N diagrams of the composite material in longitudinal, transverse and shear loadings thus eliminating the need for any further experimentation. Unlike the previous works, the present study can distinguish between the strain evolution due to fatigue and creep. The results can clearly show the contribution made by the effect of viscoelasticity to the total strain evolution during the fatigue life of the specimen. Although the effect of viscoelsticity is found to increase with temperature, its contribution to strain development during fatigue is compromised by the shorter life of the specimen when compared to lower temperatures.

Investigation of creep and fatigue in high temperature polymer matrix composites using a micromechanical approach

Polymer matrix composites (PMC’s) are widely used in critical aerospace structures due to their numerous advantageous mechanical properties. Recently, PMC’s have been considered for high temperature applications where viscoelasticity arising from the time dependent nature of the polymer matrix becomes an important consideration. This inherent viscoelasticity can significantly influence deformation, strength and failure response of these materials under different loading modes and environmental factors. With a potentially large number of plies of different fiber directions and perhaps material properties, determining a fatigue failure criterion of any degree of generality through experiments only, may seem to be an unrealistic task. This difficult situation may be mitigated through the development of suitable theoretical micro or macro mechanical models that are founded on considering the fatigue failure of the constituting laminas. The micro‐approach provides a detailed examination of the individual failure modes in each of the constituent materials i.e. fiber, matrix. In this work, a micromechanical approach is used to study the role of viscoelasticity on the fatigue behavior of polymer matrix composites. In particular, the study examines the interaction of fatigue and creep in polymer matrix composites. The matrix phase is modeled as a vicoelastic material using Schapery’s single integral constitutive equation. Taking viscoelsticity into account allows the study of creep strain evolution during the fatigue loading. The fatigue failure criterion is expressed in terms of the fatigue failure functions of the constituent materials. The micromechanical model is also used to calculate these fatigue failure functions from the knowledge of the S‐N diagrams of the composite material in longitudinal, transverse and shear loadings thus eliminating the need for any further experimentation. Unlike the previous works, the present study can distinguish between the strain evolution due to fatigue and creep. The results can clearly show the contribution made by the effect of viscoelasticity to the total strain evolution during the fatigue life of the specimen. Although the effect of viscoelsticity is found to increase with temperature, its contribution to strain development during fatigue is compromised by the shorter life of the specimen when compared to lower temperatures.

Anisotropic nature of the capillary stress tensor

The paper describes a micromechanical approach that explores the anisotropic nature of the capillary stress tensor and its evolution in pendular granular materials via Discrete Element Modeling (DEM) simulations. Dimensionless parameters are used to address the conditions under which the contribution of capillarity (or cohesive interparticle forces) to the stress transmission within a Representative Elementary Volume (REV) is expected to be considerable. From a series of suction-controlled conventional triaxial tests, numerical results show that the significance of the capillary stress and the relative magnitude of its mean to deviatoric components is directly connected to the characteristic particle size and applied stress. In addition, it is shown that the anisotropic character of the capillary stress tensor intensifies with increasing suction. Furthermore, a simple shear test is conducted at constant mean stress to reveal the development of deviatoric capillary stresses in the absence of any change in mean stress, which cannot be captured by the commonly used Bishop’s stress expression.