A “quasi-elastic” affine formulation for the homogenised behaviour of nonlinear viscoelastic polycrystals and composites

The derivation of the overall behaviour of nonlinear viscoelastic (or rate-dependent elastoplastic) heterogeneous materials requires a linearisation of the constitutive equations around uniform per phase stress (or strain) histories. The resulting Linear Comparison Material (LCM) has to be linear thermoviscoelastic to fully retain the viscoelastic nature of phase interactions. Instead of the exact treatment of this LCM (i.e., correspondence principle and inverse Laplace transforms) as proposed by the “classical” affine formulation, an approximate treatment is proposed here. First considering Maxwellian behaviour, comparisons for a single phase as well as for two-phase materials (with “parallel” and disordered morphologies) show that the “direct inversion method” of Laplace transforms, initially proposed by Schapery (1962), has to be adapted to fit correctly exact responses to creep loading while a more general method is proposed for other loading paths. When applied to nonlinear viscoelastic heterogeneous materials, this approximate inversion method gives rise to a new formulation which is consistent with the classical affine one for the steady-state regimes. In the transient regime, it leads to a significantly more efficient numerical resolution, the LCM associated to the step by step procedure being no more thermoviscoelastic but thermoelastic. Various comparisons for nonlinear viscoelastic polycrystals responses to creep as well as relaxation loadings show that this “quasi-elastic” formulation yields results very close to classical affine ones, even for high contrasts.     

A ‘stack’ model of rate-independent polycrystals

A novel ‘stack’ model of a rate-independent polycrystal, which extends the ‘ALAMEL’ model of Van Houtte et al. (2005) is proposed. In the ‘stack’ model, stacks of N neighboring ‘ALAMEL’ domains collectively accommodate the imposed macroscopic deformation while deforming such that velocity and traction continuity with their neighbors is maintained. The flow law and consistency conditions are derived and an efficient solution methodology based on the linear programming technique is given. The present model is applied to study plastic deformation of an idealized two-dimensional polycrystal under macroscopically imposed plane-strain tension and simple shear constraints. Qualitative and quantitative variations in the predicted macroscopic and microscopic response with N are presented. The constraint on individual ‘ALAMEL’ domains diminishes with stack size N but saturates for large N. Computational effort associated with the present model is analyzed and found to be well within one order of magnitude greater than that required to solve the classical Taylor model. Furthermore, implementation of the consistency conditions is found to reduce computation time by at least 50%.     

Molecular Dynamics Simulation of Impact Fracture in Polycrystalline Materials

Technique for creation of polycrystalline computer materials is presented. The method considered allows for the obtaining of not only polycrystalline particle packings with various grains sizes but also the creating of materials with the preset value of porosity. Plate impact experiments were performed to compare strength properties of mono- and polycrystalline computer materials and also to investigate influence of the material porosity on the shock wave penetration and spallation processes. The experiments show significant differences in the impact fracture processes between mono- and polycrystalline materials. Smearing the shock waves due to heterogeneity of the granular structure of the polycrystals decreases localization effects, and the fracture occupies larger areas but with the smaller level of injury. Porosity adds significant resistance due to the strong plastic deformation during the pore collapsing. This effect can strongly decrease the penetration distance of the shock wave and even prevent the spallation.     

Physico-Chemical Characterization of Yu Guo Beads(1100-771 B. C. ) in China

When was the earliest glass produced in China? This has still been a question so far. Some archaeologists have thought that Yu Guo beads are real glass, the earliest glass(1100-771 B. C. ) in China. However, more details of scientific investigations in this paper show that Yu Guo beads are mainly made of clastic quartz (>95%) with a small amount of clay and sintered under the low temperature(500-600℃). It is not a glassy body, but a kind of polycrystal ornaments.     

Perturbation approach to elastic constitutive relations of polycrystals

Herein we obtain a formula for the effective elastic stiffness tensor C^eff of an orthorhombic aggregate of cubic crystallites by the perturbation method. The effective elastic stiffness tensor of the polycrystal gives the relationship between volume average stress and volume average strain. Under Voigt's model, Reuss’ model and Man's theory, the elastic constitutive relation accounts for the effect of the orientation distribution function (ODF) up to terms linear in the texture coefficients. However, the formula derived in this paper delineates the effect of crystallographic texture on elastic response and shows quadratic texture dependence. The formula is very simple. We also consider the influence of grain shape to elastic constitutive relations of polycrystals. Some examples are given to compare computational results of the formula with those given by Voigt's model, Reuss's model, the finite element method, and the self-consistent method. In Section 3, we also present an expression of the perturbation displacement field, in which Green's function for an orthorhombic aggregate of cubic crystallites is included.     

A multi-length scale sensitivity analysis for the control of texture-dependent properties in deformation processing

Material property evolution during processing is governed by the evolution of the underlying microstructure. We present an efficient technique for tailoring texture development and thus, optimizing properties in forming processes involving polycrystalline materials. The deformation process simulator allows simulation of texture formation using a continuum representation of the orientation distribution function. An efficient multi-scale sensitivity analysis technique is then introduced that allows computation of the sensitivity of microstructure field variables such as slip resistances and texture with respect to perturbations in macro-scale forming parameters such as forging rates, die shapes and preform shapes. These sensitivities are used within a gradient-based optimization framework for computational design of material property distribution during metal forming processes. Effectiveness of the developed computational scheme is demonstrated through computationally intensive examples that address control of properties such as Young’s modulus, strength and magnetic hysteresis loss in finished products.     

The effect of element substitution on high-temperature thermoelectric properties of Ca3Co2O6 compounds

Polycrystalline Ca₃Co_1.8M_0.2O₆ (M=Mn, Fe, Co, Ni, Cu) and Ca_2.7Na_0.3Co₂O₆ were synthesized by solid-state reaction to evaluate the effect of substitution on the thermoelectric properties of Ca₃Co₂O₆. Substitution by Mn, Cu and Na appears to increase carrier density, given that electrical resistivity (ρ) and the Seebeck coefficient (S) were simultaneously reduced. Conversely, Fe substitution seems to reduce carrier density, resulting in a simultaneous increase in S and ρ. Cu and Na substitution resulted in a significant decrease in ρ due to enhancement of grain size and grain boundary connectivity, which could have a strong impact on ρ. Not only the intrinsic substitution effect on the electronic state but also this modification of the microstructure plays an important role in improvement of the thermoelectric power factor, particularly in the case of the Na-substituted sample.     

Modeling the microstructural evolution of metallic polycrystalline materials under localization conditions

In general, the shear localization process involves initiation and growth. Initiation is expected to be a stochastic process in material space where anisotropy in the elastic-plastic behavior of single crystals and inter-crystalline interactions serve to form natural perturbations to the material's local stability. A hat-shaped sample geometry was used to study shear localization growth. It is an axi-symmetric sample with an upper “hat” portion and a lower “brim” portion with the shear zone located between the hat and brim. The shear zone length was 870-890 μm with deformation imposed through a Split-Hopkinson Pressure Bar system at maximum top-to-bottom velocity in the range of 8-25 m/s. The deformation behavior of tantalum tophat samples is modeled through direct polycrystal simulations. An embedded Voronoï-tessellated two-dimensional microstructure is used to represent the material within the shear zone of the sample. A thermo-mechanically coupled elasto-viscoplastic single crystal model is presented and used to represent the response of the grains within the aggregate shear zone. In the shoulder regions away from the shear zone where strain levels remain on the order of 0.05, the material is represented by an isotropic J₂ flow theory based upon the elasto-viscoplastic Mechanical Threshold Stress (MTS) model for flow strength. The top surface stress versus displacement results were compared to those of the experiments and over-all the simulated stress magnitude is over-predicted. It is believed that the reason for this is that the simulations are two-dimensional. A region within the numerical shear zone was isolated for statistical examination. The vonMises stress state within this isolated shear zone region suggests an approximate normal distribution with a factor of two difference between the minimum and maximum points in the distribution. The equivalent plastic strain distribution within this same region has values ranging between 0.4 and 1.5 and is not symmetric. Other material state distributions are also given. The crystallographic texture within this isolated shear zone is also compared to the experimental texture and found to match reasonably well considering the simulations are two-dimensional.     

Classical and quantum molecular dynamics of cation in (CH3NH3)3 Sb2Br9 polycrystal as studied by 1H NMR.

¹H spin-lattice relaxation times and second moments were determined for polycrystalline (CH₃NH₃)₃Sb₂Br₉ sample in a wide range of temperature (5–200 K) at 24.6 and 55.2 MHz. ²H NMR spectra of (CD₃NH₃)₃Sb₂Br₉ were recorded between 5 K and room temperature. The relaxation time is interpreted as a result of motion of two different non-equivalent types of monomethylammonium cations occurring at the 2:1 proportion in a unit cell. Below 30 K, the relaxation processes via tunneling are suggested to dominate. Above 30 K, only classical behaviour of methylammonium cations is detected. Two monomethylammonium cations relax with the classical correlated C₃ reorientation and the rotational tunnelling mechanism, while the third cation exhibits only the classical correlated reorientation. The dynamic parameters of these motions have been determined.     

Two stochastic mean-field polycrystal plasticity methods

In this work, we develop two mean-field polycrystal plasticity models in which the crystal velocity gradients L^c are approximated stochastically. Through comprehensive CPFEM analyses of an idealized tantalum polycrystal, we verify that the L^c tend to follow a normal distribution and surmise that this is due to the crystal interactions. We draw on these results to develop the stochastic Taylor model (STM) and the stochastic no-constraints model (SNCM), which differ in the manner in which the crystal strain rates are prescribed. Calibration and validation of the models are performed using data from tantalum compression experiments. Both models predict the compression textures more accurately than the fully constrained model (FCM), and the SNCM predicts them more accurately than the STM. The STM is extremely computationally efficient, only slightly more expensive than the FCM, while the SNCM is three times more computationally expensive than the STM.