半晶态聚合物拉伸变形的微观机理

应用大规模分子动力学方法,采用粗粒化聚乙烯醇模型,模拟了晶区与非晶区随机交杂的半晶态聚合物模型系统,研究了半晶态聚合物在单轴拉伸变形过程中的应力-应变行为和微观结构演变.应力-应变曲线表现出4个典型变形阶段:弹性变形、屈服、应变软化和应变强化.在拉伸变形过程中,主要存在晶区折叠链之间的滑移、晶区破坏、非晶区的解缠结,以及分子链沿拉伸方向重新取向等4种主要的微结构演变形式.在屈服点附近,晶区分子链之间排列紧密程度减小而发生滑移,之后晶区变化需要的应力变小,从而形成应变软化现象.随着应变的增大,经各分子链段协同作用使非晶区分子链的解缠结和重新取向行为扩展到相对宏观尺度,导致拉伸应力增大而形成应变强化现象.      

Atomistic simulation of crystallization of a polyethylene melt in steady uniaxial extension

We present simulation results of flow-induced crystallization of a dense polymeric liquid subjected to a strong uniaxial elongational flow using a rigorous nonequilibrium Monte Carlo method. A distinct transition between the liquid and the crystalline phases occurred at critical values of flow strength, with an abrupt, discontinuous transition of the overall chain conformation. The flow-induced crystalline phase matched quantitatively the experimental X-ray diffraction data of the real crystals remarkably well, including the sharp Bragg peaks at small wavenumbers, k < 1.5 Å^?1, indicating the existence of a global long-range ordering. We also found that the enthalpy change (ΔH = 225 J/g) during the phase transition was quantitatively very similar to the experimental heat of fusion (276 J/g) of polyethylene crystals under quiescent conditions. Furthermore, a detailed analysis of the configuration-based temperature provided a sound microscopic physical origin for the effective enhancement of the crystallization (or melting) temperature that has been observed in experiments. Simulation results also allow for the deduction of potential nonequilibrium expressions for thermodynamic quantities, such as temperature and heat capacity.     

A novel efficient hybrid DSMC–dynamic collision limiter algorithm for multiscale transitional flows

A new 2D parallel multispecies polyatomic particle–based hybrid flow solver is developed by coupling the Direct Simulation Monte Carlo (DSMC) method with a novel Dynamic Collision Limiter (DCL) approach to solve multiscale transitional flows. The hybrid DSMC‐DCL solver can solve nonequilibrium multiscale flows with length scales ranging from continuum to rarefied. The DCL method, developed in this work, dynamically assigns different number of collisions in cells, which is based on the local value of K‐S parameter such that the number of collisions per time step is limited in near‐equilibrium flow regions. Present hybrid solver uses the Kolmogorov‐Smirnov statistical test as the continuum breakdown parameter, based on which, the solution domain is decomposed into near‐equilibrium and nonequilibrium flow regions. Direct Simulation Monte Carlo is used where nonequilibrium flow regions are encountered, while the DCL method is used where flow regions are found to be in near‐equilibrium state. In this work, we have studied hypersonic flow of nitrogen over a blunt body with an aerospike and supersonic flow of argon through a micronozzle. The results obtained by the hybrid DSMC‐DCL solver are compared and shown to agree well with the experimental data and with those obtained from DSMC, with significant savings in the computational cost.     

A microstructural flow-induced crystallization model for film blowing: validation with experimental data

The two-phase microstructural/constitutive model for film blowing of Doufas and McHugh (D-M) (J Rheol 45:1085–1104, 2001a) is validated against online film data of a linear low-density polyethylene (LLDPE) at a variety of processing conditions. The D-M model includes the effects of thermal and flow-induced (enhanced) crystallization (FIC) coupled with the rheological response of both the melt and semicrystalline phases under fabrication conditions. The model predictions of bubble radius, velocity, and crystallinity profiles are in quantitative agreement with available experimental data over a wide range of blow-up ratios (BUR), take-up ratios (TUR), and bubble cooling rates using the same set of material/model parameters. The model naturally predicts the location of the frost line as a consequence of system stiffening due to crystallization overcoming the pitfalls of traditional modeling approaches that impose it as an artificial boundary condition. For a wide range of processing conditions, it is found that key film mechanical properties including elongation to break, yield stress, tensile modulus, and tear strength correlate well with predicted locked-in extensional stresses and molecular orientation at the frost line enabling development of quantitative structure-process-properties relationships that are useful in product and process development. The D-M model for film blowing is physics-based including elements of molecular rheology (polymer kinetic theory), suspension, and nucleation theories as well as irreversible thermodynamics principles, yet being tractable for continuum-based numerical simulations with practical industrial applicability. The FIC enhancement factor of the model is shown to be proportional to $\exp \left (\lambda _{\text {eff},\textnormal {w}}^{2} -1\right )$ , where λ _eff,w is a molecular chain stretch ratio of the whole chain and proportional to exp (λ ² ? 1), where λ is the stretch ratio of the remaining (uncrystallized) amorphous chain, consistent with fundamental kinetic Monte Carlo simulations of flow-induced nucleation of Graham and Olmsted (Phys Rev Lett 103:115702-1–115702-4, 2009).     

A stochastic model for the temporal aspects of flow intermittency in micropillar compression

Systematic experimental investigations have demonstrated that the plastic deformation of micropillar proceeds through a sequence of intermittent bursts, the sizes of which follow power-law statistics. In this study, a stochastic model based on the power-law distribution of burst size is formulated in the framework of crystal plasticity in order to investigate the temporal aspects of flow intermittency in micropillar compression. A Monte Carlo simulation scheme is developed to determine the burst size when a burst activity is captured. This burst size is considered as the displacement boundary condition of burst deformation. Three-dimensional finite element analysis of the model is performed and its predictions are validated by comparison with results from both micro-compression experiments and simulation tests of bulk crystals using the classic crystal plasticity finite element method (CPFEM). The model provides a reasonable prediction of stress–strain responses both at the macroscopic and microscopic scales. Finally, the capability of this model is shown with applications to the intermittent plastic deformation in micropillar compressions, in particular for their burst time durations and burst velocities. The results from such stochastic finite element analysis are shown to be consistent with earlier experimental findings and results of mean-field theory.     

考虑振动非平衡的可压缩库埃特流动及其传热

新型近空间高超声速飞行器大多具有尖头薄翼的外形,驻点下游机身附近的强剪切流动及气动加热具有显著的非平衡特征.由于加热总量预估和实验测热数据辨识的需要,工程上越来越关注强剪切非平衡流动及气动加热预测问题.本文结合理论建模和直接模拟蒙特卡洛数值模拟,研究了振动非平衡条件下的可压缩库埃特流动的气动力/热问题.首先基于参考温度...     

Mechanical activation of the transfer process in polymer systems

Mechanical activation (change in reactivity or activation energy) of polymer systems with a locally nonequilibrium (relaxation) response to mechanical perturbations is studied. Mechanical activation in such systems is caused by deviation of the medium microstructure from the state of local thermodynamic equilibrium. A system of equations for shear and uniaxial (elongation) deformation modes is formulated. The influence of local nonequilibrium in the medium microstructure on the mechanism and regular features of the macroscopic transfer process and also the effect of the stressed state of the polymer system and structural, kinetic, and orientation (steric) factors on the reactivity of polymer systems are analyzed. It is demonstrated that the reactivity of systems with a complicated internal structure has an energetic entropic character and depends on the reaction zone size (effect of a “nanoreactor”). The ranges of mechanical activation parameters affecting the reactivity and activation energy of polymer systems are determined for the shear and uniaxial modes of their deformation.     

Numerical simulation of solid state sintering

This paper discusses in detail the development of a numerical model capable of simulating microstructural evolution and macroscopic deformation during sintering of complex powder compacts. The model based on the kinetic Monte Carlo (Potts) approach simulates grain growth, vacancy diffusion, and pore annihilation at grain boundaries, which is responsible for densification. Results of 2D simulations for perfect close-packed and random starting configurations are presented and discussed. The microstructural evolution is used to obtain the sintering stress––the macroscopic stress that is equivalent to the microstructural driving force for deformation.     

Theoretical modeling of microstructured liquids: a simple thermodynamic approach

A new method is presented for accounting for microstructural features of flowing complex fluids at the level of mesoscopic, or coarse-grained, models by ensuring compatibility with macroscopic and continuum thermodynamics and classical transport phenomena. In this method, the microscopic state of the liquid is described by variables that are local expectation values of microscopic features. The hypothesis of local thermodynamic equilibrium is extended to include information on the microscopic state, i.e., the energy of the liquid is assumed to depend on the entropy, specific volume, and microscopic variables. For compatibility with classical transport phenomena, the microscopic variables are taken to be extensive variables (per unit mass or volume), which obey convection-diffusion-generation equations. Restrictions on the constitutive laws of the diffusive fluxes and generation terms are derived by separating dissipation by transport (caused by gradients in the derivatives of the energy with respect to the state variables) and by relaxation (caused by non-equilibrated microscopic processes like polymer chain stretching and orientation), and by applying isotropy. When applied to unentangled, isothermal, non-diffusing polymer solutions, the equations developed according to the new method recover those developed by the Generalized Bracket [J. Non-Newtonian Fluid Mech. 23 (1987) 271; A.N. Beris, B.J. Edwards, Thermodynamics of Flowing Systems with Internal Microstructure, first ed., Oxford University Press, Oxford, 1994] and by the Matrix Model [J. Rheol. 38 (1994) 769]. Minor differences with published results obtained by the Generalized Bracket are found in the equations describing flow coupled to heat and mass transfer in polymer solutions. The new method is applied to entangled polymer solutions and melts in the general case where the rate of generation of entanglements depends nonlinearly on the rate of strain. A link is drawn between the mesoscopic transport equations of entanglements and conformation and the microscopic equation describing the configurational distribution of polymer segment stretch and orientation. Constraints are derived on the generation terms in the transport equations of entanglements and conformation, and the formula for the elastic stress is generalized to account for reversible formation and destruction of entanglements. A simplified version of the transport equation of conformation is presented which includes many previously published constitutive models, separates flow-induced polymer stretching and orientation, yet is simple enough to be useful for developing large-scale computer codes for modeling coupled fluid flow and transport phenomena in two- and three-dimensional domains with complex shapes and free surfaces.     

Monte Carlo simulation of self-avoiding lattice chains subject to oscillatory shear flow in polymer solution

 This paper has introduced a pseudo-potential in bond-fluctuation model to simulate oscillatory shear flow of multiple self-avoiding chains in three dimensions following our previous work under simple shear flow. The oscillatory flow field was reasonably reproduced by lattice Monte Carlo simulation using this pseudo-potential neglecting hydrodynamic interaction. By sampling the configuration distribution functions, the macroscopic viscoelasticity of semi-concentrated polymer solution was determined. Both Newtonian and non-Newtonian regimes were studied. The complex modulus and dynamic viscosity exhibit a reasonable power relation with oscillatory frequency, which is consistent with present theories and experiments. Consequently, lattice Monte Carlo simulation has been extended to model free-draining self-avoiding multi chains subject to oscillatory shear flow and to investigate associated viscoelasticity on the molecular level. Received: 1 October 1999 Accepted: 19 October 1999     

A Monte Carlo Algorithm for Immiscible Two-Phase Flow in Porous Media

We present a Markov Chain Monte Carlo algorithm based on the Metropolis algorithm for simulation of the flow of two immiscible fluids in a porous medium under macroscopic steady-state conditions using a dynamical pore network model that tracks the motion of the fluid interfaces. The Monte Carlo algorithm is based on the configuration probability, where a configuration is defined by the positions of all fluid interfaces. We show that the configuration probability is proportional to the inverse of the flow rate. Using a two-dimensional network, advancing the interfaces using time integration, the computational time scales as the linear system size to the fourth power, whereas the Monte Carlo computational time scales as the linear size to the second power. We discuss the strengths and the weaknesses of the algorithm.     

Homogenization of delamination growth in an ACA flip-chip joint based on micropolar theory

In the present paper the delamination mechanism of a typical internal structure of the anisotropic conductive adhesive (ACA) interconnect for electronic packaging is modeled on the basis of micropolar theory and computational homogenization. The interface is treated as a finite Representative Volume Element (RVE), across which the macroscopic deformation is expressed in terms of regularized strong displacement and rotational discontinuities. For the microstructure of the RVE, the micro-macro kinematical coupling is considered as a Taylor series expansion in the regularized macroscopic discontinuities, and, connected to that, a discontinuous fluctuation field representing the microstructural variation is included to describe delamination on the microlevel. As to the microlevel delamination modeling, on the basis of the discontinuous fluctuation field, a damage coupled to slip and dilation formulation is used to model the interface degradation. The constitutive relations are established in a thermodynamic setting, where the interfacial free energy involves internal variables of damage and plastic deformation. The parameters of the interface are calibrated so that a predefined amount of fracture energy is dissipated in mode I. In the numerical example, the response of a planar interface is considered when it is subjected to the basic modes I-II and also the non-conventional rotational discontinuity mode. Case studies on fracture and geometry parameters have also been carried out. Finally, an uncoupled thermomechanical analysis of a microsystem involving a representative ACA microstructure has been made for the understanding of the microscopic delamination during a thermal cycling procedure.     

Macroscopic theory of orientation transitions in the extensional flow of side-chain nematic polymers

A macroscopic continuum mechanical model for incompressible side-chain nematic polymers, under isothermal conditions is given. The model is a synthesis of a transient network model and the standard nematorheological model. Simplifications in the model yield constitutive equations that are identical to well known Theological models for polymer melts and for low molar mass nematics. A detailed analysis of four possible composite orientation modes of polymer backbone and mesogenic side groups in uniaxial extensional flow is given. It is shown that the thermal sensitivity of the viscoelastic parameters leads to thermally-induced orientation transitions. The extension rate sensitivity of the competition between elastic and flow orienting effects leads to flow-induced orientation transition. The role of smectic A fluctuations in thermally-induced transitions during uniaxial extensional nematic flow is elucidated. The model is able to predict and explain the experimentally observed orientation modes and thermally-induced orientation transitions of a side-chain nematic polymer subjected to uniaxial extensional flow.     

Direct Monte Carlo Simulation of Transverse Supersonic Rarefied Gas Flow around a Cylinder

Supersonic flow around a cylinder is investigated using the direct simulation Monte Carlo method over a wide rarefaction range: from the Knudsen number Kn = 0.1 to free-molecular flow. The effect of the cylinder temperature on the region of sharp nonequilibrium near the cylinder and the heat flux is studied.     

Theory of elastoplastic media with mesostructure

It is known for a long time that under elastoplastic deformation, solid matter develops certain internal structures that can be observed with instruments which make it possible to look into the interior of the solids. Such a behavior is particularly pronounced in crystalline materials in which the plastic deformation occurs by sliding over crystallographic glide planes. Internal structure or microstructure may have a different appearance on several scale levels. Hence, it is also common to speak of multilevel structures. These structures and their influence on the material behavior is the subject of this investigation. It is argued that a continuum theory of elastoplasticity with dislocations is possible only on the microscopic scale where dislocations of opposite sign are considered. The macroscopic dislocation theory takes into account only the excess dislocations of one sign per unit macro-volume. It results in a great loss of information. This means that the macroscopic dislocation theory must be classified as a mean field theory as in statistical physics. The theory can be extended by application of correlation functions. Two examples for the development of a three level structure will be discussed.     

Finite element modeling of porous titanium

The porous microstructures of metallic foams cause microscopic stress and strain localization under deformation which reduces the damage tolerance and therefore limits application of the materials. In this paper, the deformation of a relatively low porosity porous titanium is examined using two-dimensional (2D) plane strain and three-dimensional (3D) finite element models to identify the accuracy and limitations of such simulations. To generate the finite element models, a simulated microstructure was created based on micrographs of an experimental material. Compared to the 2D models, the 3D models require smaller model size to obtain convergent results. The macroscopic responses predicted by the 3D models are in reasonable agreement with experimental results while the 2D models underestimated the response. In addition, 3D models predicted more uniform microscopic field variable distributions. 2D models predicted higher probability of Von Mises stress and equivalent plastic strain exceeding a certain value and therefore overestimate the failure probability of the material.     

Formation of fibrous crystals in flowing blends of polyethylene melts

Flow induced crystallization of high density polyethylene has been studied in a two-phase flow system using low density polyethylene as the carrier phase. Extensional stresses were generated under slow flow conditions by either of two methods: one involving flow past a stationary seed, the other involving a droplet deformation and bursting mechanism. In both cases, oriented, fibrillar crystallization of the high density phase was observed optically and correlated with calculations indicating the presence of flow-induced extensional gradients. Morphological, thermal, and birefringence data indicate that the crystalline fibers produced are oriented and superheatable, and consist of a multifibrillar substructure. For fibers produced by the droplet bursting process a semi-quantitative agreement was found between fiber melting point and birefringence based on a simplified analysis for the bursting induced extensional flow. These results demonstrate that two-phase flows of crystallizable systems are a convenient means for studying the phenomenon of flow induced crystallization in polymer melts.