Ageing and rejuvenation in glassy amorphous polymers

Physical ageing of amorphous polymers well below their glass transition temperature leads to changes in almost all physical properties. Of particular interest is the increase in yield stress and post-yield strain softening that accompanies ageing of these materials. Moreover, at larger strain polymers seem to rejuvenate, i.e. aged and non-aged samples have identical stress-strain responses. Also, plastically deforming an aged sample seems to rejuvenate the polymer. In this work we use molecular dynamic simulations with a detailed force field suitable for macromolecular ensembles to simulate and understand the effects of ageing on the mechanical response of these materials. We show that within the timescales of these simulations it is possible to simulate both ageing and rejuvenation. The short range potentials play an important role in ageing and rejuvenation. A typical yield drop exhibited by glassy polymers is a manifestation of a sudden relaxation in the short range structure of an aged polymer. Moreover, the aged polymers are known to be brittle. We show that this is intimately related to its typical stress-strain response which allows it to carry arbitrarily large mean stresses ahead of a notch.     

Phenomenological theory of flow-alignment in binary nematic mixtures

A macroscopic continuum mechanical model for incompressible homogeneous (single phase) binary nematic mixtures under isothermal conditions is given. The rheological model is a generalization of the standard nematorheological model for single component uniaxial rod-like nematic liquid crystals. Its special cases include single component orthorhombic biaxial nematics and single component uniaxial nematics. Numerical solutions for rectilinear simple shear flow of the model nematic mixture are obtained and analyzed. A complete classification of all the possible shear-alignment modes for binary nematic mixtures is given. Mechanisms and parameter variations leading to alignment transitions are identified. Mixtures of two aligning nematics result in most cases in flow-aligning biaxial nematic mixtures. Mixtures of an aligning nematic with a non-aligning nematic results in a flow-aligning biaxial nematic mixture, only if sufficiently strong dynamic interactions are present. In all cases the predicted degree and type of alignment behavior is shear rate-dependent.     

Stability of the tumbled state in shear flow of a nematic liquid crystal

In shear flow of a nematic liquid crystal with ₃ 0 flow alignment cannot occur. The stability of the stationary in-plane solution, the tumbled state, is investigated using abstract techniques. Employing the existence of an elastic energy a sufficient criterion for stability is formulated. This criterion depends on the in-plane solution which is obtainable as a quadrature that is non-elementary except in special cases. It is shown that the tumbled state is stable and asymptotically stable for some physical configurations. The criterion presented is not a necessary condition for stability and thus only gives a lower bound.     

Stretch-induced wrinkling of polyethylene thin sheets: Experiments and modeling

This paper presents a study on stretch-induced wrinkling of thin polyethylene sheets when subjected to uniaxial stretch with two clamped ends. Three-dimensional digital image correlation was used to measure the wrinkling deformation. It was observed that the wrinkle amplitude increased as the nominal strain increased up to around 10%, but then decreased at larger strain levels. This behavior is consistent with results of finite element simulations for a hyperelastic thin sheet reported previously (Nayyar et al., 2011). However, wrinkles in the polyethylene sheet were not fully flattened out at large strains (>30%) as predicted for the hyperelastic sheet, but exhibited a residual wrinkle whose amplitude depended on the loading rate. This is attributed to the viscoelastic response of the material. Two different viscoelastic models were adopted in finite element simulations to study the effects of viscoelasticity on wrinkling and to improve the agreement with the experiments, including residual wrinkles and rate dependence. It is found that a parallel network model of nonlinear viscoelasticity is suitable for simulating the constitutive behavior and stretch-induced wrinkling of the polyethylene sheets.     

Fluidization behavior of graphitized glassy particles in a fluidized carbon bed cooling process for investment casting

Fluidized Carbon Bed Cooling (FCBC) is an innovative investment casting process for directional solidification of superalloy components. It takes advantage of a fluidized bed with a base of small glassy carbon beads for cooling and other low-density particles that form an insulating layer by floating to the bed surface. This so-called “Dynamic Baffle” protects the fluidized bed from the direct heat input from the high-temperature heating zone and provides the basis for an improved bed microstructure. The prerequisites for a stable casting process are stable fluidization conditions where neither collapse of the bed nor particle blow out at excessive bubble formation occur.This work aimed to investigate the fluidization behavior of spherical carbon bed material in argon and air at temperatures between 20 to 350 °C. Systematic studies at reduced pressures using the FCBC prototype device were performed to understand the stable fluidization conditions at all stages of the investment casting process. The particle shape factor and size distribution characterization and the measurement of the powder’s minimum fluidization velocity and bed voidage show that this material can be fully utilized as a cooling and buoyancy medium during the FCBC process.     

Flow and heat transfer over hyperbolic stretching sheets

The boundary layer flow and heat transfer analysis of an incompressible viscous fluid for a hyperbolically stretching sheet is presented. The analytical and numerical results are obtained by a series expansion method and a local non-similarity (LNS) method, respectively. The analytical and numerical results for the skin friction and the Nusselt number are calculated and compared with each other. The significant observation is that the momentum and the thermal boundary layer thickness decrease as the distance from the leading edge increases. The well-known solution of linear stretching is found as the leading order solution for the hyperbolic stretching.     

Phenomenological nonlinear modelling of glassy polymers

Compared with the numerous works into the constitutive equations for the mechanical behaviour of metals, very little attention has been devoted to those of polymers. However, a model is required to describe both the complex shape of the stress–strain curves and strain rate sensitivity of glassy polymers. In this Note, a unified viscoelastic-viscoplastic model is presented in which the nonlinear pre-yield behaviour, the strain softening and the strain hardening are described by internal variables, in analogy with the models developed for metals. In order to check the predictive capability of the model, the numerical results are compared with the experimental data (monotone, creep and relaxation tests) of a typical amorphous glassy polymer. To cite this article: F. Zaïri et al., C. R. Mecanique 333 (2005).     

The effects of age on viscoelasticity and deformation recovery of articular chondrocytes

本文旨在表征年龄对软骨细胞在自然生长过程中的黏弹性和恢复变形能力的影响.结果表明：年龄对软骨细胞黏弹性及其恢复变形能力产生显著影响,老年组软骨细胞各项黏弹性参数值均明显高于幼年和中年组软骨细胞(p<0.0001), 而后两组无显著差异(p>0.05); 老年组软骨细胞蠕变达到平衡态所需时间t_E显著小于幼年和中年组(p<0.05), 而幼年和中年组无显著差异(p>0.05). 老年组软骨细胞最大蠕变位移L_M显著大于幼年和中年组(p<0.005), 而幼年和中年组无显著差异(p>0.05).老年组软骨细胞恢复变形时间t_R显著大于幼年和中年组(p<0.005), 而幼年和中年组无显著差异(p>0.05). 恢复变形前8s的分析发现,幼年组软骨细胞恢复变形率K_y显著高于中年和老年组(p<0.005), 而中年组(K_a)和老年组(K_o)软骨细胞的恢复变形率无显著差异(p>0.05); 此外, 实验发现老年组软骨细胞的残余变形L_R比幼年和中年组显著增大(p<0.005), 而后两组无显著差异(p>0.05). 研究工作对于软骨组织工程、软骨细胞与支架材料相互作用以及探讨OA发生过程中的力学生物学机制具有理论意义.     

Flange earing and its control on deepdrawing of anisotropy circular sheets

The Hill's quadric anisotropy yield function and the Barlat-Lian anisotropy yield function describing well anisotropy sheet metal with stronger texture are introduced into a quadric-flow corner constitutive theory of elastic-plastic finite deformation suitable for deformation localization analysis. And then, the elastic-plastic large deformation finite element formulation based on the virtual power principle and the discrete Kirchhoff shell element model including the yield functions and the constitutive theory are established. The focus of the present research is on the numerical simulation of the flange earing of the deep-drawing of anisotropy circular sheets, based on the investigated results, the schemes for controlling the flange earing are proposed. Supported by NSFC(No. 19832020) and National Automobile Dynamic Simulation Laboratory of China.     

Peeling behavior and spalling resistance of CFRP sheets bonded to bent concrete surfaces

In this paper, the peeling behavior and the spalling resistance effect of carbon fiber reinforced polymer （CFRP） sheets externally bonded to bent concrete surfaces are firstly investigated experimentally. Twenty one curved specimens and seven plane specimens are studied in the paper, in which curved specimens with bonded CFRP sheets can simulate the concrete spalling in tunnel, culvert, arch bridge etc., whereas plane specimens with bonded CFRP sheets can simulate the concrete spalling in beam bridge, slab bridge and pedestrian bridge. Three kinds of curved specimens with different radii of curvature are chosen by referring to practical tunnel structures, and plane specimens are used for comparison with curved ones. A peeling load is applied on the FRP sheet by loading a circular steel tube placed into the central notch of beam to debond CFRP sheets from the bent concrete surface, meanwhile full-range load-deflection curves are recorded by a MTS 831.10 Elastomer Test System. Based on the experimental results, a theoretical analysis is also conducted for the specimens. Both theoretical and experimental results show that only two material parameters, the interfacial fracture energy of CFRP-concrete interface and the tensile stiffness of CFRP sheets, are needed for describing the interfacial spalling behavior. It is found that the radius of curvature has remarkable influence on peeling load-deflection curves. The test methods and test results given in the paper are helpful and available for reference to the designer of tunnel strengthening.     

Micromechanics, macromechanics and constitutive modeling of the elasto-viscoplastic deformation of rubber-toughened glassy polymers

Under certain conditions, such as sufficiently low temperatures, high loading rates and/or highly triaxial stress states, glassy polymers display an unfavorable characteristic—brittleness. A technique used for reducing the brittleness (increasing the fracture toughness) of these materials is rubber toughening. While there is significant qualitative understanding of the mechanical behavior of rubber-toughened polymers, quantitative modeling tools for the large-strain deformation of rubber-toughened glassy polymers are largely lacking.In this paper, we develop a suite of numerical tools to investigate the mechanical behavior of rubber-toughened glassy polymers, with emphasis on rubber-toughened polycarbonate. The rubber particles are modeled as voids in view of their deformation-induced cavitation early during deformation. A three-dimensional micromechanical model of the heterogeneous microstructure is developed to study the effects of initial rubber particle (void) volume fraction on the underlying elasto-viscoplastic deformation mechanisms in the material, and how these mechanisms influence the macroscopic response of the material. A continuum-level constitutive model is developed for the large-strain elasto-viscoplastic deformation of porous glassy polymers, and it is calibrated against micromechanical modeling results for porous polycarbonate. The constitutive model can be used to study various boundary value problems involving rubber-toughened (porous) glassy polymers. As an example, the case of an axisymmetric notched bar is simulated for the case of polycarbonate with varying levels of initial porosity. The quality of the constitutive model calibration is assessed using a multi-scale modeling approach.     

Plastic deformation modes in perforated sheets and their relation to yield and limit surfaces

Construction of mechanism-based plasticity theories for the homogenized response of heterogeneous materials requires identification of plastic deformation modes as a function of loading direction relative to the microstructural details. Herein, we employ an efficient homogenization theory to identify for the first time such deformation modes in plates under plane stress with hexagonal arrays of circular holes at small and intermmediate pore volume fractions, and establish their relation to the branches of initial and subsequent yield and limit surfaces. Newly introduced maps of the intrinsic geometric features of point-wise yield surfaces provide full-field picture of the investigated microstructures’ propensity for plastic strain initiation and localization. The identified characteristic plastic modes provide a rational explanation for the evolving geometric features of subsequent yield and limit surfaces whose branches represent different plastic flow mechanisms, as well as a basis for the construction of a mechanism-based homogenized plasticity theory for use in structural analysis algorithms. The results suggest the need for composite yield surfaces comprised of multiple branches in the construction of mechanism-based homogenized plasticity theory for the investigated class of porous materials.     

An analytical symplectic approach to the vibration analysis of orthotropic graphene sheets

A nonlocal continuum orthotropic plate model is proposed to study the vibration behavior of single-layer graphene sheets (SLGSs) using an analytical symplectic approach.A Hamiltonian system is established by introduc-ing a total unknown vector consisting of the displacement amplitude,rotation angle,shear force,and bending moment. The high-order governing differential equation of the vibra-tion of SLGSs is transformed into a set of ordinary differential equations in symplectic space.Exact solutions for free vibra-tion are obtianed by the method of separation of variables without any trial shape functions and can be expanded in series of symplectic eigenfunctions. Analytical frequency equations are derived for all six possible boundary con-ditions. Vibration modes are expressed in terms of the symplectic eigenfunctions.In the numerical examples,com-parison is presented to verify the accuracy of the proposed method. Comprehensive numerical examples for graphene sheets with Levy-type boundary conditions are given.A para-metric study of the natural frequency is also included.     

Constitutive modeling for anisotropic/asymmetric hardening behavior of magnesium alloy sheets

Magnesium alloy sheets have been extending their field of applications to automotive and electronic industries taking advantage of their excellent light weight property. In addition to well-known lower formability, magnesium alloys have unique mechanical properties which have not been thoroughly studied: high in-plane anisotropy/asymmetry of yield stress and hardening response. The reason of the unusual mechanical behavior of magnesium alloys has been understood by the limited symmetry crystal structure of HCP metals and thus by deformation twinning. In this paper, the phenomenological continuum plasticity models considering the unusual plastic behavior of magnesium alloy sheet were developed for a finite element analysis. A hardening law based on two-surface model was further extended to consider the general stress–strain response of metal sheets including Bauschinger effect, transient behavior and the unusual asymmetry. Three deformation modes observed during the continuous in-plane tension/compression tests were mathematically formulated with simplified relations between the state of deformation and their histories. In terms of the anisotropy and asymmetry of the initial yield stress, the Drucker–Prager’s pressure dependent yield surface was modified to include the anisotropy of magnesium alloy. The numerical formulations and characterization procedures were also presented and finally the correlation of simulation with measurements was performed to validate the proposed theory.     

Modeling slow deformation of polygonal particles using DEM

We introduce two improvements in the numerical scheme to simulate collision and slow shearing of irregular particles. First, we propose an alternative approach based on simple relations to compute the frictional contact forces. The approach improves efficiency and accuracy of the Discrete Element Method （DEM） when modeling the dynamics of the granular packing. We determine the proper upper limit for the integration step in the standard numerical scheme using a wide range of material parameters. To this end, we study the kinetic energy decay in a stress controlled test between two particles. Second, we show that the usual way of defining the contact plane between two polygonal particles is, in general, not unique which leads to discontinuities in the direction of the contact plane while particles move. To solve this drawback, we introduce an accurate definition for the contact plane based on the shape of the overlap area between touching particles, which evolves continuously in time.     

Elasto-plastic buckling and post-buckling analysis of sandwich plates with functionally graded metal-metal face sheets and interfacial damage简

Based on the elasto-plastic theory, considering the effect of spherical stress tensor on the elasto-plastic deformation and using the slicing treatment to deal with the plasticity of functionally graded coatings, the elasto-plastic increment constitutive equations of the sandwich plates with functionally graded metal-metal face sheets can be derived. Applying the weak bonded theory to the interfacial constitutive relation and taking into account the geometric nonlinearity, the nonlinear increment differential equilibrium equations of the sandwich plates with functionally graded metal-metal face sheets are obtained by the minimum potential energy principle. The finite difference method and the iterative method are used to obtain the post-buckling path. When the effect of geometrical nonlinearity of the plate is ignored, the elasto-plastic critical buckling load of the sandwich plates with functionally graded metal-metal face sheets can be solved by the Galerkin method and the iterative method. In the numerical examples, the effects of the interface damages, the induced load ratio, the functionally graded index, and the geometry parameters on the elasto-plastic post-buckling path and the elasto-plastic critical buckling load are investigated.     

The application of nonlinear gauge mathod to the analysis of local finite deformation in the necking of cylindrical bar

IntroductionNeckingandshearbandaretypicalfailureformationofplasticinstabilityofductilemetals,thephenomenaoflocalizeddeformationthatoftenaPPearinexperiments.W.JohnsonpointedoutthattheinvestigationoflocalizeddeformationcouldbetracedbacktoTresca'sexperimentalsummaryin1878.Fromtheseventies,manyresearcherswerefurthermoreconcernedaboutthisstUdyinthefieldofmaterial,mechanicsandengineering.Localdeformationexistsnotonlyintheprocessofmetalbutalsoingeotechnicssuchastheslideplaneinslopestability.Locali…     

Modeling complex plastic deformation and fracture of metals under disproportionate loading

A mathematical model is developed to describe fatigue-damage accumulation in structural materials (metals and their alloys) on multiaxial paths of disproportionate combined heat and power loading. The effect of the shape of the strain path on the fatigue life of metals was studied to obtain qualitative and quantitative estimates of the obtained constitutive relations. It is shown that the proposed constitutive relations adequately describe the main elastoplastic deformation effects and damage accumulation in structural materials for arbitrary strain paths.     

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.