Thermo-viscoelastic and viscoplastic behavior of high-density polyethylene

Observations are reported on high-density polyethylene in uniaxial tensile tests with constant strain rates and relaxation tests at various temperatures ranging from 25 to 90 °C. A constitutive model is derived for the nonlinear viscoelastic and viscoplastic behavior of semi-crystalline polymers at three-dimensional deformations. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. It is demonstrated that (i) the model correctly approximates the observations and (ii) material parameters are independent of strain rate and change consistently with temperature.     

Flow-induced crystallization of high-density polyethylene: the effects of shear and uniaxial extension

The effects of shear, uniaxial extension and temperature on the flow-induced crystallization of two different types of high-density polyethylene (a metallocene and a ZN-HDPE) are examined using rheometry. Shear and uniaxial extension experiments were performed at temperatures below and well above the peak melting point of the polyethylenes in order to characterize their flow-induced crystallization behavior at rates relevant to processing (elongational rates up to 30 s^− 1 and shear rates 1 to 1,000 s^− 1 depending on the application). Generally, strain and strain rate found to enhance crystallization in both shear and elongation. In particular, extensional flow was found to be a much stronger stimulus for polymer crystallization compared to shear. At temperatures well above the melting peak point (up to 25°C), polymer crystallized under elongational flow, while there was no sign of crystallization under simple shear. A modified Kolmogorov crystallization model (Kolmogorov, Bull Akad Sci USSR, Class Sci, Math Nat 1:355–359, 1937) proposed by Tanner and Qi (Chem Eng Sci 64:4576–4579, 2009) was used to describe the crystallization kinetics under both shear and elongational flow at different temperatures.     

Matrix FEM equation describing the large-strain deformation of an incompressible material

A tensor–matrix FEM equation describing large-strain deformation is derived. The equation is simplified and modified to describe the deformation of incompressible materials. The results of test analysis are presented     

Measurements of slip at the wall during flow of high-density polyethylene through a rectangular conduit

A hot-film probe has been used to measure slip of high-density polyethylene flowing through a conduit with a rectangular cross section. A transition from no slip to a stick-slip condition has been observed and associated with irregular extrudate shape. Appreciable extrudate roughness was initiated at the same flow rate as that at which the relationship between Nusselt number and Péclet number for heat transfer from the probe departed from the behavior expected for a no-slip condition at the conduit wall. A ₁ constant defined by eq. (A3) - C dimensionless group used in eq. (7) - C _p heat capacity - D constant in eq. (13) - f u _s/u - f _lin defined by eq. (A6) - G storage modulus - G loss modulus - k thermal conductivity - L length of hot film in thex-direction - L _eff effective length of large probe found from eq. (A3) - Nu _L Nusselt number, defined for a lengthL by eq. (2) - (Nu _L)₀ value ofNu _L atPe = 0 (eq. (A 1)) - Pe Péclet number,uL/ - Pe ₀ Péclet number in slip flow, eq. (6) - Pe ₁ Péclet number in shear flow, eq. (4) - q _L average heat flux over hot film of lengthL - R _i resistances defined by figure 8 - R _AB correlation coefficient defined by eq. (14) for signalsA andB - T temperature - T _s temperature of probe surface - T ambient temperature - T T _s –T - u average velocity - u _s slip velocity - V _b voltage indicated in figure 8 - W probe dimension (figure 6) - x distance in flow direction (figure 1) - y distance perpendicular to flow direction (figure 1) - thermal diffusivity,k/C _p - wall shear rate - _5% thickness of lubricating layer during probe calibration for introduction of an error no greater than 5%; see Appendix I - ^* complex viscosity - density - time - _c critical shear stress, eq. (13) - _w wall shear stress - frequency characterizing extrudate distortion (figures 12 and 13), or frequency of oscillation during rheometric characterization (figures 18–20) - * quantity obtained from normalized Nusselt number, eq. (A1), or complex viscosity ^* - A actual (small) probe (see Appendix I) - M model (large) probe (see Appendix I)     

爆破地震荷载作用下高密度聚乙烯波纹管动力响应试验研究

为研究爆破地震荷载作用下埋地高密度聚乙烯（high-density polyethylene,HDPE）波纹管的动力响应规律,通过现场预埋管道的爆破试验,结合爆破地震与动态应变等测试手段,分析了爆破地震荷载作用下埋地管道的动力响应特征,研究了管道振动速度及动态应变的分布特征,基于von Mises屈服准则分析评价了管道安全性,提出了爆破振动速度控制标准。试验研究结果表明：试验中管道与地表振速以及管道动态应变随爆心距的减少,随炸药量的增加而增大;爆破地震波振动主频高,管道振动主频高于地表;相同爆破工况条件下,管道上方地表振速普遍大于管道振速;管道截面背爆侧峰值轴向应变以拉应变为主,迎爆侧峰值环向应变以压应变为主;本试验管道安全控制振速可取20 cm/s,此时管道处于安全状态。

     

FEM application in phase change exchangers

Application of FEM in the analysis of condenser and vaporizer has been illustrated taking into account property variation with temperature. Accurate shell side pressure drop in a condenser has been determined by the present method taking into account the gradual reduction in vapour flow due to condensation from inlet to outlet. As the present method analyses the exchanger in small elements, analysis of an evaporator working under the conditions of partial vapour blanketing is also possible.

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Anwendung der Finite Elemente Methode bei Wärmetauschern mit Phasenwechsel

Zusammenfassung Die Verwendung der Finite Elemente Methode zur Berechnung von Kondensator und Verdampfer unter Berücksichtigung von temperaturabhängigen Stoffwerten ist hier dargestellt worden. Mit dem dargestellten Verfahren ist der genaue Druckverlust im Rohrraum eines Kondensators bestimmt worden, wobei die schrittweise Verminderung der Dampfströmung aufgrund der Kondensation von Ein-zu Auslaß mit berücksichtigt wurde. Mit der gegenwärtigen Methode, die einen Wärmeaustausch mittels kleiner Elemente berechnet, ist ebenso eine Auslegung eines Verdampfers mit einer partiellen Dampfabdeckung möglich.

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Nomenclature A heat transfer area in an elment upto any section, m² - A _c elemental heat transfer area, m² - B weightage - C UA/2 - D _e characteristic dimension, m - D _s shell diameter, cm - F _t temperature correction factor - f friction factor, m²/cm² - G mass velocity, kg/m² sec - G W/LN ^2/3 - g acceleration of gravity, m/sec² - h condensing coefficient, W/m²°C - h ₀ boiling coefficient, W/m²°C - k ₁ thermal conductivity of condensate atT _f , W/m°C - L length of tubes in the element, m - l distance of the fluid stream traverses in the element, m - LMTD log mean temperature difference, °C - N ₁,N ₂ shape functions - N _t number of tubes effective for condensation - P pressure drop, N/cm² - P _shell shell side vapour pressure drop, N/cm² - P _tube tube side stream pressure drop, N/cm² - q heat flux in the element, W/m² - S specific gravity of vapour - T _c tube side stream temperature, °C - T _c2 tube side stream exit temperature, °C - T _f (T _w +T _s )/2 - T _s saturation temperature, °C - T _w mean wall temperature in an element, °C - T ₁,T ₂ temperatures at nodes 1 and 2, °C - U overall heat transfer coefficient, W/m²°C - W ₁ tube side fluid thermal capacity rate, W/°C - W ₂ vapour mass flow rate, kg/hr - W mass of vapour condensed in any element, kg/sec - _f viscosity of condensate atT _f , N sec/m² - _f density of condensate atT _f , kg/m³     

Numerical simulation of large amplitude oscillatory shear of a high-density polyethylene melt using the MSF model

We study the flow response in large amplitude oscillatory shear of the molecular stress function (MSF) model that has recently been proposed by Wagner et al. [M.H. Wagner, P. Rubio, H. Bastian, The molecular stress function model for polydisperse polymer melts with dissipative convective constraint release, J. Rheol. 45 (2001) 1387–1412]. The MSF model is derived from molecular theory and has only two parameters to describe the non-linear material response. The model predictions are analysed in both the frequency and time domain. It shows good agreement with experimental data for a linear high-density polyethylene melt. At low and medium strains, MSF model predictions are in excellent agreement with experimental data and predictions of a six-mode Giesekus model which has six parameters to describe the non-linear material response. At medium strains, the basic Doi–Edwards model, which has no non-linear parameters, already underpredicts the data. At high strains, the MSF model predictions agree slightly better with the experimental data than the Giesekus model. Surprisingly, however, it is the Doi–Edwards model that shows excellent agreement with experimental data at high strains. For the linear melt we consider, it outperforms the models that have non-linear parameters, both in the time and frequency domain.     

On higher‐order mixed FEM for low Mach number flows: application to a natural convection benchmark problem

We consider higher‐order mixed finite elements with continuous pressures for the computation of stationary compressible flows at low Mach number. The proposed approach is based on a fully coupled treatment of the governing equations and therefore, for steady‐state calculations, does not rely on time‐stepping techniques. The non‐linear problem is solved by means of a quasi‐Newton iteration. The strongly coupled system resulting from higher‐order discretization of the linearized equations requires adequate solvers. We propose a new scheme based on multigrid methods with varying FEM ansatz orders on the grid hierarchy as well as multiplicative smoothers based on blocking techniques. Computational results are described for a benchmark configuration including a flow with heat transfer in the low Mach number regime. Furthermore, the issue of anisotropic grids is addressed in that context. Copyright © 2003 John Wiley & Sons, Ltd.     

On the application of the plastic spin concept for the description of anisotropic hardening in finite deformation plasticity

The aim of the paper is to fill the gap between the general theoretical formulation of the constitutive relations for plastic spin and practical applications for proper prediction of material behavior at finite plastic deformations and anisotropic hardening. An approximation to the representation of the general constitutive equation for plastic spin is considered and the pertinent substructure corotational rate is applied to formulate the relation for rigid-plastic material with kinematic hardening. The simple shear traction problem is analysed and the proposed model is verified with the experimental results of Swift. The merits of the present proposal vis-à-vis the existing theories are discussed.     

On the determination of deformation from strain

The problem of finding a deformation corresponding to a given Cauchy–Green strain is approached with a procedure that employs the Gram decomposition of the deformation gradient. It is shown that the rotation occurring in that decomposition can be obtained by solving a system of partial differential equations in the group of rotations or in its Lie algebra. The equivalence between the integrability conditions of these two systems and those of the systems of equations arising in the usual procedures for determining a deformation from the strain is proved. Examples of application of the proposed procedure are given.     

Rock deformation equations and application to the study on slantingly installed disc cutter

At present the mechanical model of the interac- tion between a disc cutter and rock mainly concerns indentation experiment, linear cutting experiment and tunnel boring machine （TBM） on-site data. This is not in line with the actual rock-breaking movement of the disc cutter and impedes to some extent the research on the rock-breaking mechanism, wear mechanism and design theory. Therefore, our study focuses on the interaction between the slantingly installed disc cutter and rock, developing a model in accordance with the actual rock-breaking movement. Displacement equations are established through an analysis of the velocity vector at the rock-breaking point of the disc cutter blade; the func- tional relationship between the displacement parameters at the rock-breaking point and its rectangular coordinates is established through an analysis of micro-displacement vectors at the rock-breaking point, thus leading to the geometric equations of rock deformation caused by the slantingly installed disc cutter. Considering the basically linear relationship between the cutting force of disc cutters and the rock deformation before and after the leap break of rock, we express the constitutive relations of rock deformation as generalized Hooke＇s law and analyze the effect of the slanting installa- tion angle of disc cutters on the rock-breaking force. This will, as we hope, make groundbreaking contributions to the development of the design theory and installation practice of TBM.     

On the local analysis of continuum deformation

Summary The role of the cartesian representation of the deformation gradient in the non-linear theory of continuum deformation is studied. Indeed, explicit formulae for the local analysis of deformation are obtained in terms of such a representation. Further, some connections with the multiplicative strain and rotation measures are examined.

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Sommario Si studia il ruolo della rappresentazione cartesiana del gradiente di deformazione nella teoria non-lineare della deformazione di un corpo continua tridimensionale. In termini di tale rappresentazione, si ottengono formule esplicite per le variazioni locali di lunghezza, angolo, area e volume. Si esaminano inoltre alcune connessioni con le misure multiplicative di deformazione pura e di rotazione.

     

On the derivatives of the stretch and rotation with respect to the deformation gradient

In this paper, a result involving the eigenprojections of the right stretch and its derivative with respect to the deformation gradient is derived, and a related result is found for the rotation. As an application, the form of the constitutive law for an isotropic hyperelastic material in the case when the strain energy function is expressed in terms of the right stretch, is shown to follow at once.     

On the Correlation of FEM and Experiments for Hyperelastic Elastomers

Correlation of modern finite element methods (FEM) with advanced experimental techniques for elastomers, biomedical materials, and living organs requires study and modification of the behavior of these materials. In this study, the mechanical behavior of a commonly-used elastomer, silicone rubber, which provides excellent biocompatibility, was examined under different applied loading configurations, and large deformations were investigated through both experiment and simulation. The stress-strain behaviors of silicone rubber were tested, using multiple homogeneous experiments, including uniaxial extension and equibiaxial tension, the load-apex displacement response, and digitized deformed shapes of two of the most-used structures for nonlinear hyperelasticity—the inflation of a clamped circular membrane, and indentation of the membrane by a spherical indenter. Uniaxial and equibiaxial data were evaluated simultaneously, characterized by various constitutive models for implementation in the FE simulation. These constitutive models examined the prediction of the FE simulations for the inflation and indentation tests in comparison to the results of experiments at various load-apex displacement levels. The results showed that the constitutive models calibrated with the uniaxial and equibiaxial tests, predicted nearly the same results as the actual experimental results, particularly for the applied loads that generated moderate strain. However, when the FE simulations based on the constitutive models were adjusted, employing only uniaxial or equibiaxial tests, they predicted different results, where the degree of their correlations with experimental results was incomplete or in some states simply poor. The simulations suggested that the inverse FE procedure should not be restricted to the choice of material models, while more attention should be given to the choice of ranges of deformation.     

A mesh stability study of FEM explicit algorithms for structural large-scale deformation impact responses

To FEM explicit algorithms for structural large-scale deformation impact responses, algorithm stability is discussed in the present paper. Algorithm stability is thought to include two aspects: One is called difference pattern stability and the other is called mesh stability. A self-adaptive adjusting method is proposed to ensure mesh stability with little amount of computation increased.     

A general hereditary multimechanism-based deformation model with application to the viscoelastoplastic response of titanium alloys

The formulation of a general model for the hereditary behavior of materials, in the viscoelastic and viscoplastic regimes, is presented. In this, we utilize the complete-potential structure as a general framework, together with the notion of strain- and stress- partitioning in terms of separate contributions of several submechanisms (viscoelastic and viscoplastic) to the thermodynamic functions (stored energy and dissipation). Detailed numerical treatments are given for both (i) the implicit integration algorithm for the governing flow and evolutionary rate equations of the model, and (ii) the automated parameter-estimation methodology (using the software code COMPARE) for characterization. For illustration, a specific form of the model presented is characterized for the TIMETAL 21S material using a very comprehensive test matrix, including creep, relaxation, constant strain-rate tension tests, etc. Discussion of these correlations tests, together with comparisons to several other experimental results, are given to assess the performance and predictive capabilities of the present model as well as the effectiveness and practical utility of the algorithms proposed.