Langevin-elasticity-theory-based description of the tensile properties of double network rubbers

A previously proposed and successfully tested constitutive equation denoted by the ABGIL code (a combination of the Arruda-Boyce equation based on the Langevin elasticity theory and a constraint term based on tube theories; strain-induced increase in the finite extensibility parameter is assumed) has been found to provide a good basis for quantitative interpretation of the stress-strain data recently obtained by Mott and Roland on double networks of natural rubber, prepared by introducing additional crosslinks (second network) into a first network stretched to various extents. Experimental information on properties of the first and second networks has been used to obtain their ABGIL parameters and to calculate, under the common assumption of additivity of contributions, the stress-strain properties and residual stretch of the resulting double networks. The predictive ability of the ABGIL equation has been found to be very good. Effects of the finite extensibility of network chains appear to be significant in double networks while the possible role of orientational crystallization cannot be excluded.     

Pneumatic bursting characteristics of plastics films

The bursting strength and inflated deflection of linear low density polyethylene (LLDPE), oriented polypropylene (OPP), flexible poly(vinyl chloride) (PVC), poly(ethylene terephthalate) (PET), and polyurethane (PUR) films of different thicknesses were investigated with the pneumatic bursting method. The study showed the bursting air pressure is directly proportional to the thickness of LLDPE, OPP, and PET films. The effect of different membrane diameters on the change of the bursting properties in OPP and PUR film was also investigated. The results showed that the bursting properties are inversely proportional to the membrane diameter. Furthermore, biaxial stress-strain exerted on the pole region of the tested films was studied. The results denoted that the relationship between the biaxial and uniaxial tensile stress-strain was considered for two types of film: (1) Film that presented an isotropic tensile behavior showed that the tangential stress-strain is higher than the tensile stress-strain. (2) Film that presented an anisotropic tensile behavior showed that the tangential stress-strain is determined by the weaker tensile stress-strain values between two directions.     

Comparison of recent rubber-elasticity theories with biaxial stress-strain data: the slip-link theory of Edwards and Vilgis

The Edwards-Vilgis (EV) slip-link theory (1986) derives the elastic free energy of a rubber-like network model containing stable and sliding network junctions (crosslinks and slip-links) and predicts both low-strain softening and high-strain hardening. The four-parameter stress-strain relations calculated by the theory for geometrically different deformation modes up to high strains were tested experimentally using published biaxial stress-strain data on simple covalently crosslinked networks. For networks with low degrees of strain softening and low extensibilities, the experimental dependencies could be described rather well but, generally, a simultaneous satisfactory fit to uniaxial, pure shear and equibiaxial data was not obtained. Systematic experiment-theory deviations exceeding 10% were observed and some of the parameters had a tendency to assume values lying outside the reasonably expected range. The prediction of a pronounced maximum in the strain dependence of stress supported by slip-links seems to be a reason for the discrepancy. Also, modeling of the high-strain singularity in entropy is done in the EV theory using a rather simple approximation. As a result, the finite extensibility contribution to the stress of a slip-link-free network model becomes improbably high and significantly exceeds that following, at a given modulus and locking stretch, from the rigorously derived Langevin-statistics-based eight-chain-network elasticity theory of Arruda and Boyce.     

Characterization of nonideal networks by stress-strain measurements at large extensions

It is shown how a characterization of unfilled, amorphous rubber networks can be evaluated from uniaxial stress-strain measurement data. Beside the cross-linking density, the relative scission probability during the curing procedure is evaluated, which determines the amount of dangling free chain ends and the number of trapped entanglements. These values are found from the C₂ term of the Mooney-Rivlin equation by using the predictions of a tube model. A necessary requirement for applying stress-strain measurements at large extensions is the consideration of the finite extensibility component of the reduced stress. It is taken into account by using a numerical procedure, which derives from a series expansion of the inverse Langevin approximation. The experimental results found at natural rubber networks cross-linked with thiuram (TMTD) and peroxid (DCP) show that network defects cannot be neglected in the DCP networks. They are assumed to be connected to the worse tensil strength properties compared to the TMTD networks. © 1993 John Wiley & Sons, Inc.     

Stress-strain relationships in uniaxial extension of high cis-1,4-polyisoprene networks with different molecular weight precursors

Equilibrium stress-strain relationships in uniaxial extension for high cis-1,4-polyisoprene (Shell IR 307) networks were obtained by extrapolation of relaxation measurements to infinite time through a BKZ constitutive equation. Three series of networks were investigated, each series being characterized by its polymer precursor molecular weight. Influence of crosslinking density was studied through varying amounts of dicumyl peroxide as crosslinking agent. These results were used to test Flory and Erman's recent molecular elasticity theory of imperfect networks with constraints on junctions. It was shown that this later theory treating entanglements as restrictions on junction fluctuations could be reasonably used to characterize network topology. A universal value of 0.50 for the interpenetration parameter I is confirmed and an interpretation of parameter ζ in terms of network inhomogeneity is tentatively given.     

Long time stress relaxation of amorphous networks under uniaxial tension: The Dynamic Constrained Junction Model

The constrained junction model that represents the stress-strain relations of amorphous networks in equilibrium is modified to analyze stress relaxation. Deviation of stress from equilibrium when a network is stretched suddenly is represented by a time dependent constraint contribution that is of the same form as that of the equilibrium theory. The time dependent motions of the junctions are assumed to obey the Langevin equation. The only new term in the model is a time dependent κ parameter that vanishes at long times. Results of the model are compared with uniaxial stress relaxation experiments on polyisoprene networks with different degrees of cross-linking. Experiments show that the time dependent κ parameter obeys a stretched exponential form, with β = 0.4 and τ = 40 s, both of which are the same for all extensions and cross-link densities studied. The front factor κ₀ depends on cross-link density in the same way as in the equilibrium case. Comparison with stress relaxation experiments shows satisfactory agreement at a wide range of extensions and for different degrees of cross-linking. The relatively low value of the stretched exponent parameter, β = 0.4, is interpreted in terms of a molecular picture where entanglements contribute to relaxation at a wide spectrum of time scales.     

利用正则配分函数计算实际流体的热力学性质及汽液平衡——(Ⅰ)纯流体的热力学性质

通过修改普遍化van der Waals正则配分函数的引力项,发展了一个修正的状态方程式.将表征分子间引力参数α修正为不仅依赖于温度而且与密度有关.用新的状态方程式计算纯气体、饱和蒸汽与饱和液体的压力与逸度系数的结果与实验结果符合较好.     

Viscoelastic properties of networks with low concentration of pendant chains

A good knowledge of the molecular structure of polymer networks allows to relate rheological properties with different molecular parameters. In this work we analyze the influence of low concentrations of pendant chains on the viscoelastic properties of polymer networks. Model networks, with a well defined structure, were synthesized by reacting a commercial α,ω-divinyl poly(dimethylsiloxane) (B₂) with a trifunctional cross-linker bearing silane groups (A₃) and known amounts of an anionic ω-vinyl poly(dimethylsiloxane) (B₁). The structure of the networks was predicted with a molecular model based on a mean field approach (recursive model) taking into account the initial composition of the reactants. Rheological characterization was carried out in a rotational rheometer by dynamic and stress relaxation test. Viscoelastic properties of the networks depend on both concentration and molecular weight of pendant chains. Relaxation modulus was adjusted by the empirical Chasset-Thirion equation. It was found that it provides a very good fit to the behavior of these networks prepared by end-linking. The fitting parameter m in the Chasset-Thirion equation shows a strong dependence with the molecular mass of pendant chains, but it is rhougly independent of concentration. The results agree remarkably well with the predictions of a theoretical model previously reported by our group.     

双向载荷条件下Ⅰ型裂纹的疲劳扩展

研究了双轴向应力状态下Ⅰ型穿透裂纹的疲劳扩展规律，采用构形合理且经精确标定应力强度因子值的双向十字形试样，在电液伺服双轴向疲劳试验机上对低合金钢（１６ＭｎＲ）进行了多种载荷比的疲劳裂纹扩展速率试验，得到了双轴向应力状态下的Ｐａｒｉｓ方程，为目前按缺陷评定规范依据单轴向疲劳试验所得数据对工程构件进行疲劳评定提供参考数据，并就当前研究者们对于双向应力场中横向载荷对疲劳裂纹扩展行为的影响的不同看法进行分析探讨。     

Globally optimal synthesis of heat exchanger networks. Part II: Non-minimal networks

In Part I of this work, the synthesis of minimal heat exchanger networks using the isothermal mixing stage-wise superstructure was presented. In this Part II, an extension of the algorithm presented in Part I is made to consider networks that allow multiple solutions regarding heat allocation, that is, they have energy loops where heat loads can be rearranged without changing the overall energy consumption. We extend the strategy of our Part I to use a set of nested loops to enumerate the number of units, the structure of matches, the energy consumption, different values of exchanger minimum approximation temperature (EMAT), and different locations where EMAT is active. All the models used are linear and are aided by capital cost evaluations. As in Part I, we claim global optimality based on our conjectures. Literature examples are solved to show the effectiveness of the algorithm.     

汽液平衡盐效应的分子热力学──乙醇-水-1-1型电解质系统恒压汽液平衡盐效应参数的计算

测定了6个乙醇-水-1-1型电解质系统（LiCl、LiBr、NaBr、NaAc、KCl、KI）恒压（100.8kPa）条件下的汽液平衡盐效应参数.在Pierotti定标粒子溶液理论基础上提出非电解质浓度任意变化条件下含盐双液系汽液平衡盐效应参数的计算方法.硬球作用项采用Masterton-Lee方程计算，软球作用项采用胡英等人建议的分子热力学模型计算．对于乙醇-水极性混合溶剂系统，离子-中心分子的碰撞直径考虑离子溶剂化的影响，以离子的溶剂化系数为可调参数，拟合出混合溶剂的局部介电常数与乙醇摩尔分数的关联方程．预测结果表明，在很大液相浓度范围（X_1=0.143～0.700）内14个乙醇-水-1-1型电解质系统52个盐效应参数的平均相对误差为7.76％     

Tensile creep of a long‐fibre glass mat thermoplastic (GMT) composite. II. Viscoelastic‐viscoplastic constitutive modeling

In Part I of this article, the short‐term tensile creep of a 3‐mm‐thick continuous long‐fibre glass mat thermoplastic composite was characterized and found to be linear viscoelastic up to 20 MPa. Subsequently, a nonlinear viscoelastic model has been developed for stresses up to 60 MPa for relatively short creep durations. The creep response was also compared with the same composite material having twice the thickness for a lower stress range. Here in Part II, the work has been extended to characterize and model longer term creep and recovery in the 3‐mm composite for stresses up to near failure. Long‐term creep tests consisting of 1‐day loading followed by recovery were carried out in the nonlinear viscoelastic stress range of the material, i.e., 20–80 MPa in increments of 10 MPa. The material exhibited tertiary creep at 80 MPa and hence data up‐to 70 MPa has been used for model development. It was found that viscoplastic strains of about 10% of the instantaneous strains were developed under load. Hence, a non‐linear viscoelastic–viscoplastic constitutive model has been developed to represent the considerable plastic strains for the long‐term tests. Findley's model which is the reduced form of the Schapery non‐linear viscoelastic model was found to be sufficient to model the viscoelastic behavior. The viscoplastic strains were modeled using the Zapas and Crissman viscoplastic model. A parameter estimation method which isolates the viscoelastic component from the viscoplastic part of the nonlinear model has been developed. The model predictions were found to be in good agreement with the average experimental curves. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers     

The behavior of graphite under biaxial tension

A small-deformation elastic-plastic continuum theory for describing the stressstrain behavior of graphite is examined for specimens under biaxial loading at room temperature. The continuum theory takes into account the anisotropy and plastic compressibility of graphite as well as the continuous nonlinearity of the stress-strain response. The measured strains for thin-walled cylindrical shells loaded by internal pressure are shown to agree very closely with the predictions of the theory for both loading and unloading.     

Elasticity behavior of swollen polyurethane networks

A series of polyurethane networks were prepared by reacting MDI (4,4′-diphenylmethane diisocyanate) with various mixtures of poly(oxyethylene) end-capped poly(oxypropylene) triol and diol. The uniaxial compressive properties of the polyurethane networks both in equilibrium swelling in toluene and in a dried state were measured at 27 °C. The compressive stress-strain data were analyzed according to equations based on the Gaussian theory of elasticity. Deviations from the Gaussian behavior were observed; however, as the polyether diol content increased, deviations from the Gaussian behavior decreased. The interaction parameters between the polyurethane networks and toluene at an equilibrium state were analyzed by the Flory-Huggins equation. As the polyether diol content increased, the interaction parameter, χ, increased due to the increasing content of the poly(oxyethylene) unit and urethane group concentration. With increasing polyether diol content, polyurethane networks approached phantom behavior more closely.     

PtSiO2: II. Characterization of the gel and the platinum particles by X-Ray diffraction

Modern techniques for analysis of X-ray diffraction profiles have been applied to several of the platinum-silica gel catalysts described in Part I to determine average platinum crystallite size, percentage exposed, crystallite shape, size distribution, lattice parameter, residual stresses and strains, presence or absence of faulting, and mean-square amplitude of vibration. In addition the surface area of the gel was determined with small-angle scattering (SAS). There is good agreement between the percentage exposed of platinum measured by gas adsorption in Part I and the results reported here, calculated from crystallite sizes, indicating the crystallite size is the true platinum particle size. Crystallites to sizes as small as ≈25 Å have been examined. Furthermore, the crystallites are equiaxed in shape (and definitely not cuboidal) and are strain and defect free, except in the case where the average size is near the pore size of the gel. Size distributions are sharper when the catalyst preparation is by impregnation rather than by ion exchange. The size distributions indicate that there is coalescence of some surface species during preparation rather than coarsening (Ostwald ripening). The meansquare amplitude of vibration of platinum increases by ≈30% as the particles decrease in size from ≈100 to ≈25 Å. There is no change in the lattice parameter greater than ≈0.1%. The gel surface areas determined by SAS are in agreement with those determined in Part I by physisorbtion of nitrogen.     

Mechanical properties of biaxially oriented poly(vinyl chloride)

This report describes the influence, of (a) degree of biaxial orientation, (b) stretching rate, and (c) stretching temperature on the tensile, dynamic mechanical and dielectric properties of non-impact modified PVC. A new parameter designated “planar strain” is used to correlate anisotropic property values with both equal and unequal biaxial stretching in a single two-dimensional plot, thereby providing a direct comparison of the effects of two or more biaxial stretching ratios. It is shown that optimum stretching conditions depend to some extent upon end use and that a 2 × 2 stretch ratio is optimum for impact resistance. The actual property/processing condition relationships exhibit very complicated interactions and are correlated empirically in this study. The dynamic measurements suggest that overall local segmental beta motion is increased after orientation but that the relative chain alignment makes it more difficult to activate this motion.     

Validity of the swelling method for the determination of the interaction parameter

By selecting solvents with a very weakly concentration-dependent interaction parameter χ with poly(dimethylsiloxane) (PDMS) and using experimental values of the elastic modulus of dry, end-linked PDMS networks, the Flory-Rehner theory and the phantom network assumption we obtained good agreement between the values of χ from equilibrium swelling and those obtained from intrinsic viscosity measurements on solutions of linear chains. The solvents used were 2,3-dimethylpentane and 2,2,4-trimethylpentane at 25°C.