Surface tension-driven shape-recovery of micro/nanometer-scale surface features in a Pt57.5Ni5.3Cu14.7P22.5 metallic glass in the supercooled liquid region: A numerical modeling capability

Recent experiments in the literature show that micro/nano-scale features imprinted in a Pt-based metallic glass, Pt_57.5Ni_5.3Cu_14.7P_22.5, using thermoplastic forming at a temperature above its glass transition temperature, may be erased by subsequent annealing at a slightly higher temperature in the supercooled liquid region (Kumar and Schroers, 2008). The mechanism of shape-recovery is believed to be surface tension-driven viscous flow of the metallic glass. We have developed an elastic-viscoplastic constitutive theory for metallic glasses in the supercooled liquid temperature range at low strain rates, and we have used existing experimental data in the literature for Pt_57.5Ni_5.3Cu_14.7P_22.5 (Harmon et al., 2007) to estimate the material parameters appearing in our constitutive equations. We have implemented our constitutive model for the bulk response of the glass in a finite element program, and we have also developed a numerical scheme for calculating surface curvatures and incorporating surface tension effects in finite element simulations. By carrying out full three-dimensional finite-element simulations of the shape-recovery experiments of Kumar and Schroers (2008), and using the independently determined material parameters for the bulk glass, we estimate the surface tension of Pt_57.5Ni_5.3Cu_14.7P_22.5 at the temperature at which the shape-recovery experiments were conducted. Finally, with the material parameters for the underlying elastic-viscoplastic bulk response as well as a value for the surface tension of the Pt-based metallic glass fixed, we validate our simulation capability by comparing predictions from our numerical simulations of shape-recovery experiments of Berkovich nanoindents, against corresponding recent experimental results of Packard et al. (2009) who reported shape-recovery data of nanoindents on the same Pt-based metallic glass.     

A simple method of evaluating the complex moduli of polystyrene blends

In the search for a workable mixing rule, use was made of experimental data for complex moduli of melts of narrow molar mass distribution polystyrenes and their homogeneous blends. In the course of this work two basic observations were made as to the nature of the relaxation time spectra of these blends:

1. The relaxation strength (a product of the weight fraction and the plateau modulus) of a component of large molecules is reduced by the presence of shorter molecules, the latter molecules acting like ordinary diluent molecules even if their molar masses are larger thenM _c .
2. The relaxation time of a molecule (known from measurements on the respective monodisperse component) is considerably changed by the blending. The width of the distribution of relaxation times, as expected from the known composition of the blend, is significantly reduced.

For both processes approximate empirical equations could be found. It turned out that, after the application of the required modifications, the complex moduli of the components could successfully be added in order to obtain the complex moduli of the blend at circular frequencies characteristic for the flow and rubber transition regions. On the basis of these results one may expect that for the melt of any linear polymer the linear viscoelastic properties can be evaluated with reasonable accuracy from the knowledge of the molar mass distribution.     

Thermorheological properties near the glass transition of oligomeric poly(methyl methacrylate) blended with acrylic polyhedral oligomeric silsesquioxane nanocages

Two distinct oligomeric species of similar mass and chemical functionality (M _w≈2,000 g/mol), one a linear methyl methacrylate oligomer (radius of gyration R _g≈1.1 nm) and the other a hybrid organic–inorganic polyhedral silsesquioxane nanocage (methacryl-POSS, r≈1.0 nm), were subjected to thermal and rheological tests to compare the behaviors of these geometrically dissimilar molecules over the entire composition range. The glass transition temperatures of the blends varied monotonically between the glass transition temperatures of the pure oligomer (T _g=−47.3°C) and the pure POSS (T _g=−61.0°C). Blends containing high POSS contents (with volume fraction φ _POSS≥0.90) exhibited enhanced enthalpy relaxation in differential scanning calorimetry (DSC) measurements, and the degree of enthalpy relaxation was used to calculate the kinetic fragility indices m of the oligomeric MMA (m=59) and the POSS (m=74). The temperature dependences of the viscosities were fitted by the free-volume based Williams–Landel–Ferry (WLF) and Vogel–Fulcher–Tammann (VFT) framework and a dynamic scaling relation. The calculated values of the fragility from the WLF–VFT fits were similar for the POSS (m=82) and for the oligomer (m=76), and the dynamic scaling exponent was similar for the oligomeric MMA and the POSS. Within the range of known fragilities for glass-forming liquids, the temperature dependence of the viscosity was found to be similarly fragile for the two species. The difference in shape of the nanocages and oligomer chains is unimportant in controlling the glass-forming properties of the blends at low volume fractions (φ _POSS<0.20). However, at higher volume fractions, adjacent POSS cages begin to crowd each other, leading to an increase in the fractional free volume at the glass transition temperature and the observed enhanced enthalpy relaxation in DSC.     

Detecting very low levels of long-chain branching in metallocene-catalyzed polyethylenes

The detection of long-chain branches (LCBs) is an issue of significant importance in both basic research and industrial applications, as LCBs provide excellent means to improve the processing behavior, especially in elongation-dominated processing operations. In this article, different methods for the detection of very low amounts of LCBs in metallocene-catalyzed polyethylene are presented and compared with respect to their sensitivity. Depending on the molar mass, the zero shear rate viscosity increase factor η ₀/ $\eta_{0}^{\rm lin}$ , the steady-state elastic recovery compliance $J_{e}^{0}$ , the complex modulus functions G′(ω) and G″(ω), and the thermorheological complexity were found to be sensitive. In general, the higher the molar mass, the more important the transient quantities become and the easier finding the long-chain branches gets. Although rheology is very sensitive, rheological methods in combination with size exclusion chromatography proved to be the most sensitive combination to detect even very low amounts of LCBs. Especially methods involving the elastic properties (G′(ω), $J_{\rm e}^{0}$ , and J _r(t)) react very sensitively, but these are also very distinctly influenced by the molar mass distribution.     

A linear stability analysis on the onset of thermal convection of a fluid with strongly temperature-dependent viscosity in a spherical shell

A linear stability analysis was performed in order to study the onset of thermal convection in the presence of a strong viscosity variation, with a special emphasis on the condition for the stagnant-lid (ST) convection where a convection takes place only in a sublayer beneath a highly viscous lid of cold fluid. We consider the temporal evolution (growth or decay) of an infinitesimal perturbation superimposed to a Boussinesq fluid with an infinite Prandtl number which is in a static (motionless) and conductive state in a basally heated planar layer or spherical shell. The viscosity of the fluid is assumed to be exponentially dependent on temperature. The linearized equations for conservations of mass, momentum, and internal (thermal) energy are numerically solved for the critical Rayleigh number, Ra _c , as well as the radial profiles of eigenfunctions for infinitesimal perturbations. The above calculations are repeatedly carried out by systematically varying (i) the magnitude of the temperature dependence of viscosity, E, and (ii) the ratio of the inner and outer radii of the spherical shell, γ. A careful analysis of the vertical structure of incipient flows demonstrated that the dominance of the ST convection can be quantitatively identified by the vertical profile of Δ _h (a measure of conversion between horizontal and vertical flows), regardless of the model geometries. We also found that, in the spherical shell relevant to the Earth’s mantle (γ = 0.55), the transition into ST convection takes place at the viscosity contrast across the layer ${r_\eta\simeq10^4}$ . Taken together with the fact that the threshold value of r _η falls in the range of r _η for a so-called sluggish-lid convection, our finding suggests that the ST-mode of convection with horizontally elongated convection cells is likely to arise in the Earth’s mantle solely from the temperature-dependent viscosity.     

Viscosity of Cryoprotective Agents Near Glass Transition: A New Device,Technique, and Data on DMSO,DP6, and VS55

The low strain-rate viscosity of glass-forming cryoprotective agents (CPAs) in the vicinity of the glass transition is studied experimentally. Data on the mechanical behavior in this regime is necessary to the long-term goal of developing planning tools for cryopreservation via vitrification (vitreous means glassy in Latin); such tools will provide guidelines for reducing thermal stress with its devastating effects. While the flow behavior of some glass-forming CPAs is well documented in the literature for the upper part of the cryogenic temperature range (where the CPA has a comparatively low viscosity), it is the flow behavior near the glass transition temperature (where the CPA behaves as nearly a solid with an extremely high viscosity) which is critical to the analysis of stress that develops in the cryopreserved material. If the elevated viscosity limits the material’s ability to flow—in order to accommodate the thermal strain resulting from large temperature gradients, especially at the high cooling rates necessary to form glass—structural damage may follow. Information on the behavior of the CPA in the lower part of the cryogenic temperature range is largely unavailable. A new measurement device is presented in this study, in which a solid rod is pulled from a long narrow cup containing a CPA, producing an essentially one-dimensional and isothermal field of flow. The viscosity and relaxation time of the CPA is inferred from measurements of the resulting load on the rod when extracted at a constant velocity. The current study reports on experimental data near glass transition of 7.05 M DMSO, a reference CPA solution, and the CPA cocktails VS55 and DP6.     

Rheological properties of electron beam-irradiated polypropylenes with different molar masses

Electron beam-irradiated polypropylene undergoes chain scission initiated by the loss of a proton. The resulting macroradicals can lead to branched molecules. However, the understanding of the influence of irradiation on the branching of polypropylene is still scarce. Therefore, this paper investigates structure?Cproperty relationships in such irradiated polymers. In general, irradiation yields long-chain branches, which develop from a star-like into a tree-like branching architecture with increasing dose. These conclusions can be drawn from the relation between the zero shear-rate viscosity ?? ₀ and the weight average molar mass M _w as well as from the elongational behavior.     

Linear viscoelasticity,simple and planar melt extension of linear polybutadienes with bimodal molar mass distributions

Shear oscillations, simple and planar elongations have been performed with anionically polymerized polybutadienes (PB) and their blends at room temperature. The PB components were of different molar mass averages and of narrow molar mass distributions; the blends had bimodal molar mass distributions and are represented by the weight ratio w of the high molecular component. The crossover G() = G() obtained from oscillatory measurements shows correlations with molecular parameters. For the zero shear viscosity the well-known relation ₀ M _w ^3.4 is found. The recoverable equilibrium shear compliance J _e ⁰ is nearly the same for the components; for the blends it strongly depends on w with a pronounced maximum at small w. In elongation outside the linear region strain hardening is found; its magnitude depends on M _w of the components, the composition w of the blend, the mode of elongation (simple or planar), and the elongational strain rate. The hardening revealed in the increase of the elongational viscosity above the linear viscoelastic limit increases as a function of w up to a maximum similar to J _e ⁰ such that, for both properties, the molecular processes may be the same. The elongational viscosity µ₂ (from the lateral stress in planar elongation) is above the linear viscoelastic limit for bimodal and below this limit for conventional broad molar mass distributions. In general, it can be stated that with a more narrow molar mass distribution of linear polymers the elongational behavior of the melts comes closer to the linear viscoelastic limit.Dedicated to Professor Arthur S. Lodge on the occasion of his 70th birthday and his retirement from the University of Wisconsin.Extended version of a paper presented at the Annual Conf. German Soc. of Rheology, Berlin, May 13–15, 1991.     

锆基非晶合金的动态弛豫机制和高温流变行为

非晶合金的动态弛豫机制对于理解其塑性变形, 玻璃转变行为, 扩散机制以及晶化行为都至关重要. 非晶合金的力学性能与动态弛豫机制的本征关联是该领域当前重要科学问题之一. 本文借助于动态力学分析(DMA), 探索了Zramorphous alloy,dynamic mechanical analysis,high temperature deformation,structural relaxation,quasi-points defects,1)国家自然科学基金(51971178);陕西省自然科学基金(2019JM-344);中央高校基本科研业务费专项资金(3102019ghxm007);中央高校基本科研业务费专项资金(3102017JC01003)2020-01-062020-04-10非晶合金的动态弛豫机制对于理解其塑性变形, 玻璃转变行为, 扩散机制以及晶化行为都至关重要. 非晶合金的力学性能与动态弛豫机制的本征关联是该领域当前重要科学问题之一. 本文借助于动态力学分析(DMA), 探索了Zr$_{50}$Cu$_{40}$Al$_{10}$块体非晶合金从室温到过冷液相区宽温度范围内的动态力学行为. 通过单轴拉伸实验, 研究了玻璃转变温度附近的高温流变行为. 基于准点缺陷理论(quasi-point defects theory), 对两种力学行为的适用性以及宏观力学行为变化过程中微观结构的演化规律进行描述. 研究结果表明, 准点缺陷理论可以很好地描述非晶合金损耗模量$\alpha$弛豫的主曲线. 基于非晶合金的内耗行为, 玻璃转变温度以下原子运动的激活能$U_\beta$为0.63 eV. 与准点缺陷浓度对应的关联因子$\chi $在玻璃转变温度以下约为0.38,而在玻璃转变温度以上则线性增大. Zr$_{50}$Cu$_{40}$Al$_{10}$块体非晶合金在玻璃转变温度附近, 随温度和应变速率的不同而在拉伸实验中显示出均匀的或不均匀的流变行为. 非晶合金的高温流变行为不仅可以通过扩展指数函数和自由体积理论来描述, 还可以通过基于微剪切畴(shear micro-domains, SMDs)的准点缺陷理论来描述.     

The role of short chain molecules for the rheology of polystyrene melts.

Atactic polystyrenes of narrow molar mass distribution with average molar masses larger than the critical molar massM _c were mixed with similar polystyrenes of molecular masses lower thanM _c . Linear viscoelastic melt properties of these binary blends were measured with a dynamic viscometer of the concentric cylinder type. One of the experimental findings is that the time-temperature shift factorsa _T are dependent on the composition of the samples. This can be understood, if free volume due to chain-ends is taken into account. A computer-fitted WLF-equation being modified in a proper way leads to the following results: At the glass-transition-temperature the fraction of free volume in polystyrene of infinite molar mass is only 0.015. At a temperature of 180 °C the mean value of the free volume at a chain end is 0.029 nm³ for the polystyrene investigated.     

Thermomicrohardness analysis (TμHA) of glassy materials

A thermal analysis technique and an apparatus are described which are used to study phase transformations in glassy materials by monitoring the temperature dependence of the microhardness through a phase transformation with the heating rate varied as a parameter. The method has been named Thermomicrohardness Analysis (TμHA). The glass transformation behaviors of a-As₂Se₃ xerographic photoreceptor type films have been studied to elucidate the nature of structural changes in the glass transformation region of glasses. It is shown that on an Itoh-Shishokin plot the Vickers microhardness exhibits a sharp fall in the glass transition interval due to a relaxation phenomenon similar to the relaxation of the enthalpy as determined by DSC measurements. Furthermore it is shown that the relaxation rate in both the processes is inversely proportional to the instantaneous viscosity.     

Rheological properties of branched polystyrenes: nonlinear shear and extensional behavior

Nonlinear shear and uniaxial extensional measurements on a series of graft-polystyrenes with varying average numbers and molar masses of grafted side chains are presented. Step-strain measurements are performed to evaluate the damping functions of the melts in shear. The damping functions show a decreasing dependence on strain with an increase in mass fraction of grafted side chains. Extensional viscosities of the melts of graft-polystyrenes exhibit a growing strain hardening with increasing average number of grafted side chains as long as the side branches have a sufficient molar mass to be entangled. Graft-polystyrenes with side arms below the critical molar mass M _c for entanglements of linear polystyrene but above the entanglement molar mass M _e of linear polystyrene (M _e < M _w,br < M _c) still show a distinct strain hardening. With decreasing molar mass of the grafted side chains (M _w,br < M _e) the nonlinear-viscoelastic properties of the graft-polystyrene melts approach the behavior for a linear polystyrene with comparable polydispersity.Electronic Supplementary Material Supplementary material is available for this article at     

Viscoelastic properties of ultra-high viscosity alginates

Ultra-high viscosity alginates were extracted from the brown seaweeds Lessonia nigrescens (UHV_N, containing 61% mannuronate (M) and 2% guluronate (G)) and Lessonia trabeculata (UHV_T, containing 22% M and 78% G). The viscoelastic behavior of the aqueous solutions of these alginates was determined in shear flow in terms of the shear stress σ ₂₁, the first normal stress difference N ₁, and the shear viscosity η in isotonic NaCl solutions (0.154 mol/L) at T = 298 K in dependence of the shear rate [(g)\dot]\dot{\gamma} for solutions of varying concentrations and molar masses (3–10 × 10⁵ g/mol, homologous series was prepared by ultrasonic degradation). Data obtained in small-amplitude oscillatory shear (SAOS) experiments obey the Cox–Merz rule. For comparison, a commercial alginate with intermediate chemical composition was additionally characterized. Particulate substances which are omnipresent in most alginates influenced the determination of the material functions at low shear rates. We have calculated structure–property relationships for the prediction of the viscosity yield, e.g., η–M _w–c–[(g)\dot]\dot{\gamma} for the Newtonian and non-Newtonian region. For the highest molar masses and concentrations, the elasticity yield in terms of N ₁ could be determined. In addition, the extensional flow behavior of the alginates was measured using capillary breakup extensional rheometry. The results demonstrate that even samples with the same average molar mass but different molar mass distributions can be differentiated in contrast to shear flow or SAOS experiments.     

金刚石切削Soda-lime玻璃中的刀具磨损及其对工件表面粗糙度的影响

金刚石切削加工光学玻璃时,工件表面粗糙度与刀具磨损直接相关,为研究切削距离递增下的金刚石刀具磨损及其对工件加工表面粗糙度的影响,进行了Soda-lime玻璃金刚石切削的刀具磨损试验,并对刀具磨损形貌、后刀面磨损带的材料成份、工件的表面形貌及粗糙度进行了检测.结果表明:切削距离递增下的金刚石刀具前刀面磨损表现为平滑且均匀的月牙洼磨损,后刀面磨损表现为磨损带逐渐增大,且磨损带内有沿切削方向的微沟槽产生;切削距离未达到150 m时,工件表面粗糙度Rq、Ra及Rmax值始终低于32、25及300 nm,切削距离超过150 m后,工件表面粗糙度显著增大.机械摩擦作用、热化学作用及磨料磨损作用为导致金刚石刀具磨损的主要原因.     

Mode II fracture behavior of a Zr-based bulk metallic glass

Shear band formation and fracture are characterized during mode II loading of a Zr-based bulk metallic glass. The measured mode II fracture toughness, K_IIc=75±4 MPa√m, exceeds the reported mode I fracture toughness by ∼4 times, suggesting that normal or mean stresses play a significant role in the deformation process at the crack tip. This effect is explained in light of a mean stress modified free volume model for shear localization in metallic glasses. Thermal imaging of deformation at the mode II crack tip further reveals that shear bands initiate, arrest, and reactivate along the same path, indicating that flow in the shear band leads to permanent changes in the glass structure that retain a memory of the shear band path. The measured temperature increase within the shear band is a fraction of a degree. However, heat dissipation models indicate that the temperature could have exceeded the glass transition temperature for less than 1 ms immediately after the shear band formed. It is shown that this time scale is sufficient for mechanical relaxation slightly above the glass transition temperature.     

Thermomechanics of shape memory polymers: Uniaxial experiments and constitutive modeling

Shape memory polymers (SMPs) can retain a temporary shape after pre-deformation at an elevated temperature and subsequent cooling to a lower temperature. When reheated, the original shape can be recovered. Relatively little work in the literature has addressed the constitutive modeling of the unique thermomechanical coupling in SMPs. Constitutive models are critical for predicting the deformation and recovery of SMPs under a range of different constraints. In this study, the thermomechanics of shape storage and recovery of an epoxy resin is systematically investigated for small strains (within ±10%) in uniaxial tension and uniaxial compression. After initial pre-deformation at a high temperature, the strain is held constant for shape storage while the stress evolution is monitored. Three cases of heated recovery are selected: unconstrained free strain recovery, stress recovery under full constraint at the pre-deformation strain level (no low temperature unloading), and stress recovery under full constraint at a strain level fixed at a low temperature (low temperature unloading). The free strain recovery results indicate that the polymer can fully recover the original shape when reheated above its glass transition temperature (T_g). Due to the high stiffness in the glassy state (T < T_g), the evolution of the stress under strain constraint is strongly influenced by thermal expansion of the polymer. The relationship between the final recoverable stress and strain is governed by the stress–strain response of the polymer above T_g. Based on the experimental results and the molecular mechanism of shape memory, a three-dimensional small-strain internal state variable constitutive model is developed. The model quantifies the storage and release of the entropic deformation during thermomechanical processes. The fraction of the material freezing a temporary entropy state is a function of temperature, which can be determined by fitting the free strain recovery response. A free energy function for the model is formulated and thermodynamic consistency is ensured. The model can predict the stress evolution of the uniaxial experimental results. The model captures differences in the tensile and compressive recovery responses caused by thermal expansion. The model is used to explore strain and stress recovery responses under various flexible external constraints that would be encountered in applications of SMPs.     

Testing thermodynamic constitutive equations for polymers by adiabatic deformation experiments

During adiabatic deformation experiments on polyisobutylene of various molecular weights and on polyvinylacetate, the temperature change was measured. The thermal effects occurring during the subsequent stress relaxation were also recorded. From all data, the conclusion was drawn that the entropic elasticity theory is obeyed for temperatures sufficiently above the glass transition temperature. When the value of T_g is approached, some interesting energy effects become appreciable.     

Electrorheological determination of the Leslie viscosity coefficient (α2) of a main-chain liquid crystal polymer in a nematic solvent

Analysis of the electrorheological response of thermotropic solutions of a main-chain liquid crystal polymer (MCLCP) in a low molar mass nematic solvent is performed at a fixed shear rate as a function of the applied field strength. The Leslie viscosity coefficient α₂ can be obtained by least squares fits to an equation describing the balance between the viscous and electric torques, formulated via the two dimensional Leslie-Ericksen-Parodi theory. We find that the increment Δα₂ on dissolving the MCLCP increases linearly with molecular weight, consistent with earlier light scattering measurements of the increment in the twist viscosity, Δγ₁, and also with previous electrorheological measurements of the increment in the Miesowicz viscosity Δη_c. Received: 1 December 1998 Accepted: 28 April 1999     

Effective property models for homogeneous two-phase flows

Using an analogy between thermal conductivity of porous media and viscosity in two-phase flow, new definitions for two-phase viscosity are proposed. These new definitions satisfy the following two conditions: namely (i) the two-phase viscosity is equal to the liquid viscosity at the mass quality = 0% and (ii) the two-phase viscosity is equal to the gas viscosity at the mass quality = 100%. These new definitions can be used to compute the two-phase frictional pressure gradient using the homogeneous modeling approach. These new models are assessed using published experimental data of two-phase frictional pressure gradient in circular pipes, minichannels and microchannels in the form of Fanning friction factor (f_m) versus Reynolds number (Re_m). The published data include different working fluids such as R-12, R-22, argon (R740), R717, R134a, R410A and propane (R290) at different diameters and different saturation temperatures. Models are assessed on the basis minimizing the root mean square error (eRMS). It is shown that these new definitions of two-phase viscosity can be used to analyze the experimental data of two-phase frictional pressure gradient in circular pipes, minichannels and microchannels using simple friction models.