Stress Relaxation Modulus of a Commercial Glass

The stress relaxation modulus in compression of a container glass was investigated over a wide range of strain, time, modulus, and temperature. The glass is a linear viscoelastic liquid up to 2% strain, and the modulus is a smooth function of time, with no pseudorubbery plateau apparent down to a modulus of 10° dynes/cm². The data cover 4 decades in time and a range of almost 100°C above the glass transition, T ₀ =536°C. Within experimental error, changes in temperature simply shift the modulus-vs-time curve along the time axis without altering its shape. This behavior implies that the same mechanism controls both the bulk and shear spectra. The shift factors fit the WLF equation well with values for the parameters c₁ and c₂ of 16.7±0.2 and 345±5°C, respectively. Data from the literature for silicate glasses agree with these parameters.     

Temperature Dependence of Young's Modulus and Internal Friction in Alumina, Silicon Nitride, and Partially Stabilized Zirconia Ceramics

The temperature dependence of Young's modulus and internal friction (Q⁻¹)in alumina, silicon nitride, and partially stabilized zirconia (Y-PSZ) ceramics was studied. Little change in Q⁻¹ was found for alumina, whereas Q⁻¹ for silicon nitride ceramics increased above 700°C. The Q⁻¹ of Y-PSZ increased markedly with increasing temperature up to a peak at ∼200°C.     

A Model of Structural Relaxation in Glass

Study of the time dependence of physical properties in the transformation range of glass is complicated by the "memory effect" and the inherent nonlinearity which are characteristic of structural relaxation. A multiparameter model of structural relaxation is presented that differs from earlier models in that it takes account of both these effects. This model fits available experimental data well; these data were obtained for the most part by observing the evolution of properties (such as density or refractive index) following a step change in temperature. The present model also permits prediction of the physical properties of glass subjected to arbitrary and more complex temperature-time histories. It should, therefore, also be useful in the rational design of heat treating processes such as annealing.     

Young's Modulus of Various Refractory Materials as a Function of Temperature

Young's modulus as a function of temperature was determined by a dynamic method for single-crystal sapphire and ruby and for polycrystalline aluminum oxide, magnesium oxide, thorium oxide, mullite, spinel, stabilized zirconium oxide, silicon carbide, and nickel-bonded titanium carbide. For the single crystals, Young's modulus was found to decrease linearly with increasing temperature from 100°C. to the highest temperature of measurement. For all the polycrystalline materials, except silicon carbide, stabilized zirconium oxide, and spinel, Young's modulus was found to decrease approximately linearly with increasing temperature until some temperature range characteristic of the material was reached in which Young's modulus decreased very rapidly and in a nonlinear manner with increasing temperature. This rapid decrease at high temperature is attributed to grain-boundary slip. Stabilized zirconium oxide and spinel were found to have the same rapid decrease in Young's modulus at high temperature, but they also had a decidedly nonlinear temperature dependence at low temperature.     

Stress and Structural Relaxation in Tempering Glass

Temper stresses are brought about, primarily, by a partial relaxation of transient stresses generated by rapid cooling of the glass. Stress relaxation under nonisothermal conditions is competently handled by a mathematical tempering model, in which glass is treated as a simple viscoelastic material. However, this model proved inadequate in some respects since the properties of glass depend not only on its instantaneous temperature but also on its prior thermal history. A tempering model was therefore developed that incorporates both stress and structural relaxation. Predictions of this structural model are compared with experimental data on tempering and contrasted with predictions of the viscoelastic model. Such comparisons revealed that, typically, structural relaxation accounts for approximately 24% of the total residual temper stresses.     

Dependence of the Cohesion Factor of Alkali-Silicate Glass Structure on Silica Modulus

A correlation between the structure cohesion factor and the silica modulus is identified based on analysis of calculated data. Nomograms and a prediction method are proposed to determine the specified parameters. The advisability of using the silica modulus as a structure-determining criterion in designing glass for hydrogen microcontainers is demonstrated.     

利用热膨胀仪研究硼硅酸盐玻璃的结构弛豫行为

针对目前差示扫描量热仪、红外光谱和Raman光谱等在分析不同玻璃性质弛豫行为上的局限性,提出了建立在玻璃热膨胀性能测试基础上的分析方法。在Rekhson提出的方案基础上,结合Moynihan法,采用Tool-Narayanaswamy-Moynihan唯象模型对玻璃容积在转变区内的弛豫行为进行了研究。测试了两种具有不同热历史的硼硅酸盐玻璃的热膨胀曲线,得到了相同结构弛豫参数,验证了这种方法的可靠性。结果表明:采用改进Rekhson法得到的硼硅酸盐玻璃弛豫函数在参考温度为830K时的比例系数x为0.89,活化能H为200kJ/mol,弛豫时间τr为200s,扩展指数β为0.55;对比Moynihan热容法,该方法虽在精确性上稍差,但在工业领域应用中具有非常大的潜力。     

Structural Relaxation Time of Bulk and Fiber Silica Glass as a Function of Fictive Temperature and Holding Temperature

The structural relaxation times of silica glass, both bulk glass and fiber glass at various fictive temperatures, were estimated at selected temperatures. The structural relaxation time of a glass is needed to estimate the rate of change of various glass properties in the glass transition temperature range. Traditionally, the Tool–Narayanaswamy model, in which activation energy of the relaxation time is divided into two parts, one representing the fictive temperature effect and the other representing the temperature effect, has been used. The model can explain the property changes of glass in the glass transition temperature range well when the change of the fictive temperature is small, but the model fails when the change of the fictive temperature is large, as was the case when a fiber sample was heat treated close to the glass transition temperature. The structural relaxation times estimated in the present work exhibited activation energies that varied with fictive temperature, unlike the assumption in the Tool–Narayanaswamy model. On the other hand, the relaxation time for both bulk glass and fiber glass exhibited the same temperature and fictive temperature dependence within experimental error. From these observations, one can see the source of discrepancy between the Tool–Narayanaswamy model and experimental data when the change in fictive temperature is large.     

PMMA变温松弛模量获取方法的实验研究

聚甲基丙烯酸甲酯(PMMA)在不同温度条件下进行拉伸应力松弛实验,获取了恒温条件下的松弛模量曲线,并对其进行温度修正,建立折合模量-时间对数曲线图。利用最小二乘法平移原理计算出时温等效因子,确立WLF方程参数。对其参考温度下的松弛模量进行了基于Prony级数的拟合,建立了材料Wiechert黏弹性参数模型,且实验结果与仿真结果吻合性比较好,为后续的数值仿真和实验研究提供了理论的指导作用。     

铝酸钙准二元玻璃硬度和抗碎裂性组成依赖的结构起源探究

理解玻璃的硬度和抗碎裂性与结构的关系对制备高硬耐摔功能玻璃具有重要的理论指导意义。为探究铝酸钙(CaO-Al₂O₃)准二元玻璃硬度和抗碎裂性随CaO含量的变化规律,采用激光加热气动悬浮方法,制备了组分为xCaO·(100-x)Al₂O₃(x=42.3、50.0、63.1、75.0,摩尔分数)的系列玻璃样品。利用显微维氏硬度仪、激光共聚焦显微拉曼光谱仪、X-射线衍射仪和魔角旋转固体核磁共振波谱仪,对制备的铝酸钙准二元玻璃的硬度、抗碎裂性和结构进行了详细的表征。结果表明:随着CaO含量增加,玻璃硬度逐渐下降,于x=42.3时硬度最大(8.09 GPa);而玻璃的抗碎裂性随CaO含量增加先降低后急剧增加,并于x=42.3时表现出最大的抗碎裂性(11.8 N)。随着CaO含量增加,平均键能的下降是玻璃硬度下降的原因;高铝含量(x=42.3)的铝酸钙玻璃中部分铝以五配位形式存在,在承受载荷冲击过程中容易改变配位数来耗散能量,是抗碎裂性最大的结构根源。     

Young's Modulus, Flexural Strength, and Fracture of Yttria-Stabilized Zirconia versus Temperature

The flexural strength and elastic modulus of cubic zirconia that was stabilized with 6.5 mol% yttria was determined in the temperature range of 25°–1500°C in air. Specimens were diamond machined from both hot-pressed and sintered billets that were prepared from alkoxy-derived powders. The flexural strength of the hot-pressed material decreased, from }300 MPa at 25°C to 50 MPa at 1000°C, and then increased slightly as the temperature increased to 1500°C. The flexural strength of the sintered material decreased, from 150 MPa at 25°C to 25 MPa at 750°C, and then appeared to increase slightly to }1500°C. Flexural strengths were comparable to other fully stabilized zirconia materials. The overall fracture mode was transgranular at low temperatures, mixed mode at }500°–1000°C, and intergranular at higher temperatures. Pores or pore agglomerates along grain boundaries and at triple points were fracture origins. The value of the porosity-corrected Youngs moduli was 222 GPa at 25°C, decreased to }180 GPa at 400°C, and then was relatively constant with increasing temperature to 1350°C.     

Model of Structural Relaxation in Glass with Variable Coefficients

The model of structural relaxation by Narayanaswamy deals only with the constant temperature coefficients of the glass property, p. The assumption is seldom valid for real glasses. In this work, equations are obtained for the fictive temperature of glass if the temperature coefficient, dp/dT, is a linear function of T or of 1 /T². The temperature dependence of p has no significant influence on the calculated fictive temperatures.     

Dependence of the Fictive Temperature of Glass on Cooling Rate

An equation derived by Ritland relating the cooling rate and fictive temperature for glasses without memory is extended to those with memory, i.e. those which exhibit a spectrum of relaxation times. Provided that the spectrum of relaxation times is temperature-independent, the limiting fictive temperature, T'_f , obtained when a glass is cooled through the transition region, is shown to be related to the cooling rate, q , by d In | q |/ d (1/ T'f )=-Δ h ★/ R
where R is the ideal gas constant and Δ h ★ the activation enthalpy for the relaxation times controlling the structural relaxation. Values of T'_f vs q obtained from enthalpy measurements by differential scanning calorimetry are presented for B₂O₃, 0.4Ca(NO₃)₂—0.6KNO₃, and borosilicate crown glasses; Δ h ★ is equal, within experimental error, to the activation enthalpy for shear viscosity. Values of T'_f from volume and enthalpy measurements obtained at the same cooling rate for the borosilicate crown glass are equal.     

Determination of Young's Modulus of Thin Films

An improved vibrating-reed method is described for determining Young's modulus of thin films deposited on both sides of a substrate. This technique consists of measuring the resonant frequency of a cantilever composite beam obtained by coating both sides of a substrate. The calculation procedure is presented to evaluate the film modulus from sample geometry, material density, and mechanical resonant frequency. For accurate determination of resonant frequency, the phase angle between the exciting and vibration signals is analyzed. Using the proposed technique, Young's modulus of ZrO₂ thin films is calculated, obtaining a value in agreement with literature data.