Application of a kinematic hardening viscoplasticity model with thresholds to the residual stress relaxation

The life analysis of engine components needs to take into account the residual stress relaxation induced by cyclic service loads. The paper recalls a new class of constitutive equations for cyclic viscoplasticity, using a series of kinematic hardening models with thresholds. The equations are introduced within a recently enlarged thermodynamic framework. Some attention is focused to the relations with multisurface approaches and to a specific determination procedure of the model parameters. The new model is applied to the calculation of the near surface residual stress relaxation after shot peening, when the structure is submitted to cyclic service loads. The simulated stabilized residual stresses are in good accordance with experimental results obtained on an N18 disk alloy at 650°C. In comparison, the classical model without threshold predicts the complete vanishing of the residual stresses, which is not satisfactory.     

A delta-function method for the n-th approximation of relaxation or retardation time spectrum from dynamic data

A function series g(x; n, m) is presented that converges in the limiting case n and m = constant to the delta-function located at x = = 1. For every finite n, there exists 2n+1(–nmn) approximations of the delta-function _(n)(x–x _n,m ). x _n,m is the argument where the function reaches its maximum. A formula for the calculation is given.The delta-function approximation is the starting point for the approximative determination of the logarithmic density function of the relaxation or retardation time spectrum. The n-th approximation of density functions based on components of the complex modulus (G*) or the complex compliance (J*) is given. It represents an easy differential operator of order n.This approach generalizes the results obtained by Schwarzl and Staverman, and Tschoegl. The symmetry properties of the approximations are explained by the symmetry properties of the function g(x; n, m). Therefore, the separate equations for each approximation given by Tschoegl can be subsumed in a single equation for G and G, and in another for J and J.     

Statistical mechanics of temporary polymer networks I. The equilibrium theory

In part I of this work (the present article) the equilibrium state of temporary polymer networks is treated in the framework of thermodynamics and statistical mechanics. The network is described as an open system. Thereby we use a modified spring-bead model in which the beads represent junctions that decay and reform thus adding a viscous component to the assumed elastic behaviour of the permanent network. The relevant statistical equation — analogous to Liouville's equation — is solved. The grand-canonical probability density function and two of three equations of state are derived. Explicit formulae are given for several relevant probabilities. For instance the probabilityw (z)dz that a network chain connecting two junctions has a contour length betweenz andz +dz is given by the Wien type formulaw(z) =A z ³ exp {–B z} whereA andB do not depend onz.     

Viskositätsmessung mit dem longitudinal schwingenden Band

A method for the detection of small masses with the aid of a longitudinally vibrating band is described and further applications, e.g. for viscosity and humidity measurement are discussed. The complex Young's modulus of the band can also be determined.

     

Forced oscillations of a layer of a viscoelastic material under the action of a convective pressure wave

The longitudinal and transverse components of deformation of the surface of a flat layer of a viscoelastic material glued onto a solid base under the action of a traveling pressure wave are determined. The coating compliance is described by two components corresponding to two components of surface displacement. The dimensionless compliance components depend only on the viscoelastic properties of the material, the ratio of the wave length to the layer thickness λ/H, and the ratio of the wave velocity to the velocity of propagation of shear oscillations V/C _t ⁰ . Data on the dynamic compliance are presented for 0.3 < λ/H < 30 and 0.1 < V/C _t ⁰ < 10. The compliance is demonstrated to be determined by its absolute value and by the phase lag of strain from pressure. The effect of viscous losses in the material and compressibility of the latter on the dynamic compliance is analyzed. An anomalous behavior of the compliance with the wave velocity being greater than a certain critical value is explained. __________ Translated from Prikladnaya Mekhanika i Tekhnicheskaya Fizika, Vol. 48, No. 2, pp. 90–97, March–April, 2007.     

Indentation tests investigation of mechanical behavior of two-dimensional materials

准确了解二维材料的力学性能对于推动其应用具有重要意义, 无基底压痕技术是目前最广泛采用的二维材料力学性能测试方法之一, 本文综述了二维材料压痕研究的最新进展以及所面临的问题, 并对将来的研究工作进行了展望.无基底压痕技术是将二维材料转移到带有沟槽或柱形孔的基底上, 制备二维材料"梁"和"鼓"模型, 然后利用原子力显微镜测量其在压针作用下的载荷--位移关系, 最后通过基于连续介质薄膜导出的压痕响应分析模型拟合实验结果, 估算出二维材料的弹性模量和本征强度.由于二维材料的厚度远小于连续介质薄膜, 来自于压头以及基底孔侧壁的范德华力对二维材料的压痕响应具有显著影响, 造成二维材料与传统压痕分析模型中的基本假设不符, 导致不能准确预测二维材料的弹性模量; 另外, 由于传统压痕模型无法准确描述二维材料在大变形下的非线性行为, 以及由缺陷等引起的应力集中, 导致由压痕测试表征的二维材料(特别是多晶二维材料)本征强度具有较大的偏差. 因此, 一方面需要正确了解由压痕技术获得的二维材料力学性能, 另一方面还需对目前的研究方法做进一步的改进和完善.     

A molecular mechanics approach for analyzing tensile nonlinear deformation behavior of single-walled carbon nanotubes

In this paper, by capturing the atomic information and reflecting the behaviour governed by the nonlinear potential function, an analytical molecular mechanics approach is proposed. A constitutive relation for single-walled carbon nanotubes (SWCNT’s) is established to describe the nonlinear stress-strain curve of SWCNT’s and to predict both the elastic properties and breaking strain of SWCNT’s during tensile deformation. An analysis based on the virtual internal bond (VIB) model proposed by P. Zhang et al. is also presented for comparison. The results indicate that the proposed molecular mechanics approach is indeed an acceptable analytical method for analyzing the mechanical behavior of SWCNT’s. The project supported by the National Natural Science Foundation of China (10121202, 90305015 and 10328203), the Key Grant Project of Chinese Ministry of Education (0306) and the Research Grants Council of the Hong Kong Special Administrative Region, China (HKU 7195/04E).     

薄膜结构的几何非线性分析

使用动力松弛法对薄膜结构进行静载分析，并提出一种方法处理皱折单元以确保荷载分析的可靠性。薄膜结构如果在某膜单元的单向应力方向发生皱折，其单元本身仍然能够继续承受荷载，因此提出索松弛单元和膜皱折单元处理薄膜的索松弛和膜皱折问题。就索网结构和薄膜结构分类给出算例进行静载分析，算例表明本文的方法可以有效处理索松弛单元和膜皱折单元，确保荷载分析的准确性。     

松弛与蠕变力学特性转换关系的研究

本文首先论述了拉伸应力松弛模量Ｅ（ｔ）与拉伸蠕变柔量Ｄ（ｔ）之间的近似与精确转换关系式，提出一种诊断Ｄ（ｔ）的数值积分算法，通过应力松弛模量实验给出一种固体推进剂Ｅ（ｔ）和Ｄ（ｔ）的实测与转换计算结果，计算结果有较小的误差具有重要的实用价值。     

Age dependence of the drag force in an aqueous foam

The drag force on a sphere moving through an aqueous foam is measured as the foam ages. After an initial period, the steady-state drag decreases with age T as T ^{−0.54±0.14}. As the mean bubble size R in the foam coarsens as T ^0.5, this implies that the drag force scales as The transient buildup of the force when the sphere starts to move is described by a single exponential approach to the steady-state drag while its relaxation when the motion stops is described by the sum of three exponential relaxations. This is as for fresh foam, but the coefficients and time constants vary systematically with age. For the most part, these quantities also show a power law scaling with T. The age dependence of the quantities determined in this study is discussed in terms of the mean bubble size.