Chain fragmentation under liquid-state and solid-state conditions

Thermally Activated fragmentation of copolycarbonates PC(T_xA_1-x) of bisphenol A (unit CA) and the Heat-sensitive diol 1,1,2,2-tetraethyl-1,2-di-(p-hydroxy) phenylethane (unit CT) was studied in the bulk, i.e., in the pure copolymers and in their blends with the polycarbonates of bisphenol A (PCA) or tetramethyl bisphenol A (TMPC). Fragmentation proceeds via dissociation followed by disproportionation at the central C? C bond of the unit CT. The reaction has rates that are convenient to study near the glass transition temperature. The “chemical” time constants τ for the entire reaction and τ₂ for the disproportionation step compete with the “physical” time constants δ_α for segmental motion and δ_q for fragment diffusion. A cage effect is observed below τ₂ = δ_α and effects of delayed matrix response below τ = δ_α and τ = δ_q. Owing to the two latter effects, parameters such as the glass transition temperature and the structure factor of concentration fluctuations do not respond primarily to the fragmentation, but rather to subsequent relaxation and diffusion processes in the polymer matrix.     

Edge-buckling in stretched thin films under in-plane bending

The wrinkling instabilities of a stretched rectangular thin film subjected to in-plane bending are investigated within the framework of the linearised Donnell-von Kármán bifurcation equation for thin plates. One of our principal objectives is to assess the role played by the finite bending stiffness of the film on the linear wrinkling mechanism. To this end, we employ a non-homogeneous linear pre-bifurcation solution and cast the corresponding eigenvalue problem as a singularly-perturbed differential equation with variable coefficients. Numerical simulations of this problem reveal the existence of two different regimes for the behaviour of the lowest eigenvalue. Based on this observation, a WKB analysis is carried out in order to capture the dependence of the critical wrinkling load on the wavelength of the localised oscillatory buckling pattern and the stiffness of the elastic film. The validity of the analytical results is corroborated by independent numerical computations of the eigenvalues using the method of compound matrices.     

Interlaminar fracture of multidirectional glass/epoxy laminates under mixed-mode I + II loading

The mixed-mode I + II interlaminar fracture of multidirectional glass/epoxy laminates is investigated. Mixed-mode bending (MMB) tests were performed on specimens with delaminations in 0/θ-type interfaces, with θ varying from 0 to 90°. Preliminary three-dimensional finite-element analyses validated the beam theory model (BTM) used for analysing experimental data. The compliances measured are in a good agreement with BTM predictions. The total critical energy release rate G_c varies linearly with the mode II ratio G_II/G, although some discrepancies are observed in the high-mode II results for the 0/45 and 0/90 specimens. Russian translation published in Mekhanika Kompozitnykh Materialov, Vol. 43, No. 3, pp. 349–366, May–June, 2007.     

P-version hybrid analytical finite element method for plate bending problems

Two sets of trial functions with different variables are constructed for the admissible space of the finite element analysis. The trial functions satisfy the equilibrium differential equation inside elements, while the deflections and rotations on the edges of the elements are approximated by the Peano hierarchical interpolation functions. Then, a generalized variational principle is applied to set up the p-version hybrid analytical finite element method for plate bending problems. The accuracy of finite element computation can be improved by increasing the order of the interpolation polynomials with fixed mesh. In the finite element formulation, to obtain the stiffness matrices and the load vectors, it is only necessary to perform quadrature over the edges of the elements. These matrices and vectors possess an embedding structure. The conformability between the elements can be controlled automatically.This work is supported by the Natural Science Foundation of China and the Aeronautical Science Foundation of China.     

The relationship between simple shear and pure shear for a simple fluid without coupling effects

Similarities between simple shear and pure shear or planar extension are exploited to derive equations relating stress in pure shear at constant extension rate to the stress in simple shear at constant shear rate. For the class of materials considered it follows that there are only two independent material functions required to describe simple shear. The relationships derived may also be used to estimate the ratio of first to second normal-stress differences in simple shear using experimental results from pure shear experiments.     

Boundary element bending analysis of heated elastic plates

Generally, the boundary integral equations for nonlinear and inhomogeneous problems need to be formulated in terms of boundary and domain integrals. The present paper declares the possibility of the transformation of the domain integral term into the boundary integral for the thermal bending analysis of a thin elastic plate,provided that the temperature can be expressed by a linear variation over the thickness.     

Residual stresses deriving from holographic interferometry data on a base of inverse problem solution

A transition model, which is capable of obtaining both membrane and bending residual stress components from initial experimental information, is developed for thin-walled plane structures. The determination of residual stresses is based on the combined implementing of the hole-drilling method and reflection hologram interferometry. Required input data are obtained by simultaneous measurements on through hole distortions in two principal strain directions on opposite sides of thin plane specimen. These sides are faces of the drill entrance and exit. Superimposed residual stresses field, which consists of both membrane and bending components, is a reason for the various deviations of each specific fringe pattern from an ideal form. This fact is a clear experimental indication of the bending stress contribution in a total stress field. Two ways of decomposition of superimposed residual stresses field are proposed and analysed in detail. Emphasis is laid on a careful quantitative formulation of the inverse problem needed for an accurate deriving both membrane and bending residual stress components. It is shown that an availability of two-side initial data is both an essential and necessary condition of such a formulation. Detailed analysis of an accuracy of the results obtained is performed. This analysis is based on a wide set of both actual interferograms and analogous reference fringe patterns related to superimposed residual stress field under study. Comparing residual stress values obtained proceeding from one-side and two-side data are presented for different types of superimposed field of interest.     

界面断裂韧性的实验研究

本文以铝材与浇注的环氧树脂之间的界面裂纹为研究对象，用三点弯曲和四点弯曲的试验方法，并结合有限元法的数值分析，对双材料界面裂纹的扩展判据，即裂纹扩展的临界能量释放率ＧＣ与相位角ψ↑＾的关系曲线，进行了初步验证。结果表明这一判据基本上是可取的。但是，应该注意界面裂纹的韧性与多种因素有关，实际应用ＧＣ－ψ↑＾曲线时，必须严格区分不同因素。     

Longitudinal–Transverse Bending of Layered Beams in a Three-Dimensional Formulation

Three-dimensional equations of the elasticity theory for layered beams are solved by the method of asymptotic splitting without additional hypotheses or restrictions.