Torsional statics of two-dimensionally functionally graded microtubes

A size-dependent governing equation is derived to investigate the torsional static behaviors of two-dimensionally functionally graded microtubes based on the modified couple stress theory. The shear modulus is assumed to vary along the tube’s length direction according to an exponential distribute function, and varies along the tube’s radius direction according to a power-law function. A generalized differential quadrature method is developed to determine the rotational angle and shear stresses. Some illustrative examples are given to investigate the effects of applied torques, the length scale parameter and various material compositions on the torsional angle and shear stresses.     

Finite element piezothermoelasticity analysis and the active control of FGM plates with integrated piezoelectric sensors and actuators

 An efficient finite element model is presented for the static and dynamic piezothermoelastic analysis and control of FGM plates under temperature gradient environments using integrated piezoelectric sensor/actuator layers. The properties of an FGM plate are functionally graded in the thickness direction according to a volume fraction power law distribution. A constant displacement-cum-velocity feedback control algorithm that couples the direct and inverse piezoelectric effects is applied to provide active feedback control of the integrated FGM plate in a closed loop system. Numerical results for the static and dynamic control are presented for the FGM plate, which consists of zirconia and aluminum. The effects of the constituent volume fractions and the influence of feedback control gain on the static and dynamic responses of the FGM plates are examined. Received: 13 March 2002 / Accepted: 5 March 2003 The work described in this paper was supported by a grant awarded by the Research Grants Council of the Hong Kong Special Administrative Region, China (Project No. CityU 1024/01E).     

Discrete singular convolution and its application to the analysis of plates with internal supports. Part 2: Applications

Part 2 of this series of two papers presents the applications of the discrete singular convolution (DSC) algorithm. The main purpose of this paper is to explore the utility, test the accuracy and examine the convergence of the proposed approach for the vibration analysis of rectangular plates with internal supports. Both partial internal line supports and complex internal supports are considered for 21 square plates of various combinations of edge support conditions. The effects of different size, shape and topology of the internal supports and different boundary conditions on the vibration response of plates are investigated. The partial internal line supports may vary from a central point support to a full range of cross or diagonal line supports. Several closed‐loop supports, such as ring, square and rhombus, and their combinations are studied for complex internal supports. Convergence and comparison studies are carried out to establish the correctness and accuracy of the DSC algorithm. The DSC results are compared with those in the available literature obtained by using other methods. Numerical results indicate that the DSC algorithm exhibits controllable accuracy for plate analysis and shows excellent flexibility in handling complex geometries, boundary conditions and support conditions. Copyright © 2002 John Wiley & Sons, Ltd.     

Experimental and numerical investigation of fracture in double-edge notched steel plates

Double-edge notched (DENT) steel plates were pulled until complete fracture and several experimental observations were made (using profilometry and scanning electron microscopy). The essential work of fracture (EWF) model was found to be well verified. Numerical simulations—up to the maximum load only—of some experiments were performed using the finite element method (FEM), and incorporating geometric and material non-linearities (large deformation elasto-plasticity). Some experimental measurements were compared with the corresponding numerical computations and excellent agreement was found.     

Analytical Calculation of Large-Scale Deflection of Pulse-Loaded Elliptic Plates

Large deflections of pulse-loaded elliptic and round plates made of hardenable elastoplastic materials are investigated analytically using an energy-based approach. Formulas that are convenient for engineering design have been derived.     

Recrystallization/precipitation behaviour in microalloyed steels

Microalloyed high-strength low-alloy (HSLA) steels contain additions of Nb, V, Ti, or in combination, in amounts of 0.01 to 0.1 weight percent to improve mechanical properties, which are strongly dependent on the thermomechanical interaction taking place in the course of rolling mill processes. The recrystallizatian of hat-twisted austenite has been investigated in a cylindrical specimen (f 6×50 mm) machined from hat rolled plates of 0,052 wt % Niobium microalloyed steel. Continuous and interrupted torsion test were carried out in the temperature range 1123 K to 1173 K after a solution treatment of 1.5 minutes at 1423 K and torque-twist data were analysed. The various methods were discussed for obtaining results from torsion tests. The effect of precipitation kinetics was appreciated by way of connection t_p/t_p(red), where t_p is the experimental measured time for the peak stress and t_p(red) is the newly defined reduced time. The softening ratio X and time t_0.05R for start of static recrystallization were established.

The correlation between precipitation and recrystallization is presented as a graphs for chosen requirements (temperature of austenitization, carbon and niobium content and strain rate). If temperature goes below 850°C, the restoration processes are hardly suppressed, both are limited by diffusion and Nb(CN) precipitation, which are extended dynamically in the range of strains rates 10⁻² to 1 s⁻¹.

In the present paper, an attempt is made to derive the PRTT diagram and to define all mathematical equations for describing recrystallization times t_0.05R, t_0.5R, t_0.95R and t_0.05P for the start of precipitation. In real metal forming processes such as the hot rolling of plates or strips the knowledge of these parameters and results is extremely important for the the correct microstructure and sheet quality to be obtained.     

Thermoelastic solutions for orthotropic and anisotropic composite laminates

Solutions, within the framework of linear uncoupled thermoelasticity, are presented for certain problems of flexure of composite laminates. Benchmark numerical results, useful for the validation or otherwise of approximate laminate models, are tabulated. Finally, these results are used to examine the accuracy of the classical lamination theory based on Kirchhoff's hypothesis.     

孔径法测量铜带残余应力的试验研究

介绍了用于薄板残余应力测量的新方法——孔径法,该方法是通过测量冲孔直径的变化来间接求出各方向的残余应力;文中详细阐述了残余应力的标定方法;由于可针对不同材料建立了被测材料的平均应力(σ_l)与被测板材宽度(B)、厚度(H)以及冲孔后直径变化率(△D_i/D)之间的数学模型,因而使薄板残余应力测量变得简便而经济;此外还对该方法的分辨率与测量精度进行了实验、计算与分析。     

Environmental degradation using functionally graded material approach

Attempts to model the degradation of polymer composites have been restricted to modelling the effects of selected degradation mechanisms. No comprehensive model has yet been accepted to predict the effect of the natural environment on the strength of polymer composites. From a review of available literature, it appears that the matrix of a polymer composite is most affected by exposure to the natural environment. Further, the damage appears to progress from the surface into the interior of the laminate. An approach has been developed to determine the properties of the damaged layer and combine the properties of the damaged and undamaged layer to obtain bulk material properties of the laminate.     

T-stress in orthotropic functionally graded materials: Lekhnitskii and Stroh formalisms

A new interaction integral formulation is developed for evaluating the elastic T-stress for mixed-mode crack problems with arbitrarily oriented straight or curved cracks in orthotropic nonhomogeneous materials. The development includes both the Lekhnitskii and Stroh formalisms. The former is physical and relatively simple, and the latter is mathematically elegant. The gradation of orthotropic material properties is integrated into the element stiffness matrix using a “generalized isoparametric formulation” and (special) graded elements. The specific types of material gradation considered include exponential and hyperbolic-tangent functions, but micromechanics models can also be considered within the scope of the present formulation. This paper investigates several fracture problems to validate the proposed method and also provides numerical solutions, which can be used as benchmark results (e.g. investigation of fracture specimens). The accuracy of results is verified by comparison with analytical solutions.