Thermal stresses analysis of ceramic/metal functionally gradient material cylinder

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Optimum material design for functionally gradient material plate

Summary Steady thermal stresses in a plate made of a functionally gradient material (FGM) are analyzed theoretically and calculated numerically. An FGM plate composed of PSZ and Ti-6Al-4V is examined, and the temperature dependence of the material properties is considered. A local safety factor is used for evaluation of the FGM's strength. It is assumed that top and bottom surfaces of the plate are heated and kept at constant thermal boundary conditions. The pairs of the surface temperatures, for which the minimum local safety factor can be of more than one, are obtained as available temperature regions. The temperature dependence of the material properties diminishes, available temperature region as compared with that for an FGM plate without it. The available temperature region of the FGM plate is wider than that of the two-layered plate, especially for the surface temperatures which are high at the ceramic surface and low at the metal side. The influence of different mechanical boundary conditions is examined, and available temperature regions are found to be different, depending on the mechanical boundary conditions. The influence of the intermediate composition on the thermal stress reduction is also investigated in detail for the surface temperatures which are kept at 1300 K at the ceramic surface and 300K at the metal side. Appropriate intermediate composition of the FGM plate can yield the local safety factor of one or more for the four mechanical boundary conditions at once. For the two-layered plate there does not exist, however, any appropriate pair of metal and ceramic thicknesses which would yield the local safety factor of one or more for the four mechanical boundary conditions at once. The influence of the intermediate composition on the maximization of the minimum stress ratio depends on the mechanical boundary conditions. Finally, the optimal FGM plates are determined.     

Direct calculations of material parameters for gradient plasticity

Length scale parameters introduced in gradient theories of plasticity are calculated in closed form with a continuum dislocation based theory. The similarity of the governing equations in both models for the evolution of plastic deformation of a constrained thin film makes it possible to identify parameters of the gradient plasticity theory with the dislocation based model. A one-to-one identification is not possible given that gradient plasticity does not account for individual dislocations. However, by comparing the mean plastic deformation across the film thickness we find that the length scale parameter, l, introduced in the gradient plasticity theory depends on the geometry as well as material constants.     

钨纤维复合材料穿甲弹芯侵彻时的自锐现象

对钨合金穿甲弹和钨纤维/Zr合金金属玻璃基复合材料穿甲弹进行了靶场对比侵彻实验。穿甲弹侵彻过程中,钨合金弹芯头部形成蘑菇头、头部晶粒被径向压扁;钨纤维复合材料弹芯头部在侵彻过程中,发生了绝热剪切破坏,具有自锐行为,且在弹芯头部形成很薄的边缘层,仅在这层中金属玻璃基体破碎,钨纤维断裂,温度升高,质量消蚀。钨纤维复合材料穿甲弹的侵彻能力明显高于钨合金穿甲弹。     

Anti-plane shear crack in a functionally gradient piezoelectric material

The main objective of this paper is to study the singular nature of the crack-tip stress and electric displacement field in a functionally gradient piezoelectric medium having material coefficients with a discontinuous derivative. The problem is considered for the simplest possible loading and geometry, namely, the anti-plane shear stress and electric displacement in-plane of two bonded half spaces in which the crack is parallel to the interface. It is shown that the square-root singularity of the crack-tip stress field and electric displacement field is unaffected by the discontinuity in the derivative of the material coefficients. The problem is solved for the case of a finite crack and extensive results are given for the stress intensity factors, electric displacement intensity factors, and the energy release rate. Project supported by the National Natural Science Foundation of China (No. 10072041), the National Excellent Young Scholar Fund, of China (No. 10125209) and the Teaching and Research Award Program for Outstanding Young Teachers in Higher Education Institutions of MOE, P. R. C..     

Covariant gradient continua applied to wave propagation within defective material

Riemann–Cartan geometry is used to model continuum with defects. In order to illustrate the differences induced by two possible definitions for the strain (spatial or material) in this framework, propagation of waves is studied for a simple example of infinite continuum with uniform and stationary defects density. Anisotropy and attenuation are caught by both models even if these effects are quite different. Furthermore, the spatial strain does not allow some polarizations, whereas the material one induces chirality and uniform breathing vibrations.     

Enhancing the optimization of material distributions in composite structures using gradient architectures

Many structural components encounter service conditions and hence, material performance requirements, which vary from location to location within the component resulting in a composite structure. It has been shown that abrupt transitions in material properties within a composite structure can cause concentrations of deformation, which are mitigated by gradually varying the microstructure and/or composition of materials in a gradient architecture. Structural optimization techniques, such as the homogenization method, have yet to take full advantage of gradient architectures. Many of these structural optimization techniques employ robust mathematical techniques, such as genetic algorithms (GAs), with finite element simulations to optimize material distributions in composite structures through computationally intensive stochastic, global explorations of the design search space defined by a multitude of design variables associated with the discrete representation of the composite structure. Using gradient architectures, it is demonstrated that GAs can be enhanced for composite structures by constraining the design search space through a reduction in the number of design variables, thereby substantially reducing the computational effort. For more complex material distributions, a “material gradient optimization method” is proposed that produces multiple gradient architecture constraints with more optimal solutions than obtained without using these constraints, but whose uniqueness will be dependent upon the number of layers used in the finite element simulations.     

Determination of material intrinsic length and strain gradient hardening in microbending process

Microbending experiments of pure aluminum show that the springback angles increase with the decrease of foil thickness, which indicates obvious size effects and attributes to plastic strain gradient hardening. Then a constitutive model, taking into accounts both plastic strain and plastic strain gradient hardening, is proposed to analyze the microbending process of thin foil. The model is based on the relationship between shear yield stress and dislocation density, in which the material intrinsic length is related to material properties and average grain numbers along the characteristic scale direction of part. It is adopted in analytical model to calculate the non-dimensional bending moment and predict the springback angle after microbending. It is confirmed that the predictions by the proposed hardening model agree well with the experimental data, while those predicted by the classical plasticity model cannot capture such size effects. The contribution of plastic strain gradient increases with the decrease of foil thickness and is independent on the bending angle.     

ANTI-PLANE FRACTURE ANALYSIS OF FUNCTIONALLY GRADIENT MATERIAL INFINITE STRIP WITH FINITE WIDTH

The special case of a crack under mode III conditions was treated, lying parallel to the edges of an infinite strip with finite width and with the shear modulus varying exponentially perpendicular to the edges. By using Fourier transforms the problem was formulated in terms of a singular integral equation. It was numerically solved by representing the unknown dislocation density by a truncated series of Chebyshev polynomials leading to a linear system of equations. The stress intensity factor (SIF) results were discussed with respect to the influences of different geometric parameters and the strength of the non-homogeneity. It was indicated that the SIF increases with the increase of the crack length and decreases with the increase of the rigidity of the material in the vicinity of crack. The SIF of narrow strip is very sensitive to the change of the non-homogeneity parameter and its variation is complicated. With the increase of the non-homogeneity parameter, the stress intensity factor may increase, decrease or keep constant, which is mainly determined by the strip width and the relative crack location. If the crack is located at the midline of the strip or if the strip is wide, the stress intensity factor is not sensitive to the material non-homogeneity parameter.     

Torsional vibrations of a column of fine-grained material: A gradient elastic approach

The gradient theory of elasticity with damping is successfully employed to explain the experimentally observed shift in resonance frequencies during forced harmonic torsional vibration tests of columns made of fine-grained material from their theoretically computed values on the basis of the classical theory of elasticity with damping. To this end, the governing equation of torsional vibrations of a column with circular cross-section is derived both by the lattice theory and the continuum gradient elasticity theory with damping, with consideration of micro-stiffness and micro-inertia effects. Both cases of a column with two rotating masses attached at its top and bottom, and of a column fixed at its base carrying a rotating mass at its free top, are considered. The presence of both micro-stiffness and micro-inertia effects helps to explain the observed natural frequency shift to the left or to the right of the classical values depending on the nature of interparticle forces (repulsive or attractive) due to particle charge. A method for using resonance column tests to determine not only the shear modulus but also the micro-stiffness and micro-inertia coefficients of gradient elasticity for fine-grained materials is proposed.