Molecular Dynamics Simulation Connections and Mechanical Properties of Cu/Al Explosion Shock Interface

Based on the molecular dynamics (MD) method, transient explosive welding process of Cu/Al junction point was revealed from the microscopic aspect, and mechanical properties and machinability of the Cu/Al nano-weldment were studied. The results show that kinetic energy is converted into internal energy in the system after the collision. The heterogeneous atoms penetrate into each other and the diffusion effect of copper atoms is better than aluminium atoms. The elastic modulus of the nano-weldment is 64.56 GPa, which is between copper's and aluminium's; however, its yield strength is less than those of the two monocrystals. Interactions between dislocations and disordered lattices cause the stress strengthening in the plastic deformation stage, which causes that the stress values of the weldment is larger than those of the two monocrystals. This strengthening mechanism is also reflected in the cutting process, and the weldment has the highest average cutting force 117.80 nN. A mass of dislocations nucleate in the disordered lattice areas of the weldment, and they spread at 45¯ to the cutting direction. However, dislocations pile up when their propagation is hindered by the disordered lattices and interface, which leads to the work hardening effect

Radical edge crack problem of a circular disk under circumference load

The problem of a circular disk with a radial edge crack is investigated theoretically. The disk is in an equilibrium state of generalized plane stress caused by a pair of concentrated forces loading on the disk circumference. The region of the cracked disk was mapped into the interior of a unit circle by using a conformal transformation. A boundary integral method was suggested to avoid the difficulty caused by the singularities of the transform function. The boundary value problem of the elastic cracked disk was solved analytically in a closed form. The stress intensity factor (SIF) at the tip of the crack was calculated using the complex potentials. The result shows that the smaller the load angle, the higher the value of the SIF

Nonlinear vibration of different types of functionally graded nanotubes using nonlocal strain gradient theory

Authors in this work investigate nonlinear vibration of different types of functionally graded tube in the theoretical framework of nonlocal strain graded theory. They are tubes with inside-out functionally graded distribution, tubes with circumferential functionally graded distribution and tubes with sinusoidal functionally graded distribution. At the beginning, based on the assumptions and appropriate mathematical models proposed via us, the effective material properties of new functionally graded materials are defined in the form of power-law. Then, a high order shear deformation beam model that can satisfy the stress boundary conditions on inner and outer surfaces is used to analyze respective types of FGM tube. With the aid of the Hamilton' principle, the nonlinear governing equations that include a nonlocal parameter and a material length-scale parameter are acquired, and then are solved via the perturbation method to obtain appropriate analytical solutions. Finally, parametric studies are carried out in detail for three types of functionally graded tube, including the thickness of tube, temperature, nonlocal parameter, strain gradient parameter, scale parameter ratio, slenderness ratio, volume index, different beam models, different kinds of functionally graded distribution and the size of lead

Nonlinear bending and thermal post-buckling behavior of functionally graded piezoelectric nanosize beams using a refined model

We in this paper analyze the problem of the nonlinear bending, thermal buckling and post-buckling of functionally graded piezoelectric material nanobeams based on Eringen's nonlocal elasticity theory. The beams with immovable clamped ends are exposed to the external electric voltages, a uniform transverse load as well as uniform temperature change. A refined beam model which can transform the Reddy beam model into the Timoshenko beam model is introduced into this study so that we can distinguish the role of transverse shear deformation in complicated stress field. The governing equations are induced by using the generalized variation principle, and then the approximate analytical solution of the FGP material nanobeams for nonlinear, thermal buckling, post-buckling are obtained by using a two-step perturbation method. Subsequently, detailed parametric studies are carried out to get an insight into the effects of different physical parameters, including the slenderness ratio, small scale parameter, volume fraction index and external electric voltages

Buckling and post-buckling of magneto-electro-thermo-elastic functionally graded porous nanobeams

The problem of the nonlinear thermal buckling and post-buckling of magneto-electro-thermo-elastic functionally graded porous nanobeams is analyzed based on Eringen’s nonlocal elasticity theory and by using a refined beam model. The beams with immovable clamped ends are exposed to the external electric voltages, magnetic potentials, a uniform transverse load and uniform temperature change. For the first time, the four types of porosity distribution in the nanobeam are considered and compared in complex electric–magnetic fields. Besides, the new formula of the effective material properties is proposed in this paper to simultaneously estimate the material distribution and porosity distribution in the thickness direction. The generalized variation principle is used to induce the governing equations, then the approximate analytical solution of the METE-FG nanobeams based on physical neutral surface is obtained by using a two-step perturbation technique. Finally, detailed parametric analyses are performed to get an insight into the effects of different physical parameters, including the slenderness ratio, small-scale parameter, volume fraction index, external electric voltages, magnetic potentials, porosity coefficient and different porosity distributions, for providing an effective way to improve post-buckling strength of porous beams

Nonlinear bending of functionally graded porous nanobeam subjected to multiple physical load based on nonlocal strain gradient theory

We in this paper study nonlinear bending of a functionally graded porous nanobeam subjected to multiple physical load based on the nonlocal strain gradient theory. For more reasonable analysis of nanobeams made of porous functionally graded magneto-thermo-electro-elastic materials (PFGMTEEMs), both constituent materials and the porosity appear gradient distribution in the present expression of effective material properties, which is much more suitable to the actual compared with the conventional expression of effective material properties. Besides the displacement function regarding physical neutral surface is introduced to analyze mechanical behaviors of beams made of FGMs. Then we derive nonlinear governing equations of PFGMTEEMs beams using the principle of Hamilton. To obtain analytical solutions, a two-step perturbation method is developed in nonuniform electric field and magnetic field, and then we use it to solve nonlinear equations. Finally, the analytical solutions are utilized to perform a parametric analysis, where the effect of various physical parameters on static bending deformation of nanobeams are studied in detail, such as the nonlocal parameter, strain gradient parameter, the ratio of nonlocal parameter to strain gradient parameter, porosity volume fraction, material volume fraction index, temperature, initial magnetic potentials and external electric potentials

Nonlinear thermal buckling of bi-directional functionally graded nanobeams

We in this article study nonlinear thermal buckling of bi-directional functionally graded beams in the theoretical frameworks of nonlocal strain graded theory. To begin with, it is assumed that the effective material properties of beams vary continuously in both the thickness and width directions. Then, we utilize a higher-order shear deformation theory that includes a physical neutral surface to derive the size-dependent governing equations combining with the Hamilton's principle and the von Kármán geometric nonlinearity. It should be pointed out that the established model, containing a nonlocal parameter and a strain gradient length scale parameter, can availably account for both the influence of nonlocal elastic stress field and the influence of strain gradient stress field. Subsequently, via using a easier group of initial asymptotic solutions, the corresponding analytical solution of thermal buckling of beams is obtained with the help of perturbation method. Finally, a parametric study is carried out in detail after validating the present analysis, especially for the effects of a nonlocal parameter, a strain gradient length scale parameter and the ratio of the two on the critical thermal buckling temperature of beams