Elastic-Plastic Analysis of Functionally Graded Spherical Pressure Vessels Using Strain Gradient Plasticity

In this paper, for the first time based on the nonlocal strain gradient theory the effect of size dependency in torsional vibration of bi-direction functionally graded (FG) nonlinear nano-cone is study. The material properties were assumed to vary according to the arbitrary function in radial and axial directions. The Navier equation and boundary conditions of the size-dependent bidirectional FG nonlinear nano-cone were derived by Hamilton's principle. These equations were solved by employing the generalized differential quadrature method (GDQM). The presented model can turn into the classical model if the material length scale parameters are taken to be zero. The effects of some parameters, such as inhomogeneity constant, cross-sectional area parameter and small-scale parameters, were studied. As an essential result of this study can be stated that an FG nano-cone model based on the nonlocal elasticity theory behaves softer and based on the strain gradient theory behaves harder.

The present study deals with the analysis of rotating spherical pressure vessels made of functionally graded materials (FGMs). Material properties are graded along the radial direction, which is achieved by varying volume fractions of the constituting materials according to Mori-Tanaka scheme. Shells are subjected to hydrostatic internal pressure and have free boundary condition at the outer surface. Governing equations are derived using principle of stationary total potential. The effects of grading parameter and thickness parameter on stress and deformation behavior of the shells are investigated. Results obtained show that there is a significant reduction in stress and deformation of the FGM shells as compared to homogeneous shell. Cite this Article Amit Kumar Thawait, Lakshman Sondhi, Rupesh Kumar Verma. An Investigation of Stress and Deformation States of Rotating Functionally Graded Spherical Pressure Vessels . Journal of Experimental & Applied Mechanics . 2017; 8(3): 22–3 1 p. Keywords: Functionally graded material (FGM), elastic analysis, rotating spherical pressure vessel, Mori-Tanaka scheme

Recent experiments have shown that the microscale material behavior is very different from that of bulk materials, and displays strong size effects when the characteristic length associated with the deformation is on the order of microns. Conventional continuum theories, however, can not predict this size dependence because they do not have an intrinsic length in their constitutive models. A new continuum theory, namely the strain gradient theory, has been proposed to investigate the deformation of solids at the microscale. For materials undergoing plastic deformation, the basis of strain gradient theory is the dislocation theory in materials science, and strain gradient plasticity has agreed remarkably well with experiments. For elastic materials with microstructures, it has also been established that the material behavior can be represented by an elastic strain gradient theory. A general approach to investigate fracture of materials with strain gradient effects is established. Both the near-tip asymptotic fields and the elastic full-field solutions are obtained in closed form. Due to stain gradient effects, stresses ahead of a crack tip are significantly higher than those in the classical K field. The plastic zone size surronunding a crack tip is estimated by elastic near-tip fields, as well as by the Dugdale model. It is established that the plastic zone is, in general, much more round and larger than that estimated from the classical K field.

The effective threshold for fatigue crack propagation: a plastic size effect?

In the present manuscript, the second strain gradient (SSG) is utilized to investigate the primary resonance of a nonlinear Euler-Bernoulli nanobeam is analyzed in this paper for the first time. To that end, the second strain gradient theory, a higher-order continuum theory capable of taking the size effects into account, is utilized and the governing equation of the motion for an Euler-Bernoulli nanobeam is derived with sixteen higher-order material constants. Then by implementing the Galerkin’s method,the Duffing equation for the vibration of a hinged-hinged nanobeam is obtained and its primary resonance is studied utilizing the method of multiple scales. The size effects and impact of various system parameters on the amplitude of the response are then investigated for three different materials and the results are compared to thatof the first strain gradient and classical theories. The results of this manuscript clearly shows that the nonlinear vibration of a second strain gradient nanobeam is size-dependent and although the difference between the results obtained by the second strain gradient theory and the first strain gradient theory is negligible for thicker beams, as the thickness decreases, the difference becomes more prominent. Also, the effects of nonlinearity on the forced vibration nonlinear response of an SSG beam are investigated and some observations are reported.

Micromechanical modeling of damage evolution and fracture behavior in particle reinforced metal matrix composites based on the conventional theory of mechanism-based strain gradient plasticity

Large-amplitude coupled scale-dependent behaviour of geometrically imperfect NSGT nanotubes

Free vibrations of FG elastic Timoshenko nano-beams by strain gradient and stress-driven nonlocal models

Forced vibration of a porous functionally graded (FG) cylindrical microshell due to a moving point load with constant velocity is studied for the first time. Through the thickness of microshell, there are even-type or uneven-type porosities. Therefore, material properties of the microshell become porosity-dependent and are described via modified power-law function. For micro-scale shells, small size effects due to non-uniform strain field can be considered via strain gradient theory (SGT). At first, the governing equations of the microshell are converted to new equations in Laplace domain. Then, time response of the microshell will be obtained implementing inverse Laplace transform technique. It will be demonstrated that forced vibration characteristics of a FG microshell rely on the velocity of moving load, strain gradients, porosity percentage, material/porosity distribution and its geometry.

A strain-gradient plasticity theory of bimodal nanocrystalline materials with composite structure

Increased strength-to-weight ratio and extended fatigue life are the main objectives in the optimal design of modern pressure vessels. These two goals can mutually be achieved by creating a proper residual stress field in the vessel’s wall by a process known as autofrettage. Although there are many studies that have investigated the autofrettage problem for cylindrical vessels, only a few of such studies exist for spherical ones. Because of the spherosymmetry of the problem, autofrettage in a spherical pressure vessel is treated as a one-dimensional problem and solved solely in terms of the radial displacement. The mathematical model is based on the idea of solving the elastoplastic autofrettage problem using the form of the elastic solution. Substituting Hooke’s equations into the equilibrium equation and using the strain-displacement relations yield a differential equation, which is a function of the plastic strains. The plastic strains are determined using the Prandtl–Reuss flow rule and the differential equation is solved by the explicit finite difference method. The existing 2D computer program, for the evaluation of hydrostatic autofrettage in a thick-walled cylinder, is adapted to handle the problem of spherical autofrettage. The presently obtained residual stress field is then validated against three existing solutions emphasizing the major role the material law plays in determining the autofrettage residual stress field. The new code is applied to a series of spherical pressure vessels yielding two major conclusions. First, the process of autofrettage increases considerably the maximum safe pressure that can be applied to the vessel. This beneficial effect can also be used to reduce the vessel’s weight rather than to increase the allowable internal pressure. Second, the specific maximum safe pressure increases as the vessel becomes thinner. The present results clearly indicate that autofrettaging of spherical pressure vessels can be very advantageous in various applications.

Coupled longitudinal-transverse-rotational free vibration of post-buckled functionally graded first-order shear deformable micro- and nano-beams based on the Mindlin's strain gradient theory

ABSTRACTIn this article, an analytical model for the wave propagation analysis of inhomogeneous functionally graded (FG) nanobeam in thermal environment is developed based on nonlocal strain gradient theory, in which the stress accounts for not only the nonlocal elastic stress field but also the strain gradients stress field. The nanobeam is modeled through a higher order shear deformable refined beam theory which has a trigonometric shear stress function. The temperature field supposed to have a nonlinear distribution across the nanobeam thickness. Temperature-dependent material properties of nanobeams are spatially graded based on Mori–Tanaka model. The governing equations of the temperature-dependent functionally graded (FG) nanobeam are derived using the Hamilton’s principle. Numerical examples show that the characteristics of the wave propagation of FG nanobeam are influenced by various parameters such as nonlocality parameter, length scale parameter, gradient index, and temperature changes.

Thermoelastic analysis of rotating functionally graded micro/nanodisks of variable thickness

Modeling deformation of auxetic and non-auxetic polymer gels