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

2017 ◽  
Vol 09 (08) ◽  
pp. 1750118 ◽  
Author(s):  
Hassan Shokrollahi
Keyword(s):  
Internal Pressure ◽  
Strain Gradient ◽  
Plastic Region ◽  
Pressure Vessels ◽  
Functionally Graded ◽  
Strain Gradient Plasticity ◽  
Gradient Plasticity ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Spherical Pressure

In this paper, formulation of elastic-plastic analysis of functionally graded (FG) spherical pressure vessels under internal pressure based on strain gradient plasticity is presented. The material properties are assumed to vary in a power law manner in the radial direction. A linear hardening rule for the material behavior in the plastic region is assumed. After deriving the governing differential equations, a closed form solution is obtained. At the first step, the obtained results were validated against other available results in the literature. Then the effects of changing the inner radius from a few micro-meters to one meter, FG power index and strain gradient coefficient on stress and plastic region size are studied based on classical and strain gradient theories. Also, the effect of internal pressure on the size of plastic region is studied.

Analytical Solution of a Borehole Problem Using Strain Gradient Plasticity

2002 ◽  
Vol 124 (3) ◽  
pp. 365-370 ◽  
Author(s):  
X.-L. Gao
Keyword(s):  
Analytical Solution ◽  
Strain Gradient ◽  
Plastic Region ◽  
Yield Condition ◽  
Plasticity Theory ◽  
Strain Gradient Plasticity ◽  
Spatial Gradient ◽  
Gradient Plasticity ◽  
Present Solution ◽  
Classical Plasticity

An analytical solution is presented for the borehole problem of an elasto-plastic plane strain body containing a traction-free circular hole and subjected to uniform far field stress. A strain gradient plasticity theory is used to describe the constitutive behavior of the material undergoing plastic deformations, whereas the generalized Hooke’s law is invoked to represent the material response in the elastic region. This gradient plasticity theory introduces a higher-order spatial gradient of the effective plastic strain into the yield condition to account for the nonlocal interactions among material points, while leaving other relations in classical plasticity unaltered. The solution gives explicit expressions for the stress, strain, and displacement components. The hole radius enters these expressions not only in nondimensional forms but also with its own dimensional identity, unlike classical plasticity-based solutions. As a result, the current solution can capture the size effect in a quantitative manner. The classical plasticity-based solution of the borehole problem is obtained as a special case of the present solution. Numerical results for the plastic region radius and the stress concentration factor are provided to illustrate the application and significance of the newly derived solution.

Analytical Solution for Strain Gradient Plasticity of Rotating Functionally Graded Thick Cylinders

2020 ◽  
Vol 12 (07) ◽  
pp. 2050082
Author(s):  
Saeid Varmazyari ◽  
Hassan Shokrollahi
Keyword(s):  
Analytical Solution ◽  
Strain Gradient ◽  
Yield Criterion ◽  
External Pressure ◽  
Functionally Graded ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Gradient Plasticity ◽  
Elastic Plastic ◽  
Von Mises

The elastic-plastic deformation of rotating functionally graded (FG) cylinders is investigated based on strain gradient theory. The governing equations are obtained based on the modified von Mises yield criterion, linear work hardening and plane strain assumptions. An analytical solution for the obtained equations is presented by which the deformation, strain and stress components for any point of the cylinder can be obtained. After verification of the formulation by comparing the obtained results with the reported results in the literature, some studies are presented to investigate the effects of cylinder size on the stress distribution and elastic-plastic interface radius of the rotating FG cylinder under internal and external pressure. The effects of the strain gradient coefficient, angular velocity, and the heterogeneity constant of the material are investigated. The results show that increasing the heterogeneity constant of the material and decreasing the cylinder radius lead to increasing the strength of material and decreasing the elastic-plastic interface radius. Moreover, classical theory is compared with this study and the range of the sizes in which both the theories leading to the same results, are defined.

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