Elastic-Plastic Equilibrium of a Hollow Cylinder from Inhomogeneous Perfectly Plastic Material

2013 ◽  
Vol 405-408 ◽  
pp. 3182-3185 ◽  
Author(s):  
Vladimir I. Andreev
Keyword(s):  
Cylindrical Shell ◽  
Elastic Modulus ◽  
Plastic Material ◽  
Continuous Functions ◽  
Plastic Deformations ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
External Pressures ◽  
Inner Surface ◽  
Plastic Zones

The paper presents the solution of elastic-plastic problem of the equilibrium of a thick-walled cylindrical shell under the influence of internal and external pressures. We consider a perfectly plastic material, elastic modulus and yield strength which are continuous functions of the radius. It is shown that plastic deformations may occur on both the inner surface of the shell and the inside of its wall. Defined stresses and strains in the elastic and plastic zones, as well the displacements in the shell until fracture.

Elastoplastic Equilibrium of a Hollow Cylinder from an Inhomogeneous Perfectly Plastic Material

2019 ◽  
Vol 893 ◽  
pp. 6-12
Author(s):  
Vladimir Andreev
Keyword(s):  
Elastic Modulus ◽  
Yield Strength ◽  
Hollow Cylinder ◽  
Plastic Material ◽  
Elastoplastic Problem ◽  
Plastic Deformations ◽  
Perfectly Plastic ◽  
Elastoplastic Equilibrium ◽  
Deformed State ◽  
Walled Cylinder

The article deals with the axisymmetric elastoplastic problem for a hollow thick-walled cylinder (plane deformed state), loaded from the inside and outside by uniform pressures proportional to one parameter. The material is considered to be perfectly plastic, with the elastic modulus and yield strength generally are arbitrary functions of the radius. In addition, the material is considered to be incompressible in both plastic and elastic zones. On the basis of the criteria for the plasticity of Huber - Mises and Tresca - Saint-Venant, the radius at which the first plastic deformations occur is determined. It is shown that, depending on the functions of the inhomogeneity of elastic and plastic parameters and loads, the occurrence of plastic deformations is possible both on the surfaces and on the inner walls of the cylinder.

On Determining Elastic Modulus from Instrumented Indentation

2013 ◽  
Vol 668 ◽  
pp. 616-620
Author(s):  
Shuai Huang ◽  
Huang Yuan
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Plastic Material ◽  
Instrumented Indentation ◽  
Computational Simulations ◽  
Elastic Plastic ◽  
Modified Method ◽  
Plastic Materials ◽  
Elastic Plastic Material ◽  
Elastic Plastic Materials

Computational simulations of indentations in elastic-plastic materials showed overestimate in determining elastic modulus using the Oliver & Pharr’s method. Deviations significantly increase with decreasing material hardening. Based on extensive finite element computations the correlation between elastic-plastic material property and indentation has been carried out. A modified method was introduced for estimating elastic modulus from dimensional analysis associated with indentation data. Experimental verifications confirm that the new method produces more accurate prediction of elastic modulus than the Oliver & Pharr’s method.

Case Study of Shakedown Evaluation of a Shell With Nozzle Based on Elastic-Plastic Analysis

2017 ◽  
Author(s):  
Jun Shen ◽  
Heng Peng ◽  
Liping Wan ◽  
Yanfang Tang ◽  
Yinghua Liu
Keyword(s):  
Temperature Change ◽  
Plastic Material ◽  
Material Model ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Plastic Analysis ◽  
Elastic Perfectly Plastic ◽  
Temperature Loads ◽  
The Impact

In the past, shakedown evaluation was usually based on the elastic method that the sum of the primary and secondary stress should be limited to 3Sm or the simplified elastic-plastic analysis method. The elastic method is just an approximate analysis, and the rigorous evaluation of shakedown normally requires an elastic-plastic analysis. In this paper, using an elastic perfectly plastic material model, the shakedown analysis was performed by a series of elastic-plastic analyses. Taking a shell with a nozzle subjected to parameterized temperature loads as an example, the impact of temperature change on the shakedown load was discussed and the shakedown loads of this structure at different temperature change rates were also obtained. This study can provide helpful references for engineering design.

A Note on the Path-Dependence of the J-Integral Near a Stationary Crack in an Elastic-Plastic Material With Finite Deformation

2012 ◽  
Vol 79 (4) ◽  
Author(s):  
Dorinamaria Carka ◽  
Robert M. McMeeking ◽  
Chad M. Landis
Keyword(s):  
Finite Deformation ◽  
Path Dependence ◽  
Plastic Material ◽  
Crack Tip ◽  
J Integral ◽  
Stationary Crack ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Plastic Material ◽  
Elastic Perfectly Plastic

In this technical brief, we compute the J-integral near a crack-tip in an elastic-perfectly-plastic material. Finite deformation is accounted for, and the apparent discrepancies between the prior results of the authors are resolved.

Dynamic Expansion of a Spherical Cavity in an Elastic, Perfectly Plastic Material

1968 ◽  
Vol 35 (2) ◽  
pp. 372-378 ◽  
Author(s):  
Chi-Hung Mok
Keyword(s):  
Spherical Cavity ◽  
High Speed ◽  
Numerical Solutions ◽  
Plastic Material ◽  
Numerical Technique ◽  
Nonlinear Dependence ◽  
Static Approximation ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

It is shown that initial and boundary-value problems involving high-speed elastic-plastic deformation with spherical symmetry can be solved using a finite-difference numerical technique. Numerical solutions for the dynamic expansion of a spherical cavity under a constant pressure are presented to demonstrate the nature and capability of the numerical scheme. While the solution for an elastic material agrees closely with the exact one, the solution for an elastic, perfectly plastic material also receives support from Green’s analytic predictions concerning the motion of the elastic-plastic boundary. At large times, the asymptotic solution of the dynamic elastic-plastic problem is different from the quasi-static solution. This result indicates that the concept of quasi-static approximation may not hold in dynamic plasticity. A nonlinear dependence of the plastic solution on the boundary condition is also observed.

Geometric Elements in the Elastic-Plastic Analysis of a Cylindrical Shell

1991 ◽  
Vol 44 (11S) ◽  
pp. S181-S193 ◽  
Author(s):  
S. Lukasiewicz ◽  
J. Nowinka
Keyword(s):  
Cylindrical Shell ◽  
Deformation Behavior ◽  
Geometric Approach ◽  
Radial Force ◽  
Deformation Pattern ◽  
Element Solution ◽  
Elastic Plastic ◽  
Plastic Analysis ◽  
Plastic Zones ◽  
Geometric Elements

The paper deals with an elastic-plastic analysis of a cantilever cylindrical shell loaded at its free end by a concentrated radial force. The problem is solved by means of the so-called “geometric elements” which conform to the deformation pattern of the shell. The results obtained define the large deformation behavior and the motion of plastic zones over the surface of the shell. A comparison with a standard finite element solution is made, and the advantages of the geometric approach are shown.

Lower Bound Methods in Elastic-Plastic Shakedown Analysis

2010 ◽  
Author(s):  
Wolf Reinhardt ◽  
Reza Adibi-Asl
Keyword(s):  
Lower Bound ◽  
Plastic Material ◽  
Shakedown Analysis ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Efficient Calculation ◽  
Asme Code ◽  
Elastic Shakedown ◽  
Plastic Shakedown

Several methods were proposed in recent years that allow the efficient calculation of elastic and elastic-plastic shakedown limits. This paper establishes a uniform framework for such methods that are based on perfectly-plastic material behavour, and demonstrates the connection to Melan’s theorem of elastic shakedown. The paper discusses implications for simplified methods of establishing shakedown, such as those used in the ASME Code. The framework allows a clearer assessment of the limitations of such simplified approaches. Application examples are given.

Analysis of the spherical indentation cycle for elastic–perfectly plastic solids

2004 ◽  
Vol 19 (12) ◽  
pp. 3641-3653 ◽  
Author(s):  
L. Kogut ◽  
K. Komvopoulos
Keyword(s):  
Plastic Deformation ◽  
Finite Element ◽  
Elastic Modulus ◽  
Yield Strength ◽  
Material Properties ◽  
Deformation Behavior ◽  
Plastic Material ◽  
Elastic Plastic ◽  
Loading And Unloading ◽  
Elastic Plastic Material

A finite element analysis of frictionless indentation of an elastic–plastic half-space by a rigid sphere is presented and the deformation behavior during loading and unloading is examined in terms of the interference and elastic–plastic material properties. The analysis yields dimensionless constitutive relationships for the normal load, contact area, and mean contact pressure during loading for a wide range of material properties and interference ranging from the inception of yielding to the initiation of fully plastic deformation. The boundaries between elastic, elastic–plastic, and fully plastic deformation regimes are determined in terms of the interference, mean contact pressure, and reduced elastic modulus-to-yield strength ratio. Relationships for the hardness and associated interference versus elastic–plastic material properties and truncated contact radius are introduced, and the shape of the plastic zone and maximum equivalent plastic strain are interpreted in light of finite element results. The unloading response is examined to evaluate the validity of basic assumptions in traditional indentation approaches used to measure the hardness and reduced elastic modulus of materials. It is shown that knowledge of the deformation behavior under both loading and unloading conditions is essential for accurate determination of the true hardness and reduced elastic modulus. An iterative approach for determining the reduced elastic modulus, yield strength, and hardness from indentation experiments and finite element solutions is proposed as an alternative to the traditional method.

Elastic–Plastic Response of Clamped Square Plates Subjected to Repeated Quasi-Static Uniform Pressure

2018 ◽  
Vol 10 (06) ◽  
pp. 1850067 ◽  
Author(s):  
Shiyun Shi ◽  
Ling Zhu ◽  
Tongxi Yu
Keyword(s):  
Elastic Strain ◽  
Plastic Material ◽  
Elastic Strain Energy ◽  
Uniform Pressure ◽  
Elastic Plastic ◽  
Whole Process ◽  
Perfectly Plastic ◽  
Plastic Regime ◽  
Loading And Unloading ◽  
Elastic Perfectly Plastic

In this paper, an elastic–plastic analytical method is proposed to predict the cyclic deformation of the fully clamped square plates made of elastic–perfectly plastic material under repeated quasi-static uniform pressure. The whole process can be divided into the loading and unloading phases. The loading phase is formulated as three separate regimes: the elastic regime, the mixed elastic–plastic regime and the fully plastic regime. Unloading from a status in each phase is modeled as an elastic process. The total and elastic strain energies are characterized by the loading and unloading paths together with the displacement profiles, respectively. It is theoretically revealed that the elastic strain energy and the structural stiffness of the plate increase with the increasing transverse deflection. In addition, the effect of material elasticity is highlighted in the scenario of repeated loadings. The theoretical results are validated against the numerical simulations conducted by the commercial software ABAQUS. It is shown that the proposed elastic–plastic theoretical model has reasonable accuracy and can be employed to predict pressure–deflection relationship for this class of problems.

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