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.

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.

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.

Investigation on Constraint Effect of a Reactor Pressure Vessel Subjected to Pressurized Thermal Shocks

2014 ◽  
Vol 137 (1) ◽  
Author(s):  
Guian Qian ◽  
Markus Niffenegger
Keyword(s):  
Fracture Mechanics ◽  
Pressure Vessel ◽  
Plastic Material ◽  
Crack Tip ◽  
Constraint Effect ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Crack Tip Constraint ◽  
Reactor Pressure ◽  
Thermal Shocks

The integrity of a reactor pressure vessel (RPV) related to pressurized thermal shocks (PTSs) has been extensively studied. This paper introduces the method of using fracture mechanics for the integrity analysis of a RPV subjected to PTS transients. A 3-D finite element (FE) model is used to perform thermal and fracture mechanics analyses by considering both elastic and elastic–plastic material models. The results show that the linear elastic analysis leads to a more conservative result than the elastic–plastic analysis. The variation of the T-stress and Q-stress (crack tip constraint loss) of a surface crack in a RPV subjected to PTSs is studied. A shallow crack is assumed in the RPV and the corresponding constraint effect on fracture toughness of the material is quantified by the K–T method. The safety margin of the RPV is larger based on the K–T approach than based only on the K approach. The J–Q method with the modified boundary layer formulation (MBL) is used for the crack tip constraint analysis by considering elastic–plastic material properties. For all transient times, the real stress is lower than that calculated from small scale yielding (SSY) due to the loss of crack tip constraint.

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.

scholarly journals GBT-Based Elastic-Plastic Analysis of Cold-Formed Steel Members

2019 ◽  
Author(s):  
Miguel Abambres ◽  
Dinar Camotim ◽  
Nuno Silvestre
Keyword(s):  
Plastic Material ◽  
Beam Theory ◽  
Mapping Algorithm ◽  
First Order ◽  
Elastic Plastic ◽  
Perfectly Plastic ◽  
Return Mapping ◽  
Steel Members ◽  
Shell Finite Element ◽  
Elastic Perfectly Plastic

This paper presents a formulation of Generalised Beam Theory (GBT) intended to perform thorough first-order elastic-plastic analyses of thin-walled members subjected to arbitrary deformations and made of an isotropic non-linear material. The J2-flow theory is used to model plasticity in conjunction with the Euler-Backward return-mapping algorithm. After presenting the formulation, its application is illustrated by means of the first order analysis of a simply supported Z-section beam made of an elastic-perfectly plastic material (e.g., carbon steel) and acted by a load uniformly distributed along the flanges. The set of GBT-based results comprises the load-deflection curves (equilibrium paths), displacement profiles, stress distributions (diagrams and 3D contours), and deformed shapes (modal amplitude functions and 3D configurations). These results are compared with the ones obtained from shell finite element analyses (SFEA) using ABAQUS. It is seen that the GBT results display a very good agreement with the SFEA values.

Comparison of methods for obtaining crack-tip stress distributions in an elastic-plastic material

2005 ◽  
Vol 40 (5) ◽  
pp. 431-449 ◽  
Author(s):  
C. M Davies ◽  
N. P O'Dowd ◽  
K. M Nikbin ◽  
G A Webster ◽  
F Biglari
Keyword(s):  
Principal Stress ◽  
Plastic Material ◽  
Crack Tip ◽  
Maximum Principal Stress ◽  
Stress Fields ◽  
Good Representation ◽  
Elastic Plastic ◽  
Elastic Plastic Material ◽  
Von Mises ◽  
Crack Tip Stress

Under linear elastic and elastic-plastic conditions the K field and the HRR (Hutchinson-Rice-Rosengren) field respectively are expected to provide an accurate representation of the stress field close to the crack tip in an elastic-plastic material. It has recently been proposed in French and UK defect assessment procedures that the Neuber method, originally developed for sharply curved notches, provides an alternative approach to estimate both notch and crack-tip stress fields, for use in conjunction with the sigma- d (σd) method to predict creep crack initiation times. In this work, the crack-tip stress fields under plane strain conditions, predicted from the Neuber approach, are compared with the HRR and K fields as well as those obtained from full-field finite element calculations. A compact tension and a single edge notched tension specimen have been examined; the material model used is the Ramberg-Osgood, power law plasticity model. As expected, the K field and HRR field have been found to provide a good representation of the near-tip fields at low and high loads respectively. Satisfactory solutions have also been obtained through the use of the reference stress to estimate the amplitude of the crack-tip stress in conjunction with the HRR field. The Neuber approach provides a good estimate of the equivalent (von Mises) stresses over the full range of load levels. However, but the use of the Neuber approach directly to predict the maximum principal stress in the plane of the crack provides a non-conservative prediction. A modified Neuber method, using an appropriate scaling function, has been proposed to determine the maximum principal stress in the plane of the crack from the equivalent (von Mises) stress predicted by the Neuber approach. Using the proposed method, a significantly improved estimate of the crack-tip stresses is obtained.

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