scholarly journals Influences of Material Variations of Functionally Graded Pipe on the Bree Diagram

2020 ◽  
Vol 10 (8) ◽  
pp. 2936 ◽  
Author(s):  
Aref Mehditabar ◽  
Saeid Ansari Sadrabadi ◽  
Raffaele Sepe ◽  
Enrico Armentani ◽  
Jason Walker ◽  
...  
Keyword(s):  
Internal Pressure ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Bending Moment ◽  
Yield Function ◽  
Functionally Graded ◽  
Loading Conditions ◽  
Mapping Algorithm ◽  
First Case ◽  
Backward Euler

The present research is concerned with the elastic–plastic responses of functionally graded material (FGM) pipe, undergoing two types of loading conditions. For the first case, the FGM is subjected to sustained internal pressure combined with a cyclic bending moment whereas, in the second case, sustained internal pressure is applied simultaneously with a cyclic through-thickness temperature gradient. The properties of the studied FGM are considered to be variable through shell thickness according to a power-law function. Two different designs of the FGM pipe are adopted in the present research, where the inner surface in one case and the outer surface in the other are made from pure 1026 carbon steel. The constitutive relations are developed based on the Chaboche nonlinear kinematic hardening model, classical normality rule and von Mises yield function. The backward Euler alongside the return mapping algorithm (RMA) is employed to perform the numerical simulation. The results of the proposed integration procedure were implemented in ABAQUS using a UMAT user subroutine and validated by a comparison between experiments and finite element (FE) simulation. Various cyclic responses of the two prescribed models of FGM pipe for the two considered loading conditions are classified and brought together in one diagram known as Bree’s diagram.

A Generalized Anisotropic Hardening Rule Based on the Mroz Multi-Yield-Surface Model

2008 ◽  
Author(s):  
K. S. Choi ◽  
J. Pan
Keyword(s):  
Cyclic Loading ◽  
Yield Surface ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Yield Function ◽  
Surface Model ◽  
Loading Conditions ◽  
Anisotropic Hardening ◽  
Hardening Rule ◽  
Strain Data

In this paper, a generalized anisotropic hardening rule based on the Mroz multi-yield-surface model is derived. The evolution equation for the active yield surface is obtained by considering the continuous expansion of the active yield surface during the unloading/reloading process. The incremental constitutive relation based on the associated flow rule is then derived for a general yield function. As a special case, detailed incremental constitutive relations are derived for the Mises yield function. The closed-form solutions for one-dimensional stress-plastic strain curves are also derived and plotted for the Mises materials under cyclic loading conditions. The stress-plastic strain curves show closed hysteresis loops under uniaxial cyclic loading conditions and the Masing hypothesis is applicable. A user material subroutine based on the Mises yield function, the anisotropic hardening rule and the constitutive relations was then written and implemented into ABAQUS. Computations were conducted for a simple plane strain finite element model under uniaxial monotonic and cyclic loading conditions based on the anisotropic hardening rule and the isotropic and nonlinear kinematic hardening rules of ABAQUS. The results indicate that the plastic response of the material follows the intended input stress-strain data for the anisotropic hardening rule whereas the plastic response depends upon the input strain ranges of the stress-strain data for the nonlinear kinematic hardening rule.

On the Effectiveness of Composites for Repair of Pipelines Under Various Combined Loading Conditions: A Computational Approach Using the Cohesive Zone Method

2017 ◽  
Vol 139 (2) ◽  
Author(s):  
Shahin Shadlou ◽  
Farid Taheri
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Cohesive Zone ◽  
Loading Condition ◽  
Bending Moment ◽  
Combined Loading ◽  
Loading Conditions ◽  
Original Design ◽  
Zone Method ◽  
Noticeable Effect

ASTM PCC-2 standard provides a series of equations for establishing the composite repair's thickness required for bringing the capacity of dented/damaged pipes, to their original design state. However, the accuracy of the equations' predictions for pipes subjected to various combined loadings has not been fully explored. Moreover, the influence of the state of a pipe/composite wrap (CW) interface (i.e., whether perfectly intact or not intact), in reference to the predictions of the ASTM equations, has not been studied either. In consideration of the above-mentioned issues, a comprehensive finite-element (FE) study is conducted, using the cohesive zone methodology (CZM) to simulate the response of pipes repaired with composite wraps, under single and various combined loading conditions. Moreover, the influence of perfect (or tied) and imperfect (unintact) pipe/CW interface on the load-bearing capacity of repaired pipes is systematically investigated. Finally, the effects of composite repairs' thickness and length on their efficacy are also investigated. The results show that, although the pipe/CW interface state does not have any noticeable effect when the pipe is subjected to a combined loading state of bending moment and internal pressure, it plays a crucial role when the pipe is under a combined internal pressure and uniaxial loading condition. Furthermore, the predicted values calculated according to the ASME standard are compared with the finite-element results, demonstrating that ASTM-based predictions do not provide accurate results when a repaired pipe is subjected to an axial loading condition.

On Finite Plastic Flow of Crystalline Solids and Geomaterials

1983 ◽  
Vol 50 (4b) ◽  
pp. 1114-1126 ◽  
Author(s):  
S. Nemat-Nasser
Keyword(s):  
Granular Materials ◽  
Finite Deformation ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Close Relation ◽  
Crystalline Solids ◽  
Hardening Model ◽  
First Case ◽  
Physically Based ◽  
Points Of View

Certain fundamentals of finite-deformation elastoplastic flow of crystalline solids and geomaterials are discussed from microscopic and macroscopic phenomenological points of view. In the first case, physically based constitutive relations for microelements are formulated on the basis of slip-induced plastic deformation with due account of possible frictional or pressure dependencies and inelastic volumetric changes. The close relation between the double-slip theory of single crystals and that of granular materials is discussed. The calculation of overall instantaneous moduli in terms of the local quantities for arbitrary strains and rotations is examined, and some recent results for polycrystals and granular materials are reviewed. Then, attention is focused on phenomenological constitutive relations which apply to both metals and geomaterials. Specific results are given for an isotropic-kinematic hardening model, including frictional and plastic dilatancy effects. Finally, certain fundamental thermodynamic aspects of finite-deformation inelasticity are reviewed, emphasizing conditions under which flow potentials exist.

Elastoplastic analysis of a thin-walled tube under cyclic bending and constant internal pressure: A simplified model

2014 ◽  
Vol 229 (4) ◽  
pp. 591-602 ◽  
Author(s):  
Hosein Yazdani ◽  
Ali Nayebi
Keyword(s):  
Internal Pressure ◽  
Yield Criterion ◽  
Kinematic Hardening ◽  
Elastoplastic Analysis ◽  
Simple Method ◽  
Cyclic Bending ◽  
Mapping Algorithm ◽  
Interaction Diagram ◽  
Present Solution ◽  
Thin Walled

In this study, the elastoplastic analysis of thin-walled tubes under cyclic bending and internal pressure is presented. A simple method is presented and verified. In order to predict ratcheting or shakedown behavior in the cyclic loading, von-Mises yield criterion as the yield surface and Chaboche’s nonlinear kinematic hardening model are used. The stress–strain variation is obtained with the help of return mapping algorithm. The present solution is in good agreement with experimental results. Shakedown or ratcheting behavior of the tube under various combinations of applied constant internal pressure and cyclic curvature is considered, Bree’s interaction diagram is obtained and the boundary between shakedown and ratcheting zone is determined.

scholarly journals Ratcheting Simulation of a Steel Pipe with Assembly Parts under Internal Pressure and a Cyclic Bending Load

2019 ◽  
Vol 9 (23) ◽  
pp. 5025
Author(s):  
Yang ◽  
Dai ◽  
He
Keyword(s):  
Internal Pressure ◽  
Kinematic Hardening ◽  
Three Dimensional ◽  
Bending Moment ◽  
Element Model ◽  
Steel Pipe ◽  
Cyclic Bending ◽  
Ratcheting Strain ◽  
Bending Load ◽  
Transition Points

The ratcheting behavior of a steel pipe with assembly parts was examined under internal pressure and a cyclic bending load, which has not been seen in previous research. An experimentally validated and three dimensional (3D) elastic-plastic finite element model (FEM)—with a nonlinear isotropic/kinematic hardening model—was used for the pipe’s ratcheting simulation and considered the assembly contact effects outlined in this paper. A comparison of the ratcheting response of pipes with and without assembly parts showed that assembly contact between the sleeve and pipe suppressed the ratcheting response by changing its trend. In this work, the assembly contact effect on the ratcheting response of the pipe with assembly parts is discussed. Both the assembly contact and bending moment were found to control the ratcheting response, and the valley and peak values of the hoop ratcheting strain were the transition points of the two control modes. Finally, while the clearance between the sleeve and the pipe had an effect on the ratcheting response when it was not large, it had no effect when it reached a certain value.

Pressure Sensitive Nonassociative Plasticity Model for DRA Composites

2006 ◽  
Vol 129 (2) ◽  
pp. 255-264 ◽  
Author(s):  
Xin Lei ◽  
Cliff J. Lissenden
Keyword(s):  
Plastic Deformation ◽  
Low Cycle Fatigue ◽  
Kinematic Hardening ◽  
Yield Function ◽  
Experimental Results ◽  
Plastic Strain Rate ◽  
Flow Rule ◽  
Plasticity Model ◽  
Backward Euler ◽  
Model Predictions

Discontinuously reinforced aluminum (DRA) is currently used where design considerations include specific stiffness, tailorable coefficient of thermal expansion, or wear resistance. Plastic deformation plays a role in failures due to low cycle fatigue or simple ductile overload. DRA is known to exhibit pressure dependent yielding. Plastic deformation in metals is widely regarded to be incompressible, or very nearly so. A continuum plasticity model is developed that includes a Drucker–Prager pressure dependent yield function, plastic incompressibility via a nonassociative Prandtl–Reuss flow rule, and a generalized Armstrong–Frederick kinematic hardening law. The model is implemented using a return mapping algorithm with backward Euler integration for stability and the Newton method to determine the plastic multiplier. Material parameters are characterized from uniaxial tension and uniaxial compression experimental results. Model predictions are compared to experimental results for a nonproportional compression–shear load path. The tangent stiffness tensor is nonsymmetric because the flow rule is not associated with the yield function, which means that the commonly used algorithms that require symmetric matrices cannot be used with this material model. Model correlations with tension and compression loadings are excellent. Model predictions of shear and nonproportional compression–shear loadings are reasonably good. The nonassociative flow rule could not be validated by comparison of the plastic strain rate direction with the yield function and the flow potential due to scatter in the experimental results. The model is capable of predicting the material response obtained in the experiments, but additional validation is necessary for the condition of high hydrostatic pressure.

Closed-Form Collapse Moment Equations of Elbows Under Combined Internal Pressure and In-Plane Bending Moment

2000 ◽  
Vol 122 (4) ◽  
pp. 431-436 ◽  
Author(s):  
J. Chattopadhyay ◽  
D. K. Nathani ◽  
B. K. Dutta ◽  
H. S. Kushwaha
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Internal Pressure ◽  
Closed Form ◽  
Rotation Curve ◽  
Bending Moment ◽  
Loading Conditions ◽  
Moment Equations ◽  
Element Analysis ◽  
The Moment

Elastic-plastic finite element analysis has been carried out to evaluate collapse moments of six elbows with elbow factors varying from 0.24 to 0.6. The loading conditions of combined in-plane closing/opening bending moment and varying degree of internal pressure are considered in the analysis. For each case, collapse moment is obtained by twice elastic slope method from the moment versus end-rotation curve. Based on these results, two closed-form equations are proposed to evaluate the collapse moments of elbows under combined internal pressure and in-plane closing and opening bending moment. [S0094-9930(00)00103-7]

Correlation of Test and FEA Studies on Effect of Bend Radius and Thickness on Ratcheting in Pipe Bends Subjected to Internal Pressure and In-Plane Bending Moment

2005 ◽  
Author(s):  
K. Shanmuga Sundaran ◽  
G. Thanigaiyarasu
Keyword(s):  
Internal Pressure ◽  
Analytical Study ◽  
Kinematic Hardening ◽  
Bending Moment ◽  
Material Model ◽  
Analysis Procedure ◽  
Strain Accumulation ◽  
Bend Radius ◽  
Plane Bending ◽  
Selection Of

The paper deals with the results from the analytical study on ratcheting in pipe bends. There has been no well-defined material model and analysis procedure to predict this phenomenon accurately. A recent development in parameter selection of Chaboche’s Kinematic hardening model has resulted in close predictions in ratcheting analysis [15]. A problem has been selected from existing experimental results [16, 17] published in literature, and an analysis incorporating these parameters has been carried out and presented. The amount of stresses induced and strain accumulated in pipe bends with long and short radius and subjected to internal pressure and in-plane bending moment is studied. The results and their inferences are included. The analysis was carried out on 2-inch NPS SS304 pipe bends with different bend radius and two thickness (Schedule 40 and Schedule 80) using ABAQUS, non-linear FEA software to predict the strain accumulation and their influences on ratcheting failure is presented.

Implicit Stress Integration for High-Temperature Inelastic Constitutive Models Using Linearization

2007 ◽  
Vol 340-341 ◽  
pp. 907-912
Author(s):  
Masafumi Akamatsu ◽  
Kazuhiko Nakane ◽  
Nobutada Ohno
Keyword(s):  
High Temperature ◽  
Kinematic Hardening ◽  
Constitutive Relations ◽  
Constitutive Models ◽  
Inelastic Strain ◽  
Euler Method ◽  
Joint Analysis ◽  
Integration Scheme ◽  
Implicit Integration ◽  
Backward Euler

In this study, a linearization approach is used to develop an implicit integration scheme for high-temperature inelastic constitutive models based on non-linear kinematic hardening. A non-unified model is considered in which inelastic strain rate is divided into the transient and steady parts driven, respectively, by effective stress and applied stress. By discretizing the constitutive relations using the backward Euler method, and by linearizing the resulting discretized relations, a tensor equation is derived to iteratively achieve the implicit integration of constitutive variables. The integration scheme is then programmed as a subroutine in a finite element code and applied to a lead-free solder joint analysis. It is thus demonstrated that the integration scheme affords the quadratic convergence of iteration even for considerably large increments.

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