Shakedown Limit Loads for 90 Degree Scheduled Pipe Bends Subjected to Steady Internal Pressure and Cyclic Bending Moments

2011 ◽  
Vol 133 (3) ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Pressure Vessel ◽  
Limit Load ◽  
Small Displacement ◽  
Bending Moments ◽  
Pipe Bend ◽  
Hardening Material ◽  
Cyclic Bending ◽  
Shakedown Limit

A simplified technique for determining the shakedown limit load for a long radius 90 deg pipe bend was previously developed (Abdalla, H. F., et al., 2006, “Determination of Shakedown Limit Load for a 90 Degree Pipe Bend Using a Simplified Technique,” ASME J. Pressure Vessel Technol., 128, pp. 618–624; Abdalla, H. F., et al., 2007, “Shakedown Limits of a 90-Degree Pipe Bend Using Small and Large Displacement Formulations,” ASME J. Pressure Vessel Technol., 129, pp. 287–295). The simplified technique utilizes the finite element (FE) method and employs the small displacement formulation to determine the shakedown limit load (moment) without performing lengthy time consuming full cyclic loading finite element simulations or utilizing conventional iterative elastic techniques. The shakedown limit load is determined through the calculation of residual stresses developed within the pipe bend structure. In the current paper, a parametric study is conducted through applying the simplified technique on three scheduled pipe bends, namely, nominal pipe size (NPS) 10 in. Sch. 20, NPS 10 in. Sch. 40 STD, and NPS 10 in. Sch. 80. Two material models are assigned, namely, an elastic perfectly plastic (EPP) material and an idealized elastic-linear strain hardening material obeying Ziegler’s linear kinematic hardening (KH) rule. This type of material model is termed in the current study as the KH-material. The pipe bends are subjected to a spectrum of steady internal pressure magnitudes and cyclic bending moments. The cyclic bending includes three different loading patterns, namely, in-plane closing, in-plane opening, and out-of-plane bending moment loadings of the pipe bends. The shakedown limit moments outputted by the simplified technique are used to generate shakedown diagrams of the scheduled pipe bends for the spectrum of steady internal pressure magnitudes. A comparison between the generated shakedown diagrams for the pipe bends employing the EPP- and the KH-materials is presented. Relatively higher shakedown limit moments were recorded for the pipe bends employing the KH-material at the medium to high internal pressure magnitudes.

Shakedown Limit Loads for 90-Degree Scheduled Pipe Bends Subjected to Constant Internal Pressure and Cyclic Bending Moments

2008 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Small Displacement ◽  
Bending Moments ◽  
Pipe Bend ◽  
Hardening Material ◽  
Cyclic Bending ◽  
Shakedown Limit

A simplified technique for determining the shakedown limit load for a long radius 90-degree pipe bend was previously developed [1, 2]. The simplified technique utilizes the finite element method and employs the small displacement formulation to determine the shakedown limit load (moment) without performing lengthy time consuming full cyclic loading finite element simulations or utilizing conventional iterative elastic techniques. The shakedown limit load is determined through the calculation of residual stresses developed within the pipe bend structure. In the current paper, a parametric study is conducted through applying the simplified technique on three scheduled pipe bends namely: NPS (Nominal Pipe Size) 10" Sch. No. 20, NPS 10" Sch. No. 40 STD, and NPS 10" Sch. No. 80. Two material models are assigned namely; an elastic-perfectly-plastic (EPP) material and an idealized elastic-linear strain hardening material obeying Ziegler’s linear kinematic hardening (KH) rule. This type of material model is termed in the current study as the KH-material. The pipe bends are subjected to a spectrum of constant internal pressure magnitudes and cyclic bending moments. The cyclic bending includes three different loading patterns namely: in-plane closing (IPC), in-plane opening (IPO), and out-of-plane (OP) bending moment loadings of the pipe bends. The shakedown limit moments output by the simplified technique are used to generate shakedown diagrams of the scheduled pipe bends for the spectrum of constant internal pressure magnitudes. A comparison between the generated shakedown diagrams for the pipe bends employing the EPP- and the KH-materials is presented. Relatively higher shakedown limit moments were recorded for the pipe bends employing the KH-material at the medium to high internal pressure magnitudes.

Shakedown Limit Load Determination for a Kinematically Hardening 90 deg Pipe Bend Subjected to Steady Internal Pressures and Cyclic Bending Moments

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Hany F. Abdalla ◽  
Maher Y. A. Younan ◽  
Mohammad M. Megahed
Keyword(s):  
Cyclic Loading ◽  
Internal Pressure ◽  
Limit Load ◽  
Material Model ◽  
Small Displacement ◽  
Bending Moments ◽  
Pipe Bend ◽  
Cyclic Bending ◽  
Fe Simulations ◽  
Shakedown Limit

A simplified technique for determining the lower bound shakedown limit load of a structure, employing an elastic–perfectly plastic (EPP) material model, was previously developed and successfully applied to a long radius 90 deg pipe bend (Abdalla et al., 2006, “Determination of Shakedown Limit Load for a 90 Degree Pipe Bend Using a Simplified Technique,” ASME J. Pressure Vessel Technol., 128, pp. 618–624). The pipe bend is subjected to steady internal pressure magnitudes and cyclic bending moments. The cyclic bending includes three different loading patterns, namely, in-plane closing, in-plane opening, and out-of-plane bending moment loadings. The simplified technique utilizes the finite element (FE) method and employs a small displacement formulation to determine the shakedown limit load without performing lengthy time consuming full elastic-plastic (ELPL) cyclic loading FE simulations or conventional iterative elastic techniques. In the present research, the simplified technique is further modified to handle structures employing an elastic-linear strain hardening material model following Ziegler’s linear kinematic hardening (KH) rule. The shakedown limit load is determined through the calculation of residual stresses developed within the pipe bend structure accounting for the back stresses, determined from the KH shift tensor, responsible for the rigid translation of the yield surface. The outcomes of the simplified technique showed an excellent correlation with the results of full ELPL cyclic loading FE simulations. The shakedown limit moments output by the simplified technique are utilized to generate shakedown diagrams (Bree diagrams) of the pipe bend for a spectrum of steady internal pressure magnitudes. The generated Bree diagrams are compared with the ones previously generated employing the EPP material model. These indicated relatively conservative shakedown limit moments compared with the ones employing the KH rule.

Shakedown Limit Load Determination for a Kinematically Hardening 90-Degree Pipe Bend Subjected to Constant Internal Pressure and Cyclic Bending

2007 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Finite Element ◽  
Internal Pressure ◽  
Plastic Material ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Material Behavior ◽  
Pipe Bend ◽  
Cyclic Bending ◽  
Perfectly Plastic ◽  
Shakedown Limit

A simplified technique for determining the shakedown limit load of a structure employing an elastic-perfectly-plastic material behavior was previously developed and successfully applied to a long radius 90-degree pipe bend. The pipe bend is subjected to constant internal pressure and cyclic bending. The cyclic bending includes three different loading patterns namely; in-plane closing, in-plane opening, and out-of-plane bending moment loadings. The simplified technique utilizes the finite element method and employs small displacement formulation to determine the shakedown limit load without performing lengthy time consuming full cyclic loading finite element simulations or conventional iterative elastic techniques. In the present paper, the simplified technique is further modified to handle structures employing elastic-plastic material behavior following the kinematic hardening rule. The shakedown limit load is determined through the calculation of residual stresses developed within the pipe bend structure accounting for the back stresses, determined from the kinematic hardening shift tensor, responsible for the translation of the yield surface. The outcomes of the simplified technique showed very good correlation with the results of full elastic-plastic cyclic loading finite element simulations. The shakedown limit moments output by the simplified technique are used to generate shakedown diagrams of the pipe bend for a spectrum of constant internal pressure magnitudes. The generated shakedown diagrams are compared with the ones previously generated employing an elastic-perfectly-plastic material behavior. These indicated conservative shakedown limit moments compared to the ones employing the kinematic hardening rule.

Determination of Shakedown Limit Load for a 90-Degree Pipe Bend Using a Simplified Technique

2006 ◽  
Vol 128 (4) ◽  
pp. 618-624 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Finite Element ◽  
Cyclic Loading ◽  
Internal Pressure ◽  
Bending Moment ◽  
Limit Load ◽  
Heat Fluxes ◽  
Bench Mark ◽  
Pipe Bend ◽  
Elastic Plastic ◽  
Shakedown Limit

In this paper a simplified technique is presented to determine the shakedown limit load of a 90-degree pipe bend subjected to constant internal pressure and cyclic in-plane closing bending moment using the finite element method. The simplified technique determines the shakedown limit load without performing time consuming full elastic-plastic cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown limit load is determined by performing two finite element analyses namely; an elastic analysis and an elastic-plastic analysis. By extracting the results of the two analyses, the shakedown limit load is determined through the calculation of the residual stresses developed in the pipe bend. In order to gain confidence in the simplified technique, the output shakedown limit moments are used to perform full elastic-plastic cyclic loading simulations to check for shakedown behavior of the pipe bend. The shakedown limit moments output by the simplified technique are used to generate the shakedown diagram of the pipe bend for a range of constant internal pressure magnitudes. The maximum moment carrying capacity (limit moment) the pipe bend can withstand and the elastic limit are also determined and imposed on the shakedown diagram of the pipe bend. In order to get acquainted with the simplified technique, it is applied beforehand to a bench mark shakedown problem namely, the Bree cylinder (Bree, J., 1967, J. Strain Anal., 3, pp. 226–238) problem. The Bree cylinder is subjected to constant internal pressure and cyclic high heat fluxes across its wall. The results of the simplified technique showed very good correlation with the analytically determined Bree diagram of the cylinder.

Shakedown and Limit Analysis of Kinematic Hardening Piping Elbows Under Internal Pressure and Bending Moments

2021 ◽  
Author(s):  
Heng Peng ◽  
Yinghua Liu
Keyword(s):  
Yield Strength ◽  
Internal Pressure ◽  
Limit Analysis ◽  
Kinematic Hardening ◽  
Limit Load ◽  
Bending Moments ◽  
Plastic Limit ◽  
Plastic Limit Load ◽  
Interaction Curves ◽  
Shakedown Limit

Abstract In this paper, the Stress Compensation Method (SCM) adopting an elastic-perfectly-plastic (EPP) material is further extended to account for limited kinematic hardening (KH) material model based on the extended Melan's static shakedown theorem using a two-surface model defined by two hardening parameters, namely the initial yield strength and the ultimate yield strength. Numerical analysis of a cylindrical pipe is performed to validate the outcomes of the extended SCM. The results agree well with ones from literature. Then the extended SCM is applied to the shakedown and limit analysis of KH piping elbows subjected to internal pressure and cyclic bending moments. Various loading combinations are investigated to generate the shakedown limit and the plastic limit load interaction curves. The effects of material hardening, elbow angle and loading conditions on the shakedown limit and the plastic limit load interaction curves are presented and analysed. The present method is incorporated in the commercial finite element simulation software and can be considered as a general computational tool for shakedown analysis of KH engineering structures. The obtained results provide a useful information for the structural design and integrity assessment of practical piping elbows.

scholarly journals Effect of Ovality in Inlet Pigtail Pipe Bends Under Combined Internal Pressure and In-Plane Bending for Ni-Fe-Cr B407 Material

2017 ◽  
Vol 62 (3) ◽  
pp. 1881-1887
Author(s):  
P. Ramaswami ◽  
P. Senthil Velmurugan ◽  
R. Rajasekar
Keyword(s):  
Finite Element Analysis ◽  
Finite Element ◽  
Internal Pressure ◽  
Limit Load ◽  
Outer Radius ◽  
Factor H ◽  
Geometrical Shape ◽  
Element Analysis ◽  
Pipe Bend ◽  
Plane Bending

Abstract The present paper makes an attempt to depict the effect of ovality in the inlet pigtail pipe bend of a reformer under combined internal pressure and in-plane bending. Finite element analysis (FEA) and experiments have been used. An incoloy Ni-Fe-Cr B407 alloy material was considered for study and assumed to be elastic-perfectly plastic in behavior. The design of pipe bend is based on ASME B31.3 standard and during manufacturing process, it is challenging to avoid thickening on the inner radius and thinning on the outer radius of pipe bend. This geometrical shape imperfection is known as ovality and its effect needs investigation which is considered for the study. The finite element analysis (ANSYS-workbench) results showed that ovality affects the load carrying capacity of the pipe bend and it was varying with bend factor (h). By data fitting of finite element results, an empirical formula for the limit load of inlet pigtail pipe bend with ovality has been proposed, which is validated by experiments.

Shakedown Limits of a 90-Degree Pipe Bend Using Small and Large Displacement Formulations

2006 ◽  
Author(s):  
Hany F. Abdalla ◽  
Mohammad M. Megahed ◽  
Maher Y. A. Younan
Keyword(s):  
Plastic Material ◽  
Limit Load ◽  
Material Model ◽  
Large Displacement ◽  
Small Displacement ◽  
Pipe Bend ◽  
Perfectly Plastic ◽  
Loading Patterns ◽  
Elastic Perfectly Plastic ◽  
Shakedown Limit

In this paper the shakedown limit load is determined for a long radius 90-degree pipe bend using two different techniques. The first technique is a simplified technique which utilizes small displacement formulation and elastic-perfectly-plastic material model. The second technique is an iterative based technique which uses the same elastic-perfectly-plastic material model, but incorporates large displacement effects accounting for geometric non-linearity. Both techniques use the finite element method for analysis. The pipe bend is subjected to constant internal pressure magnitudes and cyclic bending moments. The cyclic bending loading includes three different loading patterns namely; in-plane closing, in-plane opening, and out-of-plane bending. The simplified technique determines the shakedown limit load (moment) without the need to perform full cyclic loading simulations or conventional iterative elastic techniques. Instead, the shakedown limit moment is determined by performing two analyses namely; an elastic analysis and an elastic-plastic analysis. By extracting the results of the two analyses, the shakedown limit moment is determined through the calculation of the residual stresses developed in the pipe bend. The iterative large displacement technique determines the shakedown limit moment in an iterative manner by performing a series of full elastic-plastic cyclic loading simulations. The shakedown limit moment output by the simplified technique (small displacement) is used by the iterative large displacement technique as an initial iterative value. The iterations proceed until an applied moment guarantees a structure developed residual stress, at load removal, equals or slightly less than the material yield strength. The shakedown limit moments output by both techniques are used to generate shakedown diagrams of the pipe bend for a spectrum of constant internal pressure magnitudes for the three loading patterns stated earlier. The maximum moment carrying capacity (limit moment) the pipe bend can withstand and the elastic limit are also determined and imposed on the shakedown diagram of the pipe bend. Comparison between the shakedown diagrams generated by the two techniques, for the three loading patterns, is presented.

Shakedown Boundary and Limit Load Determination of a 90-Degree Back to Back Pipe Bend Subjected to Steady Internal Perssures and Cyclic In-Plane Bending Moments

2013 ◽  
Author(s):  
Hany F. Abdalla
Keyword(s):  
Limit Load ◽  
Bending Moments ◽  
Pipe Bend ◽  
Shakedown Analysis ◽  
Plane Bending ◽  
Piping Networks ◽  
Aero Engines ◽  
Shakedown Limit ◽  
Elastic Shakedown ◽  
Internal Pressures

Shakedown analysis of 90–degree back–to–back pipe bends is scarce within open literature. According the author’s knowledge, no shakedown analysis exists for such structure based on experimental data. Ninety degree back–to–back pipe bends are extensively utilized within piping networks of nuclear submarines and modern turbofan aero–engines where space limitation is considered a paramount concern. Additionally, on larger scales, 90–degree back–to–back pipe bend configurations are also found within piping networks of huge liquefied natural gas tankers. The structure analyzed is formed by bending a straight pipe to acquire the geometry of two 90–degree pipe bends set back–to–back each having a nominal pipe size (NPS) of 10 in. Schedule 40 Standard (STD). In the current research, the 90–degree back–to–back pipe bend setup analyzed is subjected to a spectrum of steady internal pressures and cyclic in–plane bending moments. A previously developed simplified technique for determining elastic shakedown limit loads is utilized to generate the elastic shakedown boundary of the 90–degree back–to–back pipe bend analyzed. In addition to determining the elastic shakedown boundary, elastic and post shakedown domains (Bree diagram), the maximum moment carrying capacities (limit moments) are also determined and imposed on the generated Bree diagram of the analyzed structure. The simplified technique outcomes showed excellent correlation with the results of full elastic–plastic cyclic loading finite element simulations.

Shakedown Boundary of a 90–Degree Back–to–Back Pipe Bend Subjected to Steady Internal Pressures and Cyclic Out–of–Plane Bending Moments

2014 ◽  
Author(s):  
Hany F. Abdalla
Keyword(s):  
Internal Pressure ◽  
Bending Moment ◽  
Bending Moments ◽  
Pipe Bend ◽  
Structure Comparison ◽  
Out Of Plane ◽  
Plane Bending ◽  
Shakedown Limit ◽  
Elastic Shakedown ◽  
Internal Pressures

Ninety degree back–to–back pipe bends are extensively utilized within piping networks of modern nuclear submarines and modern turbofan aero–engines where space limitation is considered a supreme concern. According the author’s knowledge, no shakedown analysis exists for such structure based on experimental data. In the current research, the pipe bend setup analyzed is subjected to a spectrum of steady internal pressures and cyclic out–of–plane bending moments. A previously developed direct non–cyclic simplified technique, for determining elastic shakedown limit loads, is utilized to generate the elastic shakedown boundary of the analyzed structure. Comparison with the elastic shakedown boundary of the same structure, but subjected to cyclic in–plane bending moments revealed a higher shakedown boundary for the out–of–plane bending loading configuration with a maximum bending moment ratio of 1.4 within the low steady internal pressure spectrum. The ratio decreases towards the medium to high internal pressure spectrum. The simplified technique outcomes showed excellent correlation with the results of full elastic–plastic cyclic loading finite element simulations.

Determination of Shakedown Boundary and Failure-Assessment-Diagrams of Cracked Pipe Bends

2013 ◽  
Vol 136 (1) ◽  
Author(s):  
Mostafa S. Elsaadany ◽  
Maher Y. A. Younan ◽  
Hany F. Abdalla
Keyword(s):  
Finite Element ◽  
Limit Load ◽  
Maximum Load ◽  
Fe Method ◽  
Pipe Bend ◽  
Shell Elements ◽  
Capacity Limit ◽  
Failure Assessment ◽  
Shakedown Limit

Determination of shakedown (SD) boundaries of 90-degree plain smooth pipe bends has recently received substantial attention by several researchers. However, scarce or almost no solid information is found within the literature regarding the determination of the shakedown boundary of cracked pipe bends. The current research presents two additions to the literature, namely, determination of shakedown boundary for a circumferentially cracked 90-degree pipe bend via a simplified technique utilizing the finite element (FE) method and introduction of failure-assessment diagrams (FADs) in compliance with the API 579 failure-for-service assessment of pressure vessel and piping components. The analyzed cracked pipe bend is subjected to the combined effect of steady internal pressure spectrum and cyclic in-plane closing (IPC) and opening (IPO) bending moments. Line spring elements (LSEs) are embedded in quadratic shell elements to model part-through cracks. FAD is obtained through linking the J-integral fracture mechanics parameter with the shakedown limit moments of the analyzed cracked 90-degree pipe bend. The LSE outcomes illustrated satisfactory results in comparison to the results of two verification studies: stress intensity factor (SIF) and limit load. Additionally, full elastic-plastic (ELPL) cyclic loading finite element analyses are conducted and the outcomes revealed very good correlation with the results obtained via the simplified technique. The maximum load carrying capacity (limit moment) and the elastic domain are also computed thereby generating a Bree diagram for the cracked pipe bend. Finally, Crack growth analysis is presented to complement the FAD.

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