The Effect of Modeling Parameters on the Predicted Limit Loads for Pipe Bends Subjected to Out-of-Plane Moment Loading and Internal Pressure

2000 ◽  
Vol 122 (4) ◽  
pp. 450-456 ◽  
Author(s):  
Hashem M. Mourad ◽  
Maher Y. A. Younan
Keyword(s):  
Internal Pressure ◽  
Strain Hardening ◽  
Limit Load ◽  
Factor H ◽  
Large Displacement ◽  
Small Displacement ◽  
Hardening Material ◽  
Limit Loads ◽  
Perfectly Plastic ◽  
Out Of Plane

The purpose of this study is to investigate the effect of modeling parameters on the determination of limit loads for standalone pipe bends, subjected to an out-of-plane end moment and internal pressure. A pipe bend, with bend factor h=0.1615, is modeled and analyzed using the nonlinear finite element code ABAQUS. Small and large-displacement analyses are performed with elastic-perfectly plastic and strain-hardening material models. Small-displacement analyses fail to predict the stiffening effect of pressure and give a continuously decaying limit load with increased pressure. Material strain hardening gives a higher limit load than perfectly plastic materials. In the large-displacement analysis with a strain-hardening material, the limit moment levels off as the pressure increases, and does not decrease as in the case of a perfectly plastic material. [S0094-9930(00)00804-0]

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.

Incorporation of Strain Hardening Effect Into Simplified Limit Analysis

2010 ◽  
Vol 132 (6) ◽  
Author(s):  
P. S. Reddy Gudimetla ◽  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Lower Bound ◽  
Strain Hardening ◽  
Limit Load ◽  
Element Analysis ◽  
Active Volume ◽  
Limit Loads ◽  
Reference Volume ◽  
Perfectly Plastic ◽  
Tangent Method ◽  
Elastic Perfectly Plastic

In this paper, a method for determining limit loads in the components or structures by incorporating strain hardening effects is presented. This has been done by including a certain amount of the strain hardening into limit load analysis, which normally idealizes the material to be elastic perfectly plastic. Typical strain hardening curves such as bilinear hardening and Ramberg–Osgood material models are investigated. This paper also focuses on the plastic reference volume correction concept to determine the active volume participating in plastic collapse. The reference volume concept in combination with mα-tangent method is used to estimate lower-bound limit loads of different components. Lower-bound limit loads obtained compare well with the nonlinear finite element analysis results for several typical configurations with/without crack.

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.

Plastic Response Estimation in Repeated Elastic Analyses for Strain Hardening Material Model

2013 ◽  
Vol 135 (5) ◽  
Author(s):  
S. L. Mahmood ◽  
R. Adibi-Asl ◽  
C. G. Daley
Keyword(s):  
Strain Hardening ◽  
Strain Energy ◽  
Plastic Material ◽  
Limit Load ◽  
Material Model ◽  
Element Analysis ◽  
Hardening Material ◽  
Linear Elastic ◽  
Perfectly Plastic ◽  
Elastic Perfectly Plastic

Simplified limit analysis techniques have already been employed for limit load estimation on the basis of linear elastic finite element analysis (FEA) assuming elastic-perfectly-plastic material model. Due to strain hardening, a component or a structure can store supplementary strain energy and hence carries additional load. In this paper, an iterative elastic modulus adjustment scheme is developed in context of strain hardening material model utilizing the “strain energy density” theory. The proposed algorithm is then programmed into repeated elastic FEA and results from the numerical examples are compared with inelastic FEA results.

Nonlinear Analysis of Pipe Bends Subjected to Out-of-Plane Moment Loading and Internal Pressure

2000 ◽  
Vol 123 (2) ◽  
pp. 253-258 ◽  
Author(s):  
Hashem M. Mourad ◽  
Maher Y. A. Younan
Keyword(s):  
Internal Pressure ◽  
Axial Direction ◽  
Factor H ◽  
Material Behavior ◽  
Stress And Strain ◽  
Pipe Bend ◽  
Perfectly Plastic ◽  
Out Of Plane ◽  
Elastic Perfectly Plastic ◽  
Distribution Of Stress

The behavior of a pipe bend, with bend factor h=0.1615(D=16 in.,R=24 in. and t=0.41 in.), subjected to out-of-plane bending and internal pressure is studied, taking geometric and material nonlinearity into account, using the finite element code ABAQUS. Material behavior is taken as elastic-perfectly plastic. The distribution of stress and strain along the axial direction and across the thickness of the bend is studied, with and without internal pressure, at the onset of yielding and at instability. Before instability is reached, through-the-thickness yielding appears at many points. The loaded end of the bend is found to be the most severely strained cross section. The circumferential distribution of stress and strain, and its variation with increased moment loading are then investigated for that section, at internal pressure values of zero and 1200 psi.

Incorporation of Strain Hardening Effect Into Limit Load Analysis

2010 ◽  
Author(s):  
P. S. Reddy Gudimetla ◽  
R. Adibi-Asl ◽  
R. Seshadri
Keyword(s):  
Strain Hardening ◽  
Limit Load ◽  
Active Volume ◽  
Limit Loads ◽  
Reference Volume ◽  
Perfectly Plastic ◽  
Tangent Method ◽  
Novel Method ◽  
Typical Strain ◽  
Load Analysis

In this paper a novel method for finding out limit loads in the components or structures by incorporating strain hardening effects is presented. This has been done by including certain amount of the strain hardening into limit load analysis, which normally idealizes the material to be perfectly plastic. The typical strain hardening curves including bilinear hardening and Ramberg-Osgood material models are investigated. The paper also concentrates on plastic reference volume correction concept to find the active volume participating in plastic collapse. The reference volume concept in combination with mα-Tangent method is used to estimate the lower bound limit load of different components.

Redundant Trusses of Elastic-Strain-Hardening Material

1958 ◽  
Vol 25 (2) ◽  
pp. 233-238
Author(s):  
Hans Ziegler
Keyword(s):  
Strain Hardening ◽  
Elastic Strain ◽  
Load Carrying Capacity ◽  
Hardening Material ◽  
Limit Loads ◽  
Perfectly Plastic ◽  
Load Carrying ◽  
Tension And Compression ◽  
Elastic Perfectly Plastic

Abstract W. Prager has given a geometric method for the determination of the load-carrying capacity of a redundant truss consisting of elastic, perfectly plastic bars. In the present paper this method is generalized for trusses consisting of elastic-strain-hardening bars with given limit loads in tension and compression.

Limit-Load Analysis of Pipe Bends Under Out-of-Plane Moment Loading and Internal Pressure

2001 ◽  
Vol 124 (1) ◽  
pp. 32-37 ◽  
Author(s):  
Hashem M. Mourad ◽  
Maher Y. A. Younan
Keyword(s):  
Internal Pressure ◽  
Carrying Capacity ◽  
Limit Load ◽  
Factor H ◽  
Load Carrying Capacity ◽  
Pipe Bend ◽  
Loading Mode ◽  
Load Carrying ◽  
Out Of Plane ◽  
Plane Direction

The purpose of this work is to study the load-carrying capacity of pipe bends, with different pipe bend factor h values, under out-of-plane moment loading; and to investigate the effect of internal pressure on the limit moments in this loading mode. The finite element method is used to model and analyze a standalone, long-radius pipe bend with a 16-in. nominal diameter, and a 24-in. bend radius. A parametric study is performed in which the bend factor takes ten different values between 0.0632 and 0.4417. Internal pressure is incremented by 100 psi for each model, until the limit pressure of the model is reached. The limit moments were found to increase when the internal pressure is incremented. However, beyond a certain value of pressure, the effect of pressure is reversed due to the additional stresses it engenders. Expectedly, increasing the bend factor leads to an increase in the value of the limit loads. The results are compared to those, available in the literature, of a similar analysis that treats the in-plane loading mode. Pipe bends are found to have the lowest load-carrying capacity when loaded in their own plane, in the closing direction. They can sustain slightly higher loads when loaded in the out-of-plane direction, and considerably higher loads under in-plane bending in the opening direction.

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

2006 ◽  
Vol 129 (2) ◽  
pp. 287-295 ◽  
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-deg 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 nonlinearity. 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, equal to 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.

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