Shakedown and limit load of pipe bends with local wall thinning under combined internal pressure and cyclic in-plane bending moment (original) (raw)
Related papers
Shakedown Limits of a 90-Degree Pipe Bend Using Small and Large Displacement Formulations
Journal of Pressure Vessel Technology, 2007
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 elasticplastic 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.
2007
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.
Journal of Pressure Vessel Technology, 2011
A simplified technique for determining the shakedown limit load for a long radius 90 deg pipe bend was previously developed (Abdalla, H. ). 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-ofplane 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.
European Journal of Mechanics - A/Solids
A 90° back-to-back pipe bend structure subjected to cyclic in-plane bending moment and steady internal pressures is analysed by means of the Linear Matching Method (LMM) in order to create the limit, shakedown, and ratchet boundaries. The analyses performed in this work demonstrate that the cyclic moment has a more significant impact upon the structural integrity of the pipe bend than the constant pressure. Full cyclic incremental analyses are used to verify the structural responses either side of each boundary and confirm correct responses. In addition, the shakedown boundary produced by the LMM is compared to another shakedown boundary of an identical pipe bend computed by the simplified technique and it is shown that the LMM calculates results more accurately. Parametric studies involving a change of geometry of the pipe bends and loading type are carried out. From the studies of the geometry, two semi-empirical equations are derived from correlations of the reverse plasticity limit and the limit pressure with the bend characteristic. Finally, the results presented in this paper provide a comprehensive understanding of post-yield behaviours of the 90° back-to-back pipe structure under the combined loading as well as offering essential points to be concerned for the life assessment of the piping system.
Journal of Pressure Vessel Technology, 2011
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 , "Determination of Shakedown Limit Load for a 90 Degree Pipe Bend Using a Simplified Technique," ASME J. Pressure Vessel Technol., 128,. 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.
The Influence of the Internal Pressure and In-Plane Bending Moment Loadings on Pipe Bends
2021
Circular thin-walled pipe bends are frequently used as a key part in pipeline connection either in the vertical direction or the horizontal direction due to their high flexibility. The high flexibility of pipe bends is due to the ability of their cross-section to ovalize when subjected to internal pressure and/ or bending moments that lead to high-stress concentrations at bend locations within the pipeline system. Moreover, the surface geometric characteristics of bends may cause some unbalanced outward forces caused by the induced internal pressure loading only which leads to an outward resultant force that tends to straighten out the bend causing a rise within the deformations and stress levels. This phenomenon was known as "The Bourdon effect". In addition to that, external bending moment load acting on the pipe bends may result from either occasional loadings such as; seismic loads, soil settlement, and/ or secondary loadings exerted on the pipe due to thermal expansions resulted in additional stresses. These additional stresses resulting from bending loads acting on the pipe bend are accounted for in the design codes using stress intensification factors (i) and flexibility factors (K). These factors are presented in the current American code ASME B31.3.Although they have been derived for a 90-degree pipe bend subjected to in-plane closing bending moment with long bend radius(R), they cannot be used for other loading cases such as in-plane opening moment or out-of-plane bending moment. Previous studies showed that the direction of bending moment affected the distribution and magnitude of stress levels found on the bend. However, previous studies considered only small pipe sizes of NPS 16 (406mm) and smaller under bend angles of 90 degrees or less. This paper extended the investigation on smooth pipe bends with initial circular cross-sections and uniform wall thickness with large pipe size from NPS20 (508mm) up to NPS 72 (1829mm) under a wide range of bend angles (Ø)(from 30° up to 160°). The loading considered in this study is the internal pressure and the in-plane opening/closing bending moment. In this respect, an extensive parametric study is conducted using a numerical finite element analysis (FEA) simulation using ABAQUS software to model Pipe bends with different nominal pipe sizes (NPS), bend angles (Ø), bend wall thickness (t), and various bend radius (R). The results showed that as the bend angle increases, the flexibility of the bend increases as well leading to higher stresses on the pipe bend. Finally, from the finite element analysis results depicted through curves, it could be concluded that the codes do not cover the stress distribution for large pipe bends accurately.
Elasto-Plastic collapse analysis of pipe bends using finite element analysis
2014
Conference paper,When an external load is applied to one of its ends, a pipe’s bends cross section tends to deform significantly both in and out of its end plane. This shell type behaviour characteristic of pipe bends and mainly due to their curves geometry accounts for their greater flexibility. This added flexibility is also accompanied by stresses and strains that are much higher than those present in a straight pipe. The primary goal of this research is to study the elastic-plastic behaviour of pipe bends under out of plane moment loading. It is also required to study the effects of changing the value of the pipe bend factor and the value of the internal pressure on that behaviour and to determine the value of the limit moments in each case. The results of these analyses are presented in the form of load deflection plots for each load case belonging to each model. From the load deflection curves, the limit moments of each case are obtained. The limit loads are then compared to...
General plastic collapse equations of pipe bend with or without crack under in-plane bending
2011
Elbows exhibit highly strained regions and are vulnerable to plastic collapse. It has been observed that available equations in literature for evaluation of plastic collapse load of a pipe bend have limited applicability and do not cover wide range of pipe bend radius ratios and bend angles which are used in power plant piping. Moreover, the elbow collapse load equation should approach to straight pipe collapse load as elbow bend radius increases or bend angle decreases. Generally, the available equations do not satisfy this asymptotic behaviour of an elbow. About 600 number of elastic plastic and geometric nonlinear finite element analyses of elbows having different geometric parameters bend radius, pipe radius, thickness and crack size (in case of cracked elbow), have been performed. For each of the elbow the in-plane plastic collapse moments have been evaluated from M-rotation curve by twice elastic slope (TES) method. Further two weakening factors were defined to quantify the de...