Mohammad M. Megahed

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

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.

Comparison of Pipe Bend Ratchetting/Shakedown Test Results With the Shakedown Boundary Determined via a Simplified Technique

Scarce experimental verification exits in the open literature concerning determination of the shakedown boundary for pipe bends subjected to steady internal pressure and cyclic bending loading. The objective of the present paper is to test the capability of a simplified technique presented by the authors in recent ASME JPVT publications and PVP conferences [1–4] in adequately predicting the shakedown boundary obtained through experimental testing. Recently, Chen et al. [5] published experimental and finite element (FE) simulation results on ratchetting of low-carbon steel pressurized 90-degree pipe bend specimens subjected to cyclic reversed in-plane bending forces. Chen et al. [5] performed experimental testing on a pipe bend specimen subjected to a steady internal pressure magnitude of 20.0 MPa. Through FE simulations employing a modified form of the Ohno-Wang non-linear kinematic hardening (KH) rule, Chen et al. [5] predicted a shakedown boundary for a steady internal pressure spectrum ranging from 10.0 to 25.0 MPa. Chen et al. [5] experimental and FE outcomes are utilized for comparison with the simplified technique outcomes. The simplified technique outcomes showed very good correlation with Chen et al. [5] shakedown boundary predictions for the 18.0 – 25.0 MPa steady internal pressure spectrum. On the contrary, noticeable disagreement was found for the lower magnitudes of steady internal pressure. Reasons behind the discrepancy are discussed.Copyright

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

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.

DETERMINATION OF SHAKEDOWN LIMIT LOADS FOR A CYLINDRICAL VESSEL-NOZZLE INTERSECTION VIA A SIMPLIFIED TECHNIQUE

In the current research, the shakedown limit loads for a cylindrical vessel–nozzle intersection is determined via a simplified technique. The cylindrical vessel–nozzle intersection is subjected to a spectrum of steady internal pressure magnitudes and cyclic in–plane bending moments on the nozzle. The determined shakedown limit loads are utilized to generate the Bree diagram of the cylindrical vessel–nozzle intersection. In addition, the maximum moment carrying capacity (limit moments) and the elastic limit loads are determined and imposed on the Bree diagram of the structure. The simplified technique outcomes showed excellent correlation with the results of full elastic–plastic cyclic loading finite element simulations.Copyright

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

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. DOI: 10.1115/1.4003474

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

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.Copyright

Shakedown Analysis of a Cylindrical Vessel-Nozzle Intersection Subjected to Steady Internal Pressures and Cyclic Out-of-Plane Bending Moments

In the current research, the shakedown limit loads of a cylindrical vessel–nozzle intersection are determined via a simplified technique. The cylindrical vessel–nozzle intersection is subjected to a spectrum of steady internal pressure magnitudes and cyclic out–of–plane bending moments on the nozzle. The determined shakedown limit loads, forming the shakedown boundary, are utilized to generate the Bree diagram of the cylindrical vessel–nozzle intersection. In addition to the determined shakedown boundary, the Bree diagram includes the maximum moment carrying capacity (limit moments) and the elastic limit loads. The currently generated Bree diagram is compared with previously generated Bree diagram of the same structure, but subjected to in–plane bending. Noticeable differences regarding the magnitudes of the generated shakedown boundaries are observed. Moreover, only failure due to reversed plasticity response occurs upon exceeding the generated shakedown boundary unlike cyclic in–plane bending where the structure experienced both reversed plasticity and ratchetting failure responses. The simplified technique outcomes showed excellent correlation with the results of full elastic–plastic cyclic loading finite element simulations.Copyright

Finite Element simulation of In-Service Sleeve Repair Welding of Gas Pipelines

The purpose of this study is to investigate the influence of welding sequence on the risk of burn-through, cold cracking and residual stresses during in-service sleeve repair welding of gas pipelines. Based on ABAQUS software, axisymmetric finite e1ement models were conducted to calculate transient temperature distributions and resulting residual stress field after multi-pass sleeve fillet welding of in-service API 5L-X65 36” Schedule pipes. Influence of welding sequence was investigated by comparing residual stresses and transient deformations for sequential welding; in which welding of the two circumferential pipe/sleeve fillet welds was made in sequence, to the case of performing the two welds at the same time. Sequential welding was found to reduce weld zone distortion and residual stresses due to the sleeve freedom to expand axially while conducting the first fillet weld. The upper limit of heat input was found to generate higher pipe wall peak temperature, but not to the extent of initiating pipe wall melt through.

Prediction of Ratchet Boundary for 90-Degree Smooth and Mitred Pipe Bends

The present paper attempts to predict ratchet boundary for 90-degree mitred and smooth pipe bends subjected to sustained pressure and cyclic in-plane bending. The methodology utilizes a recently published technique known as the “Uniform Modified Yielding” (UMY) technique, which relies on generation of a virtual structure with inhomogeneous reduced yield strength, whose magnitude and distribution depend on the elastic stress field due to the cyclic load. The collapse load of this virtual structure determines the threshold steady load necessary for commencement of “incremental collapse”. The technique is applied first to predict ratchet boundaries for two benchmark problems possessing analytical descriptions of ratchet boundary and uni-axial states of stress; the two-bar structure problem and the Bree cylinder. Predicted ratchet boundaries exactly coincided with the corresponding published analytical descriptions, and reasons for this correlation were discussed in this paper. The technique was then applied to three 90-degree pipe bends with similar geometries as follows: smooth pipe bend (SPB), single mitred pipe bend (SMPB), and three weld mitred pipe bend (3WMPB). Certain assumptions are adopted to enable treatment of the problem as a quasi-uniaxial one. Conservative estimates are obtained for ratchet boundaries in pipe bends that correlates well with elastic shakedown/ratchet boundary of the same problems as predicted by a recently developed non-cyclic direct technique.Copyright