Hany F. Abdalla

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

Limit and Shakedown Loads Determination for Locally Thinned Wall Pipe Branch Connection Subjected to Pressure and Bending Moments

In this paper the shakedown limit load for unreinforced locally thinned wall pipe branch connection is determined using the Simplified Technique. Loadings were considered to be internal pressure, as a steady load, with in-plane bending or with out-of-plane bending applied on the branch, as alternating loads. Two locations of local wall thinning were taken; one was on the run pipe opposite to the branch and other on the branch at the maximum tension stress side of the bending moment applied whether in in-plane or out-of-plane situation. Two Finite Element (FE) limit load models were used to verify the modeling of the pipe branch connection with its local wall thinning. First model results were compared with experimental data taken from the literature, and the second results were compared with numerical models taken also from the literature and also compared with API 579 “Fitness For Service” (FFS), part-five, level-two assessment procedure. First and second comparisons lead to good agreement but for API 579 comparison it was found that it is slightly changing with the depth of the local wall thinning but does not reflect the expected behavior of the limit load as the FEA models showed. For the results of the shakedown limit load analysis, Bree diagrams were constructed to show elastic, shakedown and plastic collapse regions. Then, comparison was made to show the effect of the local wall thinning depth and location on previous limits. Finally, the shakedown results were verified using the elastic-plastic ratcheting analysis of API 579, level three assessment and it showed successfully the shakedown, ratcheting and reversed plasticity regions. This verifications and results can prove that the Simplified Technique can be used as a level-three ratcheting assessment in API 579.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

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

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

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.Copyright

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

Determination of shakedown 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 method, and introduction of Fitness-Assessment-Diagrams (FAD) in compliance with the API 579 Fitness-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 (LSE) are embedded in quadratic shell elements to model part through cracks. Fitness assessment diagrams (FAD) are 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 and limit load. Additionally, full elastic-plastic 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.Copyright