Plastic limit load of cylindrical shells with cutouts subject to pure bending moment

This paper discusses the plastic limit load of elbows without defects and with local thinned area (LTA) in the extrados under combined pressure and in-plane closing bending moment. Finite element analysis (FEA) and experiments have been used. The results of FEA show that, for the elbows without defects, when the ratio of pressure to the limit pressure (P/PL) is smaller than 0.469, the limit moment of elbows increases with the increasing pressure; when the ratio (P/PL) is bigger than 0.469, the limit moment of elbow decreases with the increasing pressure. For the elbows with LTA, the FEA results show that with different LTA the variation of the limit load of elbows to the pressure is different. Perhaps, the limit moment of elbows always decreases with the increasing pressure. It is also likely that the limit moment of elbows increases with the increasing pressure and then decreases with the increasing pressure. The results of FEA are consistent with the experimental results. By fitting the results of FEA, the safety assessment figure for elbows under combined pressure and in-plane closing bending moment is drawn.

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Fem determination of the plastic limit load for cylindrical shells

Czasopismo Techniczne ◽

10.4467/2353737xct.19.128.11453 ◽

2019 ◽

pp. 151-162

Author(s):

Kamil Słowiński ◽

Marek Piekarczyk

Keyword(s):

Cylindrical Shells ◽

Limit Load ◽

Plastic Limit ◽

Plastic Limit Load

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Analytical Limit Loads for Tube Sections With Circumferential Degradation

Computer Technology and Applications ◽

10.1115/pvp2004-2753 ◽

2004 ◽

Author(s):

W. Reinhardt ◽

X. Wang

Keyword(s):

Analytical Solutions ◽

Load Capacity ◽

Bending Moment ◽

Limit Load ◽

Thin Wall ◽

Plastic Limit ◽

Tubes And Pipes ◽

Limit Loads ◽

Plastic Limit Load ◽

Analytical Limit

The fracture mechanics evaluation of tubes and pipes with circumferential degradation typically requires that the plastic limit load capacity be evaluated under a combination of axial force and bending moment loading. Most available analytical solutions are thin-wall approximations and may not work well for heavy-wall applications. The present paper derives an analytical limit load for a cylindrical pipe or tube with a partial circumferential, partial through-wall flaw and its bounding cases (through wall partial circumferential and uniform circumferential part-throughwall flaw). The solution is not in closed form, but can be easily solved with available mathematical software like MathCAD. The obtained limit loads for a steam generator tube are compared to those from simplified analytical solutions. The effect of tube supports on the limit load of a tube with non-axisymmetric flaw is discussed with a simplified model.

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The Numerical Investigation of Plastic Collapse Loads in Cylinders Containing Circumferential Flaws Under a Combined Loading of Internal Pressure, Tension and Bending Moment

Volume 3: Materials Technology; Ocean Space Utilization ◽

10.1115/omae2013-10741 ◽

2013 ◽

Author(s):

Liwu Wei

Keyword(s):

Surface Crack ◽

Bending Moment ◽

Limit Load ◽

Plastic Collapse ◽

Plastic Limit ◽

Integrity Assessment ◽

Reference Stress ◽

Fracture Assessment ◽

Plastic Limit Load ◽

Assessment Procedures

Fracture assessment diagram (FAD) based fracture assessment procedures are universally adopted by standards/documents including BS7910, R6, API579-1/ASME FFS-1 and FITNET. In the use of a FAD for structural integrity assessment, one important consideration is to determine the load ratio (Lr) which is defined by two equivalent definitions: Lr is either defined as the ratio of reference stress (σref) to yield strength (σY) as in BS7910, or as the ratio of applied load to plastic limit load as in R6. The solutions of reference stress or limit load are given in the assessment procedures for commonly encountered flawed structures such as a plate containing a surface crack and a cylinder containing an external surface crack. Although the solutions given in the various standards are not all the same, they were invariably derived on the basis of analysis of the force and moment equilibrium with regard to a flawed section and few of them has taken into account the effects of bi-axial stressing on a flawed section, thus remaining a question whether these solutions are still valid in situations involving bi-axial loading such as the presence of pressure in a cylinder in addition to axial tension and bending. In this work, finite element analysis (FEA) of plastic collapse was systematically performed on circumferential internal surface cracks in a cylinder subjected to various combined loads, including combined tension and pressure, combined bending moment and pressure, and combined tension, bending moment and pressure. The focus was on understanding the effects of bi-axial stressing due to pressure on plastic limit load. The investigation of these cases has demonstrated a significant effect in plastic limit load arising from the application of pressure introducing a state of bi-axial stressing. Comparison of the results of plastic limit load obtained from FEA with those derived from BS 7910 reference stress solutions was carried out to assess the applicability when the standard solutions of plastic collapse are used in the applications containing bi-axial stresses.

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

Journal of Pressure Vessel Technology ◽

10.1115/1.4051630 ◽

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.

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The Effects of Classification of Misalignment-Induced Stresses in Engineering Critical Assessments of Welded Joints With Some Misalignment

ASME 2010 Pressure Vessels and Piping Conference: Volume 3 ◽

10.1115/pvp2010-25335 ◽

2010 ◽

Author(s):

Liwu Wei

Keyword(s):

Welded Joints ◽

Driving Force ◽

Limit Load ◽

Surface Cracks ◽

Plastic Limit ◽

Secondary Stress ◽

Butt Weld ◽

Crack Driving Force ◽

Plastic Limit Load

In the ECA of a structure or component such as a pipeline girth weld, the bending stress component arising from misalignment across the weld is often classified as primary, partly because standards such as BS 7910 and API 579-1/ASME FFS-1 do not give definitive guidance on this subject. This approach may be over-conservative as the σmis is localised. In order to obtain a more realistic assessment of the structural integrity of structures containing misalignment, it is necessary to understand the conservatism or non-conservatism in an ECA associated with the classification of σmis. To address the above concerns, systematic investigations were carried out of surface cracks in a plate butt-weld including some misalignment, external circumferential surface cracks and external fully circumferential cracks in a misaligned pipe connection. FEA of these cracked welded joints with some misalignment (typically from 1mm to 2mm) was performed to calculate crack driving force and plastic limit load. The results from FEA were compared with the existing solutions of KI and σref in BS 7910 generated by assuming three options of treating the σmis. The three options were: (1) classification of σmis wholly as primary stress; (2) 15% of σmis as primary and 85% of σmis as secondary stress; and (3) classification of σmis wholly as secondary stress. Variations in parameters (eg misalignment, crack size, loading, weld overmatch and base material properties) were taken into account in order to determine the effects of these parameters on plastic limit load and crack driving force. The implication of different classifications of σmis in terms of ECAs of misaligned welded joints was revealed by conducting BS 7910 Level 2B assessments with the use of a FAD. It was found in this work that for the cases examined, use of the σmis as entirely primary bending in an ECA was over-conservative, and even treatment of σmis as entirely secondary bending was generally shown to be still conservative, when compared with the assessments based on FEA solutions. Furthermore, caution should be exercised in using the solutions of KI and σref given in the existing BS 7910 for crack-containing structures subjected to a bi-axial or tri-axial stress state. A non-conservative estimate may result from the use of these solutions which have been derived based on a uniaxial stress condition.

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