Determination of shakedown boundaries of 90-degree defect-free smooth pipe bends has received substantial attention by several researchers within the recent decades. However, scarce information is found within the literature regarding the determination of the shakedown boundary of cracked pipe bends. The current research outcomes include the determination of shakedown boundary for a circumferentially cracked 90-degree pipe bend via a simplified technique utilizing the finite element method, and introduction of Failure-Assessment-Diagrams (FAD) in compliance with the API 579 Failure-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) or opening (IPO) bending moments. Line Spring Elements (LSE) are embedded in quadratic shell elements to model part through cracks. Failure assessment diagrams (FAD) are developed 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 verification studies: stress intensity factor, Shakedown (SD) limit, and limit load. Additionally, full elastic-plastic cyclic loading finite element analyses are conducted and the outcomes revealed 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.


Mechanical Engineering Department

Degree Name

MS in Mechanical Engineering

Graduation Date


Submission Date

May 2012

First Advisor

Younan, Maher

Second Advisor

Fayek, Hany



Document Type

Master's Thesis

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Library of Congress Subject Heading 2

Composite materials.


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I know as a matter of fact that I would never be able to give the full due to everybody who helped me during the process of conducting this research. I have to thank the great generous merciful Allah for being always with me during the success times by good fortune and during stumbling times by conferring me patience and perseverance. I cannot find any manner of expression that gives the full due to my supervisor Dr. Maher Youn who was the father that direct, inspire, and encourage. My grand brother before being my supervisor Dr. Hany Fayek was the person who provides smart solutions and moral support when the road was full of obstacles. The American University in Cairo is highly acknowledged for the fincial support of this research and also for giving me the chance to utilize the state of the art computatiol facilities. Special thanks to Eng. Mohammed Abdelaal for his generous help and support. Special thanks to my colleagues Youssef Fouad and Ahmed Gaber. Last and foremost, my adored family: to my mother, words fail to express my gratitude to you. To my father, your words that you told me when I was just crawling in my road towards this day were always echoing in my ears; you have been always my inspiration. My brother Eng. Mahmoud and my little sister Magi, thanks for bearing me ever and always. To my beloved wife Dr. Alshaimaa, my dream has come to reality only when you were beside me and recently you gave me the best gift in this world, ABDELRAHAMAN who I wholeheartedly dedicate this thesis.