Three reliability methods for fatigue crack growth

Wing Kam Liu; Yijung Chen; Ted Belytschko; Yuan Jie Lua

doi:10.1016/0013-7944(95)00133-6

Three reliability methods for fatigue crack growth

Wing Kam Liu^*, Yijung Chen, Ted Belytschko, Yuan Jie Lua

^*Corresponding author for this work

Mechanical Engineering

Research output: Contribution to journal › Article › peer-review

39 Scopus citations

Abstract

In this paper, three reliability methods (1) a first order reliability method (FORM) based on the total derivative method (TDM), (2) FORM based on the Lagrange multiplier formulation (LMF) and (3) a Monte Carlo Simulation (MCS) with pseudo-exact sampling technique are applied to curvilinear fatigue crack growth problems. The crack can follow an arbitrary path which is determined by a crack direction law. A boundary integral element method is used to determine the mechanical response. With the help of the pseudo-exact sampling technique used in MCS, we are able to determine an extremely low probability of failure as low as 10^-6 with high accuracy. A comparison of the three methods shows that the LMF is the most efficient method for the general fatigue crack growth reliability problems. For the class of problems we considered, LMF agrees very well with Monte Carlo simulation, indicating that it is quite accurate.

Original language	English (US)
Pages (from-to)	733-752
Number of pages	20
Journal	Engineering Fracture Mechanics
Volume	53
Issue number	5
DOIs	https://doi.org/10.1016/0013-7944(95)00133-6
State	Published - Mar 1996

ASJC Scopus subject areas

Materials Science(all)
Mechanics of Materials
Mechanical Engineering

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title = "Three reliability methods for fatigue crack growth",

abstract = "In this paper, three reliability methods (1) a first order reliability method (FORM) based on the total derivative method (TDM), (2) FORM based on the Lagrange multiplier formulation (LMF) and (3) a Monte Carlo Simulation (MCS) with pseudo-exact sampling technique are applied to curvilinear fatigue crack growth problems. The crack can follow an arbitrary path which is determined by a crack direction law. A boundary integral element method is used to determine the mechanical response. With the help of the pseudo-exact sampling technique used in MCS, we are able to determine an extremely low probability of failure as low as 10-6 with high accuracy. A comparison of the three methods shows that the LMF is the most efficient method for the general fatigue crack growth reliability problems. For the class of problems we considered, LMF agrees very well with Monte Carlo simulation, indicating that it is quite accurate.",

author = "Liu, {Wing Kam} and Yijung Chen and Ted Belytschko and Lua, {Yuan Jie}",

note = "Funding Information: Acknowledgements--The support of the U.S. Air Force Office of Scientific Research and the National Science Foundation is gratefully acknowledged. This work was also supported, in part, by the FAA-Center for Aviation Systems Reliability, operated by the Ames Laboratory, USDOE, for the Federal Aviation Administration under Contract No. W-7405-ENG-82 for work by Iowa State University and Northwestern University.",

year = "1996",

month = mar,

doi = "10.1016/0013-7944(95)00133-6",

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pages = "733--752",

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AU - Liu, Wing Kam

AU - Chen, Yijung

AU - Belytschko, Ted

AU - Lua, Yuan Jie

N1 - Funding Information: Acknowledgements--The support of the U.S. Air Force Office of Scientific Research and the National Science Foundation is gratefully acknowledged. This work was also supported, in part, by the FAA-Center for Aviation Systems Reliability, operated by the Ames Laboratory, USDOE, for the Federal Aviation Administration under Contract No. W-7405-ENG-82 for work by Iowa State University and Northwestern University.

PY - 1996/3

Y1 - 1996/3

N2 - In this paper, three reliability methods (1) a first order reliability method (FORM) based on the total derivative method (TDM), (2) FORM based on the Lagrange multiplier formulation (LMF) and (3) a Monte Carlo Simulation (MCS) with pseudo-exact sampling technique are applied to curvilinear fatigue crack growth problems. The crack can follow an arbitrary path which is determined by a crack direction law. A boundary integral element method is used to determine the mechanical response. With the help of the pseudo-exact sampling technique used in MCS, we are able to determine an extremely low probability of failure as low as 10-6 with high accuracy. A comparison of the three methods shows that the LMF is the most efficient method for the general fatigue crack growth reliability problems. For the class of problems we considered, LMF agrees very well with Monte Carlo simulation, indicating that it is quite accurate.

AB - In this paper, three reliability methods (1) a first order reliability method (FORM) based on the total derivative method (TDM), (2) FORM based on the Lagrange multiplier formulation (LMF) and (3) a Monte Carlo Simulation (MCS) with pseudo-exact sampling technique are applied to curvilinear fatigue crack growth problems. The crack can follow an arbitrary path which is determined by a crack direction law. A boundary integral element method is used to determine the mechanical response. With the help of the pseudo-exact sampling technique used in MCS, we are able to determine an extremely low probability of failure as low as 10-6 with high accuracy. A comparison of the three methods shows that the LMF is the most efficient method for the general fatigue crack growth reliability problems. For the class of problems we considered, LMF agrees very well with Monte Carlo simulation, indicating that it is quite accurate.

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Three reliability methods for fatigue crack growth

Abstract

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