International Journal of Fracture

, Volume 145, Issue 1, pp 63–79 | Cite as

Plastic loads of elbows with local wall thinning under in-plane bending

Original Paper


Based on systematic three-dimensional (3-D), large strain FE limit analyses using elastic- perfectly plastic materials, this paper quantifies the effect of local wall thinning on plastic behavior and TES (twice-elastic-slope) plastic loads for 90° elbows under in-plane bending. The thinning geometry is assumed to be rectangular rather than circular, but the nonlinear geometry effect is fully considered. Results from systematic analyses lead to simple approximations for TES plastic loads, covering a wide range of elbow and thinning geometries. Although the proposed approximations are developed for the case when wall thinning locates in the center of the elbow, it is also shown that they can be equally applied to the case when thinning exists anywhere within the elbow. Brief discussion is made on application of the proposed approximations to estimate maximum load-carrying capacities of elbows with local wall thinning.


Elbow Large strain FE limit analysis Local wall thinning Twice-elastic-slope plastic load 






Young’s modulus


(Maximum) Depth of local wall thinning


Normalized limit moment for circumferential part-through surface crack


Normalized limit moment for sufficiently long thinning


In-plane moment


Limit in-plane moment of a defective elbow


Limit in-plane moment of a smooth elbow (without any defect)


Limit moment of a smooth straight pipe = 4σ o r 2 t


Bend radius


Mean pipe radius


Thickness of a pipe


Bend characteristic = Rt/r 2


Limiting stress of an elastic-perfectly plastic material


Half circumferential angle of wall thinning


Half longitudinal angle of wall thinning


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Copyright information

© Springer Science+Business Media B.V. 2007

Authors and Affiliations

  1. 1.Department of Mechanical EngineeringKorea UniversitySeoulKorea
  2. 2.Korea Electric Power Research InstituteYusung-gu, DaejonKorea

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