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

Abstract

Based on systematic three-dimensional (3-D), large strain FE limit analyses using elasticperfectly 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. Abbreviations TES Twice-elastic-slopeNomenclature E Young's modulus d (Maximum) Depth of local wall thinning f o Normalized limit moment for circumferential part-through surface crack f ∞ Normalized limit moment for sufficiently long thinning M In-plane moment M L Limit in-plane moment of a defective elbow M o Limit in-plane moment of a smooth elbow (without any defect) M s o Limit moment of a smooth straight pipe = 4σ o r 2 t R Bend radius r Mean pipe radius t Thickness of a pipe λ Bend characteristic = Rt/r 2 σ o

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