Effect of Loading on Stress Intensification Factors

[+] Author and Article Information
Rudolph J. Scavuzzo

 The University of Akron, Akron, OH 44325-3903rscavuzzo@uakron.edu

J. Pressure Vessel Technol 128(1), 33-38 (Oct 07, 2005) (6 pages) doi:10.1115/1.2148420 History: Received September 06, 2005; Revised October 07, 2005

The basic objective of this investigation is to determine the effect of loading on the stress intensification factors of Markl’s fatigue evaluation method for metal piping. Markl’s method is based on the fatigue testing of 4 in. schedule 40 carbon steel cantilever piping. Subsequent testing using a four-point loading showed that the S-N data were different from that predicted by the procedure and equation developed by Markl. Markl’s method is based on determining the elastic-plastic forces in a piping system by multiplying the elastic system stiffness by the actual deflection. In this manner a fictitious force is calculated to determine piping stresses assuming the elastic beam bending equation, Mc/I, applies even in partially plastic pipes. Previous analytical work on this topic by Rodabaugh and Scavuzzo (“Fatigue of Butt Welded Pipe and the Effect of Testing Methods–Report 2: Effect of Testing Methods on Stress Intensification Factors,” Welding Research Bulletin 433, July 1998) showed that these measured differences should occur between cantilever and four-point tests using Markl’s method. The basic assumption in this analytical comparison is that strain-cycle correlations lead to the correct prediction of fatigue life. Using the measured alternating strain, both types of test geometries lead to the same prediction of fatigue life using these strain-cycle correlations. In this study, the same analytical assumptions used by Rodabaugh and Scavuzzo (above) are applied to a pipe where the load is varied from a four-point loading through its extremes. Loads were varied from a cantilever to an end moment by changing the dimensions of four-point loading. Also, the shape of a bilinear stress-strain curve was varied from a perfectly plastic material to various degrees of work hardening by increasing the tangent modulus in the plastic regime. The results of the study indicate that Markl’s method is conservative by predicting too short a fatigue life for four-point loading for a given stress. As indicated by this study, the differences can be very large in the low-cycle regime for a perfectly plastic material and for a four-point loading approaching an end moment. Thus, piping could be over designed with unnecessary conservatism using the current ASME Code method based on stress intensification factors.

Copyright © 2006 by American Society of Mechanical Engineers
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Figure 1

Four-point fatigue bent test geometry

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Figure 2

Typical weld on the 112in. schedule 80 pipe. The fatigue crack location in the HAZ is Indicated by the arrow.

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Figure 3

Comparison of measured fatigue data from four-point bending tests and the ASME “Best Fit” curve using Langer’s formula (1)

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Figure 4

Bending stress versus cycles to failure compared to Markl’s equation (Eq. 1). The one low-cycle data point on Markl’s curve is from (4).

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Figure 5

The ratios of SIFs from cantilever testing, ic to those from four-point bending, I4pt(2)

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Figure 6

Deflected beam with elastic-plastic bending along length, Lm and Lp and elastic bending along length, Le

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Figure 7

The angle β is defined at the value of y when σ reaches the yield strength in the pipe wall. The stress, σ, at the angle α is shown for both α<β and α>β for the bilinear elastic-plastic material.

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Figure 8

Bilinear elastic-plastic stress-strain curve

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Figure 9

Ratios of SIFs of cantilever loading to four-point loading for β=0.065(175cycles)

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Figure 10

Ratios of SIFs of cantilever loading to four-point loading for β=0.4(11,200cycles)




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