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RESEARCH PAPERS

# Statistical and Constraint Loss Size Effects on Cleavage Fracture–Implications to Measuring Toughness in the Transition

[+] Author and Article Information
H. J. Rathbun1

University of California, Santa Barbara, CA 93106-5050palmtree@engineering.ucsb.edu

G. R. Odette, T. Yamamoto, M. Y. He, G. E. Lucas

University of California, Santa Barbara, CA 93106-5050

The analyses contained in this publication were performed to the specifications of the 1997 edition of ASTM E 1921. The changes embodied in the 2003 edition of ASTM E 1921 do not substantially affect the conclusions of this work.

Note, the Master Curve Method is explicitly for standard $1T$-($25.4mm$ thick) SEN(B) and C(T) specimens as opposed to a fully constrained, plane strain SSY condition. However, at toughness levels in the range of $100MPam$, $1T$ specimens have a relatively high level of constraint in medium-strength, pressure vessel steels.

The T-stress is a component of the elastic stress tensor. Its relative importance to crack tip stress distributions increases rapidly with deformation in the elastic regime in proportion to the load. The $T$-stress continues to provide reasonable descriptions of deviations from SSY in the elastic-plastic regime. The $T$-stress is small, and thus plays a secondary role, for the deeply cracked SEN$(B)$ specimens used in this study.

In this context, single variable means that $B$ or $b$ was varied while all other specimen and test conditions were held constant; and that within the matrix of $B$ variations there are $b-B$ combinations that are not expected to manifest significant size effects due to constraint loss.

1

Corresponding author, currently with University of California, Lawrence Livermore National Laboratory.

J. Pressure Vessel Technol 128(3), 305-313 (Jun 24, 2005) (9 pages) doi:10.1115/1.2217962 History: Received August 23, 2004; Revised June 24, 2005

## Abstract

A systematic investigation of the effects of specimen size on the cleavage fracture toughness of a typical pressure vessel steel is reported. Size dependence arises both from: (i) statistical effects, related to the volume of highly stressed material near the crack tip, that scales with the crack front length $(B)$ and (ii) constraint loss, primarily associated with the scale of plastic deformation compared to the un-cracked ligament dimension $(b)$. Previously, it has been difficult to quantify the individual contributions of statistical versus constraint loss size effects. Thus, we developed a single variable database for a plate section from the Shoreham pressure vessel using a full matrix of three point bend specimens, with $B$ from 8 to 254 mm and $b$ from 3.2 to 25.4 mm, that were tested at a common set of conditions. The University of California Santa Barbara (UCSB) $b-B$ database was analyzed using three-dimensional finite element calculation of the crack tip fields combined with a cleavage model calibrated to the local fracture properties of the Shoreham steel. This paper focuses on the possible significance of these results to the Master Curve standard as formulated in ASTM $E$ 1921. The statistical scaling procedure to treat variations in $B$ used in $E$ 1921 was found to be reasonably consistent with the UCSB $b-B$ database. However, constraint loss for three point bend specimens begins at a deformation level that is much lower than the censoring limit specified in $E$ 1921. Unrecognized constraint loss leads to a nonconservative, negative bias in the evaluation of $To$, estimated to be typically on the order of $−10°C$ for pre-cracked Charpy specimens.

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## Figures

Figure 1

Test specimen matrix. Eight tests were conducted for each specimen size and geometry.

Figure 2

(a) KJm versus logB for the UCSB b-B matrix in this study. The data at various b are slightly off-set in B for clarity. The solid curve is the fit to the b=25.4mm data. (b) Averaged KJB for all B grouped by common b plotted versus b.

Figure 3

A schematic illustration of the basis for constraint adjustment. Figure 3 illustrates an approximate condition of SSY. Here the high stress region, marked by the σ22 stress contour (not to scale), is small compared to b. Figure 3 shows that the A(σ22) contour is smaller than in Fig. 3 if the applied KJ are the same. Figure 3 shows that to achieve the same A(σ22) in smaller specimens requires a KCL>KSSY. Cleavage occurs in both cases when A=A∗ and σ22 = σ∗. Note, thicker specimens (larger B) require a smaller A∗ to achieve the same V∗

Figure 4

Nondimensional A∕b2 versus KJ4∕(Eσyb)2 trajectories for SSY and constraint loss conditions from FE simulations of crack tip stress fields used to evaluate the [KCL∕KSSY] constraint adjustment factor

Figure 5

(a) The average ⟨KJr⟩ versus B for the [KCL∕KSSY]-Kmin adjustment procedure. (b) The KJr residuals for various B. The average residuals for the various b are shown by the lines between the different B. (c) The cumulative distribution of the b-BKJr data for various b. The solid line is a fit of the data to a normal distribution function.

Figure 6

The KJm(a) and KJr(b) for the UCSB b-B database, other UCSB data and the Tregoning and Joyce database plotted versus test temperature and the master curve for To=−84°C

Figure 7

Constraint loss predicted by the [KCL∕KSSY]-constraint adjustment procedure as a function of M for the UCSB b-B database

Figure 8

(a)To determined from ASTM E1921-97 using the measured KJm data. (b) The To determined from ASTM E1921-97 using the adjusted KJr data.

Figure 9

(a) Scatter plot of To based on KJm versus KJr. (b) The To based on KJr minus that based on KJm versus ligament dimension, b.

Figure 10

Variation in To calculated using a. KJm and b. KJr

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