Enhanced levels of toughness due to loss of crack tip constraint have been related to temperature shifts in the ductile–brittle transition curve. An argument to quantify the temperature shift is developed using the self-similarity of near-tip stress fields under contained yielding combined with scaling techniques developed by Dodds and co-workers (1,2) for cleavage. This allows the temperature changes which give the same stress field at failure in constrained and unconstrained fields to be determined. The procedure is illustrated using the data of Sherry et al. (3) for an A533B pressure vessel steel. The results are consistent with empirical expressions proposed by Wallin (4), and enable a discussion of the micromechanics of cleavage.

1.
Anderson
,
T. L.
,
Dodds
,
R. H.
, and
Kirk
,
M. T.
, 1991, “
A framework to correlate a∕w ratio effects on elastic-plastic fracture toughness (Jc),
Int. J. Fract.
0376-9429,
48
, pp.
1
22
.
2.
Gao
,
X.
, and
Dodds
,
R. H.
, 2001, “
An engineering approach to assess constraint effects on cleavage fracture toughness
,”
Eng. Fract. Mech.
0013-7944,
68
, pp.
263
283
.
3.
Sherry
,
A. H.
,
Lidbury
,
D. P. G.
, and
Beardsmore
,
D. W.
, 2001, “
Validation of constraint based structural integrity assessment methods. Final report
,” Report No. AEAT∕RJCB∕ RD01329400∕R003,
AEA Technology
, UK.
4.
Wallin
,
K.
, 2001, “
Quantifying T-stress controlled constraint by the master curve transition temperature To
,”
Eng. Fract. Mech.
0013-7944,
68
, pp.
303
328
.
5.
R6, 2001, “
Assessment of the integrity of structures containing defects
,” Revision 4, British Energy Generation Ltd., Gloucester, UK, 2001.
6.
Beardsmore
,
D. W.
,
Dowling
,
A. R.
,
Lidbury
,
D. P. G.
, and
Sherry
,
A. H.
, 2003, “
The assessment of reactor pressure vessel defects allowing for crack tip constraint and its effect on the calculation of the onset of the upper shelf
,”
Int. J. Pressure Vessels Piping
0308-0161,
80
, pp.
787
795
.
7.
Sumpter
,
J. D. G.
, and
Hancock
,
J. W.
, 1991, “
Shallow crack toughness of HY80 steel: an analysis based on T stress
,”
JPVP
,
45
, pp.
207
221
.
8.
Hancock
,
J. W.
,
Reuter
,
W. A.
, and
Parks
,
D. M.
, 1993, “
Toughness and constraint parameterized by T
,” In ‘Constraint effects in fracture,’ ASTM STP 1171, American Society for Testing and Materials, Philadelphia, pp.
121
140
.
9.
Maclennan
,
I. J.
, and
Hancock
,
J. W.
, 1995, “
Constraint-Based Failure Assessment Diagrams
,”
Proc. R. Soc. London, Ser. A
1364-5021,
451
, pp:
757
777
.
10.
Ainsworth
,
R. A.
, and
O’Dowd
,
N. P.
, 1995, “
Constraint in the failure assessment diagram approach for fracture assessment
,”
Int. J. Pressure Vessels Piping
0308-0161,
117
, pp.
260
267
.
11.
O’Dowd
,
N. P.
, and
Shih
,
C. F.
, 1991, “
Family of crack tip fields characterized by a triaxiality parameter: Part I: Structure of fields
,”
J. Appl. Mech. Phys. Solids
,
39
, pp.
939
963
.
12.
Williams
,
M. L.
, 1957, “
On the stress distribution at the base of a stationary crack
,”
J. Appl. Mech.
0021-8936,
24
, pp.
111
114
.
13.
Betegón
,
C.
, and
Hancock
,
J. W.
, 1991, “
Two-parameter characterization of elastic-plastic crack-tip fields
,”
J. Appl. Mech.
0021-8936,
58
, pp.
104
110
.
14.
Ritchie
,
R. O.
,
Knott
,
J. F.
, and
Rice
,
J. R.
, 1973, “
On the relationship between critical tensile stress and fracture toughness in mild steel
,”
J. Mech. Phys. Solids
0022-5096,
21
, pp.
395
410
.
15.
Curry
,
D. A.
, 1980, “
Comparison between two models of cleavage fracture
,”
Met. Sci.
0306-3453,
14
, pp.
78
80
.
16.
Ritchie
,
R. O.
,
Server
,
W. L.
, and
Wulleart
,
R. A.
, 1979, “
Critical fracture stress and fracture strain models for prediction of lower and upper shelf toughness in nuclear pressure vessel steel
,”
Metall. Trans. A
0360-2133,
10A
, pp.
1557
1570
.
17.
Ortner
,
S. R.
, and
Hippsley
,
C. A.
, 1996, “
Two component description of ductile to brittle transition in ferritic steel
,”
Mater. Sci. Technol.
0267-0836,
12
, pp.
1035
1042
.
18.
Bowen
,
P.
,
Druce
,
S. G.
, and
Knott
,
J. F.
, 1987, “
Micromechanical modelling of fracture toughness
,”
Acta Metall.
0001-6160,
35
, pp.
1735
1746
.
19.
Beremin
,
F. M.
, 1983, “
A local criterion of cleavage fracture of a nuclear pressure vessel steel
,”
Metall. Trans. A
0360-2133,
14A
, pp.
2277
2287
.
20.
Rice
,
J. R.
, and
Tracey
,
D. M.
, 1973, “
Computational fracture mechanics
,”
Numerical and Computational Methods in Structural Mechanics
,
Academic Press
, New York.
21.
Larsson
,
S. G.
, and
Carlsson
,
A. J.
, 1973, “
Influence of non-singular stress terms and specimen geometry on small-scale yielding at crack tips in elastic plastic material
,”
Int. J. Fract.
0376-9429,
19
, pp.
263
278
.
22.
Li
,
F. Z.
,
Shih
,
C. F.
, and
Needleman
,
A.
, 1985, “
A comparison of methods for calculating energy release rates
,”
Eng. Fract. Mech.
0013-7944,
21
, pp.
405
421
.
23.
Hibbitt
,
X.
,
Carlsson
,
X.
, and
Sorrensen
,
X.
, ABAQUS Standard v5.8, Providence, RI.
24.
Recent developments in constraint-based fracture mechanics methodology with applications to the assessment of structural integrity
,”
Special Issue of Int. J. of Pressure Vessels Piping
,
80
, 2003.
25.
Lidbury
,
D. P. G.
,
et al.
, “
Effects of specimen size on the fracture toughness transition properties of a Sizewell “B” specific A508 Class 3 steel forging and comparisons with the additional RPV materials
,” AEA Technology Report No. PWR∕RDMC∕MWG∕P(89)284M, Risley, UK.
26.
Wang
,
G. Z.
,
Chen
,
J. H.
, and
Liu
,
G. H.
, 2002, “
On the characteristic distance and minimum fracture toughness for cleavage fracture in a C–Mn steel
,”
Int. J. Fract.
0376-9429,
118
, pp.
57
76
.
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