Loading a cracked structure creates a local stress concentration ahead of the crack tip. A situation

where brittle fracture initiation is likely only in this restricted area around the maximum stress corre­sponds to small-scale yielding conditions. The high stress area is localized ahead of the crack tip extending to the border of the crack tip plastic zone or three to five times the distance from the crack tip to the stress maximum.18 In such a situation, the stress distribution ahead of the crack can be described correctly with the У-integral. When loading exceeds small-scale yielding, large-scale yielding is involved and the У-integral can no longer describe the crack tip stress distribution correctly. At that point, the measuring capacity of the specimen has been exceeded.

The limit for measuring capacity is normally given as a function of the material yield strength and specimen ligament in the form of eqn [14]. The value of M has been proposed from a variety of finite element calculations to be from 50 up to 200.18 Based on present understanding and examination of many
experimental studies, a value of M = 30 can be regarded as a realistic estimate for cleavage fracture with most structural steels. Exceeding the load level given by eqn [14] will lead to gradually increasing amounts of ductile tearing before cleavage fracture initiation.

The basic analysis procedure described in ASTM E 1921 is intended for specimens and structures for which at least a moderate level of constraint (triaxial stress state) is achieved. With deep-cracked speci­mens or thick-wall structures including internal cracks, the constraint is typically high enough for the standard T0 analysis. The situation is different with low-constraint geometries like surface cracks and thin-sheet structures where the small-scale yielding condition may not prevail (note that the limit for this condition also depends on material strength properties). In principle, the basic Master Curve approach can also be applied for such low — constraint conditions, but the estimation may be overly conservative due to high plastic deformation which is outside the applied fracture model assump­tions. In ASTM E1921 test conditions, sufficient constraint is assured by defining valid tests only as those that exhibit brittle fracture initiation below or at the capacity limit value (eqn [14]) and by limiting the ductile crack extension prior to brittle fracture initiation.

The probability of cleavage initiation is controlled by the narrow zone ahead ofthe crack tip where small — scale yielding condition prevails. Several approaches like the Tstress, the Q-parameter, and small-scale yield­ing corrections have been developed to account for the effect of plastic deformation due to low constraint.19 The Tstress analysis is relatively straightforward since a simple elastic stress analysis can be used instead of a numerical large-scale yielding model. Another advan­tage of using the Tstress is that it may be performed assuming no change in temperature dependence which allows the constraint effect to be described only as a shift in T0. Consequently, the Tstress yields conservative estimates compared to the more complex Q-parameter approach. On the other hand, the Q-parameter is more accurate for very low-constraint situations. On the basis of a simplified linear-elastic analysis, the correc­tion to T0 due to low-constraint SE(B) geometry (a0/W> 0.1) with a negative Tstress has been expressed in the form19:

Tt 10MPa °C~

Tstress < 0 (for SE(B) specimens only)

where T0 is the corrected value and T0deep is the value measured for a deep crack case.

Equation [26] is an empirical result from data consisting of only SE(B) specimens (Figure 16). Additional work has been conducted to refine the expression by including test data from C(T) speci­mens and by a comparison of solutions based on Tstress and the Q-parameter. Thus, a more accurate formula for estimating the T0 from Tstress and the T0 of a deep crack case has been proposed in the form20:

T

T0 « T0 deep + — 1 for Tstress <300 MPa

0 0 deep!2MPa °C_1

(for SE(B) and C(T) specimens) [27]

The main difference between eqns [26] and [27] is that the latter also covers positive values of Tstress up to 300 MPa, whereas in eqn [26], it is assumed that only a negative T«ess has a marked effect on the value of T0.