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Table 5. Critical surface crack depth
Fracture toughness (MPa m”3 33 60 100
Critical crack depth (mm) 0.5 I .6 4.1

what appears clearly from the above results is that damage tolerance improves with increased
fracture toughness.

3.2. Final recommendations
The analyzed failures show clearly that the usual requirements for prestressing bars-i.e., yield
strength, ultimate tensile strength and ductility-are not enough to warn against brittle failures, if
the risk of damage has to be considered. In this case study, the mechanical properties (recorded in
Table 2) were higher than those required by the standards, and in spite of this, fracture occurred at
very low loads--0.3FR and 0.46FR-due to damage in the bars.
The risk of such accidents would be greatly reduced, or even avoided, if the fracture toughness
of the bars were measured (or known) and an estimation of the critical crack sizes made, by a simple
exercise of damage tolerance as shown in this paper. For the scheduled working load-0.60FR = 780
kN-the critical sizes for different toughness are given in Table 5.
These values are indicative of the defect size the designer can assume in different working
scenarios. Clearly, cracks are more dangerous than notches or pits, even though cracks are less
frequent. Nevertheless, cracks can develop from notches under repeated loads, by fatigue, or in
aggressive environments, due to stress corrosion cracking for example.
Summing up: damage tolerance procedures can be used profitably as a complementary design
criterion in prestressing with steel bars. The fracture toughness should be required as an additional
mechanical property that can be measured according to well established standards. Knowledge of
the toughness of the prestressing bars may be helpful to the designer and builder to compare, select
or reject different batches.
Acknowledgement-The authors gratefully acknowledge financial support from the Spanish Department for Industry
(Ministerio de Industria y Energia) under grant 95.0091 .OP.O2.01.

REFERENCES

1. ASTM E 399-83, Standord Test Method for Plane-Strain Fracture Toughness of Metallic Materials, 1983.
2. ASTM E 1304-89, Standard Test Method for Plane-Strain (Chevron Notch) Fracture Toughness of Metallic Materials,
1989.
3. ASTM E 813-88, Standard Test Methodfor Jlc, a Measure of Fracture Toughness, 1988.
4 Astiz, M. A., PhD thesis, Universidad Politknica de Madrid, Escuela de Ingenieros de Caminos. 1976.
5. Astiz, M. A., International Journal of Fracture, 1986,31, 105-123.
6 Astiz, M. A., Elices, M., Morton, J. and Valiente, A,, Society of Experimental Stress Analysis (SESA), Michigan
Conference, W.S.A., 198 1, pp, 211-282.
I Levan, A. and Royer, J., International Journal of Fracture, 1993, 61,71-99.
8 Elices, M., in Fracture Mechanics of Concrete: Structural Application and Numerics/ Calculation, ed. G. C. Sih and A.
DiTommaso. Martinus Nijhoff, 1985.