**Published:** Jan 1999

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**Source: **STP1332-EB

The paper presents a further development of a fatigue crack growth theory based on an energy approach first published by the author in 1981 [*1*] and later revised in 1996 [*2*]. In an ideally elastic material containing a crack the only mechanism through which energy can be absorbed during a virtual crack extension is that associated to the creation of new free surface. It is an “in-out” situation in that a crack of a given length *2a* under a stress state σ either becomes unstable or stays like it is. At variance, in a real elastic-plastic material the energy absorption rate *R* derives mainly from the energy stored ahead of the crack tip as plastic strain energy. The resistance *R* is no longer represented by a constant term, but becomes a rather complex function of crack length, increasing as the crack grows. The consequence is that even though a certain combination of crack size *2a* and stress σ does not produce instability, yet there is sufficient energy in the system to drive the crack to a point where the driving force *b* is equal to the resistance *R* and the crack stops. Unloading the system and reloading it, the crack grows by fatigue indicating that the previous condition *b* = *R* is no longer satisfied. If this happens, it is because the volume that yields ahead of the crack tip is not capable during the reloading to absorb energy with the same rate as before. This forces the crack to grow further to regain the loss of energy absorption rate through the yielding of new material and to establish again the equilibrium between *b* and *R*. The author has related this lack of material capability to develop the same energy absorption rate in any of the following cycles to a shake-down effect that takes place in the plastic enclave. In each cycle, the loss of energy absorption rate is a fraction of the elastic one. The author has related this lack of material capability to develop the same energy absorption rate in any of the following cycles to a shake down effect that takes place in the plastic enclave. In each cycle, the loss of energy absorption rate is a fraction of the elastic one. Based on this hypothesis and on the assumption that the maximum fatigue crack growth can be inferred from the extension of the stretch-zone developed at the crack tip at the moment when the material starts to tear in a monotonic loading test, i.e., at *JIc*, a fatigue crack growth equation is obtained that relates the growth rate Δ*a* not only to the stress intensity factor excursion Δ*K*, but also to the toughness *KIc* of the material, through an exponent *n*, ranging from 2 to 4, which depends on the shape of the material *J-R* curve. The theory and the equation also explain why short cracks shall grow faster than large ones and actually define what shall be considered as a real short crack. It is also explained why the fatigue crack growth rate depends on the ratio between the minimum and maximum applied stress and is practically the same in any material independently of its yield stress and toughness.

**Keywords:**

energy release rate, driving force, energy absorption rate, plastic constraint, stretch zone, crack closure

**Author Information:**

Milella, PP *Professor of machine design, University of Cassino, Dr. in Nuclear Engineering, Agenzia Nazionale per la Protezione dell'Ambiente (ANPA), Rome,*

**Committee/Subcommittee:** E08.06

**DOI:** 10.1520/STP14966S