Issue 33

F.V. Antunes et alii, Frattura ed Integrità Strutturale, 33 (2015) 199-208; DOI: 10.3221/IGF-ESIS.33.25 200 parameter, the stress intensity factor range,  K. However, the large amount of work developed showed that other parameters influence da/dN, like stress ratio or load history. Christensen  2  proposed the concept of fracture surface interaction leading to a decrease of stress intensity at the crack tip and to an increase of fatigue life. Elber  3  discussed the concept in terms of fracture mechanics parameters, promoting a strong research effort into the mechanisms and phenomena associated with fatigue crack closure. Ritchie et al  4  and Suresh  5,6  identified the main closure mechanisms, which are plasticity induced crack closure (PICC), oxide-induced crack closure and roughness induced crack closure. According to Elber’s understanding of crack closure, as the crack propagates due to cyclic loading, a residual plastic wake is formed. The deformed material acts as a wedge behind the crack tip and the contact of fracture surfaces is forced by the elastically deformed material. Crack closure concept seemed to be able to explain the influence of mean stress in both regimes I and II of crack propagation  7  , the transient crack growth behaviour following overloads  8  , the growth rate of short cracks  9  and the effect of thickness  10, 11  , among other aspects. This success in explaining different issues of fatigue crack propagation has been used to validate the crack closure concept. Pippan and Grosinger  12  demonstrated that crack closure is not only important under small scale yielding conditions, it is also essential in the regions of low cycle fatigue. The effect of specimen geometry on crack closure has been accounted for using the T-stress concept  13  . Complementary concepts have been proposed by different authors. Dai and Li  14  considered that the plastic deformation modifies the elastic stress field and defined a plasticity-corrected K to account for the effect of plasticity. This K pc was proposed as a new mechanical driving force parameter for predicting FCG rate, able to explain important phenomena associated with the plastic zone around a fatigue crack tip, such as the effects of load ratio R, single overload and the FCG behavior under cyclic compression. Ranc et al.  15  quantified the effect of heterogeneous temperature on stress intensity factor. The energy dissipated in the cyclic plastic zone ahead of crack tip produces thermal expansion of the material which affects the stress field. The stress intensity factor has to be corrected by a negative value which reduces the crack driving force. Pokluda  16  states that the effective stress field at the crack tip is a superposition of remote and local SIFs. The internal stresses created by dislocation configurations and secondary phases are to be considered as an important additional factor affecting the crack propagation rate in fatigue. Christopher et al.  17, 18  proposed a novel mathematical model of the stresses around the tip of a fatigue crack, which considers the effects of wake contact and compatibility-induced stresses at the elastic–plastic boundary. Four parameters were considered to characterize the stress field: an opening mode stress intensity factor K F , the shear stress intensity factor K S , the retardation stress intensity factor K R , and the T-stress. K R characterizes the effect of crack tip shielding arising due to plasticity both at the crack tip and in the wake. However, several questions have been raised questioning the crack closure concept, therefore the importance and even the existence of crack closure effect have been questioned by different authors. Donald and Paris  19  and Kujawski  20  introduced the concept of partial crack closure, which indicates that the contact of crack flanks at some distance from crack tip has a relatively low effect on FCGR. Some researchers suggested that closure can only occur under plane stress  21  , while others believe that it may not occur at all. Since 1993 Sadananda and Vasudevan  22-24  have advocated that because the closure occurs behind the crack tip, it has a rather limited effect on the damage process, which takes place at the ‘process zone’ in front of the crack. According to these researchers the approaches to fatigue behavior based on crack closure (i.e. on what happens behind the crack tip) should be replaced by approaches based on what happens ahead of the crack tip. They argued that closure effects on FCG behavior have been greatly exaggerated, and suggested that the fatigue crack propagation rate is controlled by a two parameter driving force, which is a function of the maximum stress intensity factor, K max , and total stress intensity factor range,  K. These two parameters account for both the applied load and the residual stress contributions. Kujawski  25  proposed a new driving force parameter for crack growth:  K effK =(K max  K + ) 0.5 , being  K + the positive part of  K. He found that without using the crack closure concept, it is possible to explain the stress ratio effect, even better than using this concept. However, Noroozi et al.  26, 27  pointed out that these models are strictly empirical and cannot explain the influence of the compressive part of the load history on fatigue crack growth. They formulated a unified two-parameter model to correlate K max and  K with the actual elastic- plastic crack tip stress–strain field. In their investigation, the difference in the stress–strain concentration at the crack tip associated with the compressive part of the loading cycle was taken into account. Clearly there is no general agreement among researchers regarding the significance of closure concept on fatigue crack behavior. The contact of crack flanks is accepted by all, because it was observed numerically and using experimental techniques, namely, digital image correlation  28  , x-ray diffraction  28,29  , potential drop  30,31  and SEM  31  . The great disagreement is about the effect of this contact on fatigue crack growth. In fact, the direct link between crack closure and crack tip fields has not been totally exploited. This might be due to experimental difficulties in measuring quantitative