numero25

A. Spagnoli et alii Frattura ed Integrità Strutturale, 25 (2013) 94-101; DOI: 10.3221/IGF-ESIS.25.14 94 Special Issue: Characterization of Crack Tip Stress Field On a kinked crack model to describe the influence of material microstructure on fatigue crack growth Andrea Spagnoli, Andrea Carpinteri, Sabrina Vantadori Department of Civil-Environmental Engineering & Architecture (DICATeA), University of Parma A BSTRACT . Threshold condition and rate of fatigue crack growth in both short and long crack regime appear to be significantly affected by the degree of crack deflection. In the present paper, a theoretical model of a periodically-kinked crack is presented to describe the influence of the degree of crack deflection on the fatigue behavior. The kinking of the crack is due to a periodic self-balanced microstress field having a length scale, d . By correlating the parameter d with a characteristic material length (e.g. average grain size in metals, maximum aggregate dimension in concrete), the possibility of using the present model to describe some experimental findings related to crack size effects in fatigue of materials is explored. Well-known experimental results concerning two different situations (fatigue threshold and fatigue crack growth in the Paris regime) are briefly analysed. K EYWORDS . Kinked crack; Crack size effect; Fatigue crack growth; Fatigue threshold; Microstress field. INTRODUCTION nder fatigue loading, cracks in both brittle and ductile materials tend to deflect because of far-field multiaxial stresses, microstructural inhomogeneities (grain boundaries, interfaces, etc.), residual stresses, etc. Threshold condition and rate of fatigue crack growth in both short and long crack regime appear to be significantly affected by the degree of crack deflection [1]. This might be induced by the fact that the value of the near-tip Stress Intensity Factor (SIF) of kinked fatigue cracks can be considerably different from that of a straight crack of the same projected length. In the case of bidimensional elastic problems, analytical solutions for SIF of kinked cracks are available in the literature [2- 7]. Some of such results have been used to gain a quantitative understanding of the relation between fatigue crack growth rate and the degree of crack deflection in the fatigue crack path (e.g. see Ref. [8]). A description of actual irregularities of kinked crack surfaces has been carried out by using the fractal geometry [9]. Successful applications of the fractal geometry to size effect-related fatigue problems have been proposed by the present authors in the past few years [10-16]. In this paper, a theoretical model of a periodically-kinked crack is discussed in order to describe the influence of the degree of deflection on the fatigue behavior. The kinking of the crack is due to a periodic self-balanced microstress field having a length scale, d [17]. By correlating the parameter d with a characteristic material length (e.g. average grain size in metals, maximum aggregate dimension in concrete), the possibility of using the present model to describe some experimental findings related to crack size effects in fatigue of materials is explored. Well-known experimental results concerning two different situations (fatigue threshold and fatigue crack growth in the Paris regime) are briefly analysed. U