Issue 35

A. Tzamtzis et alii, Frattura ed Integrità Strutturale, 35 (2016) 396-404; DOI: 10.3221/IGF-ESIS.35.45 397 material properties in the HAZ area. In the HAZ fatigue crack growth rate is influenced by the inhomogeneous overaged microstructure [11-13]. In [14] it was shown that overaging of 2024 material has significant impact on the fatigue crack growth behavior of the alloy. A relevant mechanism of 2024 alloy influenced by overaging [14], which is associated with the material’s fatigue crack growth rate is cyclic strain hardening at the crack tip. In studies [15-17], cyclic strain hardening has been linked analytically and experimentally to the closure levels of the advancing crack and hence the rate of its propagation. This dependency has been exploited in the fatigue crack growth analysis, to include the effect of local material properties on FCG with the variation in cyclic strain hardening behavior at different locations in the HAZ. The model assumes LCF conditions at the crack tip and considers incremental crack growth under fatigue loading. The results obtained analytically are compared with experimental fatigue crack growth data on overaged 2024 aluminum alloy simulating different local properties and microstructure within the HAZ. C RITICAL ENERGY DISSIPATION FOR CRACK GROWTH n the proposed model crack growth occurs incrementally after a critical number of cycles ΔΝ. The crack growth increment Δr is equal to a material element with width Δr at the crack plane (Fig. 1). Based on these assumptions, a crack propagation rate can be calculated from equation: da r dN    (1) It is assumed that the material element at the crack tip is subjected to low cycle fatigue conditions [5-9] with an average constant plastic strain range Δε pm . Under cyclic straining material failure occurs when in a stabilized hysteresis loop a critical amount of energy W f is accumulated in the material after a finite number of loading cycles Ν f . By assuming that the energy per cycle ΔW is nearly constant throughout the fatigue test, the total plastic strain energy until fracture may be approximated by [18]: 1 2 1 f f A p f n W W N N n                 (2) with σ Α the stress amplitude and n’ the cyclic strain hardening exponent. The critical amount of energy W f for failure of the material volume is estimated from the strain energy density [SED] theory [19-20]. In the SED criterion the critical strain energy density function dW/dV is associated with the critical distance r c from the crack tip for onset of crack initiation and the critical strain energy density factor S c in the form: c c c S dW dV r        (3) For plane stress the strain energy density factor becomes:   2 1 2 cr c v K S     (4) Assuming that the energy for fracture can be approximated by the critical strain energy per unit volume (dW/dV) c from the SED criterion in Eq. (3), W f in Eq. (2) can be derived with the use of Eq. (3) and the critical number of cycles N f for a crack increment Δr = r c can be obtained from (2) by:       2 1 1 4 1 cr f c p v n N r n              (5) I