C. Gandiolle et alii, Frattura ed Integrità Strutturale, 35 (2016) 232-241; DOI: 10.3221/IGF-ESIS.35.27 233 Once a crack is nucleated, depending on the loading amplitude, it will propagate or reach a crack arrest condition. The prediction of crack arrest was addressed by Araujo et al. [3] applying a short crack regime strategy. Crack propagation and crack propagation rate are usually addressed using Paris law. Numerous models exist to predict the lifetime of assemblies. Some consider that total lifetime can be approximated by the crack nucleation life and that crack propagation is negligible [4]. Others consider only the crack propagation phase [5]. Some authors also estimate the total lifetime as the sum of the crack nucleation life and the crack propagation life [6]. In the frame of this research work we investigated how to predict the crack propagation rate and the crack arrest condition of fretting fatigue test subjected to variable loading conditions. E XPERIMENTS Materials he studied material is a 32C1 steel (E=200GPa, ν=0.3). It shows low yield stress and is thus described by an elastic-plastic law. Because this study was conducted for industrial purposes, the industrial monotonic material law with isotropic hardening was used to describe the hardening of the material. Fig. 1 plots the monotonic hardening of the studied steel which was obtained from a simple tensile test and normalized by the yield strength σ y,flat . The material was tested under various fretting fatigue conditions, using a cylinder/plane contact configuration, with a cylinder of R=4.6 mm radius applied with a normal force P on the flat material. The cylinder was a FM35 steel (E=200GPa, v=0.3), but with higher yield stress (σ y_cylinder >> σ y,flat ), to investigate cracking on the plane specimen only. A similar monotonic elastic-plastic law with isotropic hardening was considered to describe its behavior (Fig. 1). Figure 1 : Monotonic elastic-plastic material laws of the flat and cylinder components (R=4.6mm). Conventional 4 points bending tests were used to identify the crack propagation law of the study material. It follows Paris law: m ΔKC dN db . (1) With b, the crack length and N the number of cycles. The parameter C and m were really close to the British Standard (BS) parameters disclosed in Tab. 1. The crack arrest condition was obtained for ΔK th_10-7 =ΔK 0 =5.7 MPa.m 1/2 , and K IC =212 MPa.m 1/2 . As several high stress ratios were applied, an effective stress intensity factor range ΔK eff was preferred to describe the overall crack propagation behavior. ΔK eff was established considering a simplification of Elber approximation proposed by V. Gros [7]: T

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