PSI - Issue 17

J.P. Pascon et al. / Procedia Structural Integrity 17 (2019) 411–418 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

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1. Introduction Damage-tolerant designs admit the pre-existence of defects and small cracks that propagate under cyclic loading and may lead to the failure of structural parts. Despite the relevance of researches on fatigue crack growth, little importance has been given to the analyses involving negative load ratios. Moreover, contradictory results have been reported upon the possible influence of the compressive loads on the growth of the crack. Dinda and Kujawski (2004) assume that the rate of crack growth is not affected by the compressive part of the cycle, whereas Mehrzadi and Taheri (2012) have shown that the compressive stresses play a critical role on fatigue crack growth. Furthermore, Silva (2004) has questioned the crack closure concept proposed by Elber to explain the cycle asymmetry effects with respect to its applicability under negative load ratios. Series 6XXX (Al-Mg-Si) are heat-treatable aluminium alloys showing good corrosion resistance and weldability, being often selected for applications in which the structure must be able to sustain occasional strikes or overloads. In a previous work, Espezua et al. (2014) presented a predictive model of fatigue crack growth in Al-Mg-Si alloys under positive and negative load ratios assuming elastic-ideally plastic material behaviour. Besides, Torres et al. (2017) delivered experimental results showing significant differences between pulsating ( R = 0) and fully reversed loading ( R = -1) fatigue crack growth behavior of 6005-T6 alloy. In that work, the simplified stress analysis assuming an elastic-ideally plastic material behavior indicated that, instead of crack closure, the explanation to the higher fatigue crack growth ratios observed for R = -1 could be given by the stress field ahead of the crack tip. The accurate knowledge of the stress-strain state near the crack tip is therefore important for damage accumulation analysis and residual life prediction. In the present paper, a numerical model via finite elements is proposed to determine the stress-strain field ahead of crack tips in plates under cyclic loading in the elastoplastic regime. The analysed centre-cracked plate simulates a M(T) specimen made of 6005-T6 alloy. In the context of finite element models, the accuracy of the stress and strain fields around the crack tip plays a major role in the correct crack growth prediction. In the work of Benz and Sander (2015), for example, the focus is on the plastic deformation mechanisms at the crack tip, as well as the crack closure behavior. In that study, the stress distribution around the crack tip is initially determined via linear elastic analysis for the specific case of a M(T) specimen and, after that, is updated according to the elastoplastic model, which includes a nonlinear kinematic hardening rule. Regarding the mesh, four- node isoparametric finite elements with an element size of 3 μm are employed around the crack growth region. The crack growth is modeled by releasing a node every two load cycles. Following the study of Benz and Sander (2015), the present authors have adopted a more enriched numerical model, in which two layers of solid tetrahedral elements of quadratic order are employed. The material behavior is described by a 3D elastoplastic model with nonlinear isotropic hardening model without imposing plane stress conditions, as performed in the aforementioned work. 2. Material and methods The material used in this work is aluminum alloy 6005 produced by direct-chill, homogenized and extruded to billets that were heat treated to the T6 temper. The chemical composition of the alloy is 0.65 Si, 0.35 Fe, 0.3 Cu, 0.5 Mn, 0.6 Mg, 0.3 Cr, 0.2 Zn and 0.1 Ti (wt. pct.). The adopted solubilization and ageing treatment lead to a material condition with 112 HV hardness, 289 MPa tensile strength and 66 GPa Young’s modulus . In order to provide a more accurate response for the numerical simulations, the cyclic stress-strain curve was determined from the low cycle fatigue test results presented by Laurito-Nascimento et al. (2013). The tests were performed at room temperature in laboratory air using a servo hydraulic machine under strain control and fully reversed strain amplitudes within the range 0.4 to 1.2%. The wave shape was triangular with constant strain rate of 0.005 s -1 . During the tests, data acquisition was performed in such a way that each recorded hysteresis loop contained 200 experimental points. Figure 1 shows the half-life stress-strain loops collected from the tests and translated to a common point of maximum compressive stress. The elastic and plastic material coefficients were determined from the experimental data assuming isotropic hardening governed by Swift's law.