PSI - Issue 17

M. Carrera et al. / Procedia Structural Integrity 17 (2019) 872–877 M. Carrera, P. Lopez-Crespo, P.J. Withers / StructuralIntegrity Procedia 00 (2019) 000 – 000

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1. Introduction

Simulations and experimental characterisation of materials have become a real necessity in modern industry. Improved predictions of the failures involving fatigue cracks in the bulk of materials can be obtained by refining our understanding of the plastic region developing ahead of a growing crack. In this context, a number of research works have focused on the plastic zone of fatigue cracks. For example, Park, Kim and Lee (1996) studied how the geometry surrounding a crack influenced its growth. They were able to characterise the fatigue crack growth rate, FCGR as a function of sample thickness, t, and evaluated the reduction in the FCGR as t increases for two different materials (304 stainless steel and Inconel 718). It was then considered that plastic zone size is a meaningful measure for FCGR predictions, in conjunction with applied load, thickness and crack closure phenomena. The relation between the plastic zone and the FCGR was also studied by some other authors. Tekin and Martin (1989) stud ied how, for a certain value of ΔK, the plastic zone size is a function of the square root of FCGR. A Ni alloy plastic zone was measured using Selected Area Channelling Patterns. Ould Chikh, Imad and Benguediab (2008) focused on 12NC6 steel, and the relationship existing between absorption energy and FCGR inside the plastic zone of the sample. Relatable is also the work made by Uguz and Martin (1996), in which several factors related to plastic zone size were revised, for fatigue and monotonic loads. It was established how the fracture toughness is related to the plastic zone size on the crack tip. However, nowadays, in order to characterize common industrial materials, it is necessary to apply different methods which give us a more practical approach. Methods such as digital image correlation (Sutton, Orteu and Schreier, (2003)) allow the surface of the material to be tested both quasi-statically (Mokhtarishirazabad et al. , (2017)) and dynamically (Mokhtarishirazabad, Lopez-Crespo and Zanganeh, (2018)). Vasco-Olmo, Díaz and Patterson (2016) measured strain maps obtained from this method for a fatigue cracked CT sample. Westergaard, Christopher-James-Patterson (CJP) and other analytic models were validated by this work. Other example of surface method is thermoelasticity. Díaz, Yates and Patterson (2004) made use of this method to observe how well it can characterise welding residual stresses and crack closure effects. Cyclic stress fields allowed also determining the stress intensity factor using this method. Although previous techniques are meaningful studying different materials, they do not give any information about what happens in the bulk of the sample. Such through-thickness information is normally assessed by numerical methods. For example, Paul and Tarafder, (2013) identified numerically both the monotonic and the reverse plastic zones on a SA333 Grade 6 C-Mn steel and observed progressive accumulation of permanent strain in the cyclic plastic zone. Besel and Breitbarth, (2016) studied the thickness effect on the evolution of forward and backward cyclic plastic zones on an aluminium alloy 2024T3 and Camas et al. , (2017) observed a complex transition between plane stress and plane strain conditions accounting both for a straight and a curved crack front. Such transition was found to depend on the load level. Lopez-Crespo et al. , (2018) characterised in great detail the size and shape of the plastic zone for different thicknesses and used the average yielded areas to infer an equivalent bi-dimensional yielded area that can be used to simplify a 3D body into a 2D problem. Recently, synchrotron based techniques, including tomography and diffraction have allowed the interior of the material to be probed experimentally. Steuwer et al. (2006) and Croft et al. , (2005) were among the first authors who provided high detail bulk strain information of a growing fatigue crack. They were able to obtain crack growing results as well as strain and stress fields for an Al Li alloy similar to AA 5091, by applying tomography and synchrotron X-ray diffraction (XRD). The experimental data were also extremely useful to validate for the first time some numerical FEM results describing the bulk behaviour. These full-field diffraction maps have been useful to estimate the stress intensity factors in the mid plane of a bainitic steel with different elastic models (Lopez-Crespo, Peralta and Withers, (2018),(Lopez-Crespo, Peralta and Withers, 2019)). Steuwer et al. , (2010) were also able to extend the methodology to the analysis of overloads and measure significant compressive residual stresses both ahead and behind the crack-tip immediately following the overload event. Lopez-Crespo et al. (2015) also studied some interaction between the plastic zone and the material hardening, obtaining a good resolution of the strain maps through XRD. Recently, the competing retardation mechanisms that take place after an overload have also been quantified and separated in the bulk of different materials with synchrotron X-ray diffraction (Salvati et al. , (2017), Simpson et al. , (2019)).