PSI - Issue 17

D. Camas et al. / Procedia Structural Integrity 17 (2019) 894–899 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

895

2

wake that acts as a shield protecting the crack tip from the nominal load applied. Therefore, the nominal load, the geometry and the contact between the crack flanks affects the crack growth rate.

Nomenclature a

crack length

b

specimen thickness

K max

Maximum stress intensity factor

Dugdale’s plastic size

r pD

R Stress ratio

Constraint factor

In the literature, a great amount of analytical, experimental and numerical work that support the crack closure concept can be easily found, although, it is fair to say that some researchers are skeptical to this phenomenon (Vasudevan et al. (2001), Sadananda and Vasudevan (2003)). Since the very beginning, numerical models have been used to analyze plasticity induced crack closure. Most of them were bi-dimensional analysis considering plane stress or plane strain states (Antunes et al. (2004)). These models allow different analysis as the effect of the compressive loads (Antunes et al. (2015)), overloads (Borrego et al. (2012)), variable amplitude loadings (Antunes et al. (2016)) or can be used to check empirical models (Antunes et al. (2015)). These numerical analyses are dependent on many different numerical parameters as the mesh size, the contact simulation, the plastic wake previously developed, the allowed penetration, the material modelling behavior, and so on. These parameters have been previously analyzed in some papers in which they were optimized to stabilize numerical results with the least numerical effort (Antunes et al. (2015), Gonzalez-Herrera and Zapatero (2005)). Some three-dimensional models can be found in the literature as those by Chermahini and Blom (1991), in which a center-cracked specimen was analyzed, and Gonzalez-Herrera and Zapatero (2008) in which a CT aluminum specimen was considered. Through these analyses, it is possible to determine the stress and strain fields as well as the crack closure and opening values, not only at the surface and at the mid-plane, but all along the thickness. Besides, bi-dimensional analyses only consider two binary states, or plane strain or plane stress, when reality is slightly different. When a mechanical component is under a certain load, there is a certain degree of plane stress or plane strain state (Lopez Crespo et al. (2018)). Another parameter that can be considered in these analyses is the crack front curvature. Bi-dimensional analyses consider an ideal straight crack front through the thickness, while it is well known that a certain curvature can be found in the crack front when the crack grows under cyclic loading conditions (Oplt et al. (2019)). This curvature has influence in the stress and strain fields around the crack front (Camas et al. (2012)). More recent papers, as those by Gardin et al. (2016), analyzed the influence of the crack front curvature in the plasticity induced crack closure results considering CT specimens of an austenitic stainless steel. These three-dimensional analyses usually consider the parameters optimized from bi-dimensional models. The present computational power allows for thorough studying of the influence of the numerical parameters on the crack opening and closure results considering three-dimensional models. The authors of the present study previously analyzed the influence of the minimum element size at the crack front considering three-dimensional models updating the previous recommendation stablished from bi-dimensional analyses (Camas et al. (2018)). The numerical models face an issue related with the validation with experimental data. Oldest techniques used to offer data obtained far from the crack tip. Digital image correlation has been recently used to validate numerical models (Camas et al. (2016), Camas et al. (2017)), but this technique only offers information of what is happening at the surface of the specimen. However, comparing these numerical and experimental results can validate the numerical models. The analysis of the crack growth scheme is a key issue. The number of loading cycles numerically applied never can reach the real one. The computational cost would be unapproachable. The usual strategy consists in applying a