PSI - Issue 5

M. Dabiri et al. / Procedia Structural Integrity 5 (2017) 385–392 M. Dabiri et al. / Structural Integrity Procedia 00 (2017) 000 – 000

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1. Introduction

The presence of geometrical discontinuities is inevitable in engineering components and structures. Experimental results show that the effective critical stress could have a lower value than the maximum stress or stress range at the notch root depending on the notch radius. This means that even stresses greater than the maximum nominal stress could exist at the notch root without causing failure. Different approaches were proposed in the literature to account for this size effect and define the effective stress/strain at the notch root required for the fatigue-life assessment of notched components. They can be broadly divided into the following groups: methods that consider the stress or stress range at a particular point (slightly distant from the notch tip) on the stress distribution, such as the well-known proposal by Peterson (Peterson, 1959). These proposals for the effective distance, however, are not supported by any physical background, and their definition depends only on the material and its mechanical properties. Other approaches named by Taylor (Taylor, 1999) as the line (such as the proposals by Neuber (Neuber, 1958) and Siebel and Stieler (Siebel & Stieler, 1955)), area, and volume (equivalent to area in 2D) methods make the same assumptions as point methods with different definitions of the effective stresses. These are the average stresses along a line distant from the notch root for the line method and over the specific area for the area method. Local strain analysis at the notch root based on the similitude concept and utilizing the numerical methods is another technique suitable for notch analysis. However, its accuracy could be affected by the approach utilized by the user and by the geometrical features of the component. That is, this method is able to predict accurate strain values at the notch root only if the detailed elastic-plastic finite element (FE) analysis using the cyclic material response is performed. Conducting the linear FE analysis equipped with the approximations, such as Neuber’s rule, to evaluate the strain could diminish its accuracy and lead to the incorrect estimation of critical spots in components, including stress raisers with different configurations (Taylor, et al., 2000). This could happen because the linear models coupled with empirical approximations do not allow the stress/strain distributions at the notch root because of plasticity. In addition, it has been shown (Fatemi, et al., 2004) (Dabiri, et al., 2016) that the accuracy of this method can be affected by notch sharpness. Alternately, the elastic-plastic reformulation of the Theory of Critical Distance (TCD) developed by Susmel and Taylor (Susmel & Taylor, 2010) (Susmel & Taylor, 2015) was proven to be an effective method for eliminating the effect of geometrical notch features on the strain analysis of the notches. Taking advantage of elastic plastic numerical models, this method is able to estimate a material characteristic length, which is a material constant (in a low cycle fatigue regime), regardless of the geometrical configuration of the notch. In this study, a series of notched round specimens made of a direct-quenched ultra-high-strength steel (UHSS) were investigated to check the accuracy of the available notch analysis methods for fatigue analysis of the material under investigation. A number of analytical approximations, such as the linear rule, Neuber’s rule (Neuber, 1961) and the strain energy density (SED) (Molski & Glinka, 1981) method, are utilized in both their standard and modified forms to account for plane stress/strain conditions. Nonlinear elastic-plastic finite element analysis was performed simultaneously to assess the stress-strain at the notch root and their distribution around it. Because most of the methods (especially the numerical models) require the cyclic stress-strain curve (CSSC) to calculate the stress-strain at the notch root, the results of strain-controlled fatigue tests conducted on the material in question, along with the obtained fatigue and cyclic properties (Dabiri, et al., 2016), were used in modelling. The TCD method was also applied to scrutinize the capability of this method for the fatigue analysis of notched components made of UHSS. The results of the predictions were compared with the experiments.

2. Material

The material used in this study is a direct-quenched ultra-high-strength steel (Strenx® 960 MC). The monotonic tensile and cyclic properties of the material are given in Table 1.

Table 1. Monotonic, cyclic and fatigue properties of Strenx® 960 MC R P0.2 (MPa) S u (MPa) E (GPa) σ ' y (MPa) K' (MPa) n'

σ ´ f (MPa) b

ε ´ f

c

1040

1240

197

833

1400.3

0.084 1636.5

-0.07 0.5 -0.65