PSI - Issue 7

Marton Groza et al. / Procedia Structural Integrity 7 (2017) 438–445 M. Groza et al. / Structural Integrity Procedia 00 (2017) 000–000

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4. The Defect Stress Gradient approach

The DSG approach was created by Nadot and Billaudeau (2006) for the multiaxial fatigue limit prediction of defective metallic materials. It has been further developed by Vincent et al. (2014), incorporating the general analytical solution of Eshelby (1957) for local stress computation near the defects, and has been successfully applied on high cycle fatigue calculations for numerous metallic materials, such as steel, aluminum and titanium. The approach characterizes the effect of the defect with the material parameter a ∇ and an estimated gradient function containing the stress difference between the hot-spot (max. stress value at the defect, max σ ) and the remote stress 0 σ divided by the size parameter area :

.max area σ σ − max Cr

.0

Cr

σ σ =

−

≤

σ

2, Cr h α σ = + J a

β

a

(1)

with

∇

,max

.max

Cr

DSG Cr

Cr

area , the max area parameter is in the current study to represent the defect size, for reasons detailed in DSG k utilization factor type quantity is used to represent the safety against crack initiation:

Instead of

Chapter 3. The

DSG DSG Cr k σ β = . Fig. 2. shows the interpretation of the far field stress

. Cr σ ∞ the hot-spot stress

.max Cr σ , the stress at

area distance

from the defect .0 Cr σ in case of homogenous (Fig. 2a.) and inhomogeneous (Fig. 2b.) stress field (or in other terms; in the presence of a structural level stress gradient). In case of nearly spherical defects (ellipsoids with a low aspect ratio) .0 . Cr Cr area σ σ ≅ , since area is a good estimation of the decay length for the local stresses. . Cr area σ , and the stress without the defect

4.1. Parameter identification and model validation

The Cr α and Cr β parameters of the Crossland equivalent stress were identified on defect free materials from three different fatigue limits, the process is shown in Fig. 3a. The a ∇ parameter of the DSG approach was identified on the R0.1 Kitagawa curve of the given NCI material. During the identification process the different defects were considered to have spherical shape, and therefore to have a theoretical stress concentration effect on the tensile stress component of 2,05 (Vincent et al. 2014). Fig. 3b. shows, that this leads to a good description of the fatigue limit as function of the defect size for defects larger than 400 m µ . The identified parameters are 1,13 ( ) Cr α = − , 255 ( ) Cr b MPa = and 209 ( ) a m µ ∇ = . In order to evaluate the identification process, the simulated Kitagawa curves are compared with the experimental results for R-1 tension and torsion, the results are plotted in Fig 3c-d. The calculations fit the experimental data for defects larger than 400 m µ well. Finite Element (FE) calculations - which can be considered as standard way for structural analysis in today’s industry- were conducted with ANSYS Academic Research Mechanical 17.5 to determine the elastic stresses at each point of the component. The surface defects were introduced in the calculation process later on, to model the industrial workflow. The localized effect of the surface defects was simulated with elastic and elastic-plastic FE-submodels and analytical calculations. The analytical EIM solution from Eshelby (1957), first applied by Vincent et al. (2014) on a similar problem, computes the disturbance in the homogenous elastic stress field inside an infinite body caused by an elliptical inclusion. 5. Calculations

5.1. Analysis example

As analysis example a complex geometry under cyclic bending loading was chosen, with the aim to investigate the limitations of a “real-world” application of the DSG approach. With the thorough analysis of three surface defects (nominated as D1-D3, Fig. 4a.) we aim to gather experience in order to establish a general assessment methodology, possibly in a much more simplified form. Two bores were fixed with rigid body elements in the 5 directions of the