PSI - Issue 23

Hynek Lauschmann et al. / Procedia Structural Integrity 23 (2019) 107–112 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

108

2

v x y

crack growth rate

index numbering locations of 3D reconstructions of the morphology of crack surface

log( v ) 1. Introduction

Conventional fractography is strongly dependent on the experience of the person analysing fracture surfaces. Objective methods arrived with quantitative fractography, when the characteristic features were described quantitatively, e.g., Chermant and Coster (1979), Banerji (1988). However, with 2D images the source of information is image brightness which is not unambiguously related to fracture morphology. It is now possible to digitalize the morphology of fracture surface in 3D, e.g. Spear et al. 2014, Khokhlov et al. (2012), Merson et al. (2018), Kaplonek et al. (2016), and automated procedures may be applied to characterize the fracture surface fully objectively. Confocal laser microscopy and scanning electron microscopy (SEM) combined with electron backscatter diffraction (EBSD) was employed by Merson et al. (2017) to quantitatively characterize the relation between standard surface morphology parameters (roughness, depth of dimples, angles between facets) and the microstructural parameters (grain size, grain orientation). The existence of such dependencies has led other authors to the idea, that it would be beneficial not only to automatically characterize a surface but also to automatically choose the morphological parameters that should be studied. In order to classify the type of the fracture, Bastidas-Rodriguez et al. (2016) have used fractal analysis together with artificial neural networks (ANN) and support vector machine (SVM). Fractal analysis has also been applied in fractography by Sahu et al. (2016) and Xu et al. (2015). For the reconstitution of the history of fatigue crack growth, textural fractography was developed - an automated analysis of textural features in SEM images of fracture surfaces, Nedbal et al. (2008), Lauschmann and Goldsmith (2009). Recently, the methods of textural fractography have been applied on 3D fracture morphologies. In this work, a novel approach is provided, using more than 1600 parameters of selected profiles and 3D reconstructions in rectangular areas. Statistical classification is used for relating fracture parameters with fatigue crack growth rate. 2. Methodology Features of a fracture surfaces in 3D. A set of 1662 features of fracture surfaces was defined, composed of three types of characteristics:  Global areal parameters: surface roughness factor, surface area, elevation relief ratio.  Line profile parameters: height parameters (height, maximum, maximum peak height, maximum valley depth, mean height of elements, total height), root mean square deviation and slope, mean width of profile elements.  Local (point) parameters: curvatures (vertical, horizontal, maximal, mean, minimal, difference, Gauss, plan, horizontal and vertical excess, total ring, total accumulation), slope parameters (gradient, steepness, direction, gradient factor, Hengl aspect), unsphericity, rotor . Line profile and point parameters are statistically evaluated producing the mean value, standard deviation, skewness, kurtosis, and quantiles related to probabilities P = 5, 10, 20, 50, 80, 90, 95 %. Relating features and crack growth rates. Due to its range and distribution, crack growth rate v = da / dN is transformed for computations as y = log( v ). According to the context, the term "crack growth rate" means transformed value. Statistical classification is a general instrument of artificial intelligence , e.g. Schlesinger and Hlaváč (2002). It consists in assessment of given objects on the basis of their numerical features to one of classes of a pre-defined set. Here classification will be applied to estimation of crack growth rate v for localities of crack surface on the basis of their characteristics. In this case, the finite set of classes is replaced by an infinite set represented by a continuous index value. Let us divide input data into two sets - training and testing one. For testing data, no suppositions are done. On the contrary, almost in all cases, training data are connected with laboratory specimens tested under fully defined conditions. Therefore, we can suppose general stochastic dependences of crack growth rate y as well as 3D features f i , i = 1,2,.., n f , on the position in fracture surface along crack length. This position may be expressed by the index numbering localities of 3D reconstruction, x = 1,2,..., n . Let 2 ( ), ( ) and ( ) i i y x f x s x are suitable regression functions