text:
\section{Introduction} \label{introduction}
A common reason for the failure of mechanical components is the accumulated fatigue damage due to cyclic loading. Considerable efforts are made in the design for reliability. In industry, these efforts predominantly include experimentation and elastic-plastic numerical simulations on the component scale, which leave the material's microstructure aside. However, the microstructure significantly affects early fatigue stages, including crack initiation determining lifetime at small strain amplitudes. More specifically, microstructure-induced life variance and the exact location of crack formation are governed by the reaction of few critical grains. In the past decades, advanced experimental techniques have been developed to observe evolving plasticity under cyclic loading. Thereby, the mechanistic understanding of material degradation is continuously improved and transcribed into materials models. Simulation models help to avoid costly and time-consuming experiments and are therefore of particular interest to the industry.

The crystal plasticity finite element (CPFE) method enables modeling the elastic-plastic deformation behavior of individual grains and clusters in polycrystals. While still limited in simulation domain size, the rapid increase in computational power renders extensive fatigue CPFE calculations feasible, see \cite{boeff2016} and \cite{natkowski_determination_2021}. The transition from predicted mechanical fields to the fatigue state is enabled through metrics for crack initiation, so-called fatigue indicator parameter (FIP) formulations. For various FIP definitions, see e.g. \cite{schaefer2019b}.

\cite{manonukul2004} propose the plastic slip accumulated over each slip system as a crack initiation criterion. Based on the work of \cite{fatemi1988}, \cite{bennett2003} propose a FIP, where the irreversibility of the plastic strain and the normal stress applied on the critical slip plane is assumed to be a driving force for crack initiation.
For a discussion of different FIP formulations, it is referred to \cite{hochhalter2010}. While these approaches can predict damage location and initiation life and are supported by a growing research community, they demand microstructural characterization and experimental benchmarks. However, an established and standardized validation procedure for micromechanical fatigue simulations is not yet available.

The validation of CPFE approaches by experimental means often involves high-resolution digital image correlation (HR-DIC) in conjunction with mechanical testing. Several of these approaches were reviewed in \cite{Pokharel2014}. \cite{guan2017} investigated single and oligo crystal nickel material with a three-point beam bending under conditions of cyclic loading. They identify slip activation with SEM images and quantify developing strain fields and localization during fatigue with HR-DIC. CPFE models are applied on microstructures under consideration of the fatigue loading such that grain-by-grain comparisons of slip can be carried out. Similarly, HR-DIC at micro tensile test specimen of a polycrystalline Ni-base superalloy has been performed by \cite{eastman2018} to benchmark a CPFE model of this material. In \cite{Zhang2018} slip bands observed in HR-DIC after tensile tests yielded good agreement with CPFE simulations concerning slip trace orientations. In prior work, \cite{Zhang2016} quantitatively compared CPFE strains in a nickel alloy grain cluster with HR-EBSD after fatigue testing. A coupling between in-situ micropillar compression of a lamellar TiAl alloy and CPFE modeling is described by \cite{chen2019}.

The aforementioned approaches have in common that few grains are analyzed, implying a small statistical basis. Furthermore, fatigue experiments are mainly performed in the low cycle fatigue (LCF) regime, while the very high cycle (VHCF) regime arguably is less understood and governed by a more pronounced impact of microstructure. The literature benchmarks fatigue phenomena predominantly up to slip band emergence utilizing experimental, image correlation-derived strain fields. While representing essential validations, slip bands do not necessarily culminate in crack initiation followed by short crack propagation.

To complement these approaches, bending resonant fatigue experiments up to short crack growth are accompanied by spatial distortion-corrected EBSD scans covering the entire highly loaded mesoscale specimen surface. The correction of such an EBSD scan facilitates its accurate alignment with damage data across the whole region of interest. Therefore, the number of considered grains can be substantially increased, and the statistical basis thereby significantly improved. While similar multimodal frameworks for large specimen areas exist \cite{charpagne2020automated, chen2018high}, they, to the best of our knowledge, have not been applied to statistically validate the damage localization of computational models. Instead of attempting validation of strain fields through DIC, SEM images were semantically segmented with the help of an accordingly trained convolutional neural network (CNN) to find locations of surface plasticity and cracks, see \cite{Thomas2020}.

The resonant bending fatigue setup by \cite{Straub2015} relies on planar mesoscale specimens with optimized geometry for a large uniform stress state at the specimen surface. The highly loaded zone typically covers an area of $500\times1000\,\upmu$m$^2$ which still can be covered by CPFE simulations for the microstructure at hand. Corresponding simulations depend on well-aligned geometry, boundary conditions, and microstructure data. Furthermore, the validation requires reference damage localization maps and cyclic damage evolution information. Thus, the data registration procedure presented in \cite{Durmaz2021}, where multiple heterogeneous data sets were spatially aligned, is employed here. Namely, in-situ light optical image series, high resolution stitched secondary electron (SE2) images, and deduced damage maps were aligned with the microtexture from 2D EBSD. The registered data is used for setting up a sub-modeling approach, where the macro model comprises the whole bending beam geometry, and the available EBSD data, confined to the highly loaded region, defines the CPFE submodel within the beam geometry. The experimental boundary conditions are translated onto the microstructure through the macro model. This unidirectional coupling allows the computation of the micromechanical stress and strain response as well as deduced FIP metrics for the actual microstructure. Such FIP maps and specifically contained hotspots are compared to damage locations identified by the aforementioned CNN for semantic segmentation. Thereby, the FIP's suitability for predicting locations of surface plasticity traces and cracks on the microstructure scale is assessed.

The experimental data for model validation, micromechanical simulation data, and the Abaqus sub-modeling routine for easy integration of user subroutines are accessible through our research data repository \cite{fordatis_repo}  and a GitHub repository \cite{github_repo}.
The latter includes detailed instructions on how to use the data and set up simulation models based upon them.
It is hoped that other researchers will find this helpful to test their micromechanical fatigue models' validity and that it will lay the foundation for a standard benchmarking approach of such.

\section{Material and experimental} \label{experimental}

The experimental procedure applied is outlined in detail in \cite{Durmaz2021}. An abridged version is presented below.

\subsection{Specimen preparation and complementing microscopy}
\label{sec:Specimen_microscopy}
The investigated material is a ferritic stainless steel EN 1.4003 (AISI 3Cr12). Table \ref{chemical_comp} shows the nominal values of the alloying elements. The as-received rod material underwent hot rolling, grinding, cold drawing, and annealing. Disks of 0.7\,mm thickness were extracted from the rod by electrical discharge machining, from which, in turn, mesoscale specimens were laser cut. Finally, state-of-the-art grinding, Struers A2 electropolishing (electrolyte composed of perchloric acid, 2-Butoxyethanol, ethanol, and water), and diamond particle/OPS polishing accomplished the specimen surface finish.

\begin{table}[hbtp]
	\centering
	\begin{tabular}{lccccccccc}
		\hline
		Material & C & Si & Mn & P & S & N & Cr & Ni & Mo \\ \hline
		\hline \vspace{-4ex} \\
		\textbf{1.4003} $\;$ & 0.013 & 0.67 & 1.08 & 0.018 & 0.021 & 0.013 & 11.9 & 0.43 & 0.33 \\
		\hline
	\end{tabular}
	\caption{Chemical composition of ferritic stainless steel 1.4003 in weight-\%.}
	\label{chemical_comp}
\end{table}

Supplementary measurements included topography-sensitive SEM secondary electron (SE2) imaging before (1) and after (2) fatigue, as well as an EBSD scan before fatigue (3). Each of these techniques was applied on the highly loaded regions and both specimen sides. A cut-out of (1) and (3) is shown in Figure \ref{fig:microstruture} a) and b), respectively. These measurements utilized a Zeiss Supra 40VP equipped with an EDAX TSL EBSD system. For EBSD data, the working distance (WD), scan step size, and aperture were chosen to be 18\,mm, 0.6\,$\upmu$m, and 60\,mm, respectively. The EBSD image reveals rather large grains with an average equivalent diameter of $d_\text{eq} \approx 25.5$\,$\upmu$m and single grains up to 100\,$\upmu$m in size. The specimen alignment relative to the rod results in slightly elongated grains in the out-of-plane direction of the specimen (not shown), where the grain size reaches up to 130\,$\upmu$m. There are manganese sulfide inclusion lamellae (type II and type III) \cite{farrar1974inclusions} which reach length of up to 50\,$\upmu$m and are oriented along the the specimen out-of-plane direction.

\begin{figure}[htbp]
	\centering
	\begin{subfigure}{0.45\textwidth}
		\def1.0\textwidth{1.0\textwidth}
		\footnotesize
		\input{figures/microstructure/rem_render.pdf_tex}
		\caption{}

	\end{subfigure}
	\hspace{10mm}
	\begin{subfigure}{0.45\textwidth}
		\def1.0\textwidth{1.0\textwidth}
		\footnotesize
		\input{figures/microstructure/ebds_render.pdf_tex}
		\caption{}

	\end{subfigure}
	\caption{Microstructure analysis of the 1.4003 ferritic steel microstructure. A SEM image is shown in (a) and an [001] EBSD map in inverse pole figure color coding illustrated in (b).}
	\label{fig:microstruture}
\end{figure}

The acquisition of the three data sets was motivated by the need for an undistorted and undeformed reference indicating prior defects (1) as well as high-resolution damage (2) and microtexture (3) information. Former allows for a spatial distortion correction of EBSD data proposed by \cite{Nolze2007, Kapur2000, Wu2002}. To reduce imaging-induced distortions in the SEM reference (1), high magnifications, long dwell times, and low working distances were utilized as suggested in \cite{Kamm2013}. For the same reason and to ensure appropriate imaging of pores and micromechanical damage, both SE2 scans were performed as stitching scans. The detailed correction approach is delineated in \cite{Durmaz2021}.

One difficulty in mapping EBSD onto other image-based modalities is the contained spatial distortions due to the 70\degree{} specimen tilt angle in EBSD measurement \cite{Nolze2007, Nolze2006}. In our case, further distortions are superimposed that arise due to the fabrication-induced specimen surface curvature. In addition to the spatial distortions, the orientation measurements are affected if large specimen surfaces are scanned, see \cite{Ram2015, Nolze2007}. Primarily, the spatial distortions in the EBSD data impede the correct assignment of damage derived from rather undistorted SEM images to its correct grain in the distorted microstructure from EBSD. This is intensified by the fact that extrusions and cracks frequently emerge at grain boundaries, see \cite{Sangid2013, Polak2003}. Therefore, the correction of large EBSD scans represents a fundamental requirement to perform reliable microstructure-property relationship analysis.

\subsection{Mesomechanical fatigue testing}
The experimentation was performed with a fatigue setup that enables resonant multiaxial loading based on \cite{Straub2015} and described in \cite{Durmaz2021}. In this work, the applied loading type is bending. The setup uses mesoscale specimens with a small, highly loaded volume in conjunction with a sophisticated control mechanism. Therewith, high sensitivity regarding initial fatigue states such as extrusion formation and crack initiation is achieved. This is enabled by a closed-loop control that adjusts the excitation frequency to adapt for degradation-induced specimen resonant frequency changes. Further, the setup is equipped with a stroboscope and camera system to capture local damage evolution in an in-situ light optical image series. Figure \ref{fig:Overview_setup} depicts the fatigue setup without the additional optics and a specimen-scale bending-induced von Mises stress distribution.

\begin{figure}[htbp]
	\centering
	\footnotesize
	\import{figures/experimental/}{Setupoverview_render.tex}
	\caption{Overview of the fatigue setup illustrating the arrangement of piezo acuators (khaki), micro sample (orange), laser (yellow) and the position sensitive device (green). The right part shows the specimen in a loaded state and the corresponding von Mises stress state.}
	\label{fig:Overview_setup}
\end{figure}

A fully reversed loading (load ratio of $R$ = -1) is applied, where the rotation angle at the unconstrained beam end acts as the controlled parameter determining the load. The specimen geometry results in a resonant frequency of $f_0$ $\approx$ 2000\,Hz. Attaining $10^9$ cycles or a relative frequency decrease of $\Delta f/f_0 = 0.1\%$ pose stopping criteria for the test. Before the fatigue experiment, the control parameter equivalent to a von Mises stress amplitude of 270\,MPa is computed by linear elastic finite element simulations.

\subsection{Multimodal image registration} \label{image}
Spatial data alignment is a prerequisite to exploit the synergies of the heterogeneous data acquired from the different imaging techniques. This process is denoted as multimodal image registration and involves challenges such as different fields of views, resolutions, contrast (e.g., topography and orientation contrast), and more. For this work, the objective is to perform and validate CPFE sub-modeling simulations.
Therefore, it is necessary to embed the EBSD-derived partially available microstructure information in the idealized specimen geometry and link them to the resulting cyclic damage evolution data and high-resolution damage localization maps. For this purpose, data from the multiple sources (s) were partially transferred to an intermediate target (it) before mapping to the target (t). Specifically, the idealized geometry (s), in-situ light optical image series (s), stitched SE2 before (it) and after fatigue (s), and a damage segmentation mask derived from the latter (s) were aligned with the EBSD scan (t). In this multi-stage registration procedure, all source data sets were first transformed to the intermediate target, the comparatively undistorted and undeformed stitched SE2 SEM image before fatigue. Subsequently, a transformation aligns all data sets with the target modality. Since minimal non-linear spatial distortions were achieved by appropriate imaging conditions and a single specimen holder throughout most of the fatigue and analytical process chain, linear affine (or alternatively rigid/similarity) transformations were adequate to achieve this alignment. The necessary transformation matrices were computed by feature-based, and intensity-based registration techniques, see \cite{Durmaz2021}. On the other hand, the latter transformation to the EBSD target modality demands distortion correction due to its inherent spatial distortions described in Section \ref{sec:Specimen_microscopy}. Hence, this alignment is achieved through an approximate affine transformation followed by an elastic transformation correction of EBSD data using point correspondences and b-spline regularization, see \cite{Sorzano2005}. In all transformation instances, owing to the feature sparsity of the polished surfaces, automatic feature detection and matching of point correspondences proved to be complicated. Therefore, features related to pores and particles common to various modalities enabled the manual feature selection and matching and thus computation of the transformations. Ultimately, the heterogeneous data were spatially aligned, and imaging-based distortions were removed to a large extent.

\section{Micromechanical fatigue simulation} \label{modeling}
The model framework consists of a CPFE model to consider the material's microstructure through grain orientations. Fatigue indicator parameters (FIPs) are introduced to quantify material fatigue during cyclic loading. These parameters are calculated from micromechanical stresses and strains obtained during the CPFE simulation. To validate the CPFE model, a sub-modeling approach is incorporated to capture realistic boundary conditions matching the experiments.

\subsection{Crystal plasticity finite element model}
A phenomenological and isothermal CPFE approach considering small strains is chosen to model elastic-plastic deformation behavior under cyclic loading for polycrystalline materials. As done by \cite{roters2010} length scale dependencies are omitted in this local formulation. A brief overview of the model is given in the following, while details can be found in \cite{kuhn_identifying_2021} and \cite{wicht_efficient_2020}.

Following \cite{asaro1977}, plastic deformation is assumed to be only caused by dislocation slip. For the BCC lattice the twelve $\{110\}$$\langle 111 \rangle$ slip systems are taken into account, which are preferentially activated, see \cite{courtney2005}. The plastic velocity gradient is thus defined as superposition of all shear rates $\dot{\gamma}^{\alpha}$ on all corresponding slip systems $\alpha$ as
\begin{equation} \label{eq:velocity_gradient}

	\dot{\strain}_\text{p} = \sum^{N_\text{Slip}}_{\alpha=1} \dot{\gamma}^{\alpha} {\bm{M}}^{\alpha} \, ,
\end{equation}
with the Schmid matrix ${\bm{M}}^{\alpha} = \bm{m}^{\alpha} \otimes \bm{n}^{\alpha}$ as a dyadic product of the projection on plane $\bm{n}^{\alpha}$ and into slip direction $ \bm{m}^{\alpha}$.

The evolution of the shear rate is adapted from \cite{rice1971} and \cite{hutchinson1976} and applied in a modified form of \cite{cailletaud1992} including kinematic hardening. It reads
\begin{equation} \label{eq:slip_rate}
	\dot{\gamma}^{\alpha} = \dot \gamma_0
	\Big \lvert \frac{\tau^{\alpha} - \chi_\text{b}^{\alpha}}{\tau_\text{c}^{\alpha}} \Big \rvert^m \, \text{sign}(\tau^{\alpha} - \chi_\text{b}^{\alpha}) \, ,
\end{equation}
where $\tau_\text{c}^{\alpha}$ is the critical resolved shear stress,
$\dot \gamma_0$ denotes the reference shear rate, and $m$ the shear rate sensitivity exponent, which are material properties. The resolved backstress on each glide system to account for kinematic hardening is described by $\chi_\text{b}^{\alpha}$.

The incorporation of kinematic hardening is necessary for the modeling of fatigue properties during cyclic loading. A kinematic hardening model for the evolution of the resolved backstress proposed by \cite{ohno_kinematic_1993} is applied and reads
\begin{equation}
	\dot{\chi_\text{b}}^{\alpha} = A_1 \dot{\gamma}^{\alpha} - A_2 \left( \frac{\lvert \chi_\text{b}^{\alpha} \rvert}{\sfrac{A_1}{A_2}}  \right)^{A_3} \chi_\text{b}^{\alpha} \lvert \dot{\gamma}^{\alpha} \rvert \, ,
\end{equation}
with the material dependent parameters $A_1$, $A_2$, and $A_3$. Implemented in a user-defined material subroutine (UMAT) of ABAQUS for user defined material models, the above introduced CPFE model provides a tool to describe micromechanical deformation under cyclic loading. The set of material parameters for the investigated ferritic steel 1.4003 is adopted from \cite{natkowski_fatigue_2021} and listed in Table \ref{cpfem_parameter}.
\begin{table}[htbp]
	\centering
	\begin{tabular}{|c|l|l|c|}

	\hline
	Parameter & Name & Value & Unit \\ \hline
	\hline \vspace{-3.5ex} \\
	$\KIC^\text{e}_{11}$ & Elastic constant                   & 263.7 & GPa \\
	$\KIC^\text{e}_{12}$ & Elastic constant                   & 120.5 & GPa \\
	$\KIC^\text{e}_{44}$ & Elastic constant                   & 79.1 & GPa \\
	$N_\text{Slip}$ & Number of slip systems           & 12 & - \\
	$\dot \gamma_0$ & Reference shear rate      & 0.001 & 1/s \\
	$m$ & Strain rate sensitivity exponent   & 100 & - \\
	$\tau_\text{c}^{\alpha}$ & Critical resolved shear stress    & 119.8 & MPa \\
	$A_1$ & Kinematic hardening 1 $\qquad$   & 25550 & MPa \\
	$A_2$ & Kinematic hardening 2 $\qquad$   & 1353 & - \\
	$A_3$ & Kinematic hardening 3 $\qquad$   & 8 & - \\
	\hline
\end{tabular}
	\caption{Material parameters for the CPFE model, according to \cite{natkowski_fatigue_2021}.}
	\label{cpfem_parameter}
\end{table}
\subsection{Fatigue indicator parameters}
Following \cite{przybyla2010}, irreversible plastic slip on the microscale causes the initiation of fatigue damage. A framework for the numerical tracking and prediction of fatigue damage in nickel-based alloys was proposed in \cite{shenoy2007, przybyla2010, castelluccio2014meso}. As a micromechanical metric for the local degradation state and a driving force for fatigue crack initiation, FIPs were introduced. FIPs are derived from stress and strain fields on the microstructure during cyclic loading. Multiple FIPs are summarized in \cite{hochhalter2010}.

\cite{manonukul2004} and \cite{mcdowell2010} propose the accumulated plastic strain as FIP. The slip rate introduced in (\ref{eq:slip_rate}) quantifies the activity of plastic gliding on each slip system $\alpha$.
The accumulated plastic slip is calculated from the resulting overall plastic strain rate. It describes the amount of accumulated plastic deformation a material has experienced during the cyclic loading history at a local material point.
It reads
\begin{equation} \label{eq:acc_pl_strain}

	\text{FIP}_\text{p}  = \int_{\text{cycle}} \sqrt{ \tfrac{2}{3} \, \dot{\strain}_\text{p} : \dot{\strain}_\text{p}} \, \mathrm{d}t \, .
\end{equation}

A second approach proposed by \cite{fatemi1988} considers the normal stress on the plane of maximum shear strain range. The FIP combines the maximum shear strain range $\Delta\gamma_\text{p,max}^\alpha$ and the maximum normal stress on the plane of maximum shear strain range $\sigma_\text{n,max}^\alpha$. This critical plane approach is determined as
\begin{equation} \label{eq:fatemie_socie}
\text{FIP}_\text{FS} = \max_{\alpha\in\left(1,...,12\right)} \left[\frac{\Delta\gamma_\text{p,max}^\alpha}{2} \Big(1+ k \frac{\sigma_\text{n,max}^\alpha}{\tau_\text{c}^{\alpha}} \Big) \right]
\end{equation}
with
\newcommand{\tilde{\tme}}{\tilde{t}}
\begin{equation} \label{eq:fatemie_socie2}
\Delta\gamma_\text{p,max}^\alpha = \max_{\tilde{\tme}}{\Big( \int_{\text{cycle start}}^{\tilde{\tme}} \dot \gamma_\text{p}^{\alpha} ~ \mathrm{d}t \Big)} - \min_{\tilde{\tme}}{\Big( \int_{\text{cycle start}}^{\tilde{\tme}} \dot \gamma_\text{p}^{\alpha} ~ \mathrm{d}t \Big)} \, ,
\end{equation}
where $\tau_\text{c}^{\alpha}$ is the critical resolved shear stress and $k$ is a constant set to 1.0 controlling the influence of the normal stress. For a discussion of this definition and the value of $k$, see \cite{boff_micromechanical_2016} and \cite{castelluccio_study_2012}.

A FIP based on a dissipation energy was introduced by \cite{korsunsky2007}. Here, the amount of energy dissipated over all slip systems under cyclic loading is considered as a measure for fatigue and the FIP is defined as
\begin{equation} \label{eq:energy_criteria}
\text{FIP}_\text{W} = \int_{\text{cycle}} \, \sum^{N_\text{Slip}}_{\alpha=1} \tau^{\alpha} ~ \dot{\gamma}^{\alpha} \, \mathrm{d}t \, .
\end{equation}
The implementation in the UMAT framework is similar to the determination of the accumulated plastic slip.
\cite{boeff2017} and \cite{schaefer2019b} compare different FIPs and their suitability for numerical prediction of fatigue crack initiation life.

Since the aforementioned FIP are primarily applicable for transgranular crack initiation but also intergranular cracks are observed, a intergranular FIP
\begin{equation}
\text{FIP}_\text{int} = \gamma_\text{p,net} \left(1+k_\text{int}\frac{\sigma_\text{n,GB}}{\tau_\text{c}^{\alpha}}\right)
\end{equation}
is employed. In contrast to the intergranular FIP proposed by \cite{przybyla_microstructure-sensitive_2013}, the critical resolved shear stress is utilized instead of the yield stress, as proposed by \cite{boff_micromechanical_2016}.
$\gamma_\text{p,net}$ is the maximum net plastic shear strain among all slip planes, $\sigma_\text{n,GB}$ is the average peak normal stress on the grain boundary and $k_\text{int}$ is a parameter, which is chosen to be $k_\text{int} = 1.0$ in analogy to the Fatemi-Socie FIP.

While aforementioned hardening and FIP formulations were shown to achieve decent damage localization capabilities in LCF settings, their applicability to VHCF is largely unknown.

\subsection{Sub-modeling approach}
To capture its exact loading condition and stress state, the microstructure domain is embedded in the macro model of the fatigue specimen using the Abaqus sub-modeling technique. The macro model is analyzed using a linear elastic material law with a Young's modulus of $210$\,GPa, and a Poisson's ratio of $0.3$. Figure \ref{fig:macro_geom} a) shows the geometry and boundary conditions of the specimen. On the right surface, marked in black, all degrees of freedom are fixed while the left surface, marked in blue, is cyclically loaded by a displacement amplitude of $u_3=0.056$\,mm along the third axis analogous to the experiment. The loading is fully reversed. Considering the static stress-strain curve, the elastic regime is not significantly exceeded by this loading, justifying the assumption of a linear elastic material for the macro model. The linear elastic material response is used as the boundary condition for the micromechanical submodel. This results in one directional coupling from the macro model to the submodel. A discretization with 116830 20-node quadratic brick elements is chosen for the specimen as shown in Figure \ref{fig:macro_geom} b). The central region for which microtexture data is available is discretized by a finer mesh, while less important areas are meshed coarsely. Three loading cycles are performed on the coupled model, at which point the cyclic FIP increment is assumed to be saturated, see for example \cite{schafer_micromechanical_2019}.
\begin{figure}[htbp]
	\centering
	\begin{subfigure}{0.47\textwidth}
		\def1.0\textwidth{1.0\textwidth}
		\footnotesize
		\import{figures/macro_geom/}{macro_geom_render.tex}
		\caption{}

	\end{subfigure}
	\hspace{5mm}
	\begin{subfigure}{0.47\textwidth}
		\def1.0\textwidth{1.0\textwidth}
		\footnotesize
		\import{figures/macro_geom/}{macro_mesh_render.tex}
		\caption{}

	\end{subfigure}
	\caption{Fatigue specimen for macroscopic FE analysis. Geometry and boundary conditions are schematically drawn in a) and the finite element mesh with 116830 C3D8 elements is depicted in b).}
	\label{fig:macro_geom}
\end{figure}

As a second step, post-processing steps are performed on the distortion corrected EBSD data in MTEX, a Matlab toolbox for crystallography. Initially, data cleaning is applied using the confidence index and image quality thresholds of 0.05 and 100, respectively. Subsequently, grains are computed, setting a 5\degree{} threshold value, and all grains consisting of less than 20 indexed pixels are discarded. Finally, the EBSD data is smoothed with a spline filter, and missing points from prior operations are filled. Based on this modified EBSD data, a discretized and extruded domain for the CPFE simulation is generated, as shown in Figure \ref{fig:embedding} a). For this purpose, the grain index and orientation acquired on a hexagonal grid are transferred to a rectangular grid by nearest-neighbor interpolation. In this manner, a 2D discretized domain is set up, which is subsequently extruded to $\sfrac{d_\text{eq}}{2}$ in the third dimension. Thus, the assumption of prismatic grains is made with grain boundaries (GB) extending into the direction normal to the specimen surface, which can be justified by the elongation of the grains in out-of-plane direction. The regular mesh for the investigated specimen microstructure counts $856\times 500\times 10 \approx 4.3 \times 10^6$ eight-node brick elements (C3D8). This 3D microstructure domain is embedded in the macro geometry as illustrated in Figure \ref{fig:embedding} b), where gaps in the lower illustration are for visualization purposes only. The deformation obtained from the continuum macro simulation is imposed on the CPFE model region's outer surfaces (sub-modeling).
Not shown in Figure \ref{fig:embedding} b) is an elastic embedding around the microstructure. It is $\SI{30}{\micro\meter}$ thick and used to limit the effects of load introduction.

The model is run on a high performance computing cluster node with 48GB RAM and 24 Intel(R) Xeon(R) \@ 2.60 GHz CPU.
The total runtime (wallclock time) of the macro model is about $1.9$\,h, and about $96$\,h for the microstructure model.
In the latter case, due to the relatively large number of elements for a CPFE simulation, ABAQUS's iterative solver is applied.

\begin{figure}[htbp]
	\centering
	\begin{subfigure}{0.47\textwidth}
		\def1.0\textwidth{1.0\textwidth}
		\footnotesize
		\import{figures/embedding/}{ebsd2abq_render.tex}
		\caption{}

	\end{subfigure}
	\hspace{5mm}
	\begin{subfigure}{0.47\textwidth}
		\def1.0\textwidth{1.0\textwidth}
		\footnotesize
		\import{figures/embedding/}{embedding_render.tex}
		\caption{}

	\end{subfigure}
	\caption{Sub-modeling CPFE approach. The processing of EBSD data to an Abaqus submodel by extrusion from 2D to 3D and subsequent discretization is described in a), where the bottom represents a 3D grain unique-color representation. In b), the embedding of the microstructure within the macro geometry is shown.}
	\label{fig:embedding}
\end{figure}

\subsection{Slip trace prediction}
\label{sec:slip_trace_prediction}
To assess the capability of the CPFE model to predict slip planes correctly, a comparison of simulation-based and actual slip traces, similar to \cite{Zhang2018}, is conducted. Slip trace prediction was enabled by considering the slip system exhibiting most plastic shear deformation and computing the intersection line (trace) of the respective slip plane with the surface plane as delineated in \cite{zhang2016b}. The surface intersecting line direction vector $\bm{c}$ can be determined by
\begin{equation} \label{eq:slip_trace_line}
	\bm{c} = \bm{n}_\text{surf} \times (\bm{R} \cdot {\bm{n}}^{\slipsysindmax}) \, ,
\end{equation}
where $\bm{n}_\text{surf}$ is the normal to the specimen surface on which the protrusions are observed, here it is assumed that $\bm{n}_\text{surf} = \left(\begin{smallmatrix}0 \\ 0 \\ 1\end{smallmatrix}\right)$. $\bm{R}$ denotes the crystal rotation matrix and ${\bm{n}}^{\slipsysindmax}$ the slip plane normal.

\section{Results} \label{results}
The proposed experimental and numerical workflow is applied to a mesoscale fatigue specimen. EBSD maps for the micromechanical simulation domain are given in Figure~\ref{fig:ebsd} for the sake of completeness. Experimentally acquired damage locations are presented together with calculated FIP distributions. In this work, damage locations refer to protrusions and crack sites. A qualitative slip trace analysis is performed on a selection of detected protrusions. Furthermore, one location in the microstructure where the proposed method fails to predict crack initiation is investigated in detail.

\begin{figure}[p]
	\centering
	\begin{subfigure}{\textwidth}
	    \centering
		\def1.0\textwidth{\textwidth}
		\footnotesize
		\import{figures/microstructure/}{ebsdx_render.pdf_tex}
		\caption{Reference direction: [100]}
	\end{subfigure}
	\\
	\begin{subfigure}{\textwidth}
	    \centering
		\def1.0\textwidth{\textwidth}
		\footnotesize
		\import{figures/microstructure/}{ebsdz_render.pdf_tex}
		\caption{Reference direction: [001]}
	\end{subfigure}
	\caption{EBSD data acquired for the considered specimen for two reference directions.}
	\label{fig:ebsd}
\end{figure}

\subsection{Comparison of FIPs with experimental damage locations}
A binary map of experimental damage locations is superimposed on normalized FIP maps in Figures \ref{fig:SDV115_Overlayed} -- \ref{fig:FIPint_Overlayed} to evaluate the ability of FIP metrics to predict hot spots for damage locations reliably and to show the feasibility of the multimodal data registration and sub-modeling approach.
Figure \ref{fig:StressMises_Overlayed} shows a similar plot for the normalized von Mises stress after the last cycle.
Normalized parameters are indicated with the notation $\overline{\left(\cdot\right)}$ subsequently. Note that the damage maps superimposed on Figures \ref{fig:SDV115_Overlayed} -- \ref{fig:FIPint_Overlayed} represent the final damage stage from the segmented SEM image. This is considered as ground truth since the damage locations are predominantly spatially-confined protrusions and to a minor extent short cracks. For such damage stages the validity of the stress/deformation fields is assumed. Alternatively, individual time steps from the in-situ imaging during the fatigue experiment can be employed but are limited in terms of optical resolution.

It is worth noting that no averaging technique is applied for the plotted FIP distributions resulting in a potential mesh-dependency of the FIP solution. However, such averaging techniques (e.g. grain-based sphere averaging) tend to not impact the qualitative result, see \cite{boff_micromechanical_2016,natkowski_fatigue_2021}.

The transgranular FIP (accumulated plastic slip, Fatemi-Socie, and dissipated energy) exhibit similarities and show roughly the same number of hotspots (yellow to red regions) in the same grains. A subset of the most pronounced hotspots where the FIP exceeds 80\% of its maximum value are annotated with red arrows for better visibility, in Figures \ref{fig:SDV115_Overlayed} -- \ref{fig:FIPint_Overlayed}. Distinct discontinuities are present in each FIP distribution in the highest loaded section of the specimen. As evident, damage locations indicated in black often arise at such discontinuities but not necessarily in the grains exhibiting the highest FIP values. Overall, from comparison to the grain maps in Figure \ref{fig:ebsd} it can be inferred that transgranular FIP distributions vary within grains and tend to localize predominantly at grain boundaries and at triple points. This is in agreement with previous investigations, e.g., by \cite{basseville_numerical_2017}, or \cite{el_shawish_combining_2017}.
The intergranular FIP is only defined at the grain boundaries themselves and is displayed in Figure \ref{fig:FIPint_Overlayed}. High values in the intergranular FIP often spatially coincide with hotspots in the other FIPs.

Ideally, the critical red areas, where the simulation predicts the highest FIP, should follow the experimentally observed damage locations. However, the majority of damage locations are located outside of highest FIP regions but rather in regions of moderately high FIP (green regions). Some of regions where FIP and ground truth are not aligned are annotated in Figure \ref{fig:SDV115_Overlayed} with box annotations exemplarily. These regions are explored subsequently.

\tikzset{align at top/.style={baseline=(current bounding box.north)}}
\newcommand{\hflip}[1]{\reflectbox{\rotatebox[origin=c]{180}{#1}}}
\begin{figure}[p]
	\centering
	\footnotesize

	\hflip{\import{figures/resultsnew/}{P8-full-sdv115-vs-seg}} \\

    \import{figures/resultsnew/}{legend-fipp}

	\caption{$\overline{\fipp}$ distribution superimposed with damage locations colored in black. The white boxes on the bottom and the top (left and right) side mark the damage spots shown in the subsequent slip trace analysis SEM images of Figure \ref{fig:slip_traces}. The additional black box annotates the region that is subsequently considered in the cyclic damage evolution analysis to investigate the inadequacies of the model. The red arrows indicate FIP values which are greater than 80\% of the maximum FIP value found with a search radius of 10 element edge lengths.}
	\label{fig:SDV115_Overlayed}
\end{figure}

\begin{figure}[p]
	\centering
	\footnotesize
	\hflip{\import{figures/resultsnew/}{P8-full-sdv116-vs-seg}}  \\
	\import{figures/resultsnew/}{legend-fipfs} \\
	\caption{$\overline{\fipfs}$ distribution superimposed with damage locations, like in Figure \ref{fig:SDV115_Overlayed}.}
	\label{fig:SDV116_Overlayed}
\end{figure}

\begin{figure}[p]
	\centering
	\footnotesize
	\hflip{\import{figures/resultsnew/}{P8-full-sdv183-vs-seg}}  \\
	\import{figures/resultsnew/}{legend-fipw} \\
	\caption{$\overline{\fipw}$ distribution superimposed with damage locations, like in Figure \ref{fig:SDV115_Overlayed}.}
	\label{fig:SDV183_Overlayed}
\end{figure}

\begin{figure}[p]
	\centering
	\footnotesize
	\hflip{\import{figures/resultsnew/}{P8-full-fipint-vs-seg}}  \\
	\import{figures/resultsnew/}{legend-fipint} \\
	\caption{$\overline{\fipint}$ distribution superimposed with damage locations, like in Figure \ref{fig:SDV115_Overlayed}.}
	\label{fig:FIPint_Overlayed}
\end{figure}

\begin{figure}[p]
	\centering
	\footnotesize
	\hflip{\import{figures/resultsnew/}{P8-full-smises-vs-seg}}  \\
	\import{figures/resultsnew/}{legend-mises} \\
	\caption{$\overline{\stressmises}$ distribution superimposed with damage locations, like in Figure \ref{fig:SDV115_Overlayed}. Arrows indicating high values are not shown.}
	\label{fig:StressMises_Overlayed}
\end{figure}

\subsection{Slip trace analysis}
The qualitative comparison of eight protrusions and their slip trace orientations with predicted slip trace orientations (according to Section \ref{sec:slip_trace_prediction}) shows good agreement. A subset of two protrusions is shown in Figure \ref{fig:slip_traces}. The white lines indicate the predicted slip traces per finite element. Angular deviations between protrusion traces and predicted traces are typically in the order of a few degrees.

\begin{figure}[htbp]
	\centering
	\footnotesize
	\adjustbox{width=0.9\textwidth,keepaspectratio}{\import{figures/resultsnew/}{Slip_trace_analysis_v4_render.tex}}
	\caption{Comparison of protrusion slip trace topography with the  simulation-derived, element-wise trace of the slip plane containing the most activated slip system (white lines). The two instances illustrated here are marked by white boxes in Figure \ref{fig:SDV115_Overlayed}. White dotted lines show the grain boundaries derived from electron backscatter diffraction}
	\label{fig:slip_traces}
\end{figure}

The dotted white lines indicate grain boundaries inferred from EBSD data. The characteristic slip traces within the protrusion in Figure \ref{fig:slip_traces} a) undergo a direction change when transitioning across the grain boundary. While the prediction in the right grain is aligned with the observed protrusion, there is a deviation observed for the left grain. This discrepancy can be ascribed to two potential reasons. One possibility is that the pore resulting from a prior manganese sulfide inclusion causes an alteration of the stress state, which is not considered in the modeling. Another option would be that the protrusion emerges in the right grain and then upon transition undergoes a direction change towards the closest aligned slip system rather than the individually highest loaded slip system in the left grain. Interestingly, while in most grains, the predicted slip traces do not vary within grains, in the right grain, the prediction is correct only in the vicinity of the actual damage location. The predicted slip trace in Figure \ref{fig:slip_traces} b) is in accordance with the visible traces in the protrusion. Aside from the shown predominant mode of single slip, few protrusions with comparatively more intricate topographies indicating multiple slip are observable in other regions.

\subsection{Cyclic evolution of crack formation and growth}
Since some damage locations occurred in regions where lower FIP metrics were predicted, the question arises which shortcoming leads to this discrepancy. Therefore, such a damage location was investigated in detail. Figure \ref{fig:time_series} depicts an image series of in-situ light optical images signifying damage (dark grayscale values) overlayed with a grain map or the accumulated plasticity FIP. The overlayed damage maps are difference images where a initial reference image was subtracted from an image associated with the specified cycle. The crack nucleates in the vicinity of a fabrication-induced pore present at the grain boundary. Crack growth occurs in both directions consecutively, indicated by the arrows in Figure \ref{fig:time_series} b). Finally, grain boundaries pose a barrier to both crack branches. Therefore, damage locations to a minor extent can be ascribed to pore-induced stress concentration. Pores present at the surface exhibit equivalent diameters of 0.1--6.0\,$\upmu$m.

\newcommand{\specialcell}[2][c]{%
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\begin{figure}[htbp]
	\centering
	\begin{subfigure}{0.65\textwidth}

		\footnotesize

        \tikzscale{0.5}
        \begin{tabularx}{0.65\textwidth}{llll}

        \specialcell{\hflip{\import{figures/resultsnew/}{P8-full-sel-grains-vs-seg-frame1323.tex}} \\ $\SI{8.00e6}{}$ cycles} &
        \specialcell{\hflip{\import{figures/resultsnew/}{P8-full-sel-grains-vs-seg-frame1335.tex}} \\ $\SI{8.98e6}{}$ cycles} &
        \specialcell{\hflip{\import{figures/resultsnew/}{P8-full-sel-grains-vs-seg-frame1349.tex}} \\ $\SI{1.01e7}{}$ cycles} &
        \specialcell{\hflip{\import{figures/resultsnew/}{P8-full-sel-grains-vs-seg-frame1367.tex}} \\ $\SI{1.15e7}{}$ cycles}  \\
        \specialcell{\hflip{\import{figures/resultsnew/}{P8-full-sel-grains-vs-seg-frame1374.tex}} \\ $\SI{1.21e7}{}$ cycles}  &
        \specialcell{\hflip{\import{figures/resultsnew/}{P8-full-sel-grains-vs-seg-frame1400.tex}} \\ $\SI{1.42e7}{}$ cycles}  &
        \specialcell{\hflip{\import{figures/resultsnew/}{P8-full-sel-grains-vs-seg-frame2500.tex}} \\ $\SI{5e8}{}$ cycles}  &
        \specialcell{\hflip{\import{figures/resultsnew/}{P8-full-sel-sdv115-vs-seg-frame2500.tex}} \\ $\SI{5e8}{}$ cycles, $\overline{\fipp}$}  \\

        \end{tabularx}
		\caption{}

	\end{subfigure}
	\hspace{2mm}
	\begin{subfigure}{0.325\textwidth}
		\def1.0\textwidth{1.0\textwidth}
		\footnotesize
		\import{figures/resultsnew/}{Time_series_analysis_2_render.tex}
		\caption{}

	\end{subfigure}
	\caption{a) Light optical grayscale image series superimposed onto the region annotated with the black box and arrow in Figure \ref{fig:SDV115_Overlayed} to track crack formation and evolution. The underlying image represents the meshed microstructure in grain color coding and for the last frame, the $\overline{\fipp}$-heatmap is shown in addition. The numbers indicate the corresponding load cycle numbers. b) Secondary electron SEM image of the final crack state (1.1$\times{}10^9$ cycles). Numbering and arrows illustrates the crack initiation and growth process. Grain boundaries analogous to a) are faintly visible through discontinuities in the grayscale contrast.}
	\label{fig:time_series}
\end{figure}

\section{Discussion} \label{discussion}
The primary objective of developing a validation methodology for fatigue damage prediction of micromechanical simulation models was satisfied. At its core, the validation evolves around automatized localization of damage locations with a convolutional neural network (1) described in \cite{Thomas2020}, multimodal image registration techniques (2), and a CPFE sub-modeling approach (3). Each of these three core elements, at their current stage, introduces specific beneficial aspects as well as limitations to the validation approach.

\subsection{Validation methodology}

From the comparison of Figure \ref{fig:time_series} a) and b) it is evident that secondary electron SEM images can provide comparatively more detail and an appropriate damage type distinction as opposed to the light optical image modality. For instance, such SEM images permit distinguishing the crack from the plasticity traces surrounding it. Since topography-information is recovered from the Everhart-Thornley SEM and applied light optical imaging techniques, only surface-altering damage exceeding these techniques' respective detection limit can be registered. A convolutional neural network based on a U-Net architecture \cite{Ronneberger2015} was trained to detect damage locations of the classes protrusion and cracks based on such topography sensitive SEM images \cite{Thomas2020}. While this model can detect such micromechanical damage reliably, individual damage object boundaries are difficult to segment accurately due to the characteristics of protrusions, and the imaging methodology \cite{Thomas2020}. To counteract this, a visual inspection and minor adjustments of the U-Net segmentation predictions were performed for the ground truth. Additionally, damage masks derived from the overlayed light optical time series data in Figure \ref{fig:time_series} a) through thresholding were considered (not shown). In that case, the SEM-derived semantic segmentation mask was used to select optimal thresholds for light optical difference images by maximizing the Jaccard index \cite{jaccard1902lois} between the SEM-derived mask and the one of the last light optical image. Therefore, a damage category-dependent threshold was selected and applied throughout the whole time series to assimilate the damage masks derived from both modalities. While their derived masks show similar patterns, damage instances appear more extensive overall in the masks derived from the light optical time series. Deviations between both damage masks exist particularly at the specimen edge. The accordance of both maps is decent but the SEM-derived map, even prior to expert corrections, provides a higher fidelity. Since damage locations in many materials tend to adhere to grain boundaries, a reliable damage detection methodology is a fundamental requirement to enable an appropriate assignment to microstructural features.

The same applies to the registration of the heterogeneous data, where the applied methodology was found to yield satisfying relative alignment between damage locations and microstructure, see \cite{Durmaz2021}. In materials with characteristic grain sizes below the micron scale, where damage is comparatively more confined, reliable damage detection proved to be more difficult, see \cite{Thomas2020} under the conditions outlined there. Moreover, such materials pose comparatively higher requirements on the data registration methodology. Therefore, the investigation of small grain materials presumably poses a limitation at the current stage. This, however, is not of concern here since the investigated material has an average grain size of 25\,$\upmu$m.

The sub-modeling approach enables translating various boundary conditions onto the microstructure domain to which the CPFE model is applied. While in this experimental case of VHCF-regime loading, the assumption of a linear elastic model on the mesoscale specimen level appears appropriate and the majority of the plasticity occurs within the microstructurally modelled CPFE domain, larger deformations could necessitate the transition to elastic-plastic models on the specimen scale and different registration methodologies. Since this model utilizes unidirectional coupling from the specimen to the microstructure scale, and not vice versa, microstructural short crack growth poses an upper bound, where the specimen-scale stress state can still be assumed to be maintained. In contrast to macroscopic specimens, the specimen-scale stress state can be altered at a relatively small absolute crack length due to the specimen's small dimensions. Remeshing-based approaches (\cite{Proudhon2016}) and XFEM techniques (\cite{Wilson2018}) can address this issue and further inherently model the stress relaxation in the vicinity of the crack.

\subsection{Assessment of FIPs with respect to experimental damage locations}

While the accumulated plastic strain $\text{FIP}_\text{p}$ is based on the notion that all slip systems contribute to fatigue crack nucleation, the Fatemi-Socie $\text{FIP}_\text{FS}$ only takes the slip system with the maximum shear strain range into account. Hence, a single slip criterion is established in $\text{FIP}_\text{FS}$ combining the effect of crystallographic slip and tensile stress on a slip plane. The measurement of dissipated energy in terms of $\text{FIP}_\text{W}$ is similar to the $\text{FIP}_\text{p}$, an accumulation of dissipated energy over all slip systems.

To achieve a quantitative comparison of the damaged area between experiment and simulation, a threshold must be applied to the FIP fields. The selection of an appropriate FIP metric threshold is hampered by the long-tailed FIP distribution arising due to the VHCF loading and the large number of grains. The selection of the most suitable metric and its ideal threshold can be facilitated by the receiver operator characteristic illustrated in Figure \ref{fig:FIP_violin}. The curve is computed by thresholding the normalized FIP metrics and von Mises stress at different values and assessing the confusion matrix elements (true-positives, true-negatives, false-positives, and false-negatives) to infer the true-positive and false-positive rates at each threshold. Therefore, the normalized damage metrics are considered class probabilities, where the boundaries zero and unity represent undamaged and damaged pixels, respectively. The SEM-derived segmentation map is taken as ground truth for the construction of this diagram, and cracks, as well as protrusions, are considered collectively as damage to formulate a binary classification problem. The area under the ROC curves is a metric (ROC-AUC) for the predictive power of the CPFEM model and the FIP formulations at hand for the given material. The same procedure is followed for the microstructure-sensitive von Mises stress. In the ROC curve, the $\text{FIP}_\text{W}$ and $\text{FIP}_\text{p}$ are nearly congruent, which is comprehensible, taking into account the similarity of their formulation. The ROC curve for $\text{FIP}_\text{FS}$ is discernable from the former two but yields similar ROC-AUC values of approximately 0.69. Interestingly, the micromechanical von Mises stress has more predictive power achieving a ROC-AUC of almost 0.73.

The surprisingly good prediction accuracy of the von Mises stress relative to the FIPs might be explained by differing mechanisms in the LCF domain and the HCF/VHCF regimes. In the Coffin-Manson-Basquin equation, the latter are governed by the elastic strain amplitude received from Basquin's law and thus dominated by a term proportional to the stress amplitude, see \cite{radaj_ermudungsfestigkeit_2007}. Furthermore, introducing a term related to stress can also be seen as a motivation for the Fatemi-Socie and dissipated energy FIPs instead of accumulated plastic strain. \cite{Schafer2019} also noted the generally limited prediction accuracy of the FIPs in the HCF regime and better accuracy of $\text{FIP}_\text{FS}$ and $\text{FIP}_\text{W}$ as opposed to $\text{FIP}_\text{p}$. However, their results also demonstrate the good lifetime prediction of the FIPs in the LCF domain.

In the FIP distributions, spatial discontinuities occur due to orientation differences between grains, i.e., at grain boundaries. Furthermore, the FIPs show a strong localization within grains towards GBs. While the FIPs reproduce the experimental tendency that damage adheres to GBs \cite{Durmaz2021}, they do not seem to most prominently indicate the correct GB locations.

\begin{figure}[htbp]
	\centering
	\footnotesize
	\includegraphics[width=0.5\textwidth]{figures/resultsnew/ROC_curve_combined.png}
	\caption{Receiver operating characteristic (ROC) curve of normalized FIP metrics and normalized von Mises stress using the segmented damage map as ground truth. This curve is constructed by sweeping the decision boundary from zero to unity and evaluating the false positive and true positive rate for each data point. The legend additionally provides the area under the ROC curve (AUC) which is a metric for the binary classification accuracy. The reference diagonal represents a classifier with no predictive power, an AUC of unity would correspond to ideal distinction of damage and no damage by the metric. Note that $\text{FIP}_\text{W}$ and $\text{FIP}_\text{p}$ almost coincide.}
	\label{fig:FIP_violin}
\end{figure}

Moreover, the damage segmentation map contains few damage locations at regions where each FIP predicts low values. Among this subset of damage locations, only the one shown in Figure \ref{fig:time_series} can be unambiguously ascribed to fabrication-induced pore defects, which were not considered in the modeling. Analogously, it cannot be excluded that elongated MnS inclusions, which are known to exist in this material, could be present beneath the specimen surface. While such defects could clearly affect damage emergence, their spatial distribution in the microstructure renders it unlikely that such defects contribute to a large portion of observed damage locations. Additional nanoscopic computer tomography experiments or similar would be required to capture those defects. Similarly, the OPS treatment results in a polishing relief, where surface steps of few tens of nm at grain boundaries (non-modelled) could contribute to damage emergence.

This leads to the conclusion that the assumptions made in the CPFE model and FIP formulations do not represent microstructural fatigue damage emergence appropriately. There is a range of incompatibilities between modeling and experiment:

\begin{enumerate}
\item The simulation considers an ideal rectangle cross-section, while the specimen possesses rounded-off edges. This influences the local stress state. However, many damage locations are not situated at the specimen edge and thus only affected to a minor degree by this stress state discrepancy.
\item Crack growth modeling is omitted. Therefore, stress release in the vicinity can not be captured by the simulation model.
\item  Grain morphology and crystallographic orientation of adjacent grains may cause elastic anisotropy as well as length scale-dependent phenomena. The used phenomenological CP model captures the elastic anisotropy. However, for the grain size effects such as the Hall-Petch relation, a non-local crystal plasticity formulation would be required.
\item Prismatic grains are assumed; however, there are many instances in the literature indicating the importance of GB inclination, e.g., \cite{Saylor2003}. Using a phenomenological model for FCC copper \cite{zeghadi2007ensemble_1, zeghadi2007ensemble_2} found that by constraining the surface microstructure and altering the sub-surface microstructure, the predicted surface plastic slip is strongly affected for uniaxial tension loading. Namely, fluctuations of more than 60\% were found for 40\% of the free surface area between different statistical volume elements with constrained surface microstructure. Moreover, in that work, the region beneath the surface that influences the surface plasticity field was twice the average grain size in depth. Despite not considering the change of the local grain boundary slip transmission characteristics when changing its inclination angle (see \cite{sangid2011a, sangid2011b}), similar to our study, they highlight the severe impact of the 3D orientation distribution. In contrast to their computational study, in our case, the influence of the 3D microstructure is somewhat alleviated since our specimen is driven in \textit{bending} resonant loading accentuating the stresses at the specimen surface. Moreover, recent computational studies suggest that the free surface's stress concentration is comparatively more pronounced when considering high symmetry crystal structures \cite{Stopka2020}, such as the BCC material characterized here.
\item Apart from the lack of 3D microstructure data, the employed Ohno-Wang kinematic hardening rule of the phenomenological CP model does not attempt to capture the influence of local slip transmission characteristics of grain boundaries on the resulting back stresses. However, these characteristics, amongst others, are presumably of high importance when it comes to localization of fatigue damage. During calibration of the Ohno-Wang kinematic hardening rule, the hardening parameters $A_1$, $A_2$ were tuned to fit the experimental macroscopic $\upsigma$-$\upepsilon$-Hysteresis in the LCF regime. There are several sets of $A_1$ and $A_2$, resulting in an adequate match. Nevertheless, only one set was taken into account in this study and used as the hardening law parameters. Possible deviations in microstructure resolved strains between these sets are neglected. An alternate calibration concept of the hardening model would be to utilize HR-DIC to directly capture local sub-grain strain fields, as shown in \cite{Zhang2016}. In \cite{Cerrone2015} a hardening rule was suggested that included a lattice incompatibility term adapted from \cite{Beaudoin2000} and a modified Voce-Kocks term, see \cite{Kocks1976}. In conjunction with similar FIPs, this hardening law yields hot spots following experimental damage and localizing to GBs in their small sample size study. However, it is unclear if these results also transfer to steel and a different parameter calibration procedure than the applied one is required for the application of this formulation.
\item Another possible cause for experimental damage not being reproduced by the FIPs is that they map the mechanical fields onto the tendency of protrusion/crack formation inaccurately. However, since the microscopic deformation field has not been validated, it is debatable whether the underlying CP models, the FIP formulations or both lead to mediocre localization. In \cite{Chen2018a}, amongst others, the same FIPs as in this work were investigated. This work can confirm their observation of corresponding FIP hot spots showing a discrepancy to experimental damage sites. Furthermore, \cite{Chen2018a} proposed an alternative FIP that succeeded in predicting fatigue crack localization in the vicinity of inclusions. This FIP is based on the stored energy per cycle. However, for this FIP computation, a non-local model capable of estimating the geometrically necessary dislocation density is required. The application of such a formulation would severely increase computational cost.
\item The hardening model parameters are derived from a low strain rate experiment, but the target fatigue experiment was cycled at frequencies of $\approx$ 2\,kHz. Therefore, the question arises whether the calibration results in a phenomenological hardening model that adequately represents the material's dislocation dynamics. It is known that through the characteristic thermally-activated screw dislocation glide, strain rate and temperature effects play an essential role in the plasticity and fatigue of BCC materials \cite{Cereceda2016, Geilen2020}. Furthermore, the strain rate sensitivity exponent is chosen in a way that strain rate effects are neglected.
Typically specimen heating affects high-frequency fatigue testing severely since frictional losses constitute approximately 95\% of the dissipated energy during plastic deformation \cite{Kamlah1997, Hodowany2000}. In contrast, for our testing methodology, we anticipate that the pronounced surface-to-volume ratio of the mesoscale specimen, the low strain amplitudes, and forced convection through specimen motion permit cycling at faster rates without notable heating on the global specimen scale. Nonetheless, thermal hotspots that alter the dislocation dynamics locally can not be excluded.
\item Even for low strain rates and room temperature, additional activation of $\{112\}$ slip systems for $\upalpha$-iron in monotonic tensile and compression tests was previously reported by \cite{Franciosi2015}. Therefore, the applied restriction to the $\{110\}$ family of slip planes in modeling could be called into question. The overall neglect of the non-Schmid behavior, see \cite{Franciosi2015, Cereceda2016} and cross-slip, a typical mechanism of screw dislocation movement in BCC materials, are potentially responsible for poor localization.
\item Additionally, the initial dislocation density, which may be of importance, is not respected. While the EBSD data step size is selected such that a geometrically necessary dislocation density estimation can be performed \cite{pantleon2008resolving, jiang2013measurement}, the statistically stored dislocation density can not be assessed with the dataset provided here. With further parametrization efforts, a non-local crystal plasticity model could take dislocation densities into consideration. However, such a model, for the present model size, might not be feasible from a computational cost point of view.
\end{enumerate}

In conclusion, it can be stated that there are multiple modeling choices, which can result in such a discrepancy to the experimental observations. These require systematic exclusion by conducting intermediate validation of strain fields, including further relevant microstructural information and potentially adapting the hardening and flow rules as well as FIP formulations. Thereby, a suitable compromise between model fidelity and computational as well as experimental model parametrization effort can be achieved.

The multimodal experimental data set stores the reality for future validations, allows for sensitivity studies to incorporate relevant features into the model purposefully, and enables, e.g., Bayesian optimization of model parameters to the experimental observation. This ultimately can lead to an improved discriminability of damaged and non-damaged regions in future predictions. The validation concept composed of deep learning damage segmentation, multimodal data registration, and submodeling is assumed to be applicable to a wide range of materials. Arguably, the deep learning networks trained in a supervised fashion pose the limiting factor in this regard since their generalization capability across datasets is known to be compromised \cite{Thomas2020}. However, novel machine learning concepts such as unsupervised domain adaptation \cite{goetz2021addressing} can render such models transferable to a wider range of materials and damage types without requiring annotated data for new target materials.

All necessary data and code to carry out micromechanical simulations and compare the results to the acquired experimental data is open sourced in \cite{fordatis_repo} and \cite{github_repo}. The provided material includes the damage time series data, EBSD data, the meshed macro model with boundary conditions and the meshed microstructure model. Furthermore, macroscopic stress-strain data with different strain amplitudes for calibration of hardening models is made available. A step-by-step guide and detailed documentation is provided. Other researchers are encouraged to set up and test their models with this validation framework.

\section{Conclusions \& Outlook}
The developed validation methodology facilitates fast semi-automatized benchmarks of micromechanical simulations, which is a requirement considering the vast material landscape and the ongoing digitization of materials. Since it relies on deep learning semantic segmentation and large corrected electron backscatter diffraction scans, it allows for statistical benchmarking of actual plasticity traces and crack formation spots. This form of validation can be especially suitable to validate fatigue indicator parameters, while high resolution digital image correlation-based techniques are essential to validate the underlying mechanical fields. The detection of dominant slip traces from micrographs, introduced in \cite{Thomas2020}, can enable automated validation of modeled slip phenomena. Multimodal registration allows for a combination of damage evolution, microtexture, exact damage localization, and prior fatigue specimen reference in one data set while maintaining the environmental testing conditions and VHCF-regime testing capabilities.

The FIP localization is shown not to agree well with the damage locations from the experiments and tends to be overpredictive. This indicates that commonly used FIP are not able to predict the location of fatigue crack initiation reliably, although they might still be applicable for fatigue lifetime prediction.

The acquired data and models are available open source to build the foundation of a more general micromechanical modeling approach. To achieve this, the data set should be extended in the future by more materials, e.g. martensitic steel, and more experimental data such as the 3D microtexture for grain boundary inclination angles or electron channeling contrast imaging for initial statistically-stored dislocation densities.

\section*{Data availability}
The research data is made available in Fordatis \cite{fordatis_repo}. The code for running the simulations and performing the validations is available in a Github repository \cite{github_repo}.

\section*{Author contributions}

\textbf{Ali Riza Durmaz:} Conceptualization, Methodology Development, Software	Programming, Validation	Verification, Formal analysis, Investigation, Data Curation, Writing - Original Draft, Writing - Review \& Editing, Visualization, and Project administration \textbf{Erik Natkowski:} Methodology Development, Software Programming, Validation Verification, Formal analysis, Investigation, Data Curation, Writing - Original Draft, Writing - Review \& Editing, and Visualization \textbf{Nikolai Arnaudov:} Conceptualization, Methodology Development, Software Programming, Validation, Verification, Formal analysis, Investigation, Writing - Original Draft, and Visualization \textbf{Stefan Weihe:} Writing - Original Draft, Writing - Review \& Editing, and Supervision \textbf{Petra Sonnweber-Ribic:} Resources, Writing - Original Draft, Writing - Review \& Editing, and Supervision \textbf{Sebastian Münstermann:} Writing - Original Draft, Writing - Review \& Editing, and Supervision \textbf{Chris Eberl:} Conceptualization, Resources, Writing - Original Draft, Writing - Review \& Editing, and Supervision \textbf{Peter Gumbsch:} Resources, Writing - Original Draft, Writing - Review \& Editing, Supervision, and Funding acquisition.

\section*{Acknowledgements}

The contribution of A.D. was funded by the Bosch-Forschungsstiftung im Stifterverband grant number T113/30074/17.

\input{nomenclature}

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redpajama_set_name: RedPajamaArXiv


text:
Der Wannig (auch Hochwannig oder Wanneck) ist ein 2.493 m hoher Gipfel der Mieminger Kette in Tirol.

Lage
Der Wannig bildet den westlichen Abschluss der Mieminger Kette. Südwestlich liegt das Dorf Nassereith im Gurgltal, im Süden der Holzleitensattel, der das Gurgltal mit dem Mieminger Plateau verbindet. Im Norden liegt der Fernpass, ein Übergang vom Gurgltal nach Biberwier im Ehrwalder Becken. Nach Osten hin setzt sich die Mieminger Kette mit den Handschuhspitzen und dem Marienbergjoch (1.789 m) fort.

Die obersten vierhundert Meter des Wannig sind von Felsen und Geröllfeldern geprägt, darunter folgt ein breiter Latschengürtel. In den tiefer gelegenen Regionen der West- und Südhänge liegen Reste alter Bergbautätigkeit, hier wurden im Revier Feigenstein Blei- und Zinkerze (Smithsonit) abgebaut.

Anstiege
Meist wird der Wannig von der nordwestlich auf 1.718 m gelegenen Nassereither Alm (auch Muthenaualm genannt) aus bestiegen, die vom Fernpass, vom Albangerle nördlich von Nassereith, von Biberwier oder vom Marienbergjoch aus erreicht werden kann. Dieser Weg führt über die Westflanke, die Grüne Wanne, zum Gipfel (Stellen UIAA I).  Ein weiterer Weg von Nassereith trifft mit diesem Anstieg auf einer Höhe von ca. 1.780 m zusammen.

Vom Marienbergjoch wird der Wannig über die Handschuhspitzen bestiegen (Stellen UIAA I), weitere Anstiege über den Nordgrat (UIAA I) und die Nordwand (UIAA III) werden selten begangen.

Literatur
 Rudolf Wutscher: Mieminger Kette. Ein Führer für Täler, Hütten und Berge (= Alpenvereinsführer. Ostalpen.). Verfasst nach den Richtlinien der UIAA. Bergverlag Rother, München 1989, ISBN 3-7633-1099-1, S. 160–161.

Weblinks

Berg in Europa
Berg in Tirol
Zweitausender
Mieminger Kette

redpajama_set_name: RedPajamaWikipedia


text:
Un aerograma o carta aèria, també anomenada aérogramme, és una fina i lleugera peça de paper plegable i engomada per a escriure cartes de trànsit aeri, en la qual la carta i el sobre estan unificats. La majoria d'aerogrames tenen el segell imprès, tant per les autoritats postals com per empreses privades. Els remitents estan obligats a escriure les seves dades al revers.

Història

L'aerograma fou força popular gràcies a la seva utilitat durant la Segona Guerra Mundial. L'1 de març de 1941, començà el servei de correu entre l'Orient Mitjà i el Regne Unit gràcies als esforços del Tinent Coronel R. E. Evans, utilitzant diverses combinacions d'hidroavions de la Imperial Airways i transport militar. La naturalesa privada del correu aeri assegurà la seva popularitat entre els usuaris. L'ús dels aerogrames fou oficialment aprovat el 1952, durant el Congrés de la Unió Postal Universal celebrat a Brussel·les. Amb la disminució de la comunicació postal, els aerogrames s'han retirat de diversos serveis postals. Els aerogrames ja no es produeixen als Estats Units des de 2006, al Regne Unit el 2012, però en 2021 encara estan disponibles a Australia Post.

Referències

Enllaços externs

 Letter Post Manual  (Universal Postal Union, Berne, 1985). Regulacions de la UPU regulations aplicables als aerogrames.
 Aerogramme Society website  Temes relacionats amb els aerogrames.
 Nota de premsa de Correos "Correos cede un aerograma a los militares en misiones de paz fuera de España para que feliciten la Navidad" - Nota de premsa de Correos en què s'explica la història dels anagrames (2014).

Correu


I certainly have you covered with these delicious Butter Caramel Nougat Keto Protein Bars.
A recipe that was originally made with leftovers of several recipes I was working on on the same day turned out perhaps better than the 3 other recipes. Once refrigerated and sampled, I was in heaven.
They are very much like a Snickers, and I swear if you added a few nuts and some sugar free milk chocolate and you would have a whole new sensation.
These are very easy to make, but you do need some Sukrin Fibre Syrups. Don't hate me for more recipes using these products, they are just so versatile for making sweets and confectionery with almost an identical consistency and flavour as their sugar-filled equivalents. Sukrin Gold fibre syrup is so much like golden syrup in cooking so it can give you those very "caramelly" flavours that golden syrup affords, as well as that "chew" in Anzac Cookies.
The clear syrup is a lot like a glucose syrup used in confectionery recipes or nougat. It is so simple to use in these recipes and unfortunately neither the clear or golden syrup have any substitutes I know of. At the moment there is only one supplier of Sukrin, in Australia but they may change in the very near future. All I can say is I have been a little bit smitten with the syrups and how I can easily recreate recipes that were otherwise impossible to make in a compliant keto version.
The above picture is just the salted caramel nougat on its own and dipped in chocolate. Super easy! Instead of splitting the mix I have just added double the WPI and Melis to the salted caramel and placed straight into a slice pan and left to set. Cut into desired size dip in a little melted dark chocolate.
The use of WPI in many of my recipes allows me to create very low carb sweets that can also benefit from a lighter texture to a slightly crisp outer edge on recipes like the Chocolate Caramel Donuts. If you do not eat any dairy, there are some great substitutes in products like Pea Protein powders (0 carb) and Egg White protein powders. Again these products do need to be sourced either online or at your local health or supplements stores. Unfortunately most supermarkets are still behind in the times and do not stock all our dietary needs (well at least for a little compliant faux food sorcery).
Check the notes within the recipe for some substitutions. This recipe is far from rocket science. Add your own flavour combinations to change this up. Delicious with coffee added, or some of the Well Naturally Chocolate Raspberry Crisp. This recipe is totally suitable to freeze and great in the lunchboxes as well.
If you are looking for a little support, a meal plan, new recipes with all macros done for you, then grab your own copy of Keto for Beginners NOW! This is a great sample of our Club Keto 365. Many of your questions answered, some great information and guidance, plus no guesswork for you.
If you love this recipe let us know below how you went, what flavours you tried and how you shaped yours up. I hope you can hide it from everyone else in the house so it doesn't get all gobbled up before you can enjoy that little piece from time to time.
These are so delicious! A tasty sugar free sweet treat.
Add WPI, Sukrin melis, vanilla and salt. Stir until thick add more protein powder if mix is not thick.
Press mixture into 6 bar mould, only fill 1/3rd of each mould. You could use half a slice tray or even mini shape moulds if you dont have a bar mould. Even braking into small balls and combining with rest of mixture into a ball shape would work.
Heat fibre syrup for 90 seconds.
Flavoured whey proteins can be used.
*For whey-free recipe, zero carb pea protein can be use. Sukrin Fibre Syrups are interchangeable.
Can I give Sukrin Gold a blast in TMX instead of using Sukrin Melis?
Thanks for that, it's just that I have ordered the Sukrin Gold and the Gold Fibre Syrup and they are on their way from WA to Tas and Aus Post take so long to deliver……..!
When I made the Choc nougat layer it seemed to have too much whey to syrup ratio as it was very dry & didn't mix in. I had to add extra syrup & even then it was a bit late and is very grainy. The other layers were perfect. I didn't have Sukrin fibre syrup but another high fibre syrup. The first two layers were perfect so I'm not sure why the last layer hasn't worked.


text:
The Internet and Plagiarism
Post by Ralph » Tue Jun 20, 2006 8:42 am
latimes.com
http://www.latimes.com/business/la-fi-t ... -headlines
From the Los Angeles Times
Teachers Adjust Lesson Plans as Web Fuels Plagiarism
By Terril Yue Jones
School term papers may be going the way of the typewriters once used to write them.
"It's so easy to cheat and steal from the Internet that I don't even assign papers anymore," said Bobbie Eisenstock, an assistant professor of journalism at Cal State Northridge. "I got tired of night after night checking for cheaters."
Across the country, teachers and professors are abandoning the traditional academic chore of tidy margins and meticulous footnotes because the Internet offers a searchable online smorgasbord of ready-made papers.
"Students are using the Internet like an 8-billion-page, cut-and-pastable encyclopedia," said John Barrie, owner of a company that makes software to detect plagiarism.
So as the academic year wraps up in Southern California and elsewhere, students increasingly are having their knowledge tested with oral exams and in-class writing exercises. Or they're being asked to demonstrate their knowledge in unconventional ways — say, by assuming the role of a colonial pamphleteer railing against the Stamp Act.
Teachers who still assign long papers — 10 pages or more with footnotes and bibliographies — often require students to attach companion essays that describe every step of their research and writing. Even then, teachers scour the Internet for suspicious turns of phrase. And some schools are paying thousands of dollars a year for software such as Barrie's that scans work for plagiarism.
Those programs reveal that about 30% of papers are plagiarized, either totally or in part.
"It's a massive, massive problem," said Barrie, whose Turn It In service evaluates 60,000 submissions a day.
To be sure, the urge to cheat is as old as school. Students have long recycled their friends' and siblings' papers with their own names on top. But the rise of the Internet has made it easier than ever: Just type in a search term and up come hundreds of cheating choices that can be assembled into a paper with a couple of mouse clicks.
A 2003 study by Rutgers University found that more than a third of college undergraduates had cut and pasted passages from the Internet without attribution. High school teachers and even elementary school instructors said that kids were starting younger, as easy access to the Internet becomes almost as ubiquitous as television.
Rather than spend all of their grading time trying to catch cheaters, teachers are changing their lesson plans.
"The number of term papers assigned over the years has decreased significantly," said Herman Clay, director of history and social sciences at Los Angeles Unified School District.
Instead, Los Angeles teachers are assigning more in-class written exams, oral reports with visual aids and PowerPoint presentations, said Clay, a former principal of Van Nuys High School.
It's unclear how many teachers nationwide are doing the same, but it's enough that some educators worry that kids are missing an important educational experience — one that requires them to seek out facts and then assemble them into a cogent, sustainable argument.
In-class writing assignments are, by necessity, much shorter exercises that can be as brief as a couple of paragraphs and rarely more than a few pages.
"Kids these days have difficulty writing in depth about anything," said Nancy Willard, executive director of the Center for Safe and Responsible Internet use. "They are used to doing PowerPoint presentations, and the level of superficiality is great compared with term papers."
Whether that matters remains to be seen.
"We're just at the first stage in college with young people who have spent significant amounts of time on the Internet and online," she said. "We have no idea where we're going and what's going to happen with kids and their brains and their ability to do schoolwork."
Ironically, the shift away from take-home writing assignments comes as standardized tests such as the SAT add essay components.
Although term papers are still required at Warren High School in Downey, a sprawling campus with 3,500 students, there is a shift toward more in-class writing and presentation-oriented projects, said Shirley Stewart, the school's advanced placement coordinator and English department chairwoman.
Under state testing guidelines, students must learn the minutiae of bibliography protocol, such as what punctuation comes after the name of the publishing company when citing a novel. But they don't necessarily have to learn it as part of a term paper.
"We're teaching formatting, and in this Internet age, that seems kind of silly," said Stewart, who noted that in-class projects combine research and organization and require a mastery of the subject at hand to present in front of teachers.
At Clovis High School outside Fresno, library media teacher Janet Groth requires students to take notes during their research and write rough drafts of papers by hand in class — then attach them to the final versions.
"It took forever to grade them," she said, "but they knew I'd be checking and that they'd have to explain any wording."
The school also fights fire with fire, paying more than $2,000 a year to use Barrie's Web-based Turn It In, which checks a student's paper against a database of 17 million essays and papers. Barrie's Oakland-based company, IParadigms, calculates that the odds of stringing the same 16 words together in the same order as somebody else is less than one in a trillion.
Barrie said he expected the number of Turn It In submissions to climb 66% to 100,000 a day when school resumes this fall.
Los Angeles Unified is experimenting with Turn It In, but the service is not in widespread use.
Students say it's easy to fall into the trap of copying too much from a website. They say they are squeezed by academics, sports, music and other extracurricular activities to make them appear more attractive to prospective colleges.
And once they're in college, students say the pressure only increases — along with the total number of assignments they're asked to turn in.
"Frequently many students plagiarize an Internet site for an essay they must write because they know the teacher will merely skim it," said Rachel Koechel, a sophomore at Washington State University, who acknowledged having shared answers for online assignments and said she had seen fellow students submit copied material. "Sometimes students don't want to spend four hours on an essay that they know isn't worth a huge amount of their grade, and/or they know it's not going to be fully read over."
Websites with names such as Cheathouse.com, Schoolsucks.com and LazyStudents.com cater to that sort of sentiment with come-ons such as "Download your workload" and "If your professor can have a research assistant, why can't you?"
Charges generally are $10 per page but can be much more for customized assignments.
"If you're as overwhelmed with homework this semester as I am, you definitely need help with at least a few essays," reads the opening page of Essayboy, which touts an inventory of more than 25,000 works. "Help is here!"
Schoolsucks.com offers essays for free to allow students to get a feel for topics and the nuances of writing, Yasha Harari, co-owner of the site, said.
"We recommend they read whatever they're writing about, get a feel for the language, see what others are writing about," Harari said. "It's a peer-to-peer study group."
Harari warned potential cheaters that they get what they pay for.
"We're the world's largest collection of free and awful homework," Harari said. "You'd be a fool to copy our papers and submit it as your own because it's fully searchable."
The idea crosses everyone's mind, said Eric Katz, a junior at the highly competitive Monta Vista High School in the Bay Area's Cupertino.
"But our school has really stressed that when you get into college, if you plagiarize, you will get caught," said Katz, who hopes to attend the University of Pennsylvania.
Despite the growing awareness that the same tools that enable plagiarism also make it easier to spot, students persist. Ted Nellen, an English teacher on New York's Long Island, this year had a student submit a beautiful sonnet — one that had been written by John Keats.
mourningstar
Post by mourningstar » Tue Jun 20, 2006 10:34 am
i have to confess .. i myself, been seduced to Plagiarism. it was a matter of time then a matter of motivation. but it mostly depends on the level of importance. i don't fool around with important papers.
i sincerely hope my ethic teacher isn't a member off this forum and most importantly that she doesn't discover my indentity.
"Desertion for the artist means abandoning the concrete."
Post by jbuck919 » Tue Jun 20, 2006 10:40 am
mourningstar wrote: i have to confess .. i myself, been seduced to Plagiarism. it was a matter of time then a matter of motivation. but it mostly depends on the level of importance. i don't fool around with important papers.
Your secret is safe with us.
The bottom line for teachers is that kids still have to learn how to write. It is a challenge but not an impossible one.
DavidRoss
Post by DavidRoss » Tue Jun 20, 2006 11:17 am
Since so many kids these days have a faulty moral compass (is it getting worse with each generation?), they are apt to do what they perceive as the easy thing rather than the right thing, and what they think will give them immediate rewards according to their MTV-addled values. Rather than knuckling under to pressure from the asylum inmates and eliminating one of the most effective educational tools in the kit, I'd like to see such cheating dealt with as it should have been ages ago: expulsion with black-balling by all accredited institutions. Otherwise we're cultivating a generation rife with Kenneth Lays and his already all too common ilk.
Who'dathunk the principle of the thin end of the wedge would be beyond the grasp of so many?
"Most men, including those at ease with problems of the greatest complexity, can seldom accept even the simplest and most obvious truth if it would oblige them to admit the falsity of conclusions which they have delighted in explaining to colleagues, which they have proudly taught to others, and which they have woven, thread by thread, into the fabric of their lives." ~Leo Tolstoy
"It is the highest form of self-respect to admit our errors and mistakes and make amends for them. To make a mistake is only an error in judgment, but to adhere to it when it is discovered shows infirmity of character." ~Dale Turner
"Anyone who doesn't take truth seriously in small matters cannot be trusted in large ones either." ~Albert Einstein
"Truth is incontrovertible; malice may attack it and ignorance may deride it; but, in the end, there it is." ~Winston Churchill
Holden Fourth
Post by Holden Fourth » Tue Jun 20, 2006 3:49 pm
Our school pays for and uses a service called "Turnitiin". All major assignments are submitted via this system and it's surprising how the originality is now coming back to kids work. Even better, once an assignment has been submitted via Turnitin it is lodged in their system forever and therefore prevents students swapping their work wih each other.
BWV 1080
Post by BWV 1080 » Wed Jun 21, 2006 9:07 pm
I must say that writing is hard work and all the marvels of modern technology haven't made it any easier. Vast resources now lie just keystrokes away, but the basic art of assembling one's thoughts into engaging prose is little changed since the days of paper and pencil. While mindless information doubles every three years, thoughtful writing still proceeds at an old fashioned pace.
Unfortunately, the timeless nature of writing isn't shared by its fraudulent imitation: plagiarism. Though nearly as ancient as writing itself, plagiarism adapts quickly to new technology. With a web full of seemingly ownerless prose, plagiarism is as easy as cut-and-paste. And if you don't see exactly what you want for free, you can buy it online at any number of "paper mills."
But a more insidious way in which technology has fostered plagiarism is by shifting our attention from content to appearance. A well-written student paper is no longer "A" work unless it's printed in color on glossy paper, with fonts and images and an accompanying multimedia presentation. Students feel expected to turn in the best papers ever written, not the best papers they can write themselves. So they assemble those papers. With hours invested in the decorations, students feel justified in stealing some or all of the text. After all, they "couldn't have said it any better" themselves.
In addition to its easy rationalization by people seeking the rewards of writing without the associated effort, plagiarism is also widely misunderstood. It isn't limited to the theft of another person's words; it also includes the theft of their ideas. More generally, plagiarism is any form of dishonesty about authorship. A reader or listener should always know whose thoughts they're hearing.
Plagiarism isn't a victimless crime. It deprives its readers of their time and trust, and its true authors of their good names. In academia, plagiarism inflates grades relative to education and devalues honest scholarship. Among authors and journalists, plagiarism cheapens the very art of writing, much as performance enhancing drugs cheapen so many sports. Plagiarism is as much a problem of morale as it is of ethics.
Plagiarism isn't an obscure tweed-collar crime. It's a sorry fact of life everywhere and any school or organization that feels untainted is probably in denial. With plagiarism so commonplace, an organization that deals openly with it deserves our support, not our condemnation. There is no scandal in cleaning house. The scandal is in tolerating or covering up plagiarism.
Unfortunately, plagiarism is openly tolerated in the most public sectors of modern life. It wasn't always that way. Lincoln didn't just perform his Gettysburg address; he actually wrote it. What happened to that tradition of intellectual honesty in public speech? With ghostwriting so ubiquitous among the rich and powerful, it's no wonder that young people see little value in learning to write well. They view writing the way they view cleaning their rooms—an unpleasant chore they'll do only until they can afford to hire someone else.
When students believe that writing assignments are merely hazing rituals, hurdles on the path to success in life, some will inevitably plagiarize. And when instructors assign writing that has no clear educational goals, how can the students value it? Having explicitly stated goals is both good discipline and a way to avoid misunderstandings. If students believe an assignment is "busy work," some will be busy cheating.
Finally, students need to be taught that the act of writing is intrinsically valuable to them. It crystallizes one's thoughts in a way that nothing else can. .

redpajama_set_name: RedPajamaCommonCrawl


text:
Q: C# divide two binary numbers Is it possible in C# to divide two binary numbers. All I am trying to do is:
Get integer value into binary format, see below
int days = 68;
string binary = Convert.ToString(days, 2);

but how do you divide the binary numbers? , what format should be used?
01000100 / 000000100 = 4

Little confused any help would be great.

A: // convert from binary representation
int x = Convert.ToInt32("01000100", 2);
int y = Convert.ToInt32("000000100", 2);

// divide
int z = x / y;

// convert back to binary
string z_bin = Convert.ToString(z, 2);

A: int a = Convert.ToInt32("01000100", 2);
int b = Convert.ToInt32("000000100", 2);
int c = a / b;

and by the way the answer is dec:17 instead of dec:4

A: it is just:
x / y

you don't have to convert integer into binary string by
int days = 68;
string binary = Convert.ToString(days, 2);

numbers are binary in memory.
or i didn't understood you

A: If you are trying to mask the bits together, youll want to use the & Operator
// convert from binary representation
int x = Convert.ToInt32("01000100", 2);
int y = Convert.ToInt32("000000100", 2);

// Bitwise and the values together
int z = x & y; // This will give you 4

// convert back to binary
string z_bin = Convert.ToString(z, 2);

A: This will help u.
 namespace BinaryExample1
        {
        class Program
        {
        static void Main(string[] args)
        {
        int i = Convert.ToInt32("01000100", 2);
        int j = Convert.ToInt32("00000100", 2);
        int z;
        z = i / j;
        Console.WriteLine(z);
        Console.ReadLine();
        }
        }
        }

redpajama_set_name: RedPajamaStackExchange


text:
New Kids is a Dutch television show.

It may also refer to:

The New Kids, a 1985 film
A series of albums by iKon:
New Kids: Begin (2016)
New Kids: Continue (2018)
New Kids: The Final (2018)
The New Kids (album) (2019)

See also
New Kids on the Block, American musical group


text:
Photo by Mark Zamora on Unsplash
A 'Back-Stage' 'Pass:'
Under the Rock with White Liberal Racism
"Negative Stereotyping of People of Color: In U.S. society today, white progressives "know" not to engage in negative stereotyping in "front-stage interactions" — settings that include white strangers or people of color. Instead whites "know" to engage in negative stereotyping only in "back-stage" settings — settings that are all-white and where participants can assume that no serious objection will be raised to the performance. In back-stage settings, the expression of the white racial frame and the lack of objection to that expression provide a 'social glue' that creates a sense of shared identity for the white group." Joe Feagin, The White Racial Frame, (127–128)
I came across this passage in a re-read of this book, which has been revised, and it reminded me of my experiences 'passing' as white, since these often allow me a 'pass' to the 'back-stage' settings described by Dr. Feagin.
About a year ago, a friend invited me to the opening of a yoga studio in the suburbs and was called away to an emergency. During the opening, S., an Indian-American woman, objected to a large sign at the front of the studio which depicted only white women doing yoga. She stated that this distorts the fact that yoga originates in India and feels like cultural appropriation. Despite the fact that this was an open meeting to discuss the yoga studio's presence in the area, this statement provoked an awkward silence in the group of mostly liberal white people. The owner, a white woman, finally broke the silence and announced that she would certainly consider it. This statement was followed by a few awkward giggles and some whispered assent, none of which was loud enough to 'implicate' any of them as individuals in actual agreement with S.. I was considering my response when the owner announced that the meeting was over.
The group headed for an informal meet 'n greet and happy hour in an adjoining room. I knew, based on the awkward silence that followed the words 'cultural appropriation,' that I was in for a back-stage treat, since I had just gotten my hair keratinized straight. Today, I was 'passing.' I plucked a few hors d'oeuvres off the table while keeping my ears peeled for the inevitable, which I've heard in some permutation many times.
A: "I'm sure she didn't mean to sound so aggressive."
B: "I know. I agree. She seems really nice. Indians are usually so…peaceable. I wonder if she's Hindu."
C: "Still. I wonder if she really meant it?"
A: "Wasn't that sign expensive?"
C: "Yes. I just…maybe I should have…."
B: "How could you know? Your sign reflects most of the people in the area. Your potential clientele. No one could blame you for making a sign that reflects the people coming here."
C: "You know, I haven't seen her around here. Maybe it would have been nice for her to mingle a little before…"
A: "…opening the conversation with a complaint? Yes. I agree. Maybe she's new to the area. I've never seen her before."
After several minutes more of this drivel, which usually falls under the rubric of 'white ignorance,' I did offer my opinion and left. Each time I 'pass' in these settings, I always leave feeling as if I've participated in what is actually a massive 'fail.' White supremacy. This is not to say that a particular shade of skin is a 'fail' but to note that a great deal of value has been placed on one relative to the other, thus creating inequity out of what is difference only for the purposes of domination. That this is classified as 'ignorance' is beginning to seem less and less plausible.
Here is what I inferred from the conversation: an Indian woman who mentions her culture is 'aggressive:' a form of subtle bullying that implies her only non-aggressive option is to subordinate (shut up); brown/black women are 'aggressive' implying they should be passive AND that white women are situated at a favorable comparison point; the stereotyped notion that Indian women should be 'peaceful,' which places pressure on her to act this way AND sets her baseline, as a brown woman, at 'obsequious;' the clientele are white and this is normative, which implies S. ultimately doesn't belong there except as an outsider; excusing each other from dealing directly with the issue at hand AND simultaneously implying that white clientele are the true natives of the general area; stating S. is a complainer: more subtle bullying ("you're whiny; shut up;"); and finally, implying she is the one who is unfriendly when the circumstances have been presented as overtly homogeneous: white.
This conversation is typical of this sort of setting, and by no means my first encounter with a situation of this nature. This context exists and involves a long list of people of color in which the final WL goal seems to be the same: appear to be liberal and open-minded but ultimately confirm white supremacy in what is hopefully a covert enough manner that one will still be perceived as 'nice' regardless of the final impact on any of a range of people of color.
Frankly, I am shocked that these sorts of comments are allowed their own free pass — yes, it's yet another — as ignorance. This is simply a lack of humanity in its willingness to 'other' another, to push an 'other' out of the space. Claiming ignorance as a substitute for moral decision-making is starting to seem like a bad excuse.
In the final analysis, this attitude conveys that these suburban whites 'own' the predominant space and belong everywhere, but that others are outsiders, even in contexts of cultural appropriation. Eventually, this profound systemic hypocrisy will have to be negotiated. The system of white supremacy in all its incarnations is one giant, protracted failure and cannot simply be excused by claims of 'ignorance' as long as those claims help sustain white supremacy.
White Denial
White Liberalism
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Alistair Mulligan
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William Bauer
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Katharine Chan, MSc, BSc, PMP in An Injustice!


On Monday, August 21st Intel INTC 50,75 +1,28 +2,59% will officially announce the newest generation (8th) of Core® processors named Coffee Lake. Intel will livestream the event at 8:00 AM PDT via its Facebook page or the Intel newsroom.
The new products are expected to have more cores than the current maximum of four in Intel's mainstream processors, with some leaks pointing at three six-core processors, which could offer 50% more performance in multithreaded tasks compared to the current Core i7-7700K – the flagship mainstream processor.
There are also rumors that Intel will be upping the core count of its Core i3 CPUs too, all of which are currently dual-core models. This is likely in response to AMD's Ryzen 3 processors, which offer four cores for a little over $100.