Metaharmonic wavelets are introduced for constructing the solution of theHelmholtz equation (reduced wave equation) corresponding to Dirichlet's orNeumann's boundary values on a closed surface approach leading to exactreconstruction formulas is considered in more detail. A scale discrete version ofmultiresolution is described for potential functions metaharmonic outside theclosed surface and satisfying the radiation condition at infinity. Moreover, wediscuss fully discrete wavelet representations of band-limited metaharmonicpotentials. Finally, a decomposition and reconstruction (pyramid) scheme foreconomical numerical implementation is presented for Runge-Walsh waveletapproximation.
The fatigue life of metals manufactured via laser-based powder bed fusion (L-PBF) highly
depends on process-induced defects. In this context, not only the size and geometry of the defect, but
also the properties and the microstructure of the surrounding material volume must be considered.
In the presented work, the microstructural changes in the vicinity of a crack-initiating defect in a
fatigue specimen produced via L-PBF and made of AISI 316L were analyzed in detail. Xenon plasma
focused ion beam (Xe-FIB) technique, scanning electron microscopy (SEM), and electron backscatter
diffraction (EBSD) were used to investigate the phase distribution, local misorientations, and grain
structure, including the crystallographic orientations. These analyses revealed a fine grain structure
in the vicinity of the defect, which is arranged in accordance with the melt pool geometry. Besides
pronounced cyclic plastic deformation, a deformation-induced transformation of the initial austenitic
phase into α’-martensite was observed. The plastic deformation as well as the phase transformation
were more pronounced near the border between the defect and the surrounding material volume.
However, the extent of the plastic deformation and the deformation-induced phase transformation
varies locally in this border region. Although a beneficial effect of certain grain orientations on the
phase transformation and plastic deformability was observed, the microstructural changes found
cannot solely be explained by the respective crystallographic orientation. These changes are assumed
to further depend on the inhomogeneous distribution of the multiaxial stresses beneath the defect as
well as the grain morphology