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A method of solving the thermo-fluid dynamics problem is presented, enabling the prediction of the shape and dimensions of the weld pool during keyhole laser welding of thick plates. It is shown that the rear weld pool boundary can be satisfactorily approximated by a set of superellipses (Lamé curves). The presence of a convex rear weld pool boundary in the mid-plane has been observed experimentally and reproduced numerically. It was shown that in this zone the concentration of liquating impurities increases and the local solidification temperature decreases, contributing to the susceptibility to hot cracking.
AbstractThe sustainable and resource-efficient production of wind energy plants requires the use of modern high-strength fine-grain structural steels. This applies to both foundation and erection structures, like mobile or ship cranes. During the assembly of steel structures, unacceptable defects can occasionally be found in the weld area. In most cases, the economical solution would be local thermal gouging of the affected areas and re-welding. Due to the high shrinkage restraint of the joint groove in the overall structure, the superposition of global and local welding-induced stresses may lead to crack formation and component failure, particularly in interaction with the degradation of the microstructure and mechanical properties of high-strength steels during the repair process. However, manufacturers hardly have any information about these issues and there is a lack of recommendations and guidelines to take these safety-relevant aspects into account in adequate repair concepts. The aim of this research is to derive recommendations for repair concepts appropriate to the stresses and materials involved providing a basis for standards and guidelines to avoid cold cracking, damage and expensive reworking especially for high-strength steels. Part 1 of this study involves systematic investigations of influences of shrinkage restraint during repair welding of two high-strength steels S500MLO for offshore application and S960QL for mobile crane structures. The quantification of the shrinkage restraint of repair weld joints was achieved by means of experimental and numerical restraint intensity analysis. In welding experiments with self-restrained slot specimens, restraint intensity and introduction of hydrogen via the welding arc using anti spatter spray were varied systematically to analyse the effect on welding result, residual stresses and cold cracking. It could be shown that increasing restraint intensities result in significantly higher transverse residual stress levels. In the case of hydrogen introduction S500MLO showed no cold cracking independent of the restraint conditions. However, S960QL was found to be considerably cold cracking sensitive if hydrogen is introduced. With increasing restraint intensity length and number of cold cracks increases significantly. Part 2 [1] of this study is focussed on microstructure and residual stresses due to gouging and stress optimization via adequate heat control parameters in repair welding.
The high potential of hydrogen as a key factor on the pathway towards a climate neutral economy, leads to rising demand in technical applications, where gaseous hydrogen is used. For several metals, hydrogen-metal interactions could cause a degradation of the material properties. This is especially valid for low carbon and highstrength structural steels, as they are commonly used in natural gas pipelines and analyzed in this work.
This work provides an insight to the impact of hydrogen on the mechanical properties of an API 5L X65 pipeline steel tested in 60 bar gaseous hydrogen atmosphere. The analyses were performed using the hollow specimen technique with slow strain rate testing (SSRT). The nature of the crack was visualized thereafter utilizing μCT imaging of the sample pressurized with gaseous hydrogen in comparison to one tested in an inert atmosphere.
The combination of the results from non-conventional mechanical testing procedures and nondestructive imaging techniques has shown unambiguously how the exposure to hydrogen under realistic service pressure influences the mechanical properties of the material and the appearance of failure.
This study investigates the room‐ and high‐temperature (650 °C) tensile and low‐cycle‐fatigue behavior of Inconel 718 produced by laser powder bed fusion (PBF‐LB/M) with a four‐step heat treatment and compares the results to the conventional wrought material. The microstructure after heat treatment is characterized on different length scales. Compared to the wrought variant, the elastic and yield properties are comparable at both test temperatures while tensile strength, ductility, and strain hardening capacity are lower. The fatigue life of the PBF‐LB/M variant at room temperature is slightly lower than that of the wrought material, while at 650 °C, it is vice versa. The cyclic stress response for both material variants is characterized by cyclic softening, which is more pronounced at the higher test temperature. High strain amplitudes (≥0.7%) at room temperature and especially a high testing temperature result in the formation of multiple secondary cracks at the transitions of regions comprising predominantly elongated grain morphology and columns of stacked grains with ripple patterns in the PBF‐LB/M material. This observation and pronounced crack branching and deflection indicate that the cracks are controlled by sharp micromechanical gradients and local crystallite clusters.
Despite the advances in hardware and software techniques, standard numerical methods fail in providing real-time simulations, especially for complex processes such as additive manufacturing applications. A real-time simulation enables process control through the combination of process monitoring and automated feedback, which increases the flexibility and quality of a process. Typically, before producing a whole additive manufacturing structure, a simplified experiment in the form of a beadon-plate experiment is performed to get a first insight into the process and to set parameters suitably. In this work, a reduced order model for the transient thermal problem of the bead-on-plate weld simulation is developed, allowing an efficient model calibration and control of the process. The proposed approach applies the proper generalized decomposition (PGD) method, a popular model order reduction technique, to decrease the computational effort of each model evaluation required multiple times in parameter estimation, control, and optimization. The welding torch is modeled by a moving heat source, which leads to difficulties separating space and time, a key ingredient in PGD simulations. A novel approach for separating space and time is applied and extended to 3D problems allowing the derivation of an efficient separated representation of the temperature.
The results are verified against a standard finite element model showing excellent agreement. The reduced order model is also leveraged in a Bayesian model parameter estimation setup, speeding up calibrations and ultimately leading to an optimized real-time simulation approach for welding experiment using synthetic as well as real measurement data.
Stresses in repair welding of high-strength steels—part 2: heat control and stress optimization
(2024)
In welding of high-strength steels, e.g. for foundations and erection structures of wind energy plants, unacceptable defects can occasionally be found in the weld area, which should be removed by thermal gouging and subsequent re-welding. High shrinkage restraint of repair welds may lead to crack formation and component failure, predominantly in interaction with degraded microstructures and mechanical properties due to repair cycles. This study aims for elaboration of recommendations for repair concepts appropriate to the stresses and materials involved to avoid cold cracking, damage and expensive reworking. In part 1 [1] of this study, systematic investigations of influences of shrinkage restraint on residual stresses and cold cracking risk during repair welding of two high-strength steels S500MLO for offshore application and S960QL for mobile crane structures were focussed. In this part 2, the microstructure, particularly hardness, and residual stresses due to gouging and influences of heat control parameters in repair welding are analysed. A clear reduction in residual stress after gouging can be observed, especially for the specimens with restrained transverse shrinkage. Gouging to a depth of approx. 2/3 of the seam height does not lead to a complete relaxation of the observed reaction forces. Particularly for the higher strength steel S960QL, there are pronounced areas influenced by the gouging process in which a degradation of the microstructure and properties should be assumed. Overall, the repair welds show a significant increase in the width of the weld and HAZ compared to the original weld, especially in the case of S960QL/G89. The repair welds show higher welding-induced stresses than the original welds, especially in the areas of the HAZ and the base metal close to the weld seam. This behaviour can be attributed overall to increased restraint conditions due to the remaining root weld or shorter gouge grooves. In good agreement with earlier investigations, the residual stresses transverse to the weld can be significantly reduced by upwardly limited working or interpass temperatures, and the reaction stresses resulting from high restraint conditions can be effectively counteracted. The influence of the heat input on the stress formation is low compared to the interpass temperature for both test materials.
For the hydrogen-based energy economy of tomorrow, the construction of the necessary infrastructure will play a central role. Most materials used to date, such as welded steels, can be prone to hydrogen embrittlement under certain conditions. This includes the classic delayed cold cracking during welding as well as degradation phenomena during service of components in hydrogen-containing environment. For the evaluation of any hydrogen effect, for example, on the mechanical properties of a welded metallic material, the hydrogen content must be precisely determined. In the case of weld seams, the carrier gas hot extraction (CGHE) according to ISO 3690 is meanwhile state-of-the-art. CGHE is based on accelerated hydrogen degassing due to the thermal activation of hydrogen at elevated temperatures. In addition to the quantification of hydrogen, thermal desorption analysis (TDA) with varying heating rates can be used to determine and evaluate the hydrogen trapping at microstructural defects in the material. For both techniques, experimental and metrological influences must be considered, which have a major effect on the result. For example, ISO 3690 suggests different sample geometries and minimum extraction times for CGHE. This study summarizes the results and experiences of numerous investigations at the Federal Institute for Materials Research and Testing (BAM) with different sample temperatures and geometries (ISO 3690 type B and cylindrical TDA samples) regarding the influence of the sample surface (polished/welded), measurement accuracy depending on the sample volume and the insufficient monitoring of the effect of PI control on the extraction temperature. A deviating extraction temperature from the target temperature can significantly falsify the measurement results. Based on the results, methods are shown which allow the desired extraction temperature to be reached quickly without physically interfering with the measuring equipment. This serves to significantly improve the reliability of the hydrogen measurement through increased signal stability and accelerated hydrogen desorption. In general, an independent temperature measurement with dummy samples is recommended for the heating procedure of choice to exclude possible undesired temperature influences before the measurement. The methods described can be transferred directly to industrial applications
In this contribution, we present a physically motivated heat source model for the numerical modeling of laser beam welding processes. Since the calibration of existing heat source models, such as the conic or Goldak model, is difficult, the representation of the heat source using so-called Lamé curves has been established, relying on prior Computational Fluid Dynamics (CFD) simulations.
Lamé curves, which describe the melting isotherm, are used in a subsequent finite-element (FE) simulation to define a moving Dirichlet boundary condition, which prescribes a constant temperature in the melt pool. As an alternative to this approach, we developed a physically motivated heat source model, which prescribes the heat input as a body load directly. The new model also relies on prior CFD simulations to identify the melting isotherm. We demonstrate numerical results of the new heat source model on boundary-value problems from the field of laser beam welding and compare it with the prior CFD simulation and the results of the Lamé curve model and experimental data.
Electromagnetic stirring is known to promote material flow, reduce porosity, uniform elements distribution, and refine grain in laser beam welding (LBW), which enhances the applicability of LBW in various industries. In this study, a phase-field model of dendrite growth in AA5754 Al alloy electromagnetic stirring laser beam welding was established. The model considered the thermal electromagnetic Lorentz force resulting from the interaction between the electric field generated by the Seebeck effect and the magnetic field, as well as the temperature gradient and solidification rate of the solidification interface obtained from the computational fluid dynamics electromagnetic stirring LBW model. The variation rules of dendrite growth with different magnetic parameters and effects are analyzed. Comprehensively, the magnetic field promotes the solidification rate, thus promoting interfacial instability and a large magnetic flux density leads to a faster interface instability. The solidification rate as well as the temperature gradient affect the growth rate, and the accelerated growth caused by the so lidification rate with a high frequency and a large magnetic flux density effectively inhibits the slow growth caused by the temperature gradient. The thermal electromagnetic Lorentz force is the main factor for the branch increment at low frequencies, while both thermal electromagnetic Lorentz force and temperature gradient in crease the number of branches at high frequencies. The calculated average branch numbers considering various factors in the stable stage under different magnetic parameters were consistent with the results of the scanning electron microscope tests.
Effect of high-pressure hydrogen environment on the physical and mechanical properties of elastomers
(2024)
This study presents the influence of high-pressure hydrogen environment on the physical and mechanical properties of two types of cross-linked hydrogenated acrylonitrile butadiene rubbers. Based on the CSA/ANSI standard, static exposures in hydrogen experiments were performed up to 100 MPa at 120 °C. Characterization before and after exposure was conducted by means of density and hardness measurements, dynamic mechanical analysis (DMA), tensile tests, compression set, FT-IR and AFM analyses to assess effects after decompression. While the effect of high-pressure exposure is significant immediately after exposure, most of the physical and mechanical properties recover after 48 hours. FT-IR, AFM, SEM and compression set results indicate, however, permanent effects.
The Varestraint test and its variant Transvarestraint are one of the most widely used techniques for evaluating a material solidification cracking sensitivity during welding. The result of such tests is a crack length which is proportional to the material’s cracking susceptibility. Nevertheless, the welding and load parameters can unintentionally influence the crack length, which in some cases can distort the material evaluation. An approach is described as to how these effects can be assessed with the aid of a digital crack analysis. The crack lengths are compared position-dependently with their possible propagation due to the weld pool movement during continuous loading. The index derived from this can be used by the operator to evaluate his test parameters. In addition, a comparison of the results of different Varestraint setups is made possible. Alongside experimental results, a numerical sensitivity analysis is presented on how individual welding and loading parameters can affect the crack lengths.
Multiple principal element alloys encompass the well-known high entropy alloys (HEA). The alloy system represents a new class of materials consisting of at least three alloying elements, each containing 5 to 35 at.%. Thus, this alloying concept differs fundamentally from conventional materials such as steel or nickel alloys. For this purpose, the alloying elements are specifically selected, the microstructures are adjusted in a single-phase and, in some cases, multi-phase manner. In particular, conflicting goals, such as the trade-off between strength and ductility in conventional steels, are overcome. However, in the last 20 years, the focus has been on material synthesis. With the increase in available material quantities, the focus is now on processing issues such as joining and welding processes. The weldability of HEAs has received very little attention so far. The experience with dissimilar metal welds is completely lacking but is essential for the application of these materials in combination with conventional materials. The present study presents comprehensive experimental results on the weldability of an equimolar CoCrFeMnNi-HEA in cold-rolled and heat-treated condition, which was joined by tungsten inert gas welding to an austenitic steel AISI 304. The mechanical properties of the dissimilar metal welds were characterized by cross-weld tensile samples, whereas the local deformation in the weld of the different welding zones was measured by digital image correlation. In accordance with the respective initial HEA condition (cold-rolled vs. heat-treated), the local strain behavior was divergent and influenced the global mechanical properties of both DMW types. Nonetheless, the experiments provided proof in principle of the weldability for dissimilar joints of the CoCrFeMnNi-HEA welded to conventional materials like austenitic stainless steels ensuring a corresponding capability for mechanical loading. This allows further considerations on the application of these innovative materials.
Numerical and experimental assessment of liquid metal embrittlement in externally loaded spot welds
(2024)
Zinc-based surface coatings are widely applied with high-strength steels in automotive industry. Some of these base materials show an increased brittle cracking risk during loading. It is necessary to examine electrogalvanized and uncoated samples of a high strength steel susceptible to liquid metal embrittlement during spot welding with applied external load. Therefore, a newly developed tensile test method with a simultaneously applied spot weld is conducted. A fully coupled 3D electrical, thermal, metallurgical and mechanical finite element model depicting the resistant spot welding process combined with the tensile test conducted is mandatory to correct geometric influences of the sample geometry and provides insights into the sample’s time dependent local loading. With increasing external loads, the morphology of the brittle cracks formed is affected more than the crack depth. The validated finite element model applies newly developed damage indicators to predict and explain the liquid metal embrittlement cracking onset and development as well as even ductile failure.
Hydrogen has great potential on the path towards decarbonization of the energy and transport sectors and can mitigate the urgent issue of global warming. It can be sustainably produced through water electrolysis with potentially zero emissions, and efficiently used (e.g., in fuel cell systems). Despite its environmental advantages, hydrogen-metal interactions could result in the degradation of the mechanical properties of several structural materials. In order to determine the magnitude of the material degradation in relation to hydrogen exposure, extensive material testing is required. The standardized procedure for in-situ testing for the quantification of the impact of compressed gaseous hydrogen (CGH2) relies on the utilization of an autoclave around the tested specimen. Such test set-up is complex, expensive, time-consuming and requires special equipment, trained personnel, and strict safety procedures. A relatively recent method to circumvent these issues and provide affordable results consists of using hollow specimens, thus applying the hydrogen pressure inside rather than outside the specimen. It allows to reduce the volume of hydrogen by several orders of magnitude and to perform the tests more efficiently and in a safer manner. This study focuses on evaluating the tensile properties of X65 vintage pipeline steel tested in a high-pressure hydrogen environment using hollow specimens. Tests are performed in 6 MPa H2 and Ar at the nominal strain rate of 10−6 s−1 to evaluate the reduced area at fracture and the elongation loss. The effect of surface finishing on crack initiation and propagation is investigated by comparing two different manufacturing techniques. In this way, this study provides insights into the applicability of a novel, reliable, and safe testing method which can be used to assess the hydrogen-assisted ductility loss in metallic materials.
A fundamental study of physical mechanisms of wineglass-shaped fusion zone profile in laser melting
(2024)
The fusion zone geometry in laser melting processes e.g., laser welding and laser-based additive manufacturing, of metallic materials has commonly a wineglass-shaped profile which is critical to the grain orientation and stress distribution. Hereby, we adopt for the first time a decoupling work through a combination of multi-physics modelling and experiments to reveal the fundamental mechanisms of this special morphology. Two physicsbased easy-to-use metal vapour models are proposed to consider the vapour’s momentum and thermal effects separately. It is found that the direct laser energy absorption and Marangoni shear stress which are widely hypothesised to dominate the wineglass-shape formation show only a minor influence. The additional heating from the metallic vapour plume rather than its momentum impact contributes predominantly to the enlarging of the molten pool top region, resulting directly in the formation of the wineglass-shaped fusion zone. The generality of the plume heating effect is also validated in two types of materials (steel and Al) in a wide range of parameters.
Die additive Fertigung mittels Schweißverfahren bietet große ökonomische Vorteile für eine ressourceneffiziente Bauteilherstellung. Offene Fragen bezüglich Homogenität, Anisotropie der Schweißgefüge und den damit verbundenen Bauteileigenschaften stehen einer wirtschaftlichen Verarbeitung oftmals im Wege. Finale Bauteilgeometrie und Oberflächengüte erfordern meist komplementäre subtraktive Fertigungsschritte. Werkstoffe für hochbelastbare Komponenten sind oftmals schwer spanbar. In einem Vorhaben der BAM und des ISAF wurde untersucht, wie die Modifikation der AM-Schweißzusätze und das ultraschallunterstützte Fräsen (US) die Zerspanungssituation verbessern. Der vorliegende Artikel stellt wesentliche Zusammenhänge zwischen Legierung, Gefüge und Zerspanung zweier schwer spanbarer Hochleistungslegierungen (FeNi und CoCr) dar. Großes Potenzial zeigte neben dem US die Modifikation mit Zr und Hf bei Zulegierung in das Schweißgut mittels Beschichtung von Massivdrähten bzw. Herstellung von Fülldrähten.
Beim Unterpulverschweißen sind die Prozessgeräusche ein Indikator für eine gute Fügequalität. Diese Beurteilung kann i.d.R. nur von einer erfahrenen Fachkraft durchgeführt werden. Eine kürzlich entwickelte künstliche Intelligenz kann automatisch das akustische Prozesssignal anhand vortrainierter Merkmale klassifizieren und die Fügequalität anhand des Geräuschs beurteilen. Der Algorithmus, einmal richtig trainiert, kann den Prüfaufwand beim Unterpulverschweißen deutlich reduzieren.
The ISO 3690 standard “Determination of hydrogen content in arc weld metal” requires a thermal activation of the diffusible hydrogen in a piece of weld metal for the subsequent ex situ concentration measurement by carrier gas hot extraction CGHE or thermal desorption spectroscopy (TCD). Laser-induced breakdown spectroscopy (LIBS) offers a time and spatially resolved, almost non-destructive, in situ measurement of hydrogen at surfaces without sample preparation. We measured hydrogen in steels, which were charged either electrochemically or by high-pressure hydrogen gas, and compared the results. Further, the feasibility of quantitative hydrogen line scan measurements with LIBS was demonstrated by measuring hydrogen at water jet cut surfaces. The hydrogen concentrations measured with the help of LIBS were compared with CGHE measurements. It was observed that hydrogen can be reliably measured with LIBS for concentrations larger than 2 wt.-ppm. The maximum hydrogen concentration achieved using electrochemical charging was 85.1 ppm. The results show that LIBS is a promising technique for time- and spatially resolved measurements of hydrogen in steels.
High-strength steels offer potential for weight optimization due to reduced wall thicknesses in modern constructions. Additive manufacturing processes such as Wire Arc Additive Manufacturing (WAAM) enable the resource-efficient production of structures. In the case of defects occurring in weld seams orWAAM components due to unstable process conditions, the economical solution is local gouging or machining and repair welding. It is important to understand the effects of machining steps on the multiaxial stress state in conjunction with the design-related shrinkage restraints. Research into how welding and slot milling of welds andWAAM structures affects residual stresses is still lacking. For this reason, component-related investigations with high-strength steels with yield strengths ≥790 MPa are carried out in our research. In-situ digital image correlation (DIC) and ex-situ X-ray diffraction (XRD) were used to analyze the stresses and strains induced on specimens during and after milling. The systematic analyses revealed a significant interaction of the stiffness and microstructure of the specimens with the initial residual stresses induced by welding. Subsequent repair welds can result in significantly higher residual stresses.
AbstractPowder Bed Fusion with Laser Beam of Metals (PBF-LB/M) has gained more industrial relevance and already demonstrated applications at a small series scale. However, its widespread adoption in various use cases faces challenges due to the absence of interfaces to established Manufacturing Execution Systems (MES) that support customers in the predominantly data-driven quality assurance. Current state-of-the-art PBF-LB/M machines utilize communication architectures, such as OPC Unified Architecture (OPC UA), Message Queuing Telemetry Transport (MQTT) and Representational State Transfer Application Programming Interface (REST API). In the context of the Reference Architecture Model Industry 4.0 (RAMI 4.0) and the Internet of Things (IoT), the assets, particularly the physical PBF-LB/M machines, already have an integration layer implemented to communicate data such as process states or sensor values. Missing is an MES component acting as a communication and information layer. To address this gap, the proposed Extract Transform Load (ETL) pipeline aims to extract relevant data from the fabrication of each build cycle down to the level of scan vectors and additionally to register process signals. The suggested data schema for archiving each build cycle adheres to all terms defined by ISO/TC 261—Additive Manufacturing (AM). In relation to the measurement frequency, all data are reorganized into entities, such as the AM machine, build cycle, part, layer, and scan vector. These scan vectors are stored in a runtime-independent format, including all metadata, to be valid and traceable. The resulting machine log represents a comprehensive documentation of each build cycle, enabling data-driven quality assurance at process level.
A steel pipeline segment of 2.5 m length was subjected to quasi-static four-point bending load in three steps for studying the initial cracking and damage accumulation based on the Acoustic Emission (AE) technique and by the direct current potential drop (DCPD) technique. For the latter, a new post-test analysis method was established.
AE is found more sensitive to crack initiation than DCPD. Formation of mesoscopic and macroscopic cracks as well as their closure and the resulting friction generate weighted peak frequencies below 400 kHz, whereas microscopic cracking produces AE with broad band spectra identifiable by weighted peak frequencies above 400 kHz. Critical states alike the maximum load level and the leak opening were accompanied by peak amplitudes above 85 dBAE. This rather fundamental study provides a data base for possibly developing advanced strategies of detection and alarm systems based on acoustic monitoring of pipelines, or at least, steel structures.
This work explores the feasibility of producing bead-on-plate welds of a CrCoNi medium entropy alloy and a CrMnFeCoNi high entropy alloy using electron beam welding. The alloys were welded in two states: one in an as-cold-rolled condition and the other in an annealed condition. In addition, the materials are welded with two different parameters. The FCC microstructure of the welds is investigated using scanning electron microscopy assisted by energy-dispersive X-ray spectroscopy and electron-backscattered diffraction. The impact of the weld on the microstructure is discussed. The heat-affected zone is negligible for the annealed condition of both medium and high entropy alloys since there is no driving force for recrystallisation and the exposure time to high temperature is insufficient for grain coarsening. The texture formed in the fusion zone is also discussed and compared to the texture in the base metal and the heat-affected zone. Although the grain growth along the (100) crystallographic direction is preferential in all cases, the crystallographic texture type differs from each weld. Higher hardness values are measured in the medium entropy alloy’s base metal and fusion zone than in the high entropy alloy.
Alloy 36 (1.3912), also known as “Invar,” is an alloy with 36% nickel. The alloy has a remarkably low thermal expansion coefficient in certain temperature ranges. This peculiarity is called the invar effect, which was discovered in 1896 by the Swiss physicist Charles Édouard Guillaume. Therefore, it is used in applications in which dimensional stability is critical, such as molding tools for composite materials in aerospace, automotive applications, or liquified natural gas (LNG) cargo tanks. Moreover, increasingly complex structures and the optimization of resource efficiency also require additive manufacturing steps for the production or repair of components. Additively manufactured components have a heterogeneous microstructure and anisotropic mechanical properties. In addition, the manufactured components require subsequent machining surface finishing, like finish milling, to achieve their final contour. Nickel iron alloys are difficult to machine. Additionally, inhomogeneous microstructure may lead to unstable cutting forces and conditions. In part I of this investigation, the initial alloy 36 is modified with the elements Ti, Zr, and Hf up to a maximum of 0.33 wt.-%. The influence of the modification elements on the microstructure as well as on the hardness of the AM components is examined. Furthermore, one modification is applied to metal arc welding process and investigated. Part II focuses on the effect of the alloy modifications on machinability as well as on the surface integrity of plasma-transferred-arc-welded (PTA) and finish milled invar components.
Duplex stainless steels (DSS) are frequently used, especially in applications requiring high strength combined with high corrosion resistance in aggressive media. Examples include power plant components and maritime structures. During welding of these steels, local variations in chemical composition can occur. This results in ferritization of the material and negatively affects the mechanical properties of the components. In this work, tungsten inert gas (TIG) welding experiments were performed with DSS. Chemical composition analysis was realized in situ by using Laser Induced Breakdown Spectroscopy (LIBS). The aim of the work is to quantitatively measure the chemical composition in the weld seam of various DSS and to identify possible influences of welding parameters on the microstructure of the material. The chemical concentrations of the main alloying elements Cr, Ni, Mn on the surface of the sample during the welding process and the cooling process were measured. Mn and Ni are austenite stabilizers and their content increases during welding by using certain high alloyed filler material. Spectra were recorded every 1.3 s at a spacing of approximately 2 mm. During the cooling process the location of the measurement was not changed. The LIBS method is proofed to be suitable for the quantitative representation of the chemical compositions during the welding process.
It is proposed to model the experimentally observed weld pool boundary with superellipses (Lamé curves) and to find the unknown parameters of the curves using optimization methods. It has been shown experimentally that during laser welding of austenitic stainless steel with a thickness of 2 mm at a speed of 20 mm/s, the rear weld pool part has a shape close to triangular which can be accurately approximated by a superellipse. Analytical dependences of the trajectory and growth rate of the crystal and its cross-sectional area on the geometry of the rear weld pool part are obtained.
Eight commercial austenitic stainless steels were tensile tested in reference atmosphere, in gaseous high-pressure hydrogen and in gaseous hydrogen precharged condition using conventional (CS) and tubular specimens (TS). For all configurations, 0.2 yield strength and ultimate tensile strength were comparable. In reference atmosphere, reduction of area of CS was higher compared to TS, whereas in gaseous high pressure hydrogen reduction of area of CS was lower compared to TS. In gaseous hydrogen precharged condition reduction of area of CS and TS were comparable for the severely affected grades. The differences in necking behavior between CS and TS are explained by different competitions between necking and hydrogen assisted crack initiation and growth especially for the tests in high pressure hydrogen gas.
For a significant increase in the strength of high-strength fine-grained structural steels with a nominal yield strength ≥690 MPa, the addition of microalloying elements such as Nb and Ti is required. The standard specifications for the chemical composition of these steels (e.g., in EN 10025-6) often only give the manufacturer limit contents to achieve the defined properties. The effect of the alloying elements in the heat affected zone (HAZ) is sometimes completely contrary.
This makes it difficult to adequately predict the batch dependency regarding weldability and the load-bearing behaviour of the welded joint. Three different micro-alloyed steels of the grade S690QL were produced on a laboratory scale, focusing on different Nb and Ti contents. To investigate the tempering effect, these were gas metal arc welded in three layers. In addition to metallographic investigations of individual HAZ areas, thermodynamic phase calculations were carried out using Thermo-Calc, following variations in the chemical composition. This provides an understanding of phase transformation, precipitation growth, and dissolution during welding as a function of temperature and cooling conditions. The results show
a divergent metallurgical behaviour in the HAZ of the three different micro-alloyed steels. Thereby, the Ti micro-alloyed grade showed a strong softening of the HAZ in contrast to the Nb micro-alloyed grade. This can be attributed to a contrary precipitation behaviour during welding.
The role of defects in the fatigue strength of Wire Arc Additively Manufactured (WAAMed) Ti-6Al-4V is analysed by means of the IBESS model, a fracture mechanics short crack growth approach based on the cyclic R-curve. Pores and crack-like defects are analysed. Estimations of the role of pore shape and size agree well with published fatigue data of WAAM Ti-6Al-4V with pores. The model is also used to explain the effect of fabrication defects on the scatter of experimental data. This demonstrates that short crack growth models represent a suitable engineering tool for the fatigue assessment of defective AM materials.
The application of anti-corrosion coated, high-strength steels in the automotive industry has increased in recent years. In combination with various zinc-based surface coatings, liquid metal embrittlement cracking can be observed in some of these materials. A high-quality, crack-free spot-welded joint is essential to realize the lightweight potential of the materials. In this work, the LME susceptibility of different coatings, which will be determined by the crack length and the occurrence rate, will be investigated using a welding under external load setup. The uncoated specimens did not show any LME. EG, GI and GA showed significantly less LME than ZM coatings. The latter coatings showed much larger crack lengths than the EG, GI and GA coatings. Furthermore, two mechanisms regarding the LME occurrence rate were observed: the occurrence of LME in zinc–magnesium coatings was theorized to be driven by the material properties of the coatings, whereas the occurrence of LME at EG, GI and GA samples was forced mainly by the application of the external tensile load.
In the experimental setup of this work, the materials were exposed to unusually high mechanical loads (up to 80% of their yield strength) to evoke LME cracks.
This article reports temperature-dependent elastic properties (Young’s modulus, shear modulus) of three alloys measured by the dynamic resonance method. The alloys Ti-6Al-4V, Inconel IN718, and AISI 316 L were each investigated in a variant produced by an additive manufacturing processing route and by a conventional manufacturing processing route. The datasets include information on processing routes and parameters, heat treatments, grain size, specimen dimensions, and weight, as well as Young’s and shear modulus along with their measurement uncertainty. The process routes and methods are described in detail. The datasets were generated in an accredited testing lab, audited as BAM reference data, and are hosted in the open data repository Zenodo. Possible data usages include the verification of the correctness of the test setup via Young’s modulus comparison in low-cycle fatigue (LCF) or thermo-mechanical fatigue (TMF) testing campaigns, the design auf VHCF specimens and the use as input data for simulation purposes.
State-of-the-art laser powder bed fusion (PBF-LB/M) machines allow pre-heating of the substrate plate to reduce stress and improve part quality. However, two major issues have been shown in the past: First, with increasing build height the apparent pre-heat temperature at the surface can deviate drastically from the nominal pre-heat temperature in the substrate plate. Second, even within a single layer the local surface pre-heat temperature can show large gradients due to thermal bottlenecks in the part geometry underneath the top surface. Both lead to unwanted changes in microstructure or defects in the final parts. In this study, a first attempt is taken to show the feasibility of pre-heating the top surface with the onboard laser beam to overcome the mentioned issues. A single layer of a group of three parts built from IN718 to a height of 33.5 mm is pre-heated in a commercially available PBF-LB/M machine to an average steady state surface temperature of 200 °C using the onboard laser beam. The parts are continuously heated, omitting powder deposition and melting step. Temperatures are measured by thermocouples underneath the surface. The experiments are supported by a thermal finite element (FE) model that predicts the temperature field in the parts. When heating the parts uniformly with the laser beam, differences in surface temperatures as large as 170 K are observed. To overcome this inhomogeneity, the heat flux supplied by the laser beam is modulated. An optimized, spatial heat flow distribution is provided by the thermal FE model and translated into a scan pattern that reproduces the optimized heat distribution on the PBF-LB/M machine by locally modulating hatch distance and scan velocity. This successfully reduces the differences in surface temperature to 20 K. Thermographic imaging shows that a homogeneous surface temperature can be achieved despite the localized heat input by the beam. The potential for industrial application of the optimized laser-heating technique is discussed.
The effect of the oscillating metal vapor plume on the keyhole and molten pool behavior during the laser beam welding of AlMg3 aluminum alloys is investigated by experimental and numerical methods. The real-time height of the metal vapor plume is measured by high-speed camera observation. The obtained experimental results are used to evaluate the additional heating source and laser beam attenuation caused by the scattering and absorption based on the Beer–Lambert theory. Furthermore, the dynamic behavior of the metal vapor plume is incorporated into a 3D transient heat transfer and fluid flow model, coupled with the ray tracing method, for the laser beam welding of the AlMg3 alloy. It is found that additional heating resulting from the scattered and absorbed laser beam energy by the metal vapor plume significantly expands the shape of the molten pool on the top region. Moreover, the oscillating metal vapor plume caused the fluctuation of the high-temperature region in the molten pool. The probability of keyhole collapse at the bottom increases 17% due to the oscillating laser power induced by the laser beam attenuation. The internal interplay between the metal vapor plume, molten pool shape, and keyhole collapse is obtained. The developed model has been validated by experiments, which shows a good agreement.
Soft polymers such as the investigated polyurethane, characterized by low Young’s moduli and prone to high shear deflection, are frequently applied in pneumatic cylinders. Their performance and lifetime without external lubrication are highly determined by the friction between seal and shaft and the wear rate. FEM simulation has established itself as a tool in seal design processes but requires input values for friction and wear depending on material, load, and velocity. This paper presents a tribological test configuration for long stroke, reciprocating movement, allowing the generation of data which meet the requirements of input parameters for FEM simulations without the geometrical influences of specific seal profiles. A numerical parameter study, performed with an FEM model, revealed the most eligible sample geometry as a flat, disc-shaped sample of the polymer glued on a stiff sample holder. At the same time, the study illustrates that the sensitivity of the contact pressure distribution to Poisson’s ratio and CoF can be minimized by the developed and verified setup. It ensures robust, reliable, and repeatable experimental results with uniform contact pressures and constant contact areas to be used in databases and FEM simulations of seals, enabling upscaling from generically shaped samples to complex seal profiles.
The strain field can reflect the initiation time of solidification cracks during the welding process. The traditional strain measurement is to first obtain the displacement field through digital image correlation (DIC) or optical flow and then calculate the strain field. The main disadvantage is that the calculation takes a long time, limiting its suitability to real-time applications. Recently, convolutional neural networks (CNNs) have made impressive achievements in computer vision.
To build a good prediction model, the network structure and dataset are two key factors. In this paper, we first create the training and test sets containing welding cracks using the controlled tensile weldability (CTW) test and obtain the real strain fields through the Lucas–Kanade algorithm. Then, two new networks using ResNet and DenseNet as encoders are developed for strain prediction, called StrainNetR and StrainNetD. The results show that the average endpoint error (AEE) of the two networks on our test set is about 0.04, close to the real strain value. The computation time could be reduced to the millisecond level, which would greatly improve efficiency.
A technique for calculating the main solidification parameters for a two-dimensional columnar crystal growth during complete penetration laser beam welding of thin steel sheets was developed. Given that the weld pool interface is described by Lamé curves (superellipses) within the horizontal plane of growth, general analytical solutions were derived for the geometry of the crystal axis and the corresponding growth rate and cross-sectional area of the crystal. A dimensionless analysis was performed to provide insights on the dependence of the solidification parameters on the shape and dimensions of the rear part of the weld pool boundary. The derived solutions were applied for the case of complete penetration laser beam keyhole welding of 2 mm thick 316L austenitic chromium-nickel steel sheets. It was shown that the reconstruction of the weld pool boundary with Lamé curves provides higher accuracy and flexibility compared to results obtained with elliptical functions. The validity of the proposed technique and the derived analytical solutions was backed up by a comparison of the obtained solutions to known analytical solutions and experimentally determined shapes and sizes of the crystals on the top surface of the sheet. The dimensions of the calculated crystal axis correlated well with the experimentally obtained results.
One of the main advantages of metal additive manufacturing (MAM) techniques is their ability to produce components with site-specific microstructural features. Nevertheless, microstructural defects and lack of repeatability are still major concerns in MAM. In this study, a laser powder bed fusion (PBF-LB/M) IN718 material, produced using two different scan length vectors, is investigated using Bragg-edge neutron 2D imaging (BENI) combined with electron backscatter diffraction (EBSD) analysis. BENI is able to detect, on a macroscopic scale, process-induced changes in texture in a large field of view covering the entire sample (20×80 mm2). In addition, high-resolution BENI (HR-BENI), with a pixel size of 12.8 µm, provides a micro-scale examination of the local variations of texture and grain morphology, otherwise undistinguishable using the standard resolution. As such, HR-BENI offers a straightforward and detailed way of screening the integrity of MAM parts at cm-length scales.
The microstructure has a great influence on short fatigue crack growth in metallic materials. Laser-based Powder Bed Fusion AlSi10Mg alloys exhibit in the as-built condition a fine fibrous Si structure and a supersaturated solid solution of Si in the α-Al matrix, which is significantly modified by heat treatments starting already at temperatures under 260 °C. This study focuses on the influence of post-process heat treatments on the microstructural evolution and the resulting fatigue crack growth resistance. As compared to the as-built condition, two heat treatments at 265 °C/1 h and at 300 °C/2 h are found to be beneficial to the fatigue crack growth resistance of the investigated material.
Understanding the void defect formation mechanism and simultaneous predicting the tool service life in friction stir welding are critical for optimizing the welding parameters. However, the void defect formation mechanism in friction stir welding is not yet elucidated. In this study, a novel integrated thermal-fluid-structure coupling model of the friction stir welding process was proposed for simultaneous prediction of the weld formation and tool service life. A new non-uniform distribution model of the tool-workpiece contact pressure was proposed to describe the interaction between the tool and the workpiece. The void defect formation mechanism was quantitatively studied using the proposed integrated thermal-fluid-structure coupling model. The results show that the plastic material flows in the horizontal direction and can completely fill the cavity behind the tool for the welding condition of forming a sound weld. While the tool-workpiece contact interfacial frictional shear stress in the rear of the tool is decreased significantly which leads to a severe decrease in the plastic material flow velocity. Therefore, after bypassing the tool from the retreating side, the plastic material at the bottom of the weld stagnates, and void defect forms in the middle and lower part of the weld at the advancing side. The difference between the maximum and the minimum tool-workpiece contact pressure could serve as a numerical criterion to predict void defects. A sound joint is formed when the difference is lower than the critical value of 15 MPa, while a void defect is formed in the weld if it is higher than this critical value. The maximum equivalent stress acting on the tool is located at the pin root with severe stress concentration at a high welding speed. The front of the tool is subjected to tensile stress while its rear is subjected to compressive stress, therefore the tool is apt to fracture at its root under an inappropriate welding condition. The average normal stress of the tool varies periodically with its period consistent with the rotation period of the tool. The service life of the tool is decreased with the increase in welding speed and the decrease in rotation speed. The model is validated by experimental results.
Aero-engine turbine disks are safety-relevant components which are operated under high thermal and mechanical stress conditions. The actual part qualification and certification procedures make use of spin-tests conducted on production-similar disks. While these tests provide, on the one hand, a reliable definition of the critical conditions for real components, on the other hand they represent a relevant cost item for engine manufacturers. The aim of this work is to present two alternative burst speed assessment methods under development based on the Failure Assessment Diagram (FAD) and a global stability criterion, respectively. In the scope of the fracture mechanics assessment, the failure modes hoop-burst and rim-peeling are investigated with semicircular surface cracks modelled at the critical regions on the turbine disk. The comparison of the predicted critical rotational speed shows good agreement between the assessment methods.
Additive manufacturing (AM) in general and laser powder bed fusion (PBF-LB/M) in particular are becoming increasingly important in the field of production technologies. Especially the high achievable accuracies and the great freedom in design make PBF-LB/M interesting for the manufacturing and repair of gas turbine blades. Part repair involves building AM-geometries onto an existing component. To minimise the offset between component and AM-geometry, a precise knowledge of the position of the component in the PBF-LB/M machine is mandatory. However, components cannot be inserted into the PBF-LB/M machine with repeatable accuracy, so the actual position will differ for each part. For an offset-free build-up, the actual position of the component in the PBF-LB/M machine has to be determined. In this paper, a camera-based position detection system is developed considering PBF-LB/M constraints and system requirements. This includes finding an optimal camera position considering the spatial limitations of the PBF-LB/M machine and analysing the resulting process coordinate systems. In addition, a workflow is developed to align different coordinate systems and simultaneously correct the perspective distortion in the acquired camera images. Thus, position characteristics can be determined from images by image moments. For this purpose, different image segmentation algorithms are compared. The precision of the system developed is evaluated in tests with 2D objects. A precision of up to 30μm in translational direction and an angular precision of 0.021∘ is achieved. Finally, a 3D demonstrator was built using this proposed hybrid strategy. The offset between base component and AM-geometry is determined by 3D scanning and is 69μm.
In 2015, the University of Manchester hosted a workshop (‘Mind the Gap’) aimed at identifying gaps in a number of structural integrity fitness-for-service procedures, including R5, R6, BS 7910 and API/ASME. The findings were subsequently summarised in a journal paper and shared with the relevant stakeholders. A second workshop, this time hosted by the University of Bristol in 2017, was intended to build on the findings of the earlier event, identifying which gaps had been filled, which remain and whether new ones have been identified in the meantime. ‘Mind the Gap 2’ was wide-ranging, including consideration of failure by fracture, fatigue crack growth, hightemperature creep and environmentally assisted crack growth, along with the use of innovative techniques to follow the progress of crack growth from the atomic to the macroscopic scale. A summary of the whole event is thus outside the scope of a single paper, so here we concentrate mainly on advances in fracture assessment, on the interface between inspection and ECA, and on how developments are being incorporated into structural integrity procedures. There is a particular emphasis on the energy transition in the UK, where the planned energy mix will include both nuclear power and offshore wind.
Hybrid laser-arc welding (HLAW) was applied for butt welding of 14.5 mm thick plates of ferritic cryogenic steel X8Ni9 containing 9% Ni, which is used for manufacturing storage and transport facilities of liquefied natural gas (LNG). The weld seam formation and the achievable metallurgical and mechanical properties of the hybrid welds were investigated experimentally for two types of filler wire, an austenitic wire dissimilar to the base metal (BM) and an experimentally produced matching ferritic wire. Safe penetration and uniform distribution of the austenitic filler metal in the narrow hybrid weld could only be achieved in the upper, arcdominated part of the weld. The pronounced heterogeneous distribution of the austenitic filler metal in the middle part and in the root area of the weld could not ensure sufficient notched impact toughness of the weld metal (WM). As a result, a decrease in the impact energy down to 17±3 J was observed, which is below the acceptance level of ≥34 J for cryogenic applications. In contrast, the use of a matching ferritic filler wire resulted in satisfactory impact energy of the hybrid welds of up to 134±52 J at the concerned cryogenic temperature of -196 °C. The obtained results contribute to an important and remarkable conversion in automated manufacturing of LNG facilities. In other words, the results will help to develop a new laser-based welding technology, where both quality and productivity are considered.The efficiency of the developed welding process has been demonstrated by manufacturing a prototype where a segment of the inner wall of large size LNG storage tank was constructed. In this concern, hybrid laser arc welding was conducted in both horizontal (2G) and vertical (3G) positions as a simulation to the actual onsite manufacturing. The prototype was fabricated twice where its quality was confirmed based on non-destructive and destructive examinations.
AbstractLaser beam welding has become widely applied in many industrial fields in recent years. Solidification cracks remain one of the most common welding faults that can prevent a safe welded joint. In civil engineering, convolutional neural networks (CNNs) have been successfully used to detect cracks in roads and buildings by analysing images of the constructed objects. These cracks are found in static objects, whereas the generation of a welding crack is a dynamic process. Detecting the formation of cracks as early as possible is greatly important to ensure high welding quality. In this study, two end-to-end models based on long short-term memory and three-dimensional convolutional networks (3D-CNN) are proposed for automatic crack formation detection. To achieve maximum accuracy with minimal computational complexity, we progressively modify the model to find the optimal structure. The controlled tensile weldability test is conducted to generate long videos used for training and testing. The performance of the proposed models is compared with the classical neural network ResNet-18, which has been proven to be a good transfer learning model for crack detection. The results show that our models can detect the start time of crack formation earlier, while ResNet-18 only detects cracks during the propagation stage.
This study was carried out to investigate the neutron transmission signal as a function of sample temperature during a welding process. A theoretical description that includes the Debye-Waller factor was used to describe the temperature influence on the neutron crosssections. Neutron imaging using a monochromatic beam helps to observe transmission variations related to the material temperature. In-situ neutron imaging of welding experiments show the distribution of the temperature in bulk steel samples. The performed finite element modelling of expected temperature distributions shows good agreement with the obtained experimental data.
Effect of Tensile Loading and Temperature on the Hydrogen Solubility of Steels at High Gas Pressure
(2023)
The hydrogen solubility in ferritic and martensitic steels is affected by hydrostatic stress, pressure, and temperature. In general, compressive stresses decrease but tensile stresses increase the hydrogen solubility. This important aspect must be considered when qualifying materials for high‐pressure hydrogen applications (e.g., for pipelines or tanks) by using autoclave systems. In this work, a pressure equivalent for compensating the effect of compressive stresses on the hydrogen solubility inside of closed autoclaves is proposed to achieve solubilities that are equivalent to those in pipelines and tanks subjected to tensile stresses. Moreover, it is shown that the temperature effect becomes critical at low temperatures (e.g., under cryogenic conditions for storing liquid hydrogen). Trapping of hydrogen in the microstructure can increase the hydrogen solubility with decreasing temperature, having a solubility minimum at about room temperature. To demonstrate this effect, the generalized law of the hydrogen solubility is parameterized for different steels using measured contents of gaseous hydrogen. The constant parameter sets are verified and critically discussed with respect to the high‐pressure hydrogen experiments.
Liquid metal embrittlement (LME) cracking is a phenomenon observed during resistance spot welding (RSW) of zinccoated advanced highstrength steels (AHSS) in automotive manufacturing. In this study, severe cracks are observed at the edge of the sheet under reduced flange widths. These cracks, traversing the AHSS sheet, culminate at the edge with a width of approximately 1.2 mm.
Through combined numerical and experimental investigations, and material testing, these cracks are identified and validated as a new type of LME crack. The mechanism behind this crack formation is attributed to unique geometric conditions that, when compared to center welding, amplify radial material flow by ninefold to 0.87 mm. The resultant tangential tensile stresses approximate 760 MPa, which exceed the yield strength of the examined advanced highstrength steel (AHSS) under heightened temperature conditions, and when combined with liquid zinc, promote the formation of this new type of LME crack.
The spatial laser energy absorption inside the keyhole is decisive for the dynamic molten pool behaviors and the resultant weld properties in high-power laser beam welding (LBW). In this paper, a numerical simulation of the LBW process, considering the 3D transient heat transfer, fluid flow, and keyhole dynamics, is implemented, in which the free surface is tracked by the volume-of-fluid algorithm. The underlying laser-material interactions, i.e., the multiple reflections and Fresnel absorption, are considered by an advanced ray-tracing method based on a localized level-set strategy and a temperature-dependent absorption coefficient. The laser energy absorption is analyzed from a time-averaged point of view for a better statistical representation. It is found for the first time that a significant drop in the time-averaged laser energy absorption occurs at the focus position of the laser beam and that the rest of the keyhole region has relatively homogeneous absorbed energy. This unique absorption pattern may lead to a certain keyhole instability and have a strong correlation with the detrimental bulging and narrowing phenomena in the molten pool. The influence of different focus positions of the laser beam on the keyhole dynamics and molten pool profile is also analyzed. The obtained numerical results are compared with experimental measurements to ensure the validity of the proposed model.
AISI 2205 duplex stainless steel is used in a variety of industries, including the chemical and petrochemical industries. This is due to its high tensile strength combined with good ductility and corrosion resistance. However, in laser beam welding, these properties are negatively afected by the high cooling rates typical of the welding process. The resulting higher ferrrite content in the weld metal than in the base material leads to a reduction in the ductility and corrosion resistance of the welded joint. To overcome this problem, in this study, thick plates were coated by direct energy deposition (DED) prior to laser beam welding, whereas a duplex powder mixture containing a higher nickel concentration was used as a coating material. To improve the weld quality for the proposed two-step process, a method of additional material deposition instead of conventional tack weld was investigated. The resulting welded joints showed a well-balanced austenite to ferrite ratio and their properties and microstructure were verifed by metallographic analysis, electron backscatter difraction and Charpy impact testing. Using the standard ASTM G48 test method, it was found that the corrosion resistance of the welds was improved by a factor of four in average compared to the conventionally welded joints. The resulting properties, such as good ductility and corrosion resistance, of the welds with pre-coated edges showed good agreement with those of the base metal and confrmed the proposed two-step process as a promising alternative to the conventional approaches for welding thick duplex stainless steel plates.
Welded joints show large variation of the weld toe geometry along the weld seam, which is one important reason for the comparably large scatter in fatigue life. Therefore, it is crucial to take the local geometry at the weld toe into account, to reduce the conservatism in fatigue assessment of welded joints. This study is based on the IBESS procedure for the calculation of the fatigue strength, whereby the evaluation of local geometrical parameters is carried out by means of 3D surface scans. The approach is validated against 26 fatigue test series. The fatigue life is in general overpredicted, whereas good agreement is achieved for high stress ratio (R = 0.5). A sensitivity analysis conducted with IBESS shows that weld toe radii ρ < 2 mm and flank angle α < 30° have a significant influence on the calculated fatigue strength. In contrast to this, no strong correlation between ρ and the fatigue strength was determined experimentally in this study.