Multi-phase metallic materials such as Advanced High-Strength Steels (AHSS) are of great importance in a wide variety of high-tech industries due to their higher strength compared to conventional (mild) forming steels. The higher strength leads to various advantages in weight, safety and environmental friendliness. In order to develop new AHHS steels, the steel industries make use of multi-scale microstructure modelling to predict mechanical properties from the microstructure features. This thesis aims at the development of relations between the features of multi-phase metallic microstructures of steels and the mechanical properties of the material. The quantitative characterization of the microstructure will be more involved than is now in use for estimations of the mechanical properties, which is a necessity because of the complexity of multi-phase microstructures. Moreover, the prediction of mechanical properties on the basis of microstructural features will be extended beyond the usual limitation of the yield stress to properties like hole expansion capacity and impact energy. Statistical approaches combined with machine learning algorithms are used to find relations between microstructure features and mechanical properties. Interpretations of the machine learning algorithms are also discussed and the possible deeply embedded relations among mechanical properties are systematically studied. The research in this thesis deepens the insight into the mechanical behaviour of the microstructure in multi-phase steels and strongly improves property predictions, not only based on microstructure features, but also on deformation properties. Results of this thesis can be directly implemented in microstructure modelling and are directly available for researchers within the steel industry for developing new materials.@en

Investigating the main determinants of the mechanical performance of metals is not a simple task. Already known physically inspired qualitative relations between 2D microstructure characteristics and 3D mechanical properties can act as the starting point of the investigation. Isotonic regression allows to take into account ordering relations and leads to more efficient and accurate results when the underlying assumptions actually hold. The main goal in this paper is to test order relations in a model inspired by a materials science application. The statistical estimation procedure is described considering three different scenarios according to the knowledge of the variances: known variance ratio, completely unknown variances, and variances under order restrictions. New likelihood ratio tests are developed in the last two cases. Both parametric and non-parametric bootstrap approaches are developed for finding the distribution of the test statistics under the null hypothesis. Finally an application on the relation between geometrically necessary dislocations and number of observed microstructure precipitations is shown.

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Abstract: The relationship between microstructure features and mechanical properties plays an important role in the design of materials and improvement of properties. Hole expansion capacity plays a fundamental role in defining the formability of metal sheets. Due to the complexity of the experimental procedure of testing hole expansion capacity, where many influencing factors contribute to the resulting values, the relationship between microstructure features and hole expansion capacity and the complexity of this relation is not yet fully understood. In the present study, an experimental dataset containing the phase constituents of 55 microstructures as well as corresponding properties, such as hole expansion capacity and yield strength, is collected from the literature. Statistical analysis of these data is conducted with the focus on hole expansion capacity in relation to individual phases, combinations of phases and number of phases. In addition, different machine learning methods contribute to the prediction of hole expansion capacity based on both phase fractions and chemical content. Deep learning gives the best prediction accuracy of hole expansion capacity based on phase fractions and chemical composition. Meanwhile, the influence of different microstructure features on hole expansion capacity is revealed. Graphical abstract: [Figure not available: see fulltext.]

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Additively manufacturing (AM) opens up the possibility for biodegradable metals to possess uniquely combined characteristics that are desired for bone substitution, including bone-mimicking mechanical properties, topologically ordered porous structure, pore interconnectivity and biodegradability. Zinc is considered to be one of the promising biomaterials with respect to biodegradation rate and biocompatibility. However, no information regarding the biodegradability and biocompatibility of topologically ordered AM porous zinc is yet available. Here, we applied powder bed fusion to fabricate porous zinc with a topologically ordered diamond structure. An integrative study was conducted on the static and dynamic biodegradation behavior (in vitro, up to 4 weeks), evolution of mechanical properties with increasing immersion time, electrochemical performance, and biocompatibility of the AM porous zinc. The specimens lost 7.8% of their weight after 4 weeks of dynamic immersion in a revised simulated body fluid. The mechanisms of biodegradation were site-dependent and differed from the top of the specimens to the bottom. During the whole in vitro immersion time of 4 weeks, the elastic modulus values of the AM porous zinc (E = 700–1000 MPa) even increased and remained within the scope of those of cancellous bone. Indirect cytotoxicity revealed good cellular activity up to 72 h according to ISO 10,993–5 and -12. Live-dead staining confirmed good viability of MG-63 cells cultured on the surface of the AM porous zinc. These important findings could open up unprecedented opportunities for the development of multifunctional bone substituting materials that will enable reconstruction and regeneration of critical-size load-bearing bone defects. Statement of significance: No information regarding the biodegradability and biocompatibility of topologically ordered AM porous zinc is available. We applied selective laser melting to fabricate topologically ordered porous zinc and conducted a comprehensive study on the biodegradation behavior, electrochemical performance, time-dependent mechanical properties, and biocompatibility of the scaffolds. The specimens lost 7.8% of their weight after4 weeks dynamic biodegradation while their mechanical properties surprisingly increased after 4 weeks. Indirect cytotoxicity revealed good cellular activity up to 72 h. Intimate contact between MG-63 cells and the scaffolds was also observed. These important findings could open up unprecedented opportunities for the development of multifunctional bone substituting materials that mimic bone properties and enable full regeneration of critical-size load-bearing bony defects.

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Additively manufactured (AM) biodegradable porous zinc exhibits great potential as a promising bone-substituting biomaterial. However, there is no information whatsoever available regarding its corrosion fatigue behavior. In this study, we used direct metal printing to fabricate topologically ordered biodegradable porous zinc based on a diamond unit cell. We compared the compression-compression fatigue behavior of AM porous zinc in air and in revised simulated body fluid (r-SBF). The fatigue strength of AM porous zinc was high in air (i.e., 70% of its yield strength) and even higher in r-SBF (i.e., 80% of its yield strength). The high value of the relative fatigue strength in air could be attributed to the good ductility of pure zinc itself. The formation of corrosion products around the strut junctions might explain the higher fatigue strength of AM zinc in r-SBF. Furthermore, we compared the fatigue behavior of a uniform design of the AM porous zinc with a functionally graded design. The functionally graded structure exhibited higher relative fatigue strengths than the uniform structure. The inspection of the fatigue crack distribution revealed that the functionally graded design controlled the sequence of crack initiation, which occurred early in the thicker struts and moved towards the thinner struts over time. The theoretical fatigue life models suggest that optimizing the functionally graded structure could be used as an effective means to improve the fatigue life of AM porous zinc. In conclusion, the favorable fatigue behavior of AM porous zinc further highlights its potential as a promising bone-substituting biomaterial. Statement of Significance: Additively manufactured (AM) biodegradable porous zinc exhibits great potential for the treatment of large bony defects. However, there is no information available regarding its corrosion fatigue behavior. Here, we compared the fatigue behavior of AM porous zinc in air and in revised simulated body fluid (r-SBF). The fatigue strength of AM porous Zn was even higher in r-SBF than in air, which were attributed to the formation of corrosion products. Furthermore, we found that the functionally graded structure controlled the sequence of crack initiation in differently sized struts and exhibited higher relative fatigue strengths than the uniform structure, suggesting that optimizing the functionally graded structure could be an effective means to improve the fatigue life of AM porous Zn.

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Understanding the relationship between microstructure features and mechanical properties is of great significance for the improvement and specific adjustment of steel properties. The relationship between mean grain size and yield strength is established by the well-known Hall-Petch equation. But due to the complexity of the grain configuration within materials, considering only the mean value is unlikely to give a complete representation of the mechanical behavior. The classical Taylor equation is often used to account for the effect of dislocation density, but not thoroughly tested in combination with grain size influence. In the present study, systematic heat treatment routes and cold rolling followed by annealing are designed for interstitial free (IF) steel to achieve ferritic microstructures that not only vary in mean grain size, but also in grain size distribution and in dislocation density, a combination that is rarely studied in the literature. Optical microscopy is applied to determine the grain size distribution. The dislocation density is determined through XRD measurements. The hardness is analyzed on its relation with the mean grain size, as well as with the grain size distribution and the dislocation density. With the help of the variable selection tool LASSO, it is shown that dislocation density, mean grain size and kurtosis of grain size distribution are the three features which most strongly affect hardness of IF steel.

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Modeling microstructures is an interesting problem not just in materials science, but also in mathematics and statistics. The most basic model for steel microstructure is the Poisson-Voronoi diagram. It has mathematically attractive properties and it has been used in the approximation of single-phase steel microstructures. The aim of this article is to develop methods that can be used to test whether a real steel microstructure can be approximated by such a model. Therefore, a general framework for testing the Poisson-Voronoi assumption based on images of two-dimension sections of real metals is set out. Following two different approaches, according to the use or not of periodic boundary conditions, three different model tests are proposed. The first two are based on the coefficient of variation and the cumulative distribution function of the cells area. The third exploits tools from to topological data analysis, such as persistence landscapes.

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The corrosion fatigue behavior of additively manufactured topologically ordered porous iron based on diamond unit cells was studied for the first time to understand its response to cyclic loading in a simulated physiological environment. The material exhibited high fatigue resistance with fatigue strengths being 70% and 65% of yield stress in air and revised simulated body fluid, respectively, mainly due to its slow degradation and excellent ductility. However, cyclic loading significantly increased biodegradation rate, especially at higher stress levels. The observed extraordinary fatigue strength, slow biodegradation and high ductility underline the importance of porous iron as a promising bone-substituting material.

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Additively manufactured (AM) biodegradable metals with topologically ordered porous structures hold unprecedented promise as potential bone substitutes. The first reports on this type of biomaterials have just recently appeared in the literature. There is, however, no information available in the literature regarding their mechanical performance under cyclic loading or the interactions between biodegradation and cyclic loading. We therefore used selective laser melting (SLM) to fabricate porous magnesium alloy (WE43) scaffolds based on diamond unit cells. The microstructure of the resulting material was examined using electron back-scattered diffraction, scanning transmission electron microscopy, and X-ray diffraction. The fatigue behaviors of the material in air and in revised simulated body fluid (r-SBF) were evaluated and compared. Biodegradation decreased the fatigue strength of the porous material from 30% to 20% of its yield strength. Moreover, cyclic loading significantly increased its biodegradation rate. The mechanistic aspects of how biodegradation and cyclic loading interacted with each other on different scales were revealed as well. On the micro-scale, cracks initiated at biodegradation pits and propagated transgranularly. In addition, dislocations became more tangled after the fatigue tests. On the macro-scale, cracks preferred initiating at the strut junctions where tensile stress concentrations were present, as revealed by the finite element analysis of the porous material under compressive loading. Most of the cracks initiated in the struts were positioned on the periphery of the specimens. Furthermore, the biodegradation pattern was found to be location-dependent with more localized biodegradation occurring in the center of the specimens. Further improvements in the biodegradation-affected fatigue performance of the AM porous Mg alloy may therefore be realized by optimizing both the topological design of the porous structure and the laser-processing parameters that determine the microstructure of the SLM porous material.

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