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This paper investigates fast and inexpensive measurement methods for defect detection in parts produced by Additive Manufacturing (AM) with special focus on lattice parts made of ceramics. By Lithography-based Ceramic Manufacturing, parts were built both without defects and with typical defects intentionally introduced. These defects were investigated and confirmed by industrial X-ray Computed Tomography. Alternative inexpensive methods were applied afterwards on the parts such as weighing, volume determination by Archimedes method and gas permeability measurement. The results showed, that defects resulting in around 20% of change in volume and mass could be separated from parts free of defects by determination of mass or volume. Minor defects were not detectable as they were in the range of process-related fluctuations. Permeability measurement did not allow to safely identify parts with defects. The measurement methods investigated can be easily integrated in AM process chains to support quality control.
The durability of concrete structures and its performance over the lifetime is strongly influenced by many interacting phenomena such as e.g. mechanical degradation due to fatigue loading, loss of prestress, degradation due to chemical reactions or creep and shrinkage. Failure due to cyclic loading is generally not instantaneous, but characterized by a steady damage accumulation.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales. A key limitation is that the models often do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles.
The objective of this paper is the presentation of numerical methods for the simulation of concrete under fatigue loading using a temporal multiscale method.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different time integration schemes.
Lifetime aspects including fatigue failure of concrete structures were traditionally only of minor importance. Because of the growing interest in maxing out the capacities of concrete, its fatigue failure under compression has become an issue. A variety of interacting phenomena such as e.g. loss of prestress, degradation due to chemical reactions or creep and shrinkage influence the fatigue resistance. Failure due to cyclic loads is generally not instantaneous, but characterized by a steady damage accumulation. Therefore, a reliable numerical model to predict the performance of concrete over its lifetime is required, which accurately captures order effects and full three-dimensional stress states.
Many constitutive models for concrete are currently available, which are applicable for specific loading regimes, different time scales and different resolution scales.
However, a key limitation of those models is that they generally do not address issues related to fatigue on a structural level. Very few models can be found in the literature that reproduce deterioration of concrete under repeated loading-unloading cycles. This is due to the computational effort necessary to explicitly resolve every cycle which exceeds the currently available computational resources. The limitation can only be overcome by the application of multiscale methods in time.
The objective of the paper is the development of numerical methods for the simulation of concrete under fatigue loading using temporal multiscale methods.
First, a continuum damage model for concrete is developed with a focus on fatigue under compressive stresses. This includes the possibility to model stress redistributions and capture size effects. In contrast to cycle based approaches, where damage is accumulated based on the number of full stress cycles, a strain based approach is developed that can capture cyclic degradation under variable loading cycles including different amplitudes and loading frequencies. The model is designed to represent failure under static loading as a particular case of fatigue failure after a single loading cycle. As a consequence, most of the material parameters can be deduced from static tests. Only a limit set of additional constitutive parameters is required to accurately describe the evolution under fatigue loading. Another advantage of the proposed model is the possibility to directly incorporate other multi-physics effects such as creep and shrinkage or thermal loading on the constitutive level.
Second, a multiscale approach in time is presented to enable structural computations of fatigue failure with a reduced computational effort. The damage rate within the short time scale corresponding to a single cycle is computed based on a Fourier based approach. This evolution equation is then solved on the long time scale using different implicit and explicit time integration schemes. Their performance and some limitations for specific loading regimes is discussed.
Finally, the developed methods will be validated and compared to experimental data.
The crack propagation rate of environmental stress cracking was studied on high-density polyethylene compact tension specimens under static loading. Selected environmental liquids are distilled water, 2 wt% aqueous Arkopal N100 solution, and two model liquid mixtures, one based on solvents and one on detergents, representing stress cracking test liquids for commercial crop protection products. The different surface tensions and solubilities, which affect the energetic facilitation of void nucleation and craze development, are studied. Crack growth in surface-active media is strongly accelerated as the solvents induce plasticization, followed by strong blunting significantly retarding both crack initiation and crack propagation. The crack propagation rate for static load as a function of the stress intensity factor within all environments is found to follow the Paris–Erdogan law. Scanning electron micrographs of the fracture surface highlight more pronounced structures with both extensive degrees of plasticization and reduced crack propagation rate, addressing the distinct creep behavior of fibrils. Additionally, the limitations of linear elastic fracture mechanisms for visco-elastic polymers exposed to environmental liquids are discussed.
Four typical high-density polyethylene container materials were used to investigate damage or stress cracking behavior in contact with model liquids for crop protection products. These model liquids are established in German regulations for the approval of dangerous goods containers and consist of typical admixtures used for crop protection products but without biological active ingredients. This study is performed with the standardized method of Full Notch Creep Test, adapting the media temperature to 40 °C according to the usual conditions where these test liquids are applied. The two model liquids differ into a water-based solution and a composition based on different organic solvents which are absorbed by the material up to significant levels. Therefore, extensive sorption measurements are performed. The fracture surfaces obtained are analyzed in detail not only by light microscopy, but also by laser scanning microscopy as well as scanning electron microscopy. Influence of pre-saturation and applied stress are addressed by respective systematic series of experiments.
The phenomenon of environmental stress cracking is still a major issue in materials engineering as well as from a scientific perspective. Especially in the case of packaging materials made of high-density polyethylene, assessing the potential of premature damage due to environmental stress cracking is complex because of the large number of components in possible liquid filling goods. As a first guideline, the well-known effect of detergents and dispersants is usually considered, but the interplay with other components, such as organic solvents is often unknown. Particularly challenging in this respect are crop protection products, consisting of several different admixtures in addition to the biologically active ingredients. This study is based on two model liquids representing these admixtures that were established for testing in this context. The model liquids as well as their constituting components were used as liquid media in the Full Notch Creep Test to characterize the environmental stress cracking behavior of a typical high-density polyethylene. Complementary to the time-to failure of a notched specimen obtained from these tests, the crack opening was monitored optically, and the fracture surface was analyzed post-failure by laser scanning microscopy as well as scanning electron microscopy. Based on the results, the effect of various surfactants as well as the influence of organic solvents on environmental stress cracking are discussed.
Packaging containers for dangerous goods that include aggressive liquids require that any packaging material that is based on high-density polyethylene has a high degree of stability and durability. This work is focused on testing the environmental stress cracking of the high-density polyethylenes used for such containers in contact with crop protection formulations, in particular, two model liquids established in Germany as standardized test media representatives for crop protection formulations containing the various admixtures typical for such products. One of the liquids is water-based and contains mostly surface-active ingredients, while the other is solvent-based and includes some emulsifiers. Originally established for pin impression tests, these model liquids and their individual components were here used for the first time as environmental media in the Full Notch Creep Test, which addresses the resistance against environmental stress cracking. The Full Notch Creep Test was carried out on five high-density polyethylene types with both model liquids, and also on one selected material with its components. The evaluation was focused on the fracture surface structures, which were visualized by a scanning electron microscope and by optical in situ imaging of the notch opening. While the water-based model liquid and its surface-active individual components induced environmental stress cracking with the characteristic pattern for a craze-crack mechanism and so-called brittle fracture on the surface, the solvent-based model liquid and its soluble ingredients exhibited rather ductile failure behavior, caused by the plasticizing effect on the polymer that reduced the yield stress of the high-density polyethylene.
For both cases, fracture surface analysis, together with side views of the crack opening, showed a clear relation between surface pattern, notch deformation (e.g., by blunting), or crack opening due to crack growth with time to failure and the solubility of the liquids in high-density polyethylene.
Polyethylen hoher Dichte (PE-HD) ist ein weit verbreitetes Material für Transportbehälter, die oft für eine längere Nutzungsdauer vorgesehen sind. Insbesondere in diesem Fall können mikroskopische Schäden im Material auch weit unterhalb der Streckgrenze auftreten, die durch eine Spannungskonzentration verursacht werden, deren Ursprung in intrinsischen Materialfehlern oder äußeren Kratzern liegt. Mit fortschreitender Schädigung bilden sich Rissstrukturen, die von verstreckten Fibrillen aufgespannt werden, bis es zum Versagen dieser Fibrillen kommt und sich der Riss ausbreitet. Dieser Schadensmechanismus des langsamen Risswachstums kann durch eine Vielzahl von Umgebungsmedien beschleunigt werden und wird dann als "environmental stress cracking" (ESC) bezeichnet. Eine international normierte Methode zur Validierung der Spannungsrissbeständigkeit von PE-HD Materialien ist der „Full Notch Creep Test“ (FNCT).
Anhand von Bruchflächenauswertungen mittels Rasterelektronenmikroskopie und Laser-Scanning-Mikroskopie, werden die typischen Schädigungsstrukturen des ESC sichtbar. Die fibrillierten Strukturen des ESC auf der Bruchfläche von PE-HD ergeben sich besonders bei oberflächenaktiven wässrigen Umgebungsmedien. In Lösungsmittel-Umgebungsmedien, im Zusammenspiel mit PE-HD, kommt es aufgrund der plastifizierenden Wirkung zur Herabsetzung der Streckspannung und Bruchflächen aus dem FNCT veranschaulichen keine signifikanten Anzeichen des Schädigungsmechanismus ESC.
Molecular orientation has a significant effect on the material properties of polymers. Preferential orientation of the microstructure (polymer chains or crystallites) in a specific direction or plane often enhances the material properties, especially if the high-strength covalent bonds are primarily exposed to loads instead of the weaker van der Waals bonds. However, the orientation-dependent microstructure and its mechanical behavior is in general already well understood by many scientific studies [1-3]. Isotropic materials are frequently required for an intrinsic material characterization without prevailing processing-induced properties, as is the case for Full Notch Creep Test (FNCT) [4] addressing environmental stress cracking (ESC) in high-density polyethylene (PE-HD) [5, 6]. Since ESC is one of the major limiting issues for long-term performance of PE-HD pipes and containers [7], which in contrast have a production-related preferential orientated microstructure due to extrusion or extrusion blow molding, it is important to additionally investigate the ESC resistance of such anisotropic microstructure.
Investigations of the slow crack growth (SCG) with respect to the molecular orientation generally obtain a factor of 1.2 up to 4.7 between crack growth perpendicular to the extrusion direction and crack growth parallel to the extrusion direction 8. Based on FNCT investigations with an aqueous detergent solution as environmental medium, hot pressed sheets with isotropic morphology are compared with extruded sheets from which specimens with different orientation angles are taken. However, the time to failure obtained by FNCT is also significantly influenced by the different cooling conditions under which the final morphology is formed. The tendency of the specimen to fail due to ESC is investigated as a function of environmental medium temperature. For a more detailed analysis of the affecting parameters in the manufacturing process, the ESC resistance is discussed considering the differences in crystallinity as revealed by thermal analysis.
Currently, the Full Notch Creep Test (FNCT) [1] method is used by material suppliers and end users in industry for the approval of container and pipe materials based on high-density polyethylene (PE-HD). The resistance to environmental stress cracking (ESC) of the material is evaluated using the time to failure of the specimen in an aqueous solution of a detergent [2, 3]. Usually specimens made of sheets with isotropic material properties, manufactured by hot pressing, are employed in order to obtain intrinsic properties of the material in terms of ESC failure. In contrast, the processes used in manufacturing to form containers and pipes, such as extrusion blow molding or extrusion, impose anisotropic properties to the material. These are mostly due to a microstructural orientation (polymer chains or crystallites) [4]. Furthermore, the different cooling conditions significantly affect the size distribution of crystallites as well as the overall morphology. It is therefore essential to understand the influence of process-induced material characteristics on failure due to ESC.
A large number of studies on material properties as a function of microstructural preferential orientation have already been conducted [5-7]. However, effects on ESC as the major failure mechanism of containers and pipes are still rather unexplored [8, 9]. The most important factor is whether primarily intramolecular high-strength covalent bonds or the substantially weaker intermolecular van der Waals forces are predominantly loaded.
In addition to the widely established classification by time to failure, the strain or crack opening displacement (COD) provides valuable information about the evolution and progression of damage as a function of time [10, 11]. Optical strain measurement using digital image correlation allows the differences in COD for isotropic and different angles of orientation of anisotropic specimens to be discussed. Also, a post-fracture surface analysis provides clarification on the craze-crack mechanism of the ESC. These different ESC-related properties of extruded and hot-pressed specimens have been investigated at different environmental medium temperatures and different initial stresses to provide a broad characterization of the fracture behavior of PE-HD.