500 Naturwissenschaften und Mathematik
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- Finite-Elemente-Methode (1)
- Fracture mechanics (1)
- Hydrauliche Bindemittel (1)
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Year of publication
- 2016 (5) (remove)
Problem definition and research objectives
1. The production of Portland cement clinker causes approx. 5% to 8% of the annual man-made CO2 emissions. This is due to the usage of mainly fossil fuel (approx. 40 % of the total CO2) and because of the decarbonation of limestone as a main component of the raw meal (approx. 60 % of the total CO2).
2. Various strategies are applied in order to reduce the green-house gas-emissions, such as optimizing the process of clinker production, the use of alternative fuel and the partial substitution of the clinker in blended cement by so-called SCM (supplementary cementitious materials). Hereby blast-furnace slag, fly ash and limestone are the most used materials.
3. Quaternary systems containing three SCM simultaneously besides Portland cement contribute to the reduction of CO2 emissions due to the decrease of the clinker content. In addition, such systems allow to use blast-furnace slag and fly ash in the most economical way and provide the possibility to account for shortages of SCM on the market.
4. Blast-furnace slag and fly ash show similarities in their principal chemical compositions such that similar hydrates are formed during their reaction in presence of Portland cement. Compared to ternary systems based on blast-furnace slag or fly ash besides limestone, quaternary systems that contain both, blast-furnace slag and fly ash, simultaneously besides limestone, are expected to perform similar in terms of phase assemblage and strength development.
5. The use of SCM as cement replacing materials is limited due to their generally slower reaction compared to neat cement which also leads to lower strength development, especially in the early stage of the hydration up to 28 d. To account for this it is necessary to study the reactivity of SCM such as blast-furnace slag and fly ash in detail in order to develop strategies to enhance the reactivity and thereby the strength development of SCM-containing systems.
6. The early hydration of clinker phases is studied in detail, mainly in diluted systems. It is unclear if processes that were found to control the reaction of such model systems are also prevailing in concentrated cement pastes under realistic water-to-solid ratios. Deeper insight to this aspect is needed to better understand interactions of neat Portland cement and SCM in the first hours of hydration.
State-of-the-art
7. Increasing Ca-concentrations lead to decreasing dissolution rates of C3S and C2S in diluted systems.
8. The hydration kinetics of C3S is controlled by the interplay of undersaturation with respect to C3S and oversaturation with respect to C-S-H.
9. Increasing Al-concentrations lead to a retardation of the hydration of C3S. It is unclear if the uptake of aluminum in C-S-H to form C-(A)-S-H which has a significantly lower growth rate than pure C-S-H or a retarding effect of Al on the dissolution of C3S causes this phenomenon.
10. The surface of limestone provides excellent conditions for the nucleation and growth of C-S-H such that significantly more C-S-H nuclei are formed in presence of limestone compared to other SCM.
11. The reactivity of blast-furnace slag and fly ash depends on the particle size as well as on the intrinsic reactivity of especially the amorphous phases.
12. An increase in network modifying oxides (e.g. CaO) in the chemical composition of amorphous (calcium)aluminosilicates leads to an increasingly depolymerized network which in turn causes increasing reactivity. The role of amphoteric oxides (Al2O3, Fe2O3) that can be present as network modifying oxides as well as network forming oxides is not completely solved.
13. CO2-containing AFm-phases are thermodynamically more stable than monosulfoaluminate. This indirectly stabilizes the voluminous ettringite which causes a higher total volume of hydrates and lower porosity whereby higher compressive strength is reached.
14. Only a few percent of limestone in blended cement reacts chemically dependent on the Al2O3 available for reaction. Al2O3 that is provided by the reaction of Portland cement but also by the dissolution of SCM, especially by fly ash, reacts to form hemicarboaluminate which is transformed to monocarboaluminate as the hydration proceeds.
Methodology
15. The influence of SCM on the early hydration of Portland cement in binary (including blast-furnace slag or fly ash or limestone or quartz) and ternary (including fly ash and limestone) systems was investigated applying isothermal calorimetry and analysis of the pore solution chemistry. Calculated saturation indices and solubility products of relevant phases were correlated with heat development. Based on the gained data it was reviewed if mechanisms that control the hydration of pure phases in diluted systems are also prevailing in cement pastes under realistic conditions.
16. The influence of the chemical composition of synthetic glasses on their dissolution at high pH was investigated in highly diluted systems using ion chromatography. Pozzolanity tests were conducted on pastes using simplified model systems and glass-blended Portland cements. The process of the glass dissolution was investigated by isothermal calorimetry and by thermogravimetry. Correlation of experimentally determined total bound water with bound water determined by mass balance calculations as a function of amount of glass reacted allowed to estimate the degree of glass reaction in the pastes. Further on selective dissolution experiments were carried out to crosscheck the results of the bound water/mass balance approach.
17. The reaction kinetics of quaternary pastes containing blast-furnace slag and fly ash simultaneously in the presence of limestone were investigated up to 28 d using isothermal calorimetry and chemical shrinkage measurements. In addition strength tests on mortar bars were carried out.
18. Pastes of quaternary blends were also investigated in terms of hydrate assemblage at ages of up to 182 d. Thermodynamic calculations regarding total volume of hydrates as a function of limestone and fly ash/blast-furnace slag content were conducted. The calculations were supported by thermogravimetric determination of bound water and portlandite content as well as qualitative X-ray diffraction. The results were correlated with strength tests on mortar bars.
19. The pore solutions of hydrated quaternary blends were extracted and investigated by means of ion chromatography at ages of up to 728 d. Based on the ion concentrations in the solutions saturation indices were calculated for relevant phases. In order to gain better insight to the blast-furnace slag reaction sulphate speciation was carried out at two blast furnace slag levels (20 and 30 wt.%) for selected samples up to 91 d of hydration and at 91 d for the whole matrix under investigation.
Main results
20. Investigations on the early hydration kinetics of binary systems showed a higher heat flow in presence of SCM compared to neat Portland cement. This is caused by the higher surface area that is available for the nucleation of hydrates and by the lower (over)saturation with respect to C-S-H. An increase in the Ca-concentration in the pore solution did not cause lower dissolution rates of C3S as was reported for pure phases in diluted systems. The highest dissolution was observed in the presence of limestone, i.e. at the highest Ca-concentration. The general trend of the reaction rate is inversely related to the degree of undersaturation with respect to C3S. The more undersaturated the faster the observed reaction. The presence of increasing Al-concentrations caused a retardation of the reaction which is in line with investigations on pure phases in diluted systems. Higher sulphate concentrations could be detected for the fly ash containing blend which possibly hindered ettringite precipitation and results in higher Al-concentrations. Correspondingly the low sulphate concentrations lead to lower Al-concentrations in the presence of quartz, blast-furnace slag and limestone compared to fly ash.
21. The early hydration kinetics of quaternary systems is significantly accelerated in the presence of limestone while fly ash leads to retardation. Compared to reference systems containing inert quartz, investigations by means of isothermal calorimetry and chemical shrinkage revealed an acceleration caused by blast-furnace slag. Additions of fly ash, limestone or mixtures thereof introduced another acceleration but differences are too small to be significant and clear distinguishing between the various SCM is not possible.
22. Investigations on the reactivity of synthetic glasses showed that increasing amounts of network modifying oxides caused an increase in reactivity and dissolution rates. The results reveal that Al2O3 acts mainly as network modifying oxide in all investigated glasses. Experimentally determined bound water (thermogravimetric experiments) in model systems and blended cements can be compared with bound water determined by mass balance calculations carried out as a function of the amount of glass reacted. This enables to estimate the degree of glass reaction.
23. The actual content of blast-furnace slag, fly ash or limestone does not exert significant influence on the development of compressive strength up to 7 d. At later ages thermodynamic calculations predict a degree of CaCO3 reaction of 2 to 5 wt.%. This leads to the formation of hemicarbonate and monocarbonate whereby ettringite is indirectly stabilized. As a result the total amount of solids is increased and compressive strength shows a slight maximum. Hereby the degree of CaCO3 reaction depends on the Al2O3 available for reaction which is not only provided by the dissolution of Portland cement but especially by the dissolution of the fly ash.
24. In general the presence of blast-furnace slag and fly ash in the presence of limestone exerts little influence on the hydrate assemblage. The substitution of some of the blast-furnace slag by fly ash leads to a slight decrease of portlandite and C-S-H and gives rise to the formation of more monocarbonate and hemicarbonate. Portlandite is consumed in a pozzolanic reaction with the fly ash whereby C-S-H is formed. However, the low reactivity of the fly ash causes a decrease in the amount of C-S-H formed. Thereby a lower total volume of hydrates is generated which is in line with slightly lower compressive strength in case of increasing fly ash content. The overall influence is small and all systems investigated reach strength class 42.5 N according to EN 196-1.
25. Corresponding to the investigations of the hydrate assemblage the pore solution chemistry of quaternary systems showed only small variations. Depending on the fly ash content the highest variations are observed for aluminium, i.e. increasing fly ash content leads to higher Al-concentrations. Another effect of increasing fly ash contents is an increasing undersaturation with respect to portlandite and a decreasing undersaturation with respect to strätlingite indicating the dissolution of portlandite.
26. The total concentration of sulfur in the pore solution is controlled by sulphate (SO42–) while the concentrations of sulphite (SO32–) and thiosulphate (S2O32–) were very low. Up to 2 d of hydration about 90 % of the total sulphur is present as SO42–. After 91 d this value is reduced to about 36 % while about 28 % are present as S2O32–. In general higher blast-furnace slag content leads to higher concentrations of sulphite and thiosulphate after 7 d.
The key objective of this research is to study fracture with a meshfree method, local maximum entropy approximations, and model fracture in thin shell structures with complex geometry and topology. This topic is of high relevance for real-world applications, for example in the automotive industry and in aerospace engineering. The shell structure can be described efficiently by meshless methods which are capable of describing complex shapes as a collection of points instead of a structured mesh. In order to find the appropriate numerical method to achieve this goal, the first part of the work was development of a method based on local maximum entropy (LME)
shape functions together with enrichment functions used in partition of unity methods to discretize problems in linear elastic fracture mechanics. We obtain improved accuracy relative to the standard extended finite element method (XFEM) at a comparable computational cost. In addition, we keep the advantages of the LME shape functions,such as smoothness and non-negativity. We show numerically that optimal convergence (same as in FEM) for energy norm and stress intensity factors can be obtained through the use of geometric (fixed area) enrichment with no special treatment of the nodes
near the crack such as blending or shifting.
As extension of this method to three dimensional problems and complex thin shell structures with arbitrary crack growth is cumbersome, we developed a phase field model for fracture using LME. Phase field models provide a powerful tool to tackle moving interface problems, and have been extensively used in physics and materials science. Phase methods are gaining popularity in a wide set of applications in applied science and engineering, recently a second order phase field approximation for brittle fracture has gathered significant interest in computational fracture such that sharp cracks discontinuities are modeled by a diffusive crack. By minimizing the system energy with respect to the mechanical displacements and the phase-field, subject to an irreversibility condition to avoid crack healing, this model can describe crack nucleation, propagation, branching and merging. One of the main advantages of the phase field modeling of fractures is the unified treatment of the interfacial tracking and mechanics, which potentially leads to simple, robust, scalable computer codes applicable to complex systems. In other words, this approximation reduces considerably the implementation complexity because the numerical tracking of the fracture is not needed, at the expense of a high computational cost. We present a fourth-order phase field model for fracture based on local maximum entropy (LME) approximations. The higher order continuity of the meshfree LME approximation allows to directly solve the fourth-order phase field equations without splitting the fourth-order differential equation into two second order differential equations. Notably, in contrast to previous discretizations that use at least a quadratic basis, only linear completeness is needed in the LME approximation. We show that the crack surface can be captured more accurately in the fourth-order model than the second-order model. Furthermore, less nodes are needed for the fourth-order model to resolve the crack path. Finally, we demonstrate the performance of the proposed meshfree fourth order phase-field formulation for 5 representative numerical examples. Computational results will be compared to analytical solutions within linear elastic fracture mechanics and experimental data for three-dimensional crack propagation.
In the last part of this research, we present a phase-field model for fracture in Kirchoff-Love thin shells using the local maximum-entropy (LME) meshfree method. Since the crack is a natural outcome of the analysis it does not require an explicit representation and tracking, which is advantageous over techniques as the extended finite element method that requires tracking of the crack paths. The geometric description of the shell is based on statistical learning techniques that allow dealing with general point set surfaces avoiding a global parametrization, which can be applied to tackle surfaces of complex geometry and topology. We show the flexibility and robustness of the present methodology for two examples: plate in tension and a set of open connected
pipes.
Piezoelectric materials are used in several applications as sensors and actuators where they experience high stress and electric field concentrations as a result of which they may fail due to fracture. Though there are many analytical and experimental works on piezoelectric fracture mechanics. There are very few studies about damage detection, which is an interesting way to prevent the failure of these ceramics.
An iterative method to treat the inverse problem of detecting cracks and voids in piezoelectric structures is proposed. Extended finite element method (XFEM) is employed for solving the inverse problem as it allows the use of a single regular mesh for large number of iterations with different flaw geometries.
Firstly, minimization of cost function is performed by Multilevel Coordinate Search (MCS) method. The XFEM-MCS methodology is applied to two dimensional electromechanical problems where flaws considered are straight cracks and elliptical voids. Then a numerical method based on combination of classical shape derivative and level set method for front propagation used in structural optimization is utilized to minimize the cost function. The results obtained show that the XFEM-level set methodology is effectively able to determine the number of voids in a piezoelectric structure and its corresponding locations.
The XFEM-level set methodology is improved to solve the inverse problem of detecting inclusion interfaces in a piezoelectric structure. The material interfaces are implicitly represented by level sets which are identified by applying regularisation using total variation penalty terms. The formulation is presented for three dimensional structures and inclusions made of different materials are detected by using multiple level sets. The results obtained prove that the iterative procedure proposed can determine the location and approximate shape of material subdomains in the presence of higher noise levels.
Piezoelectric nanostructures exhibit size dependent properties because of surface elasticity and surface piezoelectricity. Initially a study to understand the influence of surface elasticity on optimization of nano elastic beams is performed. The boundary of the nano structure is implicitly represented by a level set function, which is considered as the design variable in the optimization process. Two objective functions, minimizing the total potential energy of a nanostructure subjected to a material volume constraint and minimizing the least square error compared to a target
displacement, are chosen for the numerical examples. The numerical examples demonstrate the importance of size and aspect ratio in determining how surface effects impact the optimized topology of nanobeams.
Finally a conventional cantilever energy harvester with a piezoelectric nano layer is analysed. The presence of surface piezoelectricity in nano beams and nano plates leads to increase in electromechanical coupling coefficient. Topology optimization of these piezoelectric structures in an energy harvesting device to further increase energy conversion using appropriately modified XFEM-level set algorithm is performed .
Die thermodynamischen Grundlagen der Hydratation von Hüttensand als Hauptbestandteil von Zementen werden erforscht. Hierbei werden thermodynamische Bildungs- und Reaktionsdaten experimentell bestimmt und berechnet. Darüber hinaus wird der Prozess der Feststoffauflösung von Hüttensand in wässrigen Lösungen untersucht. Lösungs- und Fällungsprozesse werden unter verschiedenen Konditionen gemessen, ausgewertet und diskutiert. Die Ergebnisse werden im weiteren Verlauf zur Bestimmung der Hydratationsgrades in Pasten sowie zum besseren Verständnis in der Wechselwirkung zwischen Hüttensanden und Mahlhilfsstoffen genutzt und angewandt.