In the present study, a computational method was developed, validated and applied for the determination of parameters of a constitutive model for a ceramic material. An optimization algorithm, based on a direct search method, was applied to the determination of the load-displacement response of the specimen, and for the identification of the parameters of the constitutive model.A one-dimensional nonlinear initial-boundary value problem of wave propagation in a composite bar made of dissimilar materials was formulated and solved numerically. Convergence of the numerical scheme was studied, and range of convergence was established. Numerical scheme was validated for a number of benchmark problems with known analytical solutions, and for the problems solved using finite element method. Investigation of the accuracy of the displacement and strain responses was conducted; known limitations of the Kolsky's method for split Hopkinson pressure bar were revealed. For numerical examples considered in the present study, comparison of performance of the optimized finite-difference solver and of the finite element code LS-DYNA showed that the finite-difference code is about 10 times faster.Developed method and solutions were applied for the identification of the parameters of the Johnson-Holmquist constitutive model for five sets of experimental data for aluminum oxide AD995. Results of analysis revealed significant sensitivity of stress response to variation of fractured strength model parameters and damage model parameters.For the determined values of parameters, detailed parametric study of stress field, damage accumulation, and velocity field, was conducted with the help of the finite element method.It was found that the accuracy of the simulation using the JH-2 constitutive model changes with the rate of damage accumulation in the ceramic material.The damage patterns and history of damage development, obtained numerically, agreed qualitatively with the fracture history and its patterns, observed in the recovered Macor ceramics available in the literature.A method for image analysis of the photographic images of the lateral sides of the recovered specimen was proposed. It was used to quantify density of the damage in the specimen and to establish a better integral approach to predict amount of damage inside the specimen.

In this study, a cold worked tool steel and a low carbon steel ( St 37 ), which were joined by brazing, were subjected to impact and shear loading. The end product is used as paper cutting blades in the industry. Effects of different brazing filler metals on the delamination of the blades under impact loading and on the impact toughness of the blades were studied. The target is to achieve higher impact toughness values without delamination. Impact toughness of the steels, joined by Cu, CuNi and BNi brazing filler metals and separation of brazed surfaces under shear loading were studied. The microstructures that were formed as a result of each application were studied by scanning electron microscopy and x-ray diffraction. The results indicate that brittle intermetallic compounds are formed in BNi brazing filler metal application. It is observed that CuNi alloy with 24% wt Ni form stronger bonds with the base metals than pure Cu and 10% wt Ni CuNi alloy.

No description available.

<p>In an AP-HTPB propellant microstructure, the local strain rate depends on the AP crystal size and the material, while the local temperature rate depends on the impact velocity, AP crystal size, and the material.  Larger AP crystals lead to higher local strain rates and higher local temperature rates, which means hot spots are more likely to occur in AP-HTPB propellants with more large AP crystals.</p>

Strain hardening cement-based composites (SHCC) and textile reinforced concrete (TRC) are two types of novel cementitious materials which can be used for strengthening structural elements against impact loading. Under tensile loading, these composites exhibit a strain hardening behavior, accompanied with formation of multiple cracks. The multiple cracking and strain hardening behavior yield a high strain and energy absorption capacity, thus making SHCC and TRC suitable materials for impact resistant structures or protective layers. The design and optimization of such composites for impact resistant applications require a comprehensive characterization of their behavior under various impact loadings. Specifically, the rate dependent behavior of the composites and their constituents, i.e. matrix, reinforcement, and their bond, need to be described. In the context of dynamic testing, SHCC, TRC and their constituents require customized experimental setups. The geometry of the sample, ductility of the material, the need for adapters and their influence on the measurements, as well as the influence of inertia are the key aspects which should be considered in developing the impact testing setups. The thesis at hand deals with the development process of various impact testing setups for both composite scale and constituent scale. The crucial aspects to be taken into account are discussed extensively. As a result, a gravity driven split-Hopkinson tension bar was developed. The setup was used for performing impact tension experiments on SHCC, TRC and yarn-matrix bond. Moreover, its applicability for performing impact shear experiments was examined. Additionally, a mini split-Hopkinson tension bar for high speed micromechanical experiments was designed and built. In the case of compressive loading, the performance of SHCC was investigated in a split-Hopkinson pressure bar. The obtained results, with focus on tensile experiments, were evaluated concerning their accuracy, and susceptibility to inertia effects. Full-field displacement measurement obtained by digital image correlation (DIC) was used in all impact experiments as a tool for visualizing and explaining the fracture process of the material in conjunction with the standard wave analysis performed in the split-Hopkinson bars.Moreover, the rate dependent behaviors of the composites were clarified with respect to the rate dependent behavior of their constituents.

Evaluation of the performance of a product and its components under impact loading is one of the key considerations in design. In order to assess resistance to damage or ability to absorb energy through plastic deformation of a structural component, impact testing is often carried out to obtain the 'Force - Displacement' response of the deformed component. In this context, it may be noted that load cells and accelerometers are commonly used as sensors for capturing impact responses. A drop-weight impact testing set-up consisting of a moving impactor head with a lightweight piezoresistive accelerometer and a strain gage based compression load cell mounted on it is used to carry out the impact tests. The basic objective of the present study is to assess the accuracy of responses recorded by the said transducers, when these are mounted on a moving impactor head. In the present work, a novel approach of theoretically evaluating the responses obtained from this drop-weight impact testing set-up for different axially loaded specimen has been executed with the formulation of an equivalent lumped parameter model (LPM) of the test set-up. For the most common configuration of a moving impactor head mounted load cell system in which dynamic load is transferred from the impactor head to the load cell, a quantitative assessment is made of the possible discrepancy that can result in load cell response. Initially, a 3-DOF (degrees-of-freedom) LPM is considered to represent a given impact testing set-up with the test specimen represented with a nonlinear spring. Both the load cell and the accelerometer are represented with linear springs, while the impacting unit comprising an impactor head (hammer) and a main body with the load cell in between are modelled as rigid masses. An experimentally obtained force-displacement response is assumed to be a nearly true behaviour of a specimen. By specifying an impact velocity to the rigid masses as an initial condition, numerical solution of the governing differential equations is obtained using Implicit (Newmark-beta) and Explicit (Central difference) time integration techniques. It can be seen that the model accurately reproduces the input load-displacement behaviour of the nonlinear spring corresponding to the tested component, ensuring the accuracy of these numerical methods. The nonlinear spring representing the test specimen is approximated in a piecewise linear manner and the solution strategy adopted and implemented in the form of a MATLAB script is shown to yield excellent reproduction of the assumed load-displacement behaviour of the test specimen. This prediction also establishes the accuracy of the numerical approach employed in solving the LPM system. However, the spring representing the load cell yields a response that qualitatively matches the assumed input load-displacement response of the test specimen with a lower magnitude of peak load. The accelerometer, it appears, may be capable of predicting more closely the load experienced by a specimen provided an appropriate mass of the impactor system i.e. impacting unit, is chosen as the multiplier for the acceleration response. Error between input and computed (simulated) responses is quantified in terms of root mean square error (RMSE). The present study additionally throws light on the dependence of time step of integration on numerical results. For obtaining consistent results, estimation of critical time step (increment) is crucial in conditionally stable central difference method. The effect of the parameters of the impact testing set-up on the accuracy of the predicted responses has been studied for different combinations of main impactor mass and load cell stiffness. It has been found that the load cell response is oscillatory in nature which points out to the need for suitable filtering for obtaining the necessary smooth variation of axial impact load with respect to time as well as deformation. Accelerometer response also shows undulations which can similarly be observed in the experimental results as well. An appropriate standard SAE-J211 filter which is a low-pass Butterworth filter has been used to remove oscillations from the computed responses. A load cell is quite capable of predicting the nature of transient response of an impacted specimen when it is part of the impacting unit, but it may substantially under-predict the magnitudes of peak loads. All the above mentioned analysis for a 3 DOF model have been performed for thin-walled tubular specimens made of mild steel (hat-section), an aluminium alloy (square cross-section) and a glass fibre-reinforced composite (circular cross-section), thus confirming the generality of the inferences drawn on the computed responses. Further, results obtained using explicit and implicit methodologies are compared for three specimens, to find the effect, if any, on numerical solution procedure on the conclusions drawn. The present study has been further used for investigating the effects of input parameters (i.e. stiffness and mass of the system components, and impact velocity) on the computed results of transducers. Such an investigation can be beneficial in designing an impact testing set-up as well as transducers for recording impact responses. Next, the previous 3 DOF model representing the impact testing set-up has been extended to a 5 DOF model to show that additional refinement of the original 3 DOF model does not substantially alter the inferences drawn based on it. In the end, oscillations observed in computed load cell responses are analysed by computing natural frequencies for the 3 DOF lumped parameter model. To conclude the present study, a 2 DOF LPM of the given impact testing set-up with no load cell has been investigated and the frequency of oscillations in the accelerometer response is seen to increase corresponding to the mounting resonance frequency of the accelerometer. In order to explore the merits of alternative impact testing set-ups, LPMs have been formulated to idealize test configurations in which the load cell is arranged to come into direct contact with the specimen under impact, although the accelerometer is still mounted on the moving impactor head. One such arrangement is to have the load cell mounted stationary on the base under the specimen and another is to mount the load cell on the moving impactor head such that the load cell directly impacts the specimen. It is once again observed that both these models accurately reproduce the input load-displacement behaviour of the nonlinear spring corresponding to the tested component confirming the validity of the model. In contrast to the previous set-up which included a moving load cell not coming into contact with the specimen, the spring representing the load cell in these present cases yields a response that more closely matches the assumed input load-displacement response of a test specimen suggesting that the load cell coming into direct contact with the specimen can result in a more reliable measurement of the actual dynamic response. However, in practice, direct contact of the load cell with the specimen under impact loading is likely to damage the transducer, and hence needs to be mounted on the moving head, resulting in a loss of accuracy, which can be theoretically estimated and corrected by the methodology investigated in this work.

The present work aims at finding suitable mineral-bonded strengthening layers to protect steel-reinforced concrete (RC) structures from impact events. The strengthening layers are applied to the impact-facing side and absorb large parts of the impact energy. In this way, they protect the RC structures from the impact events. The multilayered strengthening layers consist of a cover layer and a damping layer. The cover layers possess a high strength and a high modulus of elasticity. The impactor directly hits the cover layer, which spreads the impact force to larger areas of the damping layer below. The strengths and moduli of elasticity of the damping layers are minor, and they absorb impact energy, converting it into friction, heat, or potential energy. Several materials have been tested as damping layers, including a concrete mixed with waste tire rubber aggregates, two types of lightweight concrete, and two types of infra-lightweight concrete. The cover layers tested include carbon-fiber-reinforced concrete and various short-fiber-reinforced concretes, some of which are reinforced with 3D hybrid pyramidal truss reinforcing structures. At first, the dynamic material properties were determined with the help of a tensile and a compressive split Hopkinson bar. The small-scale experiments serve to investigate the dynamic material behavior. At the same time, they are the basis for an eventual later numerical analysis of the strengthening layers. A numerical analysis enables the variation of the material parameters. Lastly, large-scale tests with RC cuboids that were fully supported were performed. A choice of cover and damping layer materials was compared to unstrengthened RC cuboids. The first set of experiments strived to vary the damping layer to find the most suitable one that absorbs the highest amount of incident energy, thus minimizing the damage to the RC cuboid. Afterward, the best damping layer material was combined with different cover layers to figure out the best cover layer option.:Abstract i Kurzfassung iii List of Symbols xv List of Abbreviations xix 1 Objectives, Working Program, and Structure 1 1.1 Motivation 1 1.2 Overall Objectives 1 1.3 Working Program 1 2 State of the Art and Theoretical Background 3 2.1 Impact on Structural Elements 3 2.1.1 Soft and Hard Impact 3 2.1.2 Failure Modes Under Hard Impact Conditions 3 2.1.3 Large-Scale Impact Experiments 4 2.1.4 Impact Protection Layers 4 2.2 Introduction of Impact Protection Principles 4 2.2.1 Impact Protection in Nature 4 2.2.2 Technical Impact Protection Examples 9 2.2.3 Summary of Impact Protection Principles and Usable Materials 14 2.3 Mineral-Bonded Damping Layer Materials 15 2.3.1 Waste Tire Rubber Concrete 15 2.3.2 All-Lightweight Aggregate Concrete 16 2.3.3 Infra-Lightweight Concrete 17 2.4 Mineral-Bonded Cover Layer Materials 18 2.4.1 Strain-Hardening Cementitous Composites 18 2.4.2 Textile Reinforced Concrete 19 2.4.3 Hybrid-Fiber Reinforced Concrete 19 2.5 Bond Between Different Strengthening Layers 20 3 Materials under Investigation 21 3.1 Specimen Preparation 21 3.2 Damping Layer Materials 22 3.2.1 Waste Tire Rubber Concrete (WTRC) 22 3.2.2 All-Lightweight Aggregate Concrete With Liapor Aggregates (ALWAC-L) 23 3.2.3 All-Lightweight Aggregate Concrete With Ulopor Aggregates (ALWAC-U) 23 3.2.4 Porous Lightweight Concrete (PLC) 23 3.2.5 Infra-Lightweight Concrete (ILC) 23 3.2.6 Comparison of the Damping Layer Materials 24 3.3 Cover Layer Materials 27 3.3.1 Pagel TF10 CARBOrefit With Carbon Textile Reinforcement (P-C) 27 3.3.2 Strain-Hardening Limestone Calcined Clay Cement (SHLC3) 27 3.3.3 Comparison of the Cover Layer Materials 28 3.4 Partially Loaded Areas 30 4 Methodology of Split Hopkinson Bar Experiments 35 4.1 Experimental Setup and Methodology 35 4.1.1 Compressive Split Hopkinson Bar 35 4.1.2 Tensile Split Hopkinson Bar 36 4.1.3 Instrumentation 39 4.2 Evaluation Process 39 4.2.1 Impedance 40 4.2.2 Raw Data Analysis, Filtering, and Time-Shifting of Pulses 41 4.2.3 Stresses and Strains 42 4.2.4 Deformations 50 4.2.5 Forces and Impulses 51 4.2.6 Energy Absorption 52 4.2.7 Fracture Energy 53 4.2.8 Averaging of the Results 54 5 Compressive Split Hopkinson Bar Experiments 57 5.1 Failure Modes 57 5.2 Stresses and Strains 58 5.2.1 Dynamic Compressive Strength 58 5.2.2 DIF 59 5.3 Deformations 60 5.4 Forces and Impulses 61 5.4.1 Relative Transmitted Force 61 5.4.2 Impulse Transmission 63 5.4.3 Reduction of the Pulse Inclination 64 5.5 Energy Absorption 64 5.6 Conclusions 66 6 Tensile Split Hopkinson Bar Experiments 69 6.1 Failure Modes 69 6.2 Stresses and Strains 70 6.2.1 Dynamic Tensile Strength 70 6.2.2 DIF 71 6.3 Deformations 72 6.4 Forces and Impulses 73 6.4.1 Relative Transmitted Force 73 6.4.2 Impulse Transmission 74 6.4.3 Reduction of the Pulse Inclination 75 6.5 Energy Absorption 75 6.6 Fracture Energy 77 6.7 Conclusions 78 7 Methodology of Cuboid Experiments 79 7.1 Experimental Program 79 7.1.1 Specimen Dimensions and Experimental Setup 79 7.1.2 Experimental Scheme 81 7.2 Measurements Taken During the Experiments 83 7.2.1 Light Barriers 84 7.2.2 Resistor 84 7.2.3 Strain Gauges 84 7.2.4 Laser Doppler Vibrometer 85 7.2.5 Accelerometers 85 7.2.6 Load Cells 85 7.2.7 High-Speed Cameras and DIC 85 7.3 Measurements Taken Before and After the Experiments 86 7.3.1 Impactor Indentation 86 7.3.2 Burst Mass 86 7.3.3 Ultrasonic Pulse Velocity Measurements 86 7.3.4 Stimulation 87 7.4 Evaluation Process 88 7.4.1 Fracture and Damage Process 88 7.4.2 Impactor Velocity, Deceleration, Force, Stress, and Stress Rate 88 7.4.3 Impactor Indentation, Strain, and Strain Rate 90 7.4.4 Vertical Cuboid Deformation, Velocity, and Acceleration 92 7.4.5 Lateral Cuboid Deformation, Velocity, and Acceleration 93 7.4.6 Relative Cuboid Elongation in X- and Y-Direction 93 7.4.7 Strain Measurements on the Reinforcement Bars 94 7.4.8 Path and Derivative of the Support Forces 95 7.4.9 Burst Mass 96 7.4.10 Ultrasonic Pulse Velocity Measurements 96 7.4.11 Stimulation 97 7.4.12 Impulse and Momentum Conservation 99 7.4.13 Energy Conservation 100 7.4.14 Estimation of the Eigenfrequency of the Cuboids 101 8 Damping Layer Variation in Cuboid Experiments 103 8.1 Fracture and Damage Process 103 8.2 Impactor Velocity, Deceleration, and Force 105 8.3 Impactor Indentation 108 8.4 Vertical Cuboid Deformation, Velocity, and Acceleration 110 8.5 Lateral Cuboid Deformation, Velocity, and Acceleration 113 8.6 Relative Cuboid Elongation in X- and Y-Direction 115 8.7 Path and Derivative of the Support Forces 118 8.8 Ultrasonic Pulse Velocity Measurements 120 8.9 Stimulation With the Impulse Hammer 121 8.10 Stimulation With the Steel Impactor 124 8.11 Overview Over Forces, Stresses, Strains, and Their Rates 128 8.12 Impulse and Momentum Conservation 133 8.13 Energy Conservation 135 8.14 Dimensioning of the Required Damping Layer Thickness Depending on the Loading Velocity 136 8.15 Conclusions 137 9 Cover Layer Variation in Cuboid Experiments 139 9.1 Fracture and Damage Process 139 9.2 Impactor Velocity, Deceleration, and Force 141 9.3 Impactor Indentation 144 9.4 Vertical Cuboid Deformation, Velocity, and Acceleration 145 9.5 Lateral Cuboid Deformation, Velocity, and Acceleration 147 9.6 Relative Cuboid Elongation in X- and Y-Direction 149 9.7 Path and Derivative of the Support Forces 150 9.8 Ultrasonic Pulse Velocity Measurements 152 9.9 Stimulation With the Impulse Hammer 153 9.10 Stimulation With the Steel Impactor 155 9.11 Overview Over Forces, Stresses, Strains, and Their Rates 157 9.12 Impulse and Momentum Conservation 162 9.13 Energy Conservation 163 9.14 Conclusions 164 10 Conclusions of the Cuboid Experiments 167 10.1 Main Findings 167 10.2 Most Relevant Sensor Positions and Measurements 167 10.2.1 Digital Image Correlation (DIC) of the Impactor 167 10.2.2 Lateral Acceleration 167 10.2.3 Digital Image Correlation (DIC) of the RC Cuboid 168 10.2.4 Ultrasonic Pulse Velocity (UPV) Measurements 168 10.2.5 Stimulation With the Impulse Hammer and the Steel Impactor 168 10.3 Suggested Improvements to the Setup 168 10.3.1 High-Speed Cameras (HSC) 168 10.3.2 Acceleration Sensors 169 10.3.3 Support Forces 169 10.3.4 Strain Gauges 169 10.3.5 Temperature Sensors 169 10.4 Comparison of the Material Behavior in Compressive SHB and Cuboid Experiments 169 10.4.1 Scattering of Measured Values 169 10.4.2 Failure Modes 170 10.4.3 Loading and Strain Rates 170 10.4.4 Influences of Inertia 170 10.4.5 Forces and Stresses 171 10.4.6 Energy Absorption 171 11 Summary and Conclusions 173 11.1 Compressive SHB Experiments 173 11.2 Tensile SHB Experiments 173 11.3 Damping Layer Variation in Cuboid Experiments 174 11.4 Cover Layer Variation in Cuboid Experiments 174 11.5 Conclusions 175 12 Outlook 177 12.1 Split Hopkinson Bar Testing 177 12.2 Strengthening Procedure 177 12.3 Large-Scale Impact Testing 177 12.4 Design 178 Bibliography 179 List of Figures 193 List of Tables 199 / Die vorliegende Arbeit beschäftigt sich mit der Verstärkung von Stahlbetonbauteilen gegen Impaktbeanspruchungen. Es wurden mineralisch gebundene Verstärkungsschichten entwickelt, die auf der impaktzugewandten Seite aufgebracht wurden und große Teile der Impaktenergie umwandelten, um somit die darunterliegenden Bauteile zu schützen. Die Verstärkungsschichten sind mehrlagig aufgebaut und die Materialien werden in Deck- und Dämpfungsschichten unterschieden. Dabei sind die Deckschichtmaterialien solche, die eine große Festigkeit und Steifigkeit besitzen. Sie werden direkt durch den Impaktor getroffen und sollen die Impaktlast auf einen größeren Bereich der darunterliegenden Dämpfungsschichten verteilen. Die Dämpfungsschichten sind weniger fest und steif und sollen die Impaktenergie in Reibungs-, Wärme- und innere Energie umwandeln. Als Dämpfungsschichtmaterialien wurden ein Beton mit Altgummizuschlägen, zwei unterschiedliche Leichtbetone und zwei Infraleichtbetone geprüft. Unter den geprüften Deckschichtmaterialien befanden sich ein Carbonbeton und unterschiedliche Mischungen mit Kurzfaserbetonen, die teilweise auch mit hybriden 3D Bewehrungsstrukturen bewehrt wurden. Zunächst wurden die Materialen unter dynamischer Druck- und Zugbelastung im Split-Hopkinson-Bar geprüft. Diese kleinteiligen Versuche sollen dem Verständnis des dynamischen Materialverhaltens dienen und bilden gleichzeitig die Grundlage für eine mögliche spätere numerische Analyse der Verstärkungsschichtmaterialien, die gleichzeitig die Variation der Materialeigenschaften von Verstärkungsschichten erlaubt. Anschließend wurden die unterschiedlichen Dämpfungs- und Deckschichtmaterialien in einem größeren Probenmaßstab untersucht. Die Probekörper, die unverstärkt sowie unterschiedlich verstärkt untersucht wurden, waren vollflächig gelagerte Stahlbetonquader. Zunächst wurde das Dämpfungsschichtmaterial variiert, um die Dämpfungsschicht zu finden, die am meisten Energie umwandeln und somit die Schädigung der Stahlbetonquader am effizientesten reduzieren kann. Diese wurde danach unter unterschiedlichen Deckschichten kombiniert, um das geeignetste Deckschichtmaterial zu ermitteln.:Abstract i Kurzfassung iii List of Symbols xv List of Abbreviations xix 1 Objectives, Working Program, and Structure 1 1.1 Motivation 1 1.2 Overall Objectives 1 1.3 Working Program 1 2 State of the Art and Theoretical Background 3 2.1 Impact on Structural Elements 3 2.1.1 Soft and Hard Impact 3 2.1.2 Failure Modes Under Hard Impact Conditions 3 2.1.3 Large-Scale Impact Experiments 4 2.1.4 Impact Protection Layers 4 2.2 Introduction of Impact Protection Principles 4 2.2.1 Impact Protection in Nature 4 2.2.2 Technical Impact Protection Examples 9 2.2.3 Summary of Impact Protection Principles and Usable Materials 14 2.3 Mineral-Bonded Damping Layer Materials 15 2.3.1 Waste Tire Rubber Concrete 15 2.3.2 All-Lightweight Aggregate Concrete 16 2.3.3 Infra-Lightweight Concrete 17 2.4 Mineral-Bonded Cover Layer Materials 18 2.4.1 Strain-Hardening Cementitous Composites 18 2.4.2 Textile Reinforced Concrete 19 2.4.3 Hybrid-Fiber Reinforced Concrete 19 2.5 Bond Between Different Strengthening Layers 20 3 Materials under Investigation 21 3.1 Specimen Preparation 21 3.2 Damping Layer Materials 22 3.2.1 Waste Tire Rubber Concrete (WTRC) 22 3.2.2 All-Lightweight Aggregate Concrete With Liapor Aggregates (ALWAC-L) 23 3.2.3 All-Lightweight Aggregate Concrete With Ulopor Aggregates (ALWAC-U) 23 3.2.4 Porous Lightweight Concrete (PLC) 23 3.2.5 Infra-Lightweight Concrete (ILC) 23 3.2.6 Comparison of the Damping Layer Materials 24 3.3 Cover Layer Materials 27 3.3.1 Pagel TF10 CARBOrefit With Carbon Textile Reinforcement (P-C) 27 3.3.2 Strain-Hardening Limestone Calcined Clay Cement (SHLC3) 27 3.3.3 Comparison of the Cover Layer Materials 28 3.4 Partially Loaded Areas 30 4 Methodology of Split Hopkinson Bar Experiments 35 4.1 Experimental Setup and Methodology 35 4.1.1 Compressive Split Hopkinson Bar 35 4.1.2 Tensile Split Hopkinson Bar 36 4.1.3 Instrumentation 39 4.2 Evaluation Process 39 4.2.1 Impedance 40 4.2.2 Raw Data Analysis, Filtering, and Time-Shifting of Pulses 41 4.2.3 Stresses and Strains 42 4.2.4 Deformations 50 4.2.5 Forces and Impulses 51 4.2.6 Energy Absorption 52 4.2.7 Fracture Energy 53 4.2.8 Averaging of the Results 54 5 Compressive Split Hopkinson Bar Experiments 57 5.1 Failure Modes 57 5.2 Stresses and Strains 58 5.2.1 Dynamic Compressive Strength 58 5.2.2 DIF 59 5.3 Deformations 60 5.4 Forces and Impulses 61 5.4.1 Relative Transmitted Force 61 5.4.2 Impulse Transmission 63 5.4.3 Reduction of the Pulse Inclination 64 5.5 Energy Absorption 64 5.6 Conclusions 66 6 Tensile Split Hopkinson Bar Experiments 69 6.1 Failure Modes 69 6.2 Stresses and Strains 70 6.2.1 Dynamic Tensile Strength 70 6.2.2 DIF 71 6.3 Deformations 72 6.4 Forces and Impulses 73 6.4.1 Relative Transmitted Force 73 6.4.2 Impulse Transmission 74 6.4.3 Reduction of the Pulse Inclination 75 6.5 Energy Absorption 75 6.6 Fracture Energy 77 6.7 Conclusions 78 7 Methodology of Cuboid Experiments 79 7.1 Experimental Program 79 7.1.1 Specimen Dimensions and Experimental Setup 79 7.1.2 Experimental Scheme 81 7.2 Measurements Taken During the Experiments 83 7.2.1 Light Barriers 84 7.2.2 Resistor 84 7.2.3 Strain Gauges 84 7.2.4 Laser Doppler Vibrometer 85 7.2.5 Accelerometers 85 7.2.6 Load Cells 85 7.2.7 High-Speed Cameras and DIC 85 7.3 Measurements Taken Before and After the Experiments 86 7.3.1 Impactor Indentation 86 7.3.2 Burst Mass 86 7.3.3 Ultrasonic Pulse Velocity Measurements 86 7.3.4 Stimulation 87 7.4 Evaluation Process 88 7.4.1 Fracture and Damage Process 88 7.4.2 Impactor Velocity, Deceleration, Force, Stress, and Stress Rate 88 7.4.3 Impactor Indentation, Strain, and Strain Rate 90 7.4.4 Vertical Cuboid Deformation, Velocity, and Acceleration 92 7.4.5 Lateral Cuboid Deformation, Velocity, and Acceleration 93 7.4.6 Relative Cuboid Elongation in X- and Y-Direction 93 7.4.7 Strain Measurements on the Reinforcement Bars 94 7.4.8 Path and Derivative of the Support Forces 95 7.4.9 Burst Mass 96 7.4.10 Ultrasonic Pulse Velocity Measurements 96 7.4.11 Stimulation 97 7.4.12 Impulse and Momentum Conservation 99 7.4.13 Energy Conservation 100 7.4.14 Estimation of the Eigenfrequency of the Cuboids 101 8 Damping Layer Variation in Cuboid Experiments 103 8.1 Fracture and Damage Process 103 8.2 Impactor Velocity, Deceleration, and Force 105 8.3 Impactor Indentation 108 8.4 Vertical Cuboid Deformation, Velocity, and Acceleration 110 8.5 Lateral Cuboid Deformation, Velocity, and Acceleration 113 8.6 Relative Cuboid Elongation in X- and Y-Direction 115 8.7 Path and Derivative of the Support Forces 118 8.8 Ultrasonic Pulse Velocity Measurements 120 8.9 Stimulation With the Impulse Hammer 121 8.10 Stimulation With the Steel Impactor 124 8.11 Overview Over Forces, Stresses, Strains, and Their Rates 128 8.12 Impulse and Momentum Conservation 133 8.13 Energy Conservation 135 8.14 Dimensioning of the Required Damping Layer Thickness Depending on the Loading Velocity 136 8.15 Conclusions 137 9 Cover Layer Variation in Cuboid Experiments 139 9.1 Fracture and Damage Process 139 9.2 Impactor Velocity, Deceleration, and Force 141 9.3 Impactor Indentation 144 9.4 Vertical Cuboid Deformation, Velocity, and Acceleration 145 9.5 Lateral Cuboid Deformation, Velocity, and Acceleration 147 9.6 Relative Cuboid Elongation in X- and Y-Direction 149 9.7 Path and Derivative of the Support Forces 150 9.8 Ultrasonic Pulse Velocity Measurements 152 9.9 Stimulation With the Impulse Hammer 153 9.10 Stimulation With the Steel Impactor 155 9.11 Overview Over Forces, Stresses, Strains, and Their Rates 157 9.12 Impulse and Momentum Conservation 162 9.13 Energy Conservation 163 9.14 Conclusions 164 10 Conclusions of the Cuboid Experiments 167 10.1 Main Findings 167 10.2 Most Relevant Sensor Positions and Measurements 167 10.2.1 Digital Image Correlation (DIC) of the Impactor 167 10.2.2 Lateral Acceleration 167 10.2.3 Digital Image Correlation (DIC) of the RC Cuboid 168 10.2.4 Ultrasonic Pulse Velocity (UPV) Measurements 168 10.2.5 Stimulation With the Impulse Hammer and the Steel Impactor 168 10.3 Suggested Improvements to the Setup 168 10.3.1 High-Speed Cameras (HSC) 168 10.3.2 Acceleration Sensors 169 10.3.3 Support Forces 169 10.3.4 Strain Gauges 169 10.3.5 Temperature Sensors 169 10.4 Comparison of the Material Behavior in Compressive SHB and Cuboid Experiments 169 10.4.1 Scattering of Measured Values 169 10.4.2 Failure Modes 170 10.4.3 Loading and Strain Rates 170 10.4.4 Influences of Inertia 170 10.4.5 Forces and Stresses 171 10.4.6 Energy Absorption 171 11 Summary and Conclusions 173 11.1 Compressive SHB Experiments 173 11.2 Tensile SHB Experiments 173 11.3 Damping Layer Variation in Cuboid Experiments 174 11.4 Cover Layer Variation in Cuboid Experiments 174 11.5 Conclusions 175 12 Outlook 177 12.1 Split Hopkinson Bar Testing 177 12.2 Strengthening Procedure 177 12.3 Large-Scale Impact Testing 177 12.4 Design 178 Bibliography 179 List of Figures 193 List of Tables 199

Studies on the behavior of steel fiber reinforced concrete (SFRC) and slurry infiltrated fibrous concrete (SIFCON) to impact loading have started in recent years. Using these relatively new materials, higher values of tensile and compressive strength can be obtained with greater fracture toughness and energy absorption capacity, and therefore they carry a considerable importance in the design of protective structures. In this thesis, computational analyses concerning impact loading effect on concrete, steel fiber reinforced concrete (SFRC) and slurry infiltrated fibrous concrete (SIFCON) are conducted by the aid of ANSYS AUTODYN 11.0.0 software. In the simulations, the importance of the concrete compressive and tensile strengths, and the fracture energy, together with the target and projectile erosion parameters, were investigated on the response of concrete target and projectile residual velocity. The obtained results of the simulation trials on concrete, SFRC and SIFCON have been compared with the experimental outcomes of three concrete, two SFRC and two SIFCON specimens in terms of deformed target crater radius, depth volume and striking projectile residual velocities. The simulation analyses have shown that, compressive as well as tensile strengths of the concrete, SFRC and SIFCON specimens are of great importance on the crater volume while erosion parameters have a significant effect on the projectile residual velocity. Simulation outcomes possess a higher accuracy for concrete simulations when comparisons are made with available experimental results. This accuracy deteriorates for SFRC and SIFCON specimens. It was further concluded that related material tests of the specimens must be available in order to obtain higher accuracy.

As many of the world’s nuclear power plants are near the end of their supposed life span a need arise to assess the components crucial to the safety of these plants. One of these crucial components is the concrete reactor confinement; to assess its condition, non-destructive testing (NDT) is an attractive method. Traditional testing of concrete structures has comprised of drilling out a sample and performing stress tests on it, but because of the radioactive environment inside the containment this method is far from ideal. NDT is of course possible to use at any structure but at reactor containments the benefits from not creating holes in the structure are prominent; NDT is also an attractive option from an esthetical point of view because it leaves the structure intact. The NDT method pertaining to this study is the impact echo method which comprise of applying a force on the structure, usually a hammer blow, and measuring the response with a receiver. The impact will excite waves propagating in the structure which gives rise to Lamb modes. Lamb modes are structural oscillations of the wall and it is the frequency of these modes that are used to determine the thickness of the wall. The elastic properties of the structure can in turn be obtained by measuring the velocities of the waves propagation. It is also possible to use the impact echo method to detect irregularities in the structure such as cracks or delamination. To simulate the dynamics of a system using NDT numerical methods such as finite element modeling (FEM) is often used. The purpose of this study is to assess the possibility to utilize absorbing layers using increasing damping (ALID) in models to reduce the computational time of FEM analyses. ALIDs are used at the edges to simulate an infinite system and are thus supposed to cancel out incoming waves to prevent unwanted reflection from the edges. The models in this study have all pertained to two dimensional plates utilizing infinitesimal strain theory; the decrease in computational time is significant when using ALIDs and for three dimensional models it would be even more so. The ALIDs are specified by length and maximum mass proportional Rayleigh damping (CMmax), in this study three different lengths are tested, 0.5, 1.5 and 4.5 m for CMmax ranging from 103 to 2*105 Ns/m. The damping is increased with increasing distance into the ALID with specified maximum value at the back edge. However, it should be noted that the increase in damping causes difference in impedance between elements and if this difference is too large it will cause reflections of waves at the boundary between the elements. The ALID must thus be defined so that it sufficiently cancels out the wave without causing unwanted reflections due to impedance differences. The conclusion is that the 0.5 m long ALID does not provide good results for any choice of maximum mass proportional Rayleigh damping. Both the 1.5 and 4.5 m long ALIDs are, however, concluded to be applicable; the 1.5 m ALID having 2*104 &lt; CMmax &lt;5*104 Ns/m and the 4.5 m ALID having 5*103 &lt; CMmax &lt; 104 Ns/m are choices that have shown promise in the performed simulations. The hope is that the results obtained in this study will aid in the development of numerical analysis techniques for NDT methods that can be used in the construction of new reactor confinements and/or maintenance of existing reactor confinements and other thick concrete structures. / Många av världens kärnkraftverk närmar sig slutet på sin beräknade livslängd och ett behov uppstår då att kunna utvärdera de komponenter som är väsentliga för säkerheten på dessa verk. Reaktoromslutningen i betong är en av dessa komponenter och oförstörande provning (NDT) är en attraktiv metod för att bedöma dess tillstånd. Traditionellt har utvärdering av betongkonstruktioner bestått av stresstester på borrprover men p.g.a. den radioaktiva miljön på insidan av omslutningen är denna metod ej att föredra. NDT är självklart möjligt att använda på allsköns betongkonstruktioner då det ger både konstruktionsmässiga och estetiska fördelar. NDT metoden som rör denna studie kallas impact echo och går ut på att man med en hammare slår till en punkt på väggen och mäter responsen en bit därifrån. Lasten ger upphov till vågor i form av deformation som propagerar i väggen och dessa ger i sin tur upphov till Lamb moder. Lamb moderna är strukturella oscillationer av väggen och genom att studera dess frekvenser kan väggens tjocklek bestämmas. Elastiska egenskaper i väggen erhålls utifrån de olika vågornas propageringshastigheter. Impact echo metoden kan även användas för att finna strukturella oegentligheter inuti väggen så som sprickor och delaminering. För att utföra numeriska simuleringar av dynamiska system med NDT-metoder är finita elementmetoden (FEM) användbar. Syftet med denna studie är att bedöma vilka möjligheter som finns för att implementera absorberande ränder med ökande dämpning (ALID) i datamodeller för att minska beräkningstiden av FEM-analyser. ALID används vid kanterna för att simulera ett oändligt system, dess uppgift är att dämpa bort inkommande vågor så att dessa ej reflekteras tillbaka och stör mätningarna. Samtliga modeller i denna studie är två-dimensionella med antagen oändligt liten spänning i normalriktningen. Vinsten i beräkningstid av att använda ALID är stor och ökar ytterligare om modellen utökas till tre dimensioner. Ett ALID definieras genom dess längd och maximala massproportionerlig Rayleigh-dämpning (CMmax). I denna rapport har längderna 0.5, 1.5 and 4.5 m använts med CMmax i intervallet från 103 till 2*105 Ns/m. Dämpningen ökar med ökat avstånd in i ALID med det specificerade maxvärdet vid den bakre kanten. Det bör noteras att skillnad i dämpning mellan element leder till skillnad i impedans; reflektioner av vågorna uppstår vid övergång från ett element med lägre impedans till ett med högre impedans. Ett ALID måste således vara definierat så att det dämpar bort tillräckligt av de inkommande vågorna utan att oönskade reflektioner i ALID uppstår. Studien pekar på att ett 0.5 m långt ALID inte åstadkommer önskvärda resultat för något av valen för CMmax som använts i denna rapport. Både det 1.5 och 4.5 m långa ALID har däremot get bra resultat; ett 1.5 m långt ALID bör ha 2*104 &lt; CMmax &lt;5*104 Ns/m och ett 4.5 m långt ALID 5*103 &lt; CMmax &lt; 104 Ns/m. Förhoppningen med studien är att resultaten skall underlätta utvecklingen av NDT-metoder som kan användas vid konstruktion och underhåll av reaktoromslutningar och andra tjocka betongkonstruktioner.

Milling is a common unit operation in industry for the purpose of intentional size reduction. Considerable amount of energy is consumed during a grinding process and much of the energy is dissipated as heat and sound, which often makes grinding into an energy-intensive and highly inefficient operation. Despite many attempts to interpret particle breakage during a milling process, the grindability of a material in a milling operation remains aloof and the mechanisms of particle breakage are still poorly understood. Hence the optimisation and refinement in the design and operation of milling are in great need of an improved scientific understanding of the complex failure mechanisms. This thesis aims to provide an in-depth understanding of particle breakage associated with stressing events that occur during milling. A hybrid of experimental, theoretical and numerical methods has been adopted to elucidate the particle breakage mechanics. This study covers from single particle damage at micro-scale to bulk comminution during the whole milling process. The mechanical properties of two selected materials, i.e. alumina and zeolite were measured by indentation techniques. The breakage test of zeolite granules subjected to impact loading was carried out and it was found that tangential component velocity plays an increasingly important role in particle breakage with increasing impact velocity. Besides, single particle breakage via in-situ loading was conducted under X-ray microcomputed tomography (μCT) to study the microstructure of selected particles, visualize the progressive failure process and evaluate the progressive failure using the technique of digital image correlation (DIC). A new particle breakage model was proposed deploying a mechanical approach assuming that the subsurface lateral crack accounts for chipping mechanism. Considering the limitation of existing models in predicting breakage under oblique impact and the significance of tangential component velocity identified from experiment, the effect of impact angle is considered in the developed breakage model, which enables the contribution of the normal and tangential velocity component to be rationalized. The assessment of breakage models including chipping and fragmentation under oblique impact suggests that the equivalent normal velocity proposed in the new model is able to give close prediction with experimental results sourced from the public literature. Milling experiments were performed using the UPZ100 impact pin mill (courtesy by Hosokawa Micron Ltd. UK) to measure the comminution characteristics of the test solids. Several parameters were used to evaluate the milling performance including product size distribution, relative size span, grinding energy and size reduction ratio etc. The collective data from impact pin mill provides the basis for the validation of numerical simulation results. The Discrete Element Method (DEM) is first used to model single particle breakage subject to normal impact loading using a bonded contact model. A validation of the bonded contact model was conducted where the disparity with the experimental results is discussed. A parametric study of the most significant parameters e.g. bond Young’s modulus, the mean tensile bond strength, the coefficient of variation of the strength and particle & particle restitution coefficient in the DEM contact model was carried out to gain a further understanding of the effect of input parameters on the single particle breakage behavior. The upscaling from laboratory scale (single particle impact test) to industrial process scale (impact pin mill) is achieved using Population Balance Modelling (PBM). Two important functions in PBM, the selection function and breakage function are discussed based on the single particle impact from both experimental and numerical methods. An example of predicting product size reduction via PBM was given and compared to the milling results from impact pin mill. Finally, the DEM simulation of particle dynamics with emphasis on the impact energy distribution was presented and discussed, which sheds further insights into the coupling of PBM and DEM.