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<p><b>En metod för dispersiv analys av försök med delad hopkinsonstång tillämpad på provning av granved vid hög töjningshastighet</b></p><p>Syftet var att etablera en metod för att studera sambandet mellan spänning och töjning för granved vid hög töjningshastighet. Detta åstadkoms genom att anpassa och något vidareutveckla tekniken med delad hopkinsonstång ("Split Hopkinson Pressure Bar", SHPB).</p><p>Vanligtvis har hopkinsonstavar cirkulärt tvärsnitt och en diameter som är mycket mindre än de verksamma våglängderna. Under sådana förhållanden är vågutbredningen i stängerna approximativt ickedispersiv, och en endimensionell (1D) vågutbredningsmodell kan användas. När det, som är fallet i denna studie, däremot inte kan säkerställas att stängernas tvärdimensioner är små i förhållande till våglängderna, är en helt igenom 1D vågutbredningsmodell otillräcklig, och tvärsnittets geometri, vilken var kvadratisk i denna studie, måste beaktas. Därför utvecklades med hjälp av Hamiltons princip en approximativ 3D vågutbredningsmodell för stänger med godtyckligt tvärsnitt. Modellen ger ett dispersionssamband (vågtal som funktion av vinkelfrekvens) samt medelvärden för förskjutningar och spänningar över gränsytorna mellan stänger och provstav. En kalibreringsprocedur utvecklades också.</p><p>Provning av granved genomfördes vid hög töjningshastighet (omkring 103 s-1) med den anpassade SHPB-tekniken, samt för jämförelse vid låg (8×10-3 s-1) och måttlig (17 s-1) töjningshastighet med en servohydraulisk provningsmaskin. Fukthalterna i veden motsvarade ugnstorr, fibermättnad och fullständig mättnad, och proven utfördes i radiell, tangentiell och axiell riktning i förhållande till trädets stam. För vart fall utfördes fem försök vid rumstemperatur. Resultaten visar töjningshastighetsberoendet för sambandet mellan spänning och töjning för granved under alla studerade förhållanden.</p> / <p>The aim was to establish a method for studying the relation between stress and strain in spruce wood at high strain rate. This was achieved by adapting and somewhat further developing the split Hopkinson pressure bar (SHPB) technique.</p><p>Hopkinson bars usually have a circular cross-section and a diameter much smaller than the operative wavelengths. The wave propagation in the bar is then approximately non-dispersive and a one-dimensional (1D) wave propagation model can be used. When, as in this study, it is not certain that the transverse dimensions of the bars are small in relation to the wavelengths, a solely 1D wave propagation model is insufficient and the geometry of the cross-section, which was square in this study, must be taken into account. Therefore, an approximate 3D wave propagation model for bars with arbitrary cross-section was developed using Hamilton's principle. The model provides a dispersion relation (wavenumber vs. angular frequency) and average values for displacements and stresses over the bar/specimen interfaces. A calibration procedure was also developed.</p><p>Tests on spruce wood specimens were carried out at a high strain rate (about 10³ s^-1) using the adapted SHPB technique, and for comparison at low (8×10^-3 s^-1) and medium (17 s^-1) strain rates using a servohydraulic testing machine. The moisture contents of the wood specimens corresponded to oven dry, fibre saturated and fully saturated, and the testing was performed in the radial, tangential and axial directions relative to the stem of the tree. In each case, five tests were run at room temperature. The results show the strain rate dependence of the relation between stress and strain for spruce wood under all conditions studied.</p>

<b>En metod för dispersiv analys av försök med delad hopkinsonstång tillämpad på provning av granved vid hög töjningshastighet</b> Syftet var att etablera en metod för att studera sambandet mellan spänning och töjning för granved vid hög töjningshastighet. Detta åstadkoms genom att anpassa och något vidareutveckla tekniken med delad hopkinsonstång ("Split Hopkinson Pressure Bar", SHPB). Vanligtvis har hopkinsonstavar cirkulärt tvärsnitt och en diameter som är mycket mindre än de verksamma våglängderna. Under sådana förhållanden är vågutbredningen i stängerna approximativt ickedispersiv, och en endimensionell (1D) vågutbredningsmodell kan användas. När det, som är fallet i denna studie, däremot inte kan säkerställas att stängernas tvärdimensioner är små i förhållande till våglängderna, är en helt igenom 1D vågutbredningsmodell otillräcklig, och tvärsnittets geometri, vilken var kvadratisk i denna studie, måste beaktas. Därför utvecklades med hjälp av Hamiltons princip en approximativ 3D vågutbredningsmodell för stänger med godtyckligt tvärsnitt. Modellen ger ett dispersionssamband (vågtal som funktion av vinkelfrekvens) samt medelvärden för förskjutningar och spänningar över gränsytorna mellan stänger och provstav. En kalibreringsprocedur utvecklades också. Provning av granved genomfördes vid hög töjningshastighet (omkring 103 s-1) med den anpassade SHPB-tekniken, samt för jämförelse vid låg (8×10-3 s-1) och måttlig (17 s-1) töjningshastighet med en servohydraulisk provningsmaskin. Fukthalterna i veden motsvarade ugnstorr, fibermättnad och fullständig mättnad, och proven utfördes i radiell, tangentiell och axiell riktning i förhållande till trädets stam. För vart fall utfördes fem försök vid rumstemperatur. Resultaten visar töjningshastighetsberoendet för sambandet mellan spänning och töjning för granved under alla studerade förhållanden. / The aim was to establish a method for studying the relation between stress and strain in spruce wood at high strain rate. This was achieved by adapting and somewhat further developing the split Hopkinson pressure bar (SHPB) technique. Hopkinson bars usually have a circular cross-section and a diameter much smaller than the operative wavelengths. The wave propagation in the bar is then approximately non-dispersive and a one-dimensional (1D) wave propagation model can be used. When, as in this study, it is not certain that the transverse dimensions of the bars are small in relation to the wavelengths, a solely 1D wave propagation model is insufficient and the geometry of the cross-section, which was square in this study, must be taken into account. Therefore, an approximate 3D wave propagation model for bars with arbitrary cross-section was developed using Hamilton's principle. The model provides a dispersion relation (wavenumber vs. angular frequency) and average values for displacements and stresses over the bar/specimen interfaces. A calibration procedure was also developed. Tests on spruce wood specimens were carried out at a high strain rate (about 103 s-1) using the adapted SHPB technique, and for comparison at low (8×10-3 s-1) and medium (17 s-1) strain rates using a servohydraulic testing machine. The moisture contents of the wood specimens corresponded to oven dry, fibre saturated and fully saturated, and the testing was performed in the radial, tangential and axial directions relative to the stem of the tree. In each case, five tests were run at room temperature. The results show the strain rate dependence of the relation between stress and strain for spruce wood under all conditions studied.

The aim of this thesis is to provide microstructural and mechanical characterisation of α-β titanium alloys exposed to a range of thermo-mechanical conditions, in particular under-going high rate deformation at elevated temperatures, representative of the Linear Friction Welding (LFW) manufacturing process. Three α-β titanium alloys provided by Rolls-Royce are studied: Ti-64 blade, disc and Ti-6246 disc. Ti-64 and Ti-6246 show complex deformation behaviour with strain, strain rate and temperature, especially near the transus temperature, where the low temperature α phase is transformed into the high temperature β phase. The microstructure and mechanical properties evolve in an interconnected fashion, and understanding this mutual influence is necessary to better predict the behaviour of these alloys. Characterisation of the mechanical properties was performed through uniaxial compression tests at strain rates from 0.001 to 3000 s^-1, using an Instron screw-driven machine at quasi-static rates, a servo-hydraulic machine at medium rates and a Split-Hopkinson Pressure Bar and a drop-weight tower at high strain rates. The tests were performed over a range of temperatures from room temperature to 1300 °C. The main focus was on high strain rate and high temperature tests, with the development of a gravity driven direct impact Hopkinson bar, referred as a drop-weight system, which is intended to evaluate the mechanical response of metals to high strain rate loading at temperatures up to c. 1300 °C. The design and principles of operation of the system are presented, along with calibration and validation data. Preliminary tests were performed on stock Ti-64, heated at two rates: 1 and 20 °C s^-1. The evolution of the mechanical properties was analysed, focussing on the strain rate, temperature and phases dependencies. Characterisation of the microstructure was realised by performing interrupted compression tests, first at room temperature, three plastic strains, 4%, 10% and 20%, and two different strain rates, 0.001 and 2000 s^-1; then at 4% plastic strain, a strain rate of 2000 s^-1 and three elevated temperatures, 700, 900 and 1100 °C. A better understanding of the microstructure evolution with strain, strain rates and temperature, including the macrotexture and microtexture of the specimens, was obtained using Electron Backscatter Diffraction (EBSD) to characterise the texture of the undeformed and deformed materials. The better understanding of the flow stress and microstructural evolution of both Ti-64 and its individual α and β phases with various strain rates and temperatures is intended to be used in the development of more accurate models representing the behaviour of these alloys. Predicting the microstructure evolution and then the mechanical properties of a material is essential to optimise the final mechanical properties of the alloys when welded by manufacturing processes such as the LFW process.

This master’s thesis deals with the problem of measurement for thermomechanical parameters during metal forming under higher deformation rate. The first part works up general literary studies, comprising a summary of measurement methods for required parameters. There is described a principle of their function and usage. Further assessed the current situation and recommendation of appropriate methods for the dynamic processes of forming, especially their testing. The second part is devoted to the measurement for dynamic features of the material. This is a problem specified by Split Hopkinson preassure bar test. The test is described, including the mathematical evaluation process, in the theoretical part. In the practical part, there is a detailed description of the process and evaluation of the real test with aluminum alloy AlMg4, 5Mn ,07-EN AW 5083 performed within the framework of the junior project.

Blades used on brushcutters and lawn mowers are subjected to a wide variety of working conditions. Besides continuous loads from cutting grass, the blades are also subjected to accidental impacts of branches, stones and structures. Due to exceptionally high rotational velocities, these types of impacts involve blade deformation at high strain rates. This master’s thesis aims to improve understanding and predictability of blade properties for design of future blades. The project is aimed at characterization of the mechanical response of steel used for brushcutter blades and developing a simulation model of a blade impact load case. Thus, the problem was divided into two main parts: firstly, material characterization, and secondly, numerical modeling. The objective of the material characterization part was to determine the rate dependence of the flow stress for two hardened steels. Experimental compression tests were performed at quasi-static strain rates (10-4 - 10-2 s-1) and at high strain rates (102 - 104 s-1) in order to characterize the rate dependence of each material. The objective of the numerical modeling part was to develop simulation models of an impact load case for the purpose of recreating tests performed with an experimental test setup. The simulation models were aimed to include material models for the blade based on the experimental tests performed for the two hardened steels. In preparation for the compression tests, cylindrical specimens were acquired through electrical discharge machining involving material removal from blades intended for brushcutters. Compression tests at high strain rates were performed utilizing a split-Hopkinson pressure bar apparatus which resulted in strain rates in the order of 1000 s-1 and 3000 s-1. Compression tests at quasi-static strain rates were performed with an electro-mechanical loading machine and implementation of two-dimensional digital image correlation for strain measurements. With this method, strain rates in the order of 5 · 10-2 s-1 and 5 · 10-4 s-1 were achieved. The acquired results from the experimental tests included the response of the two materials at four different strain rates in the form of true stress-true strain curves. The results were indicative of small strain rate dependency for each of the two hardened steels with a slight increase in yield stress for increasing strain rates. Both materials exhibited closely similar characteristics. At quasi-static rates, the response of both materials exhibited work-hardening of closely similar characteristics. At high strain rates, the response of both materials exhibited a close to identical decrease in stress for values of strain exceeding 10 %. This behavior was suggested to be a consequence of adiabatic heating. At all four achieved strain rates, the results were indicative of a higher yield stress with higher subsequent stresses for one of the hardened steels in comparison to the other. The impact load case aimed to be simulated involved one swing of a brushcutter against a 25 mm diameter steel rod according to standard SS-EN ISO 11806-1:2011. The steel rod was specified to be impacted horizontally by the blade at an approaching translational velocity of 1 m/s and a blade rotational velocity of 8500 rpm. The multi-physics simulation software LS-DYNA was used to develop simulation models which consisted of two main parts, the blade and the rod and included two different blade geometries. As a result of a study regarding the suitability of different discretization techniques, the decision was made to implement the mesh-free particle method Smoothed Particle Galerkin (SPG) and to perform coupling with the finite element method (FEM). Two material models were developed based on the measured stress-strain response obtained through high strain rate compression testing. Several numerical models of the impact load case were produced, all of which entailed different sets of parameters. These included selection of blade material, failure strain, rod length and blade angle relative to the horizontal plane. Finally, two models were developed which were opposite in terms of assigned element formulation for the blade tip and the rod and otherwise identical. The results of the different models were then compared, namely in terms of resulting material failure of the blade after impact. It was concluded that SPG was the most suitable method of choice for the impact load case aimed to be simulated due to its ability to handle large deformation and the inclusion of the a bond-based failure mechanism. Furthermore, implementation of the SPG method resulted in deformation and failure considered to be of greater agreement to experimental test results compared to FEM.

Dynamic tensile characterization of geo-materials is critical to the modeling and design of protective structures that are often made of concrete. One of the most commonly used techniques currently associated with this type of testing is performed with a Kolsky bar and is known as the spall technique. The validity of the data from the spall technique is highly debated because the necessary boundary conditions for the experiment are not satisfied. By using a technique called pulse shaping, a new “controlled” spall technique was developed to satisfy all boundary conditions so that the analyzed data may be useful in modeling and design. The results from this project were promising and show the potential to revolutionize the way Kolsky bar testing is performed.

The brain is a complex organ and its response to the mechanical loads at all strain rates has been nonlinear and inelastic in nature. Split-Hopkinson Pressure Bar (SHPB) high strain rate compressive tests conducted on porcine brain samples showed a strain rate dependent inelastic mechanical behavior. Finite Element (FE) modeling of the SHPB setup in ABAQUS/Explicit, using a specific constitutive model (MSU TP Ver. 1.1) for the brain, showed non-uniform stress state during tissue deformation. Song et al.’s assertion of using annular samples for negating inertial effects was also tested. FE simulation results showed that the use of cylindrical or annular did not mitigate the initial hardening. Further uniaxial stress state was not maintained is either case. Experimental studies on hydration effects of the porcine brain on its mechanical response revealed two different phenomenological trends. The wet brain (~80% water wt. /wt.) showed strain rate dependency along with two unique mechanical behavior patterns at quasi-static and high strain rates. The dry brain’s (~0% water wt. /wt.) response was akin to the response of metals. The dry brain’s response also observed to be strain rate insensitivity in its elastic modulus and yield stress variations. Uncertainty analysis of the wet brain high strain rate data revealed large uncertainty bands for the sample-to-sample random variations. This large uncertainty in the brain material should be taken into in the FE modeling and design stages. FE simulations of blast loads to the human head showed that Pressure played a dominant role in causing blast-related Traumatic Brain Injury (bTBI). Further, the analysis of shock waves exposed the deleterious effect of the 3-Dimensional geometry of the skull in pinning the location of bTBI. The effects of peak negative Pressure at injury sites have been attributed to bTBI pathologies such as Diffuse Axonal Injury (DAI), subdural hemorrhage and cerebral contusion.

A hydrocode and an explicit finite element code were used to evaluate functionally graded material impacts, meteor impacts, and split Hopkinson pressure bar specimens. Modeling impacts of functionally graded projectiles revealed that density was the primary material characteristic controlling the shock wave profile. A parametric study of material order for functionally graded armor showed that arranging the weaker material in front created the greater stopping power. By modeling an array of meteor impact scenarios, deformation and stress were shown to occur at great depths and possibly cause tectonic movement, like subduction. Three proposed Hopkinson specimens, which were designed to produce either shear or tensile reactions under compressive loading, were evaluated. For two of these specimens, improved stress and strain equations were presented.