Poly(methyl methacrylate) (PMMA) and polystyrene (PS), which are fully amorphous polymers, have been extensively studied for over a decade to discover how their mechanical behaviours vary with temperatures and strain rates. In this study, Mechanical tests were carried out at a range of strain rates and temperatures using a Hounsfield H50KM Test Machine wluch provides quasi- static rates (10-4 - 10-3 S-l) and low strain rates (10-2 - 10-1 S-l), and an in-house built Dropweight Machine which provides high strain rates (102 - 103 S-l) Mechanical tests were also performed in a high-speed photographic system, which provides high strain rates (103 S-l), to visualise the deformation of the polymers at a range of temperatures. An aluminium-heating block was built to heat up the samples to the required temperature. Strain limited tests were carried out at a range of strain rates and temperatures. Differential Scanning Calorimetry (DSC) was employed to study the glass transition temperatures and the specific heats of the samples. Dynamic Mechanical Thermal Analysis (DMTA) was adopted to study the transitions in the samples and the change of moduli with temperature densities of samples before and after high strain rate compression at certain strain were measured using a Six Column Density Apparatus The polarising microscope was used to study the orientation of the polymer chains at a range of temperatures, strains and strain rates. Eyring's theory of viscous flow was applied on yield point, 20% and 30% strain to relate the activation energy and volume with strain rate and temperature from the thermodynamic perspective. Temperature rise was calculated for high strain rate data to fit into the isothermal curve for the application of Eyring's theory and to obtain the actual smnple temperature at which the deformation took place. PMMA and PS showed ductile behaviour when tested at quasi-static and low strain rates at temperatures below their ductile-brittle transition temperatures. The densities of samples were not found to increase at different strains. The orientations of polymer chains did not influence the increase at Yield stress at high strain rates. The interpretation of activation energy and volume provided information of how the flows of chains took place at different temperatures and strain rates.

Failure of metals under impact loading is known to occur through the formation of adiabatic shear bands (ASBs). ASBs appear in materials as evidence of damage, and are known to be sites for material failure. General purpose plasticity models fail to predict the phenomenon of ASB formation. The present research validates and extends a model developed at the University of Manitoba by Feng and Bassim to predict damage due to ASBs. Parameters for the Feng and Bassim model are determined experimentally using a direct impact pressure bar to impact specimens at temperatures of 20-500oC and strain rates of 500-3000/s. A direct impact experiment is simulated in ANSYS using the model and fitted parameters. The results of the simulation show localized temperature rise and predict failure at the same locations as those observed experimentally. Nominal strain to failure is approximately 40-50% for a specimen impacted at 38 kg-m/s.

Failure of metals under impact loading is known to occur through the formation of adiabatic shear bands (ASBs). ASBs appear in materials as evidence of damage, and are known to be sites for material failure. General purpose plasticity models fail to predict the phenomenon of ASB formation. The present research validates and extends a model developed at the University of Manitoba by Feng and Bassim to predict damage due to ASBs. Parameters for the Feng and Bassim model are determined experimentally using a direct impact pressure bar to impact specimens at temperatures of 20-500oC and strain rates of 500-3000/s. A direct impact experiment is simulated in ANSYS using the model and fitted parameters. The results of the simulation show localized temperature rise and predict failure at the same locations as those observed experimentally. Nominal strain to failure is approximately 40-50% for a specimen impacted at 38 kg-m/s.

Within the aerospace industry, the reduction of costs associated with operation, manufacture and development of gas turbine engines is a primary objective. Component and assembly design optimisations can satisfy weight reductions which correspond to operational and manufacturing cost reductions. Development cost can be reduced by implementing additional numerical validation stages as an alternative to experimental validation alone. Therefore, the overarching purpose of this research is the development of a computationally efficient constitutive modelling tool, which predicts the macroscopic deformation and failure of fan system components and assemblies during dynamic and highly non-linear thermo-mechanical loading. At the macroscopic scale a series of physical deformation and failure phenomena have been identified from the literature which are necessary for accurate representation of the dynamic behaviour of Ti-6Al-4V. Across the surveyed literature these capabilities have not been implemented together within a single constitutive framework prior to the commencement of this research. Experimental support provides validation data for the subsequent constitutive modelling activities, whilst also demonstrating the importance of strain-rate sensitivity, tension-compression asymmetry and anisotropic behaviour associated with texture orientation in Ti-6Al-4V. Numerical studies were also conducted to develop a robust procedure for rapid assimilation of uni-axial experimental data within constitutive benchmarking models, for development purposes. Further parametric studies of sub-component plate impact benchmarks revealed several limitations within the commercially available solutions. These limitations are related to mesh sensitivity and damage evolution. A technique has been proposed which couples damage evolution and imposes a directional length-scale. This provides enhanced mesh insensitivity and damage evolution rate control. However, a single damage evolution mechanism was demonstrated to be insufficient when representing shear damage mechanisms in uni-axial and multi-axial loading regimes. Therefore, an additional damage mechanism has been developed and coupled with the mesh sensitivity and localisation technique. The resulting cumulative and competitive damage evolution and localisation capabilities reflect the localisation characteristics observed in the literature. The variability of alloy manufacture and the subsequent macroscopically observed behaviour remain a limitation within an isotropic framework. This has motivated the development of both asymmetric and anisotropic formulations, integrated within the newly proposed multi-mode damage localisation framework. The ability of the newly implemented non-isotropic framework successfully provides both asymmetric yielding and hardening capabilities and anisotropic evolution. These developments have been demonstrated against experimentally obtained results for validation and calibration purposes. Together these capabilities allow for accurate representation of a wide range of macroscopically observable phenomena based upon micro mechanical mechanisms.

In an effort to improve the fuel efficiency of automobiles, car designers are investigating new materials to reduce the overall vehicle weight. Magnesium alloys are good candidates to achieve that weight reduction due in part to their low density and high specific strength. To support their introduction into vehicle body structures, the dynamic behavior of magnesium alloys must be determined to assess their performance during a crash event. In this work, the tensile high strain rate behavior of AZ31B magnesium alloy sheets was characterized. Two different temper conditions were considered: AZ31B-O (fully annealed) and AZ31B-H24 (partially hardened). Three different sheet thicknesses were considered for the O temper condition, 1.0, 1.6 and 2.5 mm, while the H24 temper was 1.6 mm in thickness. The sheet condition of the magnesium alloys implies an in-plane anisotropy induced by the rolling process. Therefore, both the rolling and transverse directions were investigated in the current research. In order to characterize the constitutive behaviour of AZ31B-O and AZ31B-H24 magnesium alloy sheets, tensile tests were performed over a large range of strain rates. Quasi-static experiments were performed at nominal strain rates of 0.003s-1, 0.1s-1 and 1s-1 using a servohydraulic tensile machine. Intermediate strain rate experiments were performed at 30s-1 and 100s-1 using an instrumented falling weight impact (IFWI) apparatus, and high strain rate experimental data at 500s-1, 1000s-1 and 1500s-1 was collected using a tensile split Hopkinson bar (TSHB) apparatus. Elevated temperature experiments (up to 300°C) were also performed at high strain rates using a radiative furnace mounted on the TSHB apparatus. The tensile experiments show a significant strain rate sensitivity of the constitutive behavior of both the O and H24 temper conditions. The two tempers exhibit an average increase of stress level of 60-65 MPa over the range of strain rates considered. As the strain rate increases, the strain rate sensitivity of both tempers also increases. The strain rate has a different effect on the ductility of the two material conditions. The ductility of AZ31B-O is significantly improved under high strain rate deformations, whereas the AZ31B-H24 exhibits similar ductility at low and high strain rates. Both material conditions presented a strong in-plane anisotropy, with an average stress level in the transverse direction higher than in the rolling direction by 15 MPa and 35 MPa for the O and H24 tempers, respectively. The thermal sensitivity for both tempers at high strain rates was obtained. The two material conditions exhibit a clear thermal softening. From room temperature to 250°C, the loss in strength at 5% plastic strain was found to be 55 MPa and 125 MPa for the AZ31B-O and AZ31B-H24 materials, respectively. The thickness of the AZ31B-O sheets has a mild effect on the measured constitutive behavior. The flow stress increases with increasing thickness. An average difference of 10-15 MPa was seen between the flow stress of the 1.0mm and 2.5mm sheets. However, similar strain rate sensitivity was seen for the three thicknesses. The experimental data was fit to three constitutive models: the Johnson-Cook model, its modified version with a Cowper-Symonds strain rate sensitivity formulation, and the Zerilli-Armstrong model. The three models were evaluated by numerical simulation of the TSHB experiment under various testing conditions. It was found that the Zerilli-Armstrong model was the most accurate in predicting the flow stress of the different material conditions. However, finite element models incorporating the three constitutive fits failed to predict necking in the specimen.

In an effort to improve the fuel efficiency of automobiles, car designers are investigating new materials to reduce the overall vehicle weight. Magnesium alloys are good candidates to achieve that weight reduction due in part to their low density and high specific strength. To support their introduction into vehicle body structures, the dynamic behavior of magnesium alloys must be determined to assess their performance during a crash event. In this work, the tensile high strain rate behavior of AZ31B magnesium alloy sheets was characterized. Two different temper conditions were considered: AZ31B-O (fully annealed) and AZ31B-H24 (partially hardened). Three different sheet thicknesses were considered for the O temper condition, 1.0, 1.6 and 2.5 mm, while the H24 temper was 1.6 mm in thickness. The sheet condition of the magnesium alloys implies an in-plane anisotropy induced by the rolling process. Therefore, both the rolling and transverse directions were investigated in the current research. In order to characterize the constitutive behaviour of AZ31B-O and AZ31B-H24 magnesium alloy sheets, tensile tests were performed over a large range of strain rates. Quasi-static experiments were performed at nominal strain rates of 0.003s-1, 0.1s-1 and 1s-1 using a servohydraulic tensile machine. Intermediate strain rate experiments were performed at 30s-1 and 100s-1 using an instrumented falling weight impact (IFWI) apparatus, and high strain rate experimental data at 500s-1, 1000s-1 and 1500s-1 was collected using a tensile split Hopkinson bar (TSHB) apparatus. Elevated temperature experiments (up to 300°C) were also performed at high strain rates using a radiative furnace mounted on the TSHB apparatus. The tensile experiments show a significant strain rate sensitivity of the constitutive behavior of both the O and H24 temper conditions. The two tempers exhibit an average increase of stress level of 60-65 MPa over the range of strain rates considered. As the strain rate increases, the strain rate sensitivity of both tempers also increases. The strain rate has a different effect on the ductility of the two material conditions. The ductility of AZ31B-O is significantly improved under high strain rate deformations, whereas the AZ31B-H24 exhibits similar ductility at low and high strain rates. Both material conditions presented a strong in-plane anisotropy, with an average stress level in the transverse direction higher than in the rolling direction by 15 MPa and 35 MPa for the O and H24 tempers, respectively. The thermal sensitivity for both tempers at high strain rates was obtained. The two material conditions exhibit a clear thermal softening. From room temperature to 250°C, the loss in strength at 5% plastic strain was found to be 55 MPa and 125 MPa for the AZ31B-O and AZ31B-H24 materials, respectively. The thickness of the AZ31B-O sheets has a mild effect on the measured constitutive behavior. The flow stress increases with increasing thickness. An average difference of 10-15 MPa was seen between the flow stress of the 1.0mm and 2.5mm sheets. However, similar strain rate sensitivity was seen for the three thicknesses. The experimental data was fit to three constitutive models: the Johnson-Cook model, its modified version with a Cowper-Symonds strain rate sensitivity formulation, and the Zerilli-Armstrong model. The three models were evaluated by numerical simulation of the TSHB experiment under various testing conditions. It was found that the Zerilli-Armstrong model was the most accurate in predicting the flow stress of the different material conditions. However, finite element models incorporating the three constitutive fits failed to predict necking in the specimen.

Fibre reinforced polymers (FRP) are finding increasing use in structures subjected to high rate loading such as blast or impact. Proper design of such structures requires thorough characterisation of the material behaviour over a range of loading rates from quasi-static to impact. This thesis investigated the quasi-static and impact response of Glass Fibre Polypropylene (GFPP) in compression, bending and delamination. The bending and delamination response of Fibre Metal Laminates (FMLs) based on GFPP and aluminium was also investigated at quasi-static and impact rates. High strain rate (5x10^2 to 10^3 /s) compression tests were conducted on GFPP using a compressive Split Hopkinson Pressure Bar (SHPB) and a Direct Impact Hopkinson Pressure Bar (DIHPB), in the through-thickness and in-plane directions. In both loading directions, the peak stress of GFPP increased linearly with the logarithm of strain rate. For in-plane loading, the failure modes were dominated by localised fibre buckling and kink bands, leading to delamination. The through thickness loading produced macroscopic shear and spreading failure modes. However, both of these failure modes are linked to in-ply fibre failures, due to through thickness compression causing transverse tensile strain. Previous studies of similar materials have not explicitly stated the link between through thickness compression and fibre failure associated with transverse tensile strain. A novel test rig was developed for Three Point bend testing at impact rates. The specimen was supported at the outer points on a rigid impacter and accelerated towards a single output Hopkinson Pressure Bar (HPB), which impacted the specimen at its midspan. Previous impact bend test rigs based on HPBs were limited to testing specimens with deflections to failure up to approximately 1mm, whereas the rig implemented herein measured deflections up to approximately 10 mm. This configuration permits the output HPB to be chosen purely on the magnitude of the expected impact force, which resulted in superior force resolution to configurations used in other studies. The HPB Impact Bend rig was used to test GFPP and aluminium-GFPP FML specimens, at impact velocities ranging from 5 to 12 m/s. The flexural strength of GFPP increased with strain rate, while the flexural response of the FML specimens was relatively insensitive to strain rate. v Several candidate delamination test geometries were investigated at quasi-static displacement rates (1 mm/min), and the Single Leg Bend (SLB) test was identified as suitable for adaptation to higher rate testing. Single Leg Bend delamination tests of both GFPP and FML specimens were performed using the HPB Impact Bend rig, at impact velocities of 6 to 8 m=s. The shape of the force displacement response for the high rate testswas markedly different from the quasi-static tests, for both the GFPP and FML specimens. Finite element (FE) simulation of the quasi-static and impact rate SLB tests on GFPP indicated that the difference was probably due to the interaction of flexural vibrations and stress waves in the specimen and the impacter cross member. The experimental results and FE analysis suggest that the delamination fracture toughness of GFPP decreases slightly as strain rate increases. High rate delamination tests on FML specimens resulted in unstable crack growth.

This research focuses on the spall properties of aluminum-magnesium (Al-Mg)alloys.Aluminum alloy 5083 (Al 5083) was used as a model alloy for the work performed in this study. Al-Mg alloys represent a light-weight and corrosion resistant alloy system often used in armor plating. It is desirable to process armor plate material to yield a microstructure that provides maximum resistance to spall failure due to blast and projectile impacts. The blast and impact resistance has often been quantified based on the measurement of the spall strength and the Hugoniot elastic limit (HEL). The spall properties of Al-Mg alloys were measured for four different microstructural states resultant from varying processing conditions. The four microstructures include: (a) textured grain structure from a rolled Al 5083-H116 plate, (b) sub-micron grain structure produced using equi-channel angular pressing (ECAP),(c) equiaxed grain structure, and (d) precipitation hardened microstucture from an Al-9wt.% Mg alloy. The overall results show that grain size is not the most dominant microstructural feature affecting spall strength in aluminum alloys, when the impact conditions are the same. Texture, especially if brittle inclusions align along the grains, appears to have the most dominant effect resulting in decreased spall strength. Furthermore, one-dimensional modeling shows that the inclusion size and distribution is the controlling factor for void formation during spalling. Grain size does affect the decompression rate dependence of each microstructure, whereby smaller grain sizes result in a larger power law exponent for fits of spall strength versus decompression rate. Unlike the spall strength, the HEL shows an increasing trend with decreased grain size, as would be expected from a Hall-Petch type effect, indicating that a smaller grain size is best for penetration resistance. Samples processed using ECAP alone provide the best combination of spall strength and HEL and therefore the most promise for improved blast and penetration resistance of aluminum-magnesium alloy armor plates.

In this work, three aluminum sheet alloys, AA5754, AA5182 and AA6111, which are prime candidates for replacing mild steel in automobile structures, are tested in tension at quasi-static and high strain rates. <br /><br /> In order to characterize the constitutive response of AA5754, AA5182 and AA6111 at high strain rates, tensile experiments were carried out at strain rates between 600 s^-1 and 1500 s^-1, and at temperatures between ambient and 300??C, using a tensile split Hopkinson bar (TSHB) apparatus. As part of this research, the apparatus was modified in order to provide an improved means of gripping the sheet specimens. Quasi-static experiments also were conducted using an Instron machine. <br /><br /> The experimental data was fit to the Johnson-Cook and Zerilli-Armstrong constitutive models for all three alloys. The resulting fits were evaluated by numerically simulating the tensile experiments conducted using a finite element approach.

The main aim of this thesis is to generate a deeper understanding of the mechanical behaviour of cellular materials, specifically for their use in aerospace applications. A closed-cell polymer foam material (Rohacell) of various foam densities was chosen for this investigation, and a comprehensive experimental study was conducted which generated significant findings that hitherto have not been reported in the literature. The research presented in this study revealed the following: The quasistatic response of Rohacell foam displays a compression/tension asymmetry in moduli and strength. In-situ experiments revealed that different macroscopic collapse mechanisms at different foam densities drove this behaviour. Improved experimental methods were developed to characterise the material response at various loading rates. Under compressive loading, as the relative density and loading rate increased, a transition in material behaviour from a ductile to brittle response at very high rates (~5x10^3 s^-1) was found, and tests conducted at different temperatures were used to validate and provide a better understanding of the causes for the observed rate dependency. The compression and tension properties of pre-crushed Rohacell foam loaded in different directions were measured, and with the use of three-point-bend tests it was shown that when the foams’ tension/compression asymmetry, or the changes in stiffness and strength due to pre-crushing (i.e. strain-induced anisotropy), are neglected, this leads to incorrect predictions of the foams’ structural response. Finally, a review of some existing Finite Element foam material models was conducted, and their ability to predict the foam response under complex loading was identified. The new data and understanding generated from this thesis will allow engineers and researchers, who are developing constitutive models for predicting the response of foam materials, specifically in aerospace applications, to account for more aspects of the mechanical behaviours in their Finite Element models.