A STUDY OF THE HIGH STRAIN RATE BEHAVIOUR OF PARTICLE-REINFORCED METAL MATRIX COMPOSITES By Gilles Pageau B.Sc.A., Universiti Laval, 1981 A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF MASTER OF APPLIED SCIENCE in THE FACULTY OF GRADUATE STUDIES (Department of Metals and Materials Engineering) We accept this thesis as conforming to the required standard THE UNIVERSITY OF BRITISH COLUMBIA April 1991 © Gilles Pageau, 1991 In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives. It is understood that copying or publication of this thesis for financial gain shall not be allowed without my written permission. Department of M e t a l s and M a t e r i a l s E n g i n e e r i n g The University of British Columbia Vancouver, Canada Date A p r i l 1 1 , 1991 DE-6 (2/88) ABSTRACT This thesis presents the results of an experimental and analytical study of the high strain rate behaviour of ceramic particle-reinforced metal matrix composites (MMC). Two MMC systems, both based on the 6061-T6 aluminum matrix, were selected. The first is an alumina reinforced system, made by a liquid metallurgy (LM) route, with 10, 15 and 20% particle volume fractions. The second is a silicon carbide system, made by powder metallurgy (PM), with 0, 15 and 30% particle volume fractions. Unreinforced 6061-T6 and 7075-T6 were also included for comparison. Quasi-static tensile tests, Taylor impact tests, and high velocity penetration tests were conducted. The tension test results indicated that the reinforcement strongly affects the stiffness, strength and ductility. Some anisotropy was also observed. The Young's modulus values for both system are in good agreement with predictions from simple two-phase theoretical models. An experimental facility was constructed which is capable of accelerating small cylindrical impactors at velocities up to 1000 m/s and allow for accurate measurement of the impact velocity. The facility was designed so that both Taylor and dynamic penetration tests could be performed with only minor modifications. The Taylor test was used to characterize the strength of the MMC selected under conditions comparable to those existing in dynamic penetration. It consists of impacting short cylindrical specimens on a flat rigid anvil at velocities ranging from 150 to 300 m/s. The dynamic yield strength was deteirnined from measurements of the deformed shape of the specimen using one-dimensional analysis models. The results were shown to be quite dependent on the analysis model used for calculation. Results show that the dynamic strength is noticeably increased over the quasi-static values. The strain rate sensitivity of the MMC materials also appeared to be more pronounced. Measurements of the tested specimen profiles revealed some asymmetry ii which can be attributed to yield strength anisotropy. The MMC specimens also appeared to be more susceptible to radial cracking at the impact face. The effects of adiabatic heating and inertia within the specimen were also investigated. To assess the relative impact performance of the selected materials, dynamic penetration tests were conducted by firing small rigid tungsten rods with spherical noses on to MMC cylindrical targets with a diameter of 50 mm and a length of 150 mm. Tests were performed at three average impact velocities of 475, 750 and 920 m/s. The cavity profiles were determined from X-ray photographs. The dynamic penetration tests indicate that the PM-processed materials are more resistant to penetration than the LM-processed materials, with the difference being more significant at higher volume fractions. At low velocities (475 m/s) large scale radial cracking of the highly reinforced MMC was observed. The penetration depths were predicted using an approximate cavity expansion model developed for monolithic metals and which involves only a few measurable material properties. Sensitivity studies indicate that, for the intermediate velocity regime investigated in this study, the dynamic strength of the target material is the dominating parameter. Sliding friction at the impactor/target interface was also shown to influence the penetration behaviour to a lesser degree. Using the strength values obtained from the Taylor impact tests, the cavity expansion model predicted depths that were in reasonable agreement with the experimental results. iii TABLE OF CONTENTS Abstract ii List of Tables vi List of Figures vii List of Symbols x Acknowledgements xii Chapter 1- Introduction 1 1.1 Overview of Metal Matrix Composites 1 1.2 Importance of Material Behaviour at High Strain Rates 2 1.3 Purpose and Scope of the Present Study 4 Chapter 2 - Theoretical Basis 6 2.1 Taylor Cylinder Impact Test 6 2.1.1 Review of Different Approaches for Analyzing the Test 6 2.1.2 Selected Models 11 2.2 Dynamic Penetration Test 12 2.2.1 Review of Prediction Techniques 12 2.2.2 Selected Analysis 15 Chapter 3 - Experimental Methodology 16 3.1 Selection of Materials — 16 3.2 Quasi-Static Tensile Tests 17 3.3 Taylor Impact Tests 18 3.4 Dynamic Penetration Tests 27 iv Chapter 4 - Results and Discussions 30 4.1 Material Properties and Elastic Modulus Predictions 30 4.2 Taylor Impact Tests 33 4.3 Dynamic Penetration 41 Chapter 5 - Conclusions and Suggestions for Future Work 49 5.1 Conclusions 49 5.2 Suggestions for Future Work 51 References 52 Appendices 60 Appendix A - Analytical Models for Dynamic Strength 60 Appendix B- Equations of Cavity Expansion Model 63 Appendix C - Survey of MMC Material Suppliers 65 Appendix D - Tungsten Penetrator Material Properties 67 Appendix E - Radiographic Specifications 68 Appendix F - Chemical Compositions 69 Appendix G - Computer Program for Taylor Test Analysis 70 Appendix H- X-Ray Photographs 75 Appendix I - Computer Program for Penetration Depth Prediction 78 Tables 80 Figures 92 v LIST OF TABLES Table 1 - Typical Properties of Ceramic Particulate Reinforcements 80 Table 2 - High Strain Rate Measurement Techniques 81 Table 3 - Characteristics of Materials Used in This Work 82 Table 4 - Matrix of Tests Performed 83 Table 5 - Material Properties of Selected Particle-reinforced MMC 84 Table 6 - Taylor Impact Test Results 85 Table 7 - Shadowgraph Profile Data for Taylor Specimen 86 Table 8 - Average Dynamic Strength Values 87 Table 9 - Effect of Experimental Errors on Dynamic Strength Values 88 Table 10 - Summary of Experimental Results for Dynamic Penetration Tests 89 Table 11 - Variation of Strength with Strain Rate 91 vi LIST OF FIGURES Figure 1 - Experimental setup for quasi-static tension tests 92 Figure 2 - Geometry of the tension test specimen (dimensions in mm) 93 Figure 3 - Schematic representation of the high strain rate facility 94 Figure 4 - Overall view of the high strain rate facility 95 Figure 5 - Drawing of the 0.460 inch smooth bore launcher : 96 Figure 6 - Sub-caliber cartridge used for Taylor cylinder impact test 97 Figure 7 - Barrel extension used as blast deflector and specimen support (dimensions in mm) 98 Figure 8 - Side view of the target chamber 99 Figure 9 - Target alignment device 100 Figure 10 - Taylor test specimen design 101 Figure 11 - Measurement gauge for plastic zone determination 102 Figure 12 - Taylor test rigid target design 103 Figure 13 - Variation of impact velocity with powder mass (Hercules Bullseye) for subcaliber cartridge 104 Figure 14 - Dynamic penetration test methodology 105 Figure 15 - Geometry of tungsten impactor used in penetration tests (dimensions in mm) 106 Figure 16 - Plastic sabot design (dimensions in mm) 107 Figure 17 - Imprint on a 6061-T6 target by a plastic sabot 108 Figure 18 - Comparison of the tensile behaviour of DWA-30 MMC and unreinforced 6061-T6 Al 109 Figure 19 - Comparison of Young's modulus predictions with DURAL MMC data 110 Figure 20 - Comparison of Young's modulus predictions with DWA MMC data I l l Figure 21 - Side views (upper) and impact faces (lower) of Taylor cylinders: DWA-30, DURAL-15,7075-T6 Al, 6061-T6, undeformed 6061-T6 112 vii Figure 22 - Average deformation profile of L M 6061 Taylor specimen after impact 113 Figure 23 - Average deformation profile of DURAL-15 Taylor specimen after impact 114 Figure 24 - Average deformation profile of L M 7075 Taylor specimen after impact 115 Figure 25 - Average deformation profiles of DWA-30 axial and radial Taylor specimens after impact 116 Figure 26 - Comparison of the asymmetry of the plastic deformation profiles for axial and radial DWA-30 Taylor specimens after impact 117 Figure 27 - Comparison of Taylor test results obtained in this study and data from Wilkins and Gust for 6061-T6 Al 118 Figure 28 - Comparison of dynamic strength values from various analysis models for L M 6061, DURAL-15, DWA-30 and L M 7075 119 Figure 29 - Possible errors in dynamic strength calculations resulting from errors in final length measurements 120 Figure 30 - Cross section of crater resulting from impact of a tungsten penetrator in DWA-30 target at 850 m/s 121 Figure 31 - Radial cracks on the impact face of DWA-30 target impacted at 474 m/s 122 Figure 32 - Comparison between measured penetration depths for L M 6061, and DURALMMC 123 Figure 33 - Comparison between measured penetration depths for PM 6061, DWA-20, DWA-30, L M 7075 and L M 6061 124 Figure 34 - Variation of impact velocity as a function of propellant mass for dynamic penetration tests 125 Figure 35 - Comparison between static and dynamic friction coefficient for various materials 126 Figure 36 - Results of friction coefficient sensitivity study 127 Figure 37 - Results of Young's modulus sensitivity study 128 Figure 38 - Results of dynamic strength sensitivity study 129 Figure 39 - Measured and predicted penetration depths as a function of impact velocity for L M 6061 130 Figure 40 - Measured and predicted penetration depths as a function of impact velocity for DURAL-15 131 viii Figure 41 - Measured and predicted penetration depths as a function of impact velocity for DWA-30 132 Figure 42 - Measured and predicted penetration depths as a function of impact velocity for L M 7075 133 Figure 43 - Measured and predicted penetration depths as a function of impact velocity for L M 6061, DURAL-15, DWA-30, and LM 7075 134 Figure 44 - Variation of normalized penetration depth as a function of impact parameter 135 Figure 45 - Plastic work as a function of initial kinetic energy, (plastic zone diameter = penetrator diameter) 136 Figure 46 - Plastic work as a function of initial kinetic energy, (plastic zone diameter = 2 x penetrator diameter) 137 Figure 47 - Measured and predicted penetration depths as a function of impact velocity for DURAL-10 138 Figure 48 - Measured and predicted penetration depths as a function of impact velocity for DURAL-20 139 Figure 49 - Measured and predicted penetration depths as a function of impact velocity for DWA-20 140 Figure 50 -Measured and predicted penetration depths as a function of impact velocity for PM 6061 141 Figure 51 - Decrease in penetration depth as a function of reinforcement volume fraction for DURAL and DWA MMC for a velocity of 750 m/s 142 Figure 52 - Increase in static and dynamic strength as a function of reinforcement volume fraction for DURAL MMC 143 Figure 53 - Increase in static and dynamic strength as a function of reinforcement volume fraction for DWA MMC 144 Figure 54 - Increase in dynamic yield strength as a function of strain rate for both reinforced and unreinforced aluminum 145 Figure 55 - Geometry of Taylor cylinder specimen before and after impact showing the notation used in Appendix A 146 Figure 56 - Schematic illustration of penetrator with spherical nose showing the notation used in Appendix B 147 ix LIST OF SYMBOLS A list of important symbols is compiled here. All symbols are defined in the text when they first appear. A asymmetry (Equation 4.5) *0 specimen cross-sectional area a projectile radius aj, a2, as constants in Equation 2.1 C specific heat cltc2 constants in Equations B16 and B17 D damage parameter (Equation B14) d depth of deprression in target surface E Young's modulus e relative error in measurement of Lj (Equation 4.6) penetration resistance force h deformed length of Taylor specimen I inertia parameter (Equation 4.19) K specimen aspect ratio k ratio of Young's modulus of reinforcement and matrix initial length of Taylor specimen Le erroneous final length of Taylor specimen final length of Taylor specimen h effective projectile length P penetration depth (Equation Bll ) R maximum radius of Taylor specimen (Figure 26) r minimum radius of Taylor specimen Rm average radius X s parameter in Equation B5 room temperature Tm melting temperature ud volume of deformed material (Equation 4.13) V impact velocity vm,vr volume fraction of matrix and reinforcement w work dissipated per unit volume (Equation 4.14) w0 initial kinetic energy (Equation 4.12) X undeformed length of Taylor specimen after impact Y dynamic yield strength z normalized penetration depth (Equation B7) as, $s parameters in Equation B7 P normalized plastic wave speed (Equation A14) plastic strain (Equation A8) e m mean strain Gn normal stress on projectile nose P density of Taylor specimen or target material Pp projectile density friction coefficient V Poisson's ratio xi ACKNOWLEDGEMENTS I would like to express my sincere thanks to my advisor, Dr. A. Poursartip, for his continued encouragement and guidance during the course of this project I am also grateful to Dr. R. Vaziri for his constructive suggestions and comments. Thanks are also due to all members of the Composites Group for their patience and assistance as well as to my fellow graduate students and faculty members for their advice. I appreciate the technical assistance provided by Mr. R. McLeod (facility design and fabrication), Mr. N. Chinatambi (static testing), Ms. G. Riahi (physical properties), Mr. G. Wolf (facility drawings), and Mr. S. Milaire (electronics). Particularly, I would like to thank Mr. R. Bennett for his valued contributions throughout this work. The financial support provided by the Canadian Department of National Defence, through the Defence Research Establishment Valcartier (DREV) is gratefully acknowledged. Thanks are due to my employer, DREV, for granting me a leave of absence to work on this project. I also wish to express my gratitude to Mr. M. Clark, Mr. R. Larose and Mr. D. Leclerc of DREV for their support and encouragement. xii Cette these de maitrise est dediie d mon amie, Faye, et a mes parents pour leur support et comprehension. CHAPTER 1 INTRODUCTION 1.1 OVERVIEW OF METAL MATRIX COMPOSITES Conventional metallic materials have already been tailored to achieve close to optimum properties. However, new technological requirements ask for further improvements. Metal matrix composites (MMC), which consist of metal alloys reinforced with fibers, whiskers or particulates, have the potential of combining the high ductility and toughness of the metallic phase with the high strength and modulus of the reinforcing phase. Compared to the more developed polymer matrix composites, MMC materials offer higher service temperature capability, greater thermal and electrical conductivities, greater strength in shear and compression, and non-flammability. Currently, the interest in MMC has concentrated on the light alloys, such as aluminum, aluminum-lithium and magnesium, reinforced with particulates [Taya and Arsenault (1989)]. This interest is mainly due to the advent of new processing technologies, and the availability of ceramic particulates, such as silicon carbide and aluminum oxide, at relatively low costs. The properties of typical reinforcements are given in Table 1. The addition of ceramic particulates to a metallic matrix results in a material that is significantly stiffer and stronger than the unreinforced alloy, especially at high temperatures, and exhibits superior dimensional stability, wear and abrasion resistance. The physical and mechanical properties depend upon factors such as the constituent properties, reinforcement volume fraction and geometry (size, shape, and orientation) and interfacial bonding. Furthermore, the fact that the reinforcement is discontinuous allows the composite to be formed and machined using conventional metal working processes, and also allows the 1 selective placement of the reinforcement Because of these characteristics, particle-reinforced MMC are being considered for many weight-saving applications, including use in the aerospace, defence, automotive and recreational industries. However, as with any new material, their utilization depends on the availability of an adequate database for material properties. > 1.2 IMPORTANCE OF MATERIAL BEHAVIOUR AT HIGH STRAIN RATES In many applications, the deformation processes occur at strain rates that are well above those possible with conventional test machines. Examples include: metal forming, dynamic compaction of metal powders, explosive welding, solid particle erosion, vehicle crashworthiness, foreign object (debris or fragments) impact, satellite protection, blast loading, structure demolition, and ballistic penetration. In order to design more accurately structures that can withstand high intensity dynamic loads, it is necessary to determine the mechanical properties of the materials involved under conditions that closely match the expected deformation rates in service. Unfortunately, much of engineering design today is still based on quasi-static rather than dynamic material properties. It has long been recognized that the mechanical properties, such as strength and ductility, are influenced to some extent by strain rate. Hopkinson (1905) performed tensile-impact tests on steel and copper wires, and noted that the wires could withstand stresses above the static yield strength for a time of about 0.001 s without deforming plastically. Since that original study, the importance of such strain rate effects has been the subject of numerous studies. Strain rates experienced in engineering applications are usually classified in three categories or regimes: low strain rates (10~* s"l and below), medium strain rates (10"1 to 10^ s~l) and high strain rates (10^ s"l and above). Many materials exhibit only slight rate dependency at low and medium strain rates. However , under high strain rates conditions most structural materials show rate sensitivity, that is the dynamic flow stress is generally higher than the equivalent 2 static value. A greater dependence of the flow stress on strain rate has been observed for body centered cubic (BCC) metals, such as steel, as compared with face centered cubic (FCC) metals such as aluminum and copper [Kawata et al. (1977)]. Metals of the BCC family display high velocity brittleness with dynamic failure strains that are less than the static failure strain. Conversely, FCC metals exhibit high velocity ductility in that the dynamic failure strain is greater than the failure strain observed in the static case. For low and medium strain rates, there exist commercially available equipment, and essentially standard methods for the evaluation of the results can be used. In this range, the technique of sudden strain-rate changes can also be used to investigate rate effects. In the high strain rate regime, inertia and wave propagation effects become important, and have to be considered both in the measuring system and in the specimen. In addition, in this regime there is a change from essentially isothermal deformation to adiabatic conditions. The internal heat generated during plastic deformation does not have sufficient time to dissipate, and therefore the temperature of the specimen is increased. Since the flow stress of most materials is temperature sensitive, the adiabatic effect, especially at large strains, must also be considered in the analysis of the results [Lindholm(1971)]. The experimental work to determine the mechanical properties in the high strain rate range is difficult because the system used must be capable of producing the desired rate and of measuring the material response without affecting material behaviour. As shown in Table 2, investigations of dynamic material characteristics can be performed using a limited number of techniques such as: Split-Hopkinson pressure bar test [Kolsky (1949)], expanding ring test [Niordsen (1965)], Taylor cylinder impact test [Taylor (1946)], dynamic indentation or hardness test [Tirupataiah and Sundararajan (1991)], and plate impact test [Barker and Hollenbach (1964)]. Modes of deformation observed with these techniques can be classified into compression, tension and torsion/shear modes. Each technique has limitations that restrict the useful range of strain and strain rates attainable. Buchar et al. (1986), and Blazinski (1987) have reviewed the progress in the experimental and theoretical aspects of material behaviour at 3 high strain rates. The various experimental methods are described in detail in Volume 8 of the Ninth Edition of the Metals Handbook [Staker (1985)]. A comprehensive review of high strain rate techniques which have been applied to composite materials is presented by Sierakowski (1988). 1.3 PURPOSE AND SCOPE OF THE PRESENT STUDY With the increased use of particle-reinforced MMC as structural materials in advanced engineering applications, the need to study their behaviour under impact conditions has become more important. Although there is a large body of work concerning their quasi-static properties [see Girot et al. (1987) and Kjar et al. (1989) for reviews], there is very little available information on their behaviour at high strain rates [Ross et al. (1984), Dixon (1990)]. Earlier studies were focused on continuous fiber MMC. Schuster and Reed (1969) studied dynamic fracture under uniaxial strain impact or spall, and Awerbuch and Hahn (1976) investigated the high velocity impact damage of boron/aluminum plates. Whisker reinforced MMC have been relatively well characterized at high strain rates [Dandekar and Lopatin (1985), Harding et al. (1987), Marchand et al. (1988), and Pickard et al. (1988)]. Harding et al. (1987) found that the elastic modulus, yield strength and failure strain increase with strain rate above a certain strain rate threshold, typically 10 s"l. As far as is known, no work has yet been published in the open literature on the dynamic penetration resistance of particle-reinforced MMC. The objectives of this thesis are to: 1. Develop a facility and methodology to perform high strain rate tests. 2. Determine the strength characteristics of particle-reinforced.MMC at high strain rates and large strains using Taylor cylinder impact tests. 4 3. Investigate the ballistic performance of the selected MMC relative to that of the unreinforced matrix using dynamic penetration tests. The thesis is laid out as follows: in Chapter Two, a review of analysis methods for the Taylor test and target penetration is given. Chapter Three describes the development of the testing facility and the experimental part of this research. Results and discussions are presented in Chapter Four. Chapter Five contains the conclusions and recommendations for future work. 5 CHAPTER 2 THEORETICAL BASIS 2.1 TAYLOR CYLINDER IMPACT TEST 2.1.1 Review of Different Approaches for Analyzing the Test The Taylor cylinder impact test (often simply called the Taylor test) [Taylor (1946), Whiffin (1948)] was developed as a simple method of obtaining data to characterize the strength of a material under impact conditions. The technique consists of impacting a short cylindrical specimen on to a flat rigid target at relatively low velocities (100-300 m/s) sufficient to cause plastic deformation in the specimen without inducing any fracture. Depending on the material and the impact velocity, compressive strains of the order of 50% or more can be achieved at strain rates in the range of 10^ -10^ s~l. The final profile of the specimen and/or its deformation history may be analysed using several different methods to obtain an average dynamic strength or to derive dynamic flow curve coefficients. The experimental results can also be used for checking and refining constitutive models used in computational codes. Regnauld (1936) appears to have been the first investigator to study the dynamic impact of cylinders theoretically [ see Lips et al. (1986)]. Using a simple analytical model based on an energy balance concept, he showed how the dynamic strength can be obtained from measurements of the initial and final dimensions of the cylinder and a knowledge of its density and of the impact velocity. Taylor's analysis [Taylor (1946)], which forms the basis for most of the one-dimensional models, considers the motion and interaction of elastic and plastic waves, within a short cylindrical specimen made of a rate-independent and rigid-plastic material (elastic strains are neglected). Taylor assumed that the undeformed part of the specimen is uniformly decelerated 6 as a result of rapid elastic wave reflections between the plastic wave-front and the specimen free end. Radial inertia is neglected so that the stress can be considered constant over the entire cross-section. A discontinuity in cross-sectional area at the plastic wave-front is also assumed to exist. Using conservation of momentum across the plastic wave-front, he derived a simple relationship between the material dynamic yield strength and the final position of the plastic front which can be measured after the test. No measurements were made during the test. Since the deceleration of the rear of the cylinder is not necessarily uniform, Taylor (1948) also derived a correction formula. To support his analysis, Taylor conducted tests using short cylinders made from cast blocks of paraffin wax, and found that for this material the ratio between the dynamic yield strength and the static yield strength was about 1.8. Whiffin (1948), using the same approach and theory, carried out tests on steel, copper and lead. He observed that the convex shape predicted by Taylor's model did not compare well with the concave profiles of the deformed cylinders. Lee and Tupper (1954) extended Taylor's approach to take the elastic and work-hardening effects into account. They analysed the one-dimensional elastic-plastic wave propagation using the method of characteristics. Unfortunately, they also predicted a final convex profile for the cylinder, thus also contradicting the experimental results of Wrtiffin. The method of characteristics was also used by Ting (1966) who assumed a viscoplastic (i.e. strain-rate dependent) law, and by Raftopoulos and Davids (1967) who employed several different constitutive equations. Hawkyard et al. (1968), noting the poor correlation between experimental and predicted shapes, developed another analytical approach based on energy considerations. They estimated the dynamic strength by equating the cylinder initial kinetic energy density with the plastic work done, which is calculated from measurements of the radius of the deformed cylinder along its length. This approach was shown to provide an upper bound estimate of the dynamic strength. They conducted tests at elevated temperatures on steel and copper cylinders, which were pre-heated and transferred rapidly from the furnace to the launcher. It was observed that 7 the deformed ends of the specimens had a "double-frustum" shape, i.e. the final profile can be approximated as two collinear conical sections. They noted that if the impact velocity is too high, radial cracking occurs which invalidates the analysis. It was also shown that for steel and copper strain rates effects become more pronounced above the recrystallization temperature. Raftopoulos (1969) and Hashmi and Thompson (1977) employed a one dimensional finite-difference numerical technique to predict both the instantaneous profile and the strain distribution in the deforming cylinder. Raftopoulos's theoretical model was applied to the analysis of cylindrical specimens of equal mass and equal velocities impacting each other (symmetric Taylor test). The results of his analysis were in good agreement with experimental data for specimens striking rigid targets. Hawkyard (1969) presented a new technique essentially similar to that of Taylor , but using an energy balance, rather than a momentum balance, across the plastic wave-front. This model correcdy predicts the concavity of the mushroom region of the specimen, but is unable to predict the "double-frustum" profile observed in elevated temperature experiments. The analysis was also extended to the case of a strain-hardening material, which was shown to have considerable influence on the final profile. Balendra and Travis (1971) investigated the "double-frustum" phenomenon by conducting tests at high velocities on aluminum specimens. They were the first to study the deformation history of the specimen during impact rather than simply measuring the final deformed profile. They suggested that the double-frustum profile was due to radial inertia effects. For continuous filament reinforced composites, Ross (1971) developed an alternate analytical approach based upon strength of materials principles. He observed that impacted ductile matrix composite specimens exhibited the same general deformed shape as monolithic materials. 8 Wilkins and Guinan (1973) introduced the use of a two-dimensional finite difference computer code to predict the deformed shape of the impacted cylinder. They were able to simulate correctly the final lengths of Taylor test specimens of several metallic alloys using an elastic-plastic material model, except for the case of copper. However, the radial deformation could not be predicted accurately unless work hardening was included in the material model. It was assumed that the surface between the cylinder and the wall was frictionless. Some lack of correlation was also noted at higher impact velocities. This was attributed to a decrease in strength due to the adiabatic temperature rise. From the computer simulations, it was found that the plastic front position inside the specimen is closer to the rigid boundary in comparison with the outside measurements. They also presented an analytical model which is a simplification of the model of Taylor (1946). Their model assumed that the distance between the plastic front and the rigid boundary is only dependent on specimen initial length and independent of impact velocity. As an extension of the Wilkins and Guinan work, Gordon et al. (1977) studied the impact of composite specimens, constructed by bonding together two cylinders of different materials. Gust et al. (1978) developed a variation of the classic Taylor test to measure the dynamic strength of materials at very high temperatures. In their technique, known as the inverse (or asymmetric) Taylor test, the rigid anvil is launched on to a stationary cylindrical specimen that is preheated to the desired temperature. This method allows for good control of the specimen temperature. The analysis of the results was performed using a two-dimensional computer code. Recht (1978) extended Lee and Tupper's analysis to examine the dynamic behaviour of cylindrical projectiles and derived equations for predicting the projectile's mass loss by erosion. Hutchings (1979) showed that Taylor's theory, which is formulated for rigid-plastic materials and thus neglects elastic strains, is unsuitable for materials with large yield strains such as polymers. He developed a method based on one-dimensional elastic-plastic wave propagation 9 theory. He assumed that the plastic wave disappears after the first elastic wave interaction, which restricts the validity of the theory to low impact velocities. This approach, which is useful for determining the dynamic yield strength of polymers, is therefore only of limited applicability to metals. In order to make the Taylor test more suitable for checking and refining the dynamic stress-strain curve of materials used in computer codes, Erlich et al. (1981) introduced two modifications to the original technique. The first was to use high speed photography to record the deformation history of the cylinder. The impact experiment was simulated using a selected material model in a two dimensional computer code. The parameters of the model were varied until good agreement was obtained between the predicted and observed profiles at successive stages during the deformation history. The second modification consisted of replacing the rigid target with a stationary cylinder identical to the one being accelerated. This technique, referred to as the symmetric Taylor test, allows the impacting ends of the two cylinders to deform symmetrically. Assumptions about the rigidity of the target and sliding friction along the cylinder/target interface are no longer required, thus eliminating the uncertainties in the boundary conditions associated with the conventional configuration. For the final deformation of the two cylinders to be the same as that of a single cylinder striking a rigid target, the impact velocity must be doubled. They noted that tests in which internal voids or shear bands occur cannot be used to verify the accuracy of material deformation behaviour. Jones et al. (1987) developed a one-dimensional model representing a more precise application of the conservation of momentum at high velocities. The equation of motion was modified to include a term accounting for mass transfer across the plastic wave-front. The model which can accommodate various material constitutive relations, was applied to a rigid, perfectly plastic material in which case the relevant equations can be integrated explicitly. Gillis et al. (1987) extended Jones' analysis to incorporate the effects of work-hardening in the specimen material. In this case numerical solution of the equations is necessary. Gillis and Jones (1989) further extended their original model to the case of a rate-dependent material. 10 Hunkler (1988) developed an optimization program (CAOS) which determines the coefficients of rate dependent constitutive material models giving the best fit to the entire shape of the specimen after deformation. A two-dimensional computer code was used to perform the analysis, and the parameters of the models were systematically adjusted by CAOS until the best fit was obtained. Grady and Kipp (1989), using the void-nucleation-and-growth model of Davidson et al. (1977), were able to predict reasonably well the internal ductile void damage observed near the impact interface of aluminum cylinders. Finally, several other investigations of the Taylor test have been done, which for completeness should be mentioned: Carrington and Gayler (1948), Goldsmith (1960), Johnson (1972), Carley (1978), Papirno et al. (1980), Billington and Tate (1981), Hutchings and O'Brien (1981), Woodward and Lambert (1981), Hutchings (1982), White (1984), Johnson and Cook (1985), Kuscher (1985), Ross et al. (1985), Shockey et al. (1985), Paulus (1986), Lips et al. (1987), Macaulay (1987), Marinaro et al. (1989), and finally House (1989). 2.1.2 Selected Models To obtain the dynamic strength (Y) of the materials tested in this study, the one-dimensional models of Regnauld (1936), Taylor (1946, 1948), Hawkyard (1969), Wilkins and Guinan (1973) and Jones et al. (1987) were selected. In all these models, radial inertia and thermal softening effects are neglected, and the material is assumed to be rigid plastic. Given these assumptions closed-form solutions are obtained. The assumption of rigid-plastic behaviour is consistent with the penetration model selected (see Section 2.2.2). All the models derive Y from measurements of impact velocity, material density, and specimens initial and final length. In addition, the models of Taylor and Jones et al. require a measurement of the final 11 undeformed length of the specimen. The key equations for each of the six models are given in Appendix A. 2.2 DYNAMIC PENETRATION TEST 2.2.1 Review of Prediction Techniques Projectile impact and penetration have been the subject of many theoretical and experimental investigations for at least two centuries. Previous surveys of ballistic impact modelling have been prepared by Backman and Goldsmith (1978), Zukas et al. (1982), Walters and Zukas (1989) , and Zukas (1990). In, general, several techniques have been developed for predicting the penetration of a semi-infinite target by solid impactors. They may be grouped into four categories: empirical, semi-empirical, analytical and numerical models. Because many penetration mechanisms are possible, experimental observations usually precede and lead to the development of empirical models. Since they are based only on correlations with experimental data, empirical models do not provide even a phenomenological description of the processes involved. The reliability of empirical models is usually limited to the range of test conditions from which they are deduced. Reviews of such models for concrete have been given by Kennedy (1976), Sliter (1980) and Riera (1989). Adeli et al (1986) and Heuze" (1990) have reviewed the penetration of geological materials. Penetration of metallic materials is discussed in review articles by Brown (1985), and Muzychenko and Postnov (1986). Newton's second law of motion is the basis for most semi-empirical models and is written in a general form as: mdV/dt = aj+a2V+asV2 (2.1) where V is the instantaneous velocity of the projectile, and m is the mass of the projectile plus the target material moving with the projectile. The right hand side of Equation 2.1 corresponds 12 to the target resistance force opposing penetration. The constant aj represents the resistance resulting from the shear strength of the target material, the constant a2 represents the viscous resistance of the target and the constant aj represents the contribution arising from inertial effects. The equation of motion can be integrated with the proper initial and boundary conditions to obtain the total depth of penetration. However, the coefficients aj, a2 and 0:3 must be determined empirically from actual penetration test data. For the penetration of a ductile target by rigid cone-nosed projectiles, Brooks (1973) developed a semi-empirical model based on an aerodynamic analogy. The model, which treats the target as a rigid-plastic 'atmosphere', allows the prediction of penetration depth and cavity profile. Good agreement is reported for a variety of projectile/target combinations, however the utility of the model is somewhat reduced by the number of coefficients involved. Analytical methods for penetration mechanics are based on cavity expansion theories in which the penetration of a projectile into a target at low and intermediate velocity is simulated as a cavity (spherical or cylindrical) expanding in the target material and surrounded by a finite volume of deformed target material. The complexity of the problem is usually reduced by assuming that the projectile is nondeforming. Thermal phenomena and rigid body motion are also neglected. The resistance to penetration is usually assumed to be the sum of the shear resistance of the target, frictional resistance at the projectile-target interface and inertial effects of projectile movement in the target (also referred to as dynamic resistance). Cavity expansion theories provide closed-form solutions for the projectile penetration depth and deceleration as a function of the target properties and projectile characteristics. The foundation for such a penetration theory was first presented by Bishop et al. (1945) who studied the quasi-static penetration of a semi-mfinite strain-hardening target by a rigid punch. Goodier (1965) later extended this theory to model the penetration into an elastic-plastic , incompressible metallic target by high-velocity rigid spheres. Hanagud and Ross (1971) extended the model of Goodier to include target material compressibility. Using a similar approach, Byrnside et al. (1972) studied the impact of hard and soft spheres on aluminum targets and considered the 13 effects of projectile strength on cavity formation. The spherical cavity expansion theory approach was modified by Norwood (1974) into a cylindrical cavity expansion theory for projectiles with sharp, pointed, slender noses. The cylindrical cavity expansion approach is based on the assumption that the motion of the target material is strictly radial, which renders the problem one-dimensional in space. Considerable development followed using different target material models. Among these are the work by Forrestal et al. (1981), Norwood and Sears (1982), Longcope and Forrestal (1983), Forrestal (1986), and Luk. and Forrestal (1987). Since the 1960s, numerical techniques based on finite-difference and finite-element methods have been applied to obtain complete solutions to the penetration problems. Computer programs which handle the propagation of shock waves and solve the governing equations of impact are called "hydrodynamic" computer codes or "hydrocodes" for short. Vaziri et al. (1989) provide a comprehensive review and assessment of the various numerical methods available for penetration modelling. While numerical methods may correlate well with experimental data, their execution requires the use of expensive programs on high speed computers with large storage capabilities. In addition, a substantial amount of time is often required to execute the analysis, thus diminishing the utility of the numerical approach as a practical engineering tool for preliminary design purposes. However, this approach represents a rational way of examining the details of target and projectile behaviour and of determining which mechanisms are most important. When a compromise is desired, a simple one-dimensional finite difference model, as the one developed by Woodward (1982) for the penetration of a semi-infinite target by a cylindrical rod projectile, can be used. In this method, the projectile-target interaction is treated as that of two colliding cylinders using an approach similar to the one of Hashmi and Thompson (1977). To account for the surrounding material, the strength of the target elements is increased by a constraint factor, which is selectively applied to the projectile elements. Radial inertia and erosion effects are considered, while strain rate and thermal softening effects are neglected. 14 2.2.2 Selected Analysis For the present study, an approximate cavity expansion model, developed recently by Forrestal et al. (1988), has been selected to predict the penetration depths. This model is attractive since it leads to closed form equations involving only a few measurable parameters. Also, good agreement was reported with experimental results on the penetration of maraging steel rods into 6061-T651 aluminum targets at impact velocities ranging from 400 to 1400 m/s. The target is assumed to be semi-infinite, elastic-perfectly plastic and rate independent. The projectile is assumed to be nondeforming (rigid) and consists of a long rod with a spherical, ogival or conical nose shape. In addition the impact is assumed to occur at normal incidence, and the model considers only the forces on the nose. The derivation of the equation for the penetration depth is given in Appendix B. The principal aspects which are not taken into account are oblique impact, penetrator ductility and target thickness. The only mode of deformation considered is ductile hole growth. Failure of the target by cracking or spalling are not considered. For the perforation of target of finite thickness (e.g., plate) with rigid conical nosed rods, Forrestal et al. (1987) have presented a model which uses an approach similar to the one used for serru-infinite targets. In this case, closed-form expressions are obtained for the ballistic Umit (velocity below which there is no perforation) and the residual velocity (projectile velocity after perforation). 15 CHAPTER 3 EXPERIMENTAL METHODOLOGY 3.1 SELECTION OF MATERIALS For the present study, the material selection was based on finding a MMC system for which various reinforcement types and volume fractions were available. A survey of manufacturers was undertaken and companies in Canada, United-States, England, France and Japan were contacted. A list of suppliers from whom particle-reinforced MMC can be obtained is provided in Appendix C. Based on the information received concerning the available range of materials, mechanical properties, and cost, two material systems, both based on the 6061 aluminum matrix, were chosen. The first is an alumina ( A I 2 O 3 ) particle-reinforced system available from Dural Aluminum Composites Corp. (a division of Alcan Aluminum Corporation) and made by rheocasting (a proprietary process) with nominal 10 , 15 and 20% reinforcement volume fractions respectively. The material was first cast in 175 mm diameter billets and extruded into 50 mm cylindrical rods. The second MMC system was purchased from DWA Composites Specialties Inc. (a subsidiary of BP Metal Composites Limited). It is a powder metallurgy product and contains silicon carbide (SiC) platelets. The platelets are made from single crystals of abrasive-grade SiC that have been crushed into fine powder and separated by size. Three different volume fractions of SiC were purchased: 0, 20, and 30% reinforcement volume fraction. The 0% material serves as a control. A 55% volume fraction reinforcement was also ordered but became unavailabe due to processing difficulties. Both these MMC systems have been subjected to a standard T6 ageing treatment by the suppliers. The T6 condition provides additional second phase strengthening to the material. The high strength 7075-T6 aluminum alloy was also included in the test program for the purpose of comparison with the MMC. Table 3 provides a list of the materials selected with their respective designations. 16 The present study includes three types of tests: quasi-static tensile tests, Taylor impact tests and dynamic penetration tests. The tests performed for each material are listed in Table 4. This chapter describes the development and construction of the high strain rate facility and the testing procedures that were developed and followed. 3.2 QUASI-STATIC TENSILE TESTS The stress-strain curves for the LM-6061 and DWA-30 materials at low strain rates were determined by performing quasi-static tensile tests.The experimental setup is shown in Figure 1. The tension tests were performed with a standard screw-driven Instron machine (Model TTDL, serial # 2224) at a constant displacement rate of 0.005 cm/min. (corresponding to an initial strain rate of 0.66 x 10"4 s~l) and at room temperature. Since no standard procedure or specimen design exists for tension testing of particulate MMC, the tension tests were performed according to the ASTM B557-84 standards for aluminum products [Roebuck et al. (1989)]. As shown in Figure 2 , the specimens were small dog bone samples with a gauge diameter (D) of 4.6 mm , gauge length (L) of 18.4 mm and button ends. The reduced section aspect ratio (LID) of 4 was kept similar to the standard full size specimen as recommended by ASTM B-557. The 50 mm overall specimen length allows both the transverse (radial) and longitudinal (axial) specimens to have the same dimensions. Button-ends were preferred to threaded ends because it is difficult to machine threads on MMC specimens and threaded ends are prone to premature failure in the grip area. The MMC tensile samples were cored from the rod stock in both the longitudinal and transverse directions and finished by machining on a lathe using diamond end tools. Care was taken to avoid any marks on the gauge length surface. The diameters of the samples were measured with a micrometer at the center and at the ends of the gauge length. 17 The samples were gripped using Hounsfield grips (model #13) placed in series with a universal joint to minimize any misalignment (Figure 1). The strain was measured with a strain gauge extensometer (Instron model G51-17, serial # 1038, 12.5 mm gauge length, 15% elongation) which was previously calibrated. To verify the accuracy of the clip gauge, a narrow compact geometry strain gauge (Micro-Measurements # EA-06-125BZ-350) was also bonded on the first two specimens. The load was measured with a 90 kN Instron load cell (model D30-20, serial # 388). Load and strain data were recorded using a Schlumberger Orion Model D data logger. After each test the data was stored on compact tape and subsequently transferred to an IBM-PC for analysis. The data reduction consisted of applying the respective calibration factors to the raw data to get the true stress-true strain curves. A spreadsheet program (Lotus Symphony) was used to perform the required analysis. Yield strength was determined by the offset method at an offset of 0.2%. The tensile strength was calculated by dividing the maximum load carried by the specimen by its original cross-sectional area. The modulus of elasticity was calculated by determining the slope of the straight line portion of the stress-strain curve using a regression analysis. 3.3 TAYLOR IMPACT TESTS Background To measure the dynamic properties of the materials involved in this study, the Taylor cylinder impact technique was selected. It is one of the few techniques that can provide data in the large plastic strain (50-150%) and high strain rate (10^ s'l) regimes, which are typical of many impact events. The Taylor test is a well developed method requiring relatively simple apparatus. Furthermore the same system can also be used to perform dynamic penetration tests. 18 In the Taylor test, short cylindrical specimens of the test material are accelerated to various velocities and axially impacted against a non-deformable target at normal incidence. Upon impact, the cylinder deforms plastically in a mushroom-like shape. Depending on whether the target used is a massive rigid anvil or a short cylinder, two configurations are possible: the conventional cylinder anvil test (standard Taylor test) or the symmetric cylinder-on-cylinder impact test (symmetric Taylor test). The symmetric test simplifies the boundary conditions used in the numerical analysis, since the unknown frictional forces at the interface are eliminated by symmetry considerations. However, there are problems with alignment which the conventional massive rigid anvil does not suffer from to the same degree. For the present study both the conventional and the symmetric configurations were used for comparison. By changing the impact velocity, the average strain rate of the test can be varied. The impact velocity must be high enough that the specimen flies in a straight and stable fashion and that the specimen's deformation is measurable. The velocity must at the same time be low enough to avoid any damage (radial cracking on the perimeter, shear bands or tensile voids on the axis) to the test specimens. For brittle materials, the range of strain rates can therefore be quite limited. Experimental facility Figure 3 shows the experimental facility designed and constructed for carrying out the Taylor test. The facility consists of a smooth bore powder launcher which accelerates a cylindrical specimen into a target chamber containing either a stationary target specimen (symmetric Taylor test) or a rigid anvil (standard Taylor test). After impact, both cylinders fly into a recovery chamber filled with cotton rags (symmetric Taylor test). Figure 4 is a photograph of the facility showing the various components. The launcher, the target chamber and the recovery chamber are supported on two parallel rods which provide precise alignment between the three components. The recovery chamber can 19 slide on the rods to give access to the anvil or impact specimen while the target chamber is fixed. Launcher The launcher is used to accelerate the test cylinder to the desired impact velocity, providing the energy for the subsequent plastic deformation. While single stage gas guns have the advantages of clean environment and safe operation, they are generally relatively long (e.g. 4 meters), have large diameters (e.g. 20 mm) and are limited to velocities ranging from low to intermediate (e.g. 50 to 700 m/s). For the present work, since the same launcher is also used for the dynamic penetration tests, smokeless gun powder was chosen as the propellant. As shown in Figure 3, the main components of the launcher are the barrel, the breech block and the firing mechanism. The design of the barrel was based on the use of a standard 0.460 inch caliber Weatherby Magnum cartridge, which is one of the most powerful ammunitions available commercially. It is capable of propelling projectiles of ten grams at speeds up to 1000 m/s using a short barrel length (0.818 m). Also, its 11.68 mm diameter gives the flexibility of testing specimens of various geometries and sizes inserted in small plastic holders commonly known as sabots. The barrel (Figure 5) was machined from AISI 4340 steel, and was center-bored to an inside diameter of 11.68 mm using a gun drill. Since it was intended to be used for short distance tests, no rifling was added to the smooth bore tube. The breech end of the barrel was chambered to accept the 0.460 caliber cartridge case. After machining, the barrel was heat treated to 40 HRC to improve its strength. The thickness of the barrel, 14.8 mm, is designed to withstand internal pressures exceeding twice the ones produced by the Weatherby cartridge (400 MPa). For the Taylor tests, both the mass of the specimen and the impact velocity are relatively low. Therefore, a special sub-caliber cartridge (Figure 6) was designed with the same external 20 geometry as the .460 cartridge case but of smaller charge capacity (10 grains, i.e. 0.65 grams). The sub-caliber cartridge is primed with CCI-500 small pistol primers. In order to promote consistent performance and avoid any misfires, care should be taken to seat the primer properly in the primer pocket. Cannister grade, fast burning Hercules Bullseye smokeless pistol powder is used to load the sub-caliber. To keep the powder charge in place against the primer, a small wad of cotton was packed against the powder. This ensures a uniform burning of the propellant. The reloading process is done using a standard RCBS press, with seating and resizing dies. For safety considerations, the powder is stored in a locked cabinet. In order to reduce the disturbance when the specimen exits the barrel, a tube extension (Figure 7) with wide side slots is attached to the muzzle end of the barrel. The extension is designed to deflect the exit blast away from the velocity measurement system, as well as to provide support to the target cylinder in the symmetric Taylor configuration. To lock the cartridge assembly in the barrel chamber, a universal receiver or breech block is used. The barrel is connected to the universal receiver by means of a coupling sleeve. An opening at the back of the receiver allows the cartridge to be loaded in the barrel chamber. The opening is closed by a sliding steel block which contains a striking pin for the initiation of the primer. This design allows for a quick change of the cartridge between tests. To actuate the striking pin, an electric solenoid firing mechanism is attached to the universal receiver. For safety considerations, the firing mechanism can be activated from outside the laboratory room. The universal receiver is mounted on a steel plate which is fixed with dowel pins on a pair of blocks that can slide on the two support rods to allow rapid change of the standoff distance between the muzzle and the target The dowel pins facilitate the accurate relocation of the launcher when dismounted. As the launcher was expected to recoil with significant energy at maximum charge, an adjustable air cylinder was attached to the steel plate for recoil absorption. Tests to date have shown that only small recoil forces are generated. 21 Target chamber To contain any potential ricochet or fragments occurring during impact, as well as reduce noise and allow for the application of a vacuum, a target chamber was designed and built to serve as the target mounting area. The target chamber, shown in Figure 8 , is made from a DOM steel tube with a 305 mm inner diameter and a length of 660 mm, which is large enough to accommodate targets of various sizes. The thickness of the walls is 9.5 mm which provides the required protection against outside damage. At one end of the tube, a flange with a bronze bushing is attached to provide support to the barrel while allowing it to slide freely during recoil. Since the barrel is relatively short, no mid-supports were required. The other end of the target chamber is kept open for access to the target area and is attached to the recovery chamber during testing. The target chamber is equipped with an elongated side window on each side for visual or camera observations. There are also two round ports on the horizontal plane for the laser velocity measurement system. The side windows are covered with 9 mm thick polycarbonate sheets. An aluminum plate with a narrow slit for the laser beams is used to cover the round ports. To support the target a special holder device is attached to the base of the target chamber. The holder device consists of a V-grooved steel block fixed on a threaded rod for vertical adjustments. A swivel mechanism allows for precise control of the target orientation and ensures normal impact. To make the end of the target perpendicular to and concentric with the barrel axis, an alignment rod (Figure 9) can be inserted in the barrel and used as a reference for the adjustment of the target holder. Tests have shown that the target holder device is sturdy enough to resist the high pressure blast. 22 Recovery chamber The recovery chamber is a long cylindrical container designed for the soft recovery of the specimen and target. It is made of a 4.8 mm thick seamless steel tube 1.47 m long and 0.32 m inside diameter. A 25 mm thick steel plate is bolted on to the back end. The recovery chamber contains a heavy mesh catchment cage lightly packed with cotton rags. After impact, both the launched specimen and the target fly into the catchment cage where they are slowed down and caught by the rags without any additional damage. The recovery chamber is attached to a block which can slide on the two support rods for easy access to the target area and to allow unloading of the catch cage. During each test, the recovery chamber is bolted to the target chamber. When fixed together, both tanks can be evacuated to minimize air cushion build up between the impacting faces and to absorb the pressure generated by the burning powder. To ensure that no overpressure (i.e. a final pressure of more than one atmosphere) exists after a test, the recovery chamber was made sufficiently long for equilibrating the 400 MPa maximum gas pressure generated in the cartridge volume at full load. A vacuum of approximately 632 torr (25 inches of mercury) can be attained in 2 minutes using a vacuum pump. Specimen and measurements As shown in Figure 10, the Taylor test specimen is a circular cylinder 11.56 mm in diameter and 23.18 mm long. The specimens were first cored using an oversized diamond drill from the 50 mm bar stock and turned down to final dimensions on a lathe with diamond tipped tools. Prior to testing, the ends were polished with fine emery cloth to remove any oxide that may have formed. In order to eliminate the use of sabots, the specimens were machined to the same diameter as the barrel. Generally, sabots are used to provide a gas seal and reduce barrel wear. However, there are a number of disadvantages associated with the use of sabots. First, the added mass of the sabot influences the specimen deformation if the sabot is not discarded before impact On the other hand, they cannot be discarded before impact without reducing the velocity and/or creating instability in the flight of the specimen. To facilitate measurements of 23 the specimen, it is also desirable to have a specimen as large as possible. This is achieved when no sabots are used. The specimen length/diameter ratio (aspect ratio) of 2 was fixed by the length of the coring drill available. Large aspect ratios are desirable to nunirnize the effect of frictional forces at the specimen-anvil interface. However, specimens of aspect ratio greater than 3 are not recommended since they are prone to buckling if they strike the target at a slight angle to the normal axis. The overall lengths of the cylindrical specimens before and after testing were measured with a micrometer to an accuracy of 0.01 mm. The specimens were also weighed. For making post-impact measurements, a gauge was machined to provide accurate measurements of the undeformed length of the specimens (Figure 11). The gauge consists of a hollow brass cylinder of the same length as the specimen with an inner diameter of 11.58 mm corresponding to the specimen diameter increased by 0.02 mm. The undeformed length is defined to be the length up to the point where a 0.2% radial plastic strain occurs. As shown in Figure 11, the undeformed end of the specimen is inserted in the hole so that the plastically deformed part of the impact specimen protrudes out of the gauge end. The undeformed length is determined from the difference between the gauge length and the unfilled distance measured with a digital caliper. To examine the strain distribution and the asymmetry of the deformation, the profiles of selected specimens were obtained using a shadowgraph, also known as an optical projector. These measurements were made at DREV. The deformed profiles can be used for comparison with numerical simulations. Target and lubrication For the conventional Taylor test, the target was a hardened steel cylinder (49 HRC), 50 mm in diameter and 150 mm in length, inserted in a mild steel shell of diameter 100mm and length 250 mm (Figure 12). Both ends of the hardened target were lap-finished. The same hardened cylinder was used until noticeable deterioration of the impact face occurred, after which it was 24 reground. Tests have shown that the target used-is sufficiently massive that its motion can be neglected. For the symmetric test, as described earlier, the target consists of a stationary cylinder of the same dimensions as the cylinder being launched on to it The target cylinder is held in place using the muzzle extension which is concentric with the barrel and therefore ensures perfect alignment with the moving cylinder. In order to reduce the frictional effects as much as possible during the deformation of the cylinder against the rigid target, a lubricant must be used. It was decided not to lubricate the flat surface of the specimen so as to avoid any accumulation of debris inside the barrel. The rigid target alone was lubricated by spreading a thin film of M0S2 grease. Velocity system In addition to the measurement of the initial and final specimen dimensions, it is also necessary to measure the velocity of the specimen just before impact. Since the calculated dynamic strength varies with the square of the striking velocity (see Appendix A), it is necessary to measure the velocity as accurately as possible. The velocity measurement system consists of four parallel laser beams spaced 12 mm apart and aligned coaxially with the barrel ahead of the target The four miniature infrared solid state laser emitters are mounted on the bottom circular port of the target chamber. Each laser beam is focussed through small aperture holes on to a diode detector mounted on the top circular port. The four emitters produce a high voltage state in the detectors, which is measured with an oscilloscope. As the specimen passes through the beams, the voltage state on the oscilloscope associated with each beam drops to zero. After a test, the oscilloscope displays four voltage drops and the time interval between these drops represents the time taken by the specimen to pass through the successive beams. Knowing the distance between the beams, the average velocity can be calculated. The three values obtained provide an indication of the specimen acceleration. The time intervals between the interruption of the four laser beams are also measured independently with an electronic counter using preset 25 trigger levels. To verify the laser system, a 22 caliber and a .308 rifle barrel were mounted on the support plate. T22 Long rifle target standard velocity and 308 Winchester Accelerator 3.5 grams (55 grains) bullets were fired. The velocities determined with the laser velocity system were within 1% of the ones specified by the suppliers' ballistic charts. In order to avoid interference with the laser beams by the smoke cloud near the muzzle, most tests were performed with the barrel pulled back as much as possible (a distance of 30 cm). At such a distance the specimen is still in stable flight with only a small yawing motion. Experimental procedure Initially, no information was available on the quantity of powder necessary to obtain the velocities of interest for the various materials used as projectiles. Thus a trial and error procedure was used to determine the appropriate charges. However, after acquiring sufficient data on velocity and propellant mass, a graph was produced to provide a quick source for this information (see Figure 13). For the symmetric Taylor test, the amount of powder was doubled in order to get the same amount of deformation as with the rigid target configuration. Before each test, a number of operations were performed. The barrel and the target chamber windows were cleaned. The packing of the catch cage was checked. The target was then lubricated, installed, and aligned. The distance between the barrel end and the target was adjusted. The recovery chamber was then pushed up to the target chamber and bolted on to it. The specimen was loaded in the barrel chamber and the subcaliber cartridge was used to position the specimen at the same location in the barrel for each test. The breech block was then closed and the firing mechanism attached on to it. Vacuum was applied as required. The velocity system was reset. The firing mechanism was then armed and the safety plug inserted in the control panel. Finally the test was initiated from outside the laboratory room. After the test, the safety plug was removed first, and the combustion gases were evacuated from the target chamber using the vacuum pump. The breech was then opened and the 26 subcaliber cartridge extracted. The deformed specimen and the target were then recovered. Finally the readings from the velocity system were recorded in the log book. Initially the tests were conducted with both chambers evacuated. Later on, due to the sensitivity of the laser system to the combustion debris, vacuum was no longer applied. To prevent overpressure, a gap was allowed between the recovery chamber and the target chamber. From the preliminary tests, it was found that the specimens rebounded from the target on to the barrel extension causing damage to the undeformed sections of the specimens. A rubber pad was then added to the extension end in order to protect the specimens. 3.4 DYNAMIC PENETRATION TESTS Test configuration The dynamic penetration tests consisted of firing a small rigid tungsten rod into a semi-infinite cylinder of the material of interest (Figure 14). A semi-infinite target is defined as one whose only free surface is the impact face, so that the penetration process is not affected by the lateral or rear surfaces. In the current program, the specimen free surface was perpendicular to the penetrator axis. As shown in Figure 15, the impactors were 4.48 mm diameter and 27 mm long tungsten rods with hemispherical noses. They were machined, using electric discharge machining (EDM), from 12 mm diameter X21-C tungsten alloy bars purchased from Teledyne Firth Sterling Corp. (supplied by DREV) and had a nominal mass of 7.3 grams. As shown in Appendix D, the X21-C material has a tensile strength of 1237 MPa and a fracture strain of 13%, and is considered to be a relatively high strength and ductile alloy. Since the diameter of the 27 projectile was smaller than that of the barrel used to launch them, they were fitted in polycarbonate sabots weighing 4.5 grams (Figure 16). The targets were cylindrical specimens with nominal diameters of 50 mm which gives a target-to-penetrator diameter ratio (aspect ratio) of 11.8. Schwer et al. (1988) recommend an aspect ratio greater than 15 if large scale radial cracking of the target is to be avoided. A target length greater than twice the penetration depth is also desirable to minimize the boundary effects. As the penetration depth was not known a priori, the initial tests were conducted with 300 mm long specimens. Following these results, a target length of 150 mm was chosen for the remainder of the tests. The target specimens were cut to length with a diamond saw from the extruded bars and their impact faces were finished on a lathe with diamond tipped cutting tools. Experimental procedures The projectiles were accelerated using the smooth-bore launcher described in the previous section. Standard centre fire 0.460 Weatherby brass cartridge cases were used. They were primed with CCI 250 large rifle magnum primers. Cannister grade IMR 3031 smokeless powder was used to load the cartridge cases. The powder was covered with a small cotton wad. The sabots were then press-fitted in the cartridges using the RCBS seating die. Three powder masses were used: 3.2, 5.2 and 7.1 grams (50, 80 and 110 grains) which yielded average impact velocities of 475, 750 and 920 m/s respectively. In the same manner as for the Taylor anvil, the target was placed on the V-block holder inside the target chamber. The distance from muzzle to target was set approximately to 30 cm. Since the mass of the sabot is small, the damage caused to the target by the sabot was expected to be negligible. This was confirmed by launching an empty sabot on a target as shown in Figure 17. Since the plastic sabot does not influence the penetration depth, the use of a sabot stripper or split sabot was not required. For each test, the impact velocity was determined to within 1% accuracy using the laser velocity measurement system described previously. At maximum powder charge, the signal registered on the oscilloscope was more noisy, due to powder debris interfering with the 28 laser beams. Thick Pyrex glass sheets were added to cover and protect the laser ports from the debris. The penetration tests were conducted using the procedures described in section 3.3. Post-Impact measurements After the penetration tests were completed, all the target specimens were X-rayed to determine the cavity profiles. The dimensions were measured from the X-ray photographs with a digital caliper to an accuracy of ±0.01 mm. The X-rays were taken at the engineering consulting firm of Bacon, Donaldson & Associates. The parameters used are given in Appendix E. Some samples were sectioned using EDM machining for metallographic examinations and penetration depth measurements. The X-ray photographs were also used to ensure that the sectioning was made through the cavity center on a plane containing the impact direction. Sectioning of the DURAL-20 specimens was not possible using EDM machining. 29 C H A P T E R 4 R E S U L T S A N D D I S C U S S I O N S 4.1 MATERIAL PROPERTIES AND ELASTIC MODULUS PREDICTIONS Material Properties The properties for the selected materials are summarized in Table 5, in which the results of the tension tests are also included. The determination of the Young's modulus for the DWA-30 specimens was difficult due to the nonlinearities in the initial segment of the stress-strain curves. The low proportional limit of the MMC materials may result from various factors such as residual thermal stresses, particulate cracking, interface debonding and matrix yielding. The tensile test results indicate that the 30% SiC reinforcement increases the modulus by approximately 50% and the ultimate strength by 20%, but the ductility (elongation to failure) is drastically reduced. Representative trae-stress/true-strain curves are given in Figure 18. The stress-strain curves for the DWA-30 specimens show significant nonlinearities, with the rate of strain hardening being increased by the presence of the reinforcement. Comparison between the results for the axial and radial DWA-30 samples indicates that this MMC system is quite isotropic in strength, but the tensile elongation of the radial specimens were slightly lower than that of the axial specimens. Examination of the failed samples showed a consistent failure pattern within the gauge section and a reasonable uniformity of the yield and ultimate strengths. As expected with powder metallurgy products, the DWA-30 samples failed without any sign of external necking or of significant macroscopic plastic deformation. The densities of the DWA materials were measured by the immersion technique (according to ASTM D792-86). The addition of silicon carbide to aluminum has little influence on the overall density of the composite since the density values of aluminum and SiC are very similar. 30 For the DURAL materials, the values of the various properties were extracted from the supplier's data package. The value of density is important since it is used in the dynamic strength calculations (see Appendix A). The reinforcement content of the DWA system was measured [Vaziri and Poursartip (1991)] by dissolving the aluminum alloy matrix with a sodium hydroxide (NaOH) solution following ASTM D3553-76 procedures. Knowing the density of the unreinforced alloy and the SiC, the weight fraction of reinforcement is measured and used to obtain the volume fraction of SiC and the pore content. As the pore content was less than 1%, the composite can be considered to be free of voids. The chemical composition of the aluminum alloy used for the DURAL composites is given in Appendix F. The analysis was provided by the supplier. No analysis was provided for the DWA material. The MMCs' Poisson's ratio (v) was calculated from the rule of mixtures (ROM) [Jones (1975)] as: v = v rV r + v m V m (4.1) where v r and vm represent the Poisson's ratio of the reinforcement and matrix, and Vr and Vm represent the volume fractions of the reinforcement and matrix. The ROM value for the DWA-30 composite corresponds to the value measured previously by Tsangarakis et al. (1987) on a similar material. Table 5 shows that the DWA-20 (20% SiC) and the DURAL-20 (20% AI2O3) composites have similar elastic moduli even though AI2O3 has a much smaller Young's modulus than SiC (Table 1). This may be due to the weak interface of the SiC reinforcement, or it might be due to the higher aspect ratio of the AI2O3 reinforcement. Further study is necessary to deterrnine the exact cause. 31 Table 5 also shows that the SiC composite is significantly stronger than the AI2O3 composite. It is interesting to note that the AI2O3 reinforcement provides a similar strengthening ratio relative to its unreinforced matrix (i.e. 379/332 = 1.14) to the corresponding ratio for the SiC (i.e. 428/386 = 1.11). The strengthening mechanisms in particulate composites are still not fully understood [Nardonne (1987)]. A comparison between the properties of the 6061 alloy powder-processed (PM 6061) with the same alloy cast-processed (LM 6061) indicate that they have similar stiffnesses, but that the strength of the powder-processed aluminum is about 30% higher than that of the wrought alloy. The increase in strength can be attributed to the high dislocation density and the small subgrain size of the powder process alloy. Young's modulus prediction The Young's modulus or modulus of elasticity Ec of a composite is an important parameter for stiffness based designs (for example compression members prone to buckling). Also, as discussed in Chapter 3, the penetration resistance of materials is dependent to some degree on the Young's modulus. In order to tailor the performance of MMC to specific applications, it is necessary to be able to calculate this property. Several prediction models have been formulated which are based on three approaches: mechanics of materials, self consistent schemes, and variational methods. The models attempt to account for the various parameters that affect Ec. The predominant factor which influences the Young's modulus is the volume fraction of reinforcement. Furthermore, the Young's modulus is affected to a lesser degree by the type, size, orientation and distribution of the reinforcement. The type of matrix alloy, the processing technique and the interfacial adhesion between the matrix and the reinforcement are also important. The simplest model for Ec is a mechanics of materials approach based on the rule of mixtures (ROM): 32 Ec = ErVr + EmVm (4.2) where Er and £ m are the elastic moduli of the reinforcement and matrix, respectively. The ROM prediction provides an upper bound which can be approached with the use of continuous fiber reinforcement. For particulate reinforcements, Ahmed and Jones (1990) have presented a review of existing theories. Based on this review, the two phase models developed by Paul (1960) and Ishai (1965) were selected for comparison with the experimental data for the DWA and DURAL MMCs. For both models, the constituents are assumed to be in a state of macroscopically homogeneous stress. Adhesion is assumed to be maintained at the interface of a cubic inclusion embedded in a cubic matrix, and average stresses and strains are assumed to exist in each of the phases. Paul considered a uniform stress applied at the boundary inducing a uniform strain field in the composite, which leads to the following expression: l+(k-l)Vr2'3 F-c - Em l+(k-l)(V™-Vr) (4.3) where k = Erl Em. Ishai used the same model, but assumed a uniform strain state at the boundary of the representative volume element. He obtained the following equation: 1+ k/(k-l)-Vr1/3 (4.4) As shown in Figures 19 and 20, the measurements for the DURAL and the DWA composites fall between the values predicted by the two models. The results indicate that Paul's model gives upper bound estimates matching the DURAL data with reasonable accuracy, while Ishai's model provides a lower bound which correlates well with the DWA data. 33 4.2 TAYLOR IMPACT TESTS Test results Taylor impact tests were successfully performed on the following four materials: LM 6061, DURAL-15, DWA-30 and LM 7075. The recovered specimens had flat impact surfaces and showed axial symmetry indicating essentially normal impact with negligible obliquity due to yaw. The post-impact measurements on successfully tested specimens are summarized in Table 6. For the L M 6061 specimens, small undulations were noted on the impact face and the outside of the deformed section, which may be due to grain growth under high strain rate deformations. Typical examples of the recovered specimens are shown in Figure 21, where radial cracking of the DWA-30 specimen can also be observed. This is not unexpected since the ductility of this material is relatively low. The cracks appear to be simple tensile failures due to the large radial strains occurring at the impact face. Some of the specimens were also sectioned using EDM machining. Inspection of these specimens did not reveal any evidence of internal damage (e.g., voids). A few Taylor tests were conducted using the symmetric configuration with LM 6061 specimens. Difficulties were encountered with the measurements of the impact velocity due to the short distance between the stationary specimen and the end of the barrel. Reliable values for the velocity were obtained for only one test (specimen ST2). The overall deformation of specimen ST2 is quite close to specimen T4 which was tested with the rigid target configuration at an equivalent velocity. The results of the profile measurements of selected specimens using the shadowgraph are listed in Table 7. Since some specimens exhibited asymmetry in the radial cross-section, the radial expansion was measured along both the minor and major axis planes. Deformed profiles of each cylinder, determined from the average of both series of values, are shown in Figures 22 to 24. A comparison between the DWA-30 radial and axial specimen profiles in Figure 25 shows that the radial specimen exhibits greater deformations indicating some yield strength anisotropy. 34 To quantify the degree of asymmetry, the shape of the cross-section is assumed to be elliptical, and the asymmetry is defined as: , (R-r) A = (4.5) where: R = maximum radius, r = minimum radius, and Rm = radius of circle of equivalent area to ellipse ( R m = yjRr). The asymmetry of the DWA-30 radial and axial specimens is plotted as a function of the distance from the impact end in Figure 26. The asymmetry of the radial specimen is substantially greater than that of the axial specimen. This confirms that some strength anisotropy is present in the DWA-30 extruded bars. The extrusion process may have produced some alignment of the SiC platelets along the extrusion direction. A comparison between the LM 6061-T6 results for the length shortening ratio with data of Gust et al. (1978) and Wilkins and Guinan (1973) for the same alloy is given in Figure 27. It can be seen that the results of the present'study correlate well with their data. The variation of impact velocity with powder mass was quite linear as shown in Figure 13. The repeatability of the velocity was not particularly good due to the low powder masses involved. Dynamic strength predictions The data obtained from the Taylor impact tests was used in a computer program (Appendix G) which determines the dynamic strength according to the six models selected in Chapter 2. Since the models of Hawkyard (1969) and Jones et a/.(1987) involve transcendental equations, a subroutine ZEROIN [ Forsythe (1977)] was used to find the zero of the respective equations. This subroutine uses bisection and inverse quadratic interpolation algorithms to find a real zero of a single nonlinear equation. In the case of the model of Hawkyard (1969), the subroutine 35 allows the determination of the plastic strain EQ. For the model of Jones et al., the subroutine is used to find the non-dimensional plastic wave velocity P (see Appendix A). Results of the calculations are given in Table 6, and the average dynamic strengths are summarized in Table 8. A comparison between the various analysis models for the four materials tested is shown in bar chart form in Figure 28. It can be seen that the models of Regnauld and Jones et al. give values much higher than the other four. Also, Taylor's original model (1946) always predicts the lowest values, while the models of Wilkins and Guinan, Hawkyard and Taylor (1948) predict values that are similar and correspond to an average. Wilkins and Guinan (1973) have studied the 6061-T6 Taylor impact test using a 2-D finite difference code. Using a rigid plastic model with a strength of 420 MPa, they obtained good correlations between the measured and computed deformed profiles. The results of Table 8 indicate that the models of Wilkins and Guinan, and Hawkyard yield the closest values to 420 MPa in this study. Sensitivity analysis In order to evaluate the effect of experimental errors on the computed value of the dynamic strength, a sensitivity analysis was performed. The analysis is conducted for the Regnauld and Jones et al. models, and is based on the estimate of the level of accuracy associated with each experimental measurement. The measurements of the specimens initial length, final length and final undeformed length were estimated to be accurate to within ±0.1%, ±0.2% and ±1%, respectively. The primary source of error in the measurements of the final undeformed length is from non-symmetric deformation. When a specimen impacts the target obliquely, the plastic zone extends farther on one side of the specimen than the other. The velocity measurements were considered accurate to within ±2%. According to the model of Regnauld (Equation Al), the dynamic strength Y is directly proportional to the square of the impact velocity, therefore a ±2% error in velocity measurement leads to a relative error of ±4% in Y. For the length error sensitivity analysis, a 36 procedure similar to the one of Papirno et al. (1981) is used. The initial length of the projectile is assumed to be deteirnined without error. It is assumed that the relative error e in the measurement of the specimen final length is known, and that it can be defined as: where LQ is the initial length of the specimen, Ly is the true final length, and Le = erroneous measured final length. The relative error in dynamic strength can be written as: dY Ye , T = T~1 (4-7) where Y is the true dynamic strength, and Ye is the erroneous dynamic strength (computed using Le). Applying the model of Regnauld (Equation Al) to Y and Ye, and dividing one by the other gives: l l In(LflLQ) Y~ln(Le/L0) ^ From the definition of e (Equation 4.6), we also have: Le Lf where (Lf/ LQ) corresponds to the length shortening ratio. The relative error in dynamic strength is found by combining and rearranging equations 4.7, 4.8 and 4.9 : 37 dY In(LflLp) Y ln(l + e) +ln(Lf/ L0) -1 (4.10) Equation 4.10 was used to compute the relative error in dynamic strength as a function of Lfl LQ for three values of the final length measurement relative error, namely e = 0.1%, 0.2%, and 0.4%. The three curves obtained are shown in Figure 29 and they indicate that the sensitivity of Y increases as the amount of deformation decreases, that is as Ly/ LQ approaches 1. For the materials used in this study, the length shortening ratio varies from about 0.83 to 0.97. Inspection of Figure 29 shows that the relative error in Y can be as large as 15% in the worst case. The sensitivity analysis for the model of Jones et al. (1987) was conducted by changing each of the measured parameters independently by an amount equal to the uncertainty in that measurement and recalculating the dynamic strength. The measurements for one of the DWA-30 specimens (# T17) was chosen as the baseline data. The relative error in the dynamic strength was determined from the ratio of the difference between the strength computed using the changed measurements to the baseline value. The results for the various cases considered are given in Table 9. They indicate that the dynamic strength is much more sensitive to errors in the final length (Ly) measurements than to errors in the undeformed length (X). Also, reductions in Ly and X produce opposite effects on the computed dynamic strength value. The overall error in the dynamic strength can be determined from the square root of the sum of the squares of the individual relative errors. Using the values in Table 9, the baseline value for the DWA-30 specimen can be considered to be accurate to within ±7.5%. Effect of temperature rise on dynamic strength values During the Taylor test, as with any high-strain-rate test, the deformation of the specimen occurs too rapidly to allow temperature equilibration throughout the specimen, be it by heat conduction or by heat loss to the surroundings by convection. The Taylor impact test is 38 effectively an adiabatic, rather than an isothermal process, and therefore the plastic work of deformation is converted to thermal energy, creating large temperature increases in the highly deformed regions of the specimen. For a material with low melting temperature (TM) and low specific heat capacity (Q, the local temperature rise can be sufficient to induce a decrease in the flow strength, an effect known as thermal softening. For totally adiabatic conditions, the temperature rise AT is determined solely by the amount of energy or work dissipated per unit volume (W) and by the material density (p) and specific heat such that: W AT= - (4.11) A simple estimate of the average temperature rise may be made by assuming that all the initial kinetic energy WQ of the impacting specimen is dissipated in the volume (U^) of material undergoing plastic deformation (the mushroom portion of the specimen). The initial kinetic energy can be expressed as: pAoL0V2 W0 = 5 (4-12> where AQ is the specimen initial cross-sectional area. Knowing the original volume UQ — AQLQ , and the final undeformed length X, and assuming volume conservation, UD can then be calculated as: UD = A0(L0-X) (4.13) The energy dissipated per unit volume is: W0 W = lTd (4-14) Combining equations 4.11, 4.12, 4.13 and 4.14, the average temperature rise in the deformed section is: 39 V2 AT = 2C(1-X/L0) (4.15) For a 6061-T6 specimen, using the values of Table 6 for the highest speed tested (specimen T6), a temperature rise of 68 °C is predicted. If the energy is dissipated in a smaller volume, then the calculated temperature rise would be proportionally higher. In the extreme case, if we assume linear thermal softening relative to the melting temperature, that is Y = 0 at T = Tm, then: An effective isothermal dynamic strength (Yj) can then be calculated from the estimated temperature rise (Equation 4.15) as: where TQ is the ambient temperature (room temperature). For the case considered, equations 4.15 and 4.17 result in a 14% increase to the adiabatic strength value. Since for the MMC materials the impact velocities are lower and the specific heat values are higher, a smaller temperature rise as well as a more gradual thermal softening is anticipated. As confirmed by Wilkins and Guinan (1973) for aluminum alloys, impact velocities in excess of 400 m/s are required to produce any substantial decrease in the flow stress. Effect of radial inertia One of the most important sources of error in the characterization of materials at high strain rates is the inertia response of the specimen [Gorham (1989)]. This is due to the fact that in addition to the axial deformation, a proportion of the applied stress is used up to generate radial kinetic energy due to the Poisson's ratio effect. As the rate of deformation increases, the radial acceleration of the specimen material begins to require forces comparable with those necessary dY/dT=-Y/(Tm-T0) (4.16) Yj = Y - (dY/dT) AT = Y (l+AT/(Tm-T0)) (4.17) 40 to deform the specimen. This unavoidably affects the measured stress. At very high strain rates, the inertia of the specimen itself will result in a non-uniform stress distribution along its length. To assess the effect of inertia during the dynamic compression of the specimen, the analysis developed by Johnson (1972) is used here. This analysis assumes that frictional resistance is absent and that deformation is homogeneous. The effect of stress wave propagation is also neglected. Johnson shows that the total axial stress S exerted on a cylindrical specimen may be expressed by the following equation: S = Y(l+I) (4.18) where: Y is the current dynamic yield stress, and / is an inertia parameter expressed as: '4 pv2 I Y J K2 (4.19) In Equation 4.19, K is the specimen aspect ratio (rll), r is the current specimen radius, / is the current specimen length, p is the material density, and V = is the impact velocity. From Equations 4.18 and 4.19, it can be seen that under dynamic conditions, higher stresses are required to deform specimens having larger aspect ratios (thin specimens). Substituting into equation 4.18 the expression given by Regnauld for Y (Equation Al), and assuming the worst case corresponding to / = LQ, and r = R, where R is the radius of the impact end, then: (3/32)(R/L0)2 l= ln(LQILF) <4-20> Using the values of Table 6 and 7 for the LM 6061 material (specimen T5), the radial inertia contribution to the flow stress is 6.8%, which is smaller than the accuracy with which the dynamic strength is determined, and can therefore be considered negligible. 41 4.3 DYNAMIC PENETRATION Test results The experimental results obtained for the dynamic penetration tests are presented in Table 10. The measurements were made from the X-ray photographs using a digital caliper, and the measurements were scaled to account for the slight enlargement of the photographs. For some of the MMC specimens, penetration depth measurements were complicated by the fact that the penetrator and the cavity were bent. The curvature of the trajectory may have been caused by an area of increased strength due to higher local volume fraction of particles. Representative X-ray photographs are shown in Appendix H. Some target specimens were sectioned along the length of the cavity channel and subjected to conventional metallographic observations. The sectioned specimens were also used to measure the penetration depth. These results are also included in Table 10 and are seen to be in excellent agreement with the ones measured from the X-rays. A typical photograph of an impact-cavity cross-section is shown in Figure 30. As noted in Table 10, for the DWA-30 and LM 7075 materials at high velocity, bulging and elastic rebound of the tungsten penetrator has occurred. Figure 30 also shows the macro-cracks that grew during the sectioning of the DWA-30 target specimen. These cracks are due to the residual stresses produced by the impact. As illustrated in Figure 31, for the DWA-30 specimens tested at low speed, radial cracking has occurred during impact which was not the case for the high velocity tests. This indicates a transition from brittle to ductile behaviour as the velocity increases. Large hydrodynamic stresses (dynamic inertial pressures) occur at the penetrator-target interface because the target material is confined by the surrounding material. Since the inertial pressure increases with the square of the impact velocity [Sundararajan and Shewmon (1983)], the brittle-ductile transition may be partly caused by the pressure dependency of the failure process. This has been observed by some authors in quasi-static high pressure tensile tests [Liu et al. (1989), Vasudevan et al. (1989)]. Also, it can be seen from Table 10 that for all the tests at high velocity, the minimum cavity diameter is smaller than the initial projectile diameter, which indicates that some recovery of the cavity has occurred. 42 As reported elsewhere [Vaziri and Poursartip (1991)], metallurgical examinations of the particle distribution in an area around the cavity end indicates that there is some clustering and increased local volume fraction of the particles. A thin layer of pure aluminum has been detected on the cavity surface indicating possible local melting of the matrix phase. No shear bands were detected. Penetration depth vs impact velocity data, plotted in Figures 32 and 33, compare the performance of the DURAL and DWA composites relative to their unreinforced matrices. It can be seen that the addition of ceramic particles is quite effective in stopping the penetrator. The variation of impact velocity with propellant mass for the dynamic penetration tests is given in Figure 34. Theory predictions In order to evaluate the computational capabilities of the cavity expansion model of Forrestal et al. (Appendix B), calculations were performed for each of the tests conducted. A spreadsheet program (Borland Quattro Pro) was used for the calculations. A FORTRAN program (see Appendix I) was also written to perform the necessary steps in the model computations. Sensitivity studies The principal material parameters considered in the cavity expansion model of Forrestal et al. (1988) which may affect the performance of a target are the density (p), dynamic strength (Y), elastic modulus (E) , Poisson's ratio (v), and friction coefficient (p.). As the sliding-interface friction coefficient (p.) was not measured, the values of p. used in the calculations were based on the data available in the literature. Bowden and Freitag (1958) investigated the high-velocity sliding friction between steel and aluminum using a pin-on-disk apparatus. Velocities ranging from 150 to 700 m/s were considered. As displayed in Figure 35, the coefficient of friction decreased exponentially with velocity and varied between 43 0.5 at 150 m/s and 0.1 at 700 m/s. They explained that frictional resistance is controlled by a thin molten layer of material and is thus dominated by the material with the lower melting point. More recently, Gaffney (1976) measured shear and normal forces between steel and rock for speeds up to 30 m/s and contact stresses up to 100 MPa. The coefficient of friction was shown to decrease with increasing velocity and normal stress. Montgomery (1976) also obtained similar conclusions by measuring sliding frictional resistance on gilding rotating bands during the firing of artillery projectiles. While the pin-on-disc apparatus is limited to pressure of the order of 100 MPa, the mean pressure on rotating bands is about 350 MPa, which is similar to the pressure encountered during the dynamic penetration tests. Montgomery's data are presented in the form of a n vs PV graph, where PV is the product of bearing pressure and sliding velocity. Assuming a constant pressure of 350 MPa, the PV values were converted to velocity and the results were added to Figure 35 for comparison. As shown, the initial coefficient of friction was about 0.3 but dropped rapidly to about 0.02. According to Montgomery the friction drop is caused by the formation of a molten surface film. The only source of data on friction of MMC appears to be a paper by Rana and Stefanescu (1989). Their data indicated that the friction coefficient of SiC particulate aluminum composites at low speed was smaller than that of the unreinforced matrix. The coefficient of friction was also found to be dependent on the particle size, the weight percent of SiC particles and the dispersion of the particles. For 50 micron SiC particles and 15% reinforcement mass fraction, a value of 0.24 was obtained while for the pure matrix a value of 0.63 was measured. In order to assess the relative importance of sliding friction, target elastic modulus and strength on the predictions of depth of penetration, sensitivity studies were performed by varying each of these parameters individually. The baseline case considered was the L M 6061 material impacted by the tungsten penetrator at 750 m/s. The friction coefficient was varied between 0.02 and 0.1, the Young's modulus between 70 and 130 GPa and the dynamic strength between 44 400 and 800 MPa. The predicted penetration depths were normalized with respect to the mid-range values. The friction coefficient sensitivity study is shown in Figure 36. It can be seen that as the friction coefficient is increased from 0.02 to 0.1, the penetration depth decreases by 10% which indicates that friction is an important parameter, as expected. Figure 37 shows the effect of increasing the target modulus from 70 to 130 GPa. The 85% increase in modulus gave approximately a 12% reduction in penetration depth. The range covered corresponds to the stiffening produced by the presence of 40% SiC volume fraction. The predicted depth appears to be moderately dependent on increases in the target modulus. Figure 38 shows the variation in the predicted depth due to doubling of the target dynamic strength from 400 to 800 MPa. The 100% increase in strength gave as much as a 40% decrease in penetration depth. Of the parameters considered, the target strength seems to play the most significant role in the penetration depth and hence the performance of the target material. Plots comparing the measured and calculated results for the penetration depth of the LM 6061, DURAL-15, DWA-30 and LM 7075 materials are given in Figures 39 to 42, respectively. The two curves in each figure correspond to the Jones and Hawkyard dynamic strength values. For the friction coefficient a value of p. = 0.08 was selected in order to obtain a reasonably close fit to the measured data. The fit for each material could have been improved by selecting a different value of p.. Examination of Figures 39 to 42 shows that calculations made using Jones et al. strength values underestimate the penetration depth in the cases considered. This indicates that the model of Jones et al. tends to overestimate the dynamic strength of impacted cylinders. For the prediction corresponding to the Hawkyard strength values, the overall agreement between the calculations and the experiments is seen to be reasonably close, especially at low velocities. At high velocities for the DWA-30 material, predictions based on the strength values by 45 Hawkyard overestimate the penetration depth, whereas predictions based on the strength values by Jones et al. provides a slightly better fit. To compare the relative penetration effectiveness of the four materials, the model predictions as a function of velocity are given in Figure 43. The results demonstrate the significant influence that the dynamic strength can have on the performance, especially at high velocities. The performance of the DWA-30 composite appears to be superior to that of the LM 7075-T6, even though the strength of the LM 7075 material is 13% higher than the strength of the DWA-30 material. Besides the strength, the Young's modulus is the only parameter considered by the model of Forrestal et al. (1988) which differs significantly between the two materials. As the DWA-30 is 67% stiffer than the L M 7075 material, this indicates that a large increase in Young's modulus can have a similar effect on the penetration performance as a small increase in strength. The overall accuracy of the model of Forrestal et al. (1988) can be verified by plotting the normalized penetration depth Z as a function of the non-dimensional impact parameter (1 + D), where both terms are defined in Appendix B. Equation B12 indicates that a semi-logarithmic relationship exists between Z and (1 + D) The parameter D is similar to the damage parameter defined by Johnson (1972) to predict the deformation of the target. D is a non-dimensional number formed by the ratio of the dynamic inertial pressure and the average dynamic strength of the target material. If the strength Y is replaced by the target Brinell hardness in the expression for D, the resulting non-dimensional parameter is referred to as the Metz number [Backman and Goldsmith (1978)]. The results for the penetration tests with the LM 6061, DURAL-15, DWA-30 and L M 7075 materials have been used to determine Z and (1 + D), and have been plotted on a semi-logarithmic graph in Figure 44. It can be seen that the results are in good agreement with the straight line predicted by the model of Forrestal et al. (1988) and thus confirm its applicability to predictions of aluminum-based MMC. 46 As the mass of the target is much larger than that of the penetrator, the kinetic energy of the target after impact is small. In addition since the target is sufficiently thick, there is no residual kinetic energy in the penetrator. Neglecting the energy lost into friction, heat and elastic wave propagation, and since the penetrator deforms very little, the majority of the penetrator kinetic energy is converted to strain energy (or plastic work) by radial expansion of the target material. As a first approximation, the plastic work can be calculated as the dynamic strength multiplied by the volume of the target material undergoing plastic deformation! As a minimum, this volume can be taken as the crater volume, which for a non-deforming projectile corresponds to the product of the projectile diameter and the penetration depth. As shown in Figure 45, the plastic work done is directly proportional to the initial kinetic energy (dashed line), with a slope of approximately 0.25. If the width of the plastic zone is assumed to be twice the crater diameter, then all the kinetic energy is converted in plastic work as shown in Figure 46. However, at high velocities other energy dissipating mechanisms appear to be present as the data points deviate from the straight line. Heuze' (1990) reports that the stresses induced around the penetrator decay by an order of magnitude over a radial distance of about two and a half times the projectile diameter. For the DURAL-10, DURAL-20, DWA-20 and PM 6061 materials, the model Forrestal et al. was used to back-calculate the dynamic strength of the target material. This was done in an iterative manner where Y was varied until a reasonable fit was obtained. The model predictions giving the best fit to the experimental results are shown in Figures 47 to 50. Since all the points fall on the curves, it appears that dynamic strength is the controlling parameter. The model of Forrestal et al. can therefore be used to determine the average dynamic strength of ductile target materials penetrated by non-deforming projectiles, and it can therefore be used to assess as a first approximation the strain rate sensitivity of materials. 47 Influence of volume fraction on penetration depth and dynamic strength Figure 51 illustrates the effect of volume fraction of reinforcement of the DWA and DURAL composites on the depth of penetration for the two velocities of 475 and 750 m/s. The depth values plotted correspond to predictions from the model of Forrestal et al. using the dynamic strength values back-calculated (Table 11). As shown in Figure 51, for the DWA materials, the penetration depth decreases linearly with the reinforcement volume fraction. However, for the DURAL materials, there is a plateau in the curve between 15 and 20% volume fraction. This can be explained by looking at Figure 52 where it is seen that the DURAL-20 MMC has a dynamic strength similar to that of the DURAL-15 MMC. Figure 53 shows that on the contrary the dynamic strength of the DWA MMC is much more dependent on the volume fraction of reinforcement. Influence of strain rate on strength The values obtained from the Taylor tests (Hawkyard analysis) and the ones back-calculated from the dynamic penetration tests (Forrestal et al. analysis) are summarized in Table 11. Data from Nicholas (1981) and Ross et al. (1984) for the dynamic strength of the L M 6061, LM 7075 and DWA-30 materials have also been included in Table 11. Nicholas and Ross used the tensile split Hopkinson bar technique to measure the dynamic properties. To assess the sensitivity of the dynamic strength, the dynamic strength values are plotted as a function of the logarithm of strain rate in Figure 54. For the Taylor test, the values obtained from the model of Hawkyard were used (Table 8), and the average strain rate was assumed to be 10^ s"* as computed using Equation A4. It can be seen that the LM 6061 and LM 7075 aluminum alloys are relatively insensitive to the strain rate, while the DWA-30 composite exhibits a much more pronounced strain rate sensitivity. 48 CHAPTER 5 CONCLUSIONS AND SUGGESTIONS FOR FUTURE WORK 5.1 CONCLUSIONS The following conclusions can be drawn from the experimental and analytical work carried out in the present study: 1. The quasi-static tension test results show that reinforcement volume fraction strongly influences the stiffness, strength and ductility of the MMC, as expected. 2. The Young's modulus values for both systems are in good agreement with predictions from simple two-phase theoretical models. 3. An experimental facility has been developed to study the response of materials at high strain rates. It has been used to conduct Taylor cylinder impact tests and dynamic penetration tests on semi-infinite targets. It is capable of launching specimens at velocities up to 1000 m/s and accurate measurements of the impact velocity can be made. 4. The Taylor test results obtained for the 6061-T6 aluminum were consistent with data from previous studies. 5. Limited results indicated that the rigid target Taylor test configuration provides overall specimen deformations which are similar to the ones obtained with the more difficult to perform symmetric Taylor test configuration. 6. For the MMC specimens, the Taylor test was successfully used to determine the dynamic yield strength, but the range of velocities, and therefore the range of strain rates was quite limited. When the impact velocity was too low, there was no 49 measurable deformation, whereas when the velocity was increased cracking and fracture occurred. 7. The radial inertia effect associated with the Taylor test was investigated and was found to be within the accuracy with which the dynamic strength was determined. 8. For the Taylor tests, a simple analysis showed that the local temperature rise within the specimen during deformation affects the strength values and must therefore be considered. The correction was shown to be more important for the unreinforced alloys. 9. The 30% silicon carbide PM-processed MMC (DWA-30) was found to have a pronounced strain rate sensitivity at strain rates above 10^ s~l. The unreinforced 6061-T6 and 7075-T6 alloys were found to have a moderate strain rate dependency over a range of strain rates between 10"3 to 10^ s~l. 10. The penetration performance of the MMC is better than the unreinforced matrix, and the relative improvement increases with both increasing volume fraction and impact velocity. 11. A simple closed form cavity expansion model predicted the penetration depths well when using the dynamic strength values obtained from the Taylor test. However, it cannot provide a detailed description of the target response and also makes many assumptions. 12. A sensitivity study showed that the dynamic strength is the most important material property affecting the penetration resistance. The coefficient of friction at the targetAmpactor interface also influences the penetration depth but to a lesser extent. 13. The dynamic strength determined from the Taylor tests was found to be relatively sensitive to the model used in the analysis. From the penetration analysis, the model of 50 Hawkyard (1969) was the one for which the best correlations with the experimental results were obtained. The recent model by Jones et al. (1987) appeared to overestimate the strength for most materials, except for the DWA-30 material where it provided better agreement at high velocities. 5.2 SUGGESTIONS FOR FUTURE WORK In the present work, several aspects of the impact behaviour of particle-reinforced MMC have been considered. Due to the limited scope of the study and the time available, the impact response was analyzed using one-dimensional models which predicted the overall trends reasonably well. In order to get a more accurate and detailed description of the response of MMC at high strain rates, complementary work in the following areas could be undertaken: 1. Modelling of the Taylor test and dynamic penetration test using a hydrodynamic computer code. 2. Measurement of the deformation and temperature history of a Taylor specimen using thermocouples and high speed cameras. 3. Determination of the complete stress-strain curve of the MMC at various strain rates using a technique such as at the split-Hopkinson pressure bar method. 4. Impact testing of MMC targets of various geometries such as plates of finite thickness, so that other failure mechanisms such as spalling can be investigated. 5. In addition to the dynamic deformation behaviour, the dynamic fracture behaviour should also be investigated. 51 R E F E R E N C E S Adeli H., Arnin A.M. and Sierakowski R.L.,(1986), "Earth Penetration by Solid Impactors," Shock Vibration Digest. Vol. 18, No. 9, Sept., pp. 15-22. Ahmed, S. and Jones F.R., (1990), "A Review of Particulate Reinforcement Theories for Polymer Composites", J. Mater. Sci., Vol.25, pp. 4933-4942. ASM International (1990), Metals Handbook. Tenth Edition, Vol. 2, Properties and Selection : Nonferrous alloys and Special-purpose Materials. ASTM B557-84, (1981), "Standard Methods of Tension Testing Wrought and Cast Aluminum and Magnesium - Alloy Products", ASTM Vol 3.01. ASTM D792-86, (1988) "Standard Test Methods for Specify Gravity and Density of Plastics by Displacement", ASTM Vol. 8.11. ASTM D3553-76, (1989) "Standard Test Method for Fiber Content by Digestion of Reinforced Metal Matrix Composites", ASTM Vol. 15.03. Awerbuch, J. and Hahn, H.T., (1976), "Hard Object Impact Damage of Metal Matrix Composite", J. Comp. Mat., Vol. 10, pp 231-257. Azrin, M. et al, (1982), "Dynamic Mechanical Properties of Intercritically Rolled High Hardness Steel", Mat.Sci.Eng., Vol. 53, pp.285-289. Backman, M.E., and Goldsmith, W.E., (1978), "The Mechanics of Penetration of Projectiles into Targets" Int. J. Engng Sci., 1978, Vol. 116, pp. 1-99. Balendra, R. and Travis, F. W., (1971), "An Examination of the Double-Frustum Phenomenon in the Mushrooming of Cylindrical Projectiles Upon High-Speed Impact With A Rigid Anvil", Int. J. Mech. Sci., Vol. 13, pp. 495-505. Barker, L.M., and Hollenbach, R.E., (1964), "System for Measuring the Dynamic Properties of Materials", Rev.Sci.Instr., Vol. 35, p. 742. Billington, E.W., Tate, A., (1981), The Physics of Deformation and Flow. McGraw-Hill, New York. Bishop, R.F.,et al (1945), "The Theory of Indentation and Hardness Tests", Proc. Phys. Soc, Vol. 57, Part 3, No. 321, pp. 147-159. Bowden F.P., and Freitag E.H., "The Friction of Solids at Very High Speeds: I. Metal on Metal; II. Metal on Diamond", Proc. Royal Soc. of London, Series A, Vol. 248, pp. 350-367, 1958. 52 Blazynski, T.K., Ed. (1987), Materials at High Strain Rates. Elsevier Applied Science, New York. Brooks, P.N. (1973), On the Prediction of Crater Profiles Produced in Ductile Targets hv the Impact of Rigid Penetrators at Ballistic Velocities. Defence Research Establishment Valcartier, Report DREV R-686/73. Brown, S J (1986), "Energy Release Protection for Pressurized Systems, Part II. Review of Studies into Impact/Terminal Ballistics", Appl. Mech. Rev., Vol. 39, No. 2, pp 177-201. Buchar et al (1986), Mechanical Behavior of Metals at Extremely High Strain Rates. Trans Tech. Publ. Switzerland. Byrnside, N.C., et al, (1972), "Impact Crater Formation at Intermediate Velocities", J. Bas. Eng., Trans. ASME, June, pp.394-398. Carley, D.J., (1978), A.W.R.E., Rep. 049/78 Carrington, W.E. and Gayler, M. L. V., (1948), "The Use of Flat-Ended Projectiles for Determining Dynamic Yield Stress",: III. Changes in Microstructure Caused by Deformation Under Impact at High-Striking Velocities, Proc. Royal Soc. London, Series A, Vol. 194, pp. 323-331. Dandekar, D.P., and Lopatin, C M . , (1985), "Shock Response of SiC/2014-T4 Aluminum Composite", in Shock Waves in Condensed Matter, ed. by Y.M. Gupta, Plenum Press, New York, pp.365-369. Davidson, L. et al, (1977), "Theory of Spall Damage Accumulation in Ductile Metals", J. Mech. Phys. Sol., Vol. 25, pp. 111-28. Dixon, D.G., (1990), "Spall Failure in 6061/SiC Particulate Metal Matrix Composite", Scripta Metall., Vol. 24, pp. 577-580. Dural Aluminum Composites Corp.(1989), DURALCAN MMC Data Package, May. DWA Composite Specialties, (1985), Product Data Package. Erlich D.C. et al, (1981), "Symmetric Rod Impact Technique for Dynamic Yield Strength Determination", AIP Conf. Proc. No 78 , Second Topical Conference on Shock Waves in Condensed Matter, Menlo Park, CA., pp. 402-406. Forrestal, M.J., (1986), "Penetration into Dry Porous Rock", Lit J. Solids Structures, Vol. 22, No. 12, pp. 1485-1500. Forrestal M.J., et al, (1981), "Penetration into Targets Described by Locked Hydrostats and Shear Strength", Int. J. Solids Strut., Vol. 17, pp. 915-924. Forrestal, M.J., et al, (1987), "Perforation of Aluminum Plates With Conical-Nosed Rods", J.Appl.Mech., Vol. 54, pp. 230-232. 53 Forrestal, M J . and Luk, V.K. (1988), "Dynamic Spherical Cavity-Expansion in a Compressible Elastic-Plastic Solid", J. Appl. Mech., Vol. 55, June, pp. 275-279. Forrestal, M.J.,et al, (1988), "Penetration of 6061-T651 Aluminum Targets with Rigid Long Rods", J. Appl. Mech., Vol. 55, pp. 755-760. Forsythe, G.E. et al, (1977), Computer Methods for Mathematical Computations. Prentice-Hall, pp. 163-166. Gaffney, E.S., (1976),"Measurement of Dynamic Friction Between Rock and Steel", DNA Final Report No. DNA 4161F, Systems, Sciences and Software, La Jolla, CA., NTIS # AD-A043-708. Gillis, P.P.et al, (1987), "Some Further Results on the Taylor Impact Test," Mechanics of Material, Vol. 6, pp. 293-301. Gillis, P.P. and Jones, S.E., (1989), "A Direct Correlation of Strength with Impact Velocity in the Taylor Test", J. Eng. Mater. Tech., Vol. I l l , July, pp. 327-330. Girot, F.A. et al, (1987), "Discontinuously-Reinforced Aluminum Matrix Composites", Comp. Sci. Tech.,Vol. 30, pp. 155-184. Goldsmith, W., (1960), Impact. Edward Arnold, London. Goodier J.N., (1965), "On the Mechanics of Indentation and Cratering in solid Targets of Strain-hardening Metal, by Impact of Hard and Soft Spheres", Proc. 7th Hypervelocity Impact Symp., Vol. m. AIAA, New York, pp. 215-259. Gordon, P. et al (1977), "Influence of Dynamic Yield Point in Multimaterial Impact", J.App. Phys., Vol. 48, No. 1, pp. 172-178. Gorham, D.A., (1989), "Specimen Inertia in High Strain-Rate Compression", J.Phys. D: Appl. Phys., Vol. 22, pp. 1888-1893. Grady, D.E., and Kipp, M.E., (1989), "Fragmentation of Solids under Dynamic Loading", in Structural Failure (T. Wierzbicki and N. Jones, Eds.), Wiley, New York, pp. 1-40. Gust, W.H. et al (1978), Experimental and Computer-Simulation Study of High-Velocity Impact Deformation in Preheated Materials. Lawrence Livermore Lab Report UCRL-52621, December, NTIS #AD-A067-783. Hanagud S. and Ross B., (1971), "Large Deformation, Deep Penetration Theory for a Compressible, Strain-hardening, Target Material", AIAA J., Vol 9, No. 5, pp. 905-911. Harding J., Taya M., Derby B. and Pickard S. (1987), "An Investigation of the High Strain Rate Deformation of Sic/2124 al Composite", ICCM#6, Vol. 2, edited by Mathews F.L. et al., Elsevier, pp. 2.224-2.233. 54 Hashmi, M.S. and Thompson, P.J., (1977), "A Numerical Method of Analysis for the Mushrooming of Flat-Ended Projectiles Impinging on a Flat Rigid Anvil", IntJ.Mech.Sci., Vol.19, pp. 273-283. Hawkyard, J.B., Eaton, D. and Johnson, W., (1968) "The Mean Dynamic Yield Strength of Copper and Low Carbon Steel at Elevated Temperatures from Measurements of "Mushrooming" of Flat-Ended Projectiles", Int J. Mech. Sci., Vol. 10, pp. 929-948. Hawkyard, J.B., (1969), "A Theory for the Mushrooming of Flat-Ended Projectiles Impinging on a Flat Rigid Anvil, Using Energy considerations", Int. J. Mech. Sci, Vol. 11, pp. 313-333. Heuze\ F.E. (1990), "An Overview of Projectile Penetration into Geological Materials, with Emphasis on Rocks," Int. J. Rock Mech. Min. Sci. & Geomech. Abstr. Vol. 27, No. 1, pp. 1-14. Hopkinson, B., (1905), "The Effects of Momentary Stresses in Metals", Proc. Roy. Soc. London, Vol. 74-A, pp. 498-506. House, J.W. (1989), Tavlor Impact Testing. AFATL Report TR-89-41, Sep., NTIS # AD-A215-018. Hunkler, R., (1988), Optimisation de Modeles Numeriques pour la Description du Comportement Dvnamique des Materiaux. ISL CO 258/88, NTIS # PB-90-203357. Hutchings, I.M., (1979), "Estimation of Yield Stress in Polymers at High Strain-Rates Using G. I. Taylor's Impact Technique", J. Mech. Phys. Solids, Vol. 26, pp. 289-301. Hutchings, LM. and O'Brien, T.J., (1981), "Normal Impact of Metal Projectiles Against a Rigid Target at Low Velocities", Int.J.Mech.Sci.,Vol. 23, pp. 255-261. Hutchings, I.M., (1982), "The Behavior of Metals Under Ballistic Impact at Sub-Ordnance Velocities", in Materials Behaviour Under High Stress and Ultrahigh Loading Rates. J.Mescall et al. Ed., Plenum, New York, pp. 161-196. Ishai, O., (1965), Mag.Concr.Res., Vol. 17, No. 52, pp.148-149. Johnson, G. and Cook W.H., (1985), "Fracture Characteristics of Three Metals Subjected to Various Strains, Strain Rates, Temperatures and Pressures", Eng. Fract. Mech., Vol. 21, No. 1, pp. 31-48 Johnson, W., (1972), Impact Strength of Materials. Arnold, London. Jones, R.M.,(1975), Mechanics of Composite Materials. McGraw-Hill. Jones, S.E.,et al, (1987), "On the Equation of Motion of the Undeformed Section of a Taylor Impact Specimen," J. Appl. Phys., Vol. 61, 1987, pp. 499-502, and Erratta, Vol. 64, No. 4, 1988, p. 2249. 55 Kawata, K. et al, (1977), "Analysis of High Velocity Tension of Bars of Finite Length of BCC and FCC Metals with Their Own Constitutive Equations", in High Velocity Deformation of Solids. IUTAM Symp.1977, Springer-Verlag, pp. 1-15. Kennedy, R P (1976), "A Review of Procedures for the Analysis and Design of Concrete Structures to Resist Missile Impact Effects", Nucl.Eng.Des., Vol. 37, pp. 183-203. Kjar, A.R. et al, (1989), "Particle Reinforced Aluminium-Based Composites", in Light-Weight Alloys for Aerospace Applications. E.W. Lee et al, eds., The Minerals, Metals, Materials Soc. pp. 273-288. Kolsky, H., (1949), "An Investigation of the Mechanical Properties of Materials at Very High Rates of Loading", Proc. Roy. Soc, B, Vol. 62, p. 676. Kuscher, G.F., (1985), Nonlinear Propagation of Elastoplastic Waves in KE Penetrators. Ernst-Mach-Inst., Report 2/85, NTIS DE85011450 Lankford, J., (1981), "Mechanisms Responsible for Strain-Rate-Dependent Compressive Strength in Ceramic Materials", Communications American Ceramic Society, Feb., pp. C33 -C34. Lee, E.H. and Tupper, S. J., (1954), "Analysis of Plastic Deformation in a Steel cylinder Striking a Rigid Target", J. Appl. Mech., Vol. 21, March, pp. 63-70. Lindholm, U.S., (1971), "High Strain Rate Tests", in Techniques of Metals Research. R.F. Bunshah, Ed., Vol. 5, Part I, Wiley, pp. 199-271. Lips, H.R. et al, (1987), "Dynamic Behaviour and Properties of Heavy Metals - Experimental Approach to Separation of Parameters in the Johnson-Cook Constitutive Model", Proc. 10th Int.Symp.Bal., San Diego, CA. Liu, D.S.et al, (1989), "Effects of Superimposed Hydrostatic Pressure on the Fracture Properties of Particulate Reinforced Metal Matrix Composites", Script. Metall.,Vol. 23, pp. 253-256. Longcope D.B. and Forrestal M.J., (1983), "Penetration of Targets Described by a Mohr-Coulomb Failure Criterion with a Tension Cut-off', J.Appl.Mech.,Vol. 50, pp. 327-333 . Luk V.K. and Forrestal M.J., (1987), "Penetration into Semi-infinite Reinforced Concrete Targets with Spherical and Ogival Nose Projectiles", IntJ.Impact Engng, Vol. 6, pp. 291-301. Macaulay, M., (1987), Introduction to Impact Engineering. Chapman and Hall, London. Marchand, A., et al,(1988), "An Experimental Study of the Dynamic Mechanical Properties of an Al-SiC Composite", Eng. Frac. Mech., Vol. 30, No. 3, pp.295-315. Marinaro, D.E., et al, (1989), "Characterization of 2519-T87 Aluminum Armor Alloy for Numerical Simulation of Ballistic Phenomena", Alcoa report RR-607. 56 Montgomery, R.S., (1976), "Friction and Wear at High Sliding Speeds", Wear, Vol. 36, pp. 275-298. Muzychenko, V.P. and Postnov, V.I., (1986), "Comparative Tests on Materials in High-Speed Impact with Penetration (Review)", Zav. Lab.,Vol. 52, No. 5, May, pp.70-77. Nardonne, V.C. (1987), "Assessment of Models Used to Predict the Strength of Discontinuous Silicon Carbide Reinforced Aluminum Alloys", Script Metall., Vol. 21, No. 10, pp. 1313-1318. Nicholas, T. (1981), "Tensile Testing of Materials at High Rates of Strain", Exper. Mech., May, p.177-185. Niordsen, F.L, (1965), "A Unit for Testing Materials at High Strain Rates", Exp. Mech., Vol. 5, pp.29-32. Norwood, F.R., (1974), "Cylindrical Cavity Expansion in a Locking Soil", Sandia Laboratory Report SLA-74-0201, Jul., 34p. Norwood, F.R. and Sears, M.P., (1982), "A Nonlinear Model for the Dynamics of Penetration in Geological Targets", J.Appl.Mech., Vol. 49, pp. 26-30. Papirno, R.P. et al, (1980), "Beyond the Taylor Test to Fracture", in Proc. of Army Symp. on Solids Mech. 1980, AMMRC MS 80-4, Sept., pp. 367-385, NTIS # AD-A090-684. Paul, B., (1960), Trans. Amer. Inst. Mech. Eng., Vol. 36, p. 218. Paulus, G., (1986), "Taylor-Type Formulas for the Determination of an Average Dynamic Flow", Rapport ISL R 136/86, NTIS # PB88-148713. Pickard, S.M. et al (1988), "Strain Rate Dependence of Failure in 2124 Al/SiC Whisker composite," Scripta Metall, Vol. 22, pp. 601-606. Raftopoulos, D. and Davids, N. (1967), "Elastoplastic Impact on Rigid Targets", AIAA Journal, Vol. 5, No. 12, December, pp. 2254-2260. Raftopoulos, D., (1969), "Longitudinal Impact of Two Mutually Plastically-Deformable Missiles", IntJ.Sol.Str., Vol. 5, pp. 399-412. Rana, F. and Stefanescu, (1989), "Friction Properties of Al-1.5 Pet Mg/Sic Particulate Metal-Matrix Composites", Met. Trans. A, Vol. 20A, August, pp. 1564-1566. Recht, R.F., (1978), "Taylor Ballistic Impact Modelling Applied to Deformation and Mass Loss Determinations", Int. J. Engng.Sci., Vol. 16, pp. 809-827. Regnauld, M.P., (1936), "Note sur la d6formation d'un projectile lanc6 contre un mur indeformable", Mem. Art. Franc, Vol. 15, pp. 1-2. Riera, J.D., (1989), "Penetration, Scabbing and Perforation of Concretes Structures Hit by Solid Missiles", Nucl. Eng. Des., Vol. 115, pp. 121-131. 57 Roebuck, B., Gorley T. and McCartney L. (1989), "Mechanical Property Test Procedures for Metal Matrix Composites", Mater. Sci. Techn., Feb., Vol. 5, pp. 105-117. Ross, C.A., (1971), "Studies on Dynamic Compression of Composite Materials", Ph.D. Dissertation , University of Florida, March. Ross, C.A., Sierakowski, R.L., and Sun, C.T., (1985), Dynamic Response of Composite Materials. 2nd Ed., Soc. Exp. Mech., ISBN No. 0-912053-05-4. Ross, C.A., Cook W.H. and Wilson L.L. (1984), "Dynamic Tensile Tests of Composite Materials Using a Split-Hopkinson Pressure Bar", Exper. Techn., Vol. 8, No. 11, Nov., pp. 30-33. Schuster, D.M.,and Reed, R.P., (1969), "Fracture Behavior of Shock-Loaded Boron-Aluminum Composite Materials", J.Comp.Mat., Vol.3, pp. 562-576. Schwer, L.E., et al (1988), "An Axisymmetric Lagrangian Technique for Predicting Earth Penetration Including Penetrator Response," Int. J. Num. Anal. Meth. Geo., Vol. 12, pp. 235-262. Shockey, D.A., et al, (1985), Development of Improved Dynamic Failure Models. SRI Int., NTIS #AD-A 155 586. Sierakowski, R.L., (1988), "High Strain Rate Testing of Composites", in Dynamic Constitutive/Failure Models (A.M. Rajendran and T.Nicholas, Eds.), AFWAL-TR-88-4229, Wright-Patterson Air Force Base, OH. Sliter, G.E., (1980), "Assessment of Empirical Concrete Impact Formulas", ASCE, J.Struct.Div., May., Vol. 106, pp. 1023-1045. Staker, M.R., (1985), "High Strain Rate Testing", in Metals Handbook. 9th ed., Vol. 8, Mechanical Testing, American Society for Metals, Metals Park, pp. 185-297. Sundararajan, G. and Shewmon, P.G., (1983), "The Use of Dynamic Impact Experiments in the Determination of the Strain Rate Sensitivity of Metals and Alloys", Acta metall., Vol.31, pp. 101-109. Taya, M., Arsenault, R.J. (1989), Metal Matrix Composites Thermomechanical Behaviour. Pergamon Press, Oxford. Taylor, G.I., (1946), "The Testing of Materials at High Rates of Loading", J. Inst. Civil. Eng., No.5, pp. 486-519 Taylor, G.I., (1948), "The Use of Flat-Ended Projectiles for Determining Dynamic Yield Stress",: I. Theoretical Considerations, Proc. Royal Soc. London, Series A, Vol. 194, pp. 289-299. Ting, T.C.E., (1966), "Impact of a Nonlinear Viscoplastic Rod on a Rigid Wall", J.Appl.Mech., Sept., pp. 505-513. 58 Tirupataiah, Y., and Sundararajan G.„ (1991), "A Dynamic Indentation Technique for Obtaining the Characterization of the High Strain Rate Plastic Flow Behaviour of Ductile Metals and Alloys", J.Mech.Phys.Solids, Vol. 39, No.2, pp. 243-271. Tsangarakis, N., Andrews, B.O. and Cavallaro C , (1987), "Mechanical Properties of Some Silicon Carbide Reinforced Aluminum Composites", J.Comp.Mat., Vol. 21, May, pp. 481-492. Vasudevan, A.K., Richmond, O., Zok, F. and Embury, J.D. (1989), "The Influence of Hydrostatic Pressure on the Ductility of Al-SiC Composites", Mater. Sci. Eng. A107, pp. 63-69. Vaziri, R., Pageau, G. and Poursartip A., (1989), Review of Computer Codes for Deep Penetration Modelling of Metal Matrix Composite Materials. Report, Dept. Metals & Materials Eng., U.B.C., December. Vaziri, R. and Poursartip, A., (1991), Final contract report, University of British Columbia (in preparation). Walters, W.P., Zukas, J.A. (1989), Fundamentals of Shaped Charges. New York, Wiley-Interscience. Whiffin, A.C., (1948), "The Use of Flat-Ended Projectiles for Determining Dynamic Yield Stress,: n. Tests on Various Metallic Materials", Proc. Royal Society, London, Series A, vol. 194, pp. 300-322. White, M.P., (1984), "Impact Force of Rigid-Plastic Missile", J.AppLMech., Vol. 51, pp.102-106. Wilkins, M.L. and Guinan, W., (1973) "Impact of Cylinders on a Rigid Boundary", J. Appl. Phys., Vol. 44, No. 3, March., pp. 1200-1206. Woodward, R.L., and Lambert, J.P., (1981), "A Discussion of the Calculation of Forces in the One-Dimensional Finite Difference Model of Hashmi and Thompson", IntJ.Mech.Sci., Vol. 23, No. 8, pp. 497-501. Woodward, R.L. (1982), "Penetration of Semi-Infinite Metal Targets by Deforming Projectiles, "International Journal of Mechanical Sciences, Vol. 24, No. 2, pp. 73-87. Zukas, J.A. et al, (1982), Impact Dynamics. Wiley-Interscience, John Wiley and Sons, New York. Zukas, J.A., ed. (1990), High Velocity Impact Dynamics. Wiley, New York. 59 APPENDICES APPENDIX A ANALYTICAL MODELS FOR DYNAMIC STRENGTH The symbols used in this appendix are illustrated in Figure 55. Model of Regnauld (1936) The dynamic yield strength is: pV2 IMLQlLf) (Al) The mean strain is: em = ln (A2) Model ofTavlor (1946) YT = pV2 \(L0-X)) 2ln(L0IX)\(L0-Lf)\ (A3) If a depression in the target surface occurs during impact, then Ly must be replaced by (Lj -d) , where d is the depth of the depression. The mean strain rate during the test can be estimated as: V e = 2(L0-X) (A4) The mean strain is: Model ofTavlor (1948) YTC = 2YT L0-X I In (A5) (1-XILQ) ln(L0IX) (A6) 60 This correction formula is for length shortening ratios close to 1, that is for low impact velocities. At high velocities, it corresponds to an upper bound. Model pf Hawkyard (19(19) pV2 r r i l ) 2 Un (A7) where EQ is a measure of plastic strain defined as: E0 = l-X/L0 (A8) If measurements of X are not available, the quantity EQ can be determined implicitly in terms of the geometry of the test-piece by the following expression: j^=(l-E0)[l-ln(l-e0)J Model of Wilkins and Guinan (1973) YW = -pV2 2 In 1 - HILQ LJILQ - h!L0 where h=Lf-X, and h/LQ = 0.12. To obtain the length shortening ratio, equation A10 can be rewritten as: M. The mean strain is expressed as: exp pV2' 2Y. L0 L0-h Model of Tones etal(1987) [Lf-h pV2f3 (A9) (A10) (All) (A12) (A13) 61 where e0 is defined in Equation A8, and P .which corresponds to the plastic wave velocity in a nondimensional form, is given by the following transcendental equation: (i + fro) (1 + In .(1 + P). + ( l -Eo) (A14) 62 APPENDIX B EQUATIONS OF CAVITY EXPANSION MODEL The symbols used in this Appendix for the development of the model are illustrated in Figure 56. The incremental axial penetration resistance force {dF^ is given by: dFz = dFncosQ + dFfinQ (Bl) w h e r e : dFn=2nRonadQ (B2) dFt = \idFn (B3) R = a sin 8 (B4) and an is the normal stress on the nose induced by target resistance, u. is the sliding friction coefficient at the projectile/target interface, and other symbols are defined in Figure 56. The normal stress on the spherical nose depends on the rigid body velocity Vz and for an elastic-plastic , spherically symmetric, cavity expansion analysis [Forrestal and Luk (1988)] is approximated as: cn = (2/3)Y S + IMlpiVzCosQ)2 (B5) where S is defined as: f R 1 (B6) S = 1 + ln where Y, E, v and p are the dynamic strength, elastic modulus, Poisson's ratio and density of the target material respectively. In equation (B5), the first term corresponds to the finite pressure required to open a spherical hole quasi-statically from an initial radius of zero. The second term accounts for inertial effects. Substituting Equation B5 into Equation B l and integrating from 0 to K/2 yields: Fz = a s + p s V z 2 (B7) where a s = (2/3)na2 YS(l+im/2) (B8) f3s = 1.041(ua2 p/2)(1+\m/4) (B9) 63 Applying Newton's second law of motion gives: Fz = m(dVz/dt) = mV^dVJdz) (BIO) where m is the projectile mass and z is the current penetration depth. Introducing Equation B7 into Equation BIO and integrating from VZ = VQ to VZ = 0, gives: m P=^ln[l + VSV(f/as] where P is the final penetration depth and VQ is the impact velocity. Equation B l l can be rearranged in a nondimensional form as: Z = ln(l + D) 2P$S (Bll) where: and Z = m D = VsV(?/as (B12) (B13) (B14) The term (1+D) is defined as the impact parameter, and Z corresponds to the normalized penetration depth. The mass of the projectile can be expressed as: m = ppita2Lp (B15) where pp is the projectile density and Lp represents an effective projectile length, that is the length of a right circular rod having the same mass as the spherical nose projectile. From Equations B9 and B15, Z can be expressed as: Z = Cj p -2. [hi [pp\ (B16) where Cj is a constant The term D (Equation B14) can also be simplified if it is assumed that S (Equation B6) is a constant for aluminun based alloys. Using Equations B8 and B9, D can be expressed as: D = C2 pV2 (B17) where C2 is a constant. 64 APPENDIX C SURVEY OF MMC MATERIAL SUPPLIERS Advanced Composite Materials Corp. Mr. J.L. Cook, Vice President 1525 S. Buncombe Rd. Greer, S.C. 29651-9208 USA Alcan International Ltd. Research & Development Banbury Laboratories Southam road, Banbury Oxon, OX16 7SP Alcan International Limited Kingston R&D Centre P.O. Box 8400 Kingston, Ont., Canada, K7L 4Z4 Aluminum Company of America (Alcoa) Dr. R.R. Sawtell, Manager Innometalx Alcoa Center, Pennsylvania 15069, USA Avco Specialty Materials Subsidiary of Textron Inc. 2 Industrial Avenue Lowell, MA 01851 USA BP Metal Composites Limited Mr. D.J. Griffiths, European Sales Manager, RAE Road Farnborough, Hampshire GU14 6XE United Kingdom Cegedur-Pechiney CRV-Centr'Alp B. P. / 38340 Voreppe France C. Itoh Co. Canada Ltd. World Trade Center, Suite 770-999 Canada Place Vancouver, B.C. V6C 3E1 Comalco Research Centre Dr. A.R. Kjar 15 Edgars Road Thomastown ,Victoria, Australia 65 DOW Chemicals and Metals Department Midland, Michigan 48674 USA Dural Aluminum Composites Corporation Mr. Carol Watson, Manager 10505 Roselle Street3 San Diego, CA 92121 USA DWA Composite Specialties Inc. Mr. J.F. Dolowy, President 21119 Superior Street Chatsworth, CA 91311-4393 USA Kobe Steel Ltd. Materials Research Laboratory 3-18,1-chome, Wakinohama-cho, Chuo-ku Kobe, Japan Lanxide Corporation Dr. M.J.Hollins, Vice President One Tralee Industrial Park Newark, DE 19714-6077 USA Mitsubishi International Corp. Petroleum Div. 520 Madison Ave., 19th Fl. New York, NY 10022 USA SOURCES: Schoutens, J.E., and Dolowy, J.F. (1985), "Guide to Metal Matrix Composite Material Suppliers and Fabricators and Their Products", MMCIAC Directories and Guides Series MMCIAC No. 000666. Weeton, J.W., Peters, D.M. and Thomas K.L., (1987), "Engineers' Guide to Composite Materials" American Society of Metals. Materials Engineering (1989), "Material Selector" December. De Renzo D.J. (ed.) (1988), "Advanced Composite Materials Products and Manufacturers", Noyes Data Corp. 66 APPENDIX D TUNGSTEN PENETRATQR MATERIAL PROPERTIES Material Sintered Tungsten alloy X21-C swaged 20% Supplier Teledyne Firth Sterling Composition 92.9W, 1.3Fe, 3.7Ni, 1.8 (weight %) Co Grain diameter 20 (micron) Density 17.73 (Mg/m3) Hardness 39.5 (HRC) Young's modulus 324 (GPa) Poisson's ratio 0.303 Tensile yield strength 1215 (MPa) Ultimate tensile strength 1237 (MPa) Elongation 13 (%) 67 APPENDIX E RADIOGRAPHIC SPECIFICATIONS Performed at: Bacon Donaldson & Associates Ltd 12271 Horseshoe Way Richmond, B.C., Canada V7A 4Z1 Source X-Ray/IRI-192 Fikm Type Kodak AA Film density 1.2 Film size B (11.4x21.6 cm) Source-fillm distance 107 cm Voltage 130 KVP at 3 mA Exposure time 4.25 min. Front lead screen thickness 0.13 mm Back lead screen thickness 0.25 mm 68 APPENDIX F CHEMICAL COMPOSITIONS Chemical composition (weight %) of 6061 aluminum matrix used in DURAL MMC Material DURAL-10 (W6A-10A) DURAL-15 (W6A-15A) DURAL-20 (W6A-20A) Elements Silicon 0.64 0.65 0.67 Iron 0.15 0.16 0.07 Copper 0.26 0.266 0.28 Manganese 0.003 0.003 0.004 Magnesium 0.92 1.01 1.02 Chromium 0.10 0.098 0.11 Zirconium 0.008 0.012 0.01 Titanium 0.01 0.011 0.009 Heat treatment: solution heat treated 560 °C, 2 hours water quench 27 °C, 8 seconds aged 160 °C, 16 hours Source: DURAL data package. 69 APPENDIX G COMPUTER PROGRAM FOR TAYLOR TEST ANALYSIS C PROGRAM "TAYLOR" C WRITTEN BY Gilles Pageau UBC C DOUBLE PRECISION AX,BX,BETA,TOL,ZEROIN DOUBLE PRECISION ALPHA,LAMDA,YJ,YT,YTC,YR,YW,YH DOUBLE PRECISION Kl,K2,El,E2,E,TOLE DOUBLE PRECISION U,RHO,L,LF,X,K,STRAIN,RATE C COMMON /BLK1/L,LF,X,K EXTERNAL F EXTERNAL G C DATA INPUT WRiTE(*,l) 1 FORMAT(/ RHO(g/cm3), U(m/s), L(mm), LF(mrn), X(mm) = TJI) READ(*,2) RHO,U,L,LF,X 2 FORMAT(5F15.5) RHO=RHO*1000. L=L/1000. LF=LF/1000. X=X/1000. C JONES ANALYSIS (ALPHA-BETA) C K=l-X/L AX=.20 BX=9.9 TOL=1.0D-6 BETA=ZEROIN(AX,BX,F,TOL) C ALPHA=(L-X)/(BETA*L) LAMDA=BETA*U YJ=RHO*U*U/(ALPHA* 1.0D6) C TAYLOR ANALYSIS C YT=RHO*U*U*(L-X)/(2.0D6*(L-LF)*DLOG(L/X)) STRAIN=(L-LF)/(L-X) RATE=.5*U/(L-X) C C * CORRECTED FORMULA * Kl=l/(1-X/L) 70 K2=l/DLOG(L/X) YTC=2.*YT*(K1-K2) C C REGNAULD ANALYSIS C YR=RHO*U*U/(2.D6*DLOG(L/LF)) C C WILKINS ANALYSIS C YW=RHO*U*U/(2.D6*DLOG(.88/((LF/L)-.12))) C C HAWKYARD ANALYSIS C El=.001 E2=.999 T0LE=lD-8 E=ZER0IN(E1,E2,G,T0LE) YH=RHO*U*U/(2.D6*(DLOG(l/(l-E))-E)) C C RESULTS OUTPUT WRiTE(*,99) 99 FORMATC ******************************************************') WRTTE(*,8) 8 FORMATC -JONES') WRiTE(*,3) 3 FORMATC YJ(MPa) ALPHA BETA LAMDA') WRiTE(*,2) YJ,ALPHA,BETA,LAMDA WRiTE(*,9) 9 FORMATC -TAYLOR') WRiTE(*,4) 4 FORMATC YT(MPa) YTC(MPa) STRAIN RATE') WRTTE(*,2) YT,YTC,STRAIN,RATE WRiTE(*,5) 5 FORMATC YR(MPa) -REGNAULD') WRITE(*,2) YR WRITE(*,6) 6 FORMATC YW(MPa) -WILKINS') WRITE(*,2) YW WRiTE(*,7) 7 FORMATC YH(MPa) E(strain) -HAWKYARD") WRTTE(*,2) YH,E WRiTE(*,99) C STOP END C C DOUBLE PRECISION FUNCTION F(B) 71 DOUBLE PRECISION B,L,LF,X,K COMMON /BLK1/L,LF,X,K C C JONES ALPHA-BETA MODEL C F=((LF-X)/L)-(B*K*K/(l+B*K))+(B*X*K/(L*(l+B*K)**2))*DLOG(B*X/(L*(l &+B))) RETURN END C DOUBLE PRECISION FUNCTION G(E) DOUBLE PRECISION E,L,LF,X,K COMMON /BLK1/L,LF,X,K C C HAWKYARD MODEL C G=LF-L*(l-E)*(l+DLOG(l/(l-E))) RETURN END C C DOUBLE PRECISION FUNCTION ZEROIN(AX,BX,F,TOL) DOUBLE PRECISION AX,BX,F,TOL C SOLUTION OF NONLINEAR EQUATIONS C A ZERO OF THE FUNCTION F(X) IS COMPUTED C IN THE INTERVAL AX,BX C AX = LEFT ENDPOINT OF INTERVAL C BX = RIGHT ENDPOINT OF INTERVAL C F = FUNCTION SUBPROGRAM C TOL= TOLERANCE ON SEARCH C FROM THE BOOK "COMPUTER METHODS FOR MATHEMATICAL C COMPUTATIONS" BY FORSYTHE et al. PAGES 164-166. C DOUBLE PRECISION A,B,C,D,E,EPS,FA,FB,FC,TOLl,XM,P,Q,R,S C C COMPUTE EPS,(COMPUTER PRECISION) C EPS=1.0 10 EPS=EPS/2.0 TOL1=1.0+EPS IF(TOL1.GT.1.0) GO TO 10 C C INITIALIZATION C A=AX B=BX FA=F(A) FB=F(B) 72 c C BEGIN STEP 20 C=A FC=FA D=B-A E=D 30 IF(DABS(FC).GE.DABS(FB)) GO TO 40 A=B B=C C=A FA=FB FB=FC FC=FA C C CONVERGENCE TEST 40 TOL1=2.0*EPS*DABS(B)+0.5*TOL XM=.5*(C-B) IP(DABS(XM).LE.TOLl) GO TO 90 IF(FB.EQ.O.O) GO TO 90 C C IS BISECTION NECESSARY ? IF(DABS(E).LT.TOLl) GO TO 70 IF(DABS(FA).LE.DABS(FB)) GO TO 70 C C IS QUADRATIC INTERPOLATION POSSIBLE ? IF(A.NE.C) GO TO 50 C C LINEAR INTERPOLATION S=FB/FA P=2.0*XM*S Q=1.0-S GO TO 60 C C INVERSE QUADRATIC INTERPOLATION 50 Q=FA/FC R=FB/FC S=FB/FA P=S*(2.0*XM*Q*(Q-R)-(B-A)*(R-1.0)) Q=(Q-L0)*(R-1.0)*(S-L0) C C ADJUST SIGNS 60 IF(P.GT.O.O) Q=-Q P=DABS(P) C C IS INTERPOLATION ACCEPTABLE ? IF((2.0*P).GE.(3.0*XM*Q-DABS(TOL1*Q))) GO TO 70 IF(P.GE.DABS(0.5*E*Q)) GO TO 70 E=D 73 D=P/Q GO TO 80 C C BISECTION 70 D=XM E=D C C COMPLETE STEP 80 A=B FA=FB IF(DABS(D).GT.TOLl) B=B+D IF(DABS(D).LE.TOLl) B=B+DSIGN(TOLl,XM) FB=F(B) IF((FB*(FC/DABS(FC))).GT.0.0) GO TO 20 GO TO 30 C 90 ZEROIN=B RETURN END 74 APPENDIX H X-RAY PHOTOGRAPHS LM 6061-T6(V = 461 m/s) LM6061-T6(V = 727 m/s) 75 DWA-30 (V = 474 m/s) 76 DWA-30 (V = 920 m/s) LM 7075-T6 (V = 766 m/s) 77 APPENDIX I COMPUTER PROGRAM FOR PENETRATION DEPTH PREDICTION C PROGRAM "FORRESTAL" C DOUBLE PRECISION VI,M,D,RHO,E,U,Y,F,K,PI,A,B,AS,P,Cl,C2 C PI=3.141592654 C WRrTE(*,10) 10 FORMATC IMPACT VElX)CrTY(rn/s) ?') 1 FORMAT(F15.6) READ(*,1) VI WRrTE(*,20) 20 FORMATC PROJECTILE MASS(g) ?') READ(M) M WRITE(*,30) 30 FORMATC PROJECTILE DIA.(mm) ?') READCU) D WRITE(*,40) 40 FORMATC TARGET DENSJTY(g/cm3) ?') READ(*,1) RHO WRITE(*,50) 50 FORMATC TARGET YOUNG MODULUS(GPa) t) READ(*,1) E WRITE(*,60) 60 FORMATC POISSON RATIO ?') READ(*,1) U WRTTE(*,70) 70 FORMATC TARGET STRENGTH(MPa) ?') READCU) Y WRITE(*,80) 80 FORMATC FRICTION COEF. (.02-. 10) ?') READ(*,1) F C M=M/1000. C R=RADIUS R=D/(2*1000.) RHO=RHO*1000. E=E*1E9 Y=Y*1E6 C K=BULK MODULUS K=E/(3*(1-2*U)) C1=(1-2*U)*K 78 C2=(1-U)*Y C AS=(2*Y/(3*K))*(l+DLOG(Cl/C2)) A=PI*R*R*K*AS*(1.+(.5*PI*F)) B=.5*PI*R*R*RHO*1.041*(1.+(.25*PI*F)) P=(1000.*M/(2*B))*DLOG(l+(B*VI*ViyA)) C WRrTE(*,90) 90 FORMATC PENETRATION DEPTH(rnrn)=') WRITE(*,2) P 2 FORMAT(2X,F8.2) C STOP END 79 T A B L E S Table 1 Typical Properties of Ceramic Particulate Reinforcements Reinforcement type Alumina (AI2O3) Boron carbide ( B 4 C ) Silicon carbide (SiC) Silicon nitride ( S i 3 N 4 ) Shape platelet platelet platelet/brick whisker Mean diameter (micron) 1-3 50-100 5-20 0.5-1 Aspect ratio 10-50 1-5 Specific heat J/kgK 1300 1200 Melting point °C 2100 2450 2700 1900 Knoop hardness kg/mm^ 1800 2800 2700 Density Mg/m^ 3.98 2.52 3.21 3.18 Young's modulus GPa 270 460 440 200 Poisson's ratio 0.25 0.21 0.15 0.27 Average strength MPa 3000 2000 4000 5000 Dynamic strength MPa(l) 3500 5500 (1) [Lankford (1981)] (103 s'1) 80 Table 2 High Strain Rate Measurement Techniques Apparatus (Investigator) Mode Strain Rate Max. Strain Pressure Parameters Determined Remarks (V = speed in m/s) Split Hopkinson Bar (Kolsky, 1949) Compression 102 -104 increasing Moderate (< 0.50) Friction effects Low y(e,p,7)at various strain rates Simple test and analysis V=50 Direct compression 104 -105 Large (1.00) Low y(e,D Friction and inertia effects Tension 102-104 Small (necking) Low Y(e,p, T) and failure strain Strain Rate not constant Torsion/Shear 102-104 Large (1.00) No dispersion and inertia effects Low t(7) Modulus and Yield strength hard to measure Taylor Impact (Taylor, 1946) Compression 104-105 decreasing Large (1.00) Moderate Y Simple test V = 300 Expanding Ring (Niordsen, 1965) Tension 105 decreasing Moderate (failure) Low Non uniform strain Plate Impact (Barker, 1964) Compression/ Tension (plane impact) 105 -107 Small (plane strain) High Hugoniot Elastic Limit (HEL) spall strength Difficult to perform, need laser interferometer Shear (oblique impact) 105-107 Small High t(y) Very complex Table 3 Characteristics of Materials Used in This Work Material designation Matrix material Condition Reinforce ment type Reinforce ment vol % Process Supplier Cost $/kg PM6061 A16061 T6 PM DWA Company 200 LM6061 A16061 T6 L M 2 DURAL-10 (DURALCAN W6A-10A) A16061 T6 A1 2 0 3 11.4 L M DURAL Aluminun Company 7 DURAL-15 (DURALCAN W6A-15A) A16061 T6 A1 2 0 3 15.5 L M DURAL Aluminun Company 7.75 DURAL-20 (DURALCAN W6A-20A) A16061 T6 A 1 2 0 3 21.6 L M DURAL Aluminun Company 8.25 DWA-20 A16061 T6 SiC 18.9 PM DWA Company 200 DWA-30 A16061 T6 SiC 31.4 PM DWA Company 200 L M 7075 A17075 T6 L M 3 Note: All materials extruded in 50 mm diameter bars. Extrusion ratio of 7/2 used for DURAL materials. PM indicates powder metallurgy process route, L M indicates liquid metallurgy route. The unreinforced PM 6061 material was processed in a similar manner to the DWA-20 and DWA-30 materials. 82 Table 4 Matrix of Tests Performed Material designation Static tensile test Taylor impact test Deep penetration test PM6061 X LM6061 X X X DURAL-10 X DURAL-15 X X DURAL-20 X DWA-20 X DWA-30 X X X L M 7075 X X 83 Table 5 Material Properties of Selected Particle-reinforced MMC Material Density Young's Poisson's 0.2% Yield Ultimate Fracture (Mg/m3) modulus (GPa) ratio (1) strength (MPa) tensile strength (MPa) strain (%) PM6061 2.72 (6) 74 0.33 357 386 13.5 (3) LM6061 2.70 70 0.33 312 332 22.0 (4) DURAL-10 2.81 81 0.32 296 338 ' 7.6 (2) DURAL-15 2.86 88 0.32 317 359 5.4 (2) DURAL-20 2.94 98 0.31 359 379 2.1 (2) DWA-20 2.80 (6) 103 0.29 394 428 5.3 (3) DWA-30 2.85 (6) 132 0.27 370 461 1.9 axial (4) DWA-30 2.85 (6) 122 0.27 389 440 1.5 radial (4) L M 7075 2.80 71 0.33 503 572 11.3 (5) (1) Determined from rule-of-mixture (2) Properties from Dural data package (3) Properties from DWA data package (4) Average values from tension tests (5) Properties from ASM Metals Handbook, 10th Ed., Vol. 2. (6) Vaziri and Poursartip (1991) 84 Table 6 Taylor Impact Test Results Material Spec.# V (m/s) h (mm) Lf (mm) X (mm) (MPa) YT (MPa) YTC (MPa) YH (MPa) Yw (MPa) Yj (MPa) L M 6061 T4 162 23.18 21.34 10.86 0.921 430 314 353 384 376 460 ST2 171 (*) 23.19 21.23 10.28 0.915 449 321 364 399 392 487 T5 248 23.19 19.45 8.59 0.839 474 328 381 407 412 483 T6 261 23.18 19.22 9.93 0.829 493 364 415 422 428 452 DURAL-15 T13 156 23.08 21.73 11.54 0.942 571 425 473 517 500 622 T15 173 23.14 21.53 11.37 0.930 587 436 487 528 514 629 TJ1 189 23.22 21.22 11.46 0.914 561 421 470 499 491 577 T14 195 23.09 21.17 11.08 0.917 620 458 514 552 542 651 DWA-30 T17 137 23.14 22.32 12.95 0.965 741 573 628 685 651 811 T16 144 23.14 22.22 12.46 0.960 728 554 611 670 639 802 TJ2 181 23.16 21.52 12.78 0.929 636 497 546 571 556 639 L M 7075 T9 180 23.18 21.93 13.43 0.946 818 648 707 743 717 838 T10 207 - 23.18 21.72 14.98 0.937 922 772 828 832 808 853 T8 212 23.18 21.50 12.10 0.928 839 641 710 753 735 866 T12 233 23.19 21.16 11.71 0.912 830 629 700 737 725 840 V = Impact velocity LQ = initial length Ly= final length X = undeformed length YR = Dynamic strength using model of Regnauld (1936) Yj= Dynamic strength using model of Regnauld Taylor (1946) YJQ = Dynamic strength using model of Regnauld Taylor(1948) Yfj = Dynamic strength using model of Regnauld Hawkyard (1969) Yyy = Dynamic strength using model of Regnauld Wilkins and Guinan (1973) Yj - Dynamic strength using model of Regnauld Jones et (1987) (*) = Symmetric Taylor test Table 7 Shadowgraph Profile Data for Taylor Specimens Material LM6061 DURAL-15 DWA-30 axial DWA-30 radial LM7075 Spec. # T5 T14 T17 T16 T8 Velocity (m/s) 248 195 144 137 212 r (mm) 5.779 5.779 5.779 5.779 5.779 / (mm) dRj dR2 dRj dR 2 dRj dR2 dRj dR2 dRj dR2 (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) (mm) 0.00 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 1.25 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 2.50 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 3.75 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 5.00 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 6.25 0.000 0.015 0.000 0.000 0.000 0.000 0.000 0.000 0.000 0.000 7.50 0.015 0.030 0.010 0.000 0.000 0.000 0.000 0.000 0.000 0.000 8.75 0.030 0.050 0.022 0.015 0.000 0.020 0.000 0.010 0.000 0.000 10.00 0.080 0.112 0.028 0.028 0.000 0.030 0.000 0.020 0.000 0.000 11.25 0.180 0.210 0.050 0.048 0.016 0.040 0.010 0.030 0.000 0.010 12.50 0.336 0.382 0.084 0.088 0.026 0.050 0.030 0.040 0.010 0.036 13.75 0.578 0.604 0.156 0.164 0.060 0.080 0.046 0.080 0.054 0.090 15.00 0.890 0.938 0.260 0.274 0.096 0.124 0.082 0.124 0.116 0.186 16.25 1.238 1.306 0.404 0.424 0.152 0.170 0.130 0.196 0.226 0.338 17.50 1.752 1.792 0.598 0.614 0.218 0.234 0.202 0.282 0.380 0.536 18.75 2.320 2.326 0.836 0.848 0.312 0.314 0.294 0.392 0.606 0.774 19.45 2.540 2.540 20.00 1.082 1.096 0.396 0.396 0.402 0.500 0.820 1.022 21.17 1.308 1.350 21.25 0.464 0.480 0.514 0.608 1.018 1.240 21.50 1.156 1.257 22.22 0.572 0.672 22.32 0.546 0.566 r = undeformed radius / = distance from undefomed end dRj = radial expansion along the minor axis dR2 = radial expansion along the major axis 86 Table 8 Average Dynamic Strength Values Model Material Regnauld (1936) Taylor (1946) Taylor (1948) Hawkyard (1969) Wilkins (1971) Jones (1987) LM6061 462 332 378 403 402 471 DURAL-15 585 435 486 524 512 620 DWA-30 735 564 620 678 645 807 7075-T6 852 673 736 766 746 849 87 Table 9 Effect of Experimental Errors on Dynamic Strength Values Typical parameter error Impact velocity v0 m/s Initial length mm Final length Lf mm Undeformed length X mm Dynamic strength (Jones) MPa Strength relative error % baseline (1) 137 23.14 22.32 12.95 811 0 0.980Vo 134 23.14 22.32 12.95 776 -4.3 1.020Vo 140 23.14 22.32 12.95 847 +4.4 0.999Lo 137 23.12 22.32 12.95 833 +2.7 1.00 IL0 137 23.16 22.32 12.95 791 -2.5 0.998Ly 137 23.14 22.28 12.95 770 -5.1 1.002Ly 137 23.14 22.36 12.95 857 +5.7 0.990X 137 23.14 22.32 12.82 815 +0.5 1.010X 137 23.14 22.32 13.08 808 -0.4 1 - DWA-30, specimen #T17 88 Table 10 Summary of Experimental Results for Dynamic Penetration Tests Target material Spec.# Impact velocity (m/s) Penetration depth (1) ( mm) Minimum cavity diam. (mm) Maximum projec-tile diam. (mm) Projec-tile length (mm ) Angle of entry deg. Rem-arks (2) PM6061 P3 455 24.8 4.60 4.60 27.2 3.0 P4 483 26.5 4.52 4.52 27.2 2.0 PI 741 54.0, (55.1) 4.16 4.57 27.1 1.0 P2 755 58.3 4.12 4.56 27.1 5.0 LM6061 P28 461 29.2 4.31 4.68 27.3 1.0 P25 492 32.7 4.24 4.51 27.3 1.5 P27 727 64.7,(64.6) 4.23 4.49 27.2 2.0 P34 759 71.6 4.03 4.59 27.1 4.8 SI 850 79.0 DURAL-10 P16 471 24.1 4.64 4.64 27.2 1.5 P15 472 24.5 4.63 4.63 27.2 0.0 b P13 759 54.9 4.14 4.57 27.1 6.0 b P14 773 58.1,(58.3) 4.21 4.50 27.1 3.5 b DURAL-15 P19 468 24.5 4.64 4.64 27.2 2.0 P20 476 24.8 4.60 4.60 27.2 0.5 P18A 738 51.7 4.31 4.49 27.2 0.0 b P17A 771 54.2 4.19 4.49 27.2 2.0 b S2 850 63.0 DURAL-20 P23 450 23.2 4.48 4.48 27.1 1.5 P24 489 25.5 4.60 4.60 27.1 1.5 P21 750 50.5 4.14 4.48 27.0 1.0 P22 779 57.2 4.32 4.65 26.8 2.0 b DWA-20 P7 430 21.2 4.65 4.65 26.9 0.0 P8 455 22.5 4.64 4.64 27.1 0.0 b P17B 752 48.4, (50.7) 4.29 4.59 26.5 2.0 P18B 766 48.3 4.35 4.67 26.8 0.0 b DWA-30 P9 474 19.0, (19.6) 4.64 4.64 26.1 0.0 c P12 506 19.6 4.70 4.70 26.4 3.0 c P l l 716 36.4 4.75 4.93 25.8 5.5 b,r P10 745 37.8, (37.9) 4.70 4.87 25.5 0.0 b,r S3 850 45.0 P38 920 56.5 89 Table 10 continued Target Spec.# Impact Penetration Minimum Maximu Projec- Angle Rem-material velocity depth (1) cavity m tile of arks (m/s) ( mm) diam. projec- length entry (2) ( mm ) tile ( mm ) deg. diam. ( mm) L M 7075 P32 462 18.1,(18.9) 4.52 4.52 26.5 4.0 P33 464 18.7 4.63 4.63 26.7 1.5 P31 759 41.7 4.34 4.88 26.3 3.0 r P29 766 43.1,(43.4) 4.43 4.62 26.3 0.5 b,r S4 850 50.0 1- Penetration depths measured from X-ray photographs, values in parentheses correspond to measurement from sectioned specimens 2- Remarks designation:!) = projectile bent, r = rebound, c = radial cracks 90 Variation of Strength with Strain Rate Test type Static tension Hopkinson tension (strain rate) Rod impact (105 s"1) Dynamic Penetration Parameter UTS (MPa) UTS (MPa) Dynamic strength [Hawkyard] (MPa) Back-calculated strength (MPa) PM6061 386 470 LM606T 332 374 (1) (600/s) 403 375 DURAL-10 338 490 DURAL-15 359 524 500 DURAL-20 379 500 DWA-20 428 540 DWA-30 456 525 (2) (300/s) 678 710 L M 7075 572 747 (1) (800/s) 766 750 1 - Nicholas (1981). 2 - Ross et al. (1984) 91 FIGURES Instron machine upper head Hounsfield button-head grips tensile specimen O load cell clip gauge strain gauge O Crosshead Orion data logger 7 Tape IBM P C (analysis) Plotter Figure 1 - Experimental setup for quasi-static tension tests. 92 7.6 CO 22.0 84 7.6 1.2 R 3 R M . 6 D1A L-6.1 DIA 50.8 S C A L E : 2/1 Figure 2 - Geometry of the tension test specimen (dimensions in mm). 93 Target Chamber Recovery Chamber Launcher ^ ^ L a s e r System P r e s s u r e Gauge Vacuum Pump Support Rod Figure 3 - Schematic representation of the high strain rate facility. Figure 4 - Overall view of the high strain rate facility. 95 • 980 • .005 35.0 Figure 5 - Drawing of the 0.460 inch smooth bore launcher (dimensions in inches). 96 Figure 6 - Sub-caliber cartridge used for Taylor cylinder impact test. 97 Muzzle extension 64 DIA 3-200 Barrel Receiver ~~Tf i i ' 38 D I A n Blast deflector Laser Figure 7 - Barrel extension used as blast deflector and specimen support (dimensions in mm). 98 C e n t e r i n g F l a n g e R e c t a n g u l a r P o r t C i r c u l a r P o r t Figure 8 - Side view of the target chamber. 99 Figure 9 - Target alignment device (dimensions in inches). 100 M A S S : 6.5 grams A Figure 10 - Taylor test specimen design (dimensions in mm). 101 measurement gauge r- 11.58 r- 25.4 plastic front L 23.23 Taylor specimen X = 23.23 - R Figure 11 - Measurement gauge for plastic zone determination (dimensions in mm). 102 102 DIA r- 52 DIA 12 DIA 152 7 ~ 230 S C A L E : 1/2 Figure 12 - Taylor test rigid target design (dimensions in mm). 103 Taylor tests 700-1 0 1 2 3 4 5 6 Propellant mass (grains) Figure 13 - Variation of impact velocity with powder mass (1 grain = .065gram). 104 target V w-/y-/A>-penetrator after impact target support penetration depth Figure 14 - Dynamic penetration test methodology. 105 M A S S : 7.31 grams A S C A L E : 2/1 Figure 15 - Geometry of tungsten impactor used in penetration tests (dimensions in mm). 106 MATERIAL : P O L Y C A R B O N A T E M A S S : 4.5 grams ! / I 4.50 DIA ~7k 25 21 42 .05 5.58 "-11.66 DIA S C A L E : 2/1 Figure 16 - Plastic sabot design (dimensions in mm). 107 Figure 17 - Imprint on a 6061-T6 target by a plastic sabot. 108 600 Stress vs strain Tension test Strain Figure 18 - Comparison of the tensile behaviour of DWA-30 and unreinforced 6061-T6 Al. 109 LM 6061-T6 aluminum matrix 5 0 "I 1 1 1 1 1 1 1 1 \ 1 0 10 2 0 3 0 4 0 5 0 6 0 7 0 8 0 9 0 100 Alumina volume fraction (%) Figure 19 - Comparison of Young's modulus predictions with DURAL MMC data. 110 PM 6061-T6 aluminum matrix 50H 0 i 1 1 1— : —i 1 1 1 1 1— 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 Silicon carbide volume fraction Figure 20 - Comparison of Young's modulus predictions with DWA MMC data. Il l Figure 21 - Side views (upper) and impact faces (lower) of Taylor cylinders: DWA-30, DURAL-15, 7075-T6 Al, 6061-T6, undeformed 6061-T6. 112 Figure 22 - Average deformation profile of L M 6061 Taylor specimen after impact. 113 DURAL-15, V = 195 m/s, spec.# T14 81 : r — : r ~ Figure 23 - Average deformation profile of DURAL-15 Taylor specimen after impact. 114 LM 7075, V = 212 m/s, spec.# T8 8T : : ; — r Figure 24 - Average deformation profile of L M 7075 Taylor specimen after impact. 115 DWA-30 7-1 6.8- Radial spec. T 1 6 , V=137 m/s 6.6- Axial spec. T 1 7 , V= 144 m/s ^ 6 . 4 -w 6.2-X \ \ \ "s. \ V \ -N. \ V. \ \\ \ \ 1 6-CD C D ,_ ^ co 5.8-CD < 5.6-5.4-5.2-5- I 1 1 1 i 1 i 1 •—I 1 0 5 10 15 2 0 2 5 Distance from impact end (mm) Figure 25 - Average deformation profiles of DWA-30 axial and radial specimens after impact. 116 80-DWA-30 T 1 6 Radial specimen T 1 7 Axial specimen 0 % = Radially symmetric 5 10 15 20 Distance from impact end (mm) 25 Figure 26 - Comparison of the asymmetry of the plastic deformation profiles for axial and radial DWA-30 Taylor specimens after impact. 117 LM 6061-T6 Q Q ^ ^ ^ ^ ^ ^ ^ I 0 50 100 150 200 250 300 350 400 450 Impact velocity (m/s) Figure 27 - Comparison of Taylor test results obtained in this study and data from Wilkins and Gust for 6061-T6 Al. 118 L M 6 0 6 1 D U R A L - 1 5 D W A - 3 0 L M 7 0 7 5 Figure 28 - Comparison of dynamic strength values from various analysis models for LM 6061, DURAL-15, DWA-30 and LM 7075. 119 30 Figure 29 - Possible errors in dynamic strength calculations resulting from errors in final length measurements. 120 Figure 30 - Cross section of crater resulting from impact of a tungsten penetrator in DWA-30 target at 850 m/s. 121 Figure 31 - Radial cracks on the impact face of DWA-30 target impacted at 474 m/s. 122 100 8 0 E 7 0 E C L CD " O 6 0 5 0 o I 4 0 CD I 3 0 2 0 10 0 • • * • • *** • L M 6061 D U R A L - 1 0 D U R A L - 1 5 x D U R A L - 2 0 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1000 Impact velocity (m/s) Figure 32 - Comparison between measured penetration depths for LM 6061, and DURAL MMC. 123 100-90-8 0 " E 70-E, sz H—' 60-I J CD TJ 50-o i _ -t—• 40-CD (— CD CL 3 0 " 20-10-a 3 0 0 4 0 0 5 0 0 6 0 0 7 0 0 8 0 0 9 0 0 1000 Impact velocity (m/s) Figure 33 - Comparison between measured penetration depths for PM 6061, DWA-20, DWA-30, LM 7075 and LM 6061. 124 1000 Penetration tests Figure 34 - Variation of impact velocity as a function of propellant mass for dynamic penetration tests (1 grain = .065gram). 125 0.7 0 100 200 300 400 500 600 700 800 900 Velocity (m/s) Figure 35 - Comparison between static and dynamic friction coefficient for various materials. 126 1.5 1.4-.9 1.3-| 1.2T CD S " 1.H CD CO CO -Q 1-^ 0.9-o 1 0.8-f I 0.74, 0.64 0.5 Y=403 MPa, E=70 GPa, V=750m/s 0.02 0.03 0.04 0.05 0.06 0.07 Friction coefficient 0.08 0.09 0.1 Figure 36 - Results of friction coefficient sensitivity study. 127 70 LM 6061, Y=403 MPa, f=0.08 1.5-1 1.4-.9 1.3-•*—> 03 CD 1 2" CD ©1.1-"CD i w 1-cti ^ 0.9-o £ 0.8--t—» CD | 0 . 7 -0.6-0.5-_ • — i i i 80 90 100 110 Young's Modulus (GPa) 120 130 Figure 37 - Results of Young's modulus sensitivity study. 128 E=70 GPa, f=0.08, V=750 m/s Figure 38 - Results of dynamic strength sensitivity study. 129 LM 6061 0 100 200 300 400 500 600 700 800 900 1000 Impact velocity (m/s) Figure 39 - Measured and predicted penetration depths as a function of impact velocity for LM 6061. 130 DURAL-15 90i Impact velocity (m/s) Figure 40 - Measured and predicted penetration depths as a function of impact velocity for DURAL-15 131 DWA-30 70i Impact velocity (m/s) Figure 41 - Measured and predicted penetration depths as a function of impact velocity for DWA-30. 132 LM 7075 7Ch Impact velocity (m/s) Figure 42 - Measured and predicted penetration depths as a function of impact velocity for LM 7075. 133 100 10 450 500 550 600 650 700 750 800 850 900 950 Impact velocity (m/s) Figure 43 - Measured and predicted penetration depths as a function of impact velocity for L M 6061, DURAL-15, DWA-30, and LM 7075. 134 Figure 44 - Variation of normalized penetration depth as a function of impact parameter. 135 Plastic zone dia. = 1 x penetrator dia. Initial kinetic energy (J) Figure 45 - Plastic work as a function of initial kinetic energy, (plastic zone diameter = penetrator diameter). 136 Plastic zone dia. = 2 x penetrator dia. 1000H 5 0 0 - ^ / ° 0 500 1000 1500 2000 2500 3000 3500 Initial kinetic energy (J) Figure 46 - Plastic work as a function of initial kinetic energy, (plastic zone diameter = 2 x penetrator diameter). 137 I DURAL-10 90 Impact velocity (m/s) Figure 47 - Measured and predicted penetration depths as a function of impact velocity for DURAL-10. 138 DURAL-20 0 100 200 300 400 500 600 700 800 900 1000 Impact velocity (m/s) Figure 48 - Measured and predicted penetration depths as a function of impact velocity for DURAL-20. 139 DWA-20 80 0 100 200 300 400 500 600 700 800 900 1000 Impact velocity (m/s) Figure 49 - Measured and predicted penetration depths as a function of impact velocity for DWA-20. 140 PM 6061 Impact velocity (m/s) Figure 50 -Measured and predicted penetration depths as a function of impact velocity forPM 6061. 141 Figure 51 - Decrease in penetration depth as a function of reinforcement volume fraction for DURAL and DWA MMC for a velocity of 750 m/s. 142 600-550-500i Q_ CD C CD i_ -*—• in 0 DURAL MMC 10 ^ * Back-calculated • Static (UTS) Dynamic (Hawkyard) --i i i i 15 20 25 Alumina volume fraction (%) Figure 52 - Increase in static and dynamic strength as a function of reinforcement volume fraction for DURAL MMC. 143 800-700-^ DWA MMC Back-calculated... -• Static (UTS) Dynamic (Hawkyard) - — " - ^ " ^ -I l l I I I CO 600i CD a CD CO 500H 400; 300 200 0 5 10 15 20 25 30 Silicon carbide volume fraction (%) 35 Figure 53 - Increase in static and dynamic strength as a function of reinforcement volume fraction for DWA MMC. 144 900 Figure 54 - Increase in dynamic yield strength as a function of strain rate for both reinforced and unreinforced aluminum. 145 Rigid anvil configuration Symmetric configuration Figure 55 - Geometry of Taylor cylinder specimen before and after impact showing the notation used in Appendix A. 146 Figure 56 - Schematic illustration of penetrator with spherical nose showing the notation used in Appendix B. 147
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A study of the high strain rate behaviour of particle-reinforced metal matrix composites Pageau, Gilles 1991
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Title | A study of the high strain rate behaviour of particle-reinforced metal matrix composites |
Creator |
Pageau, Gilles |
Publisher | University of British Columbia |
Date Issued | 1991 |
Description | This thesis presents the results of an experimental and analytical study of the high strain rate behaviour of ceramic particle-reinforced metal matrix composites (MMC). Two MMC systems, both based on the 6061-T6 aluminum matrix, were selected. The first is an alumina reinforced system, made by a liquid metallurgy (LM) route, with 10, 15 and 20% particle volume fractions. The second is a silicon carbide system, made by powder metallurgy (PM), with 0, 15 and 30% particle volume fractions. Unreinforced 6061-T6 and 7075-T6 were also included for comparison. Quasi-static tensile tests, Taylor impact tests, and high velocity penetration tests were conducted. The tension test results indicated that the reinforcement strongly affects the stiffness, strength and ductility. Some anisotropy was also observed. The Young's modulus values for both system are in good agreement with predictions from simple two-phase theoretical models. An experimental facility was constructed which is capable of accelerating small cylindrical impactors at velocities up to 1000 m/s and allow for accurate measurement of the impact velocity. The facility was designed so that both Taylor and dynamic penetration tests could be performed with only minor modifications. The Taylor test was used to characterize the strength of the MMC selected under conditions comparable to those existing in dynamic penetration. It consists of impacting short cylindrical specimens on a flat rigid anvil at velocities ranging from 150 to 300 m/s. The dynamic yield strength was determined from measurements of the deformed shape of the specimen using one-dimensional analysis models. The results were shown to be quite dependent on the analysis model used for calculation. Results show that the dynamic strength is noticeably increased over the quasi-static values. The strain rate sensitivity of the MMC materials also appeared to be more pronounced. Measurements of the tested specimen profiles revealed some asymmetry which can be attributed to yield strength anisotropy. The MMC specimens also appeared to be more susceptible to radial cracking at the impact face. The effects of adiabatic heating and inertia within the specimen were also investigated. To assess the relative impact performance of the selected materials, dynamic penetration tests were conducted by firing small rigid tungsten rods with spherical noses on to MMC cylindrical targets with a diameter of 50 mm and a length of 150 mm. Tests were performed at three average impact velocities of 475, 750 and 920 m/s. The cavity profiles were determined from X-ray photographs. The dynamic penetration tests indicate that the PM-processed materials are more resistant to penetration than the LM-processed materials, with the difference being more significant at higher volume fractions. At low velocities (475 m/s) large scale radial cracking of the highly reinforced MMC was observed. The penetration depths were predicted using an approximate cavity expansion model developed for monolithic metals and which involves only a few measurable material properties. Sensitivity studies indicate that, for the intermediate velocity regime investigated in this study, the dynamic strength of the target material is the dominating parameter. Sliding friction at the impactor/target interface was also shown to influence the penetration behaviour to a lesser degree. Using the strength values obtained from the Taylor impact tests, the cavity expansion model predicted depths that were in reasonable agreement with the experimental results. |
Subject |
Metallic composites |
Genre |
Thesis/Dissertation |
Type |
Text |
Language | eng |
Date Available | 2010-11-19 |
Provider | Vancouver : University of British Columbia Library |
Rights | For non-commercial purposes only, such as research, private study and education. Additional conditions apply, see Terms of Use https://open.library.ubc.ca/terms_of_use. |
DOI | 10.14288/1.0078457 |
URI | http://hdl.handle.net/2429/30031 |
Degree |
Master of Applied Science - MASc |
Program |
Materials Engineering |
Affiliation |
Applied Science, Faculty of Materials Engineering, Department of |
Degree Grantor | University of British Columbia |
Campus |
UBCV |
Scholarly Level | Graduate |
AggregatedSourceRepository | DSpace |
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