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Parçacık takviyeli karma malzemelerdeki artık gerilmelerin sonlu elemanlar yönetimiyle analizi

Parçacık takviyeli karma malzemelerdeki artık gerilmelerin sonlu elemanlar yönetimiyle analizi

##### Dosyalar

##### Tarih

1994

##### Yazarlar

Cansun, Ali

##### Süreli Yayın başlığı

##### Süreli Yayın ISSN

##### Cilt Başlığı

##### Yayınevi

Fen Bilimleri Enstitüsü

##### Özet

Günümüzde iki veya daha fazla farklı malzemenin makro seviyede bir araya getirilmesiyle oluşturulan karma malze meler, teknolojik olarak büyük öneme sahiptirler. Bu tip malzemelerin içinde oldukça yeni olan parçacık takviyeli metal matris li karma malzemeler halen geliştirilmekte olup, üzerinde birçok araştırmalar yapılmaktadır. Bu araştırma lar, özellikle yeni üretim yöntemleri ve mekanik özellikler üzerinde yoğunlaşmıştır. Parçacık takviyeli metal matris li karma malzemelerde takviye olarak yüksek mukavemetli, rijit, gevrek ve ısıl genleşme katsayısı düşük olan seramik parçacıklar (SiC, BC, SijHı, Al*0j v.b) kullanılırken, matris malzemesi olarak ise genellikle düşük mukavemetli, sünek ve ısıl genleşme katsa yısı daha yüksek olan metal alaşımları tercih edilir. Böy lece hem matrisin, hem takviyenin en iyi özelliklerini üze rinde toplayan üstün mekanik özelliklere sahip karma malze meler elde edilir. Parçacık takviyeli metal matrisli karma malzemelerin gerek üretimi, gerekse ısıl işlemi sonrası soğuma esnasında bileşenlerinin arasındaki ısıl büzülme farklılıkları sebe biyle matriste ve takviye parçacıkta ısıl artık gerilmeler oluşur- Yapılan araştırmalarda bu iç gerilmelerin, karma malzemenin gerek mikro yapısında gerekse mekanik özellik lerinde önemli etkileri olduğu görülmüştür. Bu çalışmada sonlu elemanlar yöntemiyle analiz yapıla rak, parçacık takviyeli metal matrisli karma malzemelerdeki ısıl artık gerilmelerin seviyesi ve bu seviyelere etki eden faktörler araştırılmıştır. Sonlu elemanlar yöntemiyle ana liz ise "ANSYS 5.0" paket programı kullanılarak bilgisayar da yapılmıştır.

Modern design procedures continually strive to increase structural efficiencies through reductions in either absolute weight or increases in strength -to- weight ratio. Reductions in material density, or increases in elastic modulus, yield strength and / or ultimate tensile strength can be directly translated to reductions in structural weight. For example a 1Q percent reduction in alloy density, that can he achieved by using Al-Li alloys instead of 2000 series aluminum alloys, will lead to a 10 percent reduction in structural weight. Alternatively, a 50 percent increase in elastic modulus, which can be achieved through substitution of discontinuous silicon carbide (particulate, whisker or short fiber) reinforced aluminum alloy for an unreinforced wrought aluminum alloy, will also result in a 10 percent reduction in structural weight. System trade studies, such as outlined above, have been the primary motivating factor in the renewed interest shown in metal matrix composites. Initially, these investigations focused on continuous fiber reinforced materials emphasizing C, SiC, B, B«C, or AlîOj filaments or tows. Matrices of interest have included Al, Mg and most recently Ti. Fabrication of continuous fiber reinforced metal matrix composites has utilized plasma spraying, hot molding or superplastic diffusion bonding of foil-fiber laminates, and pressure infiltration of woven preforms. Widespread industrial application of these composites has however, been limited by the high costs of both reinforcement fiber (e.g. $135/kgm for B) and metal matrix component fabrication process. Most recent attention has therefore directed towards commercialization of discontinuous ly reinforced metal matrix composites, for example silicon carbide particulate and whisker (SiCy, Sid) and alumina / alumina-silica (AIîOj-SİOî) reinforced aluminum alloys. Discontinuous ly reinforced metal matrix composites benefit from substantially lower fiber costs, for example, $ 0.9-1.35/kg for SiC». In addition discontinuously reinforced Al matrix composites can be fabricated using standard or near- ix standard metal fabrication procedures, such as rolling, sheet forming, spinning, brazing, welding, investment casting- Finally, when careful attention is paid to processing detail, an extremely attractive combination of mechanical properties can be obtained; for example a 50 percent increase in stiffness can be achieved in SiC reinforced aluminum while maintaining adequate levels of strength, ductility, and fracture toughness. Various methods for production of particulate reinforced metal matrix composites have been developed over the last few years. Some of these manufacturing processes, that are overviewed in this thesis, are; - Powder Metallurgy Techniques - High Energy - High Rate Processes - Casting - Compocasting - Bheocasting - Kelt Infiltration - Ospray Deposition During the manufacturing or annealing processes of particulate reinforced metal matrix composites must be heated to high temperatures (e.g. 400-500*C for SiC reinforced aluminum) - Because of the mismatch in thermal expansion coefficients of metal matrix and ceramic reinforcement (e.g. 10:1 for aluminum and silicon carbide), thermal residual stresses are formed in these composites during cooling from manufacturing or annealing temperature. In this study, the thermal residual stresses in particulate reinforced metal matrix composites were analyzed by using Finite Elements Method. This finite elements analysis was done by means of a computer program "ANSYS 5.0" which is a general purpose FEA program. Different types of analysis can be done by using "ANSYS 5.0" such as: - Structural Analysis - Thermal Analysis - Magnetic Analysis - Harmonic Analysis - Spectrum Analysis - Coupled Field Analysis (e.g. thermal + structural) In order to calculate the thermal residual stresses in MMC by FEM, the popular axial symmetric cylindrical unit cell models were used according to the uniform, periodic, aligned distribution of reinforcement particles in metal matrix alloy (Figure 5-8). Based on the symmetry and periodicity arguments, the lateral surface of the cylindrical cell must remain circular and the end faces of the cell must also remain planar. Because of the axial symmetry the prohlem was solved as a two dimensional Finite Elements Analysis by using eight noded axial symmetric planar elements. These axial symmetric unit cells are subjected to a cooling from 40Q4C to the room temperature in 10 steps. In this study, the parameters, that may possibly affect the thermal residual stresses, are analyzed. These parameters are; - Reinforcement Geometry - Volume Fraction - Distribution Geometry - Matrix Material - Cooling Bate The material properties are chosen as of 1100 Al, 6061 Al alloys and SiC. The properties of 1100 aluminum alloy and SiC are taken from ref.[25]. 6061 aluminum alloy properties are taken from ref. [21]. The stress - strain curves of aluminum alloys are thought to be composed of two linear parts as shown in Figure 5-1 (Bilinear Hardening) and SiC particulates are thought to be elastic- The temperature dependency of the elastic moduli, yield strengths, thermal expansion coefficients, tangent modulus, Poisson ratios of aluminum alloys and silicon carbide can be seen in Table S-l, Table S-2 and Table S-3. Table S-l: The mechanical properties of 1100 Al alloy at different temperatures XI Table S-2: The mechanical properties of 6061 Al alloy at differ eat temperatures Table S-3: The mechanical properties of SiC particles at different temperatures In order to determine the effect of reinforcement geometry on the thermal residual stress distributions, two basic reinforcement geometries -cylinder *md sphere- were taken and for these geometries computations were done in different volume fractions. Aspect ratios for cylindrical reinforcements (the height of the cylinder / the diameter of the cylinder) of 1, 2, 3 and 4 were used in the computations while keeping the fiber volume fraction constant at 4%. The effect of volume fraction on thermal residual stress fields was identified using volume fractions of 4%, 8%, 12%, 16%, 24%, 30%, 40% for spherical and cylindrical (fiber aspect ratio was constant at 1) particulates. XXI The effect of the distribution geometry of particulates in. the metal matrix was investigated by considering cell aspect ratios of 1,2,4 and 8 with a fiber volume fraction of 4* and with a fiber aspect ratio of 1- At elevated temperatures can be expected in thermal residual stresses according to the creep properties of metal matrix alloy. Therefore during cooling process a part of thermal residual stress are relaxed by creep deformation of metal matrix alloy. The creep phenomenon is a function of time, stress and temperature. Therefore the relaxation in thermal residual stresses are strongly related to the cooling rate. In this study, the effect of cooling rate was investigated by making computations at three different cooling rates. These are; 1-) Air-cooling conditions (Figure 5-8) 2-) Furnace cooling with a rate of 0.03*C/sec 3-) Furnace cooling with a rate of 0.06*C/sec After all these computations the results listed below, were observed: 1-) After cooling from manufacturing or annealing temperature to the room temperature, considerably nonuniform distributed thermal residual stress fields occurred in this type of composites. The character of these thermal residual stress fields is compressive in the particulate and tension in the matrix. 2-) The average thermal residual stresses in the matrix increase with the volume fraction and matrix yield strength. 3-) When different distribution geometries at the constant volume fraction were investigated, it was observed that thermal residual stress fields were strongly related to the minimum spacing between particulates. 4-) The level of thermal residual stresses will affect to subsequent deformation behavior of the composite. For soft matrix materials, nearly the whole matrix deforms plastically particularly at high volume fractions. Therefore average effective residual stress levels will be greater than the matrix yield strength. And the ratio of average residual stresses to matrix yield strength is lowered as the yield strength of the matrix increases. 5-) Thermal residual stresses are concentrated near the particulates and they have a peak at the corner of the xiii cylindrical particulates. The void nucleation at the whisker ends is an important deformation mechanism controlling both the fracture and high temperature deformation of the composite. Because of the high plastic deformation and hydrostatic stress, this corner is a critical place for void nucleation. 6-) According to the analysis where the creep properties of matrix alloy were also considered, a relaxation of 5% of the average effective stresses and 20% of the maximum effective stresses were observed.

Modern design procedures continually strive to increase structural efficiencies through reductions in either absolute weight or increases in strength -to- weight ratio. Reductions in material density, or increases in elastic modulus, yield strength and / or ultimate tensile strength can be directly translated to reductions in structural weight. For example a 1Q percent reduction in alloy density, that can he achieved by using Al-Li alloys instead of 2000 series aluminum alloys, will lead to a 10 percent reduction in structural weight. Alternatively, a 50 percent increase in elastic modulus, which can be achieved through substitution of discontinuous silicon carbide (particulate, whisker or short fiber) reinforced aluminum alloy for an unreinforced wrought aluminum alloy, will also result in a 10 percent reduction in structural weight. System trade studies, such as outlined above, have been the primary motivating factor in the renewed interest shown in metal matrix composites. Initially, these investigations focused on continuous fiber reinforced materials emphasizing C, SiC, B, B«C, or AlîOj filaments or tows. Matrices of interest have included Al, Mg and most recently Ti. Fabrication of continuous fiber reinforced metal matrix composites has utilized plasma spraying, hot molding or superplastic diffusion bonding of foil-fiber laminates, and pressure infiltration of woven preforms. Widespread industrial application of these composites has however, been limited by the high costs of both reinforcement fiber (e.g. $135/kgm for B) and metal matrix component fabrication process. Most recent attention has therefore directed towards commercialization of discontinuous ly reinforced metal matrix composites, for example silicon carbide particulate and whisker (SiCy, Sid) and alumina / alumina-silica (AIîOj-SİOî) reinforced aluminum alloys. Discontinuous ly reinforced metal matrix composites benefit from substantially lower fiber costs, for example, $ 0.9-1.35/kg for SiC». In addition discontinuously reinforced Al matrix composites can be fabricated using standard or near- ix standard metal fabrication procedures, such as rolling, sheet forming, spinning, brazing, welding, investment casting- Finally, when careful attention is paid to processing detail, an extremely attractive combination of mechanical properties can be obtained; for example a 50 percent increase in stiffness can be achieved in SiC reinforced aluminum while maintaining adequate levels of strength, ductility, and fracture toughness. Various methods for production of particulate reinforced metal matrix composites have been developed over the last few years. Some of these manufacturing processes, that are overviewed in this thesis, are; - Powder Metallurgy Techniques - High Energy - High Rate Processes - Casting - Compocasting - Bheocasting - Kelt Infiltration - Ospray Deposition During the manufacturing or annealing processes of particulate reinforced metal matrix composites must be heated to high temperatures (e.g. 400-500*C for SiC reinforced aluminum) - Because of the mismatch in thermal expansion coefficients of metal matrix and ceramic reinforcement (e.g. 10:1 for aluminum and silicon carbide), thermal residual stresses are formed in these composites during cooling from manufacturing or annealing temperature. In this study, the thermal residual stresses in particulate reinforced metal matrix composites were analyzed by using Finite Elements Method. This finite elements analysis was done by means of a computer program "ANSYS 5.0" which is a general purpose FEA program. Different types of analysis can be done by using "ANSYS 5.0" such as: - Structural Analysis - Thermal Analysis - Magnetic Analysis - Harmonic Analysis - Spectrum Analysis - Coupled Field Analysis (e.g. thermal + structural) In order to calculate the thermal residual stresses in MMC by FEM, the popular axial symmetric cylindrical unit cell models were used according to the uniform, periodic, aligned distribution of reinforcement particles in metal matrix alloy (Figure 5-8). Based on the symmetry and periodicity arguments, the lateral surface of the cylindrical cell must remain circular and the end faces of the cell must also remain planar. Because of the axial symmetry the prohlem was solved as a two dimensional Finite Elements Analysis by using eight noded axial symmetric planar elements. These axial symmetric unit cells are subjected to a cooling from 40Q4C to the room temperature in 10 steps. In this study, the parameters, that may possibly affect the thermal residual stresses, are analyzed. These parameters are; - Reinforcement Geometry - Volume Fraction - Distribution Geometry - Matrix Material - Cooling Bate The material properties are chosen as of 1100 Al, 6061 Al alloys and SiC. The properties of 1100 aluminum alloy and SiC are taken from ref.[25]. 6061 aluminum alloy properties are taken from ref. [21]. The stress - strain curves of aluminum alloys are thought to be composed of two linear parts as shown in Figure 5-1 (Bilinear Hardening) and SiC particulates are thought to be elastic- The temperature dependency of the elastic moduli, yield strengths, thermal expansion coefficients, tangent modulus, Poisson ratios of aluminum alloys and silicon carbide can be seen in Table S-l, Table S-2 and Table S-3. Table S-l: The mechanical properties of 1100 Al alloy at different temperatures XI Table S-2: The mechanical properties of 6061 Al alloy at differ eat temperatures Table S-3: The mechanical properties of SiC particles at different temperatures In order to determine the effect of reinforcement geometry on the thermal residual stress distributions, two basic reinforcement geometries -cylinder *md sphere- were taken and for these geometries computations were done in different volume fractions. Aspect ratios for cylindrical reinforcements (the height of the cylinder / the diameter of the cylinder) of 1, 2, 3 and 4 were used in the computations while keeping the fiber volume fraction constant at 4%. The effect of volume fraction on thermal residual stress fields was identified using volume fractions of 4%, 8%, 12%, 16%, 24%, 30%, 40% for spherical and cylindrical (fiber aspect ratio was constant at 1) particulates. XXI The effect of the distribution geometry of particulates in. the metal matrix was investigated by considering cell aspect ratios of 1,2,4 and 8 with a fiber volume fraction of 4* and with a fiber aspect ratio of 1- At elevated temperatures can be expected in thermal residual stresses according to the creep properties of metal matrix alloy. Therefore during cooling process a part of thermal residual stress are relaxed by creep deformation of metal matrix alloy. The creep phenomenon is a function of time, stress and temperature. Therefore the relaxation in thermal residual stresses are strongly related to the cooling rate. In this study, the effect of cooling rate was investigated by making computations at three different cooling rates. These are; 1-) Air-cooling conditions (Figure 5-8) 2-) Furnace cooling with a rate of 0.03*C/sec 3-) Furnace cooling with a rate of 0.06*C/sec After all these computations the results listed below, were observed: 1-) After cooling from manufacturing or annealing temperature to the room temperature, considerably nonuniform distributed thermal residual stress fields occurred in this type of composites. The character of these thermal residual stress fields is compressive in the particulate and tension in the matrix. 2-) The average thermal residual stresses in the matrix increase with the volume fraction and matrix yield strength. 3-) When different distribution geometries at the constant volume fraction were investigated, it was observed that thermal residual stress fields were strongly related to the minimum spacing between particulates. 4-) The level of thermal residual stresses will affect to subsequent deformation behavior of the composite. For soft matrix materials, nearly the whole matrix deforms plastically particularly at high volume fractions. Therefore average effective residual stress levels will be greater than the matrix yield strength. And the ratio of average residual stresses to matrix yield strength is lowered as the yield strength of the matrix increases. 5-) Thermal residual stresses are concentrated near the particulates and they have a peak at the corner of the xiii cylindrical particulates. The void nucleation at the whisker ends is an important deformation mechanism controlling both the fracture and high temperature deformation of the composite. Because of the high plastic deformation and hydrostatic stress, this corner is a critical place for void nucleation. 6-) According to the analysis where the creep properties of matrix alloy were also considered, a relaxation of 5% of the average effective stresses and 20% of the maximum effective stresses were observed.

##### Açıklama

Tez (Yüksek Lisans) -- İstanbul Teknik Üniversitesi, Fen Bilimleri Enstitüsü, 1994

##### Anahtar kelimeler

Gerilme analizi,
Konstrüksiyon,
Malzemeler,
Sonlu elemanlar yöntemi,
Stress analysis,
Construction,
Materials,
Finite element method