Al-Sic metal matrisli karma malzemelerinin deformasyon davranışının sonlu elemanlar yöntemi ile parametrik analizi

Başlık çevirisi mevcut değil.

Tez No: 46561
Yazar: ŞAFAK YILMAZ
Danışmanlar: PROF.DR. AHMET ARAN
Tez Türü: Doktora
Konular: Makine Mühendisliği, Mechanical Engineering
Anahtar Kelimeler: Belirtilmemiş.
Yıl: 1995
Dil: Türkçe
Üniversite: İstanbul Teknik Üniversitesi
Enstitü: Fen Bilimleri Enstitüsü
Ana Bilim Dalı: Belirtilmemiş.
Bilim Dalı: Belirtilmemiş.
Sayfa Sayısı: 155

Özet

ÖZET Metal matrisli Al-SiC karma malzemeleri cazip fiziksel ve imalat özelliklerine sahiptirler. Bununla beraber, sünekliklerinin düşük olması sundukları potansiyelden tam olarak yararlanılmasını kısıtlamaktadır. Bu çalışmada SiC seramik taneciklerle takviyeli alüminyum matrislerin tek eksenli çekme yüklemesi altındaki deformasyon davranışı sonlu elemanlar yöntemi kullanarak analiz edilmiştir. Analiz parametreleri olarak; SiC takviyelerin hacim oranı, bunların matris içindeki dağılım geometrisi ve metal matrisin pekleşme üsteli dikkate alınmıştır. Uç boyutlu sonlu elemanlar analizi yapan bir bilgisayar programı hazırlanarak, sayısal gerilme-genleme eğrileri ve modellerdeki yerel gerilme-genleme dağılımları incelenmiş tir. Sürekli arabagları olan çift fazlı içyapılarda çekme deformasyonu sırasında gelişen çok eksenli gerilme alanları, bunların kısıtladığı matris içi plastik deformasyonlar, içyapı hasarları ve bu oluşumlara mikroyapı parametrelerinin etkisine ait, deneysel çalışmalarda gözlemlenemeyen veya gözlemlenmesi güç olan bilgiler elde edilmiştir. Bu bilgilerin çift fazlı malzemelerin deformasyon davranışının mekanizmalarının anlaşılmasında çok yardımcı olacağı açıktır. Artan hacim oranı ile karma malzemenin elastiklik modülü artmakta ve belli bir hacim oranındaki elastiklik modülü değerleri dağılım geometrisinden de etkilenmek tedir. Karma malzemede akmanın ilk oluştuğu andaki orantı sınırı daima, matrisin akma dayanımının altında kalmakta ve artan hacim oranı ile bu değer daha da azalmaktadır. Yerel akmalar matrisin akma dayanımının altındaki değerlerde başlıyor olmasına rağmen malzemenin deformasyonunun elastik-plastik geçişi matrisin akma dayanımının üzerinde gerçekleşmektedir. Bu davranışda 'geometrik pekleşme' olayının belirleyici olduğu ve bu etkinin dağılım geometrisine bağlılığı ortaya çıkarılmıştır. Artan takviye hacim oranı ile gerilme-genleme egriside görülen pekleşme artmak ta ve dağılım geometrisinin gerilme-genleme eğrisinin bu genel formu üzerindeki önemli etkisi olmaktadır. Elde edilen sonuçlar Al-SiC malzemesine ait özel sonuçlar ve çift fazlı malzemelerin deformasyon davranışlarına ait genel sonuçlar olarak da değerlendirilmiştir. Ayrıca, sonlu elemanlar yönteminden bu tür analizlerde nasıl yararlanabilabileceği ve analiz sonuçlarının çift fazlı malzeme tasarımlarında nasıl kullanılabileceği tartışılmıştır. xı

Özet (Çeviri)

There are many commercial materials having mixed structures with two or multi phases which can be classified as particle reinforced composite, as opposed to fiber or layer composites. The deformation characteristics of these materials have been the subject of theoretical, experi mental, and numerical investigations over the last several decades. The complicated geometry makes the prediction of their mechanical properties from those of their components a difficult task. Various kinds of factors concerning metallurgical, mechanical properties of constituent phases and character of the interface influence the mechanical properties of the two phase materials in a complex manner. For particle composites, no general method has been developed so far for the computation of its properties. There are two main approaches for interpreting the mechanical properties of these materials: One of them is the micro-mechanistic approach where the understanding is built-up from a knowledge of the deformation processes at the atomic level. The other is the continuum approach where it is assumed that the material's properties can be described by global parameters. The validity of the continuum approaches depend on particle size, and if the size of the particle is so large that the particles interact the dislocation cloud, the continuum approaches are valid. In general, the law of mixtures rule is not expected to be applicable for tensile properties of two-phase materials, for the simple reason that it assumes either constant stress (serial loading) or constant strain (parallel loading). Neither stress nor strain is constant in each phase and the stress-strain distribution occurs inhomogeneously not only between two constituent but also in the same phase. It seems difficult to clarify stress and strain distribution in two-phase composites experi mentally, and there is a lack of understanding in the stress-strain partitioning behavior of the constituents. Lacking an accurate model, the mechanical behavior of particle composites is customarily placed between the extremes of parallel loading (as in fiber composites) and series loading (as in layer composites). The analytical, Xllempirical, and semi-empirical equations are also offered for the calculation of some mechanical properties of particle composites in the literature. The analytical model to predict the thermal and mechanical properties of a particle composite was first developed by Eshelby who considered a simple ellipsoidal inclusion or inhomogeneity embedded in a infinite elastic body. Besides, recent continuum elastic and plastic calculations were considered to provide a suitable theoretical framework. These calculations have tried to elucidate important effects of the volume fraction, aspect ratio and spatial arrangement of reinforcement as well as the work hardening properties of the matrix. Hashin and Shtrikman derived more stringent bounds on composite elastic moduli than the mixture law bounds. These kind of analytical methods have the following Limitations: Many of these approaches are valid for a The more sophisticated continuum calculations based on finite element modeling are powerful approaches provided that they are based on physically realistic models. Most of the factors described above can be investigated with finite element method, simultaneously. Therefore, the elastoplastic analysis with the finite elements method (FEM) will give a lot of useful information. A.1-SİC metal matrix composites are becoming candidate materials for a variety of structural and automotive applications since these composites possess favorable combinations of mechanical properties including specific strength and stiffness, decreased thermal expansion, and high wear resistance compared to the unreinforced material. Besides, their isotropic properties retain some of the traditional f abricabi lity and formability of aluminum alloys, making them potentially more economical to produce. However the degree of strengthening depends on volume fraction, morphology and size of reinforcement. The current understanding of particle reinforced composites are going to identify some of the key factors which need to be controlled if these materials are to reach their full commercial potential. To obtain a parametric understanding of the effects of materials parameters such as the volume fraction, the shape and distribution of particles, or the matrix constitutive behavior, numerical micromechanical studies are important tools. The goal of this work is to establish a scientific xmbasis for materials design by determining the relationship between the overall material response and volume fraction, spatial distribution, and mechanical properties of constituents. FEM has been successfully used for solutions of various problems of stress analysis. It is an approximate numerical method, wherein the solution of continuum mechanics problem is approximated by polynomials on simple areas known finite elements. The division of the total area into subareas or finite elements is quite arbitrary. The finite elements may have different mechanical properties, either linear or nonlinear. The parameters of a solution, usually the values of solution at the nodes of the Finite Element Method, are determined by solving a usually large system of linear algebraic equations assembled as a result of matrix operations. These equations are expressed physical principles to the given problem. FEM modeling usually involves a computer program. The unit cell approaches were used to investigate the influence of inclusion arrangements and shape on the mechanical behavior of particle reinforced Al-SiC composites. The aspect ratio of the SiC particles is approximately 1 and particulate reinforced metal matrix composites have near isotropic properties. Since particles are equally sized, they can be modeled as sphere. In the present work, two distribution geometry models were considered. In both of these unit cell models, the spherical SiC reinforcements were embedded in a matrix in three-dimensional square packing arrangement. In the first model the particles were transversely aligned. In the second the particles were arranged in a transversely staggered array so that the poles of particles overlap. This staggered model was necessary to evaluate the effects of reinforcement overlaping on resulting composite properties. The volume element represents one-sixteenth of the unit cell. The rest of the complete model can be built by symmetry. The software developed in this study automatically produces the mesh described above. The elastic constants and the stress-strain equations of the phases, volume fraction of reinforcement, distribution type, maximum load and load steps are necessary input datas for the solution of three dimensional elasto-plastic problems. The simple- tetrahedral volume element was chosen for the construction of finite element models. The variable stiffness method was used for the elasto-plastic analysis. The program has assumed isotropic behavior of the individual phases for the analysis of elasto-plastic stress-strain behavior. Equivalent stresses of elements were calculated with the Von-Misses yield criteria for ductile Al matrix, with the total strain energy criteria for hard SiC particle. It was also assumed that the compatibility at the two-phase interface was preserved during the deformation in the FEM xivanalysis. The program determines the stresses in each element and the displacements of all nodes for each loading step or stress condition. Models with meshes of different fineness (one of them has approximately twice the number of degrees of freedom from the former) were considered to determine optimum analysis parameters. It has been determined that 550 nodes and 2187 elements are proper choices for such an analysis. The calculated elastic moduli and stress-strain curves for different composites were compared with the experimentally determined curves. The agreement between FEM calculations and experimental results was found to be excellent. The transversely aligned model was more closer to the experimental results, given in literature. The reason of this evidence is the material fabrication process. The extrusion process applied in the production stage of Al-SiC composites aligns the SiC particles in the extrusion direction. This is why the transversely aligned model much closer to the experimental results. However, both of two models are needed for a parametric analysis for determining of the mechanical property band of particulate reinforced composites. If the volume fraction of particles is so high that particles obstruct the directional alignment of each odher, the numerical results tend to be closer to the staggered model results. The general agreement of the calculated results with experimental results also emphasized that the modeling of equal size particles as spheres was a proper choice and that the spherical geometry of particles simulated the mean effect equally sized-irregular shaped particles. The agreement has also been attributed to an accurate representation of the mutual constraints of phases during deformation. On the other hand, the agreement of the stress-strain curves were valid up to a certain strain level. The numerical curves were separated from the experimental stress-strain curves after these points. The reasons for this separation are microstructural damages. If any damage occurs in microstructure, the continuum approach looses its validity. The possible microstructural damage types of the Al-SiC composites are void formation in ductile matrix, fracture of hard SiC particles and, breaking of interface. Among these, the main damage mechanism is void formation in ductile Al matrix. The necessary stress levels to initiate these damages were compared with the calculated values. It was found that the maximum equivalent stress calculated in the matrix was equal to void formation stress, where experimental and numerical results began to have different values. The maximum equivalent stress in SiC particulate was also close to the fracture strength of big particulates but the maximum interface stress was far from the interface breaking strength. This numerical damage predictions are in good agreement with the experimental damage inspections in particulate composites. These investigations also show that the finite element method is only suitable, as long as the microstructural continuity is preserved. The damage xvmechanisms can be investigated with the help of finite element method. The type of damage, the phase of damage and its starting with respect to overall deformation can be determined using finite element analysis. The nucleation and growth of damages, which relieve the hydrostatic stresses in the matrix, would therefore be expected to have strong bearing on how the microstructural parameters influences the composite response. The elastic moduli of staggered models were lower than the transversely aligned model. The stress-strain curves of the staggered model were also below the ones of the transversely aligned model. Increasing volume fraction of particles increases the elastic moduli and strain hardening tendency of both models. The stress-strain distributions were quite nonuniform in the models. Most of the stresses were taken up by the harder SiC phases and, most of the strains were in the softer Al phase, as expected. It is important to note that the local stress-strain distributions strongly depend on morphology of phases. Matrix regions over the particle poles deformed more than other matrix regions and the level of this maximum strain was higher in transversely aligned model than in the staggered one. But, for a certain volume fraction the highly strained matrix volume is larger in the staggered model than in the transversely aligned model. Therefore the elastic moduli of transversely aligned model is higher than the staggered model. The yielding nucleated between the poles of particles in both models. The proportionality limit of particulate composites was lower than the matrix yield stress. The stress intensity in the transversely aligned model was higher than in transversely staggered model. It appears that the reinforcement clustering found in real materials will affect localization of deformation and can be a determining factor in controlling properties such as ductility, toughness, and fatigue life. Although the micro yielding began at lower stresses compared with the than matrix yielding stress, the elastic-plastic transitions of stress-strain curves were above the matrix yielding stress for the both models, even if the models had an ideal plastic matrix. The causes of this evidence can be explained as fallows: The stress-strain distributions showed that transverse stresses developed in the microstructure, which were a result of the interactions between the softer Al and the harder SiC phases. Between the particle poles these transverse stresses were of tensile character and they were compressive in the gap beside the particles. The plastic yielding nucleated and grew between the poles of particles as expected. But, at the same time transverse stresses increased with the growth of the plastic deformation in the matrix. Such a change in the stress state lowered the increasing rate of the effective stress and hindered the fast growth of the xvxplastic region. Therefore it was needed to increase the overall stresses in order to continue the plastic deformation even if the matrix was ideally plastic. This event is called 'geometrical hardening'. In the transversely aligned model, such a stress state development caused the second yielding nucleation in the gap between neighboring particles. The geometrical hardening effect was weakened by the growth of this second plastic deformation region around the particles. The hardening effect was weaker in the staggered model than in the transversely aligned model. The geometrical hardening in the staggered model is completed after the plastic deformation regions neighboring come into contact. After the completion of geometrical hardening stage, plastic deformation spreaded in all matrix and the overall strain of model increased. xvii

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