Parçacık takviyeli metal matrisli karma malzemelerde bauschinger etkisinin sonlu elemanlar yöntemiyle incelenmesi
Finite element method modelling of bacuschinger effect in particulate reinforced metal matrix composites
- Tez No: 66645
- Danışmanlar: PROF. DR. AHMET ARAN
- Tez Türü: Yüksek Lisans
- Konular: Makine Mühendisliği, Mechanical Engineering
- Anahtar Kelimeler: Belirtilmemiş.
- Yıl: 1997
- Dil: Türkçe
- Üniversite: İstanbul Teknik Üniversitesi
- Enstitü: Fen Bilimleri Enstitüsü
- Ana Bilim Dalı: Makine Mühendisliği Ana Bilim Dalı
- Bilim Dalı: Belirtilmemiş.
- Sayfa Sayısı: 156
Özet
ÖZET Kullanım yerine göre istenilen özellikte malzemeler elde etme isteğinin bir sonucu olarak karma malzeme kullanımı gittikçe yaygınlık kazanmaktadır. Özellikle havacılık ve uzay sanayiinde kullanımı başlayan karma malzemeler diğer sektörlere de hızla girmektedir. Metal matrisli karma malzemeler de bu çerçevede düşünülmelidir. Bizim çalışma alanımız olan parçacık takviyeli metal matrisli karma malzemelerde yüksek dayanımlı, rijid, sert ve gevrek seramik ile sünek ve tok olan metalin özellikleri biraraya getirilmektedir. Metal matrisin bir özelliği olan“Bauschinger Etkisi”parçacık takviyeli metal matrisli karma malzemelerde de farklı özelliklerle beraber görülmektedir. Bauschinger Etkisinin büyüklükleri ve ne gibi parametrelerden etkilendiğini bulmak için özellikle 1985'ten sonra birçok deneysel çalışma yapılmıştır. Bir takım sonuçlar elde edilmiştir. Ve hale incelenmemiş bir takım özellikleri vardır. Bu çalışmada sonlu elemanlar yöntemiyle çalışan ANSYS adlı program kullanılarak metal matrisli parçacık takviyeli karma malzemelerin geometrik özellilerinin, deformasyon miktarının, elastiklik modüllerinin Bauschinger Etkisi üzerindeki etkileri incelenmiş, yapılan diğer çalışmalarla karşılaştırılarak, yeni bazı ekler yapılmaya çalışılmıştır. xı
Özet (Çeviri)
SUMMARY FINITE ELEMENT METHOD MODELING OF BACUSCHINGER EFFECT IN PARTICULATE REINGFORCED METAL MATRIX COMPOSITES Metal matrix composites combine metallic properties with ceramic properties leading to greater strength in shear, compression and higher service temperature capabilities. Materials which are used for reinforcement include carbides (SİC4), oxides (Al203,Si02), nitrides (S3N4). The attractive physical and mechanical properties such as high specific modulus, strength, thermal stability, can be obtained with metal matrix composites. We must understand the mechanical behaviour of metal matrix composites in order to design better. We must know, which properties of material change with different volume fraction, morphology. One of the important properties of metal matrix is Bauschinger effect. The knowledge of bauschinger effect in particulate reinforced metal matrix composites is not enough to use. We must learn more about the subject. Many ductile solids, after being subjected to forward deformation in tension or compression exhibit a tendency for easier plastic flow when the direction of lading is reversed than for continued forward deformation. This experimental observation is widely known as the Bauschinger effect. The aim of this study is to show the proporties of Bauschinger effect in particulate reinforced metal matrix composites. In this study, a computer program based on FEM called ANSYS was used to solve mathematical calculations. First we obtained the strees - strain curves of different metal matrix composites. First we obtained strees - strain curves for %20 volume fraction in different aspect ratios (1/d =2....1/d = 10) Then, for the same aspect ratio (1/d = 5), strees - strain curves of different volume fractions were obtained (%5, %20, %30). At last we observed the changes of strees-strain curves for different elastic modulus of ceramic. The ratio of elastic modules was selected a = 3, a = 15, a = 150 In other words the elastic modulus of ceramic was taken 210.000 MPa, 1.050.000MPa and 10.500.000 MPa(a = ESic/Eal) In the study the propertis of SiC ceramic and 6061 matrix alloy were used. For SiC particulate, Poission's ratio was taken V = 0,22, young's modulus was taken 440.000 MPa. For aluminum alloy 6061, Poisson's ratio was taken V = 0,33, Young's modulus was taken 70,000 MPa, yield strength of the alloys was taken 240MPa. The experimentally measured strees-strain curve of the 6061 alloy matrix material was approximated in the model by a bilinear curve with inital slope, E( Young' s modulus), xiiinitial yield strees, Ojy and final slope, Ep (Plastic modulus.) For computational conveience, a as the ratio of the final slope to the initial slope, a = Ep/E can be defined; thus a is a measure of the work-hardening rate, but it is not numerically equal to the logarithmic work - hardening rate, n. According to the real strees - strain curve of 6061, the measured values of 6061 were taken as E = 70 Gpa, a = 0,01. Some assumptions were made to simplify the calculations. It was studied in 2D with axisymmetric elements which act as 3D. Particulate shapes were taken as cylinders. Two of the edges in the model were constrained for displacement in X and Y directions. From the top edge of (cylinder) unit cell stresses were applied. It was considered that the unit cell acts as the all of metal matrix composites. These are good assumptions in order to model easier, by using axisymetric elements. We saved a lot of time, because there was no difference between modeling 3D and axisymmetric 2D elements. The axisymmetric properties of elements in ANSYS are great powers of the program. The solution at the nodal points is obtained by solving a large number of algebraic equations assembled as a result of matrix operations. The accuracy of the solution increases with the number of elements used to idealize the structure. The mput included a description of the elements, nodal points and constraints. In addition strees-strain curve of the matrix alloy and material properties of the particles were given as input The ANSYS computer program was used to solve these calculations. This computer program is based on FEM. We talked about the properties of the materials and dhe program, Now, we will talk about the expeirement again. We obtained all stress-strain curves. We started to investigate the Bauschinger effect in the metal matrix composite in different positions. For the same aspect ratio was equal to five (1/d = 5) and for forward strain was equal to 0,00525, we calculated Bauschinger strains and Bauschinger stress factors, for different volume fractions. (%5,%20,%30). For the same volume fraction (%20), but different aspect ratios (1/d = 2 and 1/d = 5) we calculated the Bauschiner strains and Bauschinger stress factors for forward strain was 0,00525. It was also tried to find how was changed th Bauschinger effect by different forword strains. For the aspect ratio was equal to five (1/d =5) and volume fraction was %20 it was applied 0,00835 forward strain, and was caluculated the Bauschinger strains and Bauschinger stress factors. At last for the same aspect ratio (1/d =5), for the same volume fraction (%20), it was observed in different Young's Modulus of SiC particiles how was changed the Bauschinger effect. It was applied for a =3, a = 15 and a = 150. The meaning of term“a”was explained before. The mechanism of the Bauschinger effect lies in the structure of the cold-worked state. Orowan has pointed out that during plastic deformation dislocations will accumulate at barriers in tangles and eventually from cells. Now, when the load is removed, the dislocation lines will not move appreciably because the structure is mechanically stable. However, when the direction of loading is reversed, some dislocation lines can move an appreciable distance at a low shear stress because the barriers to the rear of the dislocations are not likely to be so strong and closely spaced xiiias those immediately in front. This gives rise to initial yielding at a lower strees level when the loading direction is reversed. Same mechanism is a reality for the metal matrix of the composite. Before we discussed the results, we must talk about the studies which were made before, In some studies these results were observed about the subject. 1. The compressive yield strees of whisker and platet SiC in aluminum composites is larger than the temsile yield stress. 2. The magnitude of the strength difterential effect increases with an increase in the volume fraction of SiC. 3. The magnitude of Bauschinger effect increases with an increase in the volume fraction of SiC. 4. The magnitude of the Bauschinger effect is greater if the test is initially conducted in compression and difference, i.,e. whether tested in tension first or compression first with increasing volume fraction of SiC. 5. The asymmetric behviour of the Bauschinger Effect in the composites can be accounted for by a model based on the change in the residual strees and the work hardening of the matrix. In our model, another asumption was made. We taught that there is no residual stress in the matrix because of the cooling. The residual stress causes the strength differential and different values of Bauschinger strains and Bauschinger stress factors for tension and compression. It's very difficult to model the residual stresses in the matrix which is caused by cooling. The results were found in our study. Ao“b Asb %5 Volume fraction 1/d =5 aspect ratio 10 MPa 0,550 %8t = 0,525 %20 volume fraction 1/d = 5 aspect ratio 32MPa 0, 1 75 %et = 0,525 %30 volume fraction 1/d = 5 aspect ratio 62,5 MPa 0,125 %8f= 0,525 %20 volume fraction 1/d = 2 aspect ratio 20 MPa 0,200 %8f= 0,525 %20 volume fraction 1/d = 5 aspect ratio 145 MPa 0,550 %ef= 0,835 %20 volume fraction 1/d = 5 aspect ratio 37,5 MPa 0,200 %6f= 0,525 E, = 210 Gpa XIV%20 volume fraction 1/d = 5 aspect ratio 43,75 MPa 0, 1 50 %ef= 0,525 E,= 1050GPa %20 volume fraction 1/d = 5 aspect ratio 40 MPa 0, 1 10 %8f= 0,525 Es = 10.500 GPa We can summarize the results of the sutdy in this way: When the volume fraction of SiC particles increases, the elasticity modulus and the yield strength of the metal matrix composites increase, too. The results, which were found in our study, are the same as other studies. The increase in the values of elasticity modulus and yield strengthy are related with the shape of particles. In the cylinderic shapes, with the increase of the aspect ratio, the elasticity modulus and yield strength of the metal matrix composites increase, too. When the volume fraction of SiC particles increases, the Bauschinger stress factors increase, too. Bauschinger strains decrease when the volume fraction of SiC particles increases. In the studies which were made by others, the Bauschinger stress factors increase when the volume fraction of SiC increases. It was seen that, the value of the Bauschinger strains depended on the direction of the test. It was important that the test was begun in compression first, or in tension first. Different results were found. Bauschinger effect depends on the shape of the SiC particles The Baucshinger strese factors increase when the aspect ratio of SiC increase. By the increase of first strain value, the Bauschinger stress factors incerase, too. Also the Bauschinger strains increase. The results which were found in our study are very similiar to the results of other engineers. If the residual stresses are modedeld, better solutions can be found. Incerase in the elasticity modulus of ceramic particles, occur no change in the Bauschinger strees factors. But the Bauschinger strains decrease. In the metal matrix composites, by the increase of the volume fraction of SiC, the Baushinger stressess increase. This is seen in our model and is also seen in other studies. After the studies that are made by observers. First model was made by SHI and ARSENAULT (1993) They saw that even for high first strains for aluminum, the value of Bauschinger stress factors were too small. High Bauschinger Stress factors were found in metal matrix composites. They tried to explain this by back stress model. They taught that residual stresses were occured by different cooling condition. The explanation of Orowan for metals is not real for metal matrix composites. xvIn explaning the asymmetric BSF, a commonly used concept of ”back stress“ may be employed where the forward and reverse flow stresses can be expressed as a/ | = ay + AabF + | Aafh | (s,l) aR | = ay - AobR + | Aaa | (s,2) In these expressions, the ay is the intrinsic composite yield strength in the absence of te effects from TRS, AabF and AabR are contributions from the back stress during the forward and the reverse loading cycles respectively; and Aaa is plastic friction. The difference in the flow stress is also the definition of the BSF ob = | o/| - 1 afR| = AabF + AabR (s.3) But it was seen that the model was not good enough to explain the event. TAYA and the others (1990) made another model to explain the event. Their findings imply that the work hardening of this particulate MMC system is mainly to back stress and to forest dislocations or the source - shortening stress effect. Particulates are assumed to be spherical, of the some diameter, and distributed uniformly in the matrix. By using Eshelby's model modified for finite volume fractions of fillers, the bilinear stress - strain curve of a particulate metal matrix composite as a result of the back stress can be predicted in the following form : ay+Erep for ep>Q cr = - (s,4) Ec.e for ?,= 0 Et= _t_ (8,5) 1-E^/EC XVIo and s are the true stress and strain respectively. oy is the yield stress (it is same for tension and compression) and Ec and Etc are the Young and tangent moduli respectively. (s,6) (s,7) (s,8) Our model is very close to this model. The values are nearly same. We accepted that there was no residual stress first. ARSENAULT and PILLAI (1996) suggested to combine this two models in order to have better solution. In the simple back stress model the effects of the back stress are treated as invariant. This means that a certain percentage of the residual stress. contributes to the BSF, and this percentage does not change with the magnitude of the forward strain. In the formulation of ”Taya" the back stress again can be related to the residual stress and how the residual stress changes with strain. They assume there is zero TRS and that the residual stress (back stress) develops as a result of plastic deformation in the softer matrix in the presence of the nondeforming reinforcement. Their analysis predicts that the percentage of the residual stress which contributes to the BSF is larger than obtained by SHI and ARSENAULT (1993) and that the percentage is a function of plastic strain. Since both models of BSF are based on the relationship of residual stress and BSF, it is possible to combine the two. In other words, take into account that there is a TRS present in the sample prior to loading and that assumption of in variancy is too restrictive. The combination is given in the following equation: ah = AobF + AabR + 2 E t ep (s,9) Our Model is in good agreement with the back stress model of TAYA and the others (1990). The last model is good enough to explain the event. We must also consider the first residual stress, occurs by cooling. xvn
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