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Sünek Alüminyum Plakalarda Çatlak İlerleme Mekanizmalarının Nümerik ve Deneysel Metotlarla İncelenmesi
No full textYÖK Tez No: 685846In ductile metal plate tearing, cracks propagate in four different ways: i-) slanted, ii-) cup-cone, iii-) cup-cup, and iv-) a combination of these three. The crack propagation mechanism depends on the geometry and the material properties of the plate, as well as on the loading conditions. Several experimental studies in the literature reveal that strain hardening capacity affects the crack propagation mechanism. In high strain hardening capacity metals, a severe necking occurs at the crack tip before crack starts to propagate. The stress triaxiality reaches to considerably larger values in the center of the necking zone in comparison to that on the side faces of the plate, and therefore the crack initiates in the center and propagates in a cup-cup morphology. For low strain hardening capacity metals, on the other hand, the necking at the crack tip remains at low levels, plastic deformation localizes at shear bands and the crack propagates in either slanted or cup-cone morphology. Experimental results also show that the dominant crack propagation mechanism is cup-cup at low (quasi-static) loading rates, while it is slanted or cup-cone at high loading rates. The current literature focuses mainly on the mechanical/geometric properties of the plates; microstructure–crack morphology relationship is not yet fully clarified. This thesis aims to investigate the effects of microstructure on the crack propagation mechanism in detail. In ductile metals and metal alloys, cracks propagate predominantly by the growth and coalescence of voids nucleated by second phase particles whose size is in the order of micrometer. The fundamental hypothesis of this thesis is that, the volume fraction, the average size, the aspect ratio and spatial distribution of these particles/voids would affect crack propagation. In order to test this hypothesis, both numerical and experimental studies are performed. These studies verified the hypothesis, and the results showed that small, low aspect ratio and remotely distributed particles lead to cup-cup crack propagation, while large, elongated, and closely spaced particles favor slanted or cup-cone crack propagation. In addition, numerical calculations reveal that the orientation of elliptical nucleation sites, acting as particles, affects interactions between them and, therefore, the plastic deformation evolution in the fracture process zone. An orientation angle that allows smaller perpendicular distances between particles through the plate thickness or/and aligns particles on a shear band, promotes early localization of plastic deformation on a thin band. Consequently, this leads to a low level of plate tearing energy and, slanted or cup-cone crack propagation. In the case of an orientation angle that demotes interactions between particles, plastic localization is delayed leading to cup-cup crack propagation and a high level of plate tearing energy.Sünek metal plakaların yırtılması esnasında çatlaklar dört farklı şekilde ilerler: i-) eğik (slanted) çatlak, ii-) bardak-kapaksı (cup-cone) çatlak, iii-) bardak-bardaksı (cup-cup) çatlak ve iv-) bu üçünün karışımı. Çatlak ilerleme mekanizması, plakanın geometrisine, malzeme özelliklerine ve yükleme koşullarına göre değişmektedir. Literatürdeki birçok deneysel çalışma, plaka malzemesinin pekleşme kapasitesinin çatlak ilerleme mekanizmasında etkili olduğunu ortaya konmuştur. Yüksek pekleşme kapasitesine sahip metallerde çatlak ilerlemesinden önce oldukça yoğun çatlak ucu boyun vermesi gerçekleşmektedir. Boyun verme bölgesinin merkezindeki gerilme üç eksenliliği, plakanın yan yüzeylerindekine kıyasla oldukça yüksek değerlere ulaşmakta, dolayısıyla çatlak plakanın merkezinde oluşup, bardak-bardaksı olarak ilerlemektedir. Düşük pekleşme kapasitesine sahip metallerde ise, çatlak ucundaki boyun verme düşük düzeylerde kalmakta, plastik deformasyon kesme kuşaklarında yoğunlaşmakta ve çatlak eğik veya bardak-kapaksı olarak ilerlemektedir. Deney sonuçları ayrıca, düşük yükleme hızlarında (sanki-statik) bardak-bardaksı ilerlemenin, yüksek hızlarda ise eğik veya bardak-kapaksı ilerlemenin daha etkin bir mekanizma olduğunu ortaya koymuştur. Mevcut literatür, daha ziyade plakaların mekanik/geometrik özellikleri üzerine yoğunlaşmıştır; mikroyapı ile çatlak morfolojisi ilişkisi henüz net bir şekilde ortaya konamamıştır. Bu tezin temel amacı, mikroyapının çatlak ilerleme mekanizmasına etkilerini ayrıntılı olarak araştırmaktır. Sünek metal ve metal alaşımlarında çatlaklar, temel olarak, büyüklükleri µm mertebesinde olan ikinci faz parçacıklar tarafından peydahlanan boşlukların büyümesi ve birleşmesiyle ilerler. Tezin ana hipotezi, bu parçacıkların/boşlukların alan oranlarının, ortalama büyüklüğünün, en-boy oranının ve uzaysal dağılımlarının çatlak ilerleme mekanizmasını etkileyeceğidir. Bu hipotezi test etmek amacıyla, hem nümerik hem deneysel çalışmalar yapılmıştır. Yapılan çalışmalar hipotezi doğrulamış, elde edilen sonuçlar, ufak, dairesele yakın ve birbirine uzak parçacıkların bardak-bardaksı, büyük, ince uzun ve birbirine yakın parçacıkların ise eğik veya bardak-kapaksı çatlak ilerlemesine yol açtığını göstermiştir. Ayrıca yapılan nümerik çalışmalar, parçacıkları temsil eden eliptik boşluk peydahlanma bölgelerinin oryantasyonunun, aralarındaki etkileşimi ve kırılma oluşum bölgesi içerisindeki plastik deformasyonun gelişmini etkilediğini göstermiştir. Kalınlık boyunca parçacıklar arasındaki dik mesafenin azalmasına ve/veya parçacıkların bir kesme bandı üzerinde hizalanmasına izin veren oryantasyon açıları plastik deformasyonun ince bir bant üzerinde erken lokalizasyonunu desteklemektedir. Bu durum düşük plaka yırtılma enerjisi ve eğik/bardak-kapaksı kırılma tipi ile sonuçlanmaktadır. Parçacıklar arasındaki etkileşimleri zorlaştıran bir oryantasyon açısı ise plastik lokalizasyon geciktirerek yüksek plaka yırtılma enerjisine ve bardak-bardaksı kırılma tipine yol açmaktadır
Tüm Gerilme Oranları Sabit Tutularak Yapılan Birim Hücre Hesaplamaları
No full text16.12.2022 tarihine kadar kullanımı yazar tarafından kısıtlanmıştır.Ductile fracture in metals and metal alloys occurs through nucleation, growth, and coalescence of micron-scale voids nucleated at second phase particles. A detailed experimental investigation of the stages of ductile fracture, especially that of void nucleation and coalescence, is rather challenging and requires guidance from numerical simulations. With the studies in the literature, finite element voided unit cell calculations performed on ideal materials containing periodically distributed voids have become a convenient tool for numerical simulations of ductile fracture. In the last century, the effect of stress triaxiality on ductile fracture was well known, but shear loads were disregarded. Therefore, voided unit cell calculations were performed by prescribing only the ratios of normal stresses, i.e. ?_11=?_11/?_22 and ?_33=?_33/?_22. Experimental studies in the last decades, however, revealed a pronounced effect of shear loads on ductile fracture at low stress triaxiality, incorporated into ductile fracture simulations through the Lode parameter. In order to account for the effect of shear loads on void growth and coalescence, Tekoğlu (2014) developed a finite element framework where the stress state on a cubic unit cell containing a spheroidal void at its center is represented by three non-dimensional stress ratios, i.e. ?_11=?_11/?_22, ?_33=?_33/?_22 and ?_12=?_12/?_22. The present study attempts to extend the work of Tekoğlu (2014) by allowing a complete definition of the stress state on a unit cell with five non-dimensional stress ratios, i.e. ?_11=?_11/?_22, ?_33=?_33/?_22, ?_12=?_12/?_22, ?_13=?_13/?_22 and ?_23=?_23/?_22. Aside from being numerically efficient, the developed framework allows keeping the errors in the prescribed stress ratios below a few percent. The developed framework is generic and can be applied to any unit cells containing voids or particles. In addition to this framework, an alternative method that lowers modeling and computation costs is proposed for unit cell calculations performed only under principal stress state.Metallerde ve metal alaşımlarında sünek kırılma, ikinci faz parçacıklarda çekirdeklenen mikroskopik ölçekli boşlukların büyümesi ve birleşmesi yoluyla meydana gelmektedir. Sünek kırılma aşamalarının, özellikle boşluk çekirdeklenmesi ve birleşmesi aşamalarının ayrıntılı olarak deneysel yöntemler ile araştırılması oldukça zordur ve nümerik yöntemlerin kılavuzluğunu gerektirmektedir. Literatürde yapılan çalışmalar ile periyodik olarak dağılmış boşluklar içeren ideal malzemeler üzerinde yapılan boşluklu birim hücre sonlu elemanlar hesaplamaları, sünek kırılmanın nümerik simülasyonları için uygun bir araç haline gelmiştir. Geçen yüzyılda, gerilme üçeksenliliğinin sünek kırılma üzerindeki etkisi iyi bilinmekte, ancak kesme yükleri göz ardı edilmekteydi. Bu nedenle, boşluklu birim hücre hesaplamaları, yalnızca normal gerilimlerin oranları, yani ?_11=?_11/?_22 ve ?_33=?_33/?_22 kullanılarak gerçekleştirilmiştir. Bununla birlikte, son on yılda yapılan deneysel çalışmalar, Lode parametresi aracılığıyla sünek kırılma simülasyonlarına dahil edilen, düşük gerilme üçeksenliliğinde kesme yüklerinin sünek kırılma üzerindeki belirgin etkisini ortaya çıkarmıştır. Kayma yüklerinin boşluk büyümesi ve birleşme üzerindeki etkisini hesaba katmak için Tekoğlu (2014), merkezinde küresel bir boşluk içeren kübik birim hücre üzerindeki gerilme durumunun üç adet boyutsuz gerilme oranı, yani ?_11=?_11/?_22, ?_33=?_33/?_22 ve ?_12=?_12/?_22 ile temsil edildiği bir sonlu elemanlar çerçevesi geliştirmiştir. Bu çalışmada, Tekoğlu (2014) çalışması genişletilerek, birim hücre üzerindeki gerilme durumunun tamamının beş adet boyutsuz gerilme oranı, yani ?_11=?_11/?_22, ?_33=?_33/?_22, ?_12=?_12/?_22, ?_13=?_13/?_22 ve ?_23=?_23/?_22 ile temsil edilebildiği bir sonlu elemanlar çatısı geliştirilmiştir. Geliştirilen hesaplama çatısı, sayısal olarak verimli olmasının yanı sıra, gerilme oranlarını hesaplama boyunca düşük yüzdelerdeki (%1'in altında) hatalar ile sabit tutabilmektedir. Ayrıca, boşluklar veya parçacıklar içeren herhangi bir birim hücreye uygulanabilir olan genel bir hesaplama çatısı olma özelliğini taşımaktadır. Bu çatıya ek olarak, sadece asal gerilme durumu altında gerçekleştirilen birim hücre hesaplamaları için modelleme ve hesaplama maaliyeti daha düşük olan alternatif bir yöntem önerilmektedir
Size effects in cellular solids
Get PDFThe mechanical properties of metal foams (and other cellular solids) depend on the properties of the metal that they are made from, on their relative density, and on the cell topology (i.e., cell size, cell shape, open or closed cell morphology, etc.). The cell size of commercially available metal foams is about 1 to 10 mm. This is on the order of the smallest structural length of specimens in many applications. In such cases, the individual response to a load differs significantly from one cell to another, and the fundamental assumption of the classical continuum theory that the (physical, chemical, mechanical, etc.) properties of a material are uniformly distributed throughout its volume fails. Another situation where the classical continuum theory loses its accuracy is when the characteristic wavelength of loading is comparable to the cell size. An important technological consequence of this is the occurrence of size effects. The term "size effect" designates the effect of the macroscopic (sample) size, relative to the cell size, on the mechanical behaviour. In the last decade evidence of this appeared in a number of experimental studies (see section 1.4). To theoretically account for size effects, one may take the cellular morphology into account by discretely modelling each cell wall and/or cell face. This allows for an accurate representation of the microstructural deformation mechanisms, the bending and stretching of cell walls and faces. Such a microstructural model can predict how the overall (macroscopic) response is related to the microstructural parameters. In view of size effects, the most important feature is that it incorporates, in a physically sound manner, the material length scale in the problem, i.e. the cell size. However, such a discrete model can become computationally expensive for complex (random) microstructures, especially in three dimensions. Another approach is to use a generalized continuum theory in which many microstructural details are averaged out, but in which a "characteristic" length scale is retained. The goal of this thesis is twofold:
1) To explore the physical mechanisms that are responsible for the size-dependent elastic behaviour of cellular solids by using a discrete microstructural model.
2) To assess the capability of generalized continuum theories to capture size effects through a careful comparison with the discrete simulations.
The first chapter thesis introduces the experimental evidence for the size effects, and gives an historical overview of the generalized continuum theories used to model these size effects. In chapter 2, we use two-dimensional beam networks to mimic real (three-dimensional) foams, which allow us to account for the discreteness of their microstructure. We perform simple shear, uniaxial compression, and pure bending tests on a large variety of samples, and calculate the change in the macroscopic mechanical properties corresponding to a change in size. We close the chapter with a summary of the size effects that we observed in our calculations and discuss the possible mechanisms behind these size effects.
Chapter 3 uses the micropolar theory to capture the size effects observed in chapter 2. We fit the elastic constants of the micropolar continuum theory by comparing the analytical solution of the simple shear problem with the discrete analyses, in terms of the best agreement in the macroscopic shear stiffness of the samples. We develop a strain mapping procedure and evaluate the performance of the fitted micropolar constants in predicting the local deformation fields, the microrotations and shear strains. Finally, we solve the pure bending problem analytically for the micropolar theory and close the chapter with a discussion on the limitations of the Cosserat-type theories.
In chapter 4, we propose a generalized continuum theory (strain divergence theory), which associates energy to the divergence of strain. We derive the equilibrium equations and the boundary conditions for the strain divergence continuum, and develop a finite element implementation of the theory. We solve the simple shear and the pure bending problems analytically and compare the solutions with the discrete calculations, as well as with the analytical solutions for the couple stress theory.
Chapter 5 explores the strain concentration problem around a cylindrical hole in a field of uniaxial tension. First, we perform discrete calculations on samples with different hole sizes and show the effect of the hole size on the strain distribution near the hole. Then we compare the discrete analyses with the analytical solutions for the classical, couple stress and strain divergence theories.
Finally, in Chapter 6, we summarize the size effects that we observed in the mechanical behaviour of the two dimensional cellular solids, and we compare the different generalized continuum theories with respect to their ability in capturing size effects.
Phase-field approach to model fracture in human aorta
No full textOver the last decades the supra-physiological and pathological aspects of arterial tissues have become a prominent research topic in computational biomechanics in terms of constitutive modeling considering damage and fracture [1]. The current study presents a variational approach to the fracture of human arterial walls, featuring a thermodynamically consistent, gradient-type, diffusive crack phase-field approach. A power balance renders the Euler-Lagrange equations of the multi-field problem, i.e. the deformation and the phase-field. The respective constitutive model is essentially anisotropic and in accordance with the tissue morphology. A novel anisotropic phase-field model accounts for not only the altered crack patterns with respect to the orientation collagen fibers, but also the distinct strain-energy contributions due to isotropic and anisotropic parts [2, 3, 4]. The prediction of the crack pattern are studied via single edge-notched tests to ascertain anisotropic features of the model. Aside from that, a novel simple concept of design, i.e. an idealized cylindrical model of the multi-layered thoracic aortic wall with a notch representing the initial tear provides insights regarding the nascent crack growth associated with aortic dissection. In particular, the analysis indicates crack onset and progression around the initial tear while aligning with the direction of the first fiber family, capturing the helical pattern of the aortic dissection in the aorta [4]. The results also lay bare the need for a systematic experimental characterization of the human aorta for an inclusive parameter identificatio
Void Coalescence in Ductile Solids Containing Two Populations of Voids
No full textMany metallic alloys contain a primary and a secondary population of voids, the difference in size reaching up to orders of magnitude. The present study extends Thomason's and Benzerga-Leblond's criteria for the onset of coalescence of primary voids to incorporate the effects of a secondary population. Plastic limit load analysis is performed within a finite element (FE) framework by using three dimensional (3D) cubic unit cells. The macroscopic stress state of the unit cells corresponds to axisymmetric tension with Sigma(22) > Sigma(11) = Sigma(33). The extended versions of both criteria are able to successfully predict the critical stress for the onset of coalescence. (C) 2015 Elsevier Ltd. All rights reserved
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