FINITE ELEMENT MODELING AND ANALYSIS OF Zr35Ti30Cu8.25Be26.75 3D CELLULAR STRUCTURES FOR DUCTILITY PROJECT REPORT

INTRODUCTION

1.1 Introduction to Metallic glasses Bulk metallic glasses (BMGs) with excellent mechanical properties have become a research hotspot and promising potential as structural and functional materials. Microstructural architectures with material specific design have been proven powerful in nature and engineering applications. Natural materials, such as shells, tooth, or bone, exhibit complex hierarchical structures spanning from microscopic to macroscopic length scales and show significantly improved mechanical properties (e.g. strength and toughness) compared to base materials. Applications of engineering materials with synthetic structures range broadly, from advanced aerospace structures, structural foams, multifunctional micro lattices, and topology-optimized architectures to bio-inspired architectures. Taking cellular metals for example, the high specific strengths and large compressibility makes them powerful for energy-absorbing applications. In general, energy absorption of a cellular material scales directly with its strength and plasticity. Bulk metallic glasses have received a lot of attention for their high strength and elasticity which are consequences of their amorphous structure and concomitant lack of dislocations and associated slip planes. Bulk metallic glasses (BMGs) are a class of amorphous metals that possess very high strength. They are often not plastic in bulk forms (>1 mm) but can be very plastic at small scales (<1 mm). In addition, the significantly higher elasticity of BMGs (~2%) over crystal metals (~0.8%) or ceramics (~0.2%) offers a high possibility to develop super-elastic “spring-like” cellular structures. A combination of lithography and thermoplastic forming allows us to fabricate honeycombs from bulk metallic glass (BMG) precisely and to manipulate its structure selectively. Upon yielding, however, BMGs suffer from a strong tendency toward shear localization, which results in macroscopically brittle failure at ambient temperatures. The lack of macroscopic plasticity is considered the Achilles’ heel of BMGs and has prevented widespread proliferation of BMGs as a structural material. However when BMGs are used in geometries where one dimension is below about 10 times its critical crack length (∼ 1 mm for a medium range Zr-based BMG), they exhibit significant bending plasticity. In addition to the potential for microstructural architecture design, the unusual high ratio of yield strength over modulus of BMGs suggests that a transition from plastic yielding to elastic buckling can be realized for practical l/t ratios ( l : ligament length, t : ligament thickness). Systematic studies of such effects have been difficult since fabrication methods for stochastic foams and microstructural architecture designed by perforation- stretching provides limited control over microstructural features. BMGs are suitable to be used in such structures, and mathematical models have been developed. Furthermore, corner-fillets are used as a design tool to dissipate energy more homogenously throughout the BMG honeycombs. We consider theZr35Ti30Cu7.5Be27.5 as a typical BMG with negligible macroscopic plasticity and, as a comparison, Pt57.5Cu14.7Ni5.3P22.5, which exhibits unusually high, ∼20% compressive plasticity.

1.2 BULK METALLIC GLASSES
1.2.1 Early developments of metallic glasses
The formation of the first metallic glass of Au75Si25 was reported by Duwez at Caltech, USA, in 1960. They developed the rapid quenching techniques for chilling metallic liquids at very high rates of 105 –106 K/s. Their work showed that the process of nucleation and growth of crystalline phase could be kinetically bypassed in some alloy melts to yield a frozen liquid configuration, that is, metallic glass. Bulk Metallic Glasses BMGs are those non crystalline solids obtained by continuous cooling from the liquid state, which have a section thickness of at least a few millimeters. More commonly, metallic glasses with at least a diameter or section thickness of 1mm are considered “bulk.” (Nowadays researchers tend to consider 10mm as the minimum diameter or section thickness at which a glass is designated bulk.)

1.2.2 Characteristics of bulk metallic glasses
As will become clear in the subsequent chapters, BMGs have the following four important characteristics:
i. The alloy systems have a minimum of three components; more commonly the number is much larger and that is why they are frequently referred to as multicomponent alloy systems. There have also been reports of binary BMGs. But, the maximum diameter of the rod which could be obtained in a fully glassy condition is usually reported to be 1 or 2mm. And even in these sections, a small volume fraction of Nano crystalline precipitates have been frequently observed to be dispersed in the glassy matrix.
ii. They can be produced at slow solidification rates, typically 103 K s−1 or Less. The lowest solidification rate at which BMGs have been obtained was reported as 0.067K s−1, that is, 4K min−1 which is a really slow solidification rate.
iii. BMGs exhibit large section thicknesses or diameters, a minimum of about 1mm. The largest diameter of a bulk metallic glass rod produced till date is 72mm in a Pd40Cu30Ni10P20 alloy.
iv. They exhibit a large super cooled liquid region. The difference between the glass transition temperature, Tg, and the crystallization temperature, Tx, that is, ΔTx=Tx−Tg, is large, usually a few tens of degrees, and the highest reported value so far is 131K in a Pd43Ni10Cu27P20 alloy.

1.2.3 Glass-forming ability of BMG
The formation of multicomponent BMGs demonstrated that excellent GFA is ubiquitous and not confined to Pd-based alloys. The work of Inoue opened the door to the design of new families of BMGs and attention was once again focused on the investigation on BMG. Many kinds of BMGs have been developed including of different materials with different composition. At present, the lowest critical cooling rate for BMG formation is as low as 0.10 K/s for the Pd40Cu30Ni10P20 alloy and the maximum sample thickness reaches values as large as about 10 cm. The alloy with the largest super cooled liquid region of 135K is (Zr82.5Ti17.5)55(Ni54Cu46)18.75Be26.25. The design of the ZrTiCuNiBe glass-forming alloy family was an important progress made by Peker and Johnson. The quinary glass-former has distinct glass transition, very high stability of super cooled liquid state, and exhibits high thermal stability against crystallization. Vitalloy 1 (vit1), one of the most extensively studied BMG in the family, has the composition of Zr41Ti14Cu12.5Ni10Be22.5. Its temperature–time transition (TTT) diagram has the ‘nose’’ of the nucleation curve for crystals at time scales of the order 102 s and the critical cooling rates for glass formation in the 1 K/s range. The alloy can be cast in Cu-mold in the form of fully glassy rods with diameters ranging up to 5– 10 cm. Figure exhibits the as-cast Zr-based BMGs in different shapes prepared by the Institute of Physics, Chinese Academy of Sciences, China. The formation of the BMGs in this family requires no fluxing or special processing treatments and can form bulk glass by conventional metallurgical casting methods. It is apparent that the BMGs were developed in the sequence beginning with the expensive metallic based Pd, Pt and Au, followed by less expensive Zr-, Ti-, Ni- and Ln-based BMGs. Furthermore, it can be seen that the much cheaper Fe- and Cu-based BMGs were the most recently developed and had attracted extensive interests. Recently, the investigation on nonmagnetic bulk amorphous steel based on iron became one of the hottest topics in this field. A coordinated program has been carried out in the USA to develop new bulk ferrous metallic glasses via the exploration of novel compositions, synthesis of bulk materials, scientific underpinning of glass formability using atomistic modeling, and determination of three-dimensional atomistic structures.