Material Deforming Near their Ideal Strength By (original) (raw)

In recent years it has been shown that it is possible to design materials with strengths approaching their theoretical ideal limit. This is an intriguing development; materials typically fail at stresses that are several orders of magnitude below their theoretical limits of strength. The development of engineering alloys with usable strengths near the ideal limit would have profound technological implications. The most common approach used to increase a material's strength, is grain refinement. This method has been used to produce nanograined hollow nanospheres of CdS. Under nanoindentation these spheres show remarkable strength and deformation properties. The stresses and strains in the shells are studied with linear elastic finite element analyses and from this a failure criterion is developed. The stresses predicted by the failure criteria are 2.2 , which is very large for an inherently brittle material. We compare the failure stress to the calculated ideal strength for CdS, calculated using density functional theory. Comparing the stress predicted by the failure criteria to the ideal strength shows that the hallow nanospheres approach 70% of their ideal strength. In 2003 a new Ti, Nb based alloy "Gum Metal" was introduced by Toyota Research Corp. This alloy has strength approaching the ideal limit even in bulk form. Moreover, the material deforms in a novel fashion without the obvious participation of dislocations. A Ti-V alloy has been chosen to study the properties of this type of alloy. The BCC ideal yield surface is examined as a function of composition. Dislocation core structures are also examined as a function of composition. The results explain some experimental observations in this novel system. Contents Contents ii List of Figures iv List of Tables vii List of Figures 2.1 In (A) the Hexagonal (wurtzite) crystal structure is presented in (B) the cubic (zinc blende) crystal structure is presented. These are the most common crystal structures observed in II-VI compounds....……..…………7 2.2 Mesh representation of the four elements in the FEA model. The purple rectangle is the diamond indenter, red rectangle represents the silicon substrate, the blue curved region is the CdS nanosphere and the blue triangle represents the residual TOPO. In ANSYS mesh PLANE42 is used to represent the indenter, substrate and CdS while PLANE82 is used to represent the triangular TOPO section…………………………………………………………...……………..……… 10 2.3 Load vs. Displacement of a CdS nanosphere black dots represent experimental data. Dark blue line is FEA model prediction with ! ! = 0.74. Lite blue band considers the error in shell thickness ±7 ………………….……… 14 2.4 A Comparison of Force vs. Displacement of CdS nanosphere for 16 different experimental results with the predicted FEA curves. The black dots represent experimental data. Dark blue line is FEA model prediction with ! ! = 0.74. Lite blue band considers the error in shell thickness ±7 …………………………..15 2.5 FEA comparison of stresses and strains generated during indentation, at 10, 20 and 30 nm displacement of the top of the shell. Panel (A) shows the shear stress development in the shell, while in panel (B) the tensile development is shown. Then in panel (C) the development of the shear strains is shown. …………………………………………………………………………..…………..…. 16 2.6 Comparison experimental failures to the FEA based failure criteria. Black dots represent experimental failure, blue line the predicted failure with the average value of the inner/outer radii and the red triangles representing prediction for specific diameter and inner/outer, with the red bar being the error in the thickness. ……………………………………………………………….……..……… 18 2.7 The heavy black lines outline the planes on which slip shown to be the easiest. These planes posses short Burgers vectors. (A) Basal slip system and (B) Prismatic slip system……………………………………………………..……… 19 2.8 The heavy black lines outline the plane on which the displacement was applied. The displacement takes place in the direction of the Burgers vector……………………………………….…………………………………..……… 19 2.9 Comparison of the ideal strength for the Basal plane shear "Blue" and the Prismatic slip system. These are the two slip systems that have been reported as being active. …………..…………………………………………..…………..……… 20 v 3.1 Bain path for Ti 25 V 75 using density functional theory and k-points described in the text. The global minimum represent the BCC structure, the global maximum is the FCC structure while the local minimum is a tension formed BCT structure.…………..…………………………………………………………...……… 26 3.2 The energy surface of the Ti 25 V 75 is presented. The three variants of the Bain path are shown with the black lines. The three minimum BCC structures are shown. The white dots are the BCT saddle points that occur under extension past the FCC structure..………………………………………………..…………..……… 27 3.3 In this figure the Bain paths for four different compositions are given. In the Ti 25 V 75 composition there is a clear energy barrier in going from the BCC to BCT structure...………………………………………………………….…………..……… 28 3.4 Energy surface for Ti 25 V 75 showing the relevant energy barriers. These energy barriers are significantly larger than the energy available at room temperature…………....……………………………….………….…………..……… 30 3.5 Energy surface for Ti 85 V 15 showing that no energy barriers are visible in these calculations. The energy contours are plotted so that the smallest energy contour is equal to the energy at room temperature.…………....……..…………..……… 30 3.6 Bain paths for seven elemental BCC structures. From an examination of these it is clear that Nb and V behave qualitatively the same, thus reinforcing that Ti-V is a good approaximate to Gum Metal. It seems like the anisotropic nature of a material determins how it will transform.………….……..……… 31 4.1 Dislocation density required causing core overlap. The density is plotted as a function of the electron per atom ratio for TiV alloys. The density tends to zero as the BCC to HCP transition is approached……………….…………….…...……… 38 4.2 Supercell used for the computation of the dislocation core structures. Each cell contains 96 atoms with two screw dislocations both in the easy core configuration…………………………………………….……………..……...……… 39 4.3 Comparison of screw dislocation core structures for three different compositions. A) show the relaxed core structure for Ti 25 V 75 , which is clearly isotropic in nature. B) shows the relaxed core structure for Ti 50 V 50 which does not show much spreading of the dislocation cores. Final C) which is the relaxed core structure for composition Ti 75 V 25 clear show interaction between the dislocation cores. Every column of atoms in this structure experiences some displacements………………………………………………………….……...……… 41 4.4 Extent of the dislocation cores of screw dislocations determined by the ideal strength and elasticty of the materials. A) Ti 25 V 75 (isotropic) material shows little spreading of the cores. While in B) Ti 80 V 20 show substantial spread and interaction between the cores…………………………………….….……...……… 42 I would also like to thank my qualifying exam committee, Ron Gronsky, Andrew M. Minor, R. Ramesh and Brian Worth, for taking the time to be on my committee and showing such interest in the research. I am also grateful to my dissertation committee, Daryl C. Chrzan, Andrew M. Minor and Peter Hosemann, for their time and effort in reading my thesis. I want to thank all of my incredible officemates for their help over the years. Thank you, Lawrence Friedman and Karin Lin for helping me to understand how to perform research as a very green undergraduate. I am eternally grateful to Scott Beckman for all of his time and effort with maintaining computers and working with me on computational techniques. Also Elif Ertekin,