Pt. II C9 Alloys 2014-15 Lecture 4 Microstructural anisotropy Microstructural anisotropy in polycrystalline materials Micrograph of metal grains Image processed ! ! ! wood extruded pure Al Measure no. intercepts using grid Polar plot of mean intercept lengths ! ! Composites: fracture stress versus fibre orientation Piezoelectric effect, e.g. in perovskites Fracture stress (MPa) Fibre orientation (°) http://aluminium.matter.org.uk anisotropy module, page 5 Representation surface for diffusion in Mg B 1 Dx Need for unique direction Tensile test in single crystal: Schmid factor Flux J Concentration gradient C A τ = O F cosφ cosλ A C* 1 Dz ! adapted from www.doitpoms.ac.uk/tlplib/anisotropy/ellipsoid.php [email protected] www.doitpoms.ac.uk/tlplib/slip/slip_geometry.php Page 1 Pt. II C9 Alloys 2014-15 Lecture 4 Stereographic projection for fcc & bcc lattices Taylor factor m Schmid factor defined by τcrss = σ (cosϕ cosλ) Taylor factor m is given by σ = τcrss m i.e. m = (cosϕ cosλ)-1 and hence low m means easier slip Magnitude of m is obtained by summing the (inverse) Schmid factors of each slip system. For a polycrystal, the arithmetic mean of the Taylor factors is typically used to represent the ratio between the macroscopic flow stress and the critical resolved shear stress. Typically m ≈ 3 in polycrystalline alloys ! Diehl’s rule allows prediction of optimal slip systems Orientation dependence of m for plastic flow Assumes - weak (low Taylor factor so easy deformation) grains cannot deform much until harder are also deforming plastically, and - harder (high Taylor factor) grains deform by a combination of stress concentration and work hardening around them. Orientation dependence of τ for Cu [MPa] 111 111 2.449 100 3.674 110 3.674 100 Hosford W. F. “Mechanics of crystals and textured polycrystals”, OUP, 1993 Tensile yield stresses at different orientations – Mg single crystals 110 Honeycombe R.W.K. “Plastic deformation of metals”, Edward Arnold, p18, 1982 Rotation of slip planes towards tensile axis cosϕ cosλ Honeycombe R.W.K. “Plastic deformation of metals”, Edward Arnold, p18, 1982 [email protected] Pt. II C6 Crystallography “Deformation and texture” Page 2 Pt. II C9 Alloys 2014-15 Lecture 4 Load-extension curves for tensile deformation of two Cd crystals Effect of single crystal orientation on the Young modulus of Al geometric softening ! Two different orientations: the solid curve showing softening http://aluminium.matter.org.uk - anisotropy module Magnetocrystalline anisotropy Hysteresis loops for hard and soft magnetic materials B <100> if Fe <111> if Fe H . www9.dw-world.de/rtc/infotheque/electronic_components/inductors.html Pole figure for isotropic polycrystalline alloy 100 pole figure plotted relative to sample axes Pole figure for anisotropic polycrystalline alloy 100 pole figure plotted relative to sample axes and showing “cube” texture Problem: rotations round ND not included RD Pt. II C6 Crystallography “Deformation and texture” [email protected] Pt. II C6 Crystallography “Deformation and texture” TD Page 3 Pt. II C9 Alloys 2014-15 Lecture 4 Orientation distribution function ODF Orientation distribution function ODF Pt. II C6 Crystallography “Deformation and texture” Pt. II C6 Crystallography “Deformation and texture” Dendritic growth (cobalt, samarium, copper alloy) Rotation of slip planes towards tensile axis www.doitpoms.ac.uk/tlplib/solidification_alloys/dendritic.php Pt. II C6 Crystallography “Deformation and texture” Uniaxial stress-strain curve for recrystallised alloy 5754-O Orientation relationships between austenite & martensite (a) Bain (b) Nishiyama–Wassermann (c) Kurdjumov–Sachs ! http://aluminium.matter.org.uk/ - choose anisotropy [email protected] Blue atoms indicate a bcc unit cell. The red arrows indicate part of the motion initiating the transformation. The dashed arrows indicate the invariant direction which is shared by the parent and martensite phases. Page 4 Pt. II C9 Alloys 2014-15 Lecture 4 Deep drawing of sheet Deep drawing of sheet: earing www.custompartnet.com/wu/sheet-metal-forming www.sciencedirect.com/science/article/pii/S0045782503005176 Cube-on-edge texture & cube textures in grain oriented silicon steel Effect of Si on the equilibrium diagram of Fe-C alloys and the effect of Si on the ductile brittle transition temperature ! Goss texture http://softmagneticalloy.com/soft_magnetic_materials.htm Strength & elongation for major classes of steel . . TRIP/ TWIP www.keytometals.com/page.aspx?ID=CheckArticle&site=kts&NM=207 [email protected] Page 5