MME 131: Lecture 17 Strengthening Mechanisms Prof. A.K.M.B. Rashid Department of MME BUET, Dhaka Today s Topics Strengthening strategies: Grain strengthening Solid solution strengthening Work hardening Precipitation hardening Reference: WD Callister, Jr. Materials Science and Engineering: An Introduction, 5 th Ed., Ch. 7, pp.166-179. Lec 17, Page 1/15
General strengthening Strategy Engineering alloys are designed to have maximum strength with some ductility and toughness. The chemical composition of the alloy provides an alloy with a base mechanical properties, which can be improved if necessary. Plastic deformation depends on the ability of dislocations to move. All strengthening methods rely on impeding the motion of dislocations. To strengthen a material, the general strategy is: make it harder for dislocations to move There are 4 mechanisms by which the general strengthening strategy can be achieved: 1 Grain strengthening 2 Solid solution strengthening 3 Work/strain hardening 4 Precipitation hardening The price for enhancement of strength and hardness is in the reduction of ductility!! Lec 17, Page 2/15
#1: Grain Strengthening Obstacle: Grain boundary Creates slip plane discontinues causing difficulty in dislocation motion Grain boundaries impede the motion of dislocations. grain boundaries act as discontinuity in the lattice the slip plane in a grain does not continue in the same direction beyond the boundary dislocation needs to change direction on moving from grain A to B, which requires more energy So, dislocations are stopped by a grain boundary and pile up against it. FIGURE 7.14 ( Callister) The motion of a dislocation as it encounters a grain boundary, illustrating how the boundary acts as a barrier to continued slip. angle of misalignment Degree of obstacle increases with misorientation Small angle grain boundaries not very effective High-angle grain boundaries block slip and increase strength of the material high-angle grain boundary low-angle grain boundary angle of misalignment High angle grain boundaries cause greater mismatch along the grain boundary and offer greater resistance to dislocation motion Lec 17, Page 3/15
Phase boundaries, twin boundaries and ferroelectric or ferromagnetic domains have the same effect on providing obstacles to dislocation motion. Figure 4.11 (Callister) Dislocation movement in complex alloys are more difficult (due to the presence of twin boundary and phase boundary along with the grain boundary) Domains in ferroelectric barium titanate. Similar domain structures occur in ferromagnetic and ferrimagnetic materials. Small grain size generates high grain boundary surface area more barrier to impede dislocation motion and slip high yield strength (σ y ) and toughness Variation of yield strength of a material with its grain size according to Hall-Petch relation: s y = s 0 + k y d -½ s 0 = Yield strength at infinite grain size (i.e., single crystal) k y = Hall-Petch constant d = Average grain diameter The finer the grains, the larger the strength Halll-Petch constants for some materials Material Fe Mo Nb Cu Al Zn s 0, MPa 48 110 126 26 16 33 k y, MPa. m 0.71 1.77 0.034 0.11 0.068 0.22 Lec 17, Page 4/15
Grain Strengthening Example: Brass (70Cu-30Zn alloy) s y = s 0 + k y d -½ Figure 7.15 (Callister): The influence of grain size on the yield strength of a 70Cu-30Zn brass alloy. Note that the grain diameter increases from right to left and is not linear. Grain size d can be controlled by: the solidification process (faster cooling rates produce finer grains) plastic deformation (deformation followed by recrystallisation produces new finer crystals) appropriate heat treatment (e.g., normalising heat treatment produces new refined grains) #2: Solid Solution Strengthening Obstacle: Impurity atoms offers obstruction in dislocation motion Just like dislocations, alloying elements impose localized lattice strain in the host lattice due to the difference in size. compression tension compression tension stresses around an edge dislocation small substitutional atom large substitutional atom stresses around an impurity atom Lec 17, Page 5/15
Impurity atoms diffuse to positions where they reduce strain in lattice. smaller solute atoms sit at base of edge dislocations larger solute atoms sit at top of edge dislocations Smaller impurity atoms with their tensile strains tend to congregate in the compressive area above the slip plane Larger impurity atoms with their compressive strains tend to congregate in the tensile area below the slip plane This results partial cancellation of impurity-dislocation lattice strains, and and increase the stress required to move dislocations resistance to slip is increased As before, opposite stress around the impurity atom attracts the stress around dislocation and like stresses repeal each other. Lec 17, Page 6/15
Tensile Strength (MPa) Elongation in 2 inch (%) Principle of Alloying Alloying (i.e., making pure metal impure!) makes metals stronger and harder (almost always). Interstitial or substitutional impurities in a solution cause lattice strain. As a result, these impurities interact with dislocation strain fields and hinder dislocation motion. Impurities tend to diffuse and segregate around the dislocation core to find atomic sites more suited to their radii. This reduces the overall strain energy but anchor the dislocation. The resistance to slip will be greater because the overall lattice strain must now increase if a dislocation is torn away from them. Thus, a greater applied stress is necessary to: (1) torn away a dislocation from impurity pinning and initiate plastic deformation, and then (2) continue plastic deformation for solid solution alloys. Solid Solution Strengthening Example Alloying with Ni strengthens Cu 60 400 50 300 200 0 10 20 30 40 50 Ni Content (wt.%) 40 30 20 0 10 20 30 40 50 Ni Content (wt.%) What happens to the right side of these diagrams, i.e., alloys containing more than 50 wt.% Ni? Lec 17, Page 7/15
Figure 9.8 (Askeland). The effects of several alloying elements on the yield strength of copper. Nickel and zinc atoms are about the same size as copper atoms, but beryllium and tin atoms are much different from copper atoms. Increasing both atomic size difference and amount of alloying element increases solid-solution strengthening. #3: Strain Hardening Obstacle: Already existing dislocations offers obstruction in motion of other dislocations Also known as strain hardening, work hardening, or cold working Ductile metals become stronger when they are deformed plastically at temperatures well below the melting point. The reason for strain hardening is the increase of dislocation density with plastic deformation due to dislocation multiplication and formation of new ones The average distance between dislocations decreases and the dislocations start blocking the motion of each other. Lec 17, Page 8/15
Cold working room temperature deformation common cold working operations The percent cold work (%CW) is often used to express the degree of plastic deformation: A %CW = 0 A d A x 100 0 A 0 = original cross-section area A d = area after deformation. The percent cold work, %CW, is just another measure of the degree of plastic deformation, in addition to strain or %EL, It is also known as present reduction in area, %RA. Lec 17, Page 9/15
Yield Strength (MPa) Ductility (%EL) σ y for plastically deformed sample is higher than that for annealed sample due to hardening. (materials becomes stronger with strain). TS hardening %EL or %RA YS Stress-strain diagram showing strain hardening Effect of cold work on stress-strain diagram Work hardening: An example Yield strength and hardness increased due to strain hardening but ductility decreased (material becomes more brittle). Cold Work (%CW) Cold Work (%CW) Lec 17, Page 10/15
Anisotropy in Structure During cold working operations, the grains are deformed along the working directions and makes the material anisotropic. Isotropic material Anisotropic material Restoring Ductility after Work Hardening 1 hr heat treatment at different annealing temperatures. Effect of cold work is reversed. TS decreased while %EL increased!! Restoration of ductility in 2 steps: 1. recovery 2. recrystallisation Sometimes recrystallisation is followed by grain growth. Lec 17, Page 11/15
The effect of cold work on the properties of a Cu-35% Zn alloy and the effect of annealing temperature on the properties of a Cu-35% Zn alloy that is cold-worked 75% Recovery increased diffusion enhanced dislocation motion decreased dislocation density by annihilation, formation of low-energy dislocation configurations relieved internal strain energy Recrystallisation some residual stresses remained in some grains even after recovery stage. these strained grains replaced by new strain-free grains with low dislocation density. this occurs through nucleation and growth of new grains. Grain growth small grains merged and form larger grains with low grain boundary area. Lec 17, Page 12/15
Recrystallisation Small new crystal formed by consuming cold-worked crystals Reduced dislocation density Further recrystallisation All cold-worked crystals are consumed Grain growth At longer times, larger grains consume smaller ones Recrystallisation occurs more easily as temperature increases. Recrystallisation temperature where recrystallisation occurs in 1h ⅓ ½ of T m Recrystallisation temperature decreases as %CW is increased. %CW below which no crystallisation takes place Recrystallisation and melting temperatures of common metals and alloys Lec 17, Page 13/15
#4: Precipitation Hardening Obstacle: Hard second phase particles offers obstruction in motion of dislocations Example: Ceramics in metals (e.g., SiC in Iron or Aluminum) Hard precipitates are difficult to shear!! To Summarise: Dislocations are observed primarily in metals and alloys. Making dislocation motion difficult increases strength. Strengthening strategies: decrease grain size add solid solution impurities cold work precipitate second phase particles Heating (annealing) can reduce hardening effect by reducing dislocation density and increasing grain size. This increases ductility but decreases strength and hardness. Temperature and strain rate also affect strength and ductility. Lec 17, Page 14/15
Next Class MME 131: Lecture 18 Fracture in Metals Lec 17, Page 15/15