7 Dislocation & strengthening Mechanism in Metals

Transcription

1 7 Dislocation & strengthening Mechanism in Metals vacancy diffusion (substutional) Dislocation & plastic deformation 7.2 Basic concept Plastic deformation motion of larger number of dislocation Motion of edge dislocation Fig 7. (The process by which plastic deformation is produced by dislocation motion is tensile slip) It form an edge dislocation finally called edge dislocation Slip plane : The crystallographic plane along which the dislocation line traverses is the slip plane Dislocation density (number of dislocation) Total dislocation length per unit volume. Number of dislocation that intersect a unit area of a random section Unit mm/mm 3,or /mm 2 For carefully solidified metals 0 3 mm -2 For heavily deformed metals 0 9 ~ 0 0 mm -2 Often heat treatment 0 5 ~ 0 6 mm -2 Estimate dislocation density : 0 9 mm/mm 3

2 7.3 Characteristics of Dislocations Extra half plane : lattice strains 有 compression, tensile & shear affect the mobility of dislocation & ability to multiply compression tension Dislocation interaction: Two edge dislocation of the same sign Repulsive

3 7.4 slip system Dislocation 在不同平面不同方向的滑移能力不同有 preferred place : slip plane, slip direction Slip system 包含 slip plane & slip direction Slip system depends on crystal structure (fcc : ) atomic distortion 因 dislocation motion 最小 For FCC { } family, i.e. ( 0 -) [0 -] (- 0) Slip direction < 0> with { } plane Slip system { } < 0> 一個 plane 有可能有很多的 slip direction Dislocation in FCC & BCC slip easier than in HCP FCC & BCC metals 較 soft. HCP brittle Microstructure properties

4 7.5 Slip in single crystal Question : slip system 最簡單的 case : single crystal Although an applied stress may be more tensile or compressive, shear component exists. Force area F ' = F cosθ, shear force, τ '= σ σinθ coσθ τ = F A 0 F σinθ = = A coσθ 0 F A 0 σinθ coσθ = σ σinθ coσθ pure 拉伸應力有可能在電子平面產生 shear Resolved shear stress 分解剪應力 ψ:angle between the normal to the slip plane and the applied stress direction. τ R = σ coσφ coσλ...two ways to drive this equation. 有一個最大分的 slip systemτ = s (cosφ cosλ R ) (max) max 當 τ R 大到使 slip 開始的 stress 於 Critical resolved shear stress λ:the angle between the slip & stress direction φ + λ 90 當 single crystal 開始 deform plastically, stress=σ y, yield stress τ R = τ (max) crss s y = τ crss ( cosφ cosλ) max 當 φ = λ = 45 時, s y = 2τ crss. use τ '= σ σinφ coσφ 投影到 σ 上 σ σin φ coσφ σinφ 再投影到 slip direction, 2. use force. F 在 slip system 分力 F F " = F cosλ, 再除以 area: F" = A F" = A cosφ 0 A 0 σ σin φ coσφ coσλ = σ σinφ coσλ σinφ F cosλ cosφ 7.3 This problem asks that we compute the critical resolved shear stress for silver. In order to do this, we must employ Equation(7.3), but first it is necessary to solve for the angles λ

5 and φ from the sketch below. z [00]Direction A ψ B Direction normal to () plane λ () plane / slip plane O y x [-0] Direction / slip direction If the unit cell edge length is a, then a λ = tan = 45 a For the angle ψ, we must examine the triangle OAB. The length of line OA is just a, whereas, the length of AB is a a. Thus, a 2 λ = tan = 45 a And, finally = τ crσσ = σ y ( coσφ coσλ) (.MPa )[ cos( 54.7 ) cos( 45 )] = 0.45MPa (65.4psi) Example for slip Ex. 7.3 single crystal Slip occurs on a ( ) plane i=and in a [- 0 ] direction and it initiated at an applied tensile stress of. MPa (60psi). Compute the critical resolved shear stress. <Solution> The angle θ between the plane (h k l ) & (h 2 k 2 l 2 ) cosθ = ( h + k + l )( h + k + l ) h h 2 + k k l l 2 2 2

6 7.6 Plastic deformation of polycrystalline materials The direction of slip varies from one grain to another. Fig 7.0 On polished deformed Slip lines are visible Two slip systems operated. (00) () (0) 拉伸時會產生大規模的 plastic deformation 鄰近的 grain 一起變形 grain boundary : barer for the motion of dislocation

7 7.7 Deformation by twinning Mechanisms of strengthening in metals 材料工程師常常會被要求設計改良材料強度 High strength low ductility The ability of a metal to plastically deform depends on the ability of dislocations to move. Strengthening mechanism understand the relationship between dislocation motion & mechanical behavior of metals. Strengthening techniques Restricting or hindering dislocation motion renders a material harder and stronger Strengthening mechanism for single-phase metals. (a) Grain size reduction (b) Solid-solution alloying (c) Strain hardening

8 7.8 Strengthening by grain size reduction Grain boundary : barrier to dislocation motion For two reasons: () A dislocation asses into grain B has to change its direction of motion Misorientation, difficult to move (2) The atomic disorder in G.B results in a discontinity of slip plane from one grain into another. For high angle G.B.s, Dislocation 穿過 G.B. 會在 G.B. 處產生應力集中 active new dislocation in an adjacent grain Fine-grained material harder & stronger has greater total G.B area to impede dislocation. Hall-Petch equation ( 要背!) σ y = σ 0 + k y d -/2 σ 0 κ y : constant for a particular material How to get smaller grain size () Higher rate of solidification (2) Plastic deformation, followed by heat treatment

9 7.9 Solid- solution strengthening Add impurity atoms that go into lighter substutional or interstitial yield strength & tensile strength Mechanism : Impurity impose lattice strain on the surrounding host atoms Tensile stress imposed on hold atoms 吸引小的 solute atoms 到 dislocation 上方 reduce overall strain energy Stable 後, 要再移動 dislocation 必須有較高的能量 hard to move dislocation after the formation of solid-solution compressive

10 7.0 Strain hardening Strain hardening : A ductile metal becomes harder and stronger when it is plastically deformed. Also called work hardening 冷加工 在室溫 ( 低溫 ) 下加工 如果拉一條金屬 會越來越硬或越軟? Original cross section Cross section after deformation A0 Ad Cold work, %cw = 00% A 0 Cold working yield strength 付出的代價 ductility Strengthen mechanism dislocation dislocation strain field interaction cold working dislocation density, distance between dislocation dislocation-dislocation strain interactions are repulsive motion of dislocation becomes harder

11 7. Recovery 回覆 Plastic deformation 造成 () change in grain shape (2) strain hardening (3) an increase in dislo density The properties & structure may change back to the precold-worked states by appropriate heat treatment / annealing. 發生 : Recovery, recrystallization, grain growth Recovery : () some of internal strain energy is relieved. (2) dislocation number (3) physical properties, like electrical & thermal conductivities are recovered to their precold-worked states. - but grain is still in highs strain energy state. 7.2 Recrystallization ( 再結晶 ) - formation of a new set of strain-free & equiaxed grains - low dislocation density - mechanical properties recovered (become softer, ductile) tailor mechanical properties Driving force? Strain materials (high internal energy) unstrained material (low internal energy) Recrystallization : function (temp, time) Recrystallization temperature : the temp at which recrystallization just reaches completion in hr. ~ /3 ~ /2 of absolute melting temperature Ex. Recrystalline melting temp Al 80 (353 K) 660 (933 K)

12 7.3 Grain Growth Keep at elevated temp Grain Growth 不需經過 recovery & recrystallization 一般的 polycrystals 在室溫中也會 grow Driving force for grain growth : lower G.B Grain boundary (G.B) : high energy Grain size, total G.B, total energy d n d 0 n = kt D 0 : grain diameter at t = 0 K, n : constant, n 2