mechanical behavior of materials 1. overview of mechanical behavior 2. dislocations 3. plastic deformation in single and polycrystalline materials 4. strengthening of crystalline materials 5. high temperature deformation of crystalline materials 6. fracture mechanics 7. high temperature fracture 8. fatigue of engineering materials
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Mechanical behavior of materials 1. overview of mechanical behavior 2. dislocations 3. plastic deformation in single and polycrystalline materials 4. strengthening.
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mechanical behavior of materials
1. overview of mechanical behavior2. dislocations3. plastic deformation in single and polycrystalline materials4. strengthening of crystalline materials5. high temperature deformation of crystalline materials6. fracture mechanics7. high temperature fracture8. fatigue of engineering materials
text book: mechanical behavior of materials, thomas H. courtneyreference: the principles of engineering materials
chapter 1. overview of mechanical behavior
彈性變形Elastic deformation
Hooke's Law
The extension depends on sample dimensions
normalized force F/A 定義為 stress
normalized extension(dimensionless) 定義為 strain
l - l0 = l F
l - l0 = l F
ll 0
ε =
E 為材料特性,稱為 Young’s Modulus ,為 stiffness 的指標。E is a measure of a material’s bond strength resistant to tensile deformation.
Shear stress 剪應力 τShear strain 剪應變 γ
為材料特性,稱為 shear modulus. is a measure of resistance to bond distortion.
同樣,真應變 true strain ( based on instantaneous sample length )
=
=
= ……..= ()
= ∫𝑙 0
𝑙𝑑𝑙𝑙=𝑙𝑛 𝑙
𝑙𝑜
l0 li
= () Because l0 li
li l0
= = 1+
= () =(1+ ) = (1+)
>
(1+) <
(1+) <
Work hardening
< Eu, flow stress at work hardening > work softening due to the decreasing of cross section
Criterion for necking dF = 0T = F/ Ai F=TAi
dF = 0 = T dAi + AidT
dT/T = -dAi/Ai
Fraction increase in flow stress (dT/T) =Decrease in load-bearing area (dAi/Ai
塑性不安定 (plastic instability)
局所変形産生、只有長度L的区域有 L + dL ( dL>0 )的変形、断面積也減少 A + dA ( dA<0 )。同時、加工硬化 ( strain hardening, work-hardening) 使此区域再産生塑性変形之応力将増加 σ + dσ ( dσ>0 )、 Necking 開始条件、
体積一定条件( AL = 一定 )及由 定義、
塑性不安定条件
左辺為加工硬化率( strain hardening rate )
「加工硬化越大、 Necking越不容易発生、材料的塑性変形安定進行」
dT/T = -dAi/Ai plastic instability
Engineering - curve e > Eu : of little fundamental value fracture strain (f) : percentage of elongation is used. f = [(lf-l0 )/ l0 ]x100% lf is sample length at fracture
Material ductility
Eu is more of an inherent material property than f
resistance to neck development. Work hardening capability.
Reduction in area (R. A.) %RA = [(Ao-Af)/Ao]x100%
RA is no relative to the sample gage length.
index of material ductility
Before necking εEu εT < εE
after necking εT > εE
But always T > E
ε = /E 為 elastic tensile loading - 相當於 chemical bond strength.
但當達 plastic deformation 時,σ=Eε 已不成立。
Empirical equations
T = K(eT)n
n : strain-hardening coefficient is a measure of the material’s work hardening behavior ,
應變硬化指數 n=0.02-0.5K : strength coefficient (K: true stress at eT =1, )
B. Strain-Rate Sensitivity ( 應變速率敏感指數 ) m
Strain rate 增加, flow stress of material 增高, is a strong function of the temperature and is a specific to the materials.
經驗方程式 T = K' ( )m
: true strain rate , m : strain rate sensitivity , K' : a constant0 < m < 1 ( m = 0 , not strain rate sensitivity ; m = 1 , a viscous solid , stress increase linearly with )
Metals and alloys 在一般溫度下, strain-rate sensitivity 不明顯,例如 : 大部分材料 m=0.00-0.1 at room temperature ,但 strain-rate sensitivity 隨溫度增高而變大,某些金屬可高達 0.8
” Superplasticity ” at these strain-temperature combination.
描述 strain-rate hardening in absence of strain-hardening.
而 T = K(eT)n 描述 strain hardening without strain-rate hardening.
a measure of a material's resistance to surface penetration by an indenter having a force applied to it 。因為產生塑變,因此硬度可視為 materials' plastic flow resistance 。Brinell hardness test 最普遍 , 10mm steel ball, applied mass 3000kg,BHN is defined as the load, F, divided by the surface area of indentation.
BHN = (N/m) Stress unit
Hardness = (2.5~3.0) y
考慮 work hardening 時,一般取 3 ,Hardness is a measure of a material's plastic flow resistance.Vickers hardness test: square-based diamond pyramid indenter, applied loads 1~120 kg.