文档介绍：ChapterChapterChapter 555
55 MolecularMolecular MotionsMotions andand
TransitionsTransitions ofof PolymersPolymers
高分子的分子运动与转变高分子的分子运动与转变
ChapterChapterChapter 555
SimpleSimple MechanicalMechanical RelationshipsRelationships
基本力学参数基本力学参数
Modulus pliance
模量和柔量
• Tensile 拉伸
F
F
Tensile Stress σ= A0
拉伸应力 A0
l − l ∆l l
Tensile strain ε= 0 = 0
l
拉伸应变 l0 l0
σ
Young's Modulus E = ∆l
杨氏模量ε
F
pliance D =1 E
拉伸柔量
Numerical values of Young's modulus
Material E (Pa)
Copper × 1011
Polystyrene 3 × 109
Soft rubber 2 × 106
1Pa =1 N/m2 =10 dynes/cm2 =×10−5 kgf/cm2
F
0
A δγτ
0
τγ=
F
A
tan
=
1
G
=
δ=
=
τ G
γ J
F
0
A
剪切
剪切应力剪切应变剪切模量剪切柔量
Shear stress Shear strain Shear modulus pliance
Shear
•
• Compression 压缩
V0 V0−∆V
P
Hydrostatic pressure P
流体静压力
∆V
Volume shrink ∆=
体积收缩率 V0
P
Bulk modulus B =
本体模量∆V V0
Compressibility 1 ∆V V
= 0
可压缩度 B P
Poisson's Ratio 泊松比
−∆m m −ε
υ= 0 = T
∆l l0 ε
l0
l
Values of Poisson's ratio
Value Interpretation m0 ∆l
No volume change during stretch
m
No lateral contraction
~ Typical values for elastomers
~ Typical values for plastics
• Relationships Between E, G, B, and ν
E = 3B(1− 2ν)= 2(1+ν)G
For elastomer,v =
E ≅ 3G
Viscosity 黏度
F
Shear stress τ=
切应力
A dx
A
dx v+dv F
Shear strain γ=
F
切应变 dy v dy
. dγ dv
Shear rate γ= =
切变速率 dt dy
. η: Melt viscosity
Newton's law τ=ηγ
1Pa·s = 10 poise (泊)
modulus 复数模量
Complex modulus E ∗= E′+ iE′′ Simplified
复数模量 definition of
E' and E"
E': storage modulus *
储存模量 E = │E │
E": loss modulus
损耗模量 E′′
= tanδ
tanδ: loss tangent ′
损耗角正切,损耗因子 E
Similar definitions hold for G*, η*,
and other mechanical quantities