Mechanics of Materials
CHAPTER15 FOUNDATIONS OF THE STRESS
ANALYSIS IN EXPERIMENTS
§ 15–1 SUMMARY
§ 15–2 PRINCIPLE AND APPLICATION OF THE
STRAINOMETER OF THE RESISTANCE
§ 15–3 PRINCIPLE AND APPLICATION OF THE
PHOTOELASTICITY
第十五章 实验应力分析基础
§ 15–1 概 述
§ 15–2 电阻应变计法的原理及应用
§ 15–3 光弹性法的原理及应用
§ 15–１ Summary
一,Function of the stress analysis method in experiments,
1,Determine the reasonable dimension and the structureal form of a memberaccording to
the tested stress or strain of the model in designing,
2,Test the true stress or strain of a member in work and find out the position and the value
of the maximum stress in order to evaluate the safty and reliability of the engineering
structure and to provide the basis of improving working ability for the equipment,
3,Analyze the destroyed or failed member and propose the measures of improvement in
order to prevent it from destroying again,
4,Test the magnitude,derection and all kinds of dynamic responses of the external load,
5,Explore the new rule from tests and check the theory of stress analysis and the
calculation method,
§ 15–１ 概 述
一、实验应力分析方法的作用,
1.设计时，测定模型的应力或变形，依此来确定构件的合理尺
寸和结构形式。
2.工作中，测定构件的真实应力或变形，找出最大应力的位置
和数值，以评价工程结构的安全可靠性，并为提高设备的
工作能力提供依据。
3.对破坏或失效构件进行分析，提出改进措施，防止再次破坏。
4.测定外载的大小、方向以及各种动响应。
5.从试验中探索新的规律，并对应力分析理论和计算方法进行
校核。
二,Brief introduction of methods in the stress analysis of experiments
1.The machinery measuring method,
The figure of measuring deformations in the book annotated by Zheng
Xuan(127-200)in the east Han dynasty,
二、实验应力分析方法简介,
1,
机
械
量
测
法
东汉郑玄 (127— 200)注释的, 考工记 ?弓人, 中的测变形图
Leonardo Da Vinci( 1452-
1519).This picture is considered to
show the earliest test in Mechanics
of Materials,
The tensile test of an iron wire
designed by Leonardo Da Vinci,
里奥纳多 ?达 ?芬奇 (1452— 1519)
此图被认为是最早的材力试验
里奥纳多 ?达 ?芬奇设计的铁丝受
拉试验
tensile
Galileo (1564— 1642)
Fig.14 Sketch of the tensile test
of Galileo
Fig.15 Sketch of the bending test of Galileo
伽利略 (1564—1642)
Fig.37 Tensile-test machine of
Mushenbluic
Fig.38 Method to clamp two
ends of a tensile specimen
Mushenbluic (1692— 1761)
穆申布洛依克 (1692—1761)
Hydraulic verstile testing machine controlled by the computer
2,Other methods,
Since the early 20th century,the developments of electricity,optics acousics
and materials science have provided conditions for the productionof other
measurement methods of the stress analysis in experiments.Then the resistance-
strain method,ordinary photoelasticity method,hologram photoelasticity
method,sound launching method and so on are made fast developments and wide
applications,
2.其它方法,
20世纪初至今，电学、光学、声学和材料科学的发展，
为试验应力分析其它测量方法的产生创造了条件。于是，电
阻应变法、普通光弹法、全息光弹法、散斑法、声发射法等
方法都有了快速发展和广泛应用。
§ 15–2 Principle and application of the strainometer of the resistance
1,Resistance law,Resisance of a conductor
A
LR ??
2,Elastic law,
Land A will change after the cinductor is subjected to forces or changes in
temperatures,
TE ??? ???
3,Strain foil of resistance
?K
L
LK
R
R ????
Ｋ — Sensitive coefficient
1
2 3
4 5
Wire-coiled strain foil
1— Overburden 2— Fundus
3— Drawn line 4— Binder 5— Sensitive bar
§ 15–2 电阻应变计法的原理及应用
一、电阻定律,导体电阻
A
LR ??
二、弹性定律,导体受力或变温后,L,A都将发生改变。
TE ??? ???
三,电阻应变片,
?K
L
LK
R
R ????
Ｋ — 灵敏系数,
1
2 3
4 5
丝绕式应变片
1— 覆盖层 2— 基底 3— 引出线
4— 粘结剂 5— 敏感栅
4,Balance principle of the electric bridge
3
4
2
1
R
R
R
Rw h e n ?
0?U
After the resistance changes,
)(
4
4
4
3
3
2
2
1
1
R
R
R
R
R
R
R
REU ????????
)(
4 4321
???? ???? KE
U
R1 R
2
R4
I1,2
I3,4
A
B
C
D
Bridge with the output voltage
R3
四、电桥平衡原理
,
3
4
2
1 时
R
R
R
R ?
0?U
电阻变化后,
)(
4
4
4
3
3
2
2
1
1
R
R
R
R
R
R
R
REU ????????
)(
4 4321
???? ???? KE
U
R1 R
2
R4
I1,2
I3,4
A
B
C
D
电压输出桥
R3
5,Strainometer of resistance
4321 ????? ????m e a su re d
Transform to output voltage into the magnitude of strain,
五、电阻应变仪
4321 ????? ????读数
将输出电压转变为应变读数。
6,Arrange foils, Make the directions of foils coincide with those of principal
stresses as much as possible,
When the directions of principal stresses are un-known,the stress state of
a point must be determined by three independent quantities,
Three strain foils of 45°
0°
45°
90°
Three strain foils of 60 °
0°
60° 120°
六、布片,尽可能使片子的方向与主应力方向一致。
主应力方向未知时，必须由三个独立量才能确定一点的
应力状态。
三片 45° 应变花
0°
45°
90°
三片 60° 应变花
0°
60° 120°
yx
xy
??
?
?
?
?
?02tg
7,Relations between the principal strains and the measured strains,
???
???
???
????
?
?
?
2c o s
2
1
2s i n
22
2s i n
2
1
2c o s
22
xy
yx
xy
yxyx
?
?
?
?
?
?
?
?
? ?22
m i n
m a x
)()(
2
1
xyyxyx ?????
?
?
?????
?
?
?
yx
xy
??
?
?
?
?
?02tg
七、主应变与测量应变之间的关系,
???
???
???
????
?
?
?
2c o s
2
1
2s i n
22
2s i n
2
1
2c o s
22
xy
yx
xy
yxyx
?
?
?
?
?
?
?
?
? ?22
m i n
m a x
)()(
2
1
xyyxyx ?????
?
?
?????
?
?
?
Example 1
Three linear strains of a point are tested by the strain foil 45°,Try to determine
the principal strain of this point,
? ?][2)(
2
1 22
m a x ）（）（ yuuxyx ??????? ??????
? ?][2)(
2
1 22
m i n ）（）（ yuuxyx ??????? ??????
yx
yxu
??
???
?
?
??
?
2
2tg 0
?0
?max 45°
x
y u
[例 1 ] 用 45° 应变花测得一点的三个线应变后，求该点的主
应变。
?0
?max
? ?][2)(
2
1 22
m a x ）（）（ yuuxyx ??????? ??????
? ?][2)(
2
1 22
m i n ）（）（ yuuxyx ??????? ??????
yx
yxu
??
???
?
?
??
?
2
2tg 0
45°
x
y u
Example 2 Try to determine the principal
strain of a point after the three linear
strains of this point are tested by the strain
foil of 60° 。
2
1 2 060
21 2 0600
0
1 2 0600
m a x 3
1
33
）（）（ ??
???
?
???
? ??
??
??
??
?
120600
12060
0 2
)(3
2tg
???
??
?
??
?
?
2
12060
2120600
0
120600
m i n 3
1
33
）（）（ ??
???
?
???
? ??
??
??
??
?
Three strain foils of 60 °
0°
60° 120°
[例 2 ] 用 60° 应变花测得一点的三
个线应变后，求该点的主应变。
2
1 2 060
21 2 0600
0
1 2 0600
m a x 3
1
33
）（）（ ??
???
?
???
? ??
??
??
??
?
120600
12060
0 2
)(3
2tg
???
??
?
??
?
?
2
12060
2120600
0
120600
m i n 3
1
33
）（）（ ??
???
?
???
? ??
??
??
??
?
三片 60° 应变花
0°
60° 120°
8,Connect the bridge,
Make the stress distribute alternately;make the total bridge have a high
precision and the half bridge a low precision,The half bridhe with two arms is often
used,
9,Temperature compensation,
T
E
??? ???
It is better to realize the compensation by itself; otherwise we should use the
temperature compensator that is without any forces.We must make the working
foil and the compensation foil in the same temperature field,
八、接桥,
要使应力正负相间；全桥精度高，半桥精度低。常用半桥
双臂式桥路。
九、温度补偿,
T
E
??? ???
最好能在桥路中自补偿；否则，要用绝对不受力的温度补偿片。
工作片与补偿片要始终处于同一温度场中。
§ 15－ 3 Principle and application of the
photoelasticity
1,Principle of the photoelasticity,
①, Permanent double refraction,
②, Temporary(artificial)double
refraction,
Double refraction in the anisotropic body
due to the entering of light
e
o
§ 15－ 3 光弹性法的原理及应用
一、光测原理,
1.永久双折射,
2.暂时（人工）双折射,
光射入各向异性体产生的双折射
e
o
2,Plane stress --optics law,
2101 ?? BAnn ???
1202 ?? BAnn ???
)( 2121 ?? ??? Cnn
①,Refractive index,
C—— Stress optical coefficient of the model material
?
?1
?1
?2
?2 Plane polarized
light
The plane polarized light passes through the model subjected to forces,
So
二、平面应力 ——光学定律,
2101 ?? BAnn ???
1202 ?? BAnn ???
)( 2121 ?? ???? Cnn
1.折射率,
C—— 模型材料的应力光学系数。
?
?1
?1
?2
?2 平面
偏
振
光
平面偏振光通过受力模型
)( 21 ?? ??? Ch
②, Optical path difference,
③,The light intensity in the plane polarization field,
The model subjected to forces is in the
cross plane polarization field,
P
?1
?2 A
O
f
Light
source
Model
Analyzer
Polarizer
)( 21 ?? ??? Ch
2.光程差,
3.平面偏振场中的光强,
受力模型在正交平面偏振布置中
P
?1
?2 A
O
f
光源
模型
检偏镜
起偏镜
2)s i n2s i n(
:i n t e n s i t yi g h t
?
?
?
?
? aKI
l
,0?I
02s in ??
① Equal inclination lines
As
a black point occurs behind the analyzer,
The interference fringes formed in the
locus of the black points are called equal
inclination lines,
On the equal inclination lines,the
directions of the pricipal stresses are
same and they coincide with the
polarization axle,
Pictures of the plane polarization field taken every 150.The position of the
colored equal color lines is not changed,but the position of the black equal
inclinnation lines is changed when the polaroid rotates synchronously,
2)s i n2s i n(:
?
?? ?? aKI光强
。时，检偏镜后出现黑点 0?I
02s in ??
① 等倾线
引起的黑点的迹线形成的干
涉条纹 —— 等倾线
等倾线上,主应力方向相同
且与偏振轴重合。
0s in ????
② Equal difference lines,
The formed interference fringes--equal difference lines,
?N???
The white light is
considered to be the
light source and the
equal difference lines
aare coloured fringes,
so the equal difference
lines are also called
equal colour lines,
As N=0,they are
called the No.0 equal
difference
lines(black);
as N=1,they are called
the No.1 equal
difference lines,Simulating the plae part connected by screws and screw caps (method of pasting foils)
0s in ????
② 等差线
形成的干涉条纹 —— 等差线
?N???
以白光为光源,
等差线为彩色条
纹,故 等差线又
称 等色线
)(0
,0
黑色级等差线
称为?N
级等差线
称为
1
,1?N
h
Nf
h
N
C
??? ??? )( 21
f—— The value of the fringe of a material
a,Under the repeated loading,the equal inclination lines are not
changed,but the equal difference lines are changed
③ Distinguish equal inclination lines and equal difference lines
b,If we rotate synchronously the polarizer and the analyzer,
the equal inclination lines are changed and the equal difference
lines are not changed,
c,According to experiences,the equal inclination lines are
thick(all the black) and equal difference lines are thin(a line),
h
Nf
h
N
C
??? ??? )( 21
f—— 材料的条纹值。
a、反复加载，等倾线不变，等差线改变。
③ 区分等倾线与等差线
b、同步旋转起偏镜与检偏镜，等倾线改变，等差线不变。
c、凭经验，等倾线较粗（一片黑），等差线较细（一条线）。
,)s i n( 2?? ?? aKI
,0?I
0s in ??
?
? ?N???
There are no equal inclination lines in the cross circular polarization
field.So the equal difference lines are clear,
Light intensity,as Black points occur behind the
analyzer,
(N=0,1,2,……)
As
As
,0?m They are called the No.0.5 equal difference lines,
,1?m
They are called the No.1.5 equal difference lines,
2)s i n(:
?
? ?? aKI光强 。时，检偏镜后出现黑点 0?I
0s in ??
?
? ?N???
.0, 5,0 级等差线称为?m
.1, 5,1 级等差线为?m
正交圆偏振场中，无等倾线。故等差线比较清晰。
(N=0,1,2,……)
④, Light intensity in the cross
circular polarization field,
45° 45°
Fast
axle
Slow
axle
45° 45°
Fast
axle
Slow
axle
P
A
S
z
4.正交圆偏振场中的光强,
45° 45°
快轴 慢轴
45° 45°
快轴 慢轴
P
A
S
z
Figure of the equal difference lines of a disc subjected to radial pressures
Equal-colour lines of the spinning disc
Interference fringes of the ring
subjected to radial pressures in the
plane polarization field,
There are only equal-different
interference fringes in the circular
polarization field when the ring is
subjected to radial pressures,
CHAPTER15 FOUNDATIONS OF THE STRESS
ANALYSIS IN EXPERIMENTS
§ 15–1 SUMMARY
§ 15–2 PRINCIPLE AND APPLICATION OF THE
STRAINOMETER OF THE RESISTANCE
§ 15–3 PRINCIPLE AND APPLICATION OF THE
PHOTOELASTICITY
第十五章 实验应力分析基础
§ 15–1 概 述
§ 15–2 电阻应变计法的原理及应用
§ 15–3 光弹性法的原理及应用
§ 15–１ Summary
一,Function of the stress analysis method in experiments,
1,Determine the reasonable dimension and the structureal form of a memberaccording to
the tested stress or strain of the model in designing,
2,Test the true stress or strain of a member in work and find out the position and the value
of the maximum stress in order to evaluate the safty and reliability of the engineering
structure and to provide the basis of improving working ability for the equipment,
3,Analyze the destroyed or failed member and propose the measures of improvement in
order to prevent it from destroying again,
4,Test the magnitude,derection and all kinds of dynamic responses of the external load,
5,Explore the new rule from tests and check the theory of stress analysis and the
calculation method,
§ 15–１ 概 述
一、实验应力分析方法的作用,
1.设计时，测定模型的应力或变形，依此来确定构件的合理尺
寸和结构形式。
2.工作中，测定构件的真实应力或变形，找出最大应力的位置
和数值，以评价工程结构的安全可靠性，并为提高设备的
工作能力提供依据。
3.对破坏或失效构件进行分析，提出改进措施，防止再次破坏。
4.测定外载的大小、方向以及各种动响应。
5.从试验中探索新的规律，并对应力分析理论和计算方法进行
校核。
二,Brief introduction of methods in the stress analysis of experiments
1.The machinery measuring method,
The figure of measuring deformations in the book annotated by Zheng
Xuan(127-200)in the east Han dynasty,
二、实验应力分析方法简介,
1,
机
械
量
测
法
东汉郑玄 (127— 200)注释的, 考工记 ?弓人, 中的测变形图
Leonardo Da Vinci( 1452-
1519).This picture is considered to
show the earliest test in Mechanics
of Materials,
The tensile test of an iron wire
designed by Leonardo Da Vinci,
里奥纳多 ?达 ?芬奇 (1452— 1519)
此图被认为是最早的材力试验
里奥纳多 ?达 ?芬奇设计的铁丝受
拉试验
tensile
Galileo (1564— 1642)
Fig.14 Sketch of the tensile test
of Galileo
Fig.15 Sketch of the bending test of Galileo
伽利略 (1564—1642)
Fig.37 Tensile-test machine of
Mushenbluic
Fig.38 Method to clamp two
ends of a tensile specimen
Mushenbluic (1692— 1761)
穆申布洛依克 (1692—1761)
Hydraulic verstile testing machine controlled by the computer
2,Other methods,
Since the early 20th century,the developments of electricity,optics acousics
and materials science have provided conditions for the productionof other
measurement methods of the stress analysis in experiments.Then the resistance-
strain method,ordinary photoelasticity method,hologram photoelasticity
method,sound launching method and so on are made fast developments and wide
applications,
2.其它方法,
20世纪初至今，电学、光学、声学和材料科学的发展，
为试验应力分析其它测量方法的产生创造了条件。于是，电
阻应变法、普通光弹法、全息光弹法、散斑法、声发射法等
方法都有了快速发展和广泛应用。
§ 15–2 Principle and application of the strainometer of the resistance
1,Resistance law,Resisance of a conductor
A
LR ??
2,Elastic law,
Land A will change after the cinductor is subjected to forces or changes in
temperatures,
TE ??? ???
3,Strain foil of resistance
?K
L
LK
R
R ????
Ｋ — Sensitive coefficient
1
2 3
4 5
Wire-coiled strain foil
1— Overburden 2— Fundus
3— Drawn line 4— Binder 5— Sensitive bar
§ 15–2 电阻应变计法的原理及应用
一、电阻定律,导体电阻
A
LR ??
二、弹性定律,导体受力或变温后,L,A都将发生改变。
TE ??? ???
三,电阻应变片,
?K
L
LK
R
R ????
Ｋ — 灵敏系数,
1
2 3
4 5
丝绕式应变片
1— 覆盖层 2— 基底 3— 引出线
4— 粘结剂 5— 敏感栅
4,Balance principle of the electric bridge
3
4
2
1
R
R
R
Rw h e n ?
0?U
After the resistance changes,
)(
4
4
4
3
3
2
2
1
1
R
R
R
R
R
R
R
REU ????????
)(
4 4321
???? ???? KE
U
R1 R
2
R4
I1,2
I3,4
A
B
C
D
Bridge with the output voltage
R3
四、电桥平衡原理
,
3
4
2
1 时
R
R
R
R ?
0?U
电阻变化后,
)(
4
4
4
3
3
2
2
1
1
R
R
R
R
R
R
R
REU ????????
)(
4 4321
???? ???? KE
U
R1 R
2
R4
I1,2
I3,4
A
B
C
D
电压输出桥
R3
5,Strainometer of resistance
4321 ????? ????m e a su re d
Transform to output voltage into the magnitude of strain,
五、电阻应变仪
4321 ????? ????读数
将输出电压转变为应变读数。
6,Arrange foils, Make the directions of foils coincide with those of principal
stresses as much as possible,
When the directions of principal stresses are un-known,the stress state of
a point must be determined by three independent quantities,
Three strain foils of 45°
0°
45°
90°
Three strain foils of 60 °
0°
60° 120°
六、布片,尽可能使片子的方向与主应力方向一致。
主应力方向未知时，必须由三个独立量才能确定一点的
应力状态。
三片 45° 应变花
0°
45°
90°
三片 60° 应变花
0°
60° 120°
yx
xy
??
?
?
?
?
?02tg
7,Relations between the principal strains and the measured strains,
???
???
???
????
?
?
?
2c o s
2
1
2s i n
22
2s i n
2
1
2c o s
22
xy
yx
xy
yxyx
?
?
?
?
?
?
?
?
? ?22
m i n
m a x
)()(
2
1
xyyxyx ?????
?
?
?????
?
?
?
yx
xy
??
?
?
?
?
?02tg
七、主应变与测量应变之间的关系,
???
???
???
????
?
?
?
2c o s
2
1
2s i n
22
2s i n
2
1
2c o s
22
xy
yx
xy
yxyx
?
?
?
?
?
?
?
?
? ?22
m i n
m a x
)()(
2
1
xyyxyx ?????
?
?
?????
?
?
?
Example 1
Three linear strains of a point are tested by the strain foil 45°,Try to determine
the principal strain of this point,
? ?][2)(
2
1 22
m a x ）（）（ yuuxyx ??????? ??????
? ?][2)(
2
1 22
m i n ）（）（ yuuxyx ??????? ??????
yx
yxu
??
???
?
?
??
?
2
2tg 0
?0
?max 45°
x
y u
[例 1 ] 用 45° 应变花测得一点的三个线应变后，求该点的主
应变。
?0
?max
? ?][2)(
2
1 22
m a x ）（）（ yuuxyx ??????? ??????
? ?][2)(
2
1 22
m i n ）（）（ yuuxyx ??????? ??????
yx
yxu
??
???
?
?
??
?
2
2tg 0
45°
x
y u
Example 2 Try to determine the principal
strain of a point after the three linear
strains of this point are tested by the strain
foil of 60° 。
2
1 2 060
21 2 0600
0
1 2 0600
m a x 3
1
33
）（）（ ??
???
?
???
? ??
??
??
??
?
120600
12060
0 2
)(3
2tg
???
??
?
??
?
?
2
12060
2120600
0
120600
m i n 3
1
33
）（）（ ??
???
?
???
? ??
??
??
??
?
Three strain foils of 60 °
0°
60° 120°
[例 2 ] 用 60° 应变花测得一点的三
个线应变后，求该点的主应变。
2
1 2 060
21 2 0600
0
1 2 0600
m a x 3
1
33
）（）（ ??
???
?
???
? ??
??
??
??
?
120600
12060
0 2
)(3
2tg
???
??
?
??
?
?
2
12060
2120600
0
120600
m i n 3
1
33
）（）（ ??
???
?
???
? ??
??
??
??
?
三片 60° 应变花
0°
60° 120°
8,Connect the bridge,
Make the stress distribute alternately;make the total bridge have a high
precision and the half bridge a low precision,The half bridhe with two arms is often
used,
9,Temperature compensation,
T
E
??? ???
It is better to realize the compensation by itself; otherwise we should use the
temperature compensator that is without any forces.We must make the working
foil and the compensation foil in the same temperature field,
八、接桥,
要使应力正负相间；全桥精度高，半桥精度低。常用半桥
双臂式桥路。
九、温度补偿,
T
E
??? ???
最好能在桥路中自补偿；否则，要用绝对不受力的温度补偿片。
工作片与补偿片要始终处于同一温度场中。
§ 15－ 3 Principle and application of the
photoelasticity
1,Principle of the photoelasticity,
①, Permanent double refraction,
②, Temporary(artificial)double
refraction,
Double refraction in the anisotropic body
due to the entering of light
e
o
§ 15－ 3 光弹性法的原理及应用
一、光测原理,
1.永久双折射,
2.暂时（人工）双折射,
光射入各向异性体产生的双折射
e
o
2,Plane stress --optics law,
2101 ?? BAnn ???
1202 ?? BAnn ???
)( 2121 ?? ??? Cnn
①,Refractive index,
C—— Stress optical coefficient of the model material
?
?1
?1
?2
?2 Plane polarized
light
The plane polarized light passes through the model subjected to forces,
So
二、平面应力 ——光学定律,
2101 ?? BAnn ???
1202 ?? BAnn ???
)( 2121 ?? ???? Cnn
1.折射率,
C—— 模型材料的应力光学系数。
?
?1
?1
?2
?2 平面
偏
振
光
平面偏振光通过受力模型
)( 21 ?? ??? Ch
②, Optical path difference,
③,The light intensity in the plane polarization field,
The model subjected to forces is in the
cross plane polarization field,
P
?1
?2 A
O
f
Light
source
Model
Analyzer
Polarizer
)( 21 ?? ??? Ch
2.光程差,
3.平面偏振场中的光强,
受力模型在正交平面偏振布置中
P
?1
?2 A
O
f
光源
模型
检偏镜
起偏镜
2)s i n2s i n(
:i n t e n s i t yi g h t
?
?
?
?
? aKI
l
,0?I
02s in ??
① Equal inclination lines
As
a black point occurs behind the analyzer,
The interference fringes formed in the
locus of the black points are called equal
inclination lines,
On the equal inclination lines,the
directions of the pricipal stresses are
same and they coincide with the
polarization axle,
Pictures of the plane polarization field taken every 150.The position of the
colored equal color lines is not changed,but the position of the black equal
inclinnation lines is changed when the polaroid rotates synchronously,
2)s i n2s i n(:
?
?? ?? aKI光强
。时，检偏镜后出现黑点 0?I
02s in ??
① 等倾线
引起的黑点的迹线形成的干
涉条纹 —— 等倾线
等倾线上,主应力方向相同
且与偏振轴重合。
0s in ????
② Equal difference lines,
The formed interference fringes--equal difference lines,
?N???
The white light is
considered to be the
light source and the
equal difference lines
aare coloured fringes,
so the equal difference
lines are also called
equal colour lines,
As N=0,they are
called the No.0 equal
difference
lines(black);
as N=1,they are called
the No.1 equal
difference lines,Simulating the plae part connected by screws and screw caps (method of pasting foils)
0s in ????
② 等差线
形成的干涉条纹 —— 等差线
?N???
以白光为光源,
等差线为彩色条
纹,故 等差线又
称 等色线
)(0
,0
黑色级等差线
称为?N
级等差线
称为
1
,1?N
h
Nf
h
N
C
??? ??? )( 21
f—— The value of the fringe of a material
a,Under the repeated loading,the equal inclination lines are not
changed,but the equal difference lines are changed
③ Distinguish equal inclination lines and equal difference lines
b,If we rotate synchronously the polarizer and the analyzer,
the equal inclination lines are changed and the equal difference
lines are not changed,
c,According to experiences,the equal inclination lines are
thick(all the black) and equal difference lines are thin(a line),
h
Nf
h
N
C
??? ??? )( 21
f—— 材料的条纹值。
a、反复加载，等倾线不变，等差线改变。
③ 区分等倾线与等差线
b、同步旋转起偏镜与检偏镜，等倾线改变，等差线不变。
c、凭经验，等倾线较粗（一片黑），等差线较细（一条线）。
,)s i n( 2?? ?? aKI
,0?I
0s in ??
?
? ?N???
There are no equal inclination lines in the cross circular polarization
field.So the equal difference lines are clear,
Light intensity,as Black points occur behind the
analyzer,
(N=0,1,2,……)
As
As
,0?m They are called the No.0.5 equal difference lines,
,1?m
They are called the No.1.5 equal difference lines,
2)s i n(:
?
? ?? aKI光强 。时，检偏镜后出现黑点 0?I
0s in ??
?
? ?N???
.0, 5,0 级等差线称为?m
.1, 5,1 级等差线为?m
正交圆偏振场中，无等倾线。故等差线比较清晰。
(N=0,1,2,……)
④, Light intensity in the cross
circular polarization field,
45° 45°
Fast
axle
Slow
axle
45° 45°
Fast
axle
Slow
axle
P
A
S
z
4.正交圆偏振场中的光强,
45° 45°
快轴 慢轴
45° 45°
快轴 慢轴
P
A
S
z
Figure of the equal difference lines of a disc subjected to radial pressures
Equal-colour lines of the spinning disc
Interference fringes of the ring
subjected to radial pressures in the
plane polarization field,
There are only equal-different
interference fringes in the circular
polarization field when the ring is
subjected to radial pressures,
