柔性电子器件与制造：第4.1节柔性电子弯曲力学

Stretchability as large as 50%
Soft-hard material compound structures
of flexible electronics (Science, 2011)
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Soft-hard material compound structures is the key technology Severe mismatch between soft and hard material, so there is coupling action due to large deformation, temperature and electrical field Soft material Vs Hard material
Chapter Flexible Electronics Device & Manufacturing
Outline
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First – Failure Mode
Causing tremendous loss in daily life
Failure Modes
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Columns can fail if the applied load
外延应力产生示意图
misfit
a film asubstrate asubstrate
xx C11 C yy 12 zz C12
C12 C22 C12
C12 xx ex [100] e [010] C23 yy y C11 zz ez [001]
2 s
2 s
Film-on-substrate structures：bending
薄膜和基板中的应力 基板和薄膜界面应力
− 薄膜中： − 基板中：
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xx f
xx compression bending
tf 3t f 4t f ts xx y f f f 2 ts ts ts
Once buckled, the column’s ability to carry load is greatly reduced.
Buckling
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Buckling
新西兰6.3级地震
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Stressed-out behaviors Stress Tension Pressure
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Anxiety
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Strength failure
Mechanical failure is determined by the weakest components of devices The crack strain of inorganic brittle material is about 1-2%，and the metal is also broken after necking The freestanding metal film is different from film-on-substrate in cracking
来自百度文库
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Fracture
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Moore, G. Electronics 38, 114–117 (1965)
Fracture in microstructure
Vertical stabilizer, which separated from American Airlines Flight 587, leading to a fatal crash
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(a) Basic structures of flexible electronics; (b) the size of thin film
Film-on-substrate structures：bending
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The radius of curvature is adopted to denote the bending deformation of flexible electronics. The smaller shows better deformability.
The S.S. Schenectady split apart by brittle fracture while in harbor (1944)
Fracture: utility
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Stability failure
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Buckling is a phenomena of compression members. Once the buckling load, or critical load, is reached, the column will instantly loose stability and “kick out” to one side.
Depression
Stress engineering: bad situations
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Delamination Fatigue Crows-feet Striae gravidarum
Stress engineering: Beneficial applications
Wrinkle and buckle are ubiquitous phenomena
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where,
elastic f
1 vf E f
f

elastic s
ts 1 vs 4t f f y 2 Es t s
1 vf E f
1 vs 4t f f misfit 0 f f E t E f s s 1 v f
Stiff skin on compliant substrate: A universal model
− As a result of ageing, the soft dermis contracts, placing the system stress. − Hierarchical internal stress wrinkling by under compressive
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The misfit is resulted from the different coefficient of thermal expansion , so the thermal strain is generated when temperature changes
misfit film substrate T T0
4.1 Bending Mechanics
YongAn Huang, Ph.D
Flexible Electronics Research Center School of Mechanical Science and Engineering Huazhong University of Science and Technology
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Nature Materials 4, 271(2005) Nature Materials 4, 293(2005)
Foldable Electronics on a pliable substrate
Robustness against bending, stretching, folding
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Nature Nanotechnology 1, 201-207(2008)
Buckled Sphere
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Cao Guoxing, Chen Xi, C. R. Li, Z. X. Cao, PRL100, 2008
Peel-Pick-Place
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Mechanics of flexible electronics
Source of film stress: growth of polycrystal
非平衡状态下的沉积造成的。
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在薄膜的沉积或生长中，经常可以观测到应力的生长，这是因为薄膜在
报告提纲
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Second – Foundation
Learning the bending mechanics
Film-on-substrate structures
1 v 12 M E h3
R y R xx ( y ) R
y y R
a）纯弯结构弯矩和轴向应力分布；b）弯曲示意图
Film-on-substrate structures：bending
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对基板或薄膜施加一定的预应变或者温度变化，然后再将两者结合在一 起，当释放与应变或者温度恢复到室温后，由于基板和薄膜的应变不匹 配，会导致膜-基结构会出现弯曲变形。
0
Es 4t f 1 v t s s
Young’s modulus： ~103-105
Coefficient of heat conduction ： ~103 Coefficient of thermal expansion ： ~10-2 Soft-substrate and hard film
Source of film stress: thermal stress
t f 1 m ts 500 m
xx substrate, y

ts 4 f 2 500
薄膜应力是基板中的应力的100倍以上
Film-on-substrate structures：bending
The stress of thin film is calculated from the misfit of the thin film and substrate.
1 v 12 M 1 v 6 f h f 3 Es hs Es hs2
Stoney formula
Es h Es h f 1 v 6h f 1 v 6h f R
Stoney formula: relationship between the stress and curvature
John A. Rogers: Mechanics is the future of flexible electronics
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Features of flexible electronics: complex deformation: bend, buckle, stretch, twist Challenges: Radius of curvature as small as 1mm
E T misfit 1 v
Source of film stress: Epitaxial stresses
between film and substrate
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The epitaxial stresses occurs when there is ideal continuity
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脱氢作用dehydrogenation
Nature 419, 579(2002) Phys.Rev.Lett.90, 074302(2003)
Buckling patterns of Au on PDMS
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Scripta materialia 50, 797(2004)
Nested Buckling of Artificial Skin
exceeds the yield stress of the material.
This is a strength failure Columns can also fail by buckling. This is a stability failure
Strength failure