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Stress-Strain Relationships
• Stress is a measure of the force per unit area
• Strain is a measure of the unit change in length ( uniaxial stress) or angle (shear)
• Elastic deformation relates the stress to strain through the proportionality constant of the elastic modulus, E
• Poisson’s ratio,, relates the contraction in the x,y direction with the elongation under load in the z direction
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Relations of Stress-Strain
A) Uniaxial tension
B) Compression
C) Shear
DD) Torsion
A B
C D
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Mechanical Materials Properties
• Elastic Modulus- determines the elastic response of a material following Hooke’s law. Determines by uniaxial tensile testing, acoustic transmission, and vibrational response
• Yield Point and Ultimate Tensile Strength ( UTS)- yield point determines the onset of plastic deformation as determined by a strain offset( usually .2%), while UTS determines the maximum strength
• Coefficient of Thermal Expansion- measures the expansion over temperature, usually in microinches/in/oC. Thermally induced strains occur due to the mismatch between dissimilar materials. Measured with a dilatometer
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Typical Stress-Strain Behavior
M = Ultimate Tensile Strenght
Y.P.
Y.P. = Yield Point
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Elastic Stress-Strain Relationships
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Poisson’s Ratio
=- x / z
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Bimetal Strip
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Bimetal Strip (Cont.)
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Stress-Strain Distribution in an Adhesively Bonded Joint
Typical variations of shear and peel stressesin a single lap joint foran adhesively bonded joint.Note that the shear stress is non-zero at the ends.
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FEM Analysis of a Bonded Structure
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Stress Distribution Across Bonded Structure
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Fatigue
Materials will fail at a lower lever than the UTS when subjected to cyclic loading. This is known as fatigue. The loading can be stress induced(mechanical loading) or stain induced (thermal cycling)
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Thermal Cycle Fatigue
A ... p Nr = - 11 ,5"y) f e -- kT@,,@ A ... p Nr = - 11 ,5"y) f e -- kT@,,@ =(A\Illf,,e_ P A,y) kT@,,@
The equation that describes most metals stresses repeatedly in uniaxial tension is the Coofin-Manson equation. The generalized equation,where Nf is the number of cycles tofailure, f is the cyclic frequency, is the plastic strain and the other letters are constants is :
For Pb-Sn solders, Engelmaier developed the following model
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Literature Examples of Coffin-Manson Response
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Temperature Effects
Many mechanical properties are temperature dependent. For many of the low melting point joining materials, the mechanical properties are a “mixture” of the high and low tem-perature properties
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Creep
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Creep Response
• Steady state strain rate can be expressed as a function of the applied stress, testing temperature and microstructure
• This is known as the power law and most metals exhibit power law creep behavior.
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Room Temperature Creep Response for Eutectic Pb-Sn
Solder
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Phase Diagrams
• Phase diagrams indicate structure and interactions between metals and/or ceramics
• Eutectic - lowest melting point at eutectic composition. Transforms from a sold to liquid at eutectic temperature. Structure is a two phase lamella structure
• Solid solution- a continuos “mixing” over all compositions. Structure is single phase
• Intermetallic- unique phase at intermediate compositions, usually electronic phase such as AB, A2B,A2B3. Structure is often ordered
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Solid Solution Phase Diagram and the Lever Law
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Eutectic Transformation
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Hypoeutectic Transformation
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Two Phase Precipitation Hardening
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time0
Kinetics of Transformation
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Recovery, Recrytallization and Grain Growth
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Dislocation Movement
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Dislocations
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Image Formation on optical microscopy
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Stress- Strain Curve and the Effect of Cold Working
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Phase Diagrams
• Intermetallics typically are detrimental, especially if they exhibit limited solid solubility. Due to ordered structure, they tend to be brittle
• Phase diagrams indicate relative growth of intermetallics between two metals and can estimate growth kinetics
• Eutectic and solid solution reactions are most common in engineering applications
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Common Phase Diagrams in Packaging
• Eutectics in Pb-Sn,Sn-Bi,Sn-Ag,Pb-Sb,Ag-Cu
• Complex intermetallics in Cu-Sn,Au-Sn,Al-Au and Au-Pb
• Melting point of intermetallic indicated relative growth kinetics( Cu3Sn will grow faster than Cu6Sn5
• Intermetallics will grow and can consume parent material ( lower free energy of intermetallic
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Intermetallic Formation
A AB B
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Crystal Structures with 1:1 Atomic Ratios
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Common Phase Diagrams in Electronic Packaging
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Strength Decrease with Intermetallic Growth
Growth of intermetallics can decrease overall strengthand especially thermal shock sensitivity. Intermetallics can be strong but have no ductility and toughness
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Au Dissolution in Pb-Sn Solders
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Copper interaction with Pb-Sn Solders
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Effect of Prolonged Thermal Exposure on Pb-Sn Solders
Regular heating Prolonged Thermal Exposure
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Au-Al Intermetallic Formation
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Alloying
• Alloying changes many physical properties. Solid solution additions increase mechanical strength, raise resistivity and change the chemical potential
• Solid solution alloying can change solderability and leach resistance (example Pd in Ag)
• Alloying can decrease interdiffusion (example- Si additions to Al in IC metallization
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Solder Failure Processes
• Inferior mechanical strengths• Creep• Mechanical fatigue• Thermal fatigue• Thermal expansion anisotropy• Corrosion induced fatigue• Intermetallic compound formation• Detrimental microstructure development• Voids• Leaching• Gold Embrittlement
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Effect of Temperature on gold Embrittlement
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Aging of Au Embrittled Joint
AuSn4
Ni3Sn4Cu Ni
51 micro in Au, unaged
200 hrs @ 150o C
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Interface Failure Due to Au Embrittlement
Interfacial failure between the Ni3Sn4 and AuSn4
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Time to Embrittle for 51 microinch Au
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Intermetallic Formation
• Compatibility of solder composition to substrate
• Length of soldering cycle
• Temperature of soldering
• Post solder storage conditions
• Service conditions
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FEM Modeling of a Solder Ball