# Stress-Strain Relationships

## Presentation on theme: "Stress-Strain Relationships"— Presentation transcript:

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

Relations of Stress-Strain
A) Uniaxial tension B) Compression C) Shear A B D) Torsion D C D

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

Typical Stress-Strain Behavior
Y.P. = Yield Point M = Ultimate Tensile Strenght

Elastic Stress-Strain Relationships

Poisson’s Ratio =-  x /  z

Bimetal Strip

Bimetal Strip (Cont.)

Stress-Strain Distribution in an Adhesively Bonded Joint
Typical variations of shear and peel stresses in a single lap joint for an adhesively bonded joint.Note that the shear stress is non- zero at the ends.

FEM Analysis of a Bonded Structure

Stress Distribution Across Bonded Structure

Fatigue Materials will fail at a lower lever than the UTS

A p Nr = ,5"y) f e -- A p Nr = ,5"y) f e -- =(A\Illf,,e_ P A,y) Thermal Cycle Fatigue 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 to failure, 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

Literature Examples of Coffin-Manson Response

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

Creep

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.

Room Temperature Creep Response for Eutectic Pb-Sn Solder

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

Solid Solution Phase Diagram and the Lever Law

Eutectic Transformation

Hypoeutectic Transformation

Two Phase Precipitation Hardening

Kinetics of Transformation
time

Recovery, Recrytallization and Grain Growth

Dislocation Movement

Dislocations

Image Formation on optical microscopy

Stress- Strain Curve and the Effect of Cold Working

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

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

Intermetallic Formation
AB B

Crystal Structures with 1:1 Atomic Ratios

Common Phase Diagrams in Electronic Packaging

Strength Decrease with Intermetallic Growth
Growth of intermetallics can decrease overall strength and especially thermal shock sensitivity. Intermetallics can be strong but have no ductility and toughness

Au Dissolution in Pb-Sn Solders

Copper interaction with Pb-Sn Solders

Effect of Prolonged Thermal Exposure on Pb-Sn Solders
Regular heating Prolonged Thermal Exposure

Au-Al Intermetallic Formation

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

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

Effect of Temperature on gold Embrittlement

Aging of Au Embrittled Joint
51 micro in Au, unaged Cu Ni Ni3Sn4 AuSn4 o C

Interface Failure Due to Au Embrittlement
Interfacial failure between the Ni3Sn4 and AuSn4

Time to Embrittle for 51 microinch Au

Intermetallic Formation
Compatibility of solder composition to substrate Length of soldering cycle Temperature of soldering Post solder storage conditions Service conditions

FEM Modeling of a Solder Ball