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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

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## Stress-Strain Relationships

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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**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. M = Ultimate Tensile Strenght Y.P. = Yield Point**Poisson’s Ratio**=- x / z**Stress-Strain Distribution in an Adhesively Bonded Joint**Typical variations of shear and peelstresses in a single lap joint for an adhesively bonded joint.Note that the shear stress is non- zero at the ends.**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)**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@,,@ 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**Temperature Effects**Many mechanical properties are temperature dependent. For many of thelow melting point joining materials, the mechanical properties are a “mixture” of the high and low tem- perature properties**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.**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**Kinetics of Transformation**time 0**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**A AB B**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**Effect of Prolonged Thermal Exposure on Pb-Sn Solders**Regular heating Prolonged Thermal Exposure**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**Aging of Au Embrittled Joint**51 micro in Au, unaged Ni3Sn4 Cu Ni AuSn4 200 hrs @ 150o C**Interface Failure Due to Au Embrittlement**Interfacial failure between the Ni3Sn4 and AuSn4**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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