Presentation on theme: "Stress-Strain Relationships"— Presentation transcript:
1 Stress-Strain Relationships Stress is a measure of the force per unit areaStrain 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, EPoisson’s ratio,, relates the contraction in the x,y direction with the elongation under load in the z direction
2 Relations of Stress-Strain A) Uniaxial tensionB) CompressionC) ShearABD) TorsionDCD
3 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 responseYield 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 strengthCoefficient 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
9 Stress-Strain Distribution in an Adhesively Bonded Joint Typical variations ofshear and peel stressesin a single lap joint foran adhesively bondedjoint.Note that theshear stress is non-zero at the ends.
12 Fatigue Materials will fail at a lower lever than the UTS when subjected to cyclic loading. This is knownas fatigue. The loading can be stress induced(mechanical loading) or stain induced (thermalcycling)
13 A p Nr = ,5"y) f e -- A p Nr = ,5"y) f e -- =(A\Illf,,e_ P A,y)Thermal Cycle FatigueThe equation that describes most metals stresses repeatedlyin uniaxial tension is the Coofin-Manson equation. Thegeneralized equation,where Nf is the number of cycles tofailure, f is the cyclic frequency, is the plastic strainand the other letters are constants is :For Pb-Sn solders, Engelmaier developed the following model
15 Temperature Effects Many mechanical properties are temperature dependent. For many of the low melting point joiningmaterials, the mechanicalproperties are a “mixture”of the high and low tem-perature properties
17 Creep ResponseSteady state strain rate can be expressed as a function of the applied stress, testing temperature and microstructureThis is known as the power law and most metals exhibit power law creep behavior.
18 Room Temperature Creep Response for Eutectic Pb-Sn Solder
19 Phase DiagramsPhase diagrams indicate structure and interactions between metals and/or ceramicsEutectic - lowest melting point at eutectic composition. Transforms from a sold to liquid at eutectic temperature. Structure is a two phase lamella structureSolid solution- a continuos “mixing” over all compositions. Structure is single phaseIntermetallic- unique phase at intermediate compositions, usually electronic phase such as AB, A2B,A2B3. Structure is often ordered
29 Stress- Strain Curve and the Effect of Cold Working
30 Phase DiagramsIntermetallics typically are detrimental, especially if they exhibit limited solid solubility. Due to ordered structure, they tend to be brittlePhase diagrams indicate relative growth of intermetallics between two metals and can estimate growth kineticsEutectic and solid solution reactions are most common in engineering applications
31 Common Phase Diagrams in Packaging Eutectics in Pb-Sn,Sn-Bi,Sn-Ag,Pb-Sb,Ag-CuComplex intermetallics in Cu-Sn,Au-Sn,Al-Au and Au-PbMelting point of intermetallic indicated relative growth kinetics( Cu3Sn will grow faster than Cu6Sn5Intermetallics will grow and can consume parent material ( lower free energy of intermetallic
35 Strength Decrease with Intermetallic Growth Growth of intermetallics can decrease overall strengthand especially thermal shock sensitivity. Intermetallicscan be strong but have no ductility and toughness
41 AlloyingAlloying changes many physical properties. Solid solution additions increase mechanical strength, raise resistivity and change the chemical potentialSolid solution alloying can change solderability and leach resistance (example Pd in Ag)Alloying can decrease interdiffusion (example- Si additions to Al in IC metallization