Dynamic Property Models goals transition to deformation and fracture more secondary influences illustrations of variations more complex models key behavior patterns reinforce need for product testing

Strength-Ductility Transition below yield strength properties are generally linear with composition if deformation, flow, shape change, or fracture - everything is more complex composition is only starting point

Some Strength Factors constituent phase strength 𝜎 𝐶 = 𝜎 𝑂 𝑘 𝑓 𝑃 composition contiguity porosity grain size grain shape grain spacing homogeneity residual strain work hardening flaws, defects 𝜎 𝐶 = 𝜎 𝑂 𝑘 𝑓 𝑃 example fractional density term 𝜎 𝐶 = 𝜎 1 1−1.21 𝑉 2 2 3 𝜒 example interface cohesion term 𝜎 𝐶 = 𝜎 𝑂 + 𝐾 𝐺 𝐺 example grain size term

Example (Again) Strength-Ductility

Another Example Al-50SiC 13 µm grain size – strength = 590 MPa 165 µm grain size – strength = 390 MPa porosity role another factor, limits ductility and strength 𝛿= 𝑒𝑥𝑝 − 𝛼 (1−𝑓)

Ductility Scatter Al-Al2O3, Mg-SiC

Composition Role on Ductility 𝜀 𝐶 𝐵 = 𝜅 (1− 𝐶 2 εC = composite ductility κ = full density ductility C2 = contiguity B = about 0.7

Deformation / Fracture Parameters ductility tensile strength ponder ductility limited strength low ductility fails to reach true UTS impact energy fracture toughness creep, strain rate properties fatigue

Fracture Path Options

Other Options

More Options

And More Options

Heterogeneity

Weak Interface Role

Interface weak interface strong interface

Grain Size 290 MPa tensile strength also changes 580 MPa

Test Temperature linear thermal softening behavior

Hardness-Toughness Correlation

System Specific Optimization

Fatigue S-N Curves, R= -1

Thermal Softening Behavior

Thermal Expansion Behavior ∆𝐿 𝐿 𝑂 = 𝛼 ∆𝑇 generally scales with melting point Al (660 C) 23.8 ppm/C W (3410 C) 4.6 ppm/C linearly additive model 𝛼 𝐶 = 𝑉 𝐽 𝛼 𝐽 = 𝑉 1 𝛼 1 + 𝑉 2 𝛼 2

TEC Interaction Models add elastic properties to volume fraction 𝛼 𝐶 = 𝛼 1 − 𝐸 2 𝐸 1 3 𝑉 2 𝛼 1 − 𝛼 2 1− 𝜈 1 2 1−2 𝜈 2 𝑉 2 +2 𝑉 2 1−2 𝜈 2 +(1+ 𝜈 2 )

Thermal Expansion

Porosity Lowers TEC 𝛼 𝐶 = 𝛼 𝐶𝑂 𝑓 1/3 other models, but data are poor quality so difficult to assert validity

Creep Deformation Rate 𝑑𝜀 𝑑𝑡 = 𝐵 𝑉 2 𝑃 𝑆 𝑁 𝑒𝑥𝑝 − 𝑄 𝑅 𝑇 log (creep rate) varies with log (stress) N = 7.4

Stress-Composition Creep Rate

Thermal Shock Weakening

Thermal Fatigue 𝑁=𝐴 𝑒𝑥𝑝 𝜓 Δ𝑇 𝐿 𝛼 1 − 𝛼 2 N = number of cycles to failure ΔT function of temperature change thickness L; ψ = standard size difference in thermal expansion coefficients Δα

Design Option glass-metal seal heat spreader

Electrical Conductivity few different cases two conductors one conductor, one insulator conductor dispersed conductor percolated two insulators

Conductivity Variants

Simple Case linear rule of mixtures two conductors, ignores percolation, connectivity 𝜆 𝐶 = 𝑉 1 𝜆 1 + 𝑉 2 𝜆 2 other models very messy

Early Experiment Gurland mixed silver and bakelite

Percolation Conductivity Behavior

Loss of Conductivity from Porosity

Porosity Role on Conductivity 𝜆 𝐶 = 𝜆 𝑂 𝑓 1+ 𝜒 1−𝑓 2

Abrasive Wear Behavior 𝑀= 𝑊 𝐿 Κ 𝐻 𝐶 𝜌 M = mass loss K = wear constant W = normal load L = length of sliding ρ = density HC = hardness

Carbides Data

General Property Variations models start with linearly additive base sum relative contributions include porosity delve into contiguity may require interface term include stored energy, phase interactions need to add percolation some are just curve fitting

Key Points Dynamic Properties issues with deformation and fracture linearly additive rules not sufficient additional terms and measures required generally best to measure versus model concerns are ductility, tensile strength, fracture toughness, impact toughness, fatigue strength, creep life, thermal fatigue, …