1. 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

2. 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

3. 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 𝜒
example interface cohesion
term
𝜎 𝐶 = 𝜎 𝑂 + 𝐾 𝐺 𝐺
example grain size term

4. Example (Again) Strength-Ductility

5. 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)

6. Ductility Scatter Al-Al2O3, Mg-SiC

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

8. 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

9. Fracture Path Options

10. Other Options

11. More Options

12. And More Options

13. Heterogeneity

14. Weak Interface Role

15. Interface
weak interface
strong interface

16. Grain Size
290 MPa
tensile strength also changes
580 MPa

17. Test Temperature
linear
thermal
softening
behavior

18. Hardness-Toughness Correlation

19. System Specific Optimization

20. Fatigue S-N Curves, R= -1

21. Thermal Softening Behavior

22. 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

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

24. Thermal Expansion

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

26. 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

27. Stress-Composition Creep Rate

28. Thermal Shock Weakening

29. 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

30. Design Option
glass-metal seal
heat spreader

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

32. Conductivity Variants

33. 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

34. Early Experiment
Gurland
mixed silver
and bakelite

35. Percolation Conductivity Behavior

36. Loss of Conductivity from Porosity

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

38. 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

39. Carbides Data

40. 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

41. 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, …