1. Mechanical Properties
goals
elastic properties
yielding phenomenon
deformation, tensile strength, ductility
tensile curves
brittle versus ductile failure
fracture energy

2. Mechanical Properties
associated with “structural” applications
elastic properties
Young’s modulus or elastic modulus
Poisson’s ratio
yield strength
plastic properties
elongation
reduction in area
ultimate tensile strength
fracture energy

3. Elastic Modulus, Poisson’s Ratio
best to use ultrasonic velocity

4. Elastic Modulus
𝐸= 𝑢 2 𝜌 1+ 𝜈 (1−2 𝜈) 1− 𝜈 E = elastic modulus u = sound velocity (depends on square-root of fractional density) ρ = material density ν = Poisson’s ratio

5. Strength Definitions
strength = force over original area
engineering stress & strain
use initial size
true stress & strain
use instantaneous size

6. Stress and Load
stress = load/area

7. Compression and Tension

8. Compression Test
𝜎= 4 𝐹 𝜋 𝐷 2

9. Compression Test

10. Brazillian Test
𝜎= 2 𝐹 𝜋 𝐷 𝑇
particulate composites
D = 25 mm
T = 6 mm

11. Transverse Rupture Test

12. Transverse Rupture (TRS or MOR)

13. Strength Calculation 𝜎= 3 𝐹 𝐿 2 𝑊 𝑇 2 𝜎 𝑇𝑅𝑆 = 𝜎 𝑇𝐸𝑁 2 (𝑀+1) 2 1 𝑀
three point bending (TRS); ratio dimensions
𝜎= 3 𝐹 𝐿 2 𝑊 𝑇 2
Weibull effect
𝜎 𝑇𝑅𝑆 = 𝜎 𝑇𝐸𝑁 (𝑀+1) 𝑀
four point bending (L > G, upper gap spacing)
𝜎= 3 𝐹 (𝐿−𝐺) 2 𝑊 𝑇 2

14. Weibull Data

15. Porosity Effect

16. Disk and Ball Variant

17. Tensile Test

18. Clamping

19. Screw and Hydraulic Systems

20. Tensile Stretching - Elastic
tensile bar Ao Lo L P
 = L/Lo
stress
strain E
engineering materials all respond elastically at small strains

21. Elastic Part

22. Brittle Response x linear to fracture TS or UTS = tensile strength 
stress
brittle behavior
strain
examples: concrete, ceramics, stone

23. Ductile Response
stress
uniform

24. Ductile Options high ductility moderate ductility some, but low

25. Tensile Response
standardized test bar after ductile fracture

26. Tensile Necking
elongation versus gage length.

27. Ductility  ductility relates to strain at fracture measures
elongation
change in gauge length over initial length
reduction in area
change in gauge area over initial area 
yield
strength E E I I 
0.002

28. Example Bars initial bar very high elongation moderate elongation
brittle

29. Reduction in Area, Necking
ductile fracture - elongation and area reduction

30. Porosity Role

31. Interface Preferred Fracture

32. Transverse Rupture - Tensile

33. Impact Tester

34. Impact (Charpy) Test

35. Notch Effect
two phase stainless
unnotched impact toughness 272 J/cm2
notched impact toughness 10 J/cm2
stainless is not generally considered notch sensitive

36. Impact and Tensile
impact gives energy to fracture
tensile gives strength and elongation
area under stress-strain curve:
N/m2 {stress} by m/m {strain}
product is energy per unit volume = J/m3
tests differ in strain rates, still similar

37. Fatigue Testing

38. Fatigue
oscillating stress
bending, rotating, pulling, compression
endurance limit or fatigue strength 10 million cycles
R = -1 typical, fully reversed
fatigue strength % of tensile
composites tend to be lower range

39. Uniaxial Fatigue Tester

40. Fatigue Curve

41. Fatigue Steps

42. Fracture Toughness
resistance to crack propagation
K = stress concentration (at crack tip)
I = tensile mode (vs shear or compression)
c = critical for fracture
KIc = fracture toughness
compact tension test
Palmqvist test

43. Compact Tension Test

44. At Onset of Crack Extension
preexisting crack of size A
σ = applied stress to start crack motion
material property of fracture toughness
𝐾 𝐼𝑐 =𝑌 𝜎 𝜋 𝐴

45. Palmqvist Test (Vickers Indent)

46. Palmqvist Approach
Vickers hardness test, VHN
crack length A
𝐾 𝐼𝑐 = 𝐽 𝑉𝐻𝑁 𝑅 1/2
J conversion factor
R measured from hardness load F and crack onset load FO
𝑅= 𝐹− 𝐹 𝑂 4 𝐴

47. Some Examples
ice 0.2 MPa√m
alumina 4 MPa√m
WC-10Co 12 MPa√m
heat treated steel 100 MPa√m

48. Key Points
means to measure and specify
many possible tests
some tests are easy, widely used
chemistry, density, hardness typical
other tests are destructive
values differ between tests
best practice to specify test