# Elastic Modulus, Poisson's Ratio - Springer

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

fracture energy Mechanical Properties

associated with structural applications elastic properties Youngs modulus or elastic modulus Poissons ratio yield strength plastic properties elongation

reduction in area ultimate tensile strength fracture energy 2 Elastic Modulus, Poissons Ratio best to use ultrasonic velocity

3 Elastic Modulus E = elastic modulus u = sound velocity (depends on squareroot of fractional density) = material density

= Poissons ratio 4 Strength Definitions strength = force over original area engineering stress & strain use initial size

true stress & strain use instantaneous size 5 Stress and Load stress = load/area

Compression and Tension 7 Compression Test 4

= 2 8 Compression Test

9 Brazillian Test 2 = particulate composites

D = 25 mm T = 6 mm 10 Transverse Rupture Test 11

Transverse Rupture (TRS or MOR) 12 Strength Calculation three point bending (TRS); 1-2-4 ratio dimensions Weibull effect four point bending (L > G, upper gap spacing)

13 Weibull Data 14 Porosity Effect

15 Disk and Ball Variant 16 Tensile Test

17 Clamping 18 Screw and Hydraulic Systems

19 Tensile Stretching - Elastic tensile bar = L/Lo P

stress L Ao E Lo

strain P engineering materials all respond elastically at small strains 20 Elastic Part

21 Brittle Response linear to fracture stress

x TS or UTS = tensile strength fracture brittle behavior

strain examples: concrete, ceramics, stone Ductile Response stress uniform 23

Ductile Options high ductility moderate ductility some, but low

ductility Tensile Response standardized test bar after ductile fracture Tensile Necking

elongation versus gage length. Ductility ductility relates to strain at fracture measures

E E I I 0.002

elongation change in gauge length over initial length reduction in area change in gauge area over initial area yield strength

Example Bars initial bar very high elongation moderate elongation brittle

Reduction in Area, Necking ductile fracture - elongation and area reduction Porosity Role 30

Interface Preferred Fracture 31 Transverse Rupture - Tensile 32

Impact Tester 33 Impact (Charpy) Test 34

Notch Effect two phase stainless

unnotched impact toughness 272 J/cm2 notched impact toughness 10 J/cm2 stainless is not generally considered notch sensitive 35 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 36

Fatigue Testing 37 Fatigue oscillating stress bending, rotating, pulling, compression endurance limit or fatigue strength 10

million cycles R = -1 typical, fully reversed fatigue strength 30-50 % of tensile composites tend to be lower range 38 Uniaxial Fatigue Tester

39 Fatigue Curve 40 Fatigue Steps

41 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 42 Compact Tension Test 43

At Onset of Crack Extension preexisting crack of size A = applied stress to start crack motion material property of fracture toughness 44

Palmqvist Test (Vickers Indent) 45 Palmqvist Approach Vickers hardness test, VHN crack length A

J conversion factor R measured from hardness load F and crack onset load FO 46

Some Examples ice 0.2 MPam alumina 4 MPam

WC-10Co 12 MPam heat treated steel 100 MPam 47 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 48

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