STANDARD SAMPLE. Reduced section " Diameter. Diameter. 2" Gauge length. Radius
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1 MATERIAL PROPERTIES
2
3 TENSILE MEASUREMENT F l l 0 A 0 F
4 STANDARD SAMPLE Reduced section 2 " " Diameter 3 4 " Diameter 2" Gauge length 3 8 " Radius
5 TYPICAL APPARATUS Load cell Extensometer Specimen Moving crosshead
6 ENGINEERING STRESS F F A 0 l l 0 A 0 F
7 COMPRESSIVE LOAD F A 0 l 0 l F A 0 F ( b) T
8 SHEAR AND TORSIONAL A 0 F T F θ T F (c)
9 ENGINEERING STRESS F A 0
10 ENGINEERING STRAIN l i l 0 l 0 l l 0
11 HOOKES LAW Unload Stress Slope = modulus of elasticity Load 0 0 Strain
12 2 = Tangent modulus (at 2 ) Stress 1 = Secant modulus (between origin and 1 ) Strain
13 STRESS Force/Area
14 STRAIN Elongation
15 HOOKE S LAW E
16 Young s Modulus of Copper 110 x 10 3 MPa EXAMPLE A piece of copper originally 305 mm long is pulled in tension with a stress of 276 MPa. If the deformation is entirely elastic, what will be the resultant elongation?
17 EXAMPLE 2 A cylindrical specimen of a titanium alloy having an elastic modulus of 107 GPa and an original diameter of 3.8 mm. will experience only elastic deformation when a tensile load of 2000 N is applied. Compute the maximum length of the specimen before deformation if the maximum allowable elongation is 0.42 mm 250 mm
18 WHAT ARE WE ACTUALLY DOING HERE + Attractive force F A Attraction Unload Force F Repulsion 0 r 0 Repulsive force F R Net force F N Interatomic separation r Stress Slope = modulus of elasticity + (a) Repulsive energy E R Load Net energy E N Interatomic separation r 0 E 0 0 Strain Attractive energy E A We can see that the gradient is similar for a small region above and below the zero force (b) position (equilibrium). Potential energy E Attraction Repulsion 0
19 Force (N), Potential (J) Distance (arb)
20 ON AN ATOMIC LEVEL
21 Strongly bonded df dr r 0 Force F 0 Separation r Weakly bonded
22 U 0 r r 0 U 0 r r 0 U 0 ~ 20 kj/mol U 0 ~ 400 kj/mol Slope = E Slope = E s 109 N m r r s (10 6 psi) s 109 N m r r (10 3 psi) Figure (b) (a) Schematic diagrams showing potential energy (top) andappliedstress(bottom)
23 Temperature ( F) Modulus of elasticity (GPa) Steel Aluminum Tungsten Modulus of elasticity (10 6 psi) Temperature ( C)
24 Poisson s Ratio for Various Materials Modulus of Elasticity Shear Modulus Poisson s Material GPa 10 6 psi GPa 10 6 psi Ratio Metal Alloys Tungsten Steel Nickel Titanium Copper Brass Aluminum Magnesium Ceramic Materials
25 POISSONS RATIO ν = d/d 0 L/L 0 σ t L = L L 0 d d L 0 L s t
26 MATERIAL PROPERTIES Poisson s Ratio for Various Materials Modulus of Elasticity Shear Modulus Poisson s Material GPa 10 6 psi GPa 10 6 psi Ratio Metal Alloys Tungsten Steel Nickel Titanium Copper Brass Aluminum Magnesium Ceramic Materials
27 NEGATIVE POISSON RATI0
28 NEGATIVE POISSON RATI0
29 Elastic Plastic y Stress P Strain
30 Upper yield point Stress y Lower yield point Strain
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