Transcript Tension Test of Metals
Lab. 1: Tension Test of Metals
1. To study and conduct tension tests on several metals in which stress-strain curves are obtained for the full range of loading from zero to rupture.
2. To evaluate the following mechanical properties of each metal tested: a. Proportional limit b. Yield strength c. Ultimate strength d. Modulus of Elasticity (or Young’s Modulus) e. Percent elongation in 2 inches gage length f. Percent reduction of the critical cross sectional area g. Modulus of Resilience h. Toughness 3. To compare these experimental results with the reference values given in the textbook 4. To verify the validity of the axial elongation equation ( d = PL/AE) 5. To observe the characteristics of a tensile failure of metals 1
Material Types
can be distinguished by characteristics among the stress-strain curve.
Ductile material
: has ability to under go large deformation before fracture (rupture) or breaking. (steel)
Brittle material
: the rupture occurs along a surface perpendicular to the loading plane (glass, stone, normal concrete, aluminum) 2
Introduction to the stress-strain curve
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Proportional limit
• Stress-strain curve ( s e ) has a linear relationship • Hook’s law can be applied (Robert Hooke 1635-1703) • Slope of stress-strain curve is “E”, “Young modulas”,” Modulas of elasticity”.
Yield point “F
y
”, “
s
y
”
4
Yield Point for the brittle materials
5
Elastic range
• A stress-strain point that lies between the proportional limit and yield point. • Up to this point, the specimen can be unloaded without permanent deformation.
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Modulas of Elasticity
• Slope of the stress-strain curve.
e s = E = s 2 e 2 – – s 1 e 1 P A i A i (in 2 ) = p D i 2 4 = d L i L i = 2 in Stress (psi) s 2 s 1 s proportional limit E 0 e 1 e 2
Not a slope of Load- Deformation curve
Strain (in/in) 7
Percent elongation and Percent reduction of the critical cross section area at fracture
• Percent elongation in 2 in gage length L f – L i L i X 100 D f • Percent reduction of area A f – A i X 100 A i D 0
L i = 2 in
L f 8
Modulas of resilience (U)
Stress (lb/in 2 ) • It represents the energy per unit volume that material can absorb without yielding • The capacity of a structure to withstand a load without being permanently deformed.
• The area under the straight line of s e curve.
s pl s y 0 e pl e y Strain (in/in) 9
Modulas of resilience (U) lb-in/in
3
Stress (lb/in 2 )
U = ½ x
s pl
x
e pl s pl s y E = s pl e pl e pl = s pl E
U = ½ x
s pl
x (
s pl / E
)
Experiment ½ x s pl x e pl
(lb-in / in 3 )
U = ½ x (
s pl
)
2
/ E
0 e pl e y Strain (in/in) 10
Toughness (lb-in/in
3
)
Stress (lb/in 2 ) • The area under the s e curve. • It represents the energy per unit volume that material can absorb until failure.
s y • A 1 +A 2 +A 3 +A 4 A 2 A 3 A 4 0 A 1 e y e p e Strain (in/in) u e f 11
Engineering stress vs. True stress
Engineering stress
and strain measures incorporate
fixed
reference quantities. In this case, undeformed cross-sectional area is used.
True stress
and strain measures account for changes in cross-sectional area by using the instantaneous values for area, giving more accurate measurements for events such as the tensile test. 12
Axial Extensometer
13 www.mts.com
Load Cell
14 www.mts.com
Grip
15 www.mts.com
Approximated Values (www.matweb.com)
Can I test a steel bar with diameter of 1.0 in ?
Area of Steel ( Diameter 0.5 in)
P
x d 2 /4 = 0.196 in 2 Yield Strength Ultimate Strength Young’s Modulus
52.2 ksi 73.2 ksi
65.3 x 0.196 = 14.4 kip
29700 ksi
Percent Elongation in 2 inches
35%
(36/100 x 2) + 2 = 2.7 in Percent Reduction of Area
L f L i – L i X 100 67% Loading rate = 327 (lbs/sec)
Time of rupture : 14.4x1000/327 = 44 sec.
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Setup and Assumptions of the tensile test
• A cylindrical specimen with cross-sectional area is placed in uniaxial tension under a force. • Assumed state of
engineering stress
for a material element in the bar • Extensometer for measuring the d • Load cell and data acquisition for measuring the P • L i = 2 in, D i = ? in • L f = ? in, D f = ? in 17
Failure of materials
Highly ductile fracture Moderately ductile fracture Brittle fracture
18 Source. http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/exper/bailey/www/bailey.html
Validity of theory
• Hooke’s law (Uniaxial) • Limitation of Hooke’s law • Compare the experiment and theory 4 5 6 0 1 2 3 Deformation d (in)
Hooke’s law
d
E
e
Stress Strain L
s
L
s e
pl pl
E PL AE
Experiment d exp (in) 1 2 3 4 5 6 Theory d theory (in) d exp d theory 19
Failure of ductile materials
• The failure of many ductile materials can be attributed to cup and cone fracture. • This form of ductile fracture occurs in stages that initiate after necking begins.
• First, small microvoids form in the interior of the material. Next, deformation continues and the microvoids enlarge to form a crack. • The crack continues to grow and it spreads laterally towards the edges of the specimen. Finally, crack propagation is rapid along a surface that makes about a 45 degree angle with the tensile stress axis. The new fracture surface has a very irregular appearance. The final shearing of the specimen produces a cup type shape on one fracture surface and a cone shape on the adjacent connecting fracture surface.
20 Source: http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/exper/bailey/www/bailey.html
Failure of brittle materials
• Brittle fracture is a rapid run of cracks through a stressed material. • The cracks usually travel so fast that you can't tell when the material is about to break. In other words, there is very little plastic deformation before failure occurs • The cracks run close to perpendicular to the applied stress. This perpendicular fracture leaves a relatively flat surface at the break. Besides having a nearly flat fracture surface, brittle materials usually contain a pattern on their fracture surfaces. 21 Source: http://www.sv.vt.edu/classes/MSE2094_NoteBook/97ClassProj/exper/bailey/www/bailey.html
Experiment Calculation
d (in) P (lbf) -0.001
50 d c P c -0.001-(-0.001) 50-50 e d/ L i s P/A i 0/L i 0/A i 0.002
75 0.002-(-0.001) 75-50 0.003/L i 25/A i 0.001
90 0.001-(-0.001) 90-50 0.002/L i 40/A i 0.003
100 0.003-(-0.001) 100-50 0.004/L i 50/A i 22
Table 1-1 Material Properties of Tested Materials Experiment Material Property (Steel AISI 1022, )
Proportional Limit (unit) Yield Strength (unit) Ultimate Strength (unit) Young’s Modulus (unit) Percent Elongation in 2 inches (unit) Percent Reduction of Area (unit) Modulus of Resilience (unit) Toughness (unit) Elongation at 50% of Yield Strength (unit)
Referenced Calculated
52.2 ksi 73.2 ksi 29700 ksi 35% 67%
http://www.matweb.com/ Keywords
: carbon steel, AISI 1022, steel as rolled 23