1. Lab. 1: Tension Test of Metals
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.
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
To compare these experimental results with the reference values given in the textbook
To verify the validity of the axial elongation equation ( d = PL/AE)
To observe the characteristics of a tensile failure of metals

2. 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)

3. Introduction to the stress-strain curve

4. Proportional limit Yield point “Fy”, “sy”
Stress-strain curve (s-e) has a linear relationship
Hook’s law can be applied (Robert Hooke )
Slope of stress-strain curve is “E”, “Young modulas”,” Modulas of elasticity”.
Yield point “Fy”, “sy”

5. Yield Point for the brittle materials

6. 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.

7. Modulas of Elasticity e = Slope of the stress-strain curve. s2 – s1
Stress (psi)
Strain (in/in) s2 s1 e2 e1
s proportional limit E
Slope of the stress-strain curve.
E =
s2 – s1
e2 – e1
s = P Ai
Ai (in2) =
p Di2 4
e = d Li
Li = 2 in
Not a slope of Load- Deformation curve

8. Percent elongation and Percent reduction of the critical cross section area at fracture
Percent elongation in 2 in gage length Lf
Li= 2 in Df
Lf – Li Li
X 100
Percent reduction of area
Af – Ai Ai
X 100 D0

9. Modulas of resilience (U)
Stress (lb/in2)
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. sy
spl ey
epl
Strain (in/in)

10. Modulas of resilience (U) lb-in/in3
Stress (lb/in2)
U = ½ x spl x epl sy
spl
E =
spl
epl
epl =
spl E
Experiment
½ x spl x epl
U = ½ x spl x (spl / E)
(lb-in / in3)
U = ½ x (spl)2 / E ey
epl
Strain (in/in)

11. Toughness (lb-in/in3) The area under the s-e curve.
Stress (lb/in2)
Strain (in/in) sy ey A1 A2 A3 A4 ep eu ef
The area under the s-e curve.
It represents the energy per unit volume that material can absorb until failure.
A1+A2+A3+A4

12. 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.

13. Axial Extensometer

14. Load Cell

15. Grip

16. Approximated Values (www.matweb.com)
Can I test a steel bar with diameter of 1.0 in ?
Area of Steel ( Diameter 0.5 in)
Yield Strength
52.2 ksi
Ultimate Strength
73.2 ksi
Young’s Modulus
29700 ksi
Percent Elongation in 2 inches
35%
Percent Reduction of Area
67%
P x d2 /4 = in2
65.3 x = 14.4 kip
(36/100 x 2) + 2 = 2.7 in
Lf – Li Li
X 100
Loading rate = 327 (lbs/sec)
Time of rupture :
14.4x1000/327 = 44 sec.

17. 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
Li = 2 in, Di = ? in
Lf = ? in, Df = ? in

18. Failure of materials Highly ductile fracture
Moderately ductile fracture
Brittle fracture
Source.

19. Validity of theory Hooke’s law Hooke’s law (Uniaxial)
Limitation of Hooke’s law
Compare the experiment and theory
Load P (lbf)
Deformation d (in) 4 5 6
dexp
Experiment
Theory
dexp (in)
dtheory (in)
dtheory 3 1 2 3 4 5 6 2 1

20. 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.
Source:

21. 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.
Source:

22. Experiment Calculation
d (in)
P (lbf) dc Pc
e = d/Li
s = P/Ai
-0.001 50
(-0.001)
50-50
0/Li
0/Ai
0.002 75
0.002-(-0.001)
75-50
0.003/Li
25/Ai
0.001 90
0.001-(-0.001)
90-50
0.002/Li
40/Ai
0.003
100
0.003-(-0.001)
100-50
0.004/Li
50/Ai

23. Table 1-1 Material Properties of Tested Materials
Material Property (Steel AISI 1022, )
Experiment
Referenced
Calculated
Proportional Limit (unit)
Yield Strength (unit)
52.2 ksi
Ultimate Strength (unit)
73.2 ksi
Young’s Modulus (unit)
29700 ksi
Percent Elongation in 2 inches (unit)
35%
Percent Reduction of Area (unit)
67%
Modulus of Resilience (unit)
Toughness (unit)
Elongation at 50% of Yield Strength (unit)
Keywords: carbon steel, AISI 1022, steel as rolled