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Tensile Test Lab Report
ENGR 271
Group 3
Jesus Carrasco, Robert Demko, Joshua Jenkins, Haven Nuqui
2/27/26
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Summary
Purpose
​
The objective of this experiment is to characterize the mechanical properties of materials by
performing a standard tensile test. By subjecting a specimen to a controlled axial load until failure, the lab
aims to determine fundamental properties such as strength, ductility, and stiffness. This data allows for the
comparison of material behaviors—specifically between ductile materials (like A36 steel) and brittle
materials (like cast iron)—and the evaluation of the relationship between engineering and true
stress/strain.​
​
Background and Theory
​
A tensile test measures how a material deforms under tension. Initially, most metals exhibit
linear-elastic behavior, where deformation is temporary and follows Hooke’s Law. As the load increases,
the material undergoes plastic deformation, which is permanent. Key milestones in this process include
the yield strength (onset of noticeable plastic deformation) and tensile strength (the maximum load the
material can withstand).
A critical phenomenon in ductile materials is necking, where the specimen's cross-sectional area
begins to decrease rapidly at a localized point after reaching the maximum tensile strength. While
engineering stress is calculated using the original area, true stress accounts for this decreasing
instantaneous area, providing a more accurate representation of the material's actual strength up until the
point of fracture.
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Experimental Setup
​
The experimental procedure utilizes a standard tensile test machine equipped with a load cell to
measure applied force and a moving crosshead to provide controlled axial displacement. A "dog-bone"
shaped specimen, typically featuring a 0.505" diameter and a 2" gauge length (𝐿0), is secured in the
machine while an extensometer is attached to track precise changes in length. As the crosshead moves,
the machine records load and displacement data, which are then converted into engineering stress (σ) and
strain (ϵ) using the specimen's initial dimensions. This data allows for the calculation of the Modulus of
Elasticity (𝐸) via Hooke’s Law (σ = 𝐸ϵ) during the linear-elastic phase, and the determination of Yield
Strength (σ𝑦) using the 0.2 % offset method, where a displacement of 0.004 in is applied to a 2" sample.
As the test progresses toward failure, the resulting fracture length (𝐿𝑓) and final area (𝐴𝑓) are measured to
determine ductility through percent elongation and percent reduction in area:
Percent Elongation(%𝐸𝐿) : %𝐸𝐿 =
Percent Reduction (%𝑅𝐴) : %𝑅𝐴 =
​
𝐿𝑓−𝐿𝑜
𝐿𝑜
𝐴𝑜−𝐴𝑓
𝐴𝑜
× 100
× 100
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Calculations and Graphs
Engineering Stress vs Strain (to calculate results)
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Engineering and True Stress vs Strain Comparison (up to tensile strength, or point M)
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Data
Experimental
Theoretical
% Error
Modulus of Elasticity (ksi)
4980
30,000
83.4
Yield Strength (ksi)
69.3.6
95
0.44%
Tensile Strength (ksi)
121
148
18.20%
Fracture Strength (ksi)
56.8 N/A
N/A
Ductility (%EL)
14.3 N/A
N/A
Toughness (ksi)
14.2 N/A
N/A
Calculations
Strain Sample Calculation
∆𝐿
ε= 𝐿
𝑜
ε=
0.28547
2
ε = 0. 143𝑖𝑛/𝑖𝑛
Stress Sample Calculation
𝐹
σ= 𝐴
σ=
73.72
0.5
2
π( 0.25 )
σ = 375𝑝𝑠𝑖
True Strain Sample Calculation
ε𝑇 = 𝑙𝑛(1 + ε)
ε𝑇 = 𝑙𝑛(1 + 0. 143)
ε𝑇 = 0. 133𝑖𝑛/𝑖𝑛
True Stress Sample Calculation
σ𝑇 = σ(1 + ε)
σ𝑇 = 375(1 + 0. 00053)
σ𝑇 = 375𝑝𝑠𝑖
Modulus of Elasticity
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σ
𝑦
𝐸 = ε −0.002
𝑦
69300−0
𝐸 = 0.021675−0.002
𝐸 = 4980𝑘𝑠𝑖
Yield Strength
𝐹𝑟𝑜𝑚 𝐺𝑟𝑎𝑝ℎ: σ𝑦 = 69. 3𝑘𝑠𝑖
Tensile Strength
𝐹𝑟𝑜𝑚 𝐺𝑟𝑎𝑝ℎ: 121𝑘𝑠𝑖
Fracture Strength
𝐹𝑟𝑜𝑚 𝐺𝑟𝑎𝑝ℎ: 56. 8𝑘𝑠𝑖
Ductility
%𝐸𝐿 =
%𝐸𝐿 =
𝐿𝑓−𝐿𝑜
𝐿𝑜
* 100%
0.28547
2
* 100%
%𝐸𝐿 = 14. 3%
Toughness (Box Counting Method)
𝑢𝑡 = 35. 5 𝑏𝑜𝑥𝑒𝑠 * 0. 02𝑖𝑛/𝑖𝑛 * 20000𝑝𝑠𝑖
𝑢𝑡 = 14. 2𝑘𝑠𝑖
Modulus of Elasticity %Error
δ=|
δ=|
𝑉𝐴−𝑉𝐸
𝑉𝐸
| * 100%
4980−30000
| * 100%
30000
δ = 83. 4%
Yield Stress %Error
δ=|
δ=|
𝑉𝐴−𝑉𝐸
𝑉𝐸
| * 100%
94.6−95
| * 100%
95
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δ = 0. 444%
Tensile Strength %Error
δ=|
δ=|
𝑉𝐴−𝑉𝐸
𝑉𝐸
| * 100%
121−148
| * 100%
148
δ = 18. 2%
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Results and Discussion
​
Results
The tensile test conducted on the specimen (Group 3) yielded several key mechanical
properties. The material exhibited a Yield Strength of 69.3 ksi and a maximum Tensile Strength
of 121 ksi. In comparing experimental data to theoretical values, the Yield Strength showed an
extremely high accuracy with only a 0.44% error. However, the Modulus of Elasticity was
measured at 4,980 ksi, which represents a significant 83.4% error from the theoretical value of
30,000 ksi. This discrepancy likely stems from the sensitivity of early-stage strain measurements
or potential slip in the extensometer during the initial linear-elastic phase
The specimen demonstrated clear ductile behavior, reaching a Percent Elongation (%EL)
of 14.3% and a Fracture Strength of 56.8 ksi. The Toughness, calculated using the box-counting
method to find the area under the stress-strain curve, was determined to be 14.2 ksi.
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Discussion
1. Why does it not make much sense to calculate true stress and true strain
It does not make sense to use the standard true stress (σ𝑇 = σ(1 + ϵ ) and true strain (
ϵ𝑇 = 𝑙𝑛(1 + ϵ) equations after the maximum load (Tensile Strength) is reached because of the
phenomenon of necking. These specific equations are derived based on the assumption of
uniform deformation across the entire gauge length. Once the material reaches its peak tensile
strength, deformation becomes localized at a specific point. Because the cross-sectional area
decreases rapidly and non-uniformly in the "neck," the relationship between the original gauge
length and the instantaneous area is no longer consistent, making these specific mathematical
models invalid for the post-necking phase
2. Ductile (A36 Steel) vs. Brittle (Cast Iron) Behavior
Based on the lab objectives and general material theory, there are distinct differences in
how ductile and brittle materials deform and fracture. As a ductile material, A36 steel undergoes
significant plastic deformation and necking before failure , while a brittle material like cast iron
exhibits very little to no plastic deformation, failing almost immediately after reaching its elastic
limit. These behaviors are clearly visible on a stress-strain curve; the specimen in this lab showed
a long tail after the yield point , which is characteristic of ductile materials that "stretch" and
absorb energy. In contrast, a brittle material would produce a nearly vertical line that terminates
abruptly at the fracture point without the downward curve or necking phase seen in our
experimental Engineering Stress vs. Strain graph.
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