AMERICAN INTERNATIONAL UNIVERSITY BANGLADESH
(AIUB)
FACULTY OF ENGINEERING
DEPARTMENT OF IPE
MECHANICS OF SOLIDS
LAB
OEL REPORT
Group -03
EXPERIMENT NUMBER : 4
Experiment Name
To Determine the Shear Strength of Copper Specimen Using UTM
Supervised By
DR . MOHAMMED TAUHIDUZZAMAN
Submitted By:
NAME ID
MD.SIAM 23-54697-3
ROMANA ISLAM 23-54687-3
FARZANA ARFIN LILA 23-54432-3
MAHIHAN MAHBUB TARAN 23-54975-3
APURBO CHOWDHURY 23-55303-3
Date of Submission: 26-05-2025
1. Introduction
Understanding the mechanical properties of metals is crucial in engineering,
especially when choosing materials for structural applications. One key property is
compressive strength, which indicates how a material behaves under compressive
loads. In this experiment, a cylindrical copper specimen with a circular cross-section
was tested using a Universal Testing Machine (UTM) to observe its behavior under
compression. The test helps determine how the material deforms and allows us to
calculate important properties such as Young’s Modulus, which reflects the
material’s stiffness. By comparing the experimental results with standard theoretical
values, we can evaluate the accuracy of our testing methods and equipment.
2. Objective
The objective of this experiment is to perform a compression test on a copper
cylindrical specimen to determine its compressive strength and stress. Additionally,
the experiment aims to calculate the Young's Modulus (Elastic Modulus) of the
specimen experimentally and compute the percentage error when compared to the
standard theoretical value of Young’s Modulus for copper.
3. Apparatus and Materials
3.1. Apparatus: Universal Testing Machine (UTM), Copper cylindrical specimen,
Vernier caliper.
3.2. Specimen Details:
Material: Copper
Shape: Circular cross-section cylindrical specimen
Diameter: 18.5 mm
4. Theory
The compression test is a fundamental mechanical test where a material is subjected
to a controlled compressive force to determine its strength and deformation
characteristics. The stress-strain relationship in compression is like that in tension,
up to the yield point, after which the behavior may differ due to barreling and
material flow.
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In a compression test, a material is subjected to axial compressive force and the
corresponding deformation is recorded. For cylindrical specimens:
𝐹
Stress (σ) = ……………………………….…. (1)
𝐴
𝜋𝑑2
Where: F = Applied force (N), A = Cross-sectional area ( )
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𝛥𝑙
Strain (ε) = …………………………………… (2)
𝑙°
Where: 𝛥𝑙 = Change in length (mm), 𝑙° = Original length (mm)
Young’s Modulus (E): Ratio of stress to strain in the elastic region of the material.
𝑆𝑡𝑟𝑒𝑠𝑠
E= …………………………………. (3)
𝑠𝑡𝑟𝑎𝑖𝑛
In compression, barreling can occur due to friction at the specimen-plate interface,
leading to non-uniform deformation. Copper, being a ductile metal, tends to exhibit
significant plastic deformation after yielding, but this test focuses primarily on
its elastic behavior to calculate Young’s Modulus.
4.1. Elastic and Plastic Deformation: When a material is subjected to compressive
stress, it initially deforms elastically, meaning it will return to its original shape once
the load is removed. Beyond the elastic limit, the material undergoes plastic
deformation, where permanent changes in shape occur. Copper, being ductile,
exhibits significant plastic deformation after yielding.
4.2. Yield Point: The yield point in a compression test is the stress at which a material
begins to deform plastically. For copper, this is typically lower than the tensile yield
points due to the different nature of compressive forces.
5. Procedure
1. The diameter of the copper specimen was measured using precise instruments
to ensure accuracy.
2. The specimen was mounted centrally between the compression plates of the
Universal Testing Machine (UTM).
3. The machine was started, and the compressive load was gradually applied.
4. The maximum compressive force and the maximum compressive stress at the
point of deformation were recorded.
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5. The strain was calculated.
6. The experimental Young’s Modulus was calculated using the stress-strain
relationship.
7. The experimental value was compared with the theoretical value to calculate
the percentage error.
6. Calculation
Given Data:
Maximum force, F = 90.02 𝐾𝑁 =90.02×103 N
𝐹 90.02×103
Maximum compressive stress, σ = = N =354409448.8 N
𝐴 2.54×10−4
Ϫ𝐿 40
Strain, ∈ = = = 0.1
𝐿 400
Diameter, d = 18 mm =.018 m
Young’s Modulus from analytical: 𝐸𝑎𝑛𝑎 = 3.6 𝐺𝑃𝑎
152.57−299.59
Young’s Modulus from graph: 𝐸𝑔𝑟𝑎𝑝ℎ = 8.088−3.13 = 2.996 GPa
100
6.3 Percentage Error:
3.6−2.96
%Error = × 100% = 17.78 %
3.6
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7. Result and Discussion
Fig-1: Stress VS
strain graph.
Maximum Force Applied: 90.02×103 N
Maximum Compressive Stress: 1549397.59 N
Diameter: .0185 m
Analytical Young’s Modulus: 3.6 GPa
Young’s Modulus from graph: 2.96 GPa
Percentage Error: 17.78%
7.1. Discussion
The high percentage error observed in the experiment can be attributed to several
factors:
1. Measurement Inaccuracies: Small deformations are particularly challenging
to measure accurately. Any slight error in measuring the initial and final
lengths of the specimen can significantly impact the calculated strain and,
consequently, the Young's Modulus.
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2. Plastic Deformation Onset: If plastic deformation begins before the
measurements are recorded, it can affect the assumption of linear elasticity.
This means the material may have already started to deform plastically,
leading to an inaccurate calculation of Young's Modulus.
3. Misalignment in the UTM Machine: Any misalignment in the Universal
Testing Machine can induce uneven stress distribution across the specimen.
This uneven distribution can result in inaccurate stress readings and affect the
overall results.
7.2. Friction at Interfaces: Friction between the specimen and the compression
plates can affect the true strain measurement. This friction can cause barreling and
non-uniform deformation, leading to errors in the calculated stress and strain
values.
8. Conclusion
The compression test on the cylindrical copper specimen offered valuable insights
into the material's behavior under compressive loading. Despite the analytical
Young’s Modulus 3.6 𝐺𝑃𝑎 deviating significantly from the theoretical value (2.96
GPa), the experiment underscored the critical importance of precise strain
measurement and proper test setup. We calculated the Young's Modulus from the
graph and compared it with the experimental value, resulting in a percentage error
of 17.78%. This significant discrepancy highlights the need for improved
measurement techniques and careful calibration of equipment. To achieve more
accurate results in future experiments, incorporating advanced strain measuring
tools, such as strain gauges or extensometers, is essential. These improvements will
help minimize errors and provide closer approximations to the theoretical material
properties, thereby enhancing the reliability and validity of the findings.
