Analysis of Material Behavior Under Tensile Stress: A Report

This report details a laboratory investigation into the tensile strength and mechanical properties of four materials: A-36 steel, polymethylmethacrylate (PMMA), polycarbonate, and 6061-T6 steel alloy. The study employed an Instron load frame and BlueHill data acquisition software to subject the materials to tensile stress, measuring properties such as yield strength, modulus of elasticity, fracture strength, and percentage elongation. The report compares the materials' behaviors, analyzes stress-strain curves, and determines true stress and strain values. The results indicate that A-36 steel exhibited the highest ultimate tensile strength, while 6061-T6 steel showed a higher yield strength. The analysis includes the application of the Ramberg-Osgood model and discusses the significance of these properties in engineering design. The report also addresses the importance of elastic analysis in determining the strength of materials and its role in the design and development of new and improved materials.

First Name Last Name
Instructor
Course
07th December 2018
Part 1
Tests on tensile strength are major meant for indulgent properties of diverse materials, besides
their behavior when subjected to loading. This laboratory attempted 4 unmistakable materials,
together with A-36 steel, polymethylmethacrylate, polycarbonate, and6061-T6 steel alloy.
Respective model was attempted on various occasions by means of a BlueHill data getting
programming as well as the Instron stack diagram. The figures obtained from for each test
indicated important properties of material, for illustration, extraordinary unbending nature,
modulus of rigidity, in addition to yield feature. Additional determined properties encompassed
fractural strength, percent stretching or elongation. These measureable properties were applied
for relating the materials with one another, as well as to depict the sample as weak or pliable.
Ideal strain as well as stress were determined for 6061-T6 steel model to determine the
dissimilarity concerning the structure pressure, in addition to the genuine merits. The process of
designing pressure is a suspicion which utilizes the principal zone of the cross area, overlooking
the influences of transverse strain as well as the fluctuating cross segment. This presumption
outcomes in the descent of the designing stress strain curvature subsequent to a conclusive
rigidity, at which necking come about.
Applying the assessments of the true strain, the true plastic strain was set on for a specimen of
steel by deducting value ideal flexible strain. Graphing the logarithm of the certifiable pressure
versus the logarithm of the real plastic strain allowed the plastic piece of the real pressure strain
curve to be exhibited by the Ramberg-Osgood demonstrate as in the later area. Despite the fact
that the model did insufficiently at small plastic strains close by yielding, it attempted to
flawlessness prior to necking and a conclusive malleable strain.
The outcomes of the tractable tests exhibited that the A-36 steel was the strongest model. It
achieved the utmost extreme rigidity that is, imperative extraordinary flexibility, the unsurpassed

modulus of solidness/durability, in addition to the greatest certifiable quality of break. The 6061-
T6 steel achieved a greater yield compared to the A-36 steel, anyway an inferior inflexibility in
addition to veritable crack value as a result of softening besides cementing/setting. Most of the
materials other than the PMMA ended up being malleable, especially the polycarbonate, which
recorded 82.2% elongation. The PMMA examinations landed at the average of a percentage
extending/lengthening of simply 0.7%.
Elastic analysis is a standout concerning the record key assessments for designing, also
contributes important figures relating to a material together with its correlated properties. Such
properties can be applied for plan in addition to an enquiry of designing constructions, in
addition to developing innovative improved materials which would likely suit a predetermined
utilize.
The tensile testing investigation facility was engaged operating an Instron stack outline and the
BlueHill information securing programming. Four distinct materials were tried, including 6061-
T6 steel, A-36 hot moved steel, polymethylmethacrylate (PMMA, cast acrylic), and
polycarbonate. The samples were cask fashioned in cross area, with a lessened gage segment.
The lessened gage segment assured that the most elevated burdens materialized inside the gage,
and not close to the grasps of the Instron stack outline, forestalling strain and break of the
example close or in the holds. The moderated gage area of every example was about 12.7 mm
(0.5 inches). The examples were at that point machined to the correct measurements required for
the test, as per ASTM gauges.
Methodology
Every single specimen was assessed with the calipers to select the distance across of the cross
area. A gage length was determined (normally 50.00 mm) and scribed into the example with the
aim that the separation concerning the two trajectories could be assessed when the elastic test
was done. An average decreased gage segment illustration is indicated in Figure 1, on the
accompanying page. The BlueHill statistics obtaining programming was activated, then the
precise material was chosen. The load cell was fixated to guarantee that the equipment just
assessed the tractable load attached to the model.

The example was stacked into the jaws of the Instron stack framework with the objective that it
was correspondingly divided in the middle of the two clasps. The hub and transverse
extensometers were connected to the shrank gage segment of the specimen, guaranteeing that the
pivotal extensometer was set accurately while joining it to the gage and that the transverse
extensometer was over the entire width of the example. This precautionary measure outcomes in
enhanced figures as well as averts damage to the extensometers.
The figures was collected by making use of the product, and noted. At a fixed valuation of strain
(past the yield strain), the equipment disallowed applying figures from the extensometers, then
began saving the strain data applying the condition of the adjusting crosshead. The testing
technique was reworked for whatnot remains of the models.

Figure 1: An abridged gage fragment model made from 6061-T6 steel.

Figure 2: A distinctive Instron load frame.
Outcomes
Design Stress and design Strain
The figures so obtained were plotted on discrete charts as shown by material. Respective
illustration exhibits the stress versus the strain. Using Equation A.2, the weight was resolved. P
implies the pliable power associated with the model.

Material Properties
A conclusive rigidity meant for each material is logged in Table 1. The valuation of a conclusive
rigidity was determined utilizing equation below separately.
Table 1: a definitive elasticity meant for the each of the materials.
The yield potentials and the modulus of elasticity were determined meant for the materials. The
unfolding standard deviations for the two makings were as well determined.
Table 2: The yield quality, modulus of elasticity, as well as standard deviations for 6061-T6 steel
and A-36 steel.
The modulus of durability and the modulus of flexibility were determined as of the area in the
designing stress as opposed to constructing strain curves. Equations C.1 & C.2 are applied to
compute the modulus of elasticity.

The ideal fracture strength delivers the tangible approximation of the pressure/ stress qualified
based on the model performance when conducting tensile tests when failure is about to occur.
The ideal break feature/ fractural strength is the finest stress that the particular sample can
accommodate at yielding. The percentage lengthening and the percent reduction in area make
available data on the model’s flexibility, and the extent it inclines to be long-drawn-out before
failure.
Equation D.2 is applied to figure the percentage decrease in area.
The averages of each one of the 3 qualities for each one of the 4 materials are indicated in Table
4.
Condition D.3 is applied to establish the ideal length of the model immediately before crack.
Condition D.4 is now applied to ascertain the percentage prolongation for the model/ material.

Ideal/
genuine strain and ideal stress
One example of steel was utilized to locate the genuine stress and the genuine strain experienced
amid a tensile test, and to contrast both with the designing stress and the building strain. The
designing stress and strain does not represent the adjustment in cross sectional region, and
records for the pivotal strain in the example. The ideal strain and stress represent the adjustment
in cross sectional territory, and in this manner the ideal stress is bigger than the designing stress.
The genuine strain is likewise more noteworthy than the designing strain because of strains the
transverse way along the gage of the example. Figure 7 demonstrates the ideal strains against the
genuine/ ideal strain, alongside the building stress in addition to the designing strain for a similar
example.

A-36 steel 6061-T6 Polycarbonate PMMA
0
100
200
300
400
500
600
700
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
percent elongation vs true fracture strength
True fracture strength percent elongation, %EL
Figure showing percent elongation vs fracture strength
The genuine stress and strain at the resolve of most extreme load capacity (the point at which
ultimate elasticity ensues). 6061-T6 steel test achieved an approximation of 404.9 MPa, drawing
a distinction with a greatest rigidity of 376.6 MPa. The ideal strain at similar level achieved an
A-36 steel 6061-T6 Polycarbonate PMMA
0
100
200
300
400
500
600
700
0.00%
10.00%
20.00%
30.00%
40.00%
50.00%
60.00%
70.00%
80.00%
90.00%
percent elongation vs true
fracture strength
True fracture strength percent elongation, %EL

assessment of 0.0723 m/m, paralleled to a strain of 0.0750 m/m. The most extreme genuine
stress at break was 561.5 MPa, with a strain of 0.765 m/m. When cracking occurred, the
designing stress was marked at 261.3 MPa, having a strain of 0.182 m/m.
The Ramberg-Osgood Model
The behavior of the ideal stress for the reason that of the genuine plastic strain can be
specifically validated by making use of the Ramberg-Osgood classical. This provision help to
model the stress strain curvatures as a command setting model, throughout yielding. In figure 8,
this has been plotted against the ideal stress and strain got from the test.
1 2 3
0
50
100
150
200
250
300
350
400
450
0.001 0.01 0.05
true stress vs true plastic strain
True plastic strain(m/m) calculated stress Mpa
Series3
The assessment outcomes were reliable meant for respective materials chosen for testing, as
apparent in Figures 3-6, in which each of the 3 stress strain curvatures were evidently unevenly
casing. A fascinating discernment can be generated by employing the PMMA diagram, in which

test one abruptly loses stress during which it elongates further. This particular sample could have
yielded halfway across its area may before the occurrence of complete failure of the specimen
under test. Similarly, presence of void could have made the specimen to suddenly reach its
ultimate failure. A greater proportion of the tested samples showed expected trend of behavior of
the respective material.
From a decisive rigidity evidence in the first table, noticeably the A-36 steel was established to
be the strongest of all, 6061-T6 comes next, PMMA, and polycarbonate, correspondingly. The
majority of the standard deviations were noted to be small, not surpassing 2.606 MPa,
recommending that the figures were predictable in addition to the fact that the method of testing
was determined to be reasonable and repeatable. The ideal strength at fracture, indicated in Table
4, provides a grander viewpoint of the genuine stress at crack. The A-36 steel exhibited the most
astounding ideal strength at fracture, lagged by the 6061-T6 steel. Polycarbonate comes third
followed by PMMA.
Notwithstanding of the information that the A-36 steel was found to have a much greater
modulus of elasticity (209300 MPa, compared with 69460MPa for the 6061-T6 aluminum), as
well as an upper exciting elasticity, the yield value is approximately equivalent to the 6061-T6.
The greater stress is for the reason that of effort congealing as the material is plastically
distorted. The performance of separations diminishes individual deviations, in addition to
solidifying the material. The 6061-T6 is a toughened and seasoned combination which is as of
present precipitation hardened. In comparison, it fails to congeal/ get hard as much as the A-36
steel, producing an inferior exciting rigidity. The typical nonconformities for the yield values and
modulus of flexibility are equally diminutively differentiated with the typical qualities, validating
the reliability of the data so obtained.
Part 2
The modulus of flexibility and the modulus of durability are essential qualities in deciding the
strength which a material can assimilate prior to yielding and preceding cracking. The modulus
of versatility is the area in the building stress strain inclination pending the yield point, in
addition relates to the strength per unit volume which a given material model is capable of
retaining prior to yielding. The 6061-T6 steel accomplished the furthermost astounding modulus

of strength, lagged by A-36 steel, polycarbonate, and PMMA. The 6061-T6 had the most
noteworthy flexibility because of the high return quality, and the low modulus of versatility
(contrasted with the A-36 steel), as appeared in Table 3. The low modulus of versatility
guaranteed that the aluminum was stressed more before yielding, enabling it to ingest more
vitality.
The genuine pressure and genuine strain consider the altering region of the cross segment as it is
being stretched, and the strains that go with the evolving zone. Representing these two impacts
results in a last obvious pressure that is a lot higher than the designing crack pressure and a more
prominent measure of strain. As appeared in Figure 7, the genuine pressure achieves a greatest at
the purpose of crack. Now, the territory is a lot littler, so the example can't endure a substantial
load, which grounds the designing stress strain bend to drop off in the wake of necking. There is
no extreme tractable worry in the genuine pressure strain bend similarly as with the designing
pressure strain bend, and the genuine pressure is continually expanding up pending failure.
The Ramberg-Osgood show turned out to be superb for use in deciding ideal stress at greater
estimations of ideal plastic strain, yet incorporated most mistakes/ errors at diminutive
estimations in ideal plastic strain, particularly close to the yield strain. Particularly, the plastic
strain was fundamentally zero at this yield strain. Table 5 demonstrates a scenario whereby close
to a definitive malleable strain, the mistake is little. However close to the yield strain, the error is
notably higher marked at 19.84%. The 6160-T6 steel tests failed to exhibit the command
solidifying conduct which has been identified to be ordinary of the Ramberg-Osgood
demonstrate. The building pressure strain bend was level subsequent to yielding, besides not
curved as displayed in Figure 8. Given that the model was built-in to the information concerning
multiple instances the yield strain, in addition to a definitive ductile strain, it doesn't match the
sample adequately for little estimations of ideal plastic strain. Such error could be eased by
setting up numerous models to the curve, or by picking an alternate model which better fits the
state of the designing stress strain curvatures.
The rigidity of materials also known as tensile strength of a material is a standout amongst the
most imperative physical properties of the materials. The rigidity of the materials contributes
enormously to its quality and also its life. The quality of the materials relies upon of a wide range
of elements that influence it. Specifically, the potential in service conditions that may have
caused material failure and the structural properties of the given metals, polymer and composite

materials investigated include: temperature, molecular structure or composition. These are
discussed as follows;
Molecular structure/ Sub-atomic Structure
The sub-atomic structure of material greatly affects the elasticity of the materials. The atomic
structure is in charge of the intermolecular powers that are shaped in the material. These
intermolecular powers are in charge of restricting the distinctive atoms of the materials together
henceforth at whatever point there is an adjustment in the sub-atomic structure, the rigidity of the
material varies incredibly. This as a results causes a variation of the tensile strength of materials
during testing hence resulting in material failures.
Temperature
The temperature at which the material is being utilized, additionally greatly affects the
temperature. High temperatures make the materials delicate. At the point when the temperature is
expanded, up to some point, the tensile strength increments however past that temperature the
elasticity and flexibility of the materials particularly metals begins diminishing. The pliability
and flexibility of the metals increment with the expansion in temperature. The temperature
additionally causes changes in the sub-atomic structure. This additionally an explanation behind
the effect of temperature on the elasticity the materials as in the laboratory results.
Composition
The composition of the materials is likewise incredibly in charge of the rigidity of the materials.
For instance, unadulterated iron is weaker and has lesser rigidity while the compounds produced
using iron and different materials are particularly more grounded. The purpose for this is diverse
arrangements have distinctive atomic structures and distinctive dimensions of intermolecular ties
consequently the elasticity of these materials is additionally influenced. So as to assess the
elasticity of material, pliable testing is performed on a material with the utilization of a malleable
test machine. The instrument applies a ductile power on the test example to decide the most
extreme measure of power it can manage before disappointment. There is a heap cell furnished
with the instrument that records the power connected to the example for precise estimation and
testing results. Notwithstanding the rigidity, the machine can is likewise utilized for deciding the

young's modulus, yield quality and rate stretching in the example. The instrument is best for
evaluation of various materials and improves important actualizes for quality and quality.
Bibliography
ASTM D638 | Tensile Testing | DDL, Inc. [online], 2818. [online]. DDL Inc. Available from:
https://www.testedandproven.com/materials-testing/tensile-testing/ [Accessed 7 Dec 2018].
Metallurgical Engineering Services, 2018. Tensile Test Lab [online]. Metallurgical Engineering
Services. Available from: http://metengr.com/testing-services/mechanical-testing/tensile/
[Accessed 7 Dec 2018].