# Stress Versus Strain Essay Examples & Outline

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## Stress Versus Strain

**Aims**

The aim of this practical was to perform tensile tests on selected samples of metals and polymers with the view to gain an understanding of stress-strain behavior, ductile and brittle behavior, ultimate stress yield, Young’s modulus, Hooke’s Law and structure-property relationships. The data obtained in this experiment was compared to that published in literature.

**Introduction**

Stress is a term used to express the loading force applied to an object, which tends to deform the object. When a system is subjected to a stress, it responds by strain. In engineering, strain is the amount of deformation that occurs in a material in the direction of the force applied divided by the original length of the material. The relationship between stress and strain in a material is defined by Young’s modulus. Young’s modulus or elastic modulus measures the stiffness of a material; its ability to resist elastic deformation. When a material is loaded beyond its elastic limit, the internal stress increases and reach a point where the material starts to yield. This stress is known as the yield stress (Soboyejo, 2002).

The maximum load that a material can withstand prior to breaking is defined as the maximum tensile stress. The breaking stress is the maximum force a material can withstand prior to breaking. The amount of strain that is applied to a material before it breaks is known as the breaking strain. Hook’s law defines the relationship between the force applied and the deformation on an elastic body. It states that when an elastic material is subjected to a force, the length of the material is deformed by a distance (X) proportional to the deforming force applied (F). That is, F = kX, where k is a constant characteristic to the stiffness of a material.

A ductile material is a material that can be permanently deformed under an applied force without breaking when the applied force is removed. A brittle material is the opposite of a ductile material; when subjected to a force, a brittle material fractures without any significant deformation after the elastic limit is reached (Soboyejo, 2002).

**Experimental Procedure**

The test coupon was mounted first. The lever arm was then placed in a starting position by turning the crank in a counter-clockwise direction and pulling the lever arm further from the Force Sensor to create a gap between the liver arm and the Force Sensor Attachment. The samples were then mounted on the test coupon. Before starting to collect the data for samples, the Force Sensor was zeroed.

Analysis of Results

**METALS**

Sample 1: Annealed Steel

The data from figures 1a. – 1c are tabulated as shown in the table below

Table 1: Data for annealed steel

Mechanical properties This Practical Group 2 (2015 T2) Data from last year Literature data

Young’s modulus E 135 GPa 275 GPa 236 Gpa 200 Gpa

Yield stress 270 MPa 250 Mpa 320 Mpa 345 Mpa

Max stress 310 MPa 280 Mpa 320 Mpa 300 Mpa

Max strain, breaking strain 0.26 (26%) 0.32 (32%) 0.28 (28%) 42 - 45%

**Sample 2: Brass**

Table 2: Data for brass

Mechanical properties This Practical Last term Data from last year T2 Literature data

Young’s modulus E 187 GPa 102 GPa 115 Gpa 117 Gpa

Yield stress 430 MPa 300 Mpa 290 Mpa 310 Mpa

Max stress 640 MPa 380 Mpa 400 Mpa 430 Mpa

Max strain, breaking strain 0.22 (22%) 25%

**Sample 3: Aluminium**

Table 3: Data for aluminium

Mechanical properties This Practical Data from Group 2 (2015 T2) Literature data

Young’s modulus E 60.3 GPa 44.6 GPa 69 Gpa

Yield stress 130 MPa 155 Mpa 276 Mpa

Max stress 170 MPa 190 Mpa 145 Mpa

Max strain, breaking strain 2.6% 2% 6%

**Sample 4: Chromium Steel**

Table 4: Data for chromium steel

Mechanical properties Data from 2015 T1 Data from 2014, T2 Literature data

Young’s modulus E 157 GPa 206 GPa 205 Gpa

Yield stress 300 MPa 320 Mpa 435 Mpa

Max stress 690 MPa 670 Mpa 670 Mpa

Max strain, breaking strain 2% 3% 25.5%

**PLASTICS**

Sample 1: Polyethylene (PE)

Table 5: Data for Polyethylene

Mechanical properties Data from this practical Data from Group 2, 2015 T2 Literature data

Young’s modulus E 787 Mpa 609 Mpa 800 Mpa

Yield stress 10 MPa 10 Mpa 15 Mpa

Max stress 34 MPa 31 Mpa 34 Mpa

Max strain, breaking strain 110% 120% 125%

Sample 2: Acrylonitrile butadiene polystyrene (ABS)

**Table 6: Data for ABS**

Mechanical properties Data from this practical Data from 2014 T2 Literature data

Young’s modulus E 1370 Mpa 943 Mpa 2300 Mpa

Yield stress 10 MPa 18 Mpa 17 Mpa

Max stress 31 MPa 68 Mpa 47 Mpa

Max strain, breaking strain 28% 20%

**Sample 3: Nylon 6, 6**

Table 7: Data for Nylon 6, 6

Mechanical properties Data from this practical Data from 2014 T2 Literature data

Young’s modulus E 1190 Mpa 1390 Mpa 1800 Mpa

Yield stress 62 MPa 34 Mpa 40 Mpa

Max stress 74 MPa 60 Mpa 70 Mpa

Max strain, breaking strain 18% 22% 50%

**Sample 4: Polypropylene (PP)**

Dimensions: crosssection =2.482 mm^2

Gauge length= 19 mm

Table 8: Data for polypropylene

Mechanical properties Data from 2015 T2 Literature data

Young’s modulus E 655 Mpa 1900 Mpa

Yield stress 27 Mpa 33 Mpa

Max stress 32 Mpa 34 Mpa

Max strain, breaking strain 9%

**Sample 5: High Impact Polystyrene (HIPS)**

Young’s modulus E= 968 MPa

Yield stress=30 MPa

Max stress (Tensile strength) = 37 MPa

Table 9: Data for HIPS

Mechanical properties Data from 2015 T2 Literature data

Young’s modulus E 968 Mpa 2000 Mpa

Yield stress 30 Mpa 32 Mpa

Max stress 37 Mpa 23 Mpa

Max strain, breaking strain 40%

From table 1 – 9, it can be seen that there are slight differences between the data obtained in this practical, the previous results and the values in the literature. This may be attributed to experimental errors in mounting the coupon, such as slipping, and accuracy of the measuring instrument. Aluminium metal displays higher ductility compared to the other materials because of its more linear stress – strain curve and this means that it can be stretched – with good malleability.

Read about recycling and management of steel

Brass and chromium steel and annealed steel are less ductile. There was a significant difference between metals and all the five polymers; the polymers broke at very low strains, an indication that they are very brittle. Nylon 6,6 showed the highest strain to break while the rest show lower strain energy to break. Metals tend to be ductile because their atoms have the ability to roll over each other into other positions without altering the metallic bonds, while the plastics tend to be more brittle and break without warning under a straining force.

Questions

[C]

a)From the curve in figure 11 above:

b)Yield Strength = 31 kN/(7.854) = 394.7Mpa

c)Ultimate tensile strength = 52.49 kN/(7.854) = 668.3Mpa

d)Young’s Modulus = 835.6 N/(7.854) = 10.64Mpa

e)Stress refers to a force acting per unit area, force is the factor that causes stress within a body.

f)Extension is the change of length of a material as a result of a force acting on it, strain is extension per unit length.

[D]

**Reference**

Soboyejo, W., 2002. Mechanical Properties of Engineered Materials. 1st ed. New York: CRC Press.