STRESS STRAIN CHARACTERISTICS OF MILD STEEL BAR BY UTM

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Aim:
To study the stress strain characteristics of mild steel by Universal Testing Machine
Equipment:
Universal testing machine meter rule, dividers and scale, Test specimen
Theory:
In tension test of ductile metals, the properties usually determined are yield strength, ultimate tensile strength, modulus of elasticity, percentage of elongation etc. For brittle materials only compressive strength is determined.
The tension test is normally carried out in a Universal Testing Machine (UTM). The specimen can be in the form of a rod or a plate. The dimensions of standard specimen can be known from accepted specifications.
The following properties can be determined from the stress strain curve of the material:

1. Proportional limit: is that point on the stress strain curve at which the curve deviates from linearity, i.e. from the relation
   Stress = Young's modulus x strain
   $\sigma = E \varepsilon$
2. Elastic limit: is the point on the stress strain curve above which plastic deformation (that is permanent deformation) starts.
3. Yield strength: is the stress required to produce a small amount of permanent or plastic deformation.
   In some materials such as mild steel, where there is occurrence of sharp yield point on the stress -strain curve, the stress value at the lower yield point is taken as the yield strength. In some materials like tor steel which do not have a sharp yield point, the offset yield strength or proof stress is taken as the measure of the yield strength. This is the stress at which a line drawn parallel to the initial portion of the curve, offset by a specified strain, intersects.
   The offset value is usually a strain of 0.002 (0.2% strain). The value of the yield strength is of great importance in design calculations.
4. Tensile strength or ultimate tensile strength (UTS) is the maximum load divided by the original cross sectional area of the specimen. U.T.S. corresponds to the peak or the highest stress value in the stress -strain curve.
5. Ductility:It is usually measured as percentage elongation in length or percentage reduction in area. These measures of ductility are obtained after fracture, by keeping together the two broken parts of the specimen, and measuring the gauge length at fracture, and area of cross section at fracture.
   Percentage elongation in length = $\frac{(L_f-L_0)}{L_0}X100$
   Percentage reduction in area = $\frac{(A_f-A_0)}{A_0}X100$
   Where,
   $L_0$ and $A_0$ are initial gauge length and initial area of cross section respectively.
   $L_f$ and $A_f$ are measured gauge length at fracture and area of cross section at fracture respectively.

Procedure:

• Mark the gauge length on the test piece (according to IS1608 ${{l}_{0}}=5.65\sqrt{{{A}_{0}}}$ )
• Measure the diameter of the test piece at several sections by Vernier calipers and note down the mean diameter.
• Fix the specimen firmly to the jaws of the testing machine.
• Start the machine and gradually increase the tensile load. Collect the readings from the software assisted computer in control panel until the fracture of specimen occurs. Note down the reading where the load reaches to maximum.
• Remove the fractured specimen from the machine and measure its diameter and the final gauge length.
• Observe the stress strain curve for the tested specimen in software assisted computer in control panel and manually plot the graph between stress vs strain and mark the corresponding points listed below. a = proportionality limit
  b = elastic limit
  c = Yield point
  d = Ultimate stress
  e = Breaking stress
  A = Yield stress
• Calculate the required objective.

Observations and Calculations:
Calculation of the diameter Least count of Vernier Calipers =

S.No.	Main Scale Divisions	Vernier scale divisions	M.S.D+(V.S.D*L.C)
1
2
3
Average Value

Average diameter of the specimen (d) = _________mm
Area of the specimen ($\frac{\pi}{4}d^2$) = __________$mm^2$
Gauge length ($L_0$) = ______mm

S.No.	Load(kN)	Elongation $\Delta L$(mm)	Stress $\frac{P}{A}$ ($\frac{N}{mm^2}$)	Strain $\frac{\Delta L}{L_0}$
1
2
3
4
5
6
7

Discussion:Compare the experimental results with the theoretical values for test specimen, comment on any reason for discrepancy, comment on any instrumental/experimental errors. and area of application.
Young's modulus values of some of the metals are given below

Material	E (GPA)
Chromium	253
Nickel	211
Cobalt	211
Iron and steel	211
Manganese	162
Titanium	118
Copper	113
Silver	77
Aluminum	74
Magnesium	46
Tin	42
Lead	18