Group
Abstract
Material selection is an important stage in engineering design. Engineers use various materials with different mechanical properties in building of structures. These mechanical properties include; tensile strength, yield strength, proof stress, Young's modulus, shears modulus of rigidity and ductility amongst others. Material selection increases the performance as well as durability of the engineering component. The expected life, cost, nature of loading and working environment are some of the factors that assist engineers to select materials for particular application. Therefore, engineers and designers must be able to determine the properties of these materials before they use them. Engineers use tensile test to determine mechanical properties of different materials such as ductility, Young's modulus, percentage elongation amongst others. In this report, stress -strain behavior of mild steel and high yield steel bars have been determined experimentally to determine the various mechanical properties. The results obtained in this work are very consistent with our expectations. The experimental values for yield stress, Young's modulus, ultimate tensile strength and fracture strength of mild steel are 371 N/mm2, 164.9 KN/mm2, 407 N/mm2 and 407 N/mm2. The corresponding values for high yield steel are 533 N/mm2, 206.75 KN/mm2, 629 N/mm2 and 550 N/mm2. The experiment was very successful despite the various errors encountered.
Objectives
The following were the objectives of this experiment:
Introduction and Theory
Engineers carry out tensile test by applying opposing forces to a specimen. When this load is applied, the material gradually fails when it exceeds the maximum load the material can withstand. Engineers use tensile test to determine mechanical properties of common building materials mainly steels and their alloys. It is worth to note that steel is an alloy made from iron and carbon. Thus, steel posses the required strength requirements needed for most engineering application. There are many categories of steel depending on the ratio or percentage of carbon and iron composition. Mild steel and high yield steel bars are some of the categories of steel that engineers use in their structural work because it enhances durability, strength and safety of the building. The main objective of this experiment is to study the stress-strain behavior of mild steel and high yield stress bars. To achieve this, the experiment has focused on mechanical properties such as yield stress, Young's modulus of elasticity, ultimate tensile strength, stress at failure and the percentage elongation.
Stress refers to the magnitude of the load transmitted in the material per unit area of the cross-section. Thus, stress is equivalent to the magnitude of internal forces produced in the material. The deformation of a material under tensile loading is well is demonstrated in Figure 1.
.
Figure 1: Tensile loading
Where:
Stress is expressed as:
Stress=FA Nm2..Equation. 1
Strain is a dimensionless parameter given by the ratio of the change in length to the original length of a material subjected to tensile loading.
Strain ε=δlo
Because of material deformation, the final length is greater than the initial length. The percentage elongation of the specimen is given by:
%∆L=lf-lolo*100
Figure 2: Stress- strain graph
O-A: This denotes the elastic region characterized by a straight line from the origin. In the elastic region, tensile stress is proportional to tensile strain. The Young’s modulus is the constant of proportionality as shown in Equation 2. Deformation of the material in the elastic region is recoverable upon withdrawal of the load. Thus, the Young’s modulus is equal to the gradient of this linear section.
Young’s modulus E=stressstrain..Equation 2
A-B: The material begins to yield in this region. Ductile materials are characterizsed by a higher and lower yield point. The yield point represents the end of elastic deformation and the beginning of plastic deformation.
B-C: This is the plastic region where deformations are not recoverable. Continued loading at this region results to work hardening. Inspection of the stress-strain curve shows that in this region the stress increases at a higher rate than the strain.
Point C: This is the ultimate tensile strength or the maximum stress the material can withstand before the onset of necking.
C-D: The necking of the specimen commences after point C. Further loading of the material beyond C is accompanied by a reduction in the load and finally fracturing occurs at point D. The fracture stress of the material corresponds to point D
Methodology
Apparatus
- Extensometer and Denison extension gauge (measures cross head movement).
- 500KN Denison tensile testing machine
Experimental set-up
Figure 3: 500KN Denison tensile testing machine
Procedure
The diameter and the gauge length of the two specimens were taken after which the first specimen (mild steel) was placed on the jaws of the Denison tensile testing machine. The 500 mm extensometer was zeroed and attached to the bar. The test was then run by loading the specimen with increasing loads. The readings were recorded until the specimen failed. For each load, the corresponding extensometer and extension gauge reading were recorded. The extensometer was disengaged when the material yielded to prevent the apparatus from being damaged. The above procedure was repeated for the second specimen.
Results and Data analysis
The stress-strain curve for the two materials is as shown in Fig. 4.
Figure 4: Stress versus strain curve for mild steel and high yield steel bars
Young’s modulus or Elastic Modulus
Young’s modulus=stressstrain=gradient of linear part
For 20 mm plain round bar (high yield steel bar)
Young’s modulus=221.220.00107=206.75 KN/mm2
For 16 mm plain reinforced bar (Mild steel)
Young’s modulus=214.370.0013=164.9 KN/mm2
Percentage elongation
Percentage elongation is computed from the following expression:
%∆L=lf-lolo*100
For 20 mm plain round bar (Mild steel)
%∆L=132.9-100100*100= 32.9 %
For 16 mm plain reinforced bar (high yield steel bar)
%∆L=99.25-8080*100= 24 %
Maximum/Ultimate tensile strength
This is the maximum stress the material can withstand before it fails. This was obtained directly from the stress-strain curve as 629 N/mm2 and 407 N/mm2 for high yield stress bar and mild steel bar respectively.
Failure stress
The failure stress for the two materials were obtained directly from the stress-strain curve as 550 N/mm2 and 407 N/mm2 respectively for 16 high yield steel bar and 20 mm mild steel bar respectively.
Yield stress and proof stress
The yield stress for the two materials were obtained as 533 N/mm2 and 371 N/mm2 for 16 mm high yield steel bar and mild steel bar respectively. Finally, 0.2 % proof stress was found to be 560 N/mm2 and 410 N/mm2 for 16 mm high yield steel bar and mild steel bar respectively. Proof stress is an important property used instead of yield stress for materials that have no well-defined stress-strain curve for instance tough materials.
Discussion
The stress-strain curve for mild steel and high yield steel has been plotted in this work. Engineers obtain a number of mechanical properties of materials from this curve as shown on the previous section. This work has shown that, different materials are unique and have different mechanical properties and hence, stress-strain curve is different. For instance, ductile materials and brittle materials have different stress-strain curves. The curve is obtained from data obtained from tensile test experiment where the materials are loaded gradually in tension until it fails.
The results obtained in this work were very consistent with previous studies that have shown that steels in general have well defined stress-strain curve with a definite yield point. This was the case with the two materials (mild steel and high yield steel) investigated in this work. The stress-strain curve for the two materials are similar, the first part of the curve is linear with a gradient that equals the Young's modulus of elasticity of the material. The deformations in this region are recoverable upon removal of the load. After elastic region, the material starts yielding and thus the yield point. The yield point is characterized with a reduction in stress as some of the external energy is absorbed in effecting the deformation of the material. Yield point characterizes the onset of plastic region where deformations are not recoverable. As loading decrease, the maximum or ultimate tensile point that is the highest point on the stress-strain curve is reached. This is the maximum stress that the material can with stand. After ultimate strength point, the material begins to yield and finally fails.
The results obtained in this work are very consistent with our expectations. The yield stress, Young's modulus, ultimate tensile strength and fracture strength of mild steel were obtained as 371 N/mm2, 164.9 KN/mm2, 407 N/mm2 and 407 N/mm2. The corresponding values for high yield steel are 533 N/mm2, 206.75 KN/mm2, 629 N/mm2 and 550 N/mm2. Comparison of these values confirms the fact that high yield steel is a stronger material than mild steel as stipulated in Bs 4449. This is because high yield steel has more carbon content than mild steel making it stronger than mild steel at the expense on the ductility. That is mild steel has high percentage elongation than high yield and thus more ductile. This work has showed that stress strain curve gives mechanical properties to an engineer that allows them to select the right material depending on the loading condition. This enhances the strength, durability and safety of engineering structures.
The experimental values were consistent to theoretical values stipulated in standard manuals despite the various errors encountered in the experiment. We can attribute this small deviation to a number of experimental errors. First, lack of experience in operation the machine must have been the major contributor to the deviation. This is because there is a high probability that the vertical and horizontal cradles were not well set to coincide with the gauge length before the specimen was mounted. Secondly, the ambient temperature was not considered in the experiment. Finally, we can attribute this deviation to manufacturing errors and material deformation during preparation of the specimen.
Conclusion
The main objective of this experiment was to determine experimentally stress-strain properties of mild steel and high yield steel. The mechanical properties such as Young's modulus of elasticity, yield strength, ultimate tensile strength and stress at failure of the two samples were determined from stress strain curve. Despite the various experimental errors explained in the previous section, the results obtained were acceptable and compared well with theoretical values stated in values. The results have shown that high yield steel is stronger than mild steel but with less ductility or percentage elongation as compared to mild steel. This experiment demonstrated the versatility of tensile testing of materials in determining a number of mechanical properties of various engineering materials.
Reference List
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