# TORSION TEST Experiment

## TORSION TEST Experiment

TORSION TEST Experiment

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Experiment

TORSION TEST

Abstract

The purpose of the experiment was to examine the torsional stress-strain relationship of a cold rolled 1018 steel. The experiment was conducted by first measuring the length and diameter of the rolled 1018 steel and then fixing the bar within the grip of the torsional instron machine. The data were collected from the computer and used in analysis. The result indicated that shear was directly proportional to strain until the elastic limit was reached.

Introduction

The objective of this experiment is to examine the torsional stress-strain relationship of cold rolled 1018 steel and to determine it’s shear modulus (G) which is the slope of the linear portion and Poisson’s ratio (v) which is the ratio of transverse and axial strain. Also, to qualitatively study the relationship between torsional load and angle of twist in a full range of strains until failure by observing the pattern of angle of twist as the torsional load increases. And to determine if the material’s fracture is of ductility or brittleness. In background and theory, the torsion test is the twisting of a material under stress of angular displacement until it fails to evaluate its torsional strength and stress-strain relationship. The experiment determines properties such as shear modulus, shear stress and strain and ductility or brittleness which are important properties of in manufacturing specified products and can be used to observe the product’s quality and design. Ductile materials fail in shear to torsion breaking along perpendicular to longitudinal axis while brittle materials which are stronger in tension break perpendicular at the angle of maximum tension. With shear stress and strain, shear modulus can be determined and with a reference value of modulus of elasticity, Poisson’s ratio can be determined.

Theory

This experiment focuses on the properties that a material will have when being twisted to a certain load. Understanding torsion and its effects on different materials is very important and an understanding of the formulas is also important. The torsion formula is derived as which states that the Moment (T) multiplied by the radius ( r) is divided by the polar inertia (J). The formula forPolar inertia J is derived as where “d” is the diameter of the cross section and this formula is very important in the concept of Torsion. This lab also focuses on the angle twist which occurs when the sample is being spun on the Torsion Test Machine. This formula is and the total angle twist is where “L” is the length of the bar, “G” is the Modulus of Elasticity. This lab will also use Hooke’s Law because the torsion test machine will cause the materials to undergo shear stress and so the formula used for Shear Stress is, (where “” is the strain in radians calculated by the formula ). Strain and Shear are key factors in this lab and so the formula used to calculate the normal strain in the positive direction is . Shear modulus is calculated by combining equations 2.4 and 2.8 from the Lab manual which results in where “v” is Poisson’s Ratio. These are the key formulas regarding the Torsion Test experiment.

Procedure

The first step to conduct this experiment is to determine the initial length and diameter of the cold rolled 1018 steel bar. The diameter is measured using a caliper and a ruler to measure the length. Also, to better see the twists after the torsion process you may use a marker and draw a line on the bar. Next, fix the bar within the grip of the torsional instron machine that exhibits translational motion using a t-shape tool. Move the grip so that the bar comes in contact with the stationary grip and make sure to use the arrows on the panel to align the grips and fix the bar the same way using the tool. Close the safety door and zero the torque and rotation and start the torsion process and data acquisition. Once the bar is fractured and the machine stops, take the data that the computer displays which are rotation (degree) and the corresponding torque (lbf-in) which are needed for the calculations.

Analysis

From the Graph: Shear Modulus: G = 7E+10

Sample Calculation:

Shear Stress:

: Polar moment of Inertia:

Shear Strain:

Poisson Ratio:

Result: 1018 Cold Rolled Steel

 Experimental Theoretical % Error Modulus Elasticity E 200 GPa – – Shear Modulus G 78.0 GPa 70.0 GPa 10.3 Poisson Ratio v 0.29 0.43 48.3

Discussion/Conclusion

Torsional stresses are calculated using two formulas. The first formula is shear stress= moment (T) *radius (r)/polar inertia (J). Secondly, shear strain = elastic modulus * strain. The formula shows that shear stress is directly proportional to the moment and the radius of the rolled 1018 steel. On the other hand, an increase in the polar inertia results in decreased shear stress. The polar moment of inertia refers to the cross-section about the point of intersection. The equations hold under the following assumptions. First, the shaft material must be homogenous throughout the length with a uniform circular cross-section. The uniformity ensures that shear stress is spread throughout. Besides, the equation assumes that torsion is constant throughout the length of the steel material. Finally, the radial line must remain radial throughout the torsion and the stress applied does not exceed the elastic limit. The elasticity of the material gets destroyed when the tension exceeds the elastic limit; in such a case, the material becomes permanently deformed. The assumptions in the equation were correct as evident in the experiment.

1. What does your text tell you about the failure modes of ductile and brittle materials when they are subjected to pure shear? Did the material fail in tension, compression or shear? What observations bring you to that conclusion?

The graphs show that torque increased with the rotation until a given point when the curve becomes constant. Similarly, the shear strain increased with the shear stress until the elastic limit was achieved. The curve becomes constant beyond the elastic limit. The materials fail to conform to the modes of ductile when the tension applied exceeds the elastic limit. The material failed in tension and this is evident when shear stress remains relatively constant despite the change in the strain. The ductile material fails in shear and this means that they are likely to break when subjected to torsion. On the other hand, brittle materials fail in tension and are likely to break when subjected to torsion.

1. Describe the behavior of the material as it responds to increasing load. Pay special attention to the region above the yield where linear elastic theory no longer applies.

The material’s length increased as more loads were added. The shear increased with strain until the elastic limit was reached. The graph of the shear against strain was linear and the gradient and was used a measure of the elasticity of the material. As more load is added, the elastic limit exceeds and so that material does not proportionally respond when the load is added.

1. How do your results compare to referenced values?

The reference range may be the theoretical values expected in an experiment. The values may vary depending on precision and accuracy in the measurement of the experimental variables. The accuracy of the study findings is determined by the marginal error. In this case, the level of error recorded was significantly high, especially in the Poisson Ration experiment. The percentage error was 43.3% which is high and beyond the acceptable limits. On the other hand, the level of precision in the shear modulus G was high and this is evident in the low percentage error. The percentage error for this case was 10.3%. The theoretical values are based on an ideal experiment and so may not be the same as the results obtained from a real practical as evident in this case due to human error and the variations in the steel composition and structure among others.

Works Cited

http://matweb.com/search/datasheet.aspx?MatGUID=3a9cc570fbb24d119f08db22a53e2421

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