# ELASTIC DEFORMATION AND POISSON’S RATIO

Topics: Tensile strength, Solid mechanics, Deformation Pages: 28 (4723 words) Published: January 13, 2014
﻿

ELASTIC DEFORMATION
AND
POISSON’S RATIO

E 45 – Materials, Friday 8:00 am
September 21, 2012

Due: October 19, 2012
Abstract
A tensile test was performed on a 4140 steel sample and the axial and transverse strains were measured. Data points were collected at incremental loads and graphed to determine the elastic modulus (30.4 x 106). Poisson’s ratio was also calculated from the dataset and determined to be 0.29. These experimental values agree closely (within 2%) to the textbook values of the steel sample. A sample of 7075 Aluminum was used in a cantilever beam test. Intermediate and end loads were place on the sample and the strain was measured at various distances from the loads. Using the dataset from the individual loads, the superposition strain was calculated and agreed within 7% of the experimental strain with both loads. From the measured deflection of the cantilever beam and the dataset, Young’s Modulus for the aluminum sample was determined to be 9.1x106 psi which agrees within 8% of the textbook value. Introduction

To be able to decide on what kind of material to choose for product design, there are some critical characteristics you must consider in choosing a material prior to manufacturing. Characteristics such as material strength and flexibility are two tests that have been done on common materials for architects and engineers to reference during the design process. The purpose of this lab is to produce an elastic modulus of a material, and a predicted yield strength. Stress and strain data will be produced through tensile testing and cantilever beam testing. For a tensile test, two strain gages will be attached to the material to measure the longitudinal strain and transverse stain. The percent elongation of the specimen is directly proportional to the change in longitudinal strain. With the dimensions of the original specimen, the change in these strains can tell us the change in a cross sectional area. The stress the material is under can be calculated by the load divided by the cross sectional area. Another quantity that is useful is called the Poisson’s Ratio. This quantity compares the change in longitudinal strain and the transverse strain with the applied load. This is a common fraction used to determine roughly the change in volume distribution. For finding the deflection of a material requires a different testing process. A cantilever beam test is similar to a tensile test in that is also uses longitudinal strain gages to measure strain, however the load is applied in a perpendicular fashion to the materials major axis. Through collecting data during different load applications, a few values need to be determines such as the moment value and the elastic modulus of the beam. With the elastic modulus found in earlier, more complex situations involving more than a single applied load. This is when a very useful mathematical principal called superposition can be used to estimate the maximum deflection Through graphically interpolation, this data is showing a linear trend. With little deviation from this linear trend line, it is safe to say that we are still within the elastic deformation of the specimen. The numerical slope of this trended data is the axial strain over stress, which tells us the elastic modulus of the material. And lastly, predicted yield strength of the specimen can be calculated. This yield strength is the maximum load the specimen can undertake before inelastic deformation begins to occur. All of the data that was calculated in this lab, especially the elastic modulus and yield strength, is useful to many disciplines and industries. These critical characteristics can be determined in many materials used by engineers helps in the decision process of design.

Introduction
In this laboratory experiment the tensile test and the cantilever beam test were performed in order to measure the...