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Youngs modulus

Evaluation of Youngs modulus by three-point flexure test

Nicole Schai Assisted by Claudia Mller

Fig. 1 Substech, [1]

Report

ETH Zrich

29th of October 2011

TABLE OF CONTENT

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TABLE OF CONTENTS

1 ABSTRACT ........................................................................................................................................................... 3 2 INTRODUCTION ................................................................................................................................................... 4

2.1 YOUNGS MODULUS .................................................................................................................................................... 4 2.2 HYPOTHESIS .............................................................................................................................................................. 5

3 MATERIALS AND METHODS ................................................................................................................................. 6 3.1 PREPARATION OF COMPOSITE MATERIALS ........................................................................................................................ 6 3.2 PREPARATION OF THE SAMPLES ..................................................................................................................................... 6 3.3 THREE-POINT FLEXURE TEST .......................................................................................................................................... 6

4 RESULTS .............................................................................................................................................................. 8 4.1 PREPARATION ............................................................................................................................................................ 8 4.2 BENDING LINES .......................................................................................................................................................... 9 4.3 YOUNGS MODULUS AND BENDING STIFFNESS ................................................................................................................. 12

5 DISCUSSION ....................................................................................................................................................... 13 5.1 BENDING LINES ........................................................................................................................................................ 13 5.2 ELASTIC MODULI AND BENDING STIFFNESS ..................................................................................................................... 13

6 REFERENCES ....................................................................................................................................................... 15 6.1 LITERATURE ............................................................................................................................................................. 15 6.2 WEBSITES ............................................................................................................................................................... 15

1. ABSTRACT

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1 ABSTRACT

The Youngs modulus is a material constant that describes the elastic properties. In the following experiment, a three-point flexure test is used to measure the elastic modulus and the bending stiffness of steel, copper, aluminium and PVC. The bending stiffness of the homogeneous materials is compared to the bending stiffness determined for three different composite materials. The results show the importance of the exact measuring of the unloaded bending lines in order to get correct values for bending lines, Youngs modulus and bending stiffness. Additionally, the results show some inaccuracies due to shifts of the samples during measuring and inhomogeneous application of glue in compound materials.

2. INTRODUCTION

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2 INTRODUCTION

2.1 Youngs modulus

The Youngs modulus is an often-used term to describe materials. According to Hookes law it is defined as the ratio between tension and elongation and is therefore the slope of the stress-strain curve during the elastic deformation of a material. As this curve is a straight line during elastic deformation, the Youngs modulus is constant for different tensions applied to the material. On the other hand, Physicians derive the Youngs modulus form the bonding-potential. During this experiment we will see that both explanations are useful in different applications. The size of the Youngs modulus depends on various factors:

Type of bonding: Stronger bonds lead to a higher Youngs modulus. Primary bonds are much stronger than secondary bonds such as Van der Waals or hydrogen bonds. Within the subgroup of primary bonds, covalent bonds are stronger than ionic bonds. Metallic bonds are the weakest as they are the least direct.

Structure: Single crystals are anisotropic. Depending on what direction the tension is applied to, the Youngs modulus can vary. However, as many bulk materials are polycrystalline, the factor of direction is statistically cancelled out. Composite materials are not homogenous polycrystalline. It is not possible to evaluate a Youngs modulus for the material.

Temperature: As temperatures go close to the melting point of a certain material, the Youngs modulus drops due to higher inner energy. The temperature at which a Youngs modulus is measured has therefore a direct influence on the values. However, is the surrounding temperature far lower than the melting point, the influence is negligible.

Metals are usually not used as a pure material but as an alloy. Depending on the size of the atoms of the alloy partners, they build substitutional crystal structures (the metal with the lower percentual content takes places of the main metal, e.g. Cu-Ni) or interstitial crystal structures (small alloy partners with low percentual content sit between the main metal atoms, e.g. Fe-C). The Youngs modulus is directly proportional to the percentual alloy content. Beyond the limit of solubility the alloy consists of different phases and the elastic modulus can vary strongly. Ceramics have in comparison to polymers and metals high Youngs modulus. They might not be useful for application where stretching is required, but they are often used. Polymers chains contain covalent bonds. We therefore expect the Youngs modulus to be higher than for metals and ceramics. However, the main influence on the Youngs moduli are the Van der Waals bondings. The resistance of the polymer against elongation depends on the amount of crosslinks. The Youngs modulus can be evaluated with different such as the commonly used tension test. In the following, another way to evaluate Youngs modulus is described - the three-point flexure test. A rectangular piece of testing material is laid on two supporting pins. Force is applied to the middle of the rectangular bar and the bending of the material measured at different points between the supporting pins and the centre of the material where the load is applied. The three-point flexure test will be described more in detail in .Materials and Methods.

2. INTRODUCTION

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Table 1 shows the in literature stated Youngs modulus [2].

Tab. 1 Shows the Youngs modulus in Gigapascale taken from literature [2].

Material Youngs modulus [GPa]

Steel St37 206.0 [3] Aluminium (Al) 70.6 Copper (Cu) 129.8 Polyvinylchloride (PVC) 4.1

2.2 Hypothesis

We expect the materials to behave correspondingly to literature. The weak Van der Waals bondings of Polymers should lead to a low Youngs modulus of Polyvinylchloride (PVC). Concerning the compound materials, we expect the bending stiffness of aluminium comb core with aluminium cover to be higher than the one with Styrofoam core. This assumption is based on the strength of bee combs in nature.

3. MATERIALS AND METHODS

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3 MATERIALS AND METHODS

There were two different types of material tested, homogeneous materials like steal, copper, aluminium and PVC as well as composite and therefore heterogeneous materials. For the composite materials the Youngs modulus of Styrofoam with aluminium cover and aluminium comb with aluminium cover was measured.

3.1 Preparation of composite materials

The styropofoam-aluminium composites as well as one of the aluminium-aluminium composite were self-made. Six aluminium plates were cut to a size of 50cm x 5cm. One side was roughened with sandpaper to remove the oxidation layer and afterwards cleaned with acetone. They were put on a plastic foil. A styrofoam plate was cut to the same size as the aluminium plates. The size of the aluminium comb was about one centimetre in each direction bigger than the aluminium plates. It was cut to the right size after the gluing process. Araldite 2011 AD 80456700 was mixed by hand in a bowl and then applied to the scratched side of the aluminium plates with a spatula. The styrofoam pieces and the piece of aluminium comb were put onto the glued aluminium plates and were topped again with an aluminium plate. The composites were wrapped into plastic foil and pressed for 23 hours at room temperature using four bricks.

3.2 Preparation of the samples

The dimensions (length, width and thickness) of all samples were measured before being tested. The height a as well as the width b were measured with a calliper at three different points. For further calculations, the average was take

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