Institut für Mikro- und Nanomaterialien

Praktikum zur Vorlesung „Werkstoffe der Elektrotechnik“

Versuch: MECHANISCHE EIGENSCHAFTEN

Update: 15. Januar 2010 Autor: Mike Haddad

Outline

1. Objectives 3

2. Introduction 3

2.1 Tensile test 4

2.2 Hardness test 8

3. Carrying out the experiment 13

Tensile test and Hardness Test

4. References 14

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1. Objectives: The tensile test measures the resistance of a material to a static or slowly applied force. This laboratory experiment is designed to demonstrate the procedure used for obtaining mechanical properties as modulus of elasticity, yield strength, ultimate tensile strength (UTS), toughness, uniform elongation, and to develop the applied working knowledge of the fundamental principles of elastic and plastic deformation. Furthermore, to introduce the principles of hardness testing, emphasizing the limitations and significance of the results. 2. Introduction: Most of the materials will be under different types of loads during their use. Thus, it is vital to know the mechanical properties of these materials in order to design machine elements and members in such a way to prevent over limit deformation and fracture. The mechanical properties could be (known) by performing accurate laboratory experiments under carefully selected boundary conditions to influence as much as possible the working conditions. It is essential to perform these tests based on stipulated procedures. Professional organizations standardized the testing procedures and techniques starting from the samples selection and preparation, boundary conditions, testing procedures, and the acceptable results that we should get. In Germany, the DIN (Deutsches Institut für Normung) is the official organization that responsible for publishing the testing standards. The tensile test and the Hardness test are of the most common tests to obtain several mechanical properties such as the yield stress, the ultimate tensile strength, modulus of elasticity, hardness ….. etc.

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2.1 Tensile Test The tensile test is one of the simplest tests for determining mechanical properties of material. In this test, A specimen is deformed, usually to fracture, with a uniaxially gradually increasing applied tensile load . The applied load and the resulting elongation of the specimen are measured.

Figure 1 shows the standard configuration for tensile testing sheet material. This shape is commonly referred to as a dogbone, with wide ends and a narrow middle. The grips of the testing apparatus hold the specimen firmly at the wide ends. The midsection of the specimen has the narrower width than the grip section. This concentrates the stress in the test area, so that the fracture and most of the strain occur here. Then, the stress and the strain can be calculated from the force load on the grips and the change in the specimens gauge length using the following relations:

Figure 1: Standard setup for a tensile test

CONSTANT RATE OF MOTION

MOVABLE HEAD

GRIPS FOR HOLDING SPECIMEN FIRMLY

GAUGE MARKS

FIXED HEAD

FORCE MEASUREMENT

AP

=σ Lδε =

Where: σ = normal stress on a plane perpendicular to the longitudinal axis of the

specimen. P= applied load. A= original cross sectional area. ε = normal strain in the longitudinal direction. δ = change in the specimen’s gauge length. L= original gauge length. The resulting curve is called the Stress-Strain diagram and gives a direct indication of the materials properties. These diagrams are based on the original cross sectional area and the initial gauge length. The cross sectional area changes continuously during the test, but these changes have a negligible effect except during the final stage of the test. 4

Figure 2(a):Engineering Stress-Engineering Strain Diagram for Low Carbon Steel

Figure 2(b):True Stress-True Strain Diagram for Low Carbon Steel

Engineering stress and Engineering strain are calculated using the original specimen dimensions, while True stress and True strain are based upon the instantaneous values of cross sectional area and gauge length. As shown in figure 2(a), the initial portion of the stress-strain diagram for most materials used in engineering structures is a straight line. So, for the initial portion of the diagram, the stress σ is directly proportional to the strain ε , therefore, for a specimen subjected to a uniaxial load, we can write:

εσ E= This relationship is known as Hooke’s Law and was first recorded by Robert Hooke, an English mathematician, in 1678. The slope of the straight line portion of the stress-strain diagram is called the Modulus of Elasticity or Young’s Modulus(E), and in the shear stress-strain is called Shear Modulus or Modulus of Rigidity (G).

γτ G=

The deformation in which stress and strain are proportional is called elastic deformation and it is nonpermanent, which means that when the applied load is released, the piece returns to its original shape.

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When a tensile stress is imposed on a metal specimen, an elastic elongation and accompanying strain result in the direction of the applied strain (arbitrarily taken to be in the z direction zε ) as shown in figure 3. As a result of this elongation, there will be constrictions in the lateral (x and y) directions perpendicular to the applied stress; from these contractions, the compressive strains xε and yε may be determined.

Figure 3:Axial (z) elongation (positive strain) and lateral (x and y) contractions (negative strains) in response to an imposed tensile stress. Solid lines represent dimensions after stress application; dashed lines, before.

If the applied stress is uniaxial (only in the z direction), and the material is isotropic, then xε = yε . A parameter termed Poisson’s ratio ν is defined as the ratio of the lateral and axial strains, or

z

y

z

x

εε

εεν −=−=

At the end of the linear proportional segment comes the proportional limit stress, after this value, the stress-strain curve is no more linear and Hooke’s law ceases to be valid. And after that comes the elastic limit stress which is the maximum stress that can be applied without resulting in permanent deformation when unloaded. Then, a departure from the linearity of the stress-strain curve can be noticed this phenomenon is called the yielding and it indicates the beginning of plastic ( permanent ) deformation. In some metals, the departure from the proportional limit may be gradual, In such cases the position of this point may not be determined precisely. As a consequence, a convention has been established wherein a straight line is constructed parallel to the elastic portion of the stress–strain curve at some specified strain offset, usually 0.002. The stress corresponding to the intersection of this line and

Figure 4: Stress-Strain curve showing the 0.002 strain offset method

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the stress–strain curve as it bends over in the plastic region is defined as the yield strength yσ . This is demonstrated in Figure 4. For steels, during the yielding , a large increase in strain is noticed with little or no increase in stress and the yielding point can be determined easily. But if the specimen is strained beyond this region, An increasing stress is required to produce additional plastic deformation and the metal apparently becomes stronger and more difficult to deform. This phenomenon is called the strain hardening. The stress continues to increase with strain till it reaches a maximum point and then decreases to the fracture, the maximum point (maximum stress) on the engineering Stress-Strain curve (Figure 2a) is called the tensile strength and it is the maximum stress that can be sustained by a structure in tension and if applied and maintained fracture will result. Up to the tensile strength point, all deformation is uniform through out the gauge length area (the narrow area), but after that, a small neck (Figure 5) begins to form and all subsequent deformation will occur at this neck. This phenomenon is called necking and fracture ultimately occur at the neck. The corresponding stress at the fracture point is called the fracture strength. Figure 5: The Necking phenomenon

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2.2 Hardness Test Hardness, which is a measure of a material’s resistance to localized plastic deformation (e.g., a small dent or a scratch), is another important mechanical property. Early hardness tests were qualitative and somewhat arbitrary hardness indexing scheme was devised, termed the Mohs scale, which ranged from 1 on the soft end to 10 for diamond.

Figure 6: Hardness test

Over the years, Quantitative hardness techniques have been developed in which a small indenter is forced into the surface of a material to be tested, under controlled conditions of load and rate of application. The depth or size of the resulting indentation is measured, which in turn is related to a hardness number; the softer the material, the larger and deeper is the indentation, and the lower the hardness index number. The Hardness test is the more frequently used test for several reasons such as: 1. Simple and inexpensive, no special specimen need to be prepared, and

the testing apparatus is relatively inexpensive. 2. The test is nondestructive, the specimen is neither fractured nor

excessively deformed. 3. Other mechanical properties may be estimated from hardness data such

as tensile strength (Figure 7).

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There are several methods used to measure the hardness differs from each other in the indenter shape and dimensions, in the applied load and also in the formula used to calculate the hardness number such as Brinell hardness test, Rockwell and Rockwell Superficialhardness tests, Knoop and Vickers micro indentation Hardness tests.

In Brinell test, a hard spherical indenter ( 10 mm diameter ) is forced into the surface of the metallic specimen, the loads range between 500 and 3000 kg and maintained for a specified time. The Brinell hardness number (HB) is a function of the load and the diameter of the resulting indentation.

Figure 7: Hardness and Tensile strength

The Rockwell hardness test method consists of indenting the test material with a diamond cone or hardened steel ball indenter. The indenter is forced into the specimen under a preliminary minor load F0 (Figure 8a) usually 10 kgf. When equilibrium has been reached, an indicating device, which follows the movements of the indenter and so responds to changes in depth of penetration of the indenter is set to a datum position. While the preliminary minor load is still applied an additional major load is applied with resulting increase in penetration (Figure 8b). When equilibrium has again been reach, the additional major load is removed but the preliminary minor load is still maintained. Removal of the additional major load allows a partial recovery, so reducing the depth of penetration (Figure 8c). The permanent increase in depth of penetration, resulting from the application and removal of the additional major load is used to calculate the Rockwell hardness number.

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Figure 8: Rockwell Hardness Principle

Both the Knoop and Vickers is forced a very small diamond indenter having a pyramidal geometry into the surface of the specimen (the shape of the indenter is different in both methods as shown in figure 9). Applied loads are much smaller than Brinell and Rockwell, ranging between 1 and 1000g. The resulting indents are observed and measured under a microscope and the measurements are then converted to a hardness number. Careful specimen surface finish is necessary to assure accurate results.

Knoop

Vickers

Figure 9: Knoop and Vickers Indenters

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Har

dnes

s Te

stin

g Te

chni

ques

Sum

mar

y

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Since hardness is not a well defined material property due to the various hardness techniques dissimilarities and due to the fact that hardness depend on material type and characteristics , hardness conversion data have been determined experimentally, the most reliable conversion data exist for steel, some of them shown in figure 10 below.

Figure 10: Comparison of several hardness scales.

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3. Carrying Out The Experiment

1- Three specimens will be subjected to tensile test, Low Carbon Steel, Cupper and Zinc with the approximate dimensions shown in Figure 11.

Figure 11: Tensile specimen dimensions

50mm

80mm

100mm

2- Measure the exact dimensions for each specimen (Thickness and

Width). 3- On each sample, mark the gauge length lines (50 mm lines). 4- Run the tensile test and obtain a Load vs Elongation curve. 5- From the curve Calculate:

a. The Modulus of Elasticity. b. The Yield Stress. c. Poisson’s Ratio. d. Ultimate Tensile Strength. e. Fracture Strength. f. The Strain in the Specimen.

6- Discuss the obtained results and the obtained diagrams showing all

the regions discussed above on the curve. 7- Discuss the elastic deformation (proportional limit) and the plastic

deformation (non-recoverable region) from an atomic point of view. 8- Use another 3 specimens from the same materials used in the tensile

test and make 5 Vickers Hardness readings for each one. 9- Find the average HV number for each specimen and compare it with

the Theoretical one and find out the error percent. 10- Discuss your results and also discuss the deviation from the theoretical

values.

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4. References 1. S. Patnaik and D. Hopkins, Strength of Materials, Elsevier 2004 2. S. Timoshenko, Strength of Materials, D. Van Nostrand Co, 2nd edition 3. William D. Callister, Materials Science and Engineering, Wiley, 2007 4. www.itcsoftware.com/general_finite-eg-largestrain_files/image002.jpg 5. www.engineersedge.com