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Unformatted text preview: E 45 Laboratory Manual Lab 02 The Uniaxial Tensile Test
Objectives
1. To illustrate the basic properties of strength and toughness of materials 2. To standardize the fundamental concepts of mechanical stress and strain 3. To understand the uniaxial tensile test and the generation of "stressstrain" curves 4. To observe the microstructure of a fracture surface Overview
This experiment offers a detailed examination of the uniaxial tensile test, one of the most widely used methods for assessing the mechanical properties of metallic alloys. The test generates data on the time evolution of a material subjected to increasing load, resulting in standardized "stressstrain" curves for documenting the performance of that material up to and including its failure. Understanding how a material responds to an applied load and how to quantify its deformation and fracture behavior are the key concepts to be explored here. Equipment
Mechanical Testing 1. Tensile testing machines 2. Tensile test specimens: a. AISI 1020 plain carbon steel (0.2 wt.% C) b. AISI 4340 alloy steel (Ni, Cr, Mo, 0.4 wt% C) c. 2024T3 aluminum alloy
Metallography 1. Light optical microscopes 2. Scanning electron microscope (SEM) Copyright ⓒ 2010, Berkeley Professor Ronald Gronsky Lab 02: The Uniaxial Tensile Test Background
The elastic and plastic deformation properties of a material are most often quantified by a test that has been widely accepted throughout the engineering community, known as the “uniaxial tensile test.” A test specimen of initial length l0 and initial cross sectional area A0 is subjected to an increasing load that is applied to preserve a constant speed of a moving "crosshead" to which one side of the tensile specimen is attached, the other side being attached to a stationary platform. The configuration is “uniaxial” because the load is applied along a single axis, the long axis of the specimen, and it is “tensile” in that the applied load pulls the sample into an elongated (stretched) configuration. Both the applied load and the amount of elongation are simultaneously monitored by a computer. The data can then be displayed as a graph of “applied load” versus “elongation,” or as a graph of “stress” versus “strain” as illustrated below. Typically “engineering stress” and “engineering strain” are the parameters of interest in such studies. Engineering stress is defined as the applied load divided by the original cross sectional area, not the instantaneous cross sectional area, which changes throughout the test, and the engineering strain is the elongation (change in length) divided by the original length, not the instantaneous length, which changes throughout the test. At room temperature, metals and metallic alloys deform when a tensile load is applied. For small loads the deformation is elastic and the sample returns to its original length when the load is removed. For higher loads, the deformation can be permanent, or “plastic.” Metallic materials normally deform plastically before fracture. The initial linear portion of the stressstrain curve, up to the yield strength or elastic limit, is due to elastic (recoverable) deformation. For a plain carbon steel, the maximum stress reached in the specimen before plastic deformation occurs is called the upper yield strength (UYS). The stress immediately preceding the onset of general plastic deformation (at the end of the oscillations) is denoted the lower yield strength (LYS). This occurrence of both an upper and a lower yield is characteristic of low carbon steels, as illustrated in the stressstrain curve shown in Fig. 1. Other steels typically deform with only a single yield point. Many materials such as aluminum alloys do not show any welldefined yield points. For such materials the “0.2% offset” yield strength is used. This is the point on the stressstrain curve where a permanent, or plastic, strain of 0.2% occurs. It is established by drawing a line parallel to the elastic portion of the curve from the point on the strain axis corresponding to a 0.002 strain. The 0.2% offset yield strength is established by the intersection of this line with the stressstrain curve as illustrated in Fig. 2. page 2 of 6 Lab 02: The Uniaxial Tensile Test Stress ( ) UTS A UYS LYS Fracture Plastic strain at “A” Elastic strain at “A” Strain ( ) Figure 1 Schematic stressstrain curve for a plain carbon steel. Note the serrated yielding behavior of this material, resulting in upper and lower yield points. Stress ( ) UTS YS Fracture 0.002 Strain ( ) Figure 2 Schematic stressstrain curve for an aluminum alloy. The lack of a distinct yield point requires the use of the 0.02% offset method for determining yield strength. page 3 of 6 Lab 02: The Uniaxial Tensile Test Engineers must base their designs upon the properties of the materials they use. Among the important definitions appearing in the specification of mechanical properties are: stress, σ, (the load divided by the area supporting the load); strain, ε, (change in length divided by original length); Young's modulus, also called the Elastic Modulus, E, (ratio of a stress to strain, given by the slope of the elastic region); and Poisson's ratio, ν, (the negative value of the ratio of strain in the direction perpendicular to the loading direction to the strain in the loading direction). In addition, several other quantities can be obtained from the stressstrain curve to describe metals and alloys, as described in the following. The ultimate tensile strength (UTS) of a material is its maximum engineering stress before fracture.
UTS = Pmax Ao Fracture stress is defined as the load at fracture divided by the cross sectional area at fracture.
σf = Pf Af Reduction in area (RA) is a measure of the amount of deformation before fracture, which represents the ductility of a material. It is sometimes written as a percentage (multiply resulting fraction by 100%).
RA = Ao − Af Ao Another measure of ductility is the total elongation (TE) defined as follows, sometimes written as a percentage (multiply resulting fraction by 100%).
TE = lf − lo lo However, this is sensitive to the initial length l0. So sometimes “uniform elongation” is quoted; uniform elongation is defined as the engineering strain at maximum load. Finally, the area under the stressstrain curve indicates the capacity of a material to absorb energy. This is a rough measure of the work necessary to fracture the metal under ideal conditions, also called its toughness. Actual determinations of “toughness” however rely on other testing methods such as the "Charpy impact test" or the "fracture toughness test." The analysis of data from the uniaxial tensile test takes the form of plotting stress vs. strain in different permutations. In the most commonly used “engineering” stressstrain curve, the ordinate plots values of the engineering stress
σe = P Ao and the abscissa, the corresponding values of engineering strain, page 4 of 6 Lab 02: The Uniaxial Tensile Test εe = l − l0 l0 As the sample is deformed in tension, its length increases and cross sectional area decreases throughout the deformation process. Consequently there is an alternative “true” stresstrue strain curve that could be generated using the instantaneous (subscript i) values of these quantities, known as true stress
σtrue = P Ai and true strain
εtrue =
li l0 dl li = ln l l0 Experimental Procedures
1. Conduct uniaxial tensile tests on all three materials provided: (a) AISI 1020 (plain carbon) steel; (b) AISI 4340 (alloy) steel; and (c) 2024T6 aluminum alloy. 2. Record the initial hardness using a Rockwell hardness machine to distinguish the plain carbon steel from the alloy steel. Record the initial crosssectional area and the initial length. During the test, carefully observe the onset of yielding and where necking occurs. Record your observations in your lab notebook. At the end of each test record the final cross sectional area and final length. 3. Perform “fractography” of the fracture surfaces using optical microscopy and scanning electron microscopy.
DataSheet 1 — Uniaxial Tensile Test Material Hardness Initial area (in2) Initial gage length (in) Final area (in2) Final gage length (in) DataSheet 1 is a simple tabulation of all relevant data collected during your laboratory exercises. There should be at least three rows of data here corresponding to the three samples that were pulled in tension. This data can either be transferred to a spreadsheet or simply inserted as a table from within a wordprocessing application for inclusion in your lab report. page 5 of 6 Lab 02: The Uniaxial Tensile Test Lab Report
The report for this laboratory must include DataSheet 1, all datasets from the uniaxial tensile tests, optical micrographs, SEM images, and data analysis (calculations). Remember that all figures must have independent captions besides their descriptions in the "Results" section of your report. Writeups must also answer the following questions in the "Discussion" section of your report.
Question 1 How can you plot an “engineering stressstrain curve” from “applied load” vs. “elongation” data. Using your own data, plot engineering stressstrain curves for all three samples and explain.
Question 2 From this curve calculate the following for each of the samples: (a) Young's modulus [slope of elastic portion of the curve]; (b) yield strength [lower yield strength for steel, 0.2% offset for aluminum alloy]; (c) ultimate tensile strength; (d) fracture stress; (e) percent reduction in area at fracture; (f) total elongation; and (g) toughness [approximated as area under the curve]. Explain any anomalies in your results.
Question 3 During the tensile test the volume of the material remains constant, which can be expressed mathematically as
lo Ao = li Ai = constant Using this relation and the definitions of engineering stress, engineering strain, true stress, and true strain, derive the following relationship between true stress and engineering stress
σtrue = σe (1 + εe ) and the relationship between true strain and engineering strain
εtrue = ln(1 + εe )
Question 4 Convert your engineering stressstrain curves to true stressstrain curves.
Question 5 Where (physical location) on each sample did you observe "necking" to occur? Is this where you expected to see it? Explain.
Question 6 Compare and contrast the scanning electron “fractographs” recorded during your lab experiments. What are the distinctive features of the fracture surface? How do these features differ from sample to sample? Do these observations make physical sense with respect to their observed strength and toughness? Explain. page 6 of 6 ...
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This note was uploaded on 11/19/2010 for the course E 45 taught by Professor Gronsky during the Fall '08 term at University of California, Berkeley.
 Fall '08
 GRONSKY
 Strain, Stress

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