Mechanical Behavior of Materials

Click to edit Master title style,Click to edit Master text styles,Second Level,Third Level,Fourth Level,Fifth Level,Click to edit Master title style,Click to edit Master text styles,Second Level,Third Level,Fourth Level,Fifth Level,*,Mechanical Behavior of Materials,Know the concepts of mechanical properties of materials.,Understand the factors affecting the mechanical properties.,Be aware of the basic testing procedures that engineers use to evaluate many of these properties.,Objective,Outline,Mechanical Properties of Materials,Stress-Strain Diagram & Properties,Bend Test of Materials,Hardness Test of Materials,Impact Testing of Materials,Fracture Mechanics of Materials,Fatigue of Materials and Application,Creep of Materials , Stress Rupture, and Stress Corrosion,Evaluation of Creep & Use of Creep Data,Mechanical Behavior of Materials,Behavior and Manufacturing Properties of Materials, 2003 Brooks/Cole Publishing / Thomson Learning,Representative Strengths of Various Categories of Materials,Materials Design and Selection,Density is mass per unit volume of a material, usually expressed in units of g/cm,3,or lb/in.,3,Strength-to-weight ratio is the strength of a material divided by its density; materials with a high strength-to-weight ratio are strong but lightweight.,Most common test for determining such mechanical properties as strength, ductility, toughness, elastic modulus, and strain hardening.,The test specimen made according to standard specifications. Most specimens are solid and round, some are flat-sheet.,In this test a metal sample is pulled to failure at a constant rate.,The load displacement relationship is plotted on a moving chart graph paper, with the signals coming from a load cell fixed at the top of the testing machine, and an extensometer (strain gauge) attached to the sample.,The load displacement data obtained from the chart paper can be converted to engineering stress/strain data, and a plot of engineering stress vs. engineering strain can be constructed.,Tension Test,Mechanical Behavior of Materials,Tension Testing Machine,Tensile Specimens,Mechanical Behavior of Materials,Engineering Stress Strain Diagram For A High-Strength Aluminum Alloy.,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,A unidirectional force is applied to a specimen in the tensile test by means of the moveable crosshead. The cross-head movement can be performed using screws or a hydraulic mechanism,Mechanical Behavior of Materials,Mechanical property data obtained from the tensile test are of engineering importance for structural design. These are:,modulus of elasticity,yield strength at 0.2 percent offset,ultimate tensile strength,percent elongation at fracture,percent reduction in area at fracture,- Stress (,) = Force or load per unit area of cross-section.,- Strain (,) = Elongation change in dimension per unit length,- Youngs modulus (E)= The slope of the linear part of the stress-,strain curve in the elastic region,(stress) = E x,(strain),or E = (stress)/(strain),psi,or pa,Mechanical Behavior of Materials,Slope of stress strain plot (which is proportional to the elastic modulus) depends on bond strength of metal,Adapted from Fig. 6.7,Callister 7e.,Mechanical Behavior of Materials,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,Comparison of the elastic behavior of steel and aluminum. For a given stress, aluminum deforms elastically three times as much as does steel,Mechanical Behavior of Materials,Mechanical Behavior of Materials,In industry, components are formed into various shapes by applying external forces to the workpiece using specific tools and dies. A typical operation is rolling of a flat sheet to be processed into a car body.,Because deformation in these processes is carried out by mechanical means, an understanding of the behavior of materials in response to externally applied forces is important.,Forming operations may be carried out at room temperature or at higher temperatures and at a low or a high rate of deformation.,The behavior of a manufactured part during its expected service life is an important consideration. For example the wing of an aircraft is subjected to static as well as dynamic forces. If excessive, dynamic forces can lead to cracks and can cause failure of the component.,Mechanical Behavior of Materials,Engineering stress-strain.,Elastic range in stress-strain.,Mechanical Behavior of Materials,Engineering stress-strain curve, showing various features,Yield stress (Y), Ultimate tensile strength (UTS), and Fracture.,1. Elastic and Plastic, 2. Uniform elongation and Necking.,Mechanical Behavior of Materials,Alloying a metal with other metals or nonmetals and heat treatment can greatly affect the tensile strength and ductility of metals.,During the tensile test, after necking of the sample occurs, the engineering stress decreases as the strain increases, leading to a maximum engineering stress in the engineering stress-strain curve. Thus, once necking begins during the tensile test, the true stress is higher than the engineering stress.,Engineering stress,= P/A,0,and,Engineering strain,=(l-l,0,)/l,0,True stress,T,= F/A,i,=,(1+,) and,True strain,T,=,ln,(l,i,/l,0,) =,ln,(1+,),Mechanical Behavior of Materials,Mechanical Behavior of Materials,Engineering stress-strain curves for some metals and alloys,Chapter 4, mechanical properties of metals,Mechanical Behavior of Materials,Chapter 4, mechanical properties of metals,Comparison between engineering and tue stress-strain curve,Mechanical Behavior of Materials,Yield strength is a very important value in engineering structural design since it is the strength at which a metal or alloy begins to show,significant plastic deformation. Since there is no definite point on the stress-strain curve where elastic strain ends and plastic strain begins, the yield strength is chosen to be that at which a finite amount of plastic strain has occurred. For American structural design, the yield strength is chosen at 0.2% plastic strain.,The ultimate tensile strength (UTS) is the maximum strength reached in the engineering stress-strain curve. If the specimen develops a localized reduction in cross-sectional area (necking), the engineering stress will decrease with further strain until fracture,.,Mechanical Behavior of Materials,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,Determining the 0.2% offset yield strength in gray cast ion, and (b) upper and lower yield point behavior in a low-carbon steel,Mechanical Behavior of Materials,Resilience,U,r,Ability of a material to store energy,Energy stored best in elastic region,If we assume a linear stress-strain curve this simplifies to,Adapted from Fig. 6.15,Callister 7e.,y,y,r,2,1,U,e,s,Mechanical Behavior of Materials,The area under the elastic region is the elastic strain energy (in.lb./in.,3,), a measure of the amount of elastic energy that can be stored in each cubic inch of the specimen.,For spring steel, M,R,= 385 in.lb./in.,3,or 1355 ./lb. For rubber, M,R,= 1680 385 in.lb./in.,3,or 48,000 ./lb. Rubber can store much more energy per unit volume or weight than can steel.,Mechanical Behavior of Materials,Elastic Strain Recovery,Adapted from Fig. 6.17,Callister 7e.,1. Initial,2. Small load,3. Unload,F,d,Mechanical Behavior of Materials,The more ductile a metal is, the more the decrease in the stress on the stress-strain curve beyond the maximum stress. For high strength aluminum alloy, there is only a small decrease in stress beyond the maximum stress because this material has relatively low ductility.,The ultimate tensile strength is not used much in engineering design for ductile alloys since too much plastic deformation takes place before it is reached. However, the ultimate tensile strength can give some indication of the presence of defects. If the metal contains porosity or inclusions, these defects may cause the ultimate tensile strength of the metal to be lower than normal.,Mechanical Behavior of Materials,Ductility of metals is most commonly expressed as percent elongation and percent reduction in area. The percent elongation and percent reduction in area at fracture is of engineering importance not only as a measure of ductility but also as an index of the quality of the metal.,Percent elongation is the amount of elongation that a tensile specimen under goes during testing provides a value for the ductility of a metal.,Percent reduction in area is usually obtained from a tensile test using a specimen 0.50 in (12.7 mm) in diameter.,x 100,L,L,L,EL,%,o,o,f,-,=,100,x,A,A,A,RA,%,o,f,o,-,=,Mechanical Behavior of Materials,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,Localized deformation of a ductile material during a tensile test produces a necked region. The micrograph shows necked region in a fractured sample,Mechanical Behavior of Materials,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,The stress-strain behavior of brittle materials compared with that of more ductile materials,Mechanical Behavior of Materials,Mechanical Behavior of Materials,Chapter 4, mechanical properties of metals,Toughness:,is defined as the total area under the stress strain curve up to fracture (in.lb./in.,3,). It is a measure of the total amount of energy that can be absorbed prior to fracture. Brittle materials are not tough.,Note,:,It is not possible to make this integration unless we have some mathematical function that describes the relationship between stress and strain up to fracture (,= Ee,only describes the relationship during elastic deformation, not plastic deformation). Some possible mathematical models will be described in the following section. As an approximation, toughness can be estimated as the area under the curve using the combined areas of simple shapes such as rectangles and triangles.,Mechanical Behavior of Materials,Given the true stress strain curve, = K,n, the,toughness,(the specific energy (in.lb./in,3,) dissipated up to fracture) can be calculated by integrating with respect to strain up to the strain at fracture,(,f,),Then using the true stress strain model, = K,n,Mechanical Behavior of Materials,Example Problem,Mechanical Behavior of Materials,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,Figure 6.10 The stress-strain curve for an aluminum alloy from Table 6-1,Mechanical Behavior of Materials,Example Problem,Mechanical Behavior of Materials,Example Problem,Youngs Modulus of Aluminum Alloy,From the data in Example 6.1, calculate the modulus of elasticity of the aluminum alloy. Use the modulus to determine the length after deformation of a bar of initial length of 50 in. Assume that a level of stress of 30,000 psi is applied.,Example 6.3 SOLUTION,Mechanical Behavior of Materials,Ductility of an Aluminum Alloy,The aluminum alloy in Example 6.1 has a final length after failure of 2.195 in. and a final diameter of 0.398 in. at the fractured surface. Calculate the ductility of this alloy.,Example 6.4 SOLUTION,Mechanical Behavior of Materials,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,The effect of temperance (a) on the stress-strain curve and (b) on the tensile properties of an aluminum alloy,Mechanical Behavior of Materials,True Stress and True Strain Calculation,Compare engineering stress and strain with true stress and strain for the aluminum alloy in Example 6.1 at (a) the maximum load and (b) fracture. The diameter at maximum load is 0.497 in. and at fracture is 0.398 in.,Example 6.5 SOLUTION,Mechanical Behavior of Materials,SOLUTION (Continued),Mechanical Behavior of Materials,Compression:,Many manufacturing processes such as forging, rolling, extrusion, are performed with the work piece subjected to compressive forces. Compression test, in which the specimen is subjected to compressive load, gives information useful for these processes.,When the results of compression tests and tension tests on ductile metals are compared, the true stress-true strain curves for the two tests coincide. This comparability does not hold true for brittle materials, which are generally stronger and more ductile in compression than in tension,Mechanical Behavior of Materials,. Factor of safety,N,Often,N,is,between,1.2 and 5, Example: Calculate a diameter,d, to ensure that yield does,not occur in the 1045 carbon steel rod below. Use a,factor of safety of 5.,Design or Safety Factors,5,1045 plain,carbon steel:,s,y,= 310 MPa,TS,= 565 MPa,F,= 220,000N,d,L,o,d,= 0.067 m = 6.7 cm,Mechanical Behavior of Materials,Bend Test for Materials,Bend Test for Brittle Materials,Bend test,- Application of a force to the center of a bar that is supported on each end to determine the resistance of the material to a static or slowly applied load.,Flexural strength,-The stress required to fracture a specimen in a bend test.,Flexural modulus,- The modulus of elasticity calculated from the results of a bend test, giving the slope of the stress-deflection curve.,Mechanical Behavior of Materials,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,The bend test often used for measuring the strength of brittle materials, and (b) the deflection obtained by bending,Bend Test for Brittle Materials,Mechanical Behavior of Materials,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,Stress-deflection curve for Mg0 obtained from a bend test,Bend Test for Brittle Materials,Mechanical Behavior of Materials,Bending (Flexure):,The,Bend test is commonly used for brittle materials. It usually involves a specimen that has a rectangular cross-section. The load is applied vertically, at either one point or two: as a result, these tests are referred to as three-point and four point bend, respectively. The longitudinal stresses in these specimens are tensile at their lower surfaces and compressive at their upper surfaces.,The stress at fracture in bending is known as the,transverse rupture strength.,Bend Test for Brittle Materials,Mechanical Behavior of Materials,Hardness of Materials,Hardness is a measure of the materials resistance to localized plastic deformation (e.g. dent or scratch).,In general, hardness usually implies a resistance to deformation, and for metals the property is a measure of their resistance to permanent or plastic deformation. To a person concerned with the mechanics of materials testing, hardness is most likely to mean the resistance to indentation.,Hardness of Materials,Mechanical Behavior of Materials,Steel is harder than aluminum, and aluminum is harder than lead.,Several methods have been developed to measure the hardness of materials.,Hardness of Materials,Mechanical Behavior of Materials,Hardness and Strength,: Studies have shown that (in the same units) the hardness of a cold-worked metal is about three times its yield stress: for annealed metals, it is about five times the yield.,A relationship has been established between the ultimate tensile strength (UTS) and the Brinell hardness (HB) for steels. In SI units,UTS = 3.5*(HB), where UTS is in Mpa. Or UTS = 500*(HB), where UTS is in psi and HB is in kg/mm2, as measured for a load of 3000 kg.,Hardness of Materials,Mechanical Behavior of Materials,Hardness-Testing Procedures,: The following considerations must be taken for hardness test to be meaningful and reliable:,The zone of deformation under the indenter must be allowed to develop freely.,Indentation should be sufficiently large to give a representative hardness value for the bulk material.,Surface preparation is necessary, if conducting Rockwell test and other tests, except,Brinell,test.,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,Hardness of Materials,Mechanical Behavior of Materials,Mechanical Behavior of Materials,Hardness of Materials,Temperature Effects,: Increasing the temperature generally has the following effects on stress-strain curves:,It raises ductility and toughness,It lowers the yield stress and the modulus of elasticity,It lowers the strain-hardening exponent of most metals,Mechanical Behavior of Materials,Rate-of-Deformation (Strain Rate) Effects,: Deformation (strain) rate is defined as the speed at which a tension test is being carried out, in units of, say, mm/s.,The strain rate is a function of the specimen length. A short specimen elongates proportionately more during the same time period than does a long specimen.,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,When a ductile material is pulled in a tensile test, necking begins and voids form starting near the center of the bar by nucleation at grain boundaries or inclusions. As deformation continues a 45 shear lip may form, producing a final cup and cone fracture,Mechanical Behavior of Materials,Impact Testing of Materials,Impact test,- Measures the ability of a material to absorb the sudden application of a load without breaking.,Impact energy,- The energy required to fracture a standard specimen when the load is applied suddenly.,Impact toughness,- Energy absorbed by a material, usually notched, during fracture, under the conditions of impact test.,Fracture toughness,- The resistance of a material to failure in the presence of a flaw.,Mechanical Behavior of Materials,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,The impact test: (a) The Charpy and Izod tests, and (b) dimensions of typical specimens,Mechanical Behavior of Materials,Ductile to brittle transition temperature (DBTT),- The temperature below which a material behaves in a brittle manner in an impact test.,Notch sensitivity,- Measures the effect of a notch, scratch, or other imperfection on a materials properties, such as toughness or fatigue life.,Mechanical Behavior of Materials,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,Results from a series of Izod impact tests for a super-tough nylon thermoplastic polymer,Mechanical Behavior of Materials,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,The Charpy V-notch properties for a BCC carbon steel and a FCC stainless steel.,Mechanical Behavior of Materials,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,The area contained within the true stress-true strain curve is related to the tensile toughness. Although material,B,has a lower yield strength, it absorbs a greater energy than material,A,.,Mechanical Behavior of Materials,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,Schematic drawing of fracture toughness specimens with (a) edge and (b) internal flaws,(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning,is a trademark used herein under license.,The fracture toughness,K,c,of a 3000,000psi yield strength steel decreases with increasing thickness, eventually leveling