Mechanical Behavior of Materials

Mechanical Behavior of Materials
Objective 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.

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

Behavior and Manufacturing Properties of Materials

Representative Strengths of Various Categories of Materials
© 2003 Brooks/Cole Publishing / Thomson Learning™

Materials Design and Selection
Density is mass per unit volume of a material, usually expressed in units of g/cm3 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.

Tension Test 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 Testing Machine
Mechanical Behavior of Materials Tensile Specimens Tension Testing Machine

Engineering Stress Strain Diagram For A High-Strength Aluminum Alloy.
Mechanical Behavior of Materials (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 Engineering Stress Strain Diagram For A High-Strength Aluminum Alloy.

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 - Young’s 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

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.

(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

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.

Engineering stress-strain. Elastic range in stress-strain.

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.

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 σ = P/A0 and Engineering strain ε =(l-l0)/l0 True stress σT = F/Ai = σ (1+ ε) and True strain εT =ln (li/l0) = ln (1+ ε)

Chapter 4, mechanical properties of metals Engineering stress-strain curves for some metals and alloys

Chapter 4, mechanical properties of metals Comparison between engineering and tue stress-strain curve

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.

(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

Resilience, Ur Ability of a material to store energy Energy stored best in elastic region If we assume a linear stress-strain curve this simplifies to y r 2 1 U e s @ Adapted from Fig. 6.15, Callister 7e.

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, MR = 385 in.lb./in.3 or 1355 in.lb./lb. For rubber, MR = in.lb./in.3 or 48,000 in.lb./lb.. Rubber can store much more energy per unit volume or weight than can steel.

Elastic Strain Recovery
Mechanical Behavior of Materials Adapted from Fig. 6.17, Callister 7e. Elastic Strain Recovery 1. Initial 2. Small load 3. Unload F d

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.

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 EL % o f - = 100 x A RA % o f - =

(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

(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

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.

Given the true stress strain curve  = Kn , the toughness (the specific energy (in.lb./in3) 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

Example Problem

Example Problem (c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. Figure The stress-strain curve for an aluminum alloy from Table 6-1

Example Problem

Young’s 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

Ductility of an Aluminum Alloy The aluminum alloy in Example 6.1 has a final length after failure of in. and a final diameter of in. at the fractured surface. Calculate the ductility of this alloy. Example 6.4 SOLUTION

(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

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 in. and at fracture is in. Example 6.5 SOLUTION

SOLUTION (Continued)

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

Design or Safety Factors
Mechanical Behavior of Materials Design or Safety Factors .• 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. 1045 plain carbon steel: s y = 310 MPa TS = 565 MPa F = 220,000N d L o 5 d = m = 6.7 cm

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.

Bend Test for Brittle 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 δ obtained by bending

Bend Test for Brittle 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 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.

Hardness 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 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 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 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

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

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

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.

(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

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 material’s properties, such as toughness or fatigue life.

(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

(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.

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc
(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 Kc of a 3000,000psi yield strength steel decreases with increasing thickness, eventually leveling off at the plane strain fracture toughness Klc

Fatigue of Materials

Type of Fatigue Stresses
Typical fatigue stress cycles. (a) Reversed stress; (b) repeated stress; (c) irregular or random stress cycle Reversed cycle of stress i.e. the maximum and minimum stresses are equal. A repeated stress cycle i.e. σmax (Rmax) and σmin (Rmin) are not equal. A complicated stress cycle which might be encountered in a part such as an aircraft wing which is subjected to periodic unpredictable overloads due to gusts.

The basic method of presenting engineering fatigue data is by means of the S-N curve, a plot of stress S against the number of cycles to failure N. The value of stress that is plotted can be σa, σmax, or σmin. The most commonly used parameter is the stress ratio is R = (S min/S max). If the stresses are fully reversed, then R = -1. If the stresses are partially reversed, R = a negative number less than 1. If the stress is cycled between a maximum stress and no load, R = zero. If the stress is cycled between two tensile stresses, R = a positive number less than 1. The S-N curve is determined for a specified value of σm , R (R= σmin/σmax). The usual procedure for determining an S-N curve is to test the first specimen at a high stress where failure is expected in a fairly short number of cycles, e.g., at about two-thirds the static tensile strength of the material. The test stress is decreased for each succeeding specimen until one or two specimens do not fail in the specified numbers of cycles.

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc
(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. Examples of stress cycles. (a) Equal stress in tension and compression, (b) greater tensile stress than compressive stress, and (c) all of the stress is tensile

A fatigue failure is particularly insidious because it occurs without any obvious warning. Thermal fatigue. Thermal cycling cause expansion and contraction, hence thermal stress, if component is restrained. Corrosion fatigue. Chemical reactions induce pits which act as stress raisers. Corrosion also enhances crack propagation Fatigue tests are usually made with smooth, polished specimens under completely reversed stress conditions. Fatigue properties are frequently correlated with tensile properties. In general, the fatigue limit of cast and wrought steels is approximately 50 percent of the ultimate tensile strength. The ratio of the fatigue limit (or the fatigue strength at 106 cycles) to the tensile strength is called the fatigue ratio.

Fatigue limit (endurance limit) occurs for some materials (some Fe and Ti alloys). In this case, the S-N curve becomes horizontal at large N. The fatigue limit is maximum stress amplitude below which the material never fails, no matter how large the number of cycle is. The highest stress at which a (non-failure) is obtained is taken as the fatigue limit. For materials without a fatigue limit the test is usually terminated for practical considerations at a low stress where the life is about 108 or 5x108 cycles. The S-N curve is usually determined with about 8 to 12 specimens.

Crack initiation at the sites of stress concentration (microcracks, scratches, indents, interior corners, dislocation slip steps, etc.). Stage I: initial slow propagation along crystal planes with high resolved shear stress. Involves just a few grains, and has flat fracture surface. Stage II: faster propagation perpendicular to the applied stress. Crack grows by repetitive blunting and sharpening process at crack tip. Crack eventually reaches critical dimension and propagates very rapidly. (c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. Schematic representation of a fatigue fracture surface in a steel shaft.

Mechanical Behavior of Materials Variable affecting Fatigue
Magnitude of stress (mean, amplitude...) Quality of the surface (scratches, sharp transitions and edges). Large enough variation or fluctuation in the applied stress, and Sufficiently large number of cycles of the applied stress. Other variables include stress concentration, corrosion, temperature, overload, metallurgical structure, residual stresses, and combined stresses, which tend to alter the conditions for fatigue.

Mechanical Behavior of Materials Preventing Fatigue Failure
Introducing compressive stresses into thin surface layer by “shot peening”- firing small shot into surface to be treated. Case hardening- create C- or N-rich outer layer. Makes harder outer and also introduces compressive stresses Use materials with low thermal expansion coefficients Decrease corrosiveness of medium, if possible Add protective surface coating Add residual compressive stresses Prevent the development of surface discontinuities during processing. Reduce or eliminate tensile residual stresses caused by manufacturing.

Creep of Materials

Creep Behavior Creep is a time-dependent and permanent deformation of materials when subjected to a constant load at a high temperature (>0.4Tm). Examples: turbine blades, stream generators. Creep Testing Stages of Creep

Secondary/steady-state creep is of longest duration and is the most important parameter of the creep behavior in long-life applications έ=Δε/Δt (c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. Stages of Creep Primary/transient creep. Secondary/steady-state creep. Tertiary creep. A typical creep curve

Creep: With increasing stress or temperature, the instantaneous strain increases, the steady-state creep rate increases and the time to rupture decreases. The stress/temperature dependence of the steady-state creep rate can be described by έss= K σn exp (-Qc/RT) where Qc is the activation energy for creep, K and n are material constants. Different mechanisms are responsible for creep in different materials The mechanisms include Stress-assisted vacancy diffusion Grain boundary diffusion Grain boundary sliding Dislocation motion

Creep test - Measures the resistance of a material to deformation and failure when subjected to a static load below the yield strength at an elevated temperature. Climb - Movement of a dislocation perpendicular to its slip plane by the diffusion of atoms to or from the dislocation line. Creep rate - The rate at which a material deforms when a stress is applied at a high temperature. Rupture time - The time required for a specimen to fail by creep at a particular temperature and stress.

Stress-rupture curve - A method of reporting the results of a series of creep tests by plotting the applied stress versus the rupture time. Larson-Miller parameter - A parameter used to relate the stress, temperature, and rupture time in creep. Stress-corrosion- A phenomenon in which materials react with corrosive chemicals in the environment leading to the formation of cracks and lowering of strength.

(c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. Creep Behavior Results from a series of creep tests. (a) Stress-rupture curves for an iron-chromium-nickel alloy and (b) the Larson-Miller parameter for ductile cast iron

Mechanical Behavior of Materials

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