FACULTY OF ENGINEERING UNIVERSITY OF MAURITIUS Mechanical properties of Materials UTOSP 1293 Basics of Metallurgy Prepared by s. Venkannah MECHANICAL PROPERTIES Engineers are basically concerned with the development of machines, structures and products of various kinds. Since these constructions are usually subjected to loads and deformations, the properties of materials under the action of loads and deformation so produced for various environments become an important engineering consideration. The macroscopic properties of materials under load or force are broadly classed as mechanical properties. They are a measure of strength and lasting characteristics of a material in service and are of great importance particularly to the design engineer. Materials are selected by matching its properties to the service conditions required. Standard tests available; Destructive testing Non destructive testing. Give some examples of Destructive testing and Non-destructive testing. Destructive Testing- a proper sampling is important so that properties deduced from the test are representative of the material as a whole. It is important to note that: Properties may not be the same in all directions Properties of a product may not be the same in all parts of the material There may be different loading conditions and service conditions TENSILE TEST The tensile test is one of the most frequently used methods for determining the strength and ductility of a material. The test involves and axial load being applied to a standard specimen of circular or rectangular cross-section. The load is increased at a constant rate by mechanical or hydraulic means and this causes the specimen to elongate and finally fracture. During testing the sample is gripped at each end and in order to ensure simple uni-axial loading and to avoid fracture occurring in the region being gripped, the mid portion of the sample has a reduced cross section. This reduced section is marked with a standard length (the gauge length) from which the elongation of the specimen is measured. A plot of the elongation ΔL against load F produces a curve similar to that shown in Fig 1 below, From such graphs the following quantities can be obtained: The tensile strength, being the stress corresponding to the maximum force The yield stress, being the stress at which the material begin to yield and show plastic deformation without any increase in load 1
The proof stress, being the stress at which non proportional is equal to a specified percentage of the gauge length The tensile modulus (young s modulus) being the slope of the stress-strain graph over its proportional region. The percentage reduction in area and the percentage elongation. Mark the following points/regions on the curve (Fig 1); The elastic region The elastic limit, A The plastic region Uniform plastic deformation Localised plastic deformation (Necking) The initial part of the plot, up to the elastic limit (A), is linear and the specimen behaves in an elastic manner ie. Hooke s Law is obeyed. State Hooke s Law. If the load is released the specimen will return to its original dimensions, provided the limit of elasticity has not been exceeded. The slope of the line in the elastic region enables the Young s Modulus (E) to be determined, E = Stress/Strain = (F.L o )/( A o ΔL )= (F /ΔL) * (L o / A o ) = Slope of the elastic part of the graph * (L o / A o ) Where: F Applied Force ΔL Extension L o - Original gauge length of the specimen A o - The original cross sectional area 2
The total elastic extension that takes place is usually very small, less than.%, (e.g. for ordinary steel the elongation in the elastic stage is about.1 in per 1 in gauge length) and therefore very sensitive measuring instruments called extensometers is necessary to measure the extension in the elastic region. These instruments grip the specimens at two points on the gauge length and the separation of these points is measured during the test by either a dial gauge or an electrical transducer. Beyond point A the load/elongation curve deviates from linearity due to the specimen deforming in a plastic manner. If the load is released after the specimen has been deformed in this part of the curve, then the elastic extension will be recovered as before but it will be found that the specimen has also undergone a permanent extension. The point where the load-elongation graph ceases to be a straight line is called the limit of proportionality, and this is calculated by dividing the applied load at that point by the original cross section area of the specimen. Just beyond the limit of proportionality certain ductile materials, metals or polymers, may undergo sudden extension without a corresponding increase in load and this is referred to as the yield point. In some cases (e.g. mild steel) the load may fall temporarily producing an upper and lower yield point. The yield stress is calculated by dividing the load at yield by the original cross sectional area of the specimen. Draw the stress-strain curve for a mild steel specimen showing the upper and lower yield point. For materials that do not show a well defined yield point an offset yield stress is normally quoted. This is t he stress required to produce a specified amount of plastic deformation and is determined by drawing a line parallel to the elastic part of the graph but which is offset by an extension corresponding to.1% (or other specified amount) of the gauge length. The load at the point where the line intersects the tensile curve is determined and then divided by the original cross sectional area. For metals this offset yield stress is normally referred to as.1% proof stress. The proof stress is the stress that will cause a certain amount of permanent set because in many materials the stress at which the material changes from elastic to plastic behaviour is not easily detected. With the help of a stress-strain curve explain how the.2% proof stress of a material can be determined. Some materials, such as certain polymers and annealed copper, do not have a linear region on the curve and so the offset yield stress and Young s modulus cannot be determined. In these cases the yield stress is defined as the load to produce a total extension of.% of the gauge length divided by the original cross sectional area. In place of a Young s modulus a secant modulus is defined. The slope of the line drawn from the origin to a point on the load extension curve corresponding to an extension of.% is determined and multiplied by L o / A o. 3
With the help of a stress-strain curve explain how the.% secant modulus of a polymer can be determined. After appreciable plastic deformation has occurred the load-elongation curve reaches a maximum value. At this point the specimen has started to undergo localised plastic deformation, or necking down as it is usually called. The reduced cross sectional area in the necked region means that further deformation can occur at reduced load and hence the load/elongation curve now falls until failure finally takes place. The ultimate tensile strength.,(or Tensile Strength) of a material is calculated by dividing the maximum load by the original cross sectional area. Mark the following points on the load- extension (stress-strain) curve (Fig 1) The Fracture Strength, B The limit of proportionality, C The Ultimate Tensile Strength (UTS), D Tensile test also gives an indication of the ductility of a material. The ductility of a material can be measured in terms of the percentage reduction in area and the percentage elongation. The ductility of material is the ability of the material for being drawn plastically before failure. The ductility of the material will determine the amount of extension of the material before fracture. As the material elongates, the cross sectional area decrease. Hence a material having a high ductility will extend by a large amount and its area will decrease by a large amount. Ductile fracture: The rupture of a material after considerable amount of plastic deformation. Materials begin to neck beyond the UTS which is the max. point in the stress-strain curve. Brittle fracture: The failure of a material without apparent plastic deformation. If 2 pieces of a brittle material are fitted together, the original shape and dimensions of the specimen are restored. % Reduction in area= ((A o -A f ) / A o ) * 1 Where: A o - The cross sectional area of the specimen before testing A f The minimum cross sectional area of the specimen after fracture % Elongation = ((L f - L o ) / L o ) * 1 Where: L o - The original gauge length of the specimen before testing A f The final distance between the gauge length after fracture There is a Hounsfield tensometer in the Structural Mechanics Lab which is used to perform tensile tests on metals. Standard specimens are required. The specimen is held between grippers on the machine. It is then loaded at one end of the tensometer by a mechanical screw arrangement which is turned manually. The other end of the specimen is attached to a calibrated spring beam, the deflection of which is proportional to the applied load. This beam deflection is measured by a lever system which displaces mercury up a glass capillary tube. The movement of the mercury is followed by a cursor to which is attached a needle which can be used to punch out the value of the load onto graph paper at intervals. The graph paper 4
is mounted on a drum which rotates by an amount proportional to the elongation of the sample, the final result is a load/elongation curve onto the graph paper. The stress-strain curves for 4 materials are shown below. Which of the materials is (a) the most ductile (b) the most brittle (c) the strongest (d) the stiffest The modulus of resilience, Er, is the area under the stress-strain curve i.e. the elastic energy that a material absorbs during loading and subsequently releases when the load is removed. Compare the Young s Modulus and the tensile strength of some commonly used metals and alloys. The Poisson s ratio, μ, is the ratio; μ = - lateral strain longitudonal strain In many ductile materials, deformation does not remain uniform. At some point one region deforms more than others and a large local decrease, necking, in the cross sectional area occurs. The cross sectional area becomes smaller at this point, a lower force is required to continue its deformation. The engineering stress is the stress calculated from the original cross sectional area whereas the true stress is load at fracture divided by the actual cross sectional area after fracture.
THE BEND TEST In brittle materials (e.g. ceramics) failure occurs at the maximum load where yield strength, tensile strength and breaking strength are the same. The flexural strength and the flexural modulus are used instead to compare the properties of the materials. The flexural modulus is the modulus of elasticity in bending. Flexural strength = (3Fl)/ (2wh 2 ) Flexural modulus = (l 3 F)/ (4wh 3 δ) Where : F Fracture load l distance between the supports w- width of the plate h height of the plate δ - deflection of the plate IMPACT TEST Many materials, including steels, are prone to fracture in a brittle manner- very little plastic deformation takes place before failure. Crack growth during brittle fracture absorbs very little energy. It is also extremely rapid and occurs without any warning. The fracture surfaces have a faceted appearance sine the crack has a tendency to grow along specific crystallographic planes, called cleavage planes. The fracture surface may also show chevron markings which run back towards the origin of failure. Brittle fracture is accentuated if the material is subjected to triaxial stresses, a rapid rate of loading or low temperatures. The notched bar impact test was devised to simulate these conditions, as to test the resistance of a material to failure under the most unfavourable conditions of loading that might be encountered in service. The principle is simple; a notched specimen is struck and fractured by a swinging pendulum and the fraction of kinetic energy of the pendulum used to fracture the specimen is measured. The notch in the specimen provides a triaxial stress situation so that the test is a measure of the strength of a material under a triaxial state of stress. However, the numerical value obtained from the test cannot be translated directly to the design of large engineering components since t he results obtained from a small notched specimen will not be the same as those from an identical notch in a large component. The usefulness of the test lies in indicating whether the heat treatment or fabrication of a material has been carried out correctly. Toughness is the ability of the material to resist impact loads. Two commonly used impact tests are Charpy s Impact Test Izod s Impact Test The Izod s Impact test uses a notched specimen that is gripped at one end and held in a vertical plane. The specimen face that contains the notch is struck by a swinging pendulum released from a standard height. Some of the kinetic energy of the pendulum is used to fracture the specimen so that the pendulum swings to a point on the opposite side of the machine that is lower that the initial height from which the pendulum was released. The impact machine usually incorporates a scale that enables the value of this fracture energy to 6
be read off direct. Test pieces have standard dimensions and the strike energy of 16 J for metals and 2-2 J for polymers. The results for Izod s test for metallic materials are expressed as the number of Joules (J) required to fracture the standard sized specimen, whereas in the case of polymers the result is expressed as energy to fracture per unit area of specimen behind the notch (J/mm 2 ). The Charpy s Impact test uses a notched specimen that is supported as a simple beam and which is struck from a position behind the notch. The strike energy is 32 J for metals and.- J for polymers. The energy to fracture the specimen is measured in a similar way to that described for the Izod s test. Results for metallic specimens are expressed as the energy (J) to fracture the standard specimen, for polymers results are expressed as energy per unit area of fractured surface (J/mm 2 ). Draw a properly labelled schematic diagram of the Impact testing machine. Draw the test pieces (with dimensions) and the loading arrangements for the Izod s and Charpy s Impact tests. There has been many instances in the past of failure of metals by unexpected brittleness at low temperatures. The behaviour of materials under impact loads also depend on temperatures. The notched bar tests bar described above does not consider the temperatures of the specimens. To account of this fact the impact test can be conducted over a range of temperatures. Such tests reveal that many ductile materials become brittle over a relatively small temperature range as the temperature of testing is lowered. This is referred to as the ductile to brittle transition and for steel frequently occurs in the temperature interval to + C. Above the transition, failure takes place in a ductile manner, with extensive plastic deformation resulting in large amounts of energy being absorbed during the fracture process. Below the transition, failure occurs in a brittle manner, very little plastic deformation takes place and therefore very little energy is absorbed during fracture. Under normal conditions the stress required to cause cleavage is higher than the stress required to cause slip, but if, by some circumstances slip is suppressed, brittle fracture will occur when the internal stress increases to the value necessary to cause failure. As temperature decreases, the movement of dislocations becomes more difficult and this increases the possibility of internal stresses exceeding the yield stress at some point. Draw the Impact energy-temperature curve showing the ductile to brittle transition for ferritic and austenitic steels The transition from ductile to brittle behaviour takes place over a finite range of temperature and therefore we cannot say a material is ductile above a single specific temperature and brittle below it: we need to define the transition in some way. It is relatively easy to distinguish between the cleavage areas from the ductile areas of the fracture surface without the aid of the microscope. The cleavage areas are faceted and have a high reflectivity and bright appearance. The ductile areas are rough and fibrous and therefore have a much lower reflectivity. 7
Materials which show a ductile to brittle transition include BCC metals, HCP metals, polymers and ionic crystals. HARDNESS TEST. Hardness : Resistance of a surface to abrasion or penetration Hardness of a material may be specified in terms of some standard test involving indentation or scratching of the surface of the material. Some standard test are: Rockwell s Hardness Number (RHN) Brinell s Hardness Number (BHN) Vicker s Hardness Number (VHN) Knoop s Hardness Number (KHN) Draw the a labelled schematic diagram of the hardness testing machine FIG: Variation in properties of steel with increase in %C Rockwell s: uses a diamond cone or a steel ball and the RHN is given in terms of the depth of penetration or indentation. Various Rockwell scale (A-K) can be used depending on the indenter and load combination. Quickly made test and can be fitted in a production line. The impression is between Vicker s and Brinell s. Surface irregularity can be accommodated because of minor loads to initially locate the indentor. DIS: Not as accurate as Vicker s 8
BRINELL S: uses a hardened steel ball indenter and the BHN is given by BHN = applied force Surface area of impression Limitations Large impression and may act as stress raiser in a component May be unacceptable on grounds of surface finish The large depths precludes its use on plated or surface hardened components. Very hard materials will deform the indenter 9
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Vickers s: Uses a diamond square pyramid indenter and the VHN is given by VHN = applied force Area of indentation Suitable for hard as well as soft materials. No need to use the F/D 2 ratio for material as all impressions are geometrically similar. The Vicker s hardness range is proportional so that a material. Having VPN 4 is twice as hard as one having VPN 2 Limitations: Impression is small and the surface of the material must be polished flat. It takes a relatively long time to perform a Vicker s hardness test. Vicker s machine are more expensive than Rockwell s and Brinell s Testing machines Knoop s: uses a rhomic diamond indentor The Shore Scleroscope- a small diamond tipped tup allowed to fall on the specimen. The rebound height is measured. The harder the material, the higher the rebound. THE CREEP TEST. If we apply a stress to a material at an elevated temperature, the material may stretch and eventually fail even though the applied stress is less than the yield strength at that temperature. Plastic deformation at high temperature under a constant load is known as creep. Draw a typical creep curve showing the strain produced as a function of time for a constant stress and temperature. Show the following regions on the curve; primary creep, secondary creep and tertiary creep. Primary or transient creep- beginning at a fairly rapid rate which t hen decrease with time because work hardening sets in. Secondary or steady state creep in which the rate of strain is uniform and at its lowest value. Tertiary creep in which the rate of strain increase rapidly until fracture THE FATIGUE TEST. Many components are subjected to fluctuating loads, taking place at relatively high frequencies and under these conditions failure is found to occur at stress values much lower than that would apply for static loading. Fatigue test is the failure of a component under the action of an alternating load. The cyclical stress may occur as a result of rotation, bending or vibration. In many cases the material failed when the applied stress is below the yield strength. Failure by fatigue typically occurs in 3 stages : 1. A tiny crack initiates at the surface 2. Crack propagates as the load continues to cycle 3. Sudden fracture of material when cross section is too small to support the applied load The rotating cantilever beam test is used to test the resistance of a material to fatigue. One end of a machined, cylindrical specimen is mounted in a motor driven chuck. A weight is 11
suspended form the opposite end. Initially there a tensile force on the top and the bottom surface is compressed. After specimen rotates through 9, the locations that were in tension and compression have no stresses acting on them. After half a revolution, the material originally in tension is now in compression and the part in compression is now in tension. After a large number of rotations. the specimen may fail. The results is presented as a Stressnumber of cycles curve. The logarithmic scale is used for the number of cycles. Draw a Stress-Number. of cycles curve for a typical metal (mild steel) and a polymer showing all the important quantities Fatigue life how long a component survives a particular stress Endurance limit (fatigue limit)- the stress below which there is a % probability that failure will never occur. Fatigue strength- Maximum stress for which fatigue will not occur with a particular number of cycles. Necessary for polymers and Aluminium as they do not have the endurance limit. Endurance ratio = Endurance limit Tensile strength What do you understand by the following properties machinability, castability, malleability and weldability? STANDARD A standard is a technical specification drawn up with the aims of benefiting all concerned by ensuring consistency in quality, rationalising processes and methods of operation, promoting economic production methods providing a means of communication, protecting consumer interests, encouraging safe practices, and helping confidence in manufacturers and users. There are thousands of standards laid down by national and international bodies e.g. Bsritish Standards Institution (BS), American Society of Testing and Materials (ASTM), American Welding Society (AWS), International Organisation for Standardization (ISO), German Standards (DIN), Indian Standards (IS), Mauritius Standard Bureau (BS) etc DATA SOURCES: Data on the properties on materials is available from a range of sources such as: Specifications issued by bodies responsible for standards e.g. BS, ASM, ASTM, MS Data books e.g. ASM metal reference book (American Society for Metals, 1983), Metals Reference Book (by R. J. Smithells, Butterworth, 1987), Metals Databook (by C. Robb, The Institute of Metals, 1987), Handbook of Plastics and Elastomers (edited by C. A. Harper, Mc Graw Hill, 197), Newnes Engineering Materials Pocket Book (by W. Bolton, Heinemann-Newnes, 1989) Computerised databases which give materials and their properties e.g Cambridge Materials Selector Trade Associations e.g. the Copper Development Association, Zinc Development Association, Aluminium Federation Data sheets supplied by the suppliers In company tests- These are used to check samples of a bought in material to ensure that it conforms to the standards specified by the supplier. 12
Reference : Tensile and Impact Properties of metals by Dr. B. Noble, Tecquipment Ltd. Engineering Metallurgy by R. Higgins, th Ed. Materials Science and Engineering by Callister, 2 nd Ed. Materials for Engineering by W. Bolton Own notes Problems: UNIVERSITY OF MAURITIUS FACULTY OF ENGINEERING Tutorial 2 1. The following results were obtained from a tensile test of an aluminium alloy. The test piece had a diameter of 11.28 mm and a gauge length of 6 mm. Plot the stress-strain graph and determine (a) the tensile modulus (b) the.1% proof stress the modulus of resilience. Loa d/k N Ext/ mm 2.. 7. 1. 12. 1.8 4. 6.2 8.4 1. 1. 12. 17. 14. 6 2. 16. 3 22. 19. Loa d/k N Ext. / mm 2. 27. 3. 21.2 23. 2. 7 32. 28. 1 3. 31. 37. 3. 38. 4. 39. 61. 39. 86 2. The following results were obtained from a tensile test of a polymer. The test piece had a width of 2 mm, a thickness of 3mm and a gauge length of 8 mm. Plot the stress-strain graph and determine (a) the tensile strength (b) the secant modulus at.2% strain Load /kn 1 2 3 4 6 6 63 Ext. /mm.8.17.3.9.88 1.33 2. 2.4. 3. The following results were obtained from a tensile test of a steel specimen. The test piece had a diameter of 1 mm and a gauge length of mm. Plot the stress-strain graph and determine (a) the tensile strength (b) the.1% proof stress the yield stress and (d) the tensile modulus. Load/kN 1 1 2 2 3 32. 3.8 Ext./mm.16.33.49.6.81.97.16.2 4. The following data was obtained from a tensile test on a stainless steel test piece. Determine (a) the limit of proportionality stress (b) the tensile modulus the.2% proof stress. 13
Stress/ Mpa 9 17 2 34 49 6 7 76 8 84 88 89 Strain/ 1 1 2 3 4 6 7 8 9 1 x1-4. Describe the process through which a material undergoes (I) Ductile fracture (ii) Brittle fracture (crack formation and propagation, fracture surfaces ) 6. Describe two commonly used impact testing techniques. 7. What do you understand by the Ductile to Brittle transition of a material? 8. Fatigue and Creep are two common forms of failure. Explain the terms (I) fatigue (ii) creep. 9. Describe tests to predict the lifetime of components subjected to fatigue creep. (paying attention to terms such as fatigue limit, fatigue life, fatigue strength, steady state creep rate.) 1. List the factors that affect the fatigue life. 11. List measures to increase the resistance to fatigue of a metal alloy. 12. Give metallurgical/processing techniques that can be employed to enhance creep resistance of metal alloys. 13 The following data were collected from a 3.2 x 19.1mm rectangular test specimen of magnesium; LOAD (N) EXTENSION (mm) 138.3 278.8 63.13 743.2 814.2 987.64 128 1.91 141 3.18 1434 4.4 1383.72 12 6.99 (fracture) The initial length of the specimen was 63. mm and the final cross sectional area was 8.42 mm 2. Plot the stress - strain curve and hence determine; (a) the Young s modulus of elasticity (b) the modulus of resilience (c) the tensile strength (d) the.2% proof stress (e) the percentage elongation (f) the percentage reduction in area (g) the true stress at fracture 14 Differentiate between : 14
(i) toughness and hardness (ii) engineering stress and true stress (iii) yield strength and tensile strength (iv) creep and fatigue 1 Explain what you understand by the following terms (I) fatigue (ii) creep (iii) hardness, (iv) toughness (v) Ultimate tensile stress. 16. The following results were obtained from a tensile test on a 2-mm diameter S.G. cast iron specimen having a gauge length of 4 mm. Load (kn) Extension (mm) 2.18.37 7. 9.2 1.6 12 1.6 131 4. ( Maximum Load) 12 7.2 (fracture) After fracture, the gauge length is 47.42 mm and the diameter is 18.3 mm. Plot the data and calculate (a) the.2% proof strength (b) the tensile strength (c) the modulus of elasticity (d) the % elongation (e) the % reduction of area (f) the engineering stress at fracture (g) the true stress at fracture, and (h) the modulus of resilience. 17 What mechanical properties of a material are determined by tensile testing? What valuable information can be determined from the results of a tensile tests? 18 What is the difference between a ductile material and a malleable material? 1