Materials Engineering and Technology (MEE 1005) Winter Semester 2021-22 MEE1005 Instructor: Ariful Rahaman Contact Information Instructor: Ariful Rahaman Office: CDMM G-02 E-mail: arahaman@vit.ac.in Tensile Test specimen machine 2 Types of Loading Tensile Test Load data is obtained from Load cell Strain data is obtained from Extensometer 4 Important Mechanical Properties from a Tensile Test Young's Modulus: This is the slope of the linear portion of the stress-strain curve, it is usually specific to each material; a constant, known value. Yield Strength: This is the value of stress at the yield point, calculated by plotting young's modulus at a specified percent of offset (usually offset = 0.2%). Ultimate Tensile Strength: This is the highest value of stress on the stress-strain curve. Percent Elongation: This is the change in gauge length divided by the original gauge length. 5 Terminology Load - The force applied to a material during testing. Strain gage or Extensometer - A device used for measuring change in length (strain). Engineering stress - The applied load, or force, divided by the original cross-sectional area of the material. Engineering strain - The amount that a material deforms per unit length in a tensile test. Engineering Stress- Engineering Strain Engineering Stress- Engineering Strain σ = F/A0 where F is the force and A0 the original area of cross section The engineering stress The engineering strain, ε = (l-l0)/l0 where l is the length of the original gauge length under force F, and l0 is the original gauge length. l l 1 or 1 lo lo LO LO True Stress-True Strain 9 Poissons Ratio Problems Q1: A steel bar is 10 mm diameter and 2 m long. It is stretched with a force of 20 kN and extends by 0.2 mm. Calculate the true/engineering stress and true/engineering strain. Q2:An Aluminium tensile test specimen is 5 mm diameter with a gauge length of 50 mm. The force measure at the yield point was 982 N and the maxiumum force was 1.6 KN. Calculate the yield stress and ultimate tensile stress. At a point on the proportional section the extension was 0.03 mm and the force 800N. Calculate the modulus of elasticity. Q3: A tensile test on a cold worked brass gave the following results. The diameter of the test specimen d= 16 mm and the gauge lenth was 80 mm. After fracture the gauge length was 85 mm and the fracture point was was 15 mm diameter. The maxiumu load was 150 KN. The load and extension at the elastic limit were 70 KN and 0.5 mm, respectively. Calculate the modulus of elasticity. Calculate the % of elongation and % of reduced cross sectional area. Q4: Derive an expression for true strain as a function of D and Do for a tensile test specimen of round cross section, where D = the instantaneous diameter of the specimen and Do is its original diameter. Stress-Strain Diagram ultimate tensile strength 3 UT S necking Strain Hardening yield strength y Fracture 5 2 Elastic region slope =Young’s (elastic) modulus yield strength Plastic region ultimate tensile strength strain hardening fracture Plastic Region Elastic Region σ Eε σ E ε 4 1 σy E ε 2 ε1 ) (DL/Lo) Strain ( Stress-Strain Diagram • Elastic Region (Point 1 –2) - The material will return to its original shape after the material is unloaded( like a rubber band). - The stress is linearly proportional to the strain in this region. σ Eε σ ε or σ E ε : Stress(psi) E : Elastic modulus (Young’s Modulus) (psi) : Strain (in/in) - Point 2 : Yield Strength : a point where permanent deformation occurs. ( If it is passed, the material will no longer return to its original length.) Stress-Strain Diagram Stress-Strain Diagram Mild Steel Problems Q3: A steel bar of 25mm diameter was tested in tension and results were recorded as, limit of proportionality = 196.32kN, load at yield = 218.13kN, ultimate load = 278.20 kN. The elongation measured over a gauge length of 100mm was 0.189mm at proportionality limit, length of the bar between gauge marks after fracture was 112.62mm and minimum diameter was 23.64mm. Compute stress in the specimen at various stages, Young’s modulus, % elongation and % contraction. Q4: Derive an expression for true strain as a function of D and Do for a tensile test specimen of round cross section, where D = the instantaneous diameter of the specimen and Do is its original diameter. Problems Q1: Example: Mechanical Property Determinations from Stress–Strain Plot From the tensile stress–strain behavior for the brass specimen shown in Figure below, determine the following: (a) The modulus of elasticity (b) The yield strength at a strain offset of 0.002 (c) The maximum load that can be sustained by a cylindrical specimen having an original diameter of 12.8 mm (0.505 in.) (d) The change in length of a specimen originally 250 mm (10 in.) long that is subjected to a tensile stress of 345 MPa (50,000 psi) Tensile Properties: Ductility Ductile Materials • A ductile material is one with a large Percentage of elongation before failure. Material Percentage of Elongation Low-Carbon 37% Medium-Carbon 30% High-Carbon 25% Ductile Materials Properties of ductile materials: • • • • Easily drawn into wire or hammered thin. Easily molded or shaped. Capable of being readily persuaded or influenced tractable. Easily stretched without breaking in material strength. Problem Q3: Stress-strain data for a series of alloy steels are described in the figure below. (a) Which of these six steels has the highest yield strength? (b) Which of these steels is the most ductile? (c) For the DP 500/800 Steel, determine the: (i) Yield stress(ii) The tensile stress (iii) The elongation to failure Brittle Materials • Brittle material is one which is having very low percentage of elongation. • Brittle materials break suddenly under stress at a point just beyond its elastic limit. • A Brittle material exhibits little or no yielding before failure. • Brittle material will have a much lower elongation and area reduction than ductile ones. The tensile strength of Brittle material is usually much less than the compressive strength. Problem Q1: Three different materials, designated A, B,and C, are tested in tension using test specimens having diameters of 0.505 in. and gage lengths of 2.0 in. (see figure). At failure, the distances between the gage marks are found to be 2.13, 2.48, and 2.78 in., respectively. Also, at the failure cross sections the diameters are found to be0.484, 0.398, and 0.253 in., respectively. Determine the percent elongation and percent reduction in area of each specimen, and then, using your own judgment, classify each material as brittle or ductile. Problem Q3: (a) Show, for a tensile test, that if there is no change in specimen volume during the deformation process (i.e., Aolo = Aflf). (b) Using the result of part (a), calculate the percent cold work (% CW) experienced by naval brass when a strain value is 0.3. Stress-Strain Diagram of Ceramic/Metal/Polymer Hardness Test A measurement of a material’s resistance to penetration or localized plastic deformation Steps in hardness test: A small indenter is forced into the surface of a material to be tested with certain load. The depth / size of the resulting indentation is measured. Such data are converted to a hardness number. The softer the material, the larger and deeper the indentation, and the lower the hardness number. Hardness tests are performed more frequently than any other mechanical tests Simple / inexpensive nondestructive Other mechanical properties may be estimated from hardness data. Hardness Test •There are many hardness tests currently in use. •The neccessity for all these different hardness tests is due to the need for categorizing the great range of hardness nfrom soft rubber to hard ceramics. Two main types: Brinell and Rockwell Hardness Test Current hardness tests measure either the size of indented area or the depth of penetration (c)2003 Brooks/Cole, a division of Thomson Learning, Inc. Thomson Learning™ is a trademark used herein under license. The size of the indented area is measured The depth of penetration is measured Hardness Test Brinell Hardness Brinell-indenters Hardness Test Brinell Hardness A spherical indenter (10 mm diameter) is shot with 29 kN force at the target Frequently the indenter is steel, but for harder materials it is replaced with a tungsten carbide sphere The diameter of the indentation is recorded The indentation diameter can be correlated with the volume of the indentation. Hardness Test Brinell hardness (HB) is an accurate hardness measurement for soft materials Indenter: a hardened steel or WC sphere (10mm diameter) Load: 500-3000 kg (generally, 3000 kg) Restricted to softer steels or other softer metals Brinell Hardness •The Brinell methods consists of indenting the metal (usually) with a 10 mm diameter steel ball subjected to a load of 3000 kg. •For soft materials the load is reduced to 1500 or 500 kg, as may be required to avoid too deep an indentation •In Brinell Test, the BHN (Brinell Hardness Number) of nearly all materials is influenced by the –The magnitude of the indenting load, –Diameter of the ball indenter and –The elastic characteristics of the indenter ball. Hardness Test Typical HB values Material Softwood (e.g., pine) Hardwood Aluminum Copper Mild steel 18-8 (304) stainless steel annealed Glass Hardened tool steel Rhenium diboride Hardness 1.6 HBS 10/100 2.6–7.0 HBS 1.6 10/100 15 HB 35 HB 120 HB 200 HB 1550 HB 1500–1900 HB 4600 HB Hardness Test Disadvantages: Brinell Hardness the test machine is very heavy. the area of indentation is quite large that it affects the surface quality. This is why, sometimes it is considered as a destructive test. the thickness of the test sample also limits its use, e.g. thin sheets will bulge or be destroyed during the test. for very hard materials, the test results are unreliable. The ball gets flattened on hard surfaces. Hardness Test Rockwell Hardness Rockcell Ball indenters Basic Principle: o The indenter moves down into position on the part surface o A minor load is applied and a zero refernce position is established oThe major load is applied for a specified time period 5 mm carbide ball indenter oThe major load is released leaving the minor load applied Major load of 100 kg (for B-scale) or 150 kg (for C-scale) Rockcell Diamond indenters Hardness Test Rockwell hardness (HR) is the most widely used of all metal hardness testing methods Indenter: a small hardened steel sphere or a diamond cone Load: 10-150 kg The hardness value (based on the depth of penetration) is read directly from either a digital readout or from a rotary dial. For testing steel, the two scales most often used: ----Rockwell B scale (RB) RB 0 to RB 100: softer low-carbon steels, Al, & other softer nonferrous materials ---Rockwell C scale (RC) RC 20 to RC 70: hard steels Hardness Test Rockwell Hardness Rockwell Hardness Scales Scale A Code HRA Load Indenter Use 60 kgf 120° diamond cone Tungsten carbide Al, brass, and soft steels B HRB 100 kgf 1/16 in diameter steel sphere C D HRC HRD 150 kgf 100 kgf 120° diamond cone 120° diamond cone E HRE 100 kgf 1/8 in diameter steel sphere F HRF 60 kgf 1/16 in diameter steel sphere G HRG 150 kgf 1/16 in diameter steel sphere Harder steels 40 RHB indicates Rockwell hardness of 40 measured on B-scale 80 RHC indicates Rockwell hardness of 80 measured on C-scale Hardness Test Conversion of Hardness Conversion of hardness Standard hardness conversion tables Correlation between hardness & tensile strength For most steels, UTS(MPa) = 3.45 x HB Hardness Test Summary of Hardness Tests Hardness Test Indenter Load Brinell hardness (HB) hardened steel or WC sphere (10mm diameter) 500-3000 kg small hardened Rockwell hardness steel sphere or a (HR) diamond cone 10-150 kg Problem Q2: A cylindrical specimen of cold-worked steel has a Brinell hardness of 240. (a) Estimate its ductility in percent elongation. (b) If the specimen remained cylindrical during deformation and its original radius was 10 mm, determine its radius after deformation. Problem Q3: (a) Show, for a tensile test, that if there is no change in specimen volume during the deformation process (i.e., Aolo = Aflf). (b) Using the result of part (a), calculate the percent cold work (% CW) experienced by naval brass when a strain value is 0.3. Mechanisms of Strengthening in Metals Grain size reduction Solid solution alloying Strain hardening Precipitation Hardening Strengthening by Grain Size Reduction The grain boundary acts as a barrier to dislocation motion for two reasons Difficulty for a dislocation to pass through two different grain orientations The atomic disorder within a grain boundary region contributes to a discontinuity of slip planes from one grain to another Cont… A fine grained material is harder and stronger than one that is coarse, since the former has a greater total grain boundary area to impede dislocation motion. The relationship between the yield stress and grain size was pproposed by Hall and Petch σy Yield stress Cont… Solid Solution Strengthening Lattice strains produced by the introduction of solute atoms can be divided into: Compressive lattice strain Tensile lattice strain Solid Solution Strengthening Strain Hardening Cont… Precipitation Hardening Precipitation hardening is accomplished by two different heat treatments. Solution heat treatment is a heat treatment in which all solute atoms are dissolved to form a single phase solid solution. For an alloy of composition Co, 1. heat the alloy to a temperature within a phase field—To, and wait until all the β phase is completely dissolved. 2. rapid cool to temperature T1 to the extent that any diffusion and the formation of β phase are prevented. 3. a nonequilibrium situation of a phase solid solution supersaturated with B atoms is present. Precipitation heat treatment The supersaturated a solid solution is ordinarily heated to temperature T2 within the α + β two-phase region. 2. keep temperature and the β precipitate phase begins to form as finely dispersed particles of composition Cβ (aging). 3. after an appropriate aging time at T2, the alloy is cooled to room temperature. How the dislocations can interact with a particle? Strain Hardening Cold-Working: A process of strain hardening at room temperature to deform the material beyond the elastic range to obtain a desired property. Increase yield strength; Decrease ductility Examples of cold-working: rolling, drawing, extruding, cutting, pulling, indenting… Q1: A cylindrical rod having an initial diameter of 6 mm is to be cold worked (CW) such that cross-sectional area is reduced and final diameter is 5 mm. Determine % CW. If % CW = 20 and final diameter = 5 mm, determine original diameter? Toughness The ability of a metal to deform plastically and to absorb energy in the process before fracture is termed toughness. Fracture/Failure • The fracture of any material occurs in two steps: Crack formation Crack propagation • The failure of engineering materials is classified in terms of being: Ductile: significant plastic deformation prior to fracture Brittle: little or no plastic deformation prior to fracture Fracture behavior: %AR or %EL Very Moderately Brittle Ductile Ductile Large • Ductile fracture is usually desirable! Moderate Ductile: warning before fracture Small Brittle: No warning Example: Failure of a Pipe • Ductile failure: --one piece --large deformation • Brittle failure: --many pieces --small deformation Figures from V.J. Colangelo and F.A. Heiser, Analysis of Metallurgical Failures (2nd ed.), Fig. 4.1(a) and (b), p. 66 John Wiley and Sons, Inc., 1987. Used with permission. Ductile Fracture Ductile fracture of many engineering metals results in a “cup and cone” fracture surface. Coalescence Small cavity of Initial necking formation cavities to form a crack. This is created by a process known as microvoid coalescence. Crack propagation Final shear fracture Cont… Cup-and-cone fracture in aluminum. ductile fracture from uniaxial tensile loads ductile fracture from shear loading Brittle Fracture • Brittle fracture involves very little plastic deformation The fracture surface is usually flat and perpendicular to the applied stress. • A brittle fracture surface often shows Chevron markings, or a series of fan-like ridges or “river pattern” Chevron Brittle fracture in a mild steel. fan-like ridges Cont… • Crack propagation in brittle fracture can be either: Transgranular: through the grains (also called cleavage) Intergranular: along the grain boundaries. In both cases, the surface usually appears shiny because the facets reflect light. Cont… Crack propagation through the ineterior of grains for transgranular fracture Ductile cast iron showing a transgranular fracture surface Crack propagation along grain boundaries for Intergranular fracture Intergranular fracture surface IMPACT FRACTURE TESTING In pendulum type impact testing, the impact load is produced by swinging of an impact weight (W = m * g) from initial height (h) through the arc of a circle, thus striking and fracturing the notched specimen. After that, the weight reaches maximum height (h/). Negclecting frictional losses, the energy used to fracture the specimen (U) is then approximately defined as: Absorbed Energy = Initial Potential Energy – Final Potential Energy (energy to rupture) (energy before rupture) (energy after rupture) U = m * g * (h – h/) The absorbed energy (U), indicated on the scale of tester, is expressed in joule (i.e. N*m) .This energy value is sometimes called “impact toughness”. 62 IMPACT FRACTURE TESTING The Impact test measures a materials ability to absorb energy. This quality is often referred to as the Toughness of the material. Charpy Izod Two standardized test: Izod and Charpy Tested samples Ductile to Brittle Transition Temperature (DBTT) Deformation should be continuous across grain boundary in polycrystals for their ductile behaviour 5 independent slip systems required (absent in HCP and ionic materials) FCC crystals remain ductile upto 0 K Common BCC metals become brittle at low temperatures or at v.high strain rates f , y → y f Brittle Ductile T → DBTT Ductile – brittle transition temperature (DBTT) Ductile y < f yields before fracture Brittle y > f fractures before yielding f , y → Ductile to Brittle Transition Temperature (DBTT) f y (BCC) y (FCC) T → DBTT No DBTT Ductile y < f yields before fracture Brittle y > f fractures before yielding Ductile to Brittle Transition Temperature (DBTT) • Increasing temperature... --increases %EL and Kc • Ductile-to-Brittle Transition Temperature (DBTT)... Impact Energy FCC metals (e.g., Cu, Ni) BCC metals (e.g., iron at T < 914°C) polymers Brittle More Ductile High strength materials ( y > E/150) Temperature Ductile-to-brittle transition temperature Design Strategy: Stay Above The DBTT! • Pre-WWII: The Titanic Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(a), p. 262, John Wiley and Sons, Inc., 1996. (Orig. source: Dr. Robert D. Ballard, The Discovery of the Titanic.) • Problem: • WWII: Liberty ships Reprinted w/ permission from R.W. Hertzberg, "Deformation and Fracture Mechanics of Engineering Materials", (4th ed.) Fig. 7.1(b), p. 262, John Wiley and Sons, Inc., 1996. (Orig. source: Earl R. Parker, "Behavior of Engineering Structures", Nat. Acad. Sci., Nat. Res. Council, John Wiley and Sons, Inc., NY, 1957.) Used a type of steel with a DBTT ~ Room temp. Fatigue Fatigue is a form failure that occurs in structures subjected to dynamic and fluctuating stresses. Estimated to comprise approximately 90% of all metallic failures. Fatigue failure is brittle like in nature even in normally ductile metals. The fatigue occurs by the initiation and propagation of cracks. Fatigue under cyclic/repeated loading Cracks generally grow under repeated loading Trucks passing over bridges, Bicycle pedals May result failure or fracture: fatigue fracture Periodic inspections required for fatigue critical systems Thermal fatigue: repeated heating and cooling can cause a cyclic stress due to differential thermal expansion and contraction Fatigue Fatigue failures are often easy to identify. The fracture surface near the origin is usually smooth (Beach mark-crack initiation point). The surface becomes rougher as the crack increases in size. Concentric line patterns: the slow cyclic build up of crack growth from a surface intrusion. Line patterns are on a much finer scale and show the position of the crack tip after each cycle. Granular portion of the fracture surface: rapid crack propagation at the time of catastrophic failure Crack Initiation and Propagation Three distinct steps of fatigue failure crack initiation, wherein a small crack forms at some point of high stress concentration Crack propagation, during which this crack advances incrementally with each stress cycle Final failure, which occurs very rapidly once the advancing crack has reached a critical size The total number of cycles to failure is the sum of cycles at the first and the second stages Number of cycles for crack initiation Number of cycles to failure Nf = Ni + Np Number of cycles for crack propagation Fatigue: Cyclic Stresses Revised stress cycle; in which the stress alternates from A maximum tensile stress (+) to a maximum compressive Stress(-) of equal magnitude. Repeated stress cycle; in which maximum and minimum stresses are asymmetrical relative to the zero stress level. Random stress cycle Concepts Constant amplitude stressing Mean stress Stress amplitude (half of the range) variation about the mean Stress ratio R, Amplitude ratio Fatigue Test Fatigue testing apparatus for making rotating bending tests Result is plotted as S (stress) vs N(number of cycles to failure The most important fatigue data for engineering designs are the S-N curves, which is the Stress-Number of Cycles curves. In a fatigue test, a specimen is subjected to a cyclic stress of a certain form and amplitude and the number of cycles to failure is determined. The number of cycles, N, to failure is a function of the stress amplitude, S. A plot of S versus N is called the S-N curve. Fatigue: S-N Curve Fatigue Design Parameters • Fatigue limit, Sfat: S = stress amplitude --no fatigue if S < Sfat unsafe case for steel (typ.) Sfat safe 103 • Sometimes, the fatigue limit is zero! 105 107 109 N = Cycles to failure S = stress amplitude unsafe safe 103 105 107 109 N = Cycles to failure Adapted from Fig. 8.19(a), Callister 7e. case for Al (typ.) Adapted from Fig. 8.19(b), Callister 7e. Fatigue: S-N Curve Fatigue Limit: •For some materials such as BCC steels, the S-N curves become horizontal when the stress amplitude is decreased to a certain level. •This stress level is called the Fatigue Limit, or Endurance Limit. Fatigue Strength: For materials, which do not show a fatigue limit such as Al, Cu, and Mg (non-ferrous alloys), fatigue strength is specified as the stress level at which failure will occur for a specified number of cycles, where 107 cycles is often used. • Fatigue life: indicates how long (no. of cycles) a component survives a particular stress. Fatigue strength: is applicable to a component with No endurance limit. It is the maximum stress for which fatigue will not occur at a particular number of cycles, in general, 108 cycles for metals. Endurance ratio: the endurance limit is approximately ¼ to ½ the tensile strength. Factors that affect fatigue life Magnitude of stress (mean, amplitude...) Quality of the surface (scratches, sharp transitions and edges). --Method 1: shot peening --Method 2: carburizing C-rich gas shot put surface into compression Solutions: Polishing (removes machining flaws etc.) Introducing compressive stresses (compensate for applied tensile stresses) into thin surface layer by “Shot Peening”- firing small shot into surface to be treated. High-tech solution - ion implantation, laser peening. Case Hardening - create C- or N- rich outer layer in steels by atomic diffusion from the surface. Makes harder outer layer and also introduces compressive stresses Optimizing geometry - avoid internal corners, notches etc. 2. Remove stress concentrators. bad better Adapted from Fig. 8.25, Callister 7e. bad better Factors that affect fatigue life Thermal Fatigue: is induced at elevated temperatures by fluctuating thermal stresses. The Origin of these thernmal stresses is the restraint to the dimensional expansion and cotraction Improving Fatigue Life Eliminate restraint by design use materials with low thermal expansions. Corrosion Fatigue: failure that occurs by the simultaneous action of a cyclic stress and Chemical attack. Improving Fatigue Life add protective surface coating decrease corrosiveness of medium Add residual compressive stresses Creep Time -dependent deformation which occurs when materials are loaded above 0.4 Tmelt Sample deformation at a constant stress () vs. time , 0 t Primary Creep: slope (creep rate) decreases with time. Secondary Creep: steady-state i.e., constant slope. Tertiary Creep: slope (creep rate) increases with time, i.e. acceleration of rate. Creep: Parameters Most of component life spent here. Strain rate is constant at a given T, σ Steady state creep rate On the other hand, for many short life creep situations, time to rupture or the rupture lifetime tr, is the dominant design Creep: Stress and Temperature Effects With increasing stress and temperature The instantaneous strain at the time of stress application increases Steady state creep rate is increased The rupture lifetime is diminished stress exponent (material parameter) activation energy for creep (material parameter) strain rate Applied stress material const. Alloys For High Temperature Use Gas turbine, high temperature steam boilers, heat treating furnaces, aircraft, missiles etc Creep is generally minimized in materials with: high melting temperatures high elastic modulus large grain sizes Following materials are resilient to creep: Refractory metals, like Nb, Mo, W etc. Stainless Steel Superalloys , Co-Ni based