Fundamentals of Mechanical Properties of Metals PDF

Fundamentals of mechanical properties of metals Prof. Pasquale Russo Spena  Mechanical Properties in Design and Manufacturing Mechanical properties determine a material’s behavior when subjected to mechanical stresses  Propert...

Fundamentals of mechanical properties of metals Prof. Pasquale Russo Spena  Mechanical Properties in Design and Manufacturing Mechanical properties determine a material’s behavior when subjected to mechanical stresses  Properties include elastic modulus, ductility, hardness, and various measures of strength Resiseuze )  Dilemma: mechanical properties desirable to the mechanical designer, such as high strength, usually make manufacturing more difficult elevata resistenza  The manufacturing engineer should appreciate the design viewpoint  And the design engineer should be aware of the manufacturing viewpoint P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 2  Stress-Strain Deformation processes in manufacturing mainly involve strains of these types: a) Tensional (tensile stress), tend to stretch the material b) Compressional (compressive stresses), tend to squeeze it c) Torsional (shear stresses), tend to cause adjacent portions of material to slide against each other Linear deformation: Angular deformation: P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 3  Stress-Strain Relationships Tensile Test Gurre shoxz teloxmazione Stress-strain curve - basic relationship that describes mechanical properties for all three types of stress (tensile, compressive, and shear stresses). Tess diTraziome Tensile test is the most common test for studying stress-strain relationship, especially metals (simple and many info about metals can be evaluated). In the tensile test, a force pulls the material, elongating it (and reducing its diameter for the constancy of volume) up to fracture. P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 4  Tensile Test Specimen ISO (International Standard Organization) - UNI EN ISO 6892 ASTM (American Society for Testing and Materials) - ASTM E8 Campiona ) specify how to prepare test and specimen L0 A0 A0 Dogbone sample from sheet and plate - Dogbone sample from bulk part P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 5  Tensile Test Setup In a tensile test, crosshead speed is kept constant (e.g., 1-10 mm/min) and the resistance of the samples to this movement is measured by a load cell. v P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 6  Tensile Test Setup Example of tensile test P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 7  Tensile Test Sequence Typical progress of a tensile test: (1) beginning of test, no load; (2) uniform elongation and reduction of cross-sectional area; (3) continued elongation, maximum load reached; (4) necking begins, load begins to decrease; and (5) fracture. If pieces are put back together as in (6), final length can be measured. A1 A2 A3 F3 A0 F2 F11 deformation localizethere S Volume costout is , F1 F2 The deformatio is costant F3 P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 8  Engineering Stress Defined as force divided by original area*: F e  Ao Where: S =e = engineering stress, F = applied force Ao = original area of test specimen *Engineering stress is not the real value of the applied stress! F1 F F3  e1   e2  2  e3  Ao Ao Ao P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 9  Engineering Strain Defined as elongation divided by original length*: L  Lo e Lo Where: ideformazione e = engineering strain ) L = length at any point during elongation L1 L2 L3 Lo = original gage length *Engineering strain is not the real - value of the strain! L1  Lo L  Lo L  Lo L e1  e2  2 e3  3 Lo Lo Lo P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 10  Equipment Hydraulic or an electro-mechanical mechanism to move the crosshead. The applied force can be accurately measured by a load cell. Sample Crosshead: moves at a constant speed (e.g., 10 mm/min) v = cost Load cell: transducer that measures the applied force (P) load O sensor To mesure F Grips: clamp the sample. How ithe uppet force xesist F (or S)  e  Ao Extensometer: measures precisely the elongation of L  Lo e the gauge length Lo (ΔL = L - L0) P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 11  Stress and strain evaluation Uniform elongation Necking A1 A2 A0 F3 F2 F1 L  0 L1  L1  Lo L2  L2  Lo A3 Lo F1 F2 F3  e1   e2   e3  Ao Ao Ao F1 F2 F3 L1  Lo L2  Lo A3  Ao e1  e2  e2  Lo Lo Ao P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 12  Tensile-Test Test a Treziave å Source: aut. Kalpakjian, Manufacturing Engineering & Technology e P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 13  Stress-Strain Curves Metals with a well-defined Brittle metals elastic field (uncommon) Common Low carbon stress-strain plain steels curves for metals P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 14  Two Regions of Stress-Strain The two regions indicate two distinct forms of behavior: Curve 1. Elastic region – prior to yielding of the material Iiveca be =E.e 2. Plastic region – after yielding of the material î Yung modalms Hooke modulus F e  Ao UTS or TS Yeld stress Y Stress, σe [MPa] Uniform TS = tensile strength C Necking elongation UTS = ultimate tensile strength - Y = yield stress (or strength) ef = elongation at fracture ef l  l0 Strain, e [-] e l0 P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 15  Elastic Region in Stress-Strain Curve  Relationship between stress and strain is linear  Material returns to its original length when stress is removed Meximerm stress Hooke's Law: e = E e S =Fao where E = modulus of elasticity  E is a measure of the stiffness: Stress, σe [MPa] - Fe-based alloys 190-210 GPa - Al-based alloys 60-70 GPa times 3 less stiff  For angular deformation τ=Gγ G = shear modulus Strain, e [-] Lnenthentess P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 16  Poisson ratio Poisson’s ratio is the ratio of the lateral contraction strain to longitudinal extension strain in the direction of stretching force. It is driven by the tendency of the material to keep constant the volume SNELLA Here there is x The sereSS P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 17  Elastic costants Uniaxial stress Hooke’s Law τ Shear G γ Poisson’s ratio: ν Legati The three coefficients are not independent; they are tied through E G 2(1  ν) P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 18  Yield Point in Stress-Strain Curve  As stress increases, a point in the linear relationship is finally reached when the material begins to yield  Yield point Y can be identified by the change in slope at the upper end of the linear region or 0.2% offset  Y = a strength property  Other names for yield point = yield strength, yield stress, and elastic limit UTS P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 19  Plastic Region in Stress-Strain  Yield point marks the beginning of plastic deformation Curve  The stress-strain relationship is no longer guided by Hooke's Law  As load is increased beyond Y, elongation rate is higher than before (the slope of the curve changes dramatically), and it endures even when stress (load) is removed (plastic deformation behavior) NOTE: beyond the elastic region, material deformation is elastic-plastic and not only plastic (even though elastic deformation is negligible as compared to plastic deformation) P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 20  Tensile Strength in Stress-Strain Curve  Elongation is accompanied by a uniform reduction in cross-sectional area, consistent with maintaining constant volume  Finally, the applied load F reaches a maximum value, and engineering stress at this point is called the tensile strength TS (or UTS, Ultimate Tensile Strength) Fmax TS = UTS = Ao P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 21  Loading & Unloading In the plastic region, the true stress increases continuously*. This implies that the metal is becoming stronger as the strain increases. Hence, the name “Strain Hardening”. cincrudimento ) StaRT agein hexe couse d *Plastic deformation promotes the increase The previus plastic defr of the density of dislocations that, in turn, increase mechanical resistance. As a result, the stress must be increased to continue the plastic deformation. Flow stress (σ, σf, Y) = instantaneous value of stress required to continue deforming the material (i.e., to keep metal “flowing”): P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 22  Ductility in Tensile Test Ductility is the ability of a material to plastically strain without fracture  Ductility measure = elongation at fracture L f  L0 t Lf is measured as the distance between - (L - f -  100  100  e f gage marks after two pieces of specimen are put back together. e e P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 23  Aftex UTS Ductility in Tensile Test Percent reduction of area at fracture Af A0 Afbo A0  A f  100 A0 P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 24  Ductility in Tensile Test ductile metal brittle metal reduction of area (ductility and toughness) HIGH MEDIUM LOW/ABSENT 6 -8 % P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 25  Mechanical Properties Source: aut. Kalpakjian, Manufacturing Engineering & Technology P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 26 mun True Strain Provides a more realistic assessment of "instantaneous" elongation per unit - length To look the pattern of L1 dL defornation dL L1 .  ln L0: initial length we need to d  use L1: final length L L0 L L0 W It is possible to knt The real beformation Since volume is constant: couse need to we know Belore L1 A0 A0 not in meckel all the tefoxmetice thet deformatur Neck L0 A0  L1 A1    ln axe applied L0 A1 A1 In For a general length «L»: 2 L1 A0  D0   D0  ~   ln  ln  ln   2 ln  L0 A1  D1  un  D1  we need Aree t Äftert Only valid for round cross section cause isnit Neck Cosraut - P. Russo NOPe Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 27  m True Strain vs Eng. Strain Relationship between  and e y Aftex neck possible b no use it is mer  lne  For small deformations, e and ε are similar For large deformations, the usage of engineering strain leads to unrealistic results!! Mechenical design Mammfacutu i Note: keep in mind when discussing difference between True and Eng. stress strain curves t P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 28  True Strain vs Eng. Strain Cases  e 2 L0 2 L0  L0 L1→2L0 ln  ln 2 1 L0 L0 1 1 L1→ L0 /2 L0 L0  L0 ln 2   ln 2 2   0 ,5 L0 L0 P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 29  True Strain vs Eng. Strain Engineering Strain 1. It’s easier to calculate. 2. It’s overwhelmingly preferred in engineering analyses of materials that experience only elastic or small strains (including the common construction materials concrete, wood, and steel, for example, under normal use). 3. It’s symmetric in terms of displacements: that is, if the strain associated with being stretched a distance ∆L is e, then the strain associated with being compressed a distance ∆L is −e P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 30  True Strain vs Eng. Strain True Strain 1. It’s the exact value, not an approximation, of strain. 2. Sequential strains can be added (superposition principle): if two strains ε1 and ε2 are executed sequentially, the total strain is This is not the case with engineering strain, where the total strain is What if L2=L0? P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 31  True Strain vs Eng. Strain Example: series of successive strains. Calculation of true and engineering strain. The total engineering strain e0-3 is not equal to e0-1 + e1-2 + e2-3. The total true strain = the summation of the incremental true strains P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 32  True Stress Stress value obtained by dividing the instantaneous area into applied load F  A where  = true stress; F = applied force; A = actual (instantaneous) area resisting the load P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 33  True Stress & Eng. Stress BEFORE necking point: plastic deformation is homogeneous throughout the specimen Before wecking Aolo = LEo oAAf =Atle. o F F A0 A0 l RemEmber check    e   e   e (1  e) To - C The SIMILITUDES BW A A0 A A l0 The 2 sprain î =Eo t-t= e t - - - ! uxe True strain and stress are computed from the engineering values but only up to necking!! P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 34  True Stress & Eng. Stress AFTER necking point: plastic deformation is NOT homogeneous throughout the specimen, but localized in necking region. True strain and stress CANNOT BE computed from the engineering values.    e (1  e) load cell F A  optical A camera L P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 35  True vs. Eng. Stress-Strain Curve True stress-strain curves are considered in FEM analyses of stamping processes (e.g. forging, sheet forming). ! mecking ( MeX STRESS o ) i WHY this different trends? i Especially after necking? Note that true stress increases continuously in the plastic region even beyond necking In the engineering stress-strain curve, the significance of this is lost because stress is based on an incorrect area value P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 36. be b = -Felete) F Eao e b t-o = =lu E  True Stress - Strain curves Source: aut. Kalpakjian, Manufacturing Engineering & Technology P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 37  Plastic Flow Curve The relationship between true stress and true strain often can be modelled (i.e. approximated) with a power-law analytical function: Se o =E.e Hollomon equation cnct   K Ys n so 1000 : MPe n: strain-hardening exponent K: strength coefficient Note: K and n change with temperature P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 38  Plastic Flow Curve P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 39  Plastic Flow Curve How do “K” and “n” influence the stress-strain curve? is 8 o 8 b =KEn HuooMPa P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 40  Plastic Flow Curve How do “K” and “n” influence the stress-strain curve? P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 41  True Stress-Strain in Log-Log Plot How can “K” and “n” be evaluated from a tensile test? The plastic portion of the true stress-strain curve (or flow stress curve) plotted on a log-log scale gives ln  = ln (K*n) = ln K + n ln  the n value as the slope and the K value as the value of true stress at true strain of one. points plotted on Start of necking log-log coordinates True stress True stress   K n True strain True strain P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 42  Plastic Flow Curve  Perfectly elastic, n = 1 Flow curve σ = Kε  Elastic and perfectly plastic, n = 0 Flow curve: σ = K = Y  Elastic and strain hardening, K>Y, 0 2). The torsion test allows high deformations without too significant sample changes. Torque, torsional angle, number or rotations are measured during the test. The test is also performed on tubes to maintain the shear stress nearly constant. P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 59  Torsion test Relation between the torsional moment and maximum shear stress Polar moment of inertia P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 60  Torsion test Hot torsion test of a stainless steel strain rate 2 s-1 P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 61  Temperature and strain rate effects Many metal forming operations are performed at high temperatures. The increase in temperature involves different microstructural phenomena - than low temperature. Moreover, the strain rate has a much more significant effect on metal behavior*. The flow stress of metals is σ = f (ε , εꞏ , T) b =KEM to 8= *As a rule of thumb: f1E) at high temperature (T > Trec)  f  f ( ) if temperature is relatively low (T > P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 70 åo 200 C ooxç b =KEM E L b =cÉu  $S11),,¡])1(1 4 44 * xsf 1)*ll)S1s } )ff 1;1 Strain Rate Effects )( 4 y, ix $ f{ly{1 xD r ) ] y 1 ff HNLMNY x. " frelationship x I An empirical can be used to relate stress and strain rate 1 t 9 J Ü"... s 6,"' PI C = strength constant m = strain rate sensitivity exponent C and m change with temperature Effect of strain rate on flow stress curve at high temperature P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 71  Strain Rate Effects Plotting the flow stress as a function of the strain rate in a log-log graph, the relationship becomes linear. P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 72  Strength vs. Temperature and Strain Rate Effects of temperature on the behavior of flow stress as a function of the strain rate - Increasing temperature, C decreases and m (slope of each plot) increases - C indicated by the intersection of with the vertical dashed line at strain rate = 1.0 - At room temperature, the effect of strain rate is almost negligible. As temperature increases, strain rate becomes increasingly important in determining flow stress low carbon steel P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 73  Strain Rate P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 75  Strain Rate P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 76  Temperature and strain rate effects The combined effect of temperature, deformation, and strain rate influence the stress-strain diagrams. At high temperatures: - stress-strain curves do not show the typical increasing trend, but a softening at increasing deformation. - after reaching a stress peak, recovery and recrystallization, activated dynamically by temperature and strain rate, reduce the flow stress at increasing deformation. Hot compression test of Nymonic 115 (nickel- chromium-cobalt based alloy, strengthened with additions of molybdenum, aluminum, and titanium) P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 77  Temperature and strain rate effects thumb rule at high temperature (T > Trec)  f  f ( ) at low temperature (T σ2 > σ3 P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 80  Approach Mono-axial load Strain tensor Tri-axial load Stress tensor k σ,ε The two most common and successful yield criteria for ductile metals are 1) Tresca or Maximum shear stress (≈ 1870) 2) Von Mises or Maximum distortion energy P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 81  Tresca criterion The Tresca criterion states that a material yields at a point when the maximum shear stress τmax reaches the maximum shear stress at yielding, τ0, in a sample (of the same material) during a tensile test. τmax = 0 In a tensile test σx = σ (= σ1), σy = 0 , σz = 0 (considering x as the direction of the applied tensile load). Yield occurs when σ reaches the yield stress in tension (Y, σy…). It follows that the maximum shear stress at yielding τ0 = τmax = Tresca criterion   max   1   2 ,  1   3 ,  2   3  = 0 Y P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 82  Tresca criterion In pure shear loading, yielding occurs when  reaches the yield stress of a material in pure shear (Y). xy = xy xy σ2 = 0 xy xy σ3 = -xy in case of pure shear σ1 = xy , σ2 = 0 , σ3 = - xy , hence, σ1 = -σ3 and σ2 = 0. Tresca criterion   max   1   2 ,  1   3 ,  2   3  = 0 Y According to Tresca criterion, in pure shear yielding occurs when 2xy = Y xy = = 0.5 Y P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 83  Tresca criterion Stress analysis of a spacecraft structural member gives the state of stress shown below. If the part is made of 7075-T6 aluminum alloy with a yield strength (Y) of 500 MPa, will it exhibit yielding? NOTE: σx is a principal stress 200 0 0 0 100 -30 0 -30 -50 250 MPa 4100 MPa -1180000 MPa P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 84  Tresca criterion σ3 - 250 σ2 + 4100 σ + 1180000 σ1 = 200 MPa σ2 = 105.8 MPa σ3 = -55.8 MPa Tresca criterion   max   1   2 ,  1   3 ,  2   3  = Y _ σ = 255.8 MPa < 500 MPa The material does not yield!! P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 85  Von Mises criterion The Von Mises criterion states that a material yields at a point when the maximum distortion energy in the material Wd,max reaches the maximum distortion energy at yielding in a simple (of the same material) during a tensile test Wd,y F(σx , σy , σz , xy , xz , yz) = k Distortion energy is the part of the strain energy that corresponds to volume-preserved shape change In terms of the stress components = Y2 Von Mises criterion (or σeq) is called equivalent stress P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 88  Von Mises criterion Stress analysis of a spacecraft structural member gives the state of stress shown below. If the part is made of 7075-T6 aluminum alloy with a yield strength (Y) of 500 MPa, will it exhibit yielding? - = 224 MPa _ σ = 224 MPa < 500 MPa Von Mises The material does not yield!! _ σ = 255.8 MPa Tresca P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 89  Von Mises criterion In pure shear loading, yielding occurs when the maximum distortion energy in the material Wd,max reaches the maximum distortion energy at yielding in pure shear (Wd,y). xy Von Mises criterion xy xy xy According to Von Mises criterion, in pure shear yielding occurs when (Tresca 0.5 Y) P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 90  Von Mises criterion Von Mises criterion simplifies when the principal stresses are known:  1   2    2   3    3   1   =  1    Y0 2 2 2 2    = P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 91  PLANE STRESS conditions In case of plane stress condition one principal stress is 0. This means that the stresses are only located on a plane. For instance, in the following figures σ2 = 0 Plane stress in tension Plane stress in compression Von Mises Tresca (hypothesizing that  1   3 is the maximum value) σ  σ 12  σ 3 2  σ 1 σ 3  Y σ  σ1  σ 3  Y P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 96  PLANE STRAIN conditions Plane strain in tension: the width of the Plane strain in compression: the width of the sheet remains constant while being stretched. specimen remains constant due to the restraint by the groove. 3 1 3 1 2 2 1 ε 0  0.5 σ1  σ3 ε 2   σ 2  ν (σ1  σ 3) 2    (   ) 2 1 3 σ2  E 2 Von Mises Tresca (hypothesizing that is is the maximum value) 2 σ  σ1  σ 3   Y  1.15 Y  Y´ σ  σ1  σ 2  Y 3 P. Russo Spena - Manufacturing and Assembly Technologies - a.a. 2023-24 97