2024 MSE 316 Mechanical Behaviour of Materials Review PDF

Mechanical Behaviour of Materials (MSE316) Review Yu Zou Department of Materials Science & Engineering (MSE) University of Toronto (U of T) 1  Grading Scheme...

Mechanical Behaviour of Materials (MSE316) Review Yu Zou Department of Materials Science & Engineering (MSE) University of Toronto (U of T) 1  Grading Scheme True (T) or False (F) ~ 10-15% Focused on basic concepts and mechanisms Multiple Choice ~ 25-30% Focused on concepts, mechanisms, basic knowledge, rules, and simple calculations Calculations and long-answer questions ~ 55-65% Focused on applying rules and methods, understanding mechanisms Relatively easy, but covering a large range of the content of this course Covered in the lecture notes and relevant chapters in the textbook 2  Chapters covered 1 Overview of Mechanical Behavior 2 Elastic Behavior 3 Dislocations 4 Plastic Deformation in Single and Polycrystalline Materials 5 Strengthening of Crystalline Materials 6 Composite Materials 7 High-Temperature Deformation of Crystalline Materials 8 Deformation of Noncrystalline Materials (1-2 questions) More questions from the chapters 3, 4, 5, and 7. 3  What are true stress and strain? Are engineering stress and strain are “real” materials behaviour? On integrating from l = l0 l to l = li, 𝜀𝜀𝑇𝑇 = ln i l0 for elastic deformation for plastic deformation 4  stress/strain: True vs. Engineering Tensile test (ε > 0, before necking): True stress > Engineering stress (1+ε) >ε True strain < Engineering strain (ln(1+ε) < ε, when ε > 0) How about compression? ε < 0 True stress < Engineering stress True strain > Engineering strain MSE316 5 The range of E Which material shows the highest/lowest E? and why? Why does diamond have higher E than graphite? How about graphene? E of graphene ~ 1 TPa (the same range as diamond) Why does MgO have higher E than NaCl? Why does Ice have a lower E? Lead is the least stiff metal and OS is the stiffest Why do polymers have Low E values? Why do composite have a large range of E? MSE316 7  Poisson’s ratio (ν) Poisson’s ratio: the elastic constant that describes the proportionality between an imposed normal strain along one axis and a resulting normal strain (generally of opposite sign) along an orthogonal direction Extension (keeping terms only to first order) Contraction ν = 0.5  ΔV = 0 incompressible (e.g. Rubber) Polymers: 0.3 < ν < 0.5 most metals: 0.25 < ν < 0.45 (~1/3) ε2 ε3 Ceramics and glass: 0.1 < ν < 0.3 ν=− =− Natural cork: ν ≈ 0 (easy to compress) ε1 ε1 8  Generalized Hooke’s law The total strain in one direction is considered to be equal to the sum of the strains generated by the various stresses along that direction. an isotropic solid τ τ τ 10  Compliance and stiffness constants α, β, and γ are the direction cosines of the [hkl] direction and the , , and directions, respectively. 13  Polymers Thermoplastics: Thermosets: Polymers Polymers without cross- with many cross-links links; they have the cannot melt after they ability to melt and have been solidified. remelt; thermoplastics can be remelted back into a liquid, whereas thermoset plastics always remain in a permanent solid state. 15  Thermoplastic Behavior Thermosets: epoxy resins, melamine resin, polyurethanes, and Bakelite Thermoplastics: PS, PVC, PET, PC, PMMA The midpoint in this range is called the glass transition temperature, Tg 16  Edge dislocation and dislocation glide Shear stress Shear stress Shear stress Slip plane Unit step of slip Edge dislocation line Edge dislocation motion Dislocation glide (the most common mechanism for the motion of edge dislocations) 19  Screw dislocation Screw dislocation Spiral line in dislocation core Glide by screw dislocation motion 20  The Burgers vector (b) and Burgers Circuit Right-hand/finish-start (RH/FS) convention: 1. looking along the dislocation line, which defines the positive line sense, the circuit is taken in a clockwise fashion; 2. the Burgers vector is taken to run from the finish to the start point of the reference circuit in the perfect crystal.  b defines the dislocation slip direction, which is normal to edge dislocation line. b  In an edge dislocation, the Burgers vector and dislocation line define a unique slip plane.  Dislocation climb is possible. 21  Climb of Edge Dislocations  Dislocation glide is conservative motion.  Dislocation climb is nonconservative motion, requiring addition to the dislocation core of atoms or vacancies  climb involves diffusive motion of atoms, temperatures is required to effect it  climb occurs only at moderate to elevated temperatures (important for creep) 22 Cross slip in a face-centered cubic metal 23  Dislocation core and lattice frictional stress A D Dislocation core a The lattice friction stress (or Peierls (Peierls and Nabarro) stress） The frictional stress is low when a is large and b is small. Slip should occur most readily on close- packed atomic planes, which are characterized by the greatest separation distance Slip in close-packed directions for which the atomic slip distance is a minimum 24  Slip systems in fcc and bcc fcc bcc 25  Slip Systems Slip is expected to occur on the close-packed planes and along the close-packed atomic directions 26 The width of dislocation core w the width of the dislocation  τf decreases as dislocation width increases as a result of the smaller relative atomic displacements required for motion of a wide dislocation  The width of a dislocation is also temperature-sensitive, decreasing with decreasing temperature, and this leads to an increased frictional stress at low temperatures 27  Why ceramics are brittle? The temperature variation of dislocation width, and the friction stress, is sensitive to the nature of atomic bonding and crystal structure. Dislocation cores in covalent solids or ionic crystals (e.g. ceramics) very narrow, so their frictional stresses are very large, even larger than their fracture strength. Their dislocation motion is very difficult, resulting in stress concentration in crack tips. Stress concentration in metals leads to plastic deformation, blunting the crack tips. 28 Dislocation glide vs. twinning Since twinning and slip can be considered competitive, that mechanism requiring the lowest stress to effect it should be observed. For fcc metals, the stress required for flow via slip is almost always less than the twinning stress and so twinning is only observed in at low temperatures and high strain rates (for low SFE materials) Bcc metals are more prone to exhibit Dislocation slip twinning. This is because their yield strengths associated with slip are strongly temperature dependent Deformation twinning is important in HCP metals. As indicated, this material class has Twinning relatively few slip systems. 29 Dislocation Multiplication - Frank–Read source  Frank–Read source is a mechanism explaining the generation of multiple dislocations in specific well-spaced slip planes in crystals.  It is named after British physicist Charles Frank and Thornton Read. The stress for dislocation generation is inversely proportional to the source length. The line tension (energy per unit The smallest radius of curvature, obtained length) is T = Gb2/2 when the loop is in the form of a semicircle, The stress (𝜏𝜏) required to produce a curved corresponds to the maximum stress dislocation with a diameter of L: required to effect the process and is given by r = l/2, where I is the distance between 𝜏𝜏 = 𝐺𝐺𝐺𝐺/2𝑟𝑟 the pinned segments. 31 Plastic flow in single crystals 𝐴𝐴𝑠𝑠 = 𝐴𝐴0 /cos 𝜙𝜙 = Schmid factor ( < 1) Taylor factor ( > 1) Plastic yielding will occur most readily on the slip system possessing the greatest Schmid factor or the smallest Taylor factor. Plastic flow initiates when τRSS reaches some critical value, called critical resolved shear stress (CRSS). 33 Stress-strain behaviour of fcc and bcc metals Saturation Work hardening The strain extent of Stage hardening I decreases with increasing temperature (easier for multiple slips) the extent of Stage II is reduced as temperature easy slip is raised due to recovery Cross-slip occurs more readily in materials with high SFE, and thus the transition from Stage II to Stage III occurs at lower stress levels in I: single slip (dislocation motion, low work-hardening rate) materials having a II: multiple slip (dislocation-motion impediments) high SFE. III: Saturation (Cross-slips and dislocation rearrangement) 34 Temperature and strain rate dependence of CRSS τa is the athermal (i.e., temperature-independent) component. - long-rang internal stress fields between dislocations. τ* the thermally dependent term - "short- range" barriers. Peierl's stress and the resistance to dislocation glide Diffusion ~0.25 Tm ~0.7 Tm 35  The CRSS of fcc metals is less temperature sensitive than that of bcc metals; Alloying increases the CRSS; 36 Room-temperature yield strengths of various materials Ceramics are the strongest of the material classes. Polymers are relatively soft with low strengths, but the strongest plastics are about as strong as Al alloys. Composite strengths are a suitable average of their constituent strengths. the strengths of metals are intermediate to those of ceramics and polymers. Ultra-pure metals are quite soft. Most high-strength engineering metals are alloys; that is, they contain more than one element. Typically, a strong material is not very malleable (ductile) and vice versa. 38 strengthening mechanisms Metals: hardening mechanisms – dislocation blocking Solid solution Work hardening hardening (Composition) (Microstructure) Precipitation hardening (Composition & Microstructure) 39  Hall-Petch equation [the concept of dislocation pile-up (to be fully approved)]: A material with larger grain size is able to have more dislocations pile up, leading to a bigger driving force for dislocations to move from one grain to another. Thus you will have to apply less force to move a dislocation from a larger than from a smaller grain, leading materials with smaller grains to exhibit higher yield stress. Smaller is stronger σy is the yield stress; σo is a materials constant for the starting stress for dislocation movement (the resistance of the lattice) ky is the strengthening coefficient (a To appreciably grain-size harden a metal constant specific to each material) d is the average grain diameter typically necessitates having a grain size below 5 µm 41 Inverse Hall–Petch relation Breakdown of Hall-Petch effect below d ~10 nm : the smaller grain size, the lower strength Grain size decreasing M.A. Meyers et al. / Progress in Materials Science 51 (2006) 427–556 42  Solid-solution strengthening Both size and modulus play roles in strengthening.  Solute atoms increase the yield strength of crystalline materials.  This is a result of the interactions between a moving dislocation and solute atoms.  Introduction of a substitutional solute atom into a crystal produces a lattice dilation that typically gives rise to a spherically symmetric stress field around the solute.  since a dislocation is flexible, it spends more time at the locations of negative interaction energy. 43 Effect of the concentration of substitutional atoms 44  Precipitation hardening  Second phase particles resist dislocation penetration to a considerably greater degree than does an isolated solute atom.  particle size and volume fraction, particle shape, and the nature of the boundary between the particle and the matrix all influence hardening effect interphase boundaries (IPBs) coherent or ordered IPB Semi-coherent or partially w/ coherency strain energy ordered IPB w/ coherency incoherent or disordered IPB strain energy partially w/o coherency strain energy released A dislocation can penetrate (cutting) an ordered IPB, but not a disordered one (so, dislocation bowing occurs in this case) 45 Cutting Stress as a function of particle size (fixed volume fraction) 46  Aging effects Schematic representation of aging process at low (A), high (B), and intermediate (C) temperatures At temperatures approaching the solvus temperature, there is little driving force for the precipitation process, even though diffusion kinetics are rapid. Alternatively, precipitation of the second phase proceeds slowly at temperatures well below Ts despite the large driving force for nucleation of the second phase 47 Nondeforming Particles- Dislocation bowing 48 The Transition from Cutting to Bowing and the Maximum Particle Hardening 49 Hardening Mechanisms in Crystalline Materials 50 High-Temperature Deformation of Crystalline Materials 51  Three stages in the creep curves I: transient creep: similar to work hardening, dislocation density increases II: steady-state creep: constant creep rate, recovery effects with deformation. Nonconservative dislocation motion (climb) requires mobile vacancies. III: tertiary creep: creep rate increases continuously. recrystallization, coarsening of second-phase, formation of internal cracks or voids 52 Creep activation energies vs. self- diffusion activation energies. 53  Nabarro-Herring (NH) creep Nabarro-Herring (NH) creep is accomplished solely by diffusional mass transport (dominating at much lower stress levels and higher temperatures) NH creep is more important in creep of ceramics than in metals because of no dislocation activities the atomic volume is increased in regions experiencing a tensile stress and decreased under compression. Single crystal or individual grain 54  Coble Creep Coble creep mass transport occurs by diffusion along grain boundaries in a polycrystal or along the surface of a single crystal. DGB which represents an effective grain-boundary (or surface) diffusivity δ' is an effective grain-boundary thickness for mass transport Coble creep is more sensitive to grain size than NH creep. Coble creep will be more important in fine grained materials 55 Creep Mechanisms Involving Dislocation and Diffusional Flow - dislocation creep (or power law creep) Solute drag creep Climb-glide creep 56  Independent Processes Different creep mechanisms may operate independently (i.e., in parallel) or in sequence (i.e., in series). NH creep and Coble creep operate independently, and the resultant diffusional creep rate is the sum of the respective creep rates. Coble creep depends more strongly on grain size (~ d-3) than does NH creep ( ~ d-2). Thus, Coble creep dominates in small-grain-sized materials and vice versa. 57 Diffusional flow and dislocation (power-law) creep 58 Summary 59 deformation mechanism maps 60 Case Studies - SUPERALLOYS Superalloys are based on Fe, Ni, or Co, with the Ni-base superalloys being most important. The most demanding environments in turbine applications call for materials resistant to dislocation creep. The requirements are met with a series of Ni-base alloys based on the Ni-Al system. γ-γ' alloys; the γ refers to the fcc matrix of these materials, the γ' to the second-phase precipitate Ni3(AI,Ti). 64  Strain-Rate Sensitivity The strain-rate sensitivity varies between zero (in which case the material is not strain-rate sensitive) and unity (in which instance the stress increases linearly with strain rate and the material is called a viscous solid). High values of m indicate resistance to neck development in tension, just as do high values of the strain-hardening coefficient for most of these materials m = ~ 0.00-0.10 at room temperature. Their strain-rate sensitivities increase with temperature 65 70  Hardness vs. strength For work-hardening materials, yield strength is replaced by the flow stress corresponding to the average strain within the plastic zone. often taken as 3.0 is widely used to estimate material yield strengths from the results of hardness measurements. Both the yield stress and the work-hardening characteristics of the metal are important in determining the hardness. hardness cannot be considered a fundamental property of a metal. 73 74 Oliver-Pharr method A(hc) hc S: stiffness E: reduced modulus Reduced elastic modulus represents the elastic deformation that occurs in both sample and indenter tip. f Multiaxial Loading Conditions in actual service most materials are subjected to a variety of loading conditions (e.g., biaxial or triaxial stresses), and material response may be profoundly altered by such variations. 75 Tresca yield criterion for conditions of biaxial loading 76  The von Mises yield criterion The von Mises yield criterion is essentially an empirical criterion that nonetheless more accurately describes yielding under multi axial stress states than does the Tresca condition. The Tresca criterion, even though not as accurate as the von Mises one, is more conservative. 77 BASIC PRINCIPLES OF REINFORCEMENT The stress for the two phases are the same 79 80 the equal-strain condition is most useful for reinforcement 81 Tensile test of a fiber composite the volume fraction rule (VFR) 82 stress-strain curves of composites 84 Composite tensile strength vs. the secondary tensile strength 86 Happy to have worked with you through the course! 90 91 92  Course Evaluations Are Now Open! You will have time in class next week to provide feedback on this course Bring any of the following Check your e-mail for a link to your electronic devices to class: evaluations, or go to Smart phone http://uoft.me/openevals Tablet To access the Course Evals page Laptop on Quercus 93 Fracture and Failure Analysis (MSE419) Department of Materials Science & Engineering (MSE) University of Toronto (U of T) 96 Additive Manufacturing of Advanced Engineering Materials Summer course Yu Zou Assistant Professor and Dean's Spark Professor Department of Materials Science & Engineering Faculty of Applied Science & Engineering University of Toronto