Engineering Materials I - Essentials

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True Stress and Strain The cross-sectional area decreases rapidly in the neck region during deformation. True stress and strain account for instantaneous changes in geometry, unlike engineering stress and strain which use original dimensions. True Stress ($\sigma_T$) Defined as the applied load $F$ divided by the instantaneous cross-sectional area $A_i$: $$\sigma_T = \frac{F}{A_i}$$ During necking, $A_i$ decreases, so $\sigma_T$ is greater than engineering stress. True Strain ($\varepsilon_T$) Defined as the natural logarithm of the ratio of the instantaneous length $l_i$ to the original length $l_0$: $$\varepsilon_T = \ln \left(\frac{l_i}{l_0}\right)$$ True strain accumulates deformation, providing a more accurate measure of plastic deformation. Hardness A measure of a material's resistance to localized plastic deformation (e.g., a small dent or a scratch). Hardness tests involve forcing a small indenter into the material's surface under controlled conditions. The depth or size of the resulting indentation is measured and related to a hardness number. Softer materials result in larger and deeper indentations, and lower hardness numbers. Why Hardness Tests are Popular Simple and inexpensive, usually requiring no special specimen preparation. Nondestructive; the specimen is neither fractured nor excessively deformed. Other mechanical properties, such as tensile strength, can often be estimated from hardness data. Rockwell Hardness Test The most common method to measure hardness. Hardness is determined by the difference in depth of penetration resulting from the application of an initial minor load followed by a larger major load. Indenters include spherical hardened steel balls (various diameters: $1/16, 1/8, 1/4, 1/2$ in.) and a conical diamond (Brale) indenter (for hardest materials). Different scales are used, represented by a letter (e.g., HRB, HRC). For Rockwell, minor load is 10 kg, major loads are 60, 100, 150 kg. For superficial Rockwell tests, minor load is 3 kg, major loads are 15, 30, 45 kg. Both the hardness number and scale symbol must be indicated (e.g., 80 HRB). Rockwell Hardness - Practical Aspects Inaccuracies can result if the specimen is too thin, if an indentation is made too near a specimen edge, or if two indentations are made too close to one another. Specimen thickness should be at least ten times the indentation depth. Testing of stacked specimens is not recommended. Accuracy depends on the indentation being made into a smooth, flat surface. Brinell Hardness Test A hard, spherical indenter is forced into the surface of the metal. The Brinell hardness number (HB) is a function of both the magnitude of the load and the diameter of the resulting indentation. The indentation diameter is measured with a low-power microscope. Only one scale is generally employed with this technique. Knoop and Vickers Microindentation Hardness Test Used for very small scale hardness measurements (e.g., thin materials, coatings, small regions). A small diamond indenter with pyramidal geometry is forced into the surface. Applied loads are much smaller (1 to 1000 g) than for Rockwell and Brinell tests. The resulting impression is observed under a microscope and measured. Correlation between Hardness and Tensile Strength Both tensile strength and hardness are indicators of a metal's resistance to plastic deformation and are roughly proportional. For most steels, the Brinell hardness (HB) and tensile strength (TS, in MPa) are related by: $$\text{TS}(\text{MPa}) = 3.45 \times \text{HB}$$ Failure Modes of Engineering Materials Fracture The separation of a body into two or more pieces in response to an imposed stress. Can also occur from fatigue (cyclic stresses) or creep (time-dependent deformation at elevated temperatures). Ductile vs. Brittle Fracture Ductile Fracture: Exhibits substantial plastic deformation with high energy absorption before fracture. Classification is based on the ability of a material to experience plastic deformation. Brittle Fracture: Little or no plastic deformation with low energy absorption. Ductile fracture often gives warning (e.g., necking), while brittle fracture is sudden. Metal alloys are typically ductile; ceramics are brittle. Ductile Fracture Mechanism Necking begins. Small cavities (microvoids) form in the interior. Microvoids enlarge, come together, and coalesce to form an elliptical crack. The crack grows perpendicular to the stress direction. Final fracture occurs by rapid propagation of a crack around the outer perimeter of the neck, forming a "cup-and-cone" fracture surface. The central interior region of the surface has an irregular and fibrous appearance, indicative of plastic deformation. Brittle Fracture Characteristics Takes place without appreciable deformation and by rapid crack propagation. Crack motion is nearly perpendicular to the applied tensile stress. Yields a relatively flat fracture surface. Transgranular vs. Intergranular Brittle Fractures For most brittle crystalline materials, crack propagation (cleavage) corresponds to breaking atomic bonds along specific crystallographic planes. This is called transgranular (or transcrystalline) fracture, as the crack passes through the grains. In some alloys, crack propagation is along grain boundaries, termed intergranular fracture. Fracture Mechanics The discipline concerned with the behavior of materials containing cracks or other small flaws. A "flaw" refers to features like small pores, inclusions, or microcracks, but not atomic-level defects. Allows quantification of relationships between material properties, stress level, flaw presence, and crack propagation. Stress Concentration Measured fracture strengths are often lower than theoretical predictions due to the presence of flaws. An applied stress can be amplified or concentrated at the tip of a flaw, depending on crack orientation and geometry. The magnitude of this localized stress diminishes with distance from the crack tip. Flaws are often called "stress raisers." Fracture Toughness ($K_c$) Measures a material's ability to withstand an applied load when a flaw is present. It is the critical stress intensity factor required for a crack to propagate. Stress Intensity Factor ($K$) Quantifies the stress state at the crack tip: $$K = f\sigma\sqrt{\pi a}$$ where $f$ is a geometry factor, $\sigma$ is the applied stress, and $a$ is the flaw size. Units for fracture toughness are psi $\sqrt{\text{in.}}$ or MPa $\sqrt{\text{m}}$. Plain Strain Fracture Toughness ($K_{Ic}$) Fracture toughness depends on the sample's thickness. As thickness increases, $K_c$ decreases to a constant value, known as the plane strain fracture toughness ($K_{Ic}$). $K_{Ic}$ is a material property and does not depend on thickness. Factors Affecting Crack Growth Larger flaws reduce the permitted stress. The material's ability to deform is critical (ductile materials blunt cracks, brittle materials do not). Thicker, more rigid pieces have lower fracture toughness. Increasing the rate of application of the load (impact tests) reduces fracture toughness. Increasing the temperature normally increases fracture toughness. A small grain size generally improves fracture toughness. Stress-induced transformations in ceramics can lead to increased fracture toughness. Importance of Fracture Mechanics Allows engineers to design and select materials while accounting for inevitable flaws. Three variables: material property ($K_c$ or $K_{Ic}$), applied stress ($\sigma$), and flaw size ($a$). If two are known, the third can be determined. Applications of Fracture Mechanics Selection of a Material: Choose a material with sufficient $K_c$ or $K_{Ic}$ for known flaw size and applied stress. Design of a Component: Calculate maximum stress a component can withstand for a known flaw size and material. Design of a Manufacturing or Testing Method: Determine the maximum tolerable flaw size and design NDT techniques or manufacturing processes to ensure flaws are smaller than this critical size. Fatigue The lowering of strength or failure of a material due to repetitive stress, even if below the yield strength. Common in load-bearing components (cars, airplanes, machinery, implants). Caused by cyclic stresses (tension, compression, bending, vibration, thermal expansion/contraction). Stresses are often below yield strength, but repeated application leads to failure. Stages of Fatigue Crack Initiation: A tiny crack initiates, often at surface defects (scratches, pits, sharp corners, inclusions, grain boundaries). Crack Propagation: The crack gradually grows as the load continues to cycle. Final Fracture: Sudden fracture occurs when the remaining cross-section is too small to support the applied load. Fatigue in Engineering Materials Requires tensile stress for occurrence. Concern for metallic and polymeric materials. Ceramics typically fail by brittle fracture before fatigue becomes significant due to low fracture toughness. Polymers show fatigue, with heating near crack tips due to repetitive stresses; creep also interacts. In composites, fatigue degrades reinforcing phases, decreasing elastic modulus before fracture. Characteristics of a Fatigue Failure Fracture surface is typically smooth near the origin, becoming rougher and fibrous during final crack propagation. Beach marks (clamshell marks): Formed when the load changes intermittently during service. Striations: Finer scale marks showing the crack tip position after each cycle. Fatigue Test (Rotating Cantilever Beam Test) A conventional method to measure fatigue resistance. A cylindrical specimen is mounted in a motor-driven chuck, with a weight suspended from the other end. As the specimen rotates, any point on its surface experiences a complete sinusoidal stress cycle (from maximum tensile to maximum compressive stress). Maximum stress: $\pm\sigma = \frac{32M}{\pi d^3}$, where $M = F \cdot (L/2)$. S-N Curves (Wöhler Curves) Plot of stress amplitude ($S$) versus the logarithm of the number of cycles to failure ($N$). Used to predict component lifetime and maximum allowable loads. Fatigue Limit (Endurance Limit): The stress below which fatigue failure will not occur for an infinite number of cycles (for some materials like steels). Fatigue Life: The number of cycles a component survives at a particular stress. Fatigue Strength: The maximum stress for which fatigue will not occur within a specified number of cycles. Endurance Ratio: For some steels, the endurance limit is approximately half the tensile strength ($\text{Endurance Ratio} = \frac{\text{endurance limit}}{\text{tensile strength}} \approx 0.5$). Factors Affecting Fatigue Life Mean Stress: Increasing the mean stress level generally decreases fatigue life. Surface Effects: Fatigue life is sensitive to surface condition. Notches, grooves, holes, and sharp corners act as stress raisers. Rounded fillets improve fatigue life. Effect of Temperature: Increasing temperature generally decreases fatigue life and endurance limit. Cyclic temperature changes can cause thermal fatigue. Frequency of Stress Application: High-frequency stresses can cause heating in polymers, leading to faster failure. Creep Time-dependent permanent deformation under a constant load or stress, occurring at elevated temperatures, even if the applied stress is less than the yield strength. A significant cause of failure in components used at high temperatures. Involves mechanisms like diffusion, dislocation glide/climb, and grain boundary sliding in metallic materials. Polymeric materials also exhibit creep. Creep Test A constant stress is applied to a heated specimen, and strain is measured as a function of time. An instantaneous elastic strain ($\varepsilon_0$) occurs upon loading, followed by creep. Creep Curve (Strain vs. Time) Primary Creep (Transient): Continuously decreasing creep rate; material experiences strain hardening. Secondary Creep (Steady-State): Constant creep rate, often the longest stage. The slope of this region is the creep rate ($\text{Creep rate} = \frac{\Delta \text{Strain}}{\Delta \text{Time}}$). Tertiary Creep: Accelerating creep rate leading to rupture (failure), often due to necking, void formation, or microstructural changes. The time to failure is called rupture time . Higher stress or higher temperature reduce rupture time and increase creep rate. Applications of Creep Data Stress-Rupture Curves: Estimate the lifetime of components under specific stress and temperature combinations. Larson-Miller Parameter (L.M.P.): Consolidates stress-temperature-rupture time relationships into a single curve: $$\text{L.M.P.} = \frac{T}{1000}(A + B \ln t)$$ where $T$ is temperature in Kelvin, $t$ is time in hours, and $A, B$ are material constants. Equilibrium Phase Diagrams Solid Solutions When small amounts of elements are added to a solid material, a solid solution may form. A solid solution contains two or more types of atoms or ions dispersed uniformly throughout the material, occupying regular lattice sites or interstitial sites. Properties can be manipulated by controlling composition. Phase A phase is any portion of a system that is physically homogeneous within itself and bounded by a surface separating it from other portions. Each phase has a distinct atomic arrangement, unique properties, and a definite boundary. Phase Rule (Gibbs Phase Rule) Describes the relationship between the number of components ($C$), degrees of freedom ($F$), and phases ($P$): $$2 + C = F + P$$ "2" indicates that both temperature and pressure are allowed to change. Phase Diagrams Graphical representations showing the phases present at different temperatures, pressures, and compositions. Unary Phase Diagram (e.g., Magnesium) For a single-component system (e.g., Mg), pressure vs. temperature (P-T) diagrams show solid, liquid, and vapor phases. At atmospheric pressure, melting and boiling temperatures are shown. At very low pressures, solids can sublime directly to vapor. Along phase boundaries, two phases coexist ($F=1$). At the triple point, three phases coexist ($F=0$). Solubility and Solid Solutions Unlimited Solubility: Components can be mixed in any ratio to form a single phase (e.g., copper and nickel). Limited Solubility: Components can only dissolve up to a certain concentration in each other (e.g., salt in water, zinc in copper). Beyond this, a second phase forms. Insolubility: Components do not dissolve in each other (e.g., oil and water, copper and lead). Conditions for Unlimited Solubility (Hume-Rothery Rules) Size Factor: Atomic radii difference must be less than 15%. Crystal Structure: Must have the same crystal structure. Valence: Ions should have the same valence. Electronegativity: Atoms should have approximately the same electronegativity. Polymeric Systems Copolymers consist of different monomers (e.g., ABS polymer from acrylonitrile, butadiene, styrene). They blend properties of their constituent monomers and cannot be easily separated. Degradation of Materials Degradation Mechanisms Metals: Material loss by dissolution (corrosion) or formation of nonmetallic scale (oxidation). Ceramics: Generally resistant, but can degrade at elevated temperatures or in extreme environments (also called corrosion). Polymers: Degradation includes dissolution, swelling, and alterations to molecular structures by electromagnetic radiation (UV) and heat. Swelling and Dissolution (Polymers) Liquids diffuse into and are absorbed by the polymer, causing it to expand. Greater chemical similarity between solvent and polymer leads to greater swelling/dissolution. Bond Rupture/Scission (Polymers) The breaking of molecular chain bonds, reducing molecular weight. Caused by radiation, chemical reactions, or thermal effects. Weathering (Polymers) Degradation of polymers exposed to outdoor conditions. Primarily caused by oxidation initiated by ultraviolet radiation from the sun. Corrosion of Metals A destructive and unintentional electrochemical attack of a metal, typically beginning at the surface. Involves oxidation (metal loses electrons, $M \to M^{n+} + ne^-$ at the anode) and reduction (electrons are consumed, e.g., $2H^+ + 2e^- \to H_2$ or $O_2 + 2H_2O + 4e^- \to 4OH^-$ at the cathode). Electromotive Force (emf) Series Ranks metals by their tendency to oxidize, relative to a standard hydrogen electrode. Metals lower in the series are more active and prone to oxidation. Galvanic Series A practical ranking of metals based on their electrochemical behavior in specific environments (e.g., seawater). Metals higher in the series are more noble (cathodic) and metals lower are more active (anodic). Corrosion Rate The rate of material removal due to chemical action. Corrosion Penetration Rate (CPR): Expressed in mils per year (mpy) or millimeters per year (mm/yr). $$\text{CPR} = \frac{KW}{\rho At}$$ where $W$ is weight loss, $\rho$ is density, $A$ is exposed area, $t$ is time, and $K$ is a constant. Can also be expressed in terms of current density ($i$): $r = \frac{i}{nF}$. Forms of Corrosion Uniform Attack: Occurs with equivalent intensity over the entire exposed surface (e.g., general rusting). Galvanic Corrosion: Occurs when two dissimilar metals are electrically coupled in an electrolyte; the more active metal corrodes. Crevice Corrosion: Localized corrosion within narrow gaps or shielded areas where oxygen concentration differs. Pitting: Localized corrosion forming small pits or holes, often penetrating vertically. Intergranular Corrosion: Preferential corrosion along grain boundaries. Stress Corrosion: Results from the combined action of tensile stress and a corrosive environment. Corrosion Prevention Strategies Material Selection: Choosing corrosion-resistant materials for the specific environment. Changing the Environment: Reducing corrosiveness (e.g., deaeration, adding inhibitors). Inhibitors: Substances added to the environment to decrease corrosion. Physical Barriers: Applying films or coatings (e.g., paints, platings). Cathodic Protection: Making the metal to be protected the cathode of an electrochemical cell. This usually involves connecting it to a more active "sacrificial anode" (e.g., galvanizing steel with zinc). Materials/Processes in Industry Materials Life Cycle The entire journey of materials from raw resource extraction ("cradle") to processing, manufacturing, distribution, consumer use, and end-of-life management ("grave"). Key Stages: Material Extraction, Processing & Manufacturing, Distribution & Transportation, Use Phase, End-of-Life. Important for understanding environmental impacts and supporting circular economy models. Manufacturing Process Research & Design: Concept, market validation, detailed specifications. Prototyping & Testing: Functional models, refinement. Procurement: Sourcing materials. Production: Processing, assembly, quality control. Post-Production: Packaging, logistics, distribution. Prospective Job Roles for Materials and Process Technology Students Production Executive/Engineer, Process Executive/Engineer, Laboratory Service Technician/Engineer, Quality Controlling Executive/Manager, Project Engineer/Manager, Production Coordinator, Staff Officer – Production/Technology, Lean Supervisor/Manager, R&D Engineer/Manager, Entrepreneurs. Skills Needed Technical Knowhow, Critical Thinking, Creativity, Communication skills, Interpersonal skills, Team Work, Personality, Self-discipline, Updated knowledge and subject skills.