Math-Sci Midterm PDF

**PPT 1 - Atomic Structure, Crystal Structure and Inner Atomic Bonding** - **Atomic Structure (Freshman Chem.)** Atom is made up of: - Electrons -- [9.11 × 10^ − 31^kg]{.math.inline} - Neutrons and Protons -- [1.67 × 10^ − 27^kg]{.math.inline}  Some of the ff. pr...

**PPT 1 - Atomic Structure, Crystal Structure and Inner Atomic Bonding** - **Atomic Structure (Freshman Chem.)** Atom is made up of: - Electrons -- [9.11 × 10^ − 31^kg]{.math.inline} - Neutrons and Protons -- [1.67 × 10^ − 27^kg]{.math.inline}  Some of the ff. properties are determined by electronic structure - Chemical - Electrical - Thermal - Optical - **Electronic Structure** Electrons have wavelike and particulate properties. - **Electron Energy States** Electrons have [discrete energy states] and [tend to occupy lowest available energy state.]  - **Survey of Elements** Most elements electron configuration is [not stable] Why? Because Valence (outer) shell usually not filled completely.  - **Electron configurations** Stable elements are non-reactive so they don't need to participate in any chemical reaction Group of elements = valence electrons  - **Electronegativity** - The electronegativity from left to right and downward to upward increases. - Metals tend to give up electrons and the Non-metals (Polymers) acquire more electrons while ceramics normally sharing of a metal and non-metal - **Ionic Bonding**   - **Covalent Bonding** - similar electronegativity ∴ share electrons - bonds determined by valence -- *s* & *p* orbitals dominate bonding **PPT 2 - MATERIAL TESTING** **Material testing** - determines the physical and mechanical properties of raw materials and components. - measurement of the characteristics and behavior of such substances as metals, ceramics, or plastics under various conditions. **Types of Material Testing** (compose of destructive test and non-destructive test) Destructive Tests (also called mechanical test): - Tension/Tensile Testing - Compression Testing - Coefficient of Thermal Expansion - Beam Deflection - Shear/Torsion Test - Bend Test - Hardness Test - Impact Test - **Tension/Tensile Testing** - static tension test determines the breaking point of the material and its elongation, designated as strain. - Used to determine: - ***Yield Strength*** - which is the maximum stress that can be applied before it begins to change shape permanently. - ***Ultimate Tensile Strength*** - is the maximum stress that a material can withstand while being stretched or pulled before breaking - ***Ductility*** - Capacity of a material to deform permanently (e.g., stretch, bend, or spread) in response to stress - ***Strain Hardening Characteristics*** - process of making a metal harder and stronger through plastic deformation. This implies that the metal is becoming stronger as the strain increases. - ***Young's Modulus*** - measures the stiffness of a specimen whereby the material will return to its original condition once the load has been removed.  **Why is Tensile Testing Performed?** - **S**electing materials for an application - **P**redicting how a material will perform under different forces - **D**etermining whether the requirements of a specification, contract or standard are met - **D**emonstrating proof of concept for a new product - **P**roving characteristics for a proposed patent - **P**roviding standard quality assurance data for scientific and engineering functions - **C**omparing technical data for different material options - **M**aterial testing to provide evidence for use in legal proceedings - **Compression Test** - method for determining the behavior of materials under a compressive load. - conducted by loading the test specimen between two plates, and then applying a force to the specimen by moving the crossheads together - during the test, the specimen is compressed, and deformation versus the applied load is recorded. - Compressive Strength - Maximum compressive stress a material is capable of withstanding without fracture - Brittle materials fracture during testing and have a definite compressive strength value. - Compressive strength of ductile materials is determined by their degree of distortion during testing **Elastic Limit** - maximum stress that a material can sustain without permanent deformation after removal of the stress. **Proportional Limit** - the greatest amount of stress a material is capable of reaching without deviating from the linear relation of the stress-strain curve. proportional limit stress = measure of the onset of plasticity during monotonic loading **Yield Point** - stress in a material (usually less than the maximum attainable stress) at which an increase in strain occurs without an increase in stress. Only certain metals have a yield point. **Strain** - amount of change in the size or shape of a material due to force. - **Coefficient of Thermal Expansion** - rate at which the size of a material changes with respect to temperature change. - size considerations can be made by changes in length, area or volume, and so there are coefficients derivable for linear, area and volume expansions. - The unit of measurement for thermal expansion coefficients is the inverse of temperature, °C-1 or K-1. - Extra dimensions such as cm/cm or mm²/mm² are added to the unit so that it can be inferred whether the coefficient is linear, area or volumetric. **What is the coefficient of Thermal Expansion?** - When a material is heated, the molecules begin to agitate more, and the average distance between them rises, resulting in the material's dimensions expanding**.** - Because of their atomic bonding and molecular structures, different materials react to temperature increases in different ways.   example: - **Beam Deflection** - state of deformation of a beam from its original shape under the work of a force or load or weight. One of the most important applications of beam deflection is to obtain equations with which we can determine the accurate values of beam deflections in many practical cases. - **Shear Testing** - Designed to apply stress to a test sample so that it experiences a sliding failure along a plane that is parallel to the forces applied. - **Shear forces** cause one surface of a material to move in one direction and the other surface to move in the opposite direction so that the material is stressed in a sliding motion. - **Shear testing** applies a lateral shear force to the specimen until failure results. - Purpose of Shear Testing - to determine the **shear strength,** (maximum shear stress that the material can withstand before failure occurs) of a material. - Important design characteristics of many types of fasteners such as bolts and screws. Shear Testing - Fasteners, such as bolts, may be pulled in ***single or double shear*** to SAE(**Society of Automobile Engineers**) or ASTM (**American Standard for Testing and Materials**) specification. - A **single shear test fixture** uses **two blades** with centrally located transverse holes. One blade is kept stationary with the fastener in place while the second blade is moved in a parallel plane, which shears the fastener. - **Double shear testing** uses a **second stationary blade support** behind the shearing blade. **Lap Shear Testing** - performed to determine the shear strength of an adhesive that is applied to two metal plates and pulled to failure. It can be used to compare between adhesive types or different lots within the same adhesive. Specimens are cut and prep per ASTM (**American Standard for Testing and Materials**) standard prior to testing. Types of materials tested in Shear - **Rigid substrates** composed of metals, plastics, ceramics, composites or woods but usually come in a solid form and are used as building materials or fasteners. - **Adhesives** are used to bond two materials together and experience shear stress when the materials are pulled in opposing directions in an attempt to slide them apart. - **Layered composites** experience shear stress in a similar manner to adhesives as the shear forces are applied to the glue or laminate used to hold the layers together. - **Torsion Test** - mechanical testing that evaluates the properties of materials or devices while under stress from angular displacement. Categories: - testing raw materials like metal wires or plastic tubing to determine properties such as shear strength and modulus; or - functional testing of finished products subjected to torsion, such as screws, pharmaceutical bottles, and sheathed cables. The most common mechanical properties measured by torsion testing are **modulus of elasticity** in **shear**, **yield shear strength**, **ultimate shear strength**, **modulus of rupture in shear**, and **ductility**. Why perform a Torsion test? - For example, the metal used in vehicle drive trains experiences a complex combined loading when in use, with torsion being the main component.  An engineer trying to design a more fuel-efficient vehicle may need to change the material of the driveshaft in order to reduce vehicle weight. Torsional testing can help the engineer identify an appropriate material that will possess the required torsional strength while also - Many finished products are also subjected to torsional forces during their operation. Products such as biomedical tubing, switches, and fasteners are just a few devices subjected to torsional stresses in their everyday use. By testing their products in torsion, manufacturers are able to simulate real life service conditions,check product quality, verify designs, and ensure proper manufacturing techniques. **Different Types of Torsion Test** Torsion tests can be performed by applying only a rotational motion or by applying both axial (tension or compression) and torsional forces. Types of torsion testing vary from product to product but can usually be classified as failure, proof, or product operation testing. - **Torsion Only:** Applying only torsional loads to the test specimen. - **Axial-Torsion:** Applying both axial (tension or compression) and torsional forces to the test specimen. - **Failure Testing:** Twisting the product, component, or specimen until failure. Failure can be classified as either a physical break or a kink/defect in the specimen. - **Proof Testing:** Applying a torsional load and holding this torque load for a fixed amount of time. - **Functional Testing:** Testing complete assemblies or products such as bottle caps, switches, dial pens, or steering columns to verify that the product performs as expected under torsion loads. **What Are the Different Types of Torsion Testing Materials?** - Materials used in structural, biomedical and automotive applications are among the more common materials to experience torsion in their applications. - These materials may be composed of [metals, plastics, woods, polymers, composites, or ceramics] among others and commonly take the forms of fasteners, rods, beams, tubes and wires. - **Bend test** - Application of a force to the center of a bar that is supported on each end to determine the resistance of the material to a static or slowly applied load. **Flexural strength or modulus of rupture** -The stress required to fracture a specimen in a bend test. **Flexural modulus** - The modulus of elasticity calculated from the results of a bend test, giving the slope of the stress-deflection curve.  **Flexural Strength** - Schematic for a 3-point bending test. - Able to measure the stress-strain behavior and flexural strength of brittle ceramics. - **Flexural strength** (modulus of rupture or bend strength) is the stress at fracture.  - **Hardness of Materials** - measure of the resistance of a metal to permanent plastic deformation. - Hardness of a metal = measured by forcing an indenter into its surface. - The indenter material which is usually a [ball], [pyramid], or [cone] is made of a material much harder than the material being tested. - **Hardness Testing machine** - The indenter is pressed into the metal. - Softer materials leave a deeper indentation.  - **Brinell Hardness test** - Uses ball indenter. - Cannot be used for thin materials. - Ball may deform on very hard materials - Surface area of indentation is measured. - **Vickers Hardness Test** - Uses square pyramid indenter. - Accurate results. - Measures length of diagonal on indentation. - **Rockwell hardness test** - Gives direct reading. - **Rockwell B** (ball) used for soft materials. - **Rockwell C** (cone) uses diamond cone for hard materials. - Flexible, quick and easy to use. **PPT 3 - Fracture Toughness and Fatigue and Engineering Materials** - **Types of Fracture** - A **simple fracture** is the separation of a body into two or more pieces in response to an applied static stress at temperatures that are low relative to the melting point of the material. - Classification is based on the ability of a material to experience plastic deformation. - **Ductile Fracture (***Metals***)** is accompanied by significant plastic deformation - **Brittle Fracture(***Ceramics***)** is little or no plastic deformation and sudden or catastrophic - **Fracture Mechanism** - **Crack Propagation** - Cracks propagate due to sharpness of crack tip - A plastic material deforms at the tip, "blunting" the crack.  - **Elastic Strain Energy** - energy stored in material as it is elastically deformed - this energy is released when the crack propagates - creation of new surfaces requires energy - **Ductile Fracture** - Plastic deformation present prior to fracture (aluminum, mild steel) - "Preferred" fracture mode - Strength increases past yield - **Moderately Ductile Failure Evolution** - Necking - Void Nucleation - Coalescence of Cavities - Crack Propagation - Fracture - **Brittle Fracture** - Typical of glass(Ceramics), cast iron, chalk, HSS, plane strain situations, low temperature - Ductile to brittle transition temp - Austenitic SS for cryogenics - No or limited plastic deformation - **Comparison between Ductile and Brittle Fracture** - **Ductile fracture** has extensive plastic deformation in the vicinity of the advancing crack. The process proceeds relatively slow (stable). The crack resists any further extension (continued force) unless there is an increase in the applied stress. - In **brittle fracture,** cracks may spread very rapidly, with little deformation. These cracks are more unstable and crack propagation will continue without an increase in the applied stress.  - **Ductile Fracture** SEM -- Scanning Electron Microscope - **Brittle Fracture** - **Transgranular Fracture** - Cleavage - in most brittle crystalline materials (*Metals*), crack propagation that results from the repeated breaking of atomic bonds along specific planes. - This leads to transgranular fracture where the crack splits (cleaves) through the grains. - **Intergranular Fracture** - is typically due to elemental depletion (chromium) at the grain boundaries or some type of weakening of the grain boundary due to chemical attack, oxidation, embrittlement. - **Fracture Mechanics** Studies the relationships between: - material properties - stress level - crack producing flaws - crack propagation mechanisms - **TOUGHNESS VS. FRACTURE TOUGHNESS** **Toughness -** materials' ability to absorb energy without fracturing. ( No fracture, No Flaw, No Crack)  **Fracture Toughness** - it measures a materials resistance to fracture when a crack or flaw is present. (There's flaw and crack until it reach fracture) What is **FRACTURE TOUGHNESS?** - measures a material's resistance to brittle fracture when a crack is present. - indication of the amount of stress required to propagate a preexisting flaw which may appear may appear as [cracks, voids, metallurgical inclusions, weld defects, design discontinuities,] or some combination thereof - It is common practice to assume that flaws are present and use the linear elastic fracture mechanics (LEFM) approach to design critical components. - LEFM (**Linear Elastic Fracture Mechanics**) uses the flaw size and features, component geometry, loading conditions and the fracture toughness to evaluate the ability of a component containing a flaw to resist fracture. **Metals hold the highest values of fracture toughness.** Cracks cannot easily propagate in tough materials, making metals highly resistant to cracking under stress and gives their stress--strain curve a large zone of plastic flow. - **Test used for determining fracture toughness and fatigue** - Destructive Testing - Impact testing - Fatigue Testing - **Stress-Intensity Factor (K)** - The stress-intensity factor (K) is used to determine the fracture toughness of most materials. - A Roman numeral subscript indicates the mode of fracture and the three modes of fracture are illustrated in the image to the right. - **Mode I** fracture is the condition where the crack plane is normal to the direction of largest tensile loading. This is the most commonly encountered mode. - The stress intensity factor is a function of [loading, crack size, and structural geometry.] The stress intensity factor may be represented by the following equation: - **How to solve for Fracture Toughness** To compute for fracture toughness, three essential parameters are needed, and these parameters are **Applied Load Constant (Y), Material Critical Stress (σ~c~) **and **Length of Crack on Surface (a).** **K~c~ = Yσ~c~√(πa)** Where: **K~c~** = Fracture Toughness\ **Y** = Applied Load Constant\ **σ~c~** = Material Critical Stress\ **a** = Length of Crack on Surface Ex:  Calculating the Applied Load Constant when the Fracture Toughness, the Material Critical Stress and the Length of Crack on Surface is Given. **Y = ^K^~c~ / ~σc √(πa)~** Where: **Y** = Applied Load Constant\ **K~c~ **= Fracture Toughness\ **σ~c~** = Material Critical Stress\ **a** = Length of Crack on Surface Ex: Calculating the Material Critical Stress when the Fracture Toughness, the Applied Load Constant and the Length of Crack on Surface is Given. **σ~c~ = ^K^~c~ / ~Y\ √(πa)~** Where: **σ~c~** = Material Critical Stress\ **K~c~ **= Fracture Toughness\ **Y** = Applied Load Constant\ **a** = Length of Crack on Surface Ex: Calculating the Length of Crack on Surface when the Fracture Toughness, the Applied Load Constant and the Material Critical Stress is Given. **a = (^K^~c~ / ~Yσc~)^2^ x ^1^ / ~π~** Where: **a** = Length of Crack on Surface\ **K~c~ **= Fracture Toughness\ **Y** = Applied Load Constant\ **σ~c~** = Material Critical Stress Ex: **Fatigue** - is a failure mechanism that involves the cracking of materials and structural components due to cyclic (or fluctuating) stress.   - **FATIGUE TESTING** - From Latin \"**Fatigare**\" meaning **\"to tire."** - Engineering terminology: - **damage and failure of materials under cyclic loads.** -  **Fatigue testing **is defined as the **process of progressive localized permanent structural change** occurring in a material subjected to conditions that produce fluctuating stresses and strains at some point or points and that may culminate in cracks or complete fracture after a sufficient number of fluctuations. - **The process of fatigue consists of three key stages:** - **Types of Fatigue** - **High-Cycle Fatigue: **This occurs when materials are subjected to stresses much lower than their yield strength, over a high number of cycles. - **Low-Cycle Fatigue:** transpires when materials are subjected to higher stresses, typically exceeding the yield strength over a smaller number of cycles. This can cause structural failure within thousands or even hundreds of cycles. - **Thermal Fatigue: **This is a specific type of fatigue caused by cyclic thermal loads, usually as a result of fluctuating temperatures. This fluctuation causes materials to expand and contract, leading to stress build-up and eventual crack propagation. - **Fatigue Analysis** There are two primary things in understanding fatigue: 1. **Initiate a crack** - **The stress field near a fatigue crack tip can be divided into three types:** - **Impact Tests** - measure the ability of a material to resist deformation in response to a sudden load. These tests are normally conducted according to test methods and standards published by ASTM International. - **4 types of impact tests:** Charpy, Izod, drop-weight, and dynamic tear test. - Different materials testing standards, such as ASTM E23, ASTM A370, and ASTM D256 govern the exact testing procedure and test specimen requirements for each type of impact test, and for different material groups (e.g., metals vs. plastics). How does Impact Test Work? An impact test works by striking a properly prepared and fixtures test specimen with a weight, either from the side or from above. - For **Charpy and IZOD impact tests**, a pendulum with a weighted hammer is released from a specific height. The arc of its motion strikes the vertically oriented test specimen on its side. - For **drop-weight impact tests and dynamic tear tests**, a weight is guided by rails and dropped directly onto a test specimen from above. For each type of impact test, a notch is cut into the test specimen, forcing the fracture of the specimen to occur at a repeatable location. **The CHARPY Impact test** - The Charpy Impact Test was invented in 1900 by Georges Augustin Albert Charpy (1865-1945). The **Charpy impact test** measures the **energy absorbed by a standard notched specimen while breaking under an impact load.** The Charpy impact test continues to be used as an economical quality control method to determine the notch sensitivity and impact toughness of engineering materials. - The Charpy Impact Test is **commonly used on metals**, but is also applied to composites, ceramics and polymers. With the Charpy impact test one most commonly evaluates the relative toughness of a material, and as such, it is **used as a quick and economical quality control device.** **The IZOD Impact test** - **Izod impact testing **is an  **ASTM  standard method of determining the impact resistance of materials**. A pivoting arm is raised to a specific height (constant  potential energy) and then released. The arm swings down hitting the sample, breaking the specimen. The energy absorbed by the sample is calculated from the height the arm swings to after hitting the sample. A notched sample is generally used to determine impact energy and notch sensitivity. - The test is similar to the  Charpy impact test but uses a different arrangement of the specimen under test. The Izod impact test differs from the Charpy impact test in that the sample is held in a cantilevered beam configuration as opposed to a three-point bending configuration. - The test is named after the English engineer Edwin Gilbert Izod (1876--1946), who described it in his 1903 address to the British Association, subsequently published in Engineering. **The Drop-Weight Impact Test** - The drop-weight impact test, also known as the **Pellini test**, uses a  weight suspended over a simply supported horizontal test specimen and then dropped to produce the impact. - A tube or rails guide the weight during its "free-fall" onto the specimen. Unlike Charpy and Izod tests, the height of the weight before and after it strikes the test specimen cannot be used to determine the energy absorbed by the test specimen. Instead, results only pass or fail since energy absorbed by the test specimen cannot be adequately determined. - Fracture is not the only criterion for failure, deformation or the formation of a crack can also be considered a failure. **The Dynamic Tear test** - The dynamic tear test is similar to the drop-weight impact test. In the dynamic tear test, a notched test specimen is simply supported on both ends. A weight is dropped on the face opposite the notched side and subjecting the test specimen to a bending impact load and 3-point bending. The primary difference between drop-weight impact testing and dynamic tear testing is that dynamic tear testing is often used for test specimens with a thickness less than 5/8" while drop-weight impact testing is for test specimens thicker than 5/8". - **Fatigue Test** - helps determine a material's ability to withstand cyclic fatigue loading conditions. By design, a material is selected to meet or exceed service loads that are anticipated in fatigue testing applications. - Cyclic fatigue tests produce repeated loading and unloading in tension, compression, bending, torsion or combinations of these stresses. - Fatigue tests are commonly loaded in tension -- tension, compression -- compression and tension into compression and reverse. **What is the Purpose of Fatigue Testing?** 1\. to determine the lifespan that may be expected from a material subjected to cyclic loading. - *However, fatigue strength and crack resistance are commonly sought values as well.* - *The fatigue life of a material is the total number of cycles that a material can be subjected to under a single loading scheme.* 2\. To determine the maximum load that a sample can withstand for a specified number of cycles. - *All of these characteristics are extremely important in any industry where a material is subject to fluctuating instead of constant forces.* **How to Perform a Fatigue Test?** - To perform a fatigue test, a sample is loaded into a fatigue tester or fatigue test machine and loaded using the pre-determined test stress, then unloaded to either zero load or an opposite load. - This cycle of loading and unloading is then repeated until the end of the test is reached. The test may be run to a pre-determined number of cycles or until the sample has failed depending on the parameters of the test. **PPT 4 - CORROSION PREVENTION AND CONTROL** - [Corrosion] slow but continuous eating away of metallic components by chemical or electrochemical attack.   - **Three factors govern corrosion**. 1\. The metal from which the component is made. 2\. The protective treatment the component surface receives. 3\. The environment in which the component is kept. - Noble Metals - highly resistant to oxidation and corrosion due to their low reactivity *(Ex: Gold, platinum, silver)* - Prevention processes - unable to prevent the inevitable failure of the component by corrosion. - only slow down the process to a point where the component will have worn out or been discarded for other reasons before failing due to corrosion. - **Types of corrosion** 1.Atmospheric Corrosion 2\. Galvanic Corrosion 3\. Corrosion Accelerated by Mechanical Stresses a\. Stress Corrosion b\. Corrosion Fatigue c\. Fretting Corrosion d\. Impingement Corrosion - **Atmospheric Corrosion** - gradual degradation of a material, typically metals, due to chemical reactions with elements present in the atmosphere, such as oxygen, water vapor, carbon dioxide, and pollutants. - **Factors influencing Atmospheric Corrosion** 1\. High humidity accelerates corrosion as water acts as an electrolyte, enabling electrochemical reactions. 2\. Pollutants (Ex: Chlorides and Sulfur Compounds) 3\. Temperature -- high temp increase reaction rates 4\. Material composition 5\. Time of Wetness 6\. Atmospheric categories - **Mechanism of Atmospheric Corrosion** 1\. Formation of a thin water film on the metal surface (due to humidity, dew, or rain). 2\. Dissolution of oxygen and pollutants in the water film, creating an electrolyte. 3\. Electrochemical reactions between the metal and oxygen, resulting in corrosion products like rust (for iron) or patinas (for copper). - **Prevention of Atmospheric Corrosion** - **Protective Coatings.** Paints, powder coatings, or galvanization (zinc coating) protect the metal surface. - **Corrosion-Resistant Materials.** Use materials like stainless steel, aluminum, or titanium. - **Environmental Control.** Reduce exposure to pollutants and humidity (e.g., dehumidifiers in storage areas). - **Regular Maintenance.** Cleaning surfaces to remove corrosive agents like salt or dust. - **Cathodic Protection.** Using sacrificial anodes to redirect corrosion away from critical metal structures. - **Galvanic Corrosion** - occurs when two dissimilar metals are in electrical contact with each other in the presence of an electrolyte (such as water or moisture) **ELECTROCHEMICAL CELL** **Anode Reactions** - **Factors Influencing Galvanic Corrosion** **1. Electrochemical Potential Difference.** The greater the difference in potential between the two metals, the faster the corrosion. **2. Size of Anode and Cathode.** A small anode and a large cathode accelerate corrosion of the anode. **3. Distance Between Metals.** Corrosion decreases with increased physical separation in the electrolyte. **4. Environment.** Saltwater or polluted environments accelerate galvanic corrosion due to better conductivity. **5. Coatings.** Coatings on the cathode may inadvertently increase corrosion of the anode if the coating fails locally. **Prevention of Galvanic Corrosion** - **Material Selection.** Use metals close to each other in the Galvanic Series to reduce potential differences. - **Insulation.** Use non-conductive barriers (plastic washers, gaskets) to prevent electrical contact. - **Protective Coatings.** Apply coatings to one or both metals to isolate them from the electrolyte. - **Sacrificial Anodes.** Introduce a more reactive metal (e.g., zinc) to protect both metals in the system. - **Environmental Control.** Reduce exposure to moisture or corrosive environments