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MFGT 290 MFGT Certification Class

MFGT 290 MFGT Certification Class. 8: Strength of Materials Chapter 11: Material Properties. Professor Joe Greene CSU, CHICO. MFGT 290. Chap 8: Strength of Materials. Stress and Strain Axial Loading Torsional Loading Beam Loading Column Loading Practice Problems.

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MFGT 290 MFGT Certification Class

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  1. MFGT 290MFGT Certification Class 8: Strength of Materials Chapter 11: Material Properties Professor Joe Greene CSU, CHICO MFGT 290

  2. Chap 8: Strength of Materials • Stress and Strain • Axial Loading • Torsional Loading • Beam Loading • Column Loading • Practice Problems

  3. Mechanical Test Considerations P P A P P P P shear compression tension • Normal and Shear Stresses • Force per unit area • Normal force per unit area • Forces are normal (in same direction) to the surface • Shear force per unit area • Forces are perpendicular (right angle) to the surface • Direct Normal Forces and Primary types of loading • Prismatic Bar: bar of uniform cross section subject to equal and opposite pulling forces P acting along the axis of the rod. • Axial loads: Forces pulling on the bar • Tension= pulling the bar; Compression= pushing; torsion=twisting; flexure= bending; shear= sliding forces Normal Forces Shear Forces

  4. Stress-Strain Diagrams Forces Test Sample Fixed • Equipment • Tensile Testing machine • UTM- Universal testing machine • Measures • Load, pounds force or N • Deflection, inches or mm • Data is recorded at several readings • Results are averaged • e.g., 10 samples per second during the test. • Calculates • Stress, Normal stress or shear stress • Strain, Linear strain • Modulus, ratio of stress/strain

  5. Stress-Strain Diagrams Linear (Hookean) Stress Non-Linear (non-Hookean) Strain • Stress-strain diagrams is a plot of stress with the corresponding strain produced. • Stress is the y-axis • Strain is the x-axis

  6. Modulus and Strength Modulus Yield Strength Proportional Limit Stress Strain • Modulus: Slope of the stress-strain curve • Can be Initial Modulus, Tangent Modulus or Secant Modulus • Secant Modulus is most common • Strength • Yield Strength • Stress that the material starts to yield • Maximum allowable stress • Proportional Limit • Similar to yield strength and is the point where Hooke’s Law is valid • If stress is higher than Hooke’s Law is not valid and can’t be used. • Ultimate strength • Maximum stress that a material can withstand • Important for brittle materials Ultimate Strength

  7. Allowable Axial Load • Structural members are usually designed for a limited stress level called allowable stress, which is the max stress that the material can handle. • Equation 8-2 can be rewritten • Required Area • The required minimum cross-sectional area A that a structural member needs to support the allowable stress is from Equation 9-1 Example 8-2.1 Hinged Beam • Statics review • Sum of forces = 0 • Sum of Moments = 0. Moment is Force time a distance to solid wall

  8. Strain  L • Strain: Physical change in the dimensions of a specimen that results from applying a load to the test specimen. • Strain calculated by the ratio of the change in length, , and the original length, L. (Deformation) • Where, •  = linear strain ( is Greek for epsilon) •  = total axial deformation (elongation of contraction) = Lfinal –Linitial = Lf - L • L = Original length • Strain units (Dimensionless) • Units • When units are given they usually are in/in or mm/mm. (Change in dimension divided by original length) • % Elongation = strain x 100%

  9. Strain 0.1 in 1 in 10in • Example • Tensile Bar is 10in x 1in x 0.1in is mounted vertically in test machine. The bar supports 100 lbs. What is the strain that is developed if the bar grows to 10.2in? What is % Elongation? •  =Strain = (Lf - L0)/L0 = (10.2 -10)/(10)= 0.02 in/in • Percent Elongation = 0.02 * 100 = 2% • What is the strain if the bar grows to 10.5 inches? • What is the percent elongation? 100 lbs

  10. Tensile Modulus and Yield Strength • Modulus of Elasticity (E) (Note: Multiply psi by 7,000 to get kPa) • Also called Young’s Modulus is the ratio of stress to corresponding strain • A measure of stiffness • Yield Strength: (Note: Multiply psi by 7,000 to get kPa) • Measure of how much stress a material can withstand without breaking • Modulus (Table 8-1) Yield Strength • Stainless Steel E= 28.5 million psi (196.5 GPa) 36,000 psi • Aluminum E= 10 million psi 14,000 psi • Brass E= 16 million psi 15,000 psi • Copper E= 16 million psi • Molybdenum E= 50 million psi • Nickel E= 30 million psi • Titanium E= 15.5 million psi 120,000 psi • Tungsten E= 59 million psi • Carbon fiber E= 40 million psi • Glass E= 10.4 million psi • Composites E= 1 to 3 million psi 15,000 psi • Plastics E= 0.2 to 0.7 million psi 5,000 to 12,000 psi

  11. Hooke’s Law • Hooke’s Law relates stress to strain by way of modulus • Hooke’s law says that strain can be calculated as long as the stress is lower than the maximum allowable stress or lower than the proportional limit. • If the stress is higher than the proportional limit or max allowable stress than the part will fail and you can’t use Hooke’s law to calculate strain. • Stress = modulus of elasticity, E, times strain • Stress=  = load per area, P/A • Strain=  = deformation per length,  /L • Rearrange Hooke’s law • Solving for deformation is • With these equations you can find • How much a rod can stretch without breaking. • What the area is needed to handle load without breaking • What diameter is needed to handle load without breaking • Example 10-1 • Example 10-3 Eqn 8-3

  12. Problem solving techniques • Steps to solve most Statics problems • Set-up problem • Draw picture and label items (D, L, P, Stress, etc..) • List known values in terms of units. • Solve problem • Make a Force balance with Free body diagram • Identify normal forces • Identify shear forces • Write stress as Force per unit area • Calculate area from set-up, or • Calculate force from set-up • Write Hooke’s law • Rearrange for deflections • Write deflections balance • Solve for problem unknowns Eqn 8-3

  13. Safety Factor • Allowable Stresses and Factor of Safety • Provide a margin of safety in design for bridges, cars, buildings, rockets, space shuttles, air planes, etc… • Structural members and machines are designed so that columns, plates, trusses, bolts, see much less than the stress that will cause failure. • Ductile materials: If the stress is greater than the yield strength or proportional limit of the material. • Brittle materials: If the stress is greater than the ultimate strength of the material.Since they do not show any yielding, just fracturing.

  14. Stress Concentrations • Stresses can be higher near holes, notches, sharp corners in a part or structural member. • Stress concentration factor, K = stresses near hole stresses far away from hole • K is looked up in a table or on a graph • Stress at hole can be calculated to see if part will fail. • Where b is the net width at hole section and t is the thickness.

  15. Thermal Stresses • Most materials expand when heated as the temperature increases. • As the temperature goes up, the material expands and results in forces that cause stress in the part. As temperature increases the stresses increase in part. • Examples, • Cast iron engine block heat up to 500F and expands the cast iron block which causes stresses at the bolts. The bolts must be large enough to withstand the stress. • Aluminum heats up and expands and then cools off and contracts. • Sometimes the stresses causes cracks in the aluminum block. • Space shuttle blasts off and heats up, goes into space and cools down (-200F), and reenters Earths atmosphere and heats up (3000F) • Aluminum melts at 1300F so need ceramic heat shields • Aluminum structure expands and cools. • The amount the material expands is as follows: • Change in length that is causes by temperature change (hot or cold) • Where, •  = change in length •  = the CLTE (coefficient of linear thermal expansion • T = change in temperature (Thot – Tcold) • L = length of member • Examples

  16. Strain and Poisson’s Ratio Transverse Strain Axial Strain P, Load • Axial strain is the strain that occurs in the same direction as the applied stress. • Transverse strain is the strain that occurs perpendicular to the direction of the applied stress. • Poisson’s ratio is ratio of lateral strain to axial strain. Poisson’s ratio = lateral strain axial strain • Example • Calculate the Poisson’s ratio of a material with lateral strain of 0.002 and an axial strain of 0.006 • Poisson’s ratio = 0.002/0.006 = 0.333 • Example • Note: For most materials, Poisson’s ratio is between 0.25 and 0.5 • Plastics: Poisson’s ratio 0.3 • Table 8-1 Metals: Poisson’s ratio = 0.3 steel, 0.33 Al, 0.35 Mg, 0.34 Ti

  17. Chapter 11: Material Properties • Structure of Matter • Material Testing Agencies • Physical Properties • Mechanical Properties and Test Methods • Stress and Strain • Fatigue Properties • Hardness • Practice Problems

  18. Fatigue Properties S, stress N, number of cycles • Fatigue Properties • All materials that are subjected to a cyclic loading can experience fatigue • Failure occurs through a maximum stress at any cycle. • Test methods • Subject the material to stress cycles and counting the number of cycles to failure, then • Fatigue properties are developed. • Table of properties for each material • How many cycles a material can experience at a certain stress level before failing. • S-N diagrams are developed (Stress and Number of cycles) • Specify fatigue as a stress value • Design for less than fatigue stress

  19. Fundamentals of Hardness • Hardness is thought of as the resistance to penetration by an object or the solidity or firmness of an object • Resistance to permanent indentation under static or dynamic loads • Energy absorption under impact loads (rebound hardness) • Resistance toe scratching (scratch hardness) • Resistance to abrasion (abrasion hardness) • Resistance to cutting or drilling (machinability) • Principles of hardness (resistance to indentation) • indenter: ball or plain or truncated cone or pyramid made of hard steel or diamond • Load measured that yields a given depth • Indentation measured that comes from a specified load • Rebound height measured in rebound test after a dynamic load is dropped onto a surface

  20. Hardness Mechanical Tests • Brinell Test Method • One of the oldest tests • Static test that involves pressing a hardened steel ball (10mm) into a test specimen while under a load of • 3000 kg load for hard metals, • 1500 kg load for intermediate hardness metals • 500 kg load for soft materials • Various types of Brinell • Method of load application:oil pressure, gear-driven screw, or weights with a lever • Method of operation: hand or electric power • Method of measuring load: piston with weights, bourdon gage, dynamoeter, or weights with a lever • Size of machine: stationary (large) or portable (hand-held)

  21. Brinell Test Conditions • Brinell Test Method (continued) • Method • Specimen is placed on the anvil and raised to contact the ball • Load is applied by forcing the main piston down and presses the ball into the specimen • A Bourbon gage is used to indicate the applied load • When the desired load is applied, the balance weight on top of the machine is lifted to prevent an overload on the ball • The diameter of the ball indentation is measured with a micrometer microscope, which has a transparent engraved scale in the field of view

  22. Brinell Test Example • Brinell Test Method (continued) • Units: pressure per unit area • Brinell Hardness Number (BHN) = applied load divided by area of the surface indenter Where: BHN = Brinell Hardness Number L = applied load (kg) D = diameter of the ball (10 mm) d = diameter of indentation (in mm) • Example: What is the Brinell hardness for a specimen with an indentation of 5 mm is produced with a 3000 kg applied load. • Ans:

  23. Brinell Test Method (continued) • Range of Brinell Numbers • 90 to 360 values with higher number indicating higher hardness • The deeper the penetration the higher the number • Brinell numbers greater than 650 should not be trusted because the diameter of the indentation is too small to be measured accurately and the ball penetrator may flatten out. • Rules of thumb • 3000 kg load should be used for a BHN of 150 and above • 1500 kg load should be used for a BHN between 75 and 300 • 500 kg load should be used for a BHN less than 100 • The material’s thickness should not be less than 10 times the depth of the indentation

  24. Advantages & Disadvantages of the Brinell Hardness Test • Advantages • Well known throughout industry with well accepted results • Tests are run quickly (within 2 minutes) • Test inexpensive to run once the machine is purchased • Insensitive to imperfections (hard spot or crater) in the material • Limitations • Not well adapted for very hard materials, wherein the ball deforms excessively • Not well adapted for thin pieces • Not well adapted for case-hardened materials • Heavy and more expensive than other tests ($5,000)

  25. Rockwell Test • Hardness is a function of the degree of indentation of the test piece by action of an indenter under a given static load (similar to the Brinell test) • Rockwell test has a choice of 3 different loads and three different indenters • The loads are smaller and the indentation is shallower than the Brinell test • Rockwell test is applicable to testing materials beyond the scope of the Brinell test • Rockwell test is faster because it gives readings that do not require calculations and whose values can be compared to tables of results (ASTM E 18)

  26. Rockwell Test Description • Specially designed machine that applies load through a system of weights and levers • Indenter can be 1/16 in hardened steel ball, 1/8 in steel ball, or 120° diamond cone with a somewhat rounded point (brale) • Hardness number is an arbitrary value that is inversely related to the depth of indentation • Scale used is a function of load applied and the indenter • Rockwell B- 1/16in ball with a 100 kg load • Rockwell C- Brale is used with the 150 kg load • Operation • Minor load is applied (10 kg) to set the indenter in material • Dial is set and the major load applied (60 to 100 kg) • Hardness reading is measured • Rockwell hardness includes the value and the scale letter

  27. Rockwell Values • B Scale: Materials of medium hardness (0 to 100HRB) Most Common • C Scale: Materials of harder materials (> 100HRB) Most Common • Rockwell scales divided into 100 divisions with each division (point of hardness) equal to 0.002mm in indentation. Thus difference between a HRB51 and HRB54 is 3 x 0.002 mm - 0.006 mm indentation • The higher the number the harder the number

  28. Rockwell and Brinell Conversion • For a Rockwell C values between -20 and 40, the Brinell hardness is calculated by • For HRC values greater than 40, use • For HRB values between 35 and 100 use

  29. Rockwell and Brinell Conversion • For a Rockwell C values, HRC, values greater than 40, • Example, • Convert the Rockwell hardness number HRc 60 to BHN • Review Questions

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