IM417 - Mechanical Behavior of Materials I

Course Information

• Course title: IM417 - Failure Analysis
• Lecture topic: Mechanical Behavior of Materials I
• Lecturer: Dr. Mohamed Khamis
• Department: Industrial and Management Engineering

Technological Tools

• Mechanical Testing
  • Hardness, micro-hardness, tensile, shear, physical testing
• Stress Analysis/FEA
  • Magnitude, principal direction, sensitivity
• Instrumentation
  • Strain gauges, accelerometers, thermocouples, etc.
• Non-Destructive Testing (NDT)

Mechanical Testing

• Lab testing: Up to 100,000 lbf
• Field testing: Over 1 million lbf
• Output:
  • Stress versus Strain
  • Elastic Deformation
  • Plastic Deformation
  • Elastic limit
  • Tensile strength, Necking
  • Hooke's Law
  • Poisson's ratio
  • Modulus of resilience(E)
  • Tensile toughness
  • Ductility

Measuring Components

• Load cell: Measures load (P)
• Extensometer: Measures gage length (L) and diameter (d)
• Data acquisition under computer control
  • Fast data collection: Disk storage problems
  • Slow data collection: Resolution problems
• Convert load-extension to stress-strain

Tensile Test

• Specimen: Stainless Steel

Stress vs Strain

• Mechanical Properties
  • Deal with elastic or inelastic behavior of a material under load
  • Describe material behavior under applied forces in terms of stress and resulting strain or applied strain and resulting stress
  • Example: 100 kg force on a rod stretches it, measured as strain

Strength

• Ability of a material to resist load without rupture
  • Ultimate strength: Maximum force per cross-sectional area
  • Yield strength: Force at yield point per cross-sectional area

Stiffness

• Resistance of a material to deform under load in an elastic state
  • Measured by the Modulus of Elasticity (Stress/strain)

Testing Procedures

• Primary measurements: Load applied and effects of load application
• Parameters of test: Method of loading, condition of the specimen during the test and surrounding conditions during testing
• Primary types of tests
  • Tensile, Compression, Shear, Torsion, Flexure

Mechanical Test Considerations

• Tests classification - Load application
  • Kind of stress induced: Single load or multiple loads
  • Rate at which stress is developed: Static versus dynamic
  • Number of cycles of load application: Single versus fatigue

Tensile Test (Details)

• Unidirectional force applied to a specimen via a movable crosshead
• Crosshead movement can be performed using screws or a hydraulic mechanism

Tensile Stress-Strain Curves

• Different material types display varying stress-strain curves
  • Metal (graph)
  • Thermoplastic material above Tg (graph)
  • Elastomer (graph)
  • Ceramics, glasses, and concrete (graph)

Stiffness and Resilience

• Stiffness: Extent to which an object resists deformation in response to an applied force
  • Flexibility: The inverse of stiffness
• Stiffness (k) measure of resistance of an elastic body to deformation (e.g., stretching, compression)
• k = F / δ (F = force, δ = displacement)
• Resilience: Ability of a material to absorb energy when deformed elastically and release it upon unloading
• Modulus of resilience: Maximum energy absorbed per unit volume without a permanent distortion
  • Calculated by integrating the stress-strain curve from zero to the elastic limit

The Output of Tensile Test

• Data displayed from a tensile test on an aluminum alloy test bar (graph)

Yield Strength

• Determining yield strength (graph)
  • 0.2 % offset yield strength (graph a and graph b)

Yield Strength & Plasticity

• Offset yield strength (0.2%)
  • Method to determine yield strength of materials without an easily discernible yield point
• Irreversible deformation
• Yielding: Onset of plastic deformation

Perfectly Plastic

• Yield stress: Solid flows like a liquid
• No volume changes during plastic flow

Strain Hardening

• Requires increasing stress for further straining
• Power law hardening
  • σ = σ₁ + Hεⁿ (σ₁ = initial yield stress, H = hardening modulus, n = hardening exponent, ε = strain)

Engineering & True Stresses-Strain

• Engineering Stress (σ) = P/A₀ (P = load, A₀ = initial cross-sectional area)
• True stress (σₜ) = P/A (A = instantaneous cross-sectional area)
• No difference for small strain
• Necking: Plastic instability, localized plastic deformation

Engineering & True Strains

• Engineering axial strain (ε) = (L - L₀) / L₀ (L = final length, L₀ = initial length)
• True axial strain (εₜ) = ln(L/L₀)
• Transverse strain (ε'ₙ) = ln(d/d₀) (d = final diameter, d₀ = initial diameter)
• No difference for small strain

Example: Young's Modulus of Aluminum Alloy

• Calculation of Young's Modulus (E) using stress and strain data

Example: True Stress, True Strain Calculations

• Calculation of true stress, true strain at maximum load and at fracture using data from a tensile test

Mechanical Test Modes

• Primary types of loading: Tension, compression, shear, torsion, flexure

Compression Test

• Specimens are short, large diameter
• Stress: Force per unit area
• Strain: Change in length relative to original length

Shear Test

• Direct shear: Parallel forces in opposite directions
• Single shear: On a single plane
• Double shear: On two planes simultaneously

Torsion Test

• Torsional shear stress/torsional stress: Twisting in a shaft due to a couple
• Torque: Force x distance
• Relationship between torsional stress (τ), torque (T), radius (r), and second moment of inertia (J): τ = Tr / J

This quiz covers the fundamental concepts of mechanical behavior of materials as outlined in the Failure Analysis course. Topics include mechanical testing methods, stress analysis, and key properties such as tensile strength and elastic deformation. Familiarize yourself with key terms and measurement techniques relevant to this field.