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Open CalculatorAll Metallurgical and Materials PE Equations (9)
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Arrhenius Relation (Diffusion / Reaction Rate)
Temperature dependence of diffusion coefficient or rate constant.
intermediate -
Corrosion Rate from Current Density
Use Faraday’s law to convert corrosion current density to penetration rate.
intermediate -
Norton Creep Law (Steady-State)
Steady-state creep strain rate as a power law of applied stress with Arrhenius temperature dependence.
intermediate -
Basquin High-Cycle Fatigue Relation
Empirical power-law relation between stress amplitude and life in high-cycle regime.
intermediate -
Fick’s First Law of Diffusion
Steady-state diffusion flux proportional to concentration gradient.
intermediateHigh Frequency -
Mode I Stress Intensity Factor
Mode I stress intensity factor for a crack in an infinite plate with a geometry factor.
intermediateHigh Frequency -
Hall–Petch Grain Size Strengthening
Yield strength increase with decreasing grain size.
intermediate -
Hooke’s Law (Uniaxial)
Linear elastic relation between stress, strain, and Young’s modulus for small strains.
basicHigh Frequency -
True vs Engineering Stress and Strain
Conversion between engineering and true stress–strain for tensile tests.
intermediate
Frequently Asked Questions
How do I use Arrhenius Relation (Diffusion / Reaction Rate) on the PE exam?
Always convert temperature to Kelvin! The gas constant R = 8.314 J/(mol·K) is universal. For PE exam problems, activation energies are typically given in J/mol or cal/mol. Remember that doubling absolute temperature doesn't double the diffusion rate - the exponential relationship makes small temperature changes very significant.
How do I use Corrosion Rate from Current Density on the PE exam?
CRITICAL: Use correct K constant - 0.129 for mpy with µA/cm², 3.27×10⁻³ for mm/year with A/cm². Equivalent weight depends on oxidation state (Fe²⁺ vs Fe³⁺). Always verify units match between icorr and K constant.
How do I use Norton Creep Law (Steady-State) on the PE exam?
Norton creep law is critical for high-temperature design problems. Always verify temperature is in Kelvin (add 273 to °C). The stress exponent n typically ranges 3-8 for metals. Remember that small changes in temperature or stress create large changes in creep rate due to exponential and power law dependencies.
How do I use Basquin High-Cycle Fatigue Relation on the PE exam?
Basquin equation applies only to high-cycle fatigue (typically Nf > 10³-10⁴ cycles). For low-cycle fatigue, use Coffin-Manson strain-life relation. Always check if mean stress corrections (Goodman, Gerber) are needed. The fatigue strength exponent b is always negative.
How do I use Fick’s First Law of Diffusion on the PE exam?
Remember the negative sign - flux always flows from high to low concentration. For PE exam problems, you'll often need to look up or calculate D using the Arrhenius equation: D = D₀e^(-Q/RT). Concentration gradients are typically given as weight percent differences.