What Is the Johnson-Cook Dynamic Plastic Flow Stress Calculator?
The Johnson-Cook model is an empirical constitutive law describing how metals strengthen under rapid deformation and soften under high temperatures.
How Does the Johnson-Cook Dynamic Plastic Flow Stress Calculator Work?
Multiplies three terms: isotropic strain hardening (A + B*eps^n), logarithmic strain rate enhancement, and homologous temperature softening.
Johnson-Cook Dynamic Plastic Flow Stress Calculator Formula & Variables
The core mathematical equation utilized by this calculator is expressed as:
sigma = left[ A + B arepsilon_p^n
ight] left[ 1 + C lnleft( rac{dot{ arepsilon}}{dot{ arepsilon}_0}
ight)
ight] left[ 1 - left( rac{T - T_{ ext{ref}}}{T_{ ext{melt}} - T_{ ext{ref}}}
ight)^m
ight]
Johnson-Cook dynamic constitutive equation coupling work hardening, rate sensitivity, and thermal softening.
How to Use the Johnson-Cook Dynamic Plastic Flow Stress Calculator
- Input material parameters (A, B, n, C, m), plastic strain, strain rate in s⁻¹, and temperature in Kelvin.
Step-by-Step Example Calculation
AISI 4340 Steel High-Rate Deformation
Input Values:
aYieldMpa:792
bHardeningMpa:510
nHardeningExp:0.26
cStrainRateCoeff:0.014
mThermalExp:1.03
plasticStrain:0.2
strainRatePerSec:1000
currentTempK:500
Worked Steps: Flow stress sigma = 1,185 MPa with 1.10x strain rate boost and 86% thermal retention.
Understanding Your Result
Displays net dynamic flow stress, static work hardening stress, and individual rate/temperature multipliers.
Factors That Affect the Result
- Extreme strain rates (explosive/ballistic) drastically elevate flow stress; high adiabatic temperatures degrade strength.
When Should You Use This Calculator?
- Finite element explicit dynamics (LS-DYNA, Abaqus), crashworthiness analysis, machining chip formation, and armor penetration.
Assumptions & Limitations
- Assumes isotropic hardening without kinematic backstress or phase transformation.
Frequently Asked Questions
Calculation Accuracy & Reference Note
Standard Johnson-Cook explicit formulation.