Davis Triaxiality Factor Calculator

TFD = (σ1 + σ2 + σ3) / σVM · NX Simcenter SOL 401 · v1.0
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Davis Triaxiality Factor
1.000
-1
0
~1.0 Plane Stress
2
≥3.0 Plane Strain
Strain Margin of Safety
Per Davis TFD failure theory — strain ratio margin, not load-based margin. MS must be ≥ 0 at SFu (or above) to verify positive margins.
Approach 1 — Reduce allowable by TFD
MS_u = (ε_true_ult × 2^(1-TFD)) / ε_point - 1
Approach 2 — Compute triaxial strain first
ε_triaxial = ε_point / 2^(1-TFD)
MS_u_ε = ε_true_ult / ε_triaxial - 1
Both approaches yield identical MS. Approach 2 isolates ε_triaxial for direct entry in post-processor.
Detailed breakdown
How to read this. TFD = 1 is uniaxial tension (the reference state for tensile-test allowables). TFD < 1 means the stress state is more compressive / less constrained than uniaxial; the material has more ductility available than the tensile-test value, so 2(1-TFD) > 1 increases the allowable strain. TFD > 1 means the stress state is more constrained (approaching plane strain or hydrostatic tension); ductility is suppressed and 2(1-TFD) < 1 reduces the allowable. At TFD = 3.0 (plane strain) the available ductility is one-quarter of the tensile-test value. Use the strain margin to verify a critical point in FEA passes against the local stress state, not just the global uniaxial allowable.
Formulas
TFD = (σ1 + σ2 + σ3) / σVM   [Davis-Connelly 1959]
MS_u = (ε_true_ult × 2^(1-TFD)) / ε_point - 1
ε_triaxial = ε_point / 2^(1-TFD)
MS_u_ε = ε_true_ult / ε_triaxial - 1
η_Wierzbicki = TFD / 3
μ_Lode = (2·Mid - Max - Min) / (Max - Min)
Simcenter quick calc: TFD = (Max + Mid + Min Principal) / Von-Mises
Davis TFD reference values
Stress state TFD Classification 2(1-TFD)
Uniaxial Compression-1TFD < 1 (compressive)4.00
Pure Shear0TFD < 1 (compressive)2.00
Uniaxial Tension~1.0Plane Stress1.00
Equibiaxial Tension21 < TFD < 30.50
Plane Strain≥ 3.0Plane Strain0.25
Hydrostatic Tension∞Fully constrained→ 0
Theory and limitations
Davis triaxiality factor (Davis & Connelly, 1959) was developed to correlate the available plastic ductility of a stressed point against the uniaxial tensile-test ductility. It uses the ratio of the first stress invariant (sum of principals = 3 × mean stress) to the von Mises equivalent stress.

Strain margin theory: a tensile-test elongation ε_true_ult is measured at TFD = 1. At any other stress state the available ductility scales by 2(1-TFD) — a heuristic Davis fit to test data across a range of triaxialities. The margin check ensures the FEA point strain at the design factor of safety remains within the available (TFD-corrected) ductility envelope.

Wierzbicki triaxiality η = TFD / 3 = (mean stress) / (von Mises) is the more modern form used in damage / fracture models (Bao-Wierzbicki, Johnson-Cook, GTN). The two are direct multiples; the Davis form survives in legacy aerospace stress reports.

Lode parameter μ distinguishes between stress states with the same triaxiality but different shear character (uniaxial tension μ = -1, pure shear μ = 0, uniaxial compression μ = +1).

References:
  • Davis, E.A. & Connelly, F.M. (1959), "Stress distribution and plastic deformation in rotating cylinders of strain-hardening material"
  • Wierzbicki, T. & Bao, Y. (2005), Int. J. Mech. Sci. 47
  • Bridgman, P.W. (1944), "Stress distribution at the neck of a tension specimen"
  • NX Simcenter SOL 401 documentation (stress output post-processing)
Limitations: the Davis 2(1-TFD) ductility correction is empirical and was originally fit for steels and aluminum alloys. It may overcorrect for materials with limited inherent ductility (CFRP, brittle alloys) or undercorrect for highly anisotropic materials. For fatigue / fracture, use a true damage model (Johnson-Cook, GTN) calibrated to the specific material. The TFD itself is sensitive to von Mises in the denominator — near pure hydrostatic stress (σ_VM → 0) it explodes to infinity, so use the dial classification rather than the raw number for nearly-hydrostatic states.