TrimLab | Neuber Notch Analysis

Method & Assumptions

Neuber rule + Ramberg–Osgood material response

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Elastic notch input

The elastic predictor can either be calculated from nominal stress and Kt or entered directly as an elastic FEM peak.

σe = Kt · σnom or σe = σpeak,FEM

Neuber rule

The local elastic-plastic stress-strain state is constrained to the same stress-strain product as the elastic notch solution.

σ · ε = σe² / E

Material model

The intersection is found numerically on a monotonic Ramberg–Osgood curve.

ε = σ/E + (σ/K)^(1/n)

Failure assessment

Allowables are checked against the Neuber-corrected local state. Yielding itself is not treated as failure.

Uσ = SF·|σlocal|/σallow Uεp = SF·|εp|/εp,allow

PASS if governing utilization ≤ 1

Assumptions

uniaxial local notch state
isotropic symmetric tension/compression response
monotonic Ramberg–Osgood parameters
small-scale local plasticity; no gross-section collapse
FEM peak must be a valid linear-elastic local peak
entered allowables must be appropriate for the design case

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Parameters

Nominal loading, notch factor and material model

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Loading & Notch

Nominal stress + KtCalculate the elastic peak from Kt · σnom.

Direct elastic peakEnter a linear-elastic peak stress, e.g. from FEM.

Load direction

Nominal stress magnitude [MPa]

Theoretical stress concentration Kt [-]

Use the elastic geometric concentration factor from handbook or an analytical solution.

Material — Ramberg–Osgood

Elastic modulus E [MPa]

Yield strength Rp0.2 [MPa]

Strength coefficient K [MPa]

Hardening exponent n [-]

Failure Criterion

Assessment method

Safety factor SF [-]

Allowable local stress [MPa]

Allowable plastic strain [%]

Engineering allowable, entered as plastic strain percentage.

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Results

Elastic predictor and corrected local notch state

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Local Stress

–

Local Strain

–

Plastic Strain

–

Material State

–

Allowable Check

–

Detailed Results

Quantity	Value	Unit
Nominal stress σnom	–	MPa
Elastic notch / FEM peak stress σe	–	MPa
Elastic notch strain	–	%
Neuber local stress	–	MPa
Neuber local strain	–	%
Local plastic strain	–	%
Effective stress concentration Kσ	–	–
Effective strain concentration Kε	–	–
Kσ · Kε / Kt²	–	–
Local stress / yield strength	–	–

Failure Assessment

Stress utilization–

Plastic-strain utilization–

Assessment quantity	Value	Unit
Governing criterion	–	–
Governing utilization	–	–
Reserve factor RF	–	–
Margin of safety MS	–	–

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Visualization

Neuber hyperbola intersection and notch stress redistribution

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Stress–Strain Intersection

Absolute axes are used for readability; compression results retain a negative sign in the result table.

Ramberg–Osgood

Neuber hyperbola

Elastic predictor

Stress allowable

Corrected local state

Notch Redistribution

Schematic comparison of elastic peak and Neuber-corrected state.