Stress Gradient Effect
Stress gradient effect based on FKM guideline method.
It is supported for both shells and solid elements. For solid elements, the stress gradient effect is only available with grid point stress in fatigue analysis using results of static analysis. For solid elements, SURFSTS field on FATPARM is automatically set to GP when Stress Gradient effect is activated.
The Stress Gradient method is supported for Uniaxial and Multiaxial SN, EN and FOS Fatigue. It is not supported for Weld, Vibration, and Transient Fatigue analyses.
FKM Guideline Method
In the FKM guideline method, stress gradient effect is considered by increasing fatigue strength by a factor calculated using a rule in FKM guidelines. In HyperLife implementation of FKM guideline method, 6 components of a stress tensor at each time step is reduced by the factor provided by FKM guidelines.
To activate Stress Gradient effect using FKM guideline method, the GRD field on FATPARM should be set to GRDFKM.
- Calculate stress gradient of 6 components of a stress tensor, Δσij(t)ΔzΔσij(t)Δz , at each time step after linear combination of stress history. z-direction is an outward surface normal. For a solid element, the gradient is calculated by finite difference between stress at surface and stress at 1mm below the surface. The stress at 1mm below surface is an interpolated stress from grid point stresses of an element of interest. In case of 2nd order solid elements, only grid point stresses at corners are used for interpolation. For shell elements, the gradient is calculated from stresses of both layers and its thickness.
- Using the stress gradient obtained in Step 1, a gradient of equivalent stress in the surface normal direction, Δσeq(t)ΔzΔσeq(t)Δz , is calculated in an analytical way at each time step. The equivalent stress can be either von Mises stress or absolute maximum principal stress.
- The related stress gradient,
GσGσ
is calculated using the following
normalization.
(1) ˉG(t)σ=1σeq(t)Δσeq(t)Δz¯¯¯G(t)σ=1σeq(t)Δσeq(t)Δz - Calculate the correction factor nσ(t)nσ(t) . Refer to Correction Factor Calculation.
- Apply the correction factor
nσnσ
to the surface stress tensor to obtain
reduced surface stress. Apply the same
nσnσ
to corresponding strain tensor to obtain
reduced strain tensor when EN fatigue analysis is to be carried out with
nonlinear analysis.
(2) σ'ij(t)=σij(t)nσ(t)σ'ij(t)=σij(t)nσ(t)
Correction Factor Calculation
Correction factor calculation is based on relationship between nσnσ and GσGσ described in the FKM guidelines.
- If ˉGσ≤0.1 mm−1nσ=1+ˉGσ⋅mm⋅10−(aG−0.5+RmbG⋅MPa)If ¯¯¯Gσ≤0.1 mm−1nσ=1+¯¯¯Gσ⋅mm⋅10−(aG−0.5+RmbG⋅MPa)
- If 0.1 mm−1<ˉGσ≤1 mm−1nσ=1+√ˉGσ⋅mm⋅10−(aG+RmbG⋅MPa)If 0.1 mm−1<¯¯¯Gσ≤1 mm−1nσ=1+√¯¯¯Gσ⋅mm⋅10−(aG+RmbG⋅MPa)
- If 1 mm−1<ˉGσ≤100 mm−1nσ=1+4√ˉGσ⋅mm⋅10−(aG+RmbG⋅MPa)If 1 mm−1<¯¯¯Gσ≤100 mm−1nσ=1+4√¯¯¯Gσ⋅mm⋅10−(aG+RmbG⋅MPa)
Constants | Stainless Steel | Other steels | GS | GGG | GT | GG | Wrought Al-Alloys | Cast Al- Alloys |
---|---|---|---|---|---|---|---|---|
aGaG | 0.40 | 0.50 | 0.25 | 0.05 | -0.05 | -0.05 | 0.05 | -0.05 |
bGbG | 2400 | 2700 | 2000 | 3200 | 3200 | 3200 | 850 | 3200 |
- GS
- Cast Steel and Heat Treatable cast steel for general purposes.
- GGG
- Nodular Cast Iron.
- GT
- Malleable Cast Iron.
- GG
- Cast Iron with lamellar graphite (grey cast iron).
RmRm is UTS in MPa and dimension of GσGσ is mm. HyperLife takes care of the unit system for RmRm and GσGσ through stress units defined in MATFAT and stress unit and length unit defined in FATPARM. aGaG and bGbG values are user input in MATFAT after keyword STSGRD. Since the stress gradient has to be calculated in length dimension of mm, define the length units so that HyperLife can properly locate a point that is 1mm below the surface. If GσGσ is negative, nσnσ is set to 1.0. If GσGσ is greater than 100 mm-1, nσnσ is set to 1.0 with a warning message.
User-defined Relationship
User-defined relationship between nσnσ and GσGσ can be specified through TABLES1 Bulk Data. Pairs of (xi,yi) = ( GσGσ , nσnσ ) can be defined on the TABLES1 entry. A TABLES1 that defines the relationship between nσnσ and GσGσ should be referenced in MATFAT after keyword STSGRD. If GσGσ falls outside the range of xi, extrapolation behavior follows usual TABLES1 behavior. This means that nσnσ can be lower than 1.0 when GσGσ is negative depending on how GσGσ is treated when being negative or greater than 100mm-1. The user-defined relationship takes precedence over the one in FKM guidelines.
Input to Activate Stress Gradient Effect
Choose a method (FKM guideline) to use on the GRD field after keyword STRESS in FATPARM. If FKM guideline method is chosen, the equivalent stress σeqσeq method to calculate stress gradient should be specified on the SCBFKM field in FATPARM. Material properties required for stress gradient effect are to be input after keyword STSGRD in MATFAT.