XXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXXX''"> Rules for Changing Young’s Modulus
It is possible to select a new material for use in the fatigue analysis in either FEFAT or PCRACK to explore the effect on life. However, the user must be careful to ensure that the stress or strain values calculated from the FE analysis still apply. For example, if a steel is changed to an aluminum alloy, the value of E will drop by about a factor of three. This means that the FE results which were calculated for steel are no longer appropriate and need modification to allow for the new Young’s Modulus.
There are two scenarios that need to be considered in order to decide which correction method should be used. These are where firstly the load (P) is the constant and secondly where the displacement (U) is fixed. In a test machine, these would be described respectively as “load” and “displacement” controlled tests. The type of loading scenario is easily worked out by considering the loading applied in the FE analysis.
The general equation for linear static analysis is:
(3‑4)
Where P = force, K = structural stiffness, and U = displacement.
If we rewrite the structural stiffness as a function of geometry and the Young’s Modulus then the force becomes:
(3‑5)
(i) For load controlled situations,
(3‑6)
and since the displacements are proportional to the strains,
(3‑7)
If the Young’s Modulus (E) changes, then the stresses remain unchanged but the strains are factored by the ratio of E/E' where E' is the new value of Young’s Modulus, i.e.,
(3‑8)
(ii) For displacement controlled situations,
U is defined and hence the strains are prescribed, and so from
.
(3‑9)
If the Young’s Modulus (E) changes, then the strains remain unchanged but the stresses are factored by the ratio E'/E where E' is the new value of Young’s Modulus, i.e,
(3‑10)
Implementation in MSC Fatigue
For a more complete assessment of the effects of a change in the Young’s Modulus, a full reanalysis of the FE model will be required. However, a first approximation may be made using FEFAT or PCRACK. To do this properly, the user will need to factor the strains or stresses by the appropriate ratio of Young’s Moduli. This scale factor may be applied using the Scale Factor option in the main FEFAT or PCRACK analysis menus. For example, in a load controlled situation if E changes from 210,000 MPa to 70,000 MPa, the stresses will remain the same and the strains will increase by a factor of 3.0. This correction must be applied carefully using the following rules:
1. Total Life Analysis
Since the analysis is only ever dealing with stresses, the following applies:
load controlled | No change in the stresses and no factor needs to be applied. Simply select the new material. |
displacement controlled | Select the new material and apply a factor E'/E using the Scale Factor option. |
2. Crack Initiation Analysis
Since the analysis uses both stresses and strains, the following applies:
load controlled | No change in the stresses, select new materials and apply the factor E'/E using Scale Factor option. |
displacement controlled | No Scale Factor required by the user since strains must be kept constant and the new value of E will automatically adjust the stresses. |
3. Crack Growth Analysis
Since the analysis is only ever dealing with stresses, the following applies:
load controlled | No change in the stresses and no factor needs to be applied. Simply select the new material. |
displacement controlled | Select the new material and apply a factor E/E' using the Scale Factor option. |
4. Spot Weld Analysis.
The analysis uses forces and moments from the FE model. If these are likely to be modified the FE analysis should be rerun. The forces and moments are likely to change if the modulus of the whole structure is not changed, if the component is in displacement or strain control, if the sheet thicknesses are also changed. Otherwise there is no problem.