GROWTH
GROWTH is the module for running Crack Growth analyses in 2D and 3D FEMs.
2D FEM case:
By means of this module, the following can be done in case of 2D structures.
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Running the analysis at a user defined FEM sub-model (provided this is a planar structure). An internal FEM solver handling plane-stress or plane strain elements is used.
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Calculating Stress Intensity Factors with J-Integral or displacement correlation methods, in conjunction with the use of quarter point elements.
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Propagating one or multiple introduced cracks (GROWTH remeshes the FEM automatically).
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Introduce holes or crack stop drill holes in the structure (and accounting of such modifications).
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Calculating crack growth Life based on the NASGRO crack growth mathematical model (without or with the Generalized Willemborg Retardation model), once the Stress Intensity Factor curves are calculated at the crack propagation phase.
When a FEM sub-part is selected for a crack propagation simulation, the program converts the model to the 2nd order.
Boundary conditions of the selected sub-part are defined by importing the FEM result file (the program reads displacements and grid point force balance at the automatically identified edges of the selected sub-part).
The crack(s) can be introduced with the GUI in a simple manner. The user can control the crack size, orientation and FEM refinement. At the crack tip a rosette of 8 quarter point triangular elements is placed.
This allows the calculation of SIFs, Stress Intensity Factors (KI and KII), using J-Integral approach, with high fidelity.
With a similar GUI interaction process, the analyst can introduce holes or stop drills.
Once the 'damaged' model is defined, the analysis is performed as follows.
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Two nodes are constrained (even if the sub-part is self balanced, for numerical reasons the FEM must be properly conditioned). Typically these are selected in a location sufficiently far from the crack propagation region.
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A reference condition is defined by importing load case related sequences and selecting the instant for which the internal stresses have to be considered.
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It is defined whether the propagation has to be 'straight' or whether the crack can deviate according to the calculated ratios KII/KI.
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It is defined whether plane stress or plane strain elements have to be used (the analyst must decide in advance, depending on the thickness and fracture toughness.
In case of multiple propagating cracks, the program detects the faster crack and propagates the other(s) by scaling the propagation increments on the basis of the Paris exponent (user defined).
The propagation simulation delivers a set of SIF curves (one curve for each crack, made of 'points' collected by considering the SIFs at each propagation steps).
The SIF curves are used then as main input for calculating Crack Growth Life.
Modification factors can be defined (such as additional SIFs or scaling factors defined at each propagation steps). This is particularly relevant in case the analyst wants to account residual stress conditions.
da/dN can be provided as NASGRO equation model or in tabular format (in this case a simple logarithmic interpolation or Walker point-by-point interpolation is then performed).
When LIFING is installed the NASGRO database file is installed.
The Generalized Willemborg Retardation model can be used.
The workflow is summarized below.
3D FEM case:
From release 3.4, the module GROWTH includes the capability to calculate Stress Intensity Factors with M-Integral in 3D FEM (with data imported by file or from a FEM generated with the QUICK2DFEM module by extrusion).
From release 4.5 the cracks can be automatically propagated.
The workflow is summarized below.
At the crack front, where the template of elements shown on the left is used, the SIFs are calculated using the M-integral.
The propagation, from a given crack front is performed in two steps:
1. generation of new '1st trial' crack front shifted of a user-defined distance. The FEM is solved with this 'temporary' configuration.
2. the crack growth integration is performed considering a linear variation of SIFs from the current crack front to the temporary one. The propagation is done at all points in the crack front or a user-defined selection. At each integration step, i.e. cycle, the resulting crack front is interpolated with an elliptical shape.
when one of the crack front points touches the temporary front, the integration is stopped and the adjacent crack front is redefined and the FEM is regenerated.