1 Advances I n Crack Growth Modelling Of 3D Aircraft Structures Sharon Mellings, John Baynham, Bob Adey C M BEASY Ltd C BEASY 2009
2 Contents � Introduction � Overview of methodology � Model creation � Crack growth examples � Fatigue loading with mixed mode growth � Contact on crack faces � Conclusions C BEASY 2009
3 I ntroduction � Effective fracture analysis and crack growth prediction can be invaluable in airframe structural design � Critical crack sizes can be determined � Inspection intervals can be computed � Failure modes can be simulated C BEASY 2009
4 Crack growth analytical methods used � A variety of techniques can be used to predict the rate and in some cases the paths for crack growth in structures including � Reference solution methods (“Cook Book” Solutions) � Finite element analysis � Boundary element analysis � Each of these has their own advantages and disadvantages. C BEASY 2009
5 Boundary elements analysis � This analysis is ideal for crack growth analysis as it deals purely with the boundary of the model. � However boundary element models of the part generally do not exist and it would be necessary to create the BEM model as well as defining the loads and restraints. � This methodology will be used in this paper overcomes these difficulties, with a tool that automatically creates a BEM model using existing FE models. C BEASY 2009
6 Crack growth process � Create model � Add initial crack � Solve to compute stress intensity factors � Determine where the crack is growing to and how far � Grow the crack � Add the grown crack to the un-cracked model C BEASY 2009
7 Example Model � The analysis process will be demonstrated using a number of models. � All of the examples in this presentation demonstrate crack growth within a curved, machined, stiffened panel. � The initial model is a finite element representation of part of a stiffened panel. � The part is modelled in ABAQUS using tetrahedral elements. C BEASY 2009
8 Finite element model of a panel (ABAQUS) Detailed crack growth to be studied in this area. C BEASY 2009
9 Crack growth process � Create loaded model � Add initial crack � Solve to compute stress intensity factors � Determine where the crack is growing to and how far � Grow the crack � Add the grown crack to the un-cracked model C BEASY 2009
10 Model creation � The ABAQUS FE model will be used to create a boundary element sub-model. � A group of FE elements is selected from the full ABAQUS model � The external surfaces of the group are used to create boundary elements � Loading is created on the boundary element model to give the same load condition as in the finite element model. C BEASY 2009
11 Section of ABAQUS model selected for analysis C BEASY 2009
12 Boundary element mesh of the selected sub-model Triangular boundary elements created from the tetrahedral finite elements. C BEASY 2009
13 Crack growth process � Create loaded model � Add initial crack � Solve to compute stress intensity factors � Determine where the crack is growing to and how far � Grow the crack � Add the grown crack to the un-cracked model C BEASY 2009
14 Crack growth process � Using the sub-model a number of different crack growth studies will be performed. � This will look at how crack front shapes change through the thickness transitions in the model. � In the initial examples, a uniaxial tension loading is applied to the model. � Subsequent studies will look at crack turning and compressive loads, resulting from multi-axial loading. C BEASY 2009
15 Examples of crack growth studies in the model Example 2 Example 1 Cracks are initiated at three different Example 3 locations in the model C BEASY 2009
16 Adding the crack � In the analysis process the user is simply required to select the type of crack and then add it to the model. � The cracks used are selected from a list of “library” cracks. C BEASY 2009
17 Example 1 � In the first example, a through crack will be placed at the top of the stiffener itself. � The changing shape of the crack front will be examined as the crack grows. � First we will look at the tools used to generate this crack growth model. � Note that in this analysis, we will not be looking at the fatigue life, but just the shape of the grown crack. C BEASY 2009
18 Selection of library crack C BEASY 2009
19 Diagram of added crack Through thickness Crack depth Crack Growth C BEASY 2009
20 Specify crack size C BEASY 2009
21 Fatigue properties C BEASY 2009
22 Mesh after the initial crack is added C BEASY 2009
23 Crack growth process � Create loaded model � Add initial crack � Solve to compute stress intensity factors � Determine where the crack is growing to and how far � Grow the crack � Add the grown crack to the un-cracked model C BEASY 2009
24 Adding the crack to the model � The stresses and displacements are computed using the Dual Boundary Element method. � This model is then solved to give the stress intensity factors. � These are computed using the J-Integral ⎛ ⎞ ⎛ ⎞ ∂ ∂ ∂ ∂ θ u u ∫ ∫ ∫ ⎜ ⎟ ⎜ = − ⎟ σ Γ − σ Ω + σ δ α Ω i i J Wn d d d ⎜ ⎟ ⎜ ⎟ ∂ ∂ ∂ ∂ 1 1 ij i 3 ij ij ⎝ ⎠ ⎝ ⎠ x x x x Ω Ω 1 3 1 1 C C BEASY 2009
25 Stress intensity factors along the crack front 6.0000E+00 5.0000E+00 4.0000E+00 Note fully mixed Mode 1 SIF mode Ki, Kii and Kiii 3.0000E+00 Mode 2 Mode 3 are predicted 2.0000E+00 1.0000E+00 0.0000E+00 0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000 1.0000 xi C BEASY 2009
26 Crack growth process � Create loaded model � Add initial crack � Solve to compute stress intensity factors � Determine where the crack is growing to and how far � Grow the crack � Add the grown crack to the un-cracked model C BEASY 2009
27 Crack growth rate � In this analysis, the crack growth is modelled using the Paris equation: ( ) da = Δ n C K dN � For this equation we need a single dK value. � From the analysis we have 3 independent stress intensity factor values � These are combined into a Keff value ( ) ( ) = + 2 + 2 K K K 2 K eff I III II = − max min dK K K eff eff eff C BEASY 2009
28 Crack growth direction � The Paris equation determines how fast the crack is growing. � The direction for the crack growth depends on the loading direction. � For this example, the crack growth direction is determined to be the direction in which the strain energy density is minimised. � This computation uses both the K1 and K2 values C BEASY 2009
29 Predict the crack growth � In the simulation process the crack front is grown using δ A values which vary along the front. The average δ A is used to limit the growth. � This distance is pre-defined before the analysis is started. � The crack is grown, using successive recalculations of the da/dN crack growth rate until the required growth increment is reached. C BEASY 2009
30 Predicted new crack front positions Predict new crack C BEASY 2009
31 Crack growth process � Create loaded model � Add initial crack � Solve to compute stress intensity factors � Determine where the crack is growing to and how far � Grow the crack � Add the grown crack to the un-cracked model C BEASY 2009
32 Grow the crack � The predicted crack growth positions are used to create a new crack surface � This grown crack is added to the un- cracked model � A new cracked model is produced and the new stress intensity factors are computed. C BEASY 2009
33 Crack mesh after first growth step C BEASY 2009
34 Crack growth through stiffener C BEASY 2009
35 Crack surfaces after breakthrough. C BEASY 2009
36 Example 2 � In the previous example, the initial crack was a straight through-crack. � However would the crack growth be different if the initial crack was a smaller, corner crack, for example? � In this second example the initial crack is changed. � Note this just requires a change of the selected crack, not a completely new model. C BEASY 2009
37 View of the crack added to the model C BEASY 2009
38 Crack growing in the stiffener C BEASY 2009
39 Comparison of growth between different cracks � The resultant crack shape is similar to the through crack growth performed earlier. � However any computed life would not include the growth from the corner crack. Growth from Growth from through crack corner crack C BEASY 2009
40 Example 3 � For the third example we now look at a crack that is growing in the main panel itself. � In this example we are simulating a crack that is growing through the panel towards the stiffened section. C BEASY 2009
41 Crack growth through base panel C BEASY 2009
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