Tool development for automating the structural integrity assessment of aircrafts’ components

4.1. Numerical simulation and FE model description

A parametric FE model of the damaged component is developed within ANSYS software based on the output data of the image processing algorithm. The ANSYS scripting language is utilised to declare the geometric characteristics or import a geometry from a computer aided design (CAD) software, the material properties and boundary conditions of the damaged component. The respective loading conditions (UL) are then applied to the FE model and a non-linear stress-strain analysis is carried out. The plates considered are assumed to be a small portion of an aircraft’s skin structure, therefore flat and curved plates are considered. The metallic plates are analysed under tension and the composite plate under compression. The cases where compression is applied a buckling analysis has been considered to determine the critical buckling load reduction of the damaged component. In Table 1, the plates’ characteristics and the desired residual strength values for calculation are depicted.

4.2. Metallic plates

Regarding the metallic plates two parametric FE models have been developed. The first model concerns flat plates and the second curved. From those two generic models a wide range of plates with arbitrary cracks can be built and analysed. The crack(s) of the plate is/are declared by parameters, which have been acquired from the image processing algorithm. To demonstrate the respective numerical models, the geometric characteristics of the metallic plates of Table 1 are utilised. The flat and the curved plates are assumed to have the following material properties; $E_{11}$ = 72 GPa and Poisson ratio of $\nu$ = 0.33. Furthermore, material nonlinearity is also considered to the numerical analysis by inserting a bilinear representation of the stress-strain curve. Finally, for each plate, a reference model referred hereafter as “Reference Plate”, with no cracks, is analysed for comparison purposes.

The mesh for both metallic plates has been carefully selected based on a convergence study. For the boundary conditions, the nodes of one end of the plate are fully constrained creating a fixed support, while the opposite end only $y$ and $z$-direction is constraint ($U_y=U_z=0$). An incremental forced displacement, in the $x$-direction ($U_x$), is applied to the latest edge to achieve tension. A representation of the plates is available in Figs. 2-3. The aforementioned FE models have been validated using the case studies from the ANSYS verification manual.

Fig. 2Geometry of flat plate with crack (a), FE model of flat plate with crack (b)

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Fig. 3Geometry of curved plate with crack FE model of curved plate with crack (b)

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The cracked areas of the plates have been introduced to the FE model using the XFEM method because it eliminates the need to remesh crack-tip regions. The method has some strong advantages, since it extends the conventional FEM to account for cracks based on the concept of partition of unity [16, 17]. Within the XFEM method, the Phantom-Node Method [18-21] is preferred because it considers only the displacement jump across the crack faces and ignores the crack-tip singularity contributions. The parameters applied for simulating the crack growth during tension, using the Phantom-Node method of the XFEM, are presented in Table 2.

4.3. Monolithic composite plates

For the case of the composite flat plate a parametric FE model has been also developed as previously. From this generic FE model a wide range of plates with arbitrarily located and sized delaminations can be built and analysed. The delamination(s) of the plate is/are declared by parameters from the image processing algorithm. To demonstrate the plate’s numerical model, the geometric characteristics of Table (1) are utilised. The material properties have the following representative values; $E_{11}$ = 32.3 GPa, $E_{22}$ = $E_{33}$ = 8.5 GPa and $G_{12}$ = 2.03, $G_{23}$ = $G_{13}$ = 1.01 GPa, while the Poisson ratio is ${\nu }_{12}$ = ${\nu }_{23}$ = ${\nu }_{13}$ = 0.29. A reference model, referred hereafter as “Reference-PDM”, where no delaminations are considered, is developed for comparison purposes. The reference FE model has PDM features to detect failure according to failure criteria.

The mesh size has been carefully selected based on a convergence study, as well as model validation has been also performed. The same boundary conditions with those mentioned to the respective metallic plate are considered. One edge is loaded by applying incremental forced displacement in the $x$-direction, so that plate’s compression is achieved. The forced displacement corresponds to the UL that has to withstand the plate. The characteristics of the composite plate are shown in Fig. 4. It has also to be noted that the developed FE model is not limited to generate plates with midplane through delaminations, but it can also generate multiple and randomly located delaminations.

Fig. 4Geometry of composite flat plate with delamination (a), FE model of flat plate with delamination (b)

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The FE model described assumes that the delamination growth is initiated in the loading direction and the delamination is driven by local buckling of a thin delaminated region referred hereafter as sub-laminate. Additionally, it is assumed that the base substrate remains flat before sub-laminate buckling, in the local post buckled regime and at propagation. Finally, the released strain energy of delamination growth in the longitudinal yields to Mode I fracture of the resin material. In reality, the propagation is more complex than assumed, since growth is mixed mode, [22]. However, taking into account only Mode I for delamination due to buckling has shown to produce accurate numerical predictions [23].

In the current application, a bilinear form of the CZM model is used, employing the relation between normal cohesive traction $T_n$ and normal displacement jump ${\delta }_n$, Eq. 1, [24].

where, $D_n$ is the damage parameter associated with Mode I dominated bilinear cohesive law. The bilinear form has been selected as the most suitable form for the numerical solution of delamination problems due to buckling, assuming that Mode I governs the failure analysis. The parameters applied for simulating the delamination growth during buckling, using the bilinear form of the CZM model, are presented in Table 3.

Apart from the CZM modelling technique that simulates delamination and delamination growth, PDM has been also considered. It is well known that the material can experience enough damage in local failure level that eventually the structure is not able to withstand the UL. Hence, in order the developed application to be able to calculate the strength reduction of the material, due to concentrated local failure, the appropriate ANSYS subroutines for PDM have been employed.

To obtain PDM calculation, damage initiation and evolution criteria are set to analyse the progression of damage within the composite structure. Damage initiation criteria are used for declaring the failure criteria that determine the onset of material damage under loading. Two different failure criteria have been employed for the aforementioned purpose; Maximum Stress and Tsai-Wu failure criteria. Aim is to determine the most appropriate one. Furthermore, the Hashin and the Puck damage evolution laws are selected to define the material damage progression after the initiation of damage, referred hereafter as Hashin-PDM and Puck-PDM.

5.1. Metallic plates

For the metallic plates the existence of crack(s) is/are expected to reduce the tensile strength of the plates due to their propagation. A force-displacement graph for each FE model (flat and curved plate) is extracted from the FE model and it is presented in Figs. 5-6 respectively. In the same graph, the respective reference FE model, where no crack is considered, is also depicted for comparison reasons. According to Section 3, if tensile strength reduction is detected before the UL is reached, then the plate is not able to operate properly and it has to be substituted. To visualize the displacements of the plates and the crack propagation the axial displacement of the cracked plates are also available in Figs. 5-6.

Fig. 5Contour plot of axial displacement-Flat plate (a), force vs. axial displacement-flat plate (b)

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As it can be observed from Figs. 5-6 for small values of axial load, the force-displacement plot of the damaged plates coincide with the respective of the reference. This occurs due to the fact that the crack is not propagating yet. The propagation of the crack starts when a minimum load has reached (2.7 kN for the flat and 200 N for the curved plate), at these points the force-displacement plots start to deviate from the references plots. No UL is available for the analysed plates, hence comments for specific loads cannot be made. However, the following condition can be expressed for covering the requirements of the structural assessment rules of CS-25 book. If the UL of the plate is larger than the point where this deviation occurs then the plate cannot function any more under this static load and vice versa. This method can be adopted to examine the residual tensile strength of any structural component. It is also worth mentioning that the reference plots of both plates appear a bilinear behaviour due to the bilinear stress-strain plot that has been inserted as material properties. However, the change of slope (after yield stress) of the reference plots is not available in Figs. 5-6 for scaling reasons; it occurs at higher loads.

Fig. 6Contour plot of axial displacement-curved plate (a), force vs. axial displacement-curved plate (b)

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5.2. Monolithic composite plates

The monolithic composite flat plate are subjected to compression load as it is mentioned in Table 1. As a result, buckling due to compression may appear to the plate. The fact that delamination(s) exist(s) may lead buckling to occur in lower critical buckling load. Therefore, in this section, a buckling analysis is performed for the composite monolithic plate, so that a comparison between the critical buckling load of the delaminated composite plates and the respective reference (plate with no delaminations) to be carried out. The force-displacement graph has been plotted for the FE model in Fig. 7. In the same graph, the respective reference FE model (Reference-PDM), where no delaminations exist, is also demonstrated in order to observe whether the delamination has caused critical buckling load reduction.

Fig. 7Force vs. axial displacement-curved plate

In Fig. 7, the force-displacement curve of the delaminated composite plate is demonstrated using Hashin and Puck damage evolution laws (Hashin-PDM and Puck-PDM respectively). Both evolution laws produce similar results regarding the prediction of the critical buckling load. The prediction of the onset of damage has been calculated using the Max-Stress and Tsai-Wu criterion. From the graph, it can be observed that both criteria yield the same force and displacement where damage growth occurs. Up to the aforementioned point the two analyses (Hashin-PDM and Puck-PDM) predict the same behaviour for the delaminated plate. Therefore, both damage evolution laws are adequate for the buckling analysis of delaminated plates under uniaxial compression. Moreover, in Fig. 7 the force-displacement curve for a reference plate (no delamination) is also plotted for comparison reasons. It can be observed that the critical buckling load of the delaminated plate, as analysed using the different PDM subroutines, appears to have a decrease of 3.33 %, in comparison with the respective reference plate.

To determine whether the delaminated plate is suitable under static load to continue to operate, its UL has to be considered. Assuming that the UL is the critical buckling load of the reference plate, then the delaminated plate has to be substituted by a new one, since strength reduction has occurred according to Fig. 7. In case that the UL is less than 29 kN then the component, under static load, has adequate residual strength to continue functioning. The observed critical buckling load reduction is relative small because the considered delamination has been assumed to exist in the midplane of the composite plate. In case that an eccentric delaminations exist, it is expected to have larger critical buckling load reduction in comparison with the respective reference.