Application of the cohesive model for predicting the residual strength of a large scale fuselage structure with a two-bay crack
Introduction
The requirements for high loading capacity, weight reduction and low production cost of engineering structures, combined with high structural safety, particularly in transportation industry, have to be met by new design concepts, materials, production technologies, and assessment methods. When safety of a new airplane has to be demonstrated during the development stage, extremely expensive test programs are required. The residual strength of the fuselage, for instance, has to satisfy aerospace certification requirements. A longitudinal crack of twice the distance between two stiffeners is inserted into a full-scale barrel section representing the fuselage design which is then subjected to internal pressure [1]. The required residual strength of that cracked structure has to be at least 1.15 times the internal cabin pressure.
In order to reduce testing costs, Airbus in Germany in cooperation with IMA1 have developed a new, cost-saving, test procedure for fuselages. Instead of a complete barrel, only a section of it is loaded by internal pressure and biaxial tension. The inner side of the IMA panel is sealed against a chamber so that internal pressure can be built-up. Tests can be done under monotonically increasing and cyclic loads [2]. Although this test rig is quite complex, it allows testing a range of design solutions with much less efforts than the classical barrel test. Furthermore, simulations applying advanced models of fracture and damage mechanics would reduce test efforts even more, since as soon as the finite element model of a panel has been made up parameter variations with respect to geometrical parameters, boundary conditions and material properties can be effectively studied.
Thin-walled light-weight structures such as the fuselage of an aeroplane may exhibit a large amount of crack extension before final failure ensues. The ability of treating large amounts of ductile crack extension can in general be met by a number of assessment procedures and numerical models. It is a common practice to treat ductile crack extension in the form of a crack extension resistance curve (R-curve), with crack extension expressed as a function of either of crack tip parameters like the stress intensity factor, K, the J integral, or crack tip opening displacement (CTOD) [3]. Among CTOD the δ5 crack tip opening displacement method with a fixed gauge length at the crack tip is extensively validated for dealing with large amounts of crack extensions [4], [5], [6], [7], [8] and is now standardised by ASTM [9] and ISO [10].
Besides these classical fracture mechanics methods, numerical damage mechanics models are being increasingly used. Their advantage over the classical fracture mechanics methods is that they avoid an intrinsic problem of the latter: The essential transferability problem inherent in fracture mechanics can be better handled by damage mechanics models.
Numerical damage models such as the cohesive model, see e.g. general overviews in [11], [12], [13], [14] and its application to thin-walled structures in [15], [16], [17], [18], [19], [20] or porous plasticity models, e.g. [21], [22], [23], [24], have already been extensively validated by means of numerous tests on laboratory test pieces, e.g. [15], [16], [17], [25], [26], [27]. However, only few investigations can be found on the application to complex large scale structural components. e.g. [28]. Earlier investigations carried out on a realistic fuselage component are based on the crack tip opening angle (CTOA) [29].
In the work described in the present paper, the cohesive model was chosen for simulating the residual strength of a cracked large scale and stiffened structural component. This choice was motivated by the suitability of this model for analysing large amounts of crack extension, the current lack of structural applications, and by the experience of our group with this model. In order to test the versatility of the cohesive model for structural behaviour, the results of a panel test performed by IMA were made available to the authors. This panel is shown in Fig. 1 and will henceforth be called “IMA panel”.
The paper starts with a description of the IMA panel test, as the details of the test setup are needed for the boundary conditions of the numerical model. Then the cohesive model applied in this paper is introduced in detail. A description of the determination of the various material parameters follows. The following section deals with the finite element model of the panel and the results of its deformation behaviour. The paper concludes with the lessons learned during this exercise. The following step-by-step procedure was set up:
- (i)
The tensile properties of all materials of the panel were experimentally determined.
- (ii)
Fracture mechanics tests were performed on modified Kahn specimens made of the skin material taken from the tested IMA panel. The test results – together with the tensile properties – served for determining the cohesive parameters.
- (iii)
With the thus generated cohesive parameters the load carrying behaviour of the IMA panel was analysed.
Section snippets
Panel design
The IMA panel is a part of a wide-body fuselage with an outer diameter of 5640 mm, Fig. 2a. Geometry and dimensions of the panel are shown in Fig. 2b. The 1.8 mm thick skin is stiffened by seven frames (C1–C7) and eight stringers (P1–P8). The details of the riveted design near the crack tip in frame C3 are displayed in Fig. 3. The frame assembly consisted of several components. The stringers are adhesively bonded to the skin, representing a specific feature of this fuselage design. The other
Stress–strain data
The fuselage panel consisted of components made of five materials as specified in Fig. 4. The stress–strain curves were determined on the small flat tensile specimens, depicted in Fig. 4. Elongation was measured with a clip of 7.0 mm initial gauge length. The tensile specimens were taken from all components of the IMA panel.
Three of the stress–strain curves belong to one group, whose individual curves are similar, namely skin, clip and lower frame. The stringer and the upper frame profiles have
Traction-separation law
Cohesive models describe various kinds of decohesion processes by its constitutive behaviour, which is a relation between surface tractions, generally having one normal and two tangential components, and the corresponding material separations. In an FE model, the cohesive surface is introduced by interface elements at the boundaries of solid elements along a pre-defined crack path. Cohesive elements are surface elements in 3D structures and line elements in 2D structures. They do not have an
FE mesh
A 3D CAD was generated and meshed using the programme IDEAS.3 All construction profiles are connected by rivet blocks, see Fig. 10a. The two-bay crack was manually inserted. The FE model consisted of 77,208 solid elements with 551,086 nodes. The elements had 20 nodes and eight integration points (ABAQUS type C3D20R). A refined crack tip mesh block was placed at each of the two crack tips.
Cohesive elements were inserted ahead of both crack tips, in axial
Deformation and plastic zone extension
First, the global deformation and the distribution of plastic zones are presented, as determined at the failure pressure of the test and for the initial crack length. The largest deformation appears along the free edges of the two-bay crack as depicted in Fig. 12a, with two maxima in the middle of the two bays. Most important for the understanding of the deformation behaviour and the evaluation of the boundary conditions is the radial deformation along frame C4, shown in Fig. 12b for case A and
Conclusions
A residual strength analysis of a curved fuselage panel with riveted-on frames containing a two-bay crack has been successfully conducted using a 3D FE analysis in combination with the cohesive model. The main conclusions from this study are as follows:
- •
A hybrid method combining experiments and simulations for determining the cohesive parameters of a thin-walled Aluminium sheet with combined normal and slant fracture modes is verified and successfully applied to the fuselage panel.
- •
It has been
Acknowledgments
Authors gratefully acknowledge Dr. H.-J. Schmidt and Dr. Assler with Airbus Deutschland in Hamburg as well Dr. T. Fleischer and Dipl.-Ing. M. Semsch with IMA Materialforschung und Anwendungstechnik GmbH in Dresden for their kind cooperation and support of this study with valuable information on the fuselage test setup. Our colleague Dipl.-Ing. V. Heitmann is gratefully appreciated for supporting experiments on small specimens.
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