Application of the cohesive model for predicting the residual strength of a large scale fuselage structure with a two-bay crack

Abstract

The residual strength of a curved and stiffened panel containing a two-bay crack was assessed using the cohesive model. This panel represents a section of a wide-body aeroplane fuselage. The tests were conducted at IMA GmbH Dresden in cooperation with Airbus Industries Germany. The structural panel was modelled using 3D finite elements and a layer of cohesive elements ahead of each crack tip allowing for 70 mm crack extension. Identification of the cohesive parameters was done on small laboratory test pieces. Special effort was made for the transfer of these parameters to the structure. Reasonably conservative predictions of the residual strength of the panel were achieved. The boundary conditions of the loading devices of the test rig are shown to have substantial influence on the predictions.

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:

• The tensile properties of all materials of the panel were experimentally determined.

• 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.

• With the thus generated cohesive parameters the load carrying behaviour of the IMA panel was analysed.