Issue 30

R. Baptista et alii, Frattura ed Integrità Strutturale, 30 (2014) 118-126; DOI: 10.3221/IGF-ESIS.30.16 119 I NTRODUCTION he study of biaxial fatigue life behavior is very important, as Shanyavskiy [1] and Cláudio et al. [2] have demonstrated, when considering the main applications of aluminum alloys or composite materials. Recently different types of specimens and biaxial fatigue testing machines have been developed by the scientific community and therefore new challenges must be solved in order to assess the material properties. Using the latest generation of in- plane biaxial fatigue testing machines, like the one developed by Cláudio et al. [3], using smaller and more efficient electrical motors, requires new specimens, with an optimal geometry, allowing to attain higher stress levels using lower loads. The cruciform specimen, a two-dimensional analogue of the uniaxial tensile specimen, has been used by different authors, but there is not a design accepted by all. Hanabusa et al. [4], developed a cruciform geometry using slits on the specimen arms in order to promote an uniform stress and strain distribution on the specimen center, and to reduce the stress concentration on the specimen arms corner, independently of the load ratio applied. On the other hand, Müller et al. [5], used notches on the specimen arms corners as a mean to achieve higher stress levels on the specimen center and to reduce the stress concentration on the specimen arms. Finally several different types of specimens with a reduce thickness in the center, have been reviewed by Bruschi et al. [6] or Leotoing et al. [7]. This reduction drives the maximum stress and strains to occur on the specimen center, rather than on the specimen arms, while it still allows for a uniform strain and stress level to occur. This reduction can be achieved using a straight or curved profile, but Leotoing et al. [7] have achieved excellent results, using a revolved spline profile. Unfortunately there is still no specimen design standard, and one must choose all the available design variables very wisely in order to achieve the best results possible. An optimization process is one of the possible solutions to solve this problem. Yu et al. [8] developed an optimization process in order to produce optimal center thickness on their specimens, while Smits et al. [9] and Makris et al. [10] have also used an optimization process to develop optimal geometries for their cruciform specimens. The aforementioned specimens all use reduced central thicknesses and similar specimen arms fillets, in order to achieve higher stress levels on the specimen center, while maintain uniform strain distributions. In the present paper a cruciform specimen geometry design is optimized for the use with low capacity test machine, [3]. The optimization process used the Direct Multi-Search methodology to obtain several Pareto Fronts relating to two objectives functions: a) maximizing the stress level on the specimen center; b) maximizing the stress uniformity on the specimen center. All the cruciform specimens use a reduced center thickness and elliptical fillet on the arms corners in order to drive the optimization process. C RUCIFORM SPECIMEN DESIGN he geometry presented in this paper (Fig. 1) was achieved after an extensive literature review and using the authors previous experience, [11]. This geometry has proven to be efficient by Poncelet et al. [12] and Ackermann et al. [13], for metallic specimens, but also by Lamkanf et al. [14] for composite materials specimens. There were two main goals to achieve with this geometry, the first one was to guarantee that the maximum stress level occurred on the specimen center, while the second one was to assure the stress distribution on the specimen center was almost uniform. Therefore one can expect the fatigue crack initiation to occur exactly on the specimen center. The geometry is derived from a cruciform geometry, with reduced thickness in the center of the specimen and uses an elliptical fillet in order to reduce the stress concentration in the arms corners. Therefore one can aim to achieve the maximum stress level on the center of the specimen, while the stress level on the arms will be considerably lower, as shown by Cláudio et al. [2]. The specimen center reduced thickness is achieved by using a revolved spline, in order to reduce the stress concentration between the original material thickness and the specimen center, while it is also possible to achieve a uniform stress level on the specimen center, within a radius of 1 mm, as reported by Makinde et al. [15]. This geometry is defined by nine variables. Two of them where considered constant, the specimen arm length with a value of 200 mm and the specimen arm width with a value of 30 mm for finite element modeling purposes. These dimensions have no influence on the final results. The specimen arm width is also a possible variable for future optimization problems, as it will influence the applied load in order to achieve a desirable stress level. Tab. 1 shows five of the other variables which were used in the optimization problem. The center thickness (tt) is a value of the arms thickness (t) (material base) and ratios of 15% and 17% were considered, while the spline exit angle (theta) is a very important variable ensuring a smooth geometrical transition to avoid stress concentration in the critical region. The center spline radius (rr) defines the area where the specimen thickness is reduced, using the above referenced revolved spline, that has a tangency T T