Issue 48

F. V. Antunes et alii, Frattura ed Integrità Strutturale, 48 (2019) 676-692; DOI: 10.3221/IGF-ESIS.48.64 677 specimen, where the crack is positioned. Recently, Lo et al.  9  suggested a third version similar to the original one but with a different positioning of the holes. Other geometries have been used to study mixed mode I/II loading namely the compact mixed-mode specimen, CMM  10  , the asymmetric three-point single edge notch bend specimen, aSENB3, and the asymmetric four-point single edge notch bend specimen, aSENB4  11  . For mixed mode I/III loading a modified compact tension specimen (MCT) was developed  12  . For materials submitted to compressive loads (like glass) alternative specimens were developed, namely the cracked brazilian disc specimen, CBD  13  and the double clivage drilled compression, DCDC  14  . Richard et al.  15  obtained K I and K II solutions for the original CTS geometry, presented in Appendix A, considering that the crack was plane and normal to lateral faces. These solutions are adequate for fracture studies, since pre-cracks are obtained under mode I loading therefore do not suffer crack deflection. However, cracks submitted to mixed mode fatigue loading change orientation searching mode I loading and Richard’s solutions can be inadequate since they have been developed for straight cracks. Therefore, the objective of the present work is the development of K I , K II solutions for the CTS mixed mode specimen which include the influences of crack length, loading angle and crack orientation. This way, literature solution is extended for fatigue studies under mixed mode loading. Several crack geometries were studied numerically by the finite element method in order to obtain K I , K II , and analytical solutions were fitted to the numerical predictions. N UMERICAL P ROCEDURE ig. 1 presents the geometry of the Compact Tension Shear (CTS) specimen studied here. It has a width of 90 mm, a total height of 148 mm, and a thickness of 3 mm, and is identical to Richard’s specimen  1  , except in the thickness. The thickness affects the shape of crack front, but a reduced effect on crack orientation may be expected. A pre-crack submitted to cyclic loading changes its direction approaching direction normal to remote loading, i.e., approaching mode I. A main geometrical parameter is therefore the slope at the crack tip,  . The specimens used in the experimental work had an initial notch depth a 0 =42.5 mm, however cracks with less extent were studied numerically to enable the reduction of initial notch depth in posterior studies. This specimen geometry was tested with the loading device shown in Fig. 2. This apparatus was based on the mixed-mode fracture testing technique originally developed by Richard  16  . The loading device allows to apply pure mode-I, pure mode-II, as well as mixed-mode loading to the CTS specimen just by changing the loading angle  between the longitudinal axis of the specimen and the load direction applied by a uniaxial tension testing machine. Fig. 3 defines load direction,  , and boundary conditions. The specimen has circular holes but the loading device has elongated holes. The holes 1, 3, 4, 6 are elongated in the direction parallel to the crack so that forces F 1 , F 3 , F 4 and F 6 are normal to the crack plane. On the other hand, holes 2 and 5 are elongated perpendicular to the crack so that only the forces F 2 and F 5 parallel to the crack can be transmitted from the load device to the specimen. The uniaxial load F is related with punctual loads according  16  : 1 c F F F.( cosα sin ) 1 6 2 b     2 5 F F F.sinα   3 4 1 c F F F.( cosα sin ) 2 b     (1) The material studied was the AlMgSi1 (6082) aluminium alloy with a T6 heat treatment. The T6 heat treatment corresponds to a conversion of heat-treatable material to the age-hardened condition by solution treatment, quenching and artificial age-hardening. The chemical composition and the mechanical properties of the alloy are shown in Tabs. 1 and 2, respectively. Si Mg Mn Fe Cr Cu Zn Ti Other 1.05 0.80 0.68 0.26 0.01 0.04 0.02 0.01 0.05 Table 1 : Chemical composition of 6082-T6 aluminium alloy (wt. %). F