PSI - Issue 25

R. Baptista / Procedia Structural Integrity 25 (2020) 186–194

189

4

Author name / Structural Integrity Procedia 00 (2019) 000–000

σ yy

α

σ xx

β

Fig. 1 Cruciform specimen design and dimensions, detail A) initial crack direction, detail B) modified cruciform specimen with two anti symmetrical holes.

Loads and boundary conditions were applied to the cruciform specimen arms external limits, Fig. 1. On both axis symmetric periodic boundary conditions were applied, while restricting movement and rotation on the remaining axis. These boundary condition made sure that the specimen center remains on a central position, and therefore the stress field is not affected by specimen bending or distortion. An average of 35000 nodes per model was achieved in each simulation. All simulations used quadratic quadrilateral elements and SIF and T-Stress were extracted considering the contour integral technique applied to the crack front. Special spider-web meshes were defined on the crack front, using singular collapsed elements. With an average element size of 0.025 mm, five contour integrals were extracted around the crack tip. SIF and T-Stress values were obtained from the averages of these five contours. 2.3. Loading Paths Biaxial loading conditions were applied to the cruciform specimens. The nominal applied stress on both axes was 100 MPa and the applied stress ratio R was -1. Proportional and non-proportional loading can be defined by altering the stress phase angle φ . Under proportional conditions φ may assume a value of 0 rad or rad (180º). In this paper several non-proportional (out-of-phase) loading conditions were also considered, including phase angle values of ⁄ (30º), (60º) and rad (90º). �� � ���� � �� (8) �� � ���� � (9) Biaxial stress ratio can also be used to modify the loading path, by altering the maximum stress value on the xx axis. Two different values of were considered, 1 and 1.5. 2.4. T-Stress analysis As mentioned, SIF and T-Stress were extracted from the Finite Element Analysis (FEA) models considering the contour integral technique. T-Stress values also depend on the crack propagating direction, Breitbarth et al. (2018). As on this paper FCG was modeled considering FCG to occur accordingly to the MTS criterion, T-Stress values were extracted for the critical direction θ defined by this criterion. In order to analyze T-Stress values and compare them for the different loading conditions applied, a normalized value was considered. The biaxiality ratio B , defined by Leevers and Radon (1982), is a dimensionless value of T in regards to both mode I and mode II SIF.