Issue 38

M.A. Meggiolaro et alii, Frattura ed Integrità Strutturale, 38 (2016) 67-75; DOI: 10.3221/IGF-ESIS.38.09 71 could be filtered out if associated with a non-damaging low peak-stress level, while another event with the same amplitude could be preserved if happening under a damaging high peak-stress level. However, this is easier said than done. The filter amplitude must be calculated in real time (or else it would lose efficiency), so it cannot be a function of the peak or mean stresses along a load event, which would require cycle identification and information about future events. Instead, mean/maximum-stress effects are modeled in the filter in a simplified way, as a function of the current (instantaneous) hydrostatic  h or normal   stress along the load path, respectively for invariant-based and critical-plane models, as briefly outlined in [6]. Crossland’s invariant-based model [7], e.g., adopts an infinite-life criterion Mises C h C max 2 (3 )          (4) where  Mises is a path-equivalent von Mises shear stress range,  hmax is the peak hydrostatic component, and  C and  C are material constants. If this damage model is adopted, then the stress history could be represented in the previously defined 5D deviatoric space s   , assuming a  h -dependent variable filter amplitude Mises Mises C C h r 2 3 2 ( 3) (3 3 )             (5) On the other hand, Findley’s critical-plane model [9] assumes that F F max 2          (6) where  and   max are the shear stress range and peak normal stress on the critical plane, and  F and  F are material constants. Using this damage model, the shear stress history on the considered candidate plane could be represented in the 2D shear stress space  A  B  T , while adopting a   - dependent variable filter amplitude F F r max 2          (7) Fatemi-Socie’s critical-plane model [10] assumes that b c c FS c Yc N N S G max 1 (2 ) (2 ) 2                    (8) where  and   max are the shear strain range and peak normal stress on the critical plane, N is the associated fatigue life in cycles, G and S Yc are the material’s shear modulus and cyclic yield strength, and  FS ,  c ,  c , b  and c  are material constants. For this damage model, the shear strain history on the considered candidate plane could be represented in the 2D shear strain space  A  B  T , while adopting a   - dependent variable filter amplitude b c c c FS L L Yc r N N G S (2 ) (2 ) 1 2                          (9) where N L is the number of cycles associated with the stress-life fatigue limit, or any other user-defined fatigue life level. A high-cycle variation of the above variable filter amplitude can also be defined, based on a shear stress instead of shear strain amplitude, giving   L U U r S 1        (10) where  L is the shear fatigue limit under zero mean stresses,  U is a material constant and S U is its ultimate strength. In all above cases for Crossland’s, Findley’s and Fatemi-Socie’s models or its variations, the filter amplitude r becomes instantaneously smaller for higher  h or   stress levels, to avoid filtering out damaging events. Analogously, similar expressions for such a variable r could be easily derived for other multiaxial fatigue damage models.