13th International Conference on Fracture June 16–21, 2013, Beijing, China -6- ‐0.2 0 0.2 0.4 0.6 0.8 1 0 5000 10000 15000 20000 25000 30000 Normalised K value ( K / max K in the cycle) Time (s) Normalised K term K range ‐ cycle 1 K range ‐ cycle 2 K range ‐ cycle 3 K range ‐ cycle 4 Figure 6. Normalised K time history and cyclic events The calculation of crack growth for a single crack front position through one load cycles using Eqn. 2 and Eqn. 3 then proceeds by integrating the sequence of K vs t segments with discrete da/dn effects added as the fatigue cycles occur. The procedure of extracting a full K vs t time history from a finite element analysis and carrying out a combined fatigue and time integration has been implemented for a general 3D crack in version 7.8 of Zencrack [11]. A number of aspects of the integration process cannot be described fully here but are mentioned briefly: • The finite element analysis provides K vs t data for one crack size and one load cycle. The integration scheme modifies the basic K vs t history to account for changes due to the increased crack size as the crack grows. When the mesh is updated to a new crack position and submitted for a new finite element analysis, a new baseline K vs t solution is generated. • The definition of cyclic events as a result of the cycle counting process will, in general, lead to different temperatures at minimum and maximum conditions for a fatigue cycle. When calculating da/dn for the cycle, an appropriate temperature assumption must be made. • Mode mixity and local changes of growth direction through the load cycle are possible. Two examples of integration output from this process are shown in Figure 7. The da/dt contributions are only non-zero when the temperature is above the threshold temperature defined for the da/dt growth law. The first (and largest) cyclic event produces a visible instantaneous (vertical segment) on the da plot. Cyclic events 2, 3 and 4 have much lower da/dn values and the vertical segment da contributions from them are too small to be seen on the scale of this figure. 1.0E‐09 1.0E‐08 1.0E‐07 1.0E‐06 1.0E‐05 1.0E‐04 0 100 200 300 400 500 600 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 da/dt [m/s] Temperature [degrees C] Number of flight cycles Tthr=475 degC Temperature da/dt 1.0E‐07 1.0E‐06 1.0E‐05 1.0E‐04 1.0E‐03 1.0E‐02 1.0E‐01 1.0E+00 0 0.001 0.002 0.003 0.004 0.005 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 da/dn [mm/cycle] Crack growth [mm] Number of flight cycles Crack growth da/dn Figure 7. T, da/dt, da/dn and da through integration of a load cycle
RkJQdWJsaXNoZXIy MjM0NDE=