Page 63 - Biaxial Multiaxial Fatigue and Fracture

48 E LABESSE-JIED ET AL.

Ta(t)=Z(t)-? (7)

The damage associated with each cycle is calculated by using Miner’s linear rule and the
material fatigue strength curve expressed in the form of Basquin’s law [7].

The lifetime is calculated by maximising the damage over all the examined planes. In other
words, it means that the critical plane enforces its fatigue life to the material.

EVALUATION OF THE METHOD ON SPECIMENS
The local approach is assessed on cylindrical and tubular shaft specimens from experiments
reported in the round-robin program performed by the SAE in the 80’s 181. The shafts are
submitted to proportional or non-proportional strain-controlled tension and torsion loading.
The strain amplitudes are constant or variable. The random spectra come fi-om measurements
made on log skidder and agriculture tractor axles and recorded as Markov matrix. Fatigue tests
are pedormed on shaft specimens with different deterministic or random amplitudes until
complete fracture. Calculations are carried out according to the local approach flowchart (Fig.
4). Starting from the deterministic or random strain cycles, the stress states are calculated by
using a cyclic constitutive law with non-linear kinematical and isotropic hardening. Then, the
damage corresponding to the cycles extracted by the rainflow method is calculated and
cumulated. The life corresponding to each strain sequence is then calculated by using the most
damaged facet.
The shafl is made up of C45 carbon steel. The mechanical properties of this steel are
summarised in Table 1.

Table 1. Monotonic and cyclic properties of C45 carbon steel (from [SI)

OY K n cf7Y K’ n’ cf’f Z’f b
(MPa) (M Pa) (MPa) (MPa) (MPa) (MPa)
280 1185 0.23 180 1258 0.208 948 505 - 0.092

Figure 6 gives the comparison between the experiments and calculated lives for all kinds of
loading: deterministic uniaxial tension, proportional tension-torsion, non proportional tension-