Fatigue Crack Paths 2003

amplitude multiaxial loading (in-phase and out-of-phase) that the number of cycles to

initiation was deduced from simple analytical expressions. The damage accumulation

under variable loading of the same loading mode (tension, torsion, combined tension

and torsion) is rather easy to estimate with this model but some problems have to be

faced with non similar variable loading conditions, i.e. with a loading history showing

different successive stress states.

This approach will be used to detail how the successive applications of a torsion

loading, a tension loading (and a combined tension and torsion loading) can lead to an

increase or a decrease of the accumulated damage. The interaction mechanisms between

the microcracks nucleated under these different load conditions (and then on different

critical planes) is discussed. The predictions of the critical plane fatigue damage model

are compared to fatigue tests under sequence of tension and torsion carried out on a

mild steel. Other data from the literature relative to sequence of non similar load

conditions are also analyzed.

T W OS C A L ECRITICAPLL A N DE A M A GMEO D E L

To depict the fatigue crack initiation phenomenomin polycrystalline metallic materials,

two scales of description of a material can be distinguished : the usual macroscopic

scale and a mesoscopic one. The macroscopic scale is defined with the help of an

elementary volume V determined at any point O of a body as the smallest sample of the

material surrounding O that can be considered to be homogeneous. Usually, engineers

use stresses and strains measured or estimated at this scale. V contains a large number

of grains (crystals) and the mesoscopic scale is defined as a small portion of this

volume. In the high cycle fatigue regime, some grains undergo local plastic strain while

the rest of the matrix behaves elastically (the overall plastic strain is negligible). To

reach the stress and strain fields at the grain scale, Dang Van [5] proposed to use the

Lin-Taylor localisation rule that assumes that the macroscopic strain is equal to the

mesoscopic strain. According to this first order approximation of the localisation

problem and a microplasticity analysis, one can compute for any type of multiaxial

loading the cyclic response of the plastically deforming grains. Dang Van assumed that

a fatigue limit occurs if, at all scales (macroscopic and mesoscopic), an elastic

shakedown state is reached or, in other words, if the grains tend to recover a purely

elastic response. Since the fatigue crack nucleation is a phenonemon different from a

simple cyclic plasticity mechanism, it is assumed that the condition of elastic

shakedown is modified by the hydrostatic stress (or in a similar way by the normal

stress acting on the critical plane).

Now, when dealing with crack initiation and related fatigue life, this concept of

elastic shakedown is no more enough. One has to give a damage evolution law coherent

with the experimental observations in high cycle fatigue. First of all, the shear stress and

the hydrostatic stress are considered as the proper mechanical parameters responsible of

damage increase. Second, the damage evolution is assumed to be mainly due to the

accumulation of mesoscopic plastic strain itself influenced by the hydrostatic stress