A novel approach to model mixed mode plasticity at crack tip and crack growth. Experimental validations using velocity fields from digital image correlation

Predicting the growth of fatigue cracks under multi-axial loading conditions remains difficult for at least two main reasons. Firstly, the crack path can be very complicated, which makes the determination of stress intensity factors difficult and induces non-linear effects due to contact and friction between the faces of the crack. Secondly, the elastic-plastic behaviour of the crack tip region also introduces non-linear effects on both the growth rate and the crack path. This paper is devoted to the experimental analysis of plastic flow within the crack tip region. A set of specific experiments were conducted so as to validate a novel approach to model the mixed mode elastic-plastic behaviour of a cracked component. The velocity field at the vicinity of the crack tip was determined using digital image correlation in I + II mixed mode loading conditions. The mode I and mode II components of the experimental velocity field were extracted using symmetry considerations with respect to a coordinate system attached to the crack tip. Each mode was then partitioned into elastic and plastic parts and each part was approached by the product of an intensity factor and a spatial reference field, constructed once for all. With this approach, the experimental velocity field is described using only four degrees of freedom, which are respectively the mode I and mode II intensity factors of the elastic and plastic part of the velocity field. The experimental results showed that the error associated with this approximation is small. A criterion was proposed to determine the yield surface, and it was shown that the experimental yield surface agrees well with the theoretical one. In particular it is shown that the LEFM framework can still be used in elastic-plastic conditions provided that the centre of the elastic domain is allowed to evolve with plastic flow. The plastic flow direction was also measured and is consistent the hypothesis of a normality flow rule that is used in the model. And finally, the measured transient evolutions the plastic flow in complex loading conditions are consistent with the hypotheses of the model.