Modeling size effects associated with tensile fracture initiation from a wellbore

This paper investigates different tensilefractureinitiation criteria on the plane-strain configuration of a defect-free openhole wellbore. It aims to model the effect of the internal pressurization of awellbore drilled in the direction of one of the principal stresses. We compare a brittle initiation model that accounts for both the necessary stress and energy conditions (mixed criteria) for the development of afracture with a bilinear cohesive zone model which can degenerate either to the Dugdale rectangular softening model or the linear softening model. Moreover, we propose an approximation of the mixed criteria which amounts to solving a single scalar nonlinear equation. The effect of the wellboresize on the load at fractureinitiation observed experimentally is well reproduced by these different models which all provide a similar response. The sizeeffect on tensile failure is governed by the ratio I between a material lengthscale lm over a structural lengthscale ls: I=lm/ls. The material lengthscale is defined as the square of the ratio between the material fracture toughness over its tensile strength , while the structural lengthscale is here simply the wellbore radius . For small values of I (i.e., I<0.1), tensile crack initiation is dominated by strength with vanishingly small sizeeffects, while for large value of I (I>10), crack initiation is dominated by energy requirements and the initiation pressure increases with I. The far-field stresses modify the transition between a strength-dominated to an energy-dominated tensile failure as a function of I. A higher mean compressive far-field stress tends to make the failure more strength-driven, while higher differential far-field compressive stress promotes an energy-driven tensile failure.