Modeling size effects associated with tensile fracture initiation from a wellbore

Abstract

This paper investigates different tensile fracture initiation criteria on the plane-strain configuration of a defect-free openhole wellbore. It aims to model the effect of the internal pressurization of a wellbore 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 a fracture 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 wellbore size on the load at fracture initiation observed experimentally is well reproduced by these different models which all provide a similar response. The size effect 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 ℓm=KIc2/σT2, while the structural lengthscale is here simply the wellbore radius ℓs=a. For small values of I (i.e., I<0.1), tensile crack initiation is dominated by strength with vanishingly small size effects, 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.