A 3-D Failure Initiation Criterion from a Sharp V-notch Edge in Elastic Brittle Structures

A three-dimensional failure initiation criterion in brittle materials containing a sharp V-notch is presented and validated by experiments. It is based on simultaneous fulfilment of the stress requirement and a finite fracture mechanics energy release rate (ERR) requirement. Since the ERR cannot determine failure initiation direction for dominant mode III loading, the failure initiation orientation is determined solely by stress considerations and the force at fracture is determined by both ERR and stress requirements. Experiments on PMMA, Graphite and MACOR V-notched specimens loaded by three modes demonstrated that predicted fracture load was mostly within 6.5% (RMS) of experimental values. ∗Corresponding author Email address: [email protected] (Zohar YOSIBASH) Preprint submitted to European Journal of Mechanics A/Solids May 28, 2016 Nomenclature General Symbol Meaning δΠ The difference in the potential energy between a V-notched 3D linear elastic domain with and without a small crack Hij Geometric functions G Energy release rate Gc Critical energy release rate in mode I KI , KII , KIII Mode I, II and III stress intensity factors KIc Mode I fracture toughness Fc Failure load of the specimen σ Stress tensor σn Stress normal to the rotated plane σn,avg Average stress normal to the rotated plane σc Critical stress αi Eigenvalues Si(θ ) Eigen-stress associated with the eigenvalue αi Ai(z) Generalized Edge Stress Intensity Functions S Crack area R Outer radius of integration h V-notch height (depth) γ V-notch inclination angle in relation to the side faces ω V-notch solid angle (complementary to 2π with the notch opening angle) E Young’s modulus ν Poisson’s ratio α Counter clockwise rotation angle around the y axis (from the yz reference plane which is the V-notch bisector) θ Counter clockwise rotation angle around the z axis (from the yz reference plane which is the V-notch bisector)/ an angle measured from the V-notch bisector so that − 2 ≤ θ ≤ ω 2 2 Coordinate systems (r, θ, z) Cylindrical coordinates, the z axis coincides with the V-notch edge and θ is measured from the bisector plane α, θ Failure initiation rotation angles around V-notch bisector plane rp, θp Polar coordinate system in the plane rotated by α, θ ∗ around bisector plane θp1, θp2 Integration limits on the circular sector in the rotated plane