Fracture mechanics Subjects of interest Introduction/ objectives Stress intensity factor Determination of fracture toughness Fracture toughness and design Plasticity correction Crack opening displacement R curve Probabilistic aspects of fracture mechanics

Crack and stress intensity approach The unit of KI is MPam

Stresses near and tip of the crack

Loading types In all loading1/r singularity may occur at the tip of the crack. K (stress intensity factor) and fij (dimensionless shape correction factor) depend on laoding type and shape geomety. (i,j=1,3) There are three ways of applying a force to enable a crack to propagate: Mode I fracture : opening mode(a tensile stress normal to the plane of the crack). Mode II fracture : sliding mode (a shear stress acting parallel to the plane of the crack and perpendicular to the crack). Mode III fracture : Tearing mode (a shear stress acting parallel to the plane of the crack and parallel to the crack front)

Cauchy stress around a crack tip and Stress Intensity Factors Crack deformation mode. K value can be evaluated using standard mathematical approaches, Mode I: tension, opening Mode II: In plane shear, sliding Mode III: Out of plane shear, tearing

ac : is the critical crack length in an infinite plate Stress intensity factor K can be described as fracture toughness KIC of materials (material resistance to crack propagation) under conditions of Brittle fracture In the presence of sharp crack Under critical tensile loading KIC : is the critical stress intensity factor for plane strain condition in mode I failure. ac : is the critical crack length in an infinite plate app : is the applied stress LEFM- Linear Elastic Fracture Mechanics DEÜ, Makina MÜhendisliği Bölümü

Stress intensity factor types in a plate including crack Mode I and Mode II calculations of a plate subjected to tension. (Mixed Mode Loading)

Stresses in the systems with crack When the crack at the center of a plate the stress and stress intensity factors terms can be given as : : Shape correction factor DEÜ, Makina MÜhendisliği Bölümü

Center crack in an infinite plate subjected to tension Stress Intensity Factor Aprroach K : h 2a b P where w = 2b

Types of Stress: Plane stress problem : the stress in z direction becomes zero. z = xz = yz = 0, Plane strain problem : the strain in z direction becomes zero xz = yz = 0 and z =  (x + y).

Geometries of Fracture Center crack and finite plate: Stress intensity factor infinite plate:

Single sided notch, subjected to stress Stress intensity factor One-sided cracked plate if( a w) semi infinite plate β=1.12

Stress intensity factor Double-sided notch : Stress intensity factor a) if( a w) semi infinite plate β=1.12 b) DEÜ, Makina MÜhendisliği Bölümü

Stress intensity factors Y wrt a/w ratio

Eliptic Crack

Semi Eliptic Surface crack

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