Elastic Plastic Fracture Mechanics Application of LEFM ve

Elastic - Plastic Fracture Mechanics Application of LEFM ve EPFM with respect to Fracture Behaviour LEFM: 1) For high strength materials at Plane Strain Case 2 ) For high strength materials at Plane Stress Case EPFM: 1) For high strength materials at Plane Stress Case 2) For Ductile Materials at Plane Stress Case or Plane Strain Case 3) Ductile materials that have plasticity Plastic Failure: Fully plastic Deformation of ductile materials Doç. Dr. M. Evren Toygar, DEÜ

LEFM and EPFM In LEFM, K is the stress intensity factor that identifies stress and displacement at the tip of the crack. K indentifies not only stress and strain magnitudes but also resistance of materials and the crack tip behaviours due to loading. K value depends on both stress and crack length. The stress statements near the crack tip for plane strain case when the crack a exists Doç. Dr. M. Evren Toygar, DEÜ

LEKM For =0 Tekillik bölgesi According to Irwin: if the plastic zone size less than the size of singularity then, LEFM is valid. If not, Dugdale yield model for plane sterss case is: ASTM: a, B, W-a 2. 5 , namely , specimen dimension. Doç. Dr. M. Evren Toygar, DEÜ

EPFM • Two parameters used in EPFM : • crack opening displacement (Çatlak ucu deplasmanı) (COD) veya crack tip opening displacement (çatlak ucu açılma miktarı) (CTOD). • J-integral. All two parameters give the fracture toughness measurement results independent of geometry. y Sharp crack x Blunt crack Doç. Dr. M. Evren Toygar, DEÜ ds

CRACK TIP OPENING DISPLACEMENTCTOD n WELLS, has obtained the relations between CTOD and stress intensity factors with approximate analysis. n IRWIN has obtained the effective crack length a + rp due to plasticity at the tip of the crack. Doç. Dr. M. Evren Toygar, DEÜ

EPFM • According to Wells: In LEFM conditons, at structural steel to do KIC measurement, the thickness of specimen has to be large and the plastic deformation makes the crack tip as blunt. Sharp crack Blunt crack ; • Irwin’s effective crack length, a + rp and plane stress case: Doç. Dr. M. Evren Toygar, DEÜ

CTOD Plane Strain Energy Release Rate • Equation can be obtained when the small-scale yield occurs. Here CTOD is related with G (strain energy release rate). • Wells : is valid for large –scale yield and it is related with J integral • Dugdale yields strip model: is the opening amount at the tip of the crack Crack tip opening displacement with respect to yield strip model Doç. Dr. M. Evren Toygar, DEÜ

CTOD Plane Strain Energy Release Rate Infinite plate with a crack Taylor series expansion, If and Obtained as: Doç. Dr. M. Evren Toygar, DEÜ can be

CTOD Plane Strain Energy Release Rate Generally: Dugdale Model: Dugdale : examined the plastic zone size for thick plate at plane stress case Doç. Dr. M. Evren Toygar, DEÜ

CTOD Blunted crack Sharp crack Blunted crack Original displacement at he crack tip Displacement at 900 line intersection, suggested by Rice CTOD Measurement by using bending specimen deplasman Vp Doç. Dr. M. Evren Toygar, DEÜ ' ' '

SENB Specimen Elastic-plastic analyses V, P Here, has the value 0. 44 for SENT specimen • ASTM E 1290 -89 standards: At experiments both CT and SENT specimens can be used. • cross sectional area: for rectangle W=2 B; or for square W=B can be taken the following equation KI can be used CTOD Equation Doç. Dr. M. Evren Toygar, DEÜ

J-kontur Integral y x ds Define the path around the crack ( ) tanımlayalım. J-integral : Here w is the strain energy density and , Ti is the component of the perpendicular traction vector. Doç. Dr. M. Evren Toygar, DEÜ

J- Integral 1) Linear Elastic Behavior : J Integral : G (is the strain energy release rate for the unit crack extansion) : Plane stress case : Plane strain case Doç. Dr. M. Evren Toygar, DEÜ

J- Integral 2) J Integral for both Elastic and Plastic Behaviour : : the path at the crack around w : is the strain energy density T : is the perpendicular traction vector n : normal to the surface u : displacement vector ds: is the inctement of the length along the path Doç. Dr. M. Evren Toygar, DEÜ

J- Integral J = Jelastic+ J plastic For the edge notch specimen when the plane strain case Doç. Dr. M. Evren Toygar, DEÜ