Basic principles of metallic fracture Author: Miha Povšič Mentor: izred. prof. dr. Leon Cizelj Co-mentor: dr. Samir El Shawish Ljubljana, January 2016

Introduction fracture mechanics is a science about cracks rapid expansion after World War II categories of fracture mechanics: linear elastic fracture mechanics (LEFM) elastic-plastic fracture mechanics (EPFM) fracture analysis: the energy criterion the stress intensity approach

Microscopic view of material fracture material fracture : applied stress is sufficient to break the bonds between the atoms cohesive stress σC of the order of E/π

Microscopic view of material fracture stress for global fracture several orders of magnitude lower flaws in the material flaws magnify the local stress and cause the global strength to decrease propagation of breakings failure stress σf

Stress concentration at crack tip singularity in stress amplitude stress field near the crack tip: stress intensity factor K: critical stress intensity factor KIc :

Modes of loading Mode I – Opening Mode II – In-Plane Shear Mode III – Out-0f-Plane Shear

Critical stress intensity factor defined by Irwin in 1957 measure for fracture toughness higher value means tougher material Material KIc [MPam1/2] Steel alloy (4340) 50 Aluminium 14-28 Soda lime glass 0,7-0,8 Concrete 0,2-1,4 Polystyrene 0,7-1,1 Silica aerogels 0,0008–0,0048

Energy criterion approach Griffith, 1920 energy available for crack growth > resistance of the material we define potential energy Π from strain energy U and work of internal forces F

Energy criterion approach – LEFM energy release rate G: critical energy release rate: connection with critical stress intensity factor:

Energy criterion approach – EPFM energy release rate J: J is equal to: connection with G:

Resistance curve - LEFM crack growth stability R; material resistance to crack extension depend on crack length a stability criterion stable unstable

Resistance curve - EPFM similar to LEFM R -> JR includes plasticity stability criterion stable unstable

Experimental methods – Charpy impact test determines the amount of energy absorbed by the material during the fracture absorbed energy is measure of material's notch toughness widely applied in industry easy, cheap, quick

Experimental methods – unloading compliance method method for monitoring the crack growth behaviour single-specimen test technique measurements of a crack length during the loading with this method we can calculate R curve

Simulation limitation of analytical calculation -> simulation 2D approximation of 3D plane strain plane stress Abaqus FEA finite element analysis

Simulation - preparation homogeneous compact tension (CT) specimen material: 18MnD5 ferritic steel geometry: mesh:

Simulation – stress distribution elastic and elastic - plastic material under the same load higher stress concentration at the crack tip for elastic material

Simulation - J - integral J integral vs. load diagram J contour integral plane stress is more conservative approximation

Conclusion cracks are important in fracture mechanics fracture toughness - crack initiation: simple one-parametric approaches for describing fracture critical stress intensity factor KIC, critical crack driving force GIC , critical J contour integral JIC stability of crack growth: R curve or JR curve

References [1] T. L. Anderson, Fracture mechanics: Fundamentals and application, Third edition (CRC Press, 2005) [2] Irwin, G.R., "Analysis of Stresses and Strains near the End of a Crack Traversing a Plate," Journal of Applied Mechanics, Vol. 24, pp. 361-364, 1957. [3] https://en.wikipedia.org/wiki/Fracture_toughness [4] Griffith, A.A., "The Phenomena of Rupture and Flow in Solids," Philosophical Transactions, Series A, Vol. 221, pp. 163-198, 1920 [5] I. Simonovski, O. Martin, G. Machina, WP4.2 K/J Value Estimation of different Specimen Designs Part 1: Homogeneous Specimens - Report on Round2 results, January 2015 [6] http://www.twi-global.com/technical-knowledge/faqs/material-faqs/faq-what-is-charpy-testing/