Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education 1 /10 M.Chrzanowski: Strength of Materials 3 SM3-03: F racture 3. Mechanics of cracks growth Linear Fracture Mechanics (LFM)

Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education 2 /10 M.Chrzanowski: Strength of Materials 3 SM3-03: F racture SPACE PROCESS OF FATIGUE DETERIORATION MATERIAL DETERIORATION IN TIME SPACE Typical stages of fatigue failure development, and its fraction of failure process 1,2,3 – nucleation - small area - up to 80% of the life-time 4,5,6 – fatigue deterioration - large area - up to 20% of the life-time 7 – instantaneous fracture - large area - below 1 % of the life-time SPACE DOMAIN TIME DOMAIN Initial cumullation of damages Continuum Damage Mechanics (CDM) Sub-critical propagation of micro-ckracs Linear Fracture Mechanics (LFM) Post-critical propagation of a main crack Dynamical Fracture Mechnaics (DFM)

Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education 3 /10 M.Chrzanowski: Strength of Materials 3 SM3-03: F racture SS Schenctady T2 transporter cracked on , Portland, OR

Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education 4 /10 M.Chrzanowski: Strength of Materials 3 SM3-03: F racture De Havilland „Comet” the first passenger jet – analysis of disaster Catastrophic failures Production Introduced to the service

Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education 5 /10 M.Chrzanowski: Strength of Materials 3 SM3-03: F racture Stress-based approach q[Pa] y x σ y = 3q G.Kirsch, 1898 – Thin plate of unlimited width containing a circular hole solids/77450/Stress-concentrations-and-fracture?anchor=ref611555

Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education 6 /10 M.Chrzanowski: Strength of Materials 3 SM3-03: F racture q[Pa] y x G.V. Kolosow 1910 & C.E.Inglis, 1913 – Thin plate of unlimited width containing an elliptical hole a b b  0 σ  a  b σ  3q INDEPENDENT OF THE MAGNITUDE OF a !!!

Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education 7 /10 M.Chrzanowski: Strength of Materials 3 SM3-03: F racture H.M.Westergaard, 1939, N.I.Muskhelischvili, 1943 – 2D analysis of the stress field around the notch tip yy AA r  x  0 0 Dla Singularity ! Stress intensity factor a

Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education 8 /10 M.Chrzanowski: Strength of Materials 3 SM3-03: F racture To stystemise above, three cases are distinguished: Stress intensity factors for different orientation of crack plane and loading has been calculated around 1960 (G.Sih) Mode I - Tearing; crack surfaces open perpendicular to the planes of its movement KIKI K II K III Mode II – Out-of-plane shear; crack surfaces slide perpendicular to the planes of its movement Mode III - Out-of-plane shear; crack surfaces slide paralell to the planes of its movement

Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education 9 /10 M.Chrzanowski: Strength of Materials 3 SM3-03: F racture Stress-based approach Safe design requires following conditions to be fulfilled: K I < K Ic K II < K IIc K III < K IIIc where K Ic, K IIc, K IIIc are critical values of responsible stress intensity factors, experimentally determined

Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European Union within the confines of the European Social Fund and realized under surveillance of Ministry of Science and Higher Education 10 /10 M.Chrzanowski: Strength of Materials 3 SM3-03: F racture Simple example showing importance of Facture Mechanics (after J.Hult, Bära Brista, Almqvist&Wiksell, 1975) 2l2l q q c c What is the length of central crack which can be introduced without dimintion of load carrying of the specimen (no interaction between cracks is assumed) For edge crack: For central crack: E.g. if c = 2 cm l  2,5 cm 2l  5 cm