Project “The development of the didactic potential of Cracow University of Technology in the range of modern construction” is co-financed by the European.

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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 M.Chrzanowski: Strength of Materials 3 SM3-0 5 : Damage 1/9 Fracture Mechanics 5.Continuum Damage Mechanics (CDM)

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 M.Chrzanowski: Strength of Materials 3 SM3-0 5 : Damage 2/9 What did happen between these two stages?

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 M.Chrzanowski: Strength of Materials 3 SM3-0 5 : Damage 3/9 voids growth voids coalescencefinal failure of RVE initial structure What did happen between these two stages?

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 M.Chrzanowski: Strength of Materials 3 SM3-0 5 : Damage 4/9 Initiation and slow growth of defects (material deterioration) FATIGUE Low Cycle Fatigue (LCF) High Cyle Fatigue (HCF) Dctile Creep Fracture (DCF) Brittle Creep Fracture (BCF) b n m log t * log  log N * log ε 1 CREEP 1 1 1,3 < β < 2,5 Coffin-Manson < b < 20 Basquin 1910 Shanley < n < 15 Hoff ,5 < m < 10 Robinson β

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 M.Chrzanowski: Strength of Materials 3 SM3-0 5 : Damage 5/9 FATIGUE Low Cycle Fatigue (LCF) High Cyle Fatigue (HCF) Dctile Creep Fracture (DCF) Brittle Creep Fracture (BCF) CREEP 1,3 < β < 2,5 Coffin-Manson < b < 20 Basquin 1910 Shanley < n < 15 Hoff ,5 < m < 10 Robinson 1952 dl/dN = F(  a,pl ) Solomon 1972 dl/dN = f(  K) Paris 1964 dε/dt =  (  ) Hoff 1953 dω/dt = g (  ω) Kachanov 1958 Life Fraction Rule (LFR) Creep fatigue interaction Palmgren 1924 Miner 1945

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 M.Chrzanowski: Strength of Materials 3 SM3-0 5 : Damage 6/9 Physical quantities (measurable) Mathematical quantities (non-measurable) Dynamics Kinematics Hooke, 1678 Navier, 1822 Cohesion Measurable and non-measurable quantities in constitutive equations Griffith, 1920 Kachanov, 1958

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 M.Chrzanowski: Strength of Materials 3 SM3-0 5 : Damage 7/9 LFR for FATIGUELFR for CREEP Göteborg (1973) Life Fraction Rule (LFR) Creep fatigue interaction Palmgren 1924Miner 1945 Cape Canaveral (1992)Moskwa (1969)

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 M.Chrzanowski: Strength of Materials 3 SM3-0 5 : Damage 8/9 Creep-Fatigue Interaction happens here!

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 M.Chrzanowski: Strength of Materials 3 SM3-0 5 : Damage 9/9 FATIGUE CREEP N 1 or t 1 N 2 or t 2 N 3 or t 3 N 1 or t 1 N 2 or t 2 4,93 10,70 15,02 Block A = 2,61  D A =2,61/15,02=0,174 Block B = 4,15  D B =4,15/10,7= 0,412 Block C = 3,45  D C =3,45/4,93= 0,700 Sequence 0: A+B Sequence 1: A+B+C Sequence 2: A+B+A Sequence 3: A+B+A+B = 0,174+0,412=0586<1 = 0,586+0,700=1,286>1 = 0,586+0,174=0,760<1 = 0,760+0,412=1,172>1 Sequence SAFE Sequence UNSAFE SAFETY FIRST !