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Fracture Mechanics

This text delves into the intricate relationship between continuum damage mechanics (CDM), void growth, and the final failure of representative volume elements (RVE). It examines the stages of defect initiation, slow growth, and their implications in material deterioration under various conditions, including fatigue and creep. The document references key models and historical studies, such as those by Robinson, Hoff, and Basquin, to elucidate the complex behaviors of brittle and ductile creep fractures. It also discusses measurable and non-measurable quantities relevant to material behavior under stress.

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Fracture Mechanics

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  1. Fracture Mechanics Continuum Damage Mechanics (CDM)

  2. What did happen between these two stages?

  3. What did happen between these two stages? voids growth initial structure final failure of RVE voids coalescence

  4. log ε 1 β log N* Initiation and slow growth of defects (material deterioration) FATIGUE CREEP Brittle Creep Fracture (BCF) Dctile Creep Fracture (DCF) High Cyle Fatigue (HCF) Low Cycle Fatigue (LCF) log  n 1 1 1 m b log t* 1,5 < m< 10 Robinson 1952 2 < n < 15 Hoff 1953 5 <b < 20 Basquin 1910 Shanley 1955 1,3 <β < 2,5 Coffin-Manson 1954

  5. FATIGUE CREEP Brittle Creep Fracture (BCF) Dctile Creep Fracture (DCF) High Cyle Fatigue (HCF) Low Cycle Fatigue (LCF) 1,5 < m< 10 Robinson 1952 2 < n < 15 Hoff 1953 5 <b < 20 Basquin 1910 Shanley 1955 1,3 <β < 2,5 Coffin-Manson 1954 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) Palmgren 1924 Miner 1945 Creep fatigue interaction

  6. Measurable and non-measurable quantities in constitutive equations Cohesion Kinematics Dynamics Griffith, 1920 Physical quantities (measurable) Hooke, 1678 Kachanov, 1958 Mathematical quantities (non-measurable) Navier, 1822

  7. LFR for FATIGUE LFR for CREEP Göteborg (1973) Moskwa (1969) Cape Canaveral (1992) Life Fraction Rule (LFR) Palmgren 1924 Miner 1945 Creep fatigue interaction

  8. Creep-Fatigue Interaction happens here!

  9. CREEP FATIGUE Sequence UNSAFE N2 or t2 Sequence SAFE Sequence UNSAFE Sequence SAFE N1 or t1 15,02 10,70 4,93 N1 or t1 Block A = 2,61  DA=2,61/15,02=0,174 N2 or t2 Block B = 4,15  DB=4,15/10,7= 0,412 N3 or t3 Block C = 3,45  DC=3,45/4,93= 0,700 Sequence 0: A+B = 0,174+0,412=0586<1 SAFETY FIRST ! Sequence 1: A+B+C = 0,586+0,700=1,286>1 Sequence 2: A+B+A = 0,586+0,174=0,760<1 Sequence 3: A+B+A+B = 0,760+0,412=1,172>1

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