Linear Fracture Mechanics LFM 3 Mechanics of cracks

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Linear Fracture Mechanics (LFM) 3. Mechanics of cracks growth

Linear Fracture Mechanics (LFM) 3. Mechanics of cracks growth

LFM – fatigue revisited Typical stages of fatigue failure development, and its fraction of

LFM – fatigue revisited Typical stages of fatigue failure development, and its fraction of the whole process of failure 1, 2, 3 – nucleation up to 80% 4, 5, 6 – fatigue deterioration up to 20% 7 – instantaneous fracture Linear Fracture Sub-critical propagation Mechanics (LFM) of micro-cracks Post-critical Dynamic propagation Fracture Mechanics of a main crack (DFM) SPACE DOMAIN Continuum Damage Initial cumullation of Mechanics (CDM) damages below 1 % SPACE PROCESS OF FATIGUE DETERIORATION

SS Schenectady T 2 transporter cracked on 16. 01. 1943, Portland, OR

SS Schenectady T 2 transporter cracked on 16. 01. 1943, Portland, OR

De Havilland „Comet” – first passenger jet Production -1949 Catastrophic failures 3. 03. 1953

De Havilland „Comet” – first passenger jet Production -1949 Catastrophic failures 3. 03. 1953 10. 01. 1954 8. 04. 1954 Introduced to the service 1952 De Havilland „Comet” – analysis of 10. 01. 1954 disaster

LFM – Linear Fracture Mechanics Stress-based approach q[Pa] G. Kirsch, 1898 – Thin plate

LFM – Linear Fracture Mechanics Stress-based approach q[Pa] G. Kirsch, 1898 – Thin plate of unlimited width containing a circular hole http: //www. britannica. com/EBchecked/topic/553306/mechanics-ofsolids/77450/Stress-concentrations-and-fracture? anchor=ref 611555 y σy= 3 q x q[Pa]

LFM – Linear Fracture Mechanics G. V. Kolosow 1910 & C. E. Inglis, 1913

LFM – Linear Fracture Mechanics G. V. Kolosow 1910 & C. E. Inglis, 1913 – Thin plate of unlimited width containing an elliptical hole q[Pa] y b a b 0 q[Pa] σ a b INDEPENDENT OF THE MAGNITUDE OF a !!! σ 3 q x

LFM – Linear Fracture Mechanics H. M. Westergaard, 1939, N. I. Muskhelischvili, 1943 –

LFM – Linear Fracture Mechanics H. M. Westergaard, 1939, N. I. Muskhelischvili, 1943 – 2 D analysis of the stress field around the notch tip 0 A y r x Dla a Singularity ! Stress intensity factor

LFM – Linear Fracture Mechanics Stress intensity factors for different orientation of crack plane

LFM – Linear Fracture Mechanics Stress intensity factors for different orientation of crack plane and loading has been calculated around 1960 (G. Sih) To systemise above, three cases are distinguished: KI KIII Mode I - Tearing; crack surfaces open perpendicular to the planes of its movement Mode II - In-plane shear; crack surfaces slide perpendicular to the crack front Mode III - Out-of-plane shear; crack surfaces slide parallel to the crack front

LFM – Linear Fracture Mechanics • stress intensity factors (SIF) definitions

LFM – Linear Fracture Mechanics • stress intensity factors (SIF) definitions

LFM – Linear Fracture Mechanics Stress-based approach Safe design requires following conditions to be

LFM – Linear Fracture Mechanics Stress-based approach Safe design requires following conditions to be fulfilled: KI < KIc where KII < KIIc KIII < KIIIc KIc , KIIIc are critical values of responsible stress intensity factors, experimentally determined

Simple example showing application of Facture Mechanics (after J. Hult, Bära Brista, Almqvist&Wiksell, 1975)

Simple example showing application of Facture Mechanics (after J. Hult, Bära Brista, Almqvist&Wiksell, 1975) q What is the length of central crack to be introduced without reduction of load carrying specimen (no interaction between cracks is assumed) For edge crack: c c For central crack: 2 l q E. g. if c = 2 cm 2 l 5 cm

Dependence of Fracture Toughness on thickness

Dependence of Fracture Toughness on thickness

Materials Data. Book, Cambridge University Engineering Department

Materials Data. Book, Cambridge University Engineering Department