By G. Pluvinage
An unlimited majority of disasters emanate from tension concentrators reminiscent of geometrical discontinuities. The function of tension focus used to be first highlighted by means of Inglis (1912) who provides a pressure focus issue for an elliptical disorder, and later via Neuber (1936). With the development in computing, it really is now attainable to compute the genuine pressure distribution at a notch tip. This distribution isn't uncomplicated, yet seems like pseudo-singularity as in precept the facility dependence with distance is still. This distribution is ruled by way of the notch pressure depth issue that is the root of Notch Fracture Mechanics. Notch Fracture Mechanics is linked to the volumetric process which postulates that fracture calls for a actual quantity. when you consider that fatigue additionally wishes a actual procedure quantity, Notch Fracture Mechanics can simply be prolonged to fatigue emanating from a rigidity focus.
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Extra info for Fracture and Fatigue Emanating From Stress Concentrators
K V . k H ! k t2 . 4] has proposed a modification of Neuber’s rule based on a material parameter m. 30) C1m . C12 m 1 , with kV kH ,C2 . 33) where n and K are respectively the hardening exponent and coefficient of the Ludwik’s law of the material and E Young’s modulus. This relationship is differs little from plane stress to plane strain conditions. 5, we obtain again Neuber’s rule. For the elastic case: for elastoplastic case : kV kH kt ; ; C1 C 2 1, kV kt ; k H ! kt ; C1 1 ; C 2 ! 1 . 5] MolskiíGlincka’s method considers the strain energy density at the notch tip W*.
Kt n 1 K » « 2 »¼ «¬ x Expression for ] We define the ]parameter as: §¨ © n 1 2 k t2 kV . k H 1 V 2max V max V max . ·¸ ¹ K n . Hg x k t2 . k t2 . k t2 . §¨ 1 ©2 . §¨ n 2 ·¸ , ¨ V g . 49) k t2 § n2 · ¸¸ . k V . 50) This leads to: [ § n2 · ¸¸ . H V « max max max . « V g . ¨ 2 n 1 ¹¼ © ¬ ª 1 ·º §1 ¸» , «V max . H max . 55) ] = 1 and we found again the Neuber’s rule. 56) E k t 1 E 1 k t 1. s , E where Es is the secant modulus defined by: or kV V max . H max Es The elastoplastic strain concentration factor is given: Es , kH kH .
40) K n . 41) Assuming that the gross stress remains elastic, the strain energy density is equal to : G PLUVINAGE 50 V 2g W 02 2E . 42) leads to: k t2 . V 2g 2 2 n 1 1 V 2max V max V max . K n . 43) By extension to the case for Re < Vg 1 º ª n» « V 2g V g V g 2 » « . kt n 1 K » « 2 »¼ «¬ x Expression for ] We define the ]parameter as: §¨ © n 1 2 k t2 kV . k H 1 V 2max V max V max . ·¸ ¹ K n . Hg x k t2 . k t2 . k t2 . §¨ 1 ©2 . §¨ n 2 ·¸ , ¨ V g . 49) k t2 § n2 · ¸¸ . k V . 50) This leads to: [ § n2 · ¸¸ .