TECHICAL Series MATHEMATICS • INFORMATICS • PHYSICS Series PHILOLOGY Series ECONOMIC SCIENCES Sereies EDUCATIONAL SCIENCES Series LAW AND SOCIAL SCIENCES Series
The Paris Formula for the Crack Propagation Rate, Approached as a Temperature and Asymmetry Coefficient Complex Function
(Formula lui Paris pentru viteza de propagare a fisurii, abordare ca o funcţie complexă de temperatură şi coeficient de asimetrie)
Vol LXV • No. 4/2013
Vâlcu Roşca, Cosmin Miriţoiu, Alina Romanescu
Universitatea din Craiova, Facultatea de Mecanică, Str. Calea Bucureşti nr. 107, Craiova
e-mail: rosca_valcu@yahoo.com

 Keywords   crack, asymmetry coefficient, stress intensity factor, temperature, Paris formula

 Abstract
The paper presents the propagation rate of the crack according to the Paris formula from a new point of view by taking into account the temperature T variation and the asymmetry coefficient R. The fatigue loadings by axial-eccentric tensile test were made of CT specimens made by stainless steel V2A class, 10TiNiCr175 mark. The loading temperatures were: 213K, 253K and 273K, and the asymmetry factors were: R=0.1, R=0.3 and R=0.5. By using the Paris formula, da/dN= C∙(ΔK)m with adequate mathematical programs, C(R,T) and m(R,T) parameters were determined as compound functions, using approximations by second degree parabolas. By simultaneously varying the loading temperature T and asymmetry factor R, there were drawn the variation surfaces, into a three orthogonal axes system, for the C and m parameters. Finally, with the C and m expressions, as functions of two variables (R and T), there was made a complex study for the propagation of the cracking speed da/dN, expressed by various drawn graphics.

 Rezumat
Lucrarea îşi propune studiul vitezei de propagare a fisurii conform relaţiei lui Paris printr-o abordare nouă a analizei ţinând seama simultan de variaţia temperaturii T şi a coeficientului de asimetrie R. Încercările de oboseală prin întindere axial- excentrică au fost efectuate pe epruvete tip CT executate din oţel inoxidabil clasa V2A, marca 10TiNiCr175. Temperaturile de încercare au fost 213K, 253K şi 293K, iar coeficienţii de asimetrie ai solicitării: R=0.1, R=0.3 şi R=0.5. Folosind formula lui Paris, da/dN=C(deltaK)m, cu programe matematice adecvate, s-au determinat parametrii C(R,T) şi m(R,T), ca funcţii compuse, utilizând aproximarea prin parabole de gradul al doilea. Variind simultan temperatura de încercare T şi coeficientul de asimetrie R, au fost trasate suprafeţele de variaţie, într-un sistem de axe triortogonale, pentru parametrii C şi m. În final, cu expresiile pentru C şi m, ca funcţii de două variabile, (R şi T), s-a făcut un studiu amplu pentru viteza de propagare a fisurii da/dN, materializat prin diverse grafice trasate.



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