Consolidated derivation of fracture mechanics parameters and fatigue theoretical evolution models: basic review
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Consolidated derivation of fracture mechanics parameters and fatigue theoretical evolution models: basic review E. S. Ameh1 Received: 9 July 2019 / Accepted: 22 September 2020 © Springer Nature Switzerland AG 2020
Abstract Presence of cracks lead to structural steels failure below critical yield strength. The primary aim of the present article is to simplify and consolidate mathematical derivation of stress concentration, fracture stress, stress intensity factor, crack tip opening displacement and J-integral parameters from the first principle as well as application to fatigue. The review explains the mathematical derivation of fracture mechanics parameters from the theoretical concept, including alternatives to fatigue life prediction with strain-based approach method. The stress concentration around a notch can only be performed if the radius of the notch is far greater than zero and the stress field at sharp crack shows singularity when the crack tip radius is equal to zero. Furthermore, blunted crack tip violates stress singularity, while the crack tip opening displacement and J-integral parameters show the solution of a crack extending beyond zero crack tip radius, thus are used to characterize material stress fields with blunted crack tip. The review highlights benefit of characterizing fatigue crack growth with J-integral and crack tip opening displacement parameters over stress intensity factor. This paper would benefit majorly engineers and specialists in nuclear, aviation, oil and gas industries. Keyword Crack tip opening displacement · Fatigue · J-integral · Plastic zone · Stress intensity factor Abbreviations Δk Applied stress intensity factor Γ Close path dv Change in load displacement n Constant for deeply notched specimen 𝜓, 𝜒 Complex analytical function z Conjugate function a Crack length Δa Change in crack length kop Crack opening stress factor ΔCTOD Crack tip opening displacement kc Critical fracture toughness of material 𝜌c Critical dislocation density r Crack tip radius k I Cyclic strength coefficient nI Cyclic strain hardening exponent 𝜌 Density Ud Dislocation strain energy
ux,y Displacement field in X and Y direction ui Displacement vector ds Displacement along contour Δkeff Effective stress intensity factor range 𝛾s Elastic surface energy 𝜌∗ Elementary material block size 𝛼 Ellipse coordinate lines G Energy release rate da∕dN Fatigue crack growth rate 𝜀If Fatigue ductility coefficient c Fatigue ductility exponent 𝜎fI Fatigue strength coefficient d Fatigue strength exponent Φ General stress function 𝛽 Hyperbola coordinate lines da Incremental crack length dN Incremental number of stress cycle (z) Integral of complex function
* E. S. Ameh, [email protected] | 1Department of Mechanical Engineering, University of Benin, Benin, Edo State, Nigeria. SN Applied Sciences
(2020) 2:1800
| https://doi.org/10.1007/s42452-020-03563-8
Vol.:(0123456789)
Review Paper
SN Applied Sciences
(2020) 2:1800
da Incremental crack length ΔJ J-integral range R St
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