Methodology for assessing embryonic cracks development in structures under high‐cycle multiaxial random vibrations

Abstract

A B S T R A C T The myriad applicability of the frequency-domain critical plane criterion is outlined in order to evaluate and track the progression of fatigue damage in metallic structures subjected to high-cycle multiaxial random vibrations. The fatigue assessment using the given criterion is performed according to the following stages: (i) critical plane definition, (ii) power spectral density evaluation of an equivalent normal stress and (iii) computation of the damage precursor and fatigue life. The frequency-domain critical plane criterion is validated using experimental results related to (a) AISI 1095 steel cantilever beams under nonlinear base vibration, (b) 18G2A steel and (c) 10HNAP steel round specimens under random non-proportional combined flexural and torsional loads.Keywords damage precursor; frequency domain; high-cycle fatigue; multiaxial loading; random loading; vibration fatigue. Z ' = rotated frame Puvw = reference system related to the critical plane S eq (ω) = equivalent PSD function s xyz (t) = stress vector in PXYZT = time interval of observation T cal = fatigue life determined through calculations T exp = fatigue life through experiments α n = nth bandwidth parameter, with n = 1,2,3, … γ = rotation about the w axiŝ 1;2 and3 = rotation about the X ' axis λ n = nth spectral moment, with n = 1,2,3, … σ af = fatigue limit for fully reversed normal stress (R = À 1) σ 2 6';6' = variance of s 6 ' t ð Þ σ 2 6};6} = variance of s 6 } t ð Þ τ af = fatigue limit for fully reversed shear stress (R = À 1) ω = pulsation Correspondence: S. Vantadori.

An efficient procedure to speed up critical plane search in multiaxial fatigue: Application to the Carpinteri-Spagnoli spectral criterion

“…(3). The first step in the CS method is to scan the angles and (in intervals 0 ≤ ≤ 2 and 0 ≤ ≤ ) in order to find that particular direction ′ (defined by * and * ) which maximizes the expected maximum peak of normal stress z ′ ( ) in time [2][3][4]:…”

“…This article, in particular, deals with the Carpinteri-Spagnoli (CS) spectral method, in which a sequence of five rotations (Fig. 1) is used to identify the critical plane onto which an equivalent stress is finally defined [2][3][4].…”

“…If, to implement the CS method, a routine is written by following exactly the algorithm as described in several literature articles [2][3][4], it seems that the outcome is a numerical code that is not very efficient and thus slow. This occurs for two main reasons.…”

Prediction of multiaxial fatigue life for complex three‐dimensional stress state considering effect of additional hardening

“…Some other models took the effect of loading environments into account in the process of establishing fatigue damage parameter, such as FS model, Li model, and Shang‐Wang model . Unfortunately, neither of these models can be accepted generally to coordinate the effect of material properties and loading environments, even though some other attempts have been made . Against this background, the priority of multiaxial fatigue life prediction is to analyse the induced mechanisms of additional cyclic hardening.…”

“…33,34 Unfortunately, neither of these models can be accepted generally to coordinate the effect of material properties and loading environments, even though some other attempts have been made. 20,[35][36][37] Against this background, the priority of multiaxial fatigue life prediction is to analyse the induced mechanisms of additional cyclic hardening.…”