Fatigue life prediction via the time‐dependent evolution of linear and nonlinear mechanical parameters determined via Fourier transform of the stress

Abstract

This study proposes a new concept for the lifetime prediction of solid polymers under mechanical fatigue. The time evolution of linear and nonlinear mechanical parameters was studied using polystyrene (PS), polymethylmethacrylate (PMMA), and styrene‐acrylonitrile (SAN) samples in strain controlled (large amplitude) oscillatory shear (torsion). Higher harmonics of the stress were detected and quantified via Fourier transform (FT). Besides storage and loss modulus (G′, G″), the ratio of the third (I3) harmonic over the fundamental one, I1 (I3/1), was analyzed. After an initial transient period (regime I), the three parameters (G′, G″, and I3/1) linearly de/increase with the cycle number (N) (regime II) before failure onset (regime III) occurs. In regime II, the absolute values of the rates of change (derivative) of G′, G″, and I3/1 (dG′/dN, dG″/dN, and dI3/1/dN) were correlated with the lifetime (Nf). An inverse proportionality between the rate of change and lifetime was found allowing better prediction while testing. © 2018 Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2018, 135, 46634.

Fourier transform fatigue analysis of the stress in tension/tension of HDPE and PA6

“…With ongoing fatigue, the nonlinear mechanical parameter I 3/1 was found to monotonously increase (for rectangular and notched specimens). [ 4, 16, 17 ] On the other hand, the even higher harmonics can be associated with asymmetries caused by the loading conditions, such as T/T, or an anisotropy in the specimen, such as cracks, plastic deformation, or buckling. Therefore, the first even higher harmonic ( I 2/1 ) was found to be a very sensitive parameter towards crack detection.…”

“…Recently, a framework was developed to analyze, quantify, and predict the fatigue behavior via the discrete Fourier transform of the stress response by individually analyzing each higher harmonic for brittle polymers under torsion and tension. Three concepts based on the higher harmonics were introduced: (1) the detection of macroscopic cracks via the I 2/1 intensity, [ 16 ] (2) the prediction of fatigue failure via the rate of change of the I 3/1 intensity, [ 17 ] and (3) the cumulative nonlinearity Q f as a fatigue criterion. [ 23 ]…”

“…For PMMA and PS specimen and different specimen geometries, Equation (10) was shown to have a much lower standard deviations between 26% and 35% than the standard strain‐life curve, which had standard deviations up to 83%. [ 4, 17 ]…”

“…[ 23 ] As for dI 3/1 /dN and N f , Q f and ε 0 were found to have a better correlation with standard deviations between 30% and 52% compared to 35% to 83% for the strain‐life curves. [ 4, 17 ]…”

Analysis and prediction of the width of spreading carbon fiber tow based on gray system theory

“…A new control method to improve the quality and production efficiency of carbon fiber tow was found. [13][14][15] After studying many predictive control models, we found that some production systems have certain internal and external disturbances. [16][17][18] Complicated uncertainties are difficult to calculate accurately so we are limited and cannot analyze all of the influencing factors.…”