Fatigue behavior of polystyrene (PS) analyzed from the Fourier transform (FT) of stress response: First evidence of I2/1(N) and I3/1(N) as new fingerprints

Polymer Engineering & Sci

Wilhelm

Rodrigue

2020

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Mechanical fatigue under strain controlled tension/tension (T/T) of rectangular un‐notched and notched specimens of high density polyethylene and polyamide 6 was performed. Under large amplitude oscillatory elongation, the stress response is nonlinear asymmetric due to a different stress response during loading and unloading and was analyzed via discrete Fourier transform. Dynamic strain (ε0) sweep tests revealed odd (I3/1 α ε02) and even (I2/1 α ε01) harmonics in the stress, well described by the Neo‐Hooke's law. Before crack onset for the Nc specimens, the storage and loss moduli and I2/1 are constant, but I3/1 increases with fatigue. The first derivative of I3/1 (dI3/1/dN) and the cumulative nonlinearity Qf parameter (integral of I3/1/ε02) were found to be strong criteria predicting fatigue. To break the unnotched specimens in the low and high cycle fatigue regime, large strain amplitudes were applied, resulting for both materials in initial plastic deformation followed by buckling when a critical compression force is exceeded. This results in a different time evolution of the linear and nonlinear parameters, especially as a minimum in the I2/1 curve. Finally, a model is proposed to describe the nonlinear viscoelastic specimen response under T/T and the effect of buckling.

σ = \sum_{n = 0}^{\infty} I_{n} e^{italicinωt + δ_{n}}

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Section: Theorymentioning

confidence: 99%

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

Polymer Engineering & Sci

Wilhelm

Rodrigue

2020

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“…In regime III, after a crack is initiated and a macroscopic crack occurred, the decrease in G ′ typically accelerates, while G ″ and I 3/1 finally increase rapidly near failure. The occurrence of a macroscopic crack [a crack clearly visible by the naked eye (>1 mm), i.e., in contrast to crazes] and the transition from regime II to regime III was confirmed by the video camera and by the nonlinear fingerprint for crack detection: the increased intensity of the second higher harmonic ( I 2/1 ) (see also supplementary material).…”

Section: Resultsmentioning

confidence: 95%

“…The tests were performed with commercial polystyrene [PS, Ineos Nova 3900, M w = 250 kg/mol, PDI = 2.5, melt flow index MFI (200 °C/5 kg) = 38, density = 1.04 g/cm 3 ], polymethylmethacrylate [PMMA, Arkema VM‐100, M w = 100 kg/mol, PDI = 1.8, MFI = 14.5 g/10 min (230 °C, 3.8 kg), density = 1.18 g/cm 3 ] and styrene‐acrylonitrile [SAN, M w = 180 kg/mol, PDI = 2.1, 76 wt % styrene, MFI = 3.9 g/10 min (230 °C, 3.8 kg), density = 1.10 g/cm 3 ] on a strain controlled rotational rheometer (ARES, TA Instruments, New Castle, Delaware) using a torsion rectangular geometry . The rheometer is connected to a computer with the standard firm software (TA Orchestrator) recording and calculating the linear properties ( G ′ , G ″), as well as to a second computer recording the strain and stress/torque time data (200 points/cycle) with a custom written LabView program.…”

Section: Fatigue Testingmentioning

confidence: 99%

“…In the literature, a stress analysis can be used to calculate a damage rate, to follow the dissipated energy based on the stress amplitude time evolution, or to describe specific events during fatigue. For example, failure onset was investigated via an increase of the so‐called viscoelastic nonlinear parameter (sum of n higher harmonics normalized to the fundamental one, with up to n = 100) or the occurrence of a macroscopic crack via the first even higher harmonic of the stress ( I 2/1 ) …”

Section: Introductionmentioning

confidence: 99%

“…For example, the relative intensity of the third harmonic ( I 3 ) is represented as I 3/1 . More information on the basics of FT analysis, FT‐rheology and FT application in fatigue testing can be found elsewhere …”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

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

J of Applied Polymer Sci

Wilhelm

Rodrigue

2018

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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.

Nonlinear Schapery viscoelastic material model for thermoplastic polymers

Zink

Kehrer

J of Applied Polymer Sci

et al. 2021

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The nonlinear mechanical behavior of viscoelastic materials is modeled based on the Schapery integral model containing internal variables. In this context, a new approach for the strain-dependent material properties is introduced considering a one-dimensional formulation with strain-dependent nonlinear functions for an oscillatory load case. In addition to the viscoelastic storage and loss modulus, the higher order harmonic oscillations in the stress response are computed and compared to experimental data from Fourier transform rheology of Polyamide 6 (PA6). The comparison reveals a good agreement between the predictions of the nonlinear model and the experimental data for the higher harmonic intensity I 2=1 .