Large Strain Amplitudes Research Articles

Combining mechanical and thermal surface fourier transform analysis to follow the dynamic fatigue behavior of polymers

This work investigates the phenomena of self-heating, also called intrinsic heating, and thermoelastic coupling during non-linear dynamic mechanical fatigue testing via surface temperature measurement coupled with the mechanical behavior of polymers. Static tensile tests and dynamic strain controlled fatigue tests under tension/tension were performed at a frequency of ω1/2π = 5 Hz, as well as in the low cycle fatigue regime at ω1/2π = 0.2 Hz, on six polymers: high density polyethylene (HDPE), low density polyethylene (LDPE), ultra high molecular weight polyethylene (UHMWPE), polyamide 6 (PA6), and two grades of polypropylene (PP).In dynamic testing, the surface temperature rises to a plateau value (ΔT) when an equilibrium between the viscous/plastic dissipated energy and heat convection is reached. Power-law correlations were found between the strain amplitude (ε0) and ΔT, as well as between ε0 and the calculated dissipated energy density (Wdiss,p) obtained from the mechanical stress response, with similar exponents for both correlations. Thermoelastic coupling is firstly investigated in uniaxial tension, revealing a linear relation between the strain rate and the rate of temperature decrease, which is more distinct with decreasing polymer chain mobility. In dynamic fatigue testing, the surface temperature was found to oscillate with an amplitude T1, which was analyzed via Fourier transform. A direct relation between T1 and ε0 at small deformations was observed. At large strain amplitudes, T1 (ε0) follows a similar trend as the complex modulus E*(ε0). At low frequencies and large strain amplitudes, additional higher harmonics at two (T2) and three (T3) times the fundamental frequency were also detected as fingerprints of plastic deformation, resulting in additional heat dissipated during the loading half cycle. From the results obtained, the advantages of the calculated dissipated energy density over the surface temperature analysis was analyzed to predict the fatigue behavior. This analysis is believed to be valid for all materials due to the mathematical/physical principles involved. The results are thus expected to hold for other materials such as composites, rubbers, ceramics and metals.

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

AbstractMechanical 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.

Dynamic Characterization of Tire Derived Aggregates

Despite the recent efforts in characterizing and investigating the dynamic properties of tire-derived aggregates (TDA) and its use in civil engineering applications, the size of TDA used in most of the previous work was significantly smaller than the TDA size range mentioned in ASTM D6270 standards. There are two types of TDA, Type A and Type B, in which the maximum aggregate size of Types A and B are 200 and 450 mm, respectively. Thus, the availability of experimental data and shear modulus reduction curves for the dynamic behavior of TDA of larger sizes are deemed necessary for practical engineers to assess and investigate the behavior of such material under dynamic loads. This paper provides the results of large-scale undrained cyclic triaxial tests performed on Type A TDA at large strain amplitudes. The tests were performed under confining pressures ranging from 25 to 200 kPa and shear strain levels ranging from 0.1% to 10%. Furthermore, each test consisted of successive stages in which the number of cycles and axial strain levels varied. The shear modulus of Type A TDA has a range of 245–1,796 kPa, with a decreasing trend with increasing shear strain amplitudes. Furthermore, the dampening ratios were found to range from 11% to 23.5%. Finally, the shear modulus reduction curves were obtained through curve fitting techniques and nonlinear regression.

Influence of carbon black on the Payne effect of filled natural rubber compounds

The incorporation of carbon black (CB) in natural rubber (NR) enhances the Payne effect while the mechanism has not been clearly clarified so far. Herein the Payne effect of CB filled NR compounds under large strain amplitudes is investigated via simultaneous measurement of rheological response and electrical conduction. Low temperature and high frequency accelerate the Payne effect. The destruction and recovery of CB agglomerates are not synchronized with the appearance of the Payne effect, indicating that the structural evolution of the filler phase is not the main factor dominating the Payne effect. The investigation would be illuminating for understanding the molecular mechanisms of strain softening in rubber nanocomposites.

Experimental investigation and constitutive modeling of the behaviour of highly plastic Lower Rhine clay under monotonic and cyclic loading

A new experimental series on the highly plastic (plasticity index, IP = 34%) Lower Rhine clay (LRC) is presented. The study comprises tests on normally as well as overconsolidated samples under monotonic and cyclic loading. The loading velocity has been varied to evaluate the strain rate dependency of the LRC behaviour, testifying the well-known reduction of undrained shear strength with decreasing displacement rate. Isotropic consolidation followed by a cyclic loading with constant deviatoric stress amplitude leads to a failure due to large strain amplitudes with eight-shaped effective stress paths in the final phase of the tests. The inherent anisotropy has been additionally evaluated using samples cut out in either the vertical or the horizontal direction. Furthermore, the behaviour of LRC is compared with the behaviour of low plastic kaolin silt (IP = 12.2%). A new visco-hypoplastic-type constitutive model with a historiotropic yield surface has been used to simulate some of the experiments with cyclic loading. Even the eight-shaped stress loops at cyclic mobility are reproduced well with this model. The data of this paper can be also used by other researchers for the examination, calibration, improvement, or development of constitutive models dedicated to fine-grained soils under monotonic and cyclic loading.

Modeling Payne effect with a framework of multiple natural configurations

Payne effect is the complex nonlinear response of filled elastomers to oscillatory loading. Although usually characterized by the decrease in the storage modulus with strain amplitude, and by the bell-shaped curve of loss modulus with strain amplitude, the response has many other peculiar features. The manner of decrease in storage modulus with strain amplitude does not change when the frequency of the test is changed. Static strain offsets do not change the relationship between storage modulus and strain amplitude. In addition, when tested at relatively large strain amplitude levels, the material behavior changes and requires a certain period of time before it returns to what was initially observed. In this study, a model is developed to describe Payne effect using a framework of multiple natural configurations. Assuming appropriate functional forms for the Helmholtz potential and the rate of dissipation, and maximizing the rate of dissipation over all allowable mechanical processes, the constitutive equations were obtained. In a simple one-dimensional setup, the model was able to describe many aspects of Payne effect reasonably well, including the independence of the nature of modulus decrease on the frequency of loading and static strain offsets.

Characterization of nonlinear viscoelasticity of magnetorheological grease under large oscillatory shear by using Fourier transform-Chebyshev analysis

Magnetorheological (MR) grease, which is a type of magneto-sensitive smart material, exhibits complex viscoelastic behavior under different magnetic fields. Storage and loss moduli from oscillatory test are commonly used to characterize such field-dependent viscoelastic behavior. However, they are not able to represent the higher harmonic nonlinearity appeared in oscillatory responses under large amplitude oscillatory (LAOS) shear. In this paper, an investigation is conducted on the characterization of the filed-dependent nonlinearity of MR grease under LAOS by utilizing of Fourier transform (FT)-Chebyshev analysis. To capture the higher harmonic nonlinearity for the modeling and analysis, a comprehensive test program has been conducted. Firstly, MR grease with 70% weight percentage of carbonyl iron particles (MRG-70) is prepared and the stress response of MRG-70 under the oscillatory shear from small to large strain amplitudes with different magnetic field are measured. Then the higher harmonics in stress response signal are used to detect the intercycle nonlinearity of MRG-70 and compare with the traditional analysis method of dynamic modulus. Further, the elastic and viscous measures from FT-Chebyshev analysis are obtained to capture the inter-/intracycle nonlinear behaviors, that is, strain stiffening/softening, shear thickening/thinning, of MRG-70 under LAOS. It is found that, in the presence of magnetic fields, the onset of the intercycle nonlinearities of MRG-70 is originated from shear thickening of MR grease. With the further increase of the shear strain, MRG-70 exhibits the nonlinearities with different combinations of strain stiffening/softening and shear thickening/thinning.

A modified one-dimensional constitutive model of pseudoelastic SMAs and its application in simulating the force–deformation relationship of SMA helical springs

The Graesser–Cozzarelli constitutive model of shape memory alloys (SMAs) has been widely applied in seismic engineering due to its concise functions with well-defined material parameters. However, this model has some limitations, e.g. it fails to model the hardening behavior of SMAs under relatively large strain amplitudes and the effects of ambient temperature. In this paper, a modified Graesser–Cozzarelli constitutive model of pseudoelastic SMAs is proposed, through consideration of the changes of the elastic moduli of SMAs induced by different martensite fractions, the effects of ambient temperature on the pseudoelastic characteristics, the hardening behavior and the phenomenon of degradation of the pseudoelasticity of SMAs under large strain amplitudes. Furthermore, the modified model was validated by the results of experiments on SMA wires under different strain amplitudes and ambient temperatures. The modified model was then utilized to simulate the force–deformation relationship of SMA helical springs for the first time. In the procedure used to simulate the springs, the torsional and bending moments on the cross-section of the coiled wire of the springs were considered simultaneously, and the effect of the pitch angle was also included. Moreover, the spring simulation procedure was verified by tensile tests of SMA helical springs with complex loading patterns and existing simulated results of the effects of ambient temperature. The research results indicate that the spring simulation procedure based on the modified model can simulate the force–deformation relationship of the springs under different complex loading conditions and ambient temperature reasonably well. Furthermore, the effects of the spring index and the initial height of the springs on the characteristics of the force–deformation relationship were investigated in detail.

Effect of Tensile Mean Strain on Fatigue Behavior of Al-Li Alloy 2099

In this study, the effect of tensile mean strain on the fatigue behavior of aluminum alloy 2099-T83 was experimentally examined for the first time. In order to elucidate the effect of tensile mean strain on fatigue lives, strain-control fatigue testing was conducted at three strain ratios (R = − 1, 0.1, 0.7). Experimental results show that the application of greater mean strains during cyclic deformation resulted in shorter fatigue lives, particularly at lower strain amplitudes. At these lower strain amplitudes, the mean stress response to deformation did not fully relax as it did when subjected to larger strain amplitudes, where the effect of mean strains on fatigue performance was negligible. The Morrow and Smith–Watson–Topper mean strain correction models were implemented using monotonic and fully reversed fatigue properties in order to account for the damage associated with the relaxed mean stresses. A new model is presented that incorporates a mean stress sensitivity material property to capture, within a scatter band of three, the effects of tensile mean strains on the fatigue behavior of AA2099.

Interfacial dilatational rheology as a bridge to connect amphiphilic heterografted bottlebrush copolymer architecture to emulsifying efficiency

HypothesisMolecular architecture and composition of amphiphilic bottlebrush copolymers will dictate the dominant interfacial relaxation modes and the corresponding dilatational rheology for adsorbed layers at oil/water interfaces in a way that will correlate with the emulsifying efficiency of different bottlebrush copolymers. ExperimentsAmphiphilic, xylene-soluble poly(ethylene oxide)-poly(n-butyl acrylate) (PEO-PBA) heterografted bottlebrush copolymers with controlled differences in backbone length, hydrophilicity and arm length were synthesized by atom transfer radical polymerization. Dilatational rheology of adsorbed layers at the xylene/water interface was probed via pendant drop tensiometry by measuring the interfacial stress response to either large-amplitude strain cycling or small-amplitude strain oscillation. The rheological response was recorded as a function of interfacial pressure for adsorbed layers under different compression states. Emulsifying efficiency was determined as the lowest copolymer concentration that yielded water-in-xylene emulsions with at least one-month stability against coalescence. FindingsThe more hydrophilic copolymers with longer PEO arms exhibited non-hysteretic stress-strain response curves in large-amplitude strain cycling and a tendency for the modulus to increase with increasing interfacial pressure. These were more efficient emulsifiers than less hydrophilic copolymers that exhibited hysteretic interfacial rheology. Mere existence of significant moduli did not correlate with high emulsifying efficiency, while an increase in modulus with increasing interfacial pressure did so.

The combined and interactive effects of orientation, strain amplitude, cycle number, stacking fault energy and hydrogen doping on microstructure evolution of polycrystalline high-manganese steels under low-cycle fatigue

We studied the combined and interactive effects of crystallographic orientation, strain amplitude, cycle number, stacking fault energy (SFE) and hydrogen doping on the microstructure evolution of polycrystalline high-manganese steels (HMnSs) under low-cycle fatigue (LCF). An integrated experimental approach combining digital image correlation (DIC), electron backscatter diffraction (EBSD) and electron channelling contrast imaging (ECCI) at interrupted cycles was performed in the same region of interest on the bulk shear samples, which enables us to systematically compare the dislocation patterns of grains with defined loading conditions at a much larger field of view and less artefacts compared to transmission electron microscopy (TEM). We found that Taylor factor (M) works well with describing the effect of crystallographic orientation, which was further proved by the crystal plasticity finite element method (CPFEM). In detail, grains with a medium M value (3.3–3.9) tend to form more complex dislocation pattern, which is defined as sensitive value. Generally, increasing strain amplitude and cycle number both promote the evolution of dislocation pattern while their efficiencies depend strongly on grain orientation. The promotion effect of SFE on dislocation evolution becomes obvious at larger strain amplitudes (>0.4%) and non-sensitive M value. Hydrogen can strongly assist the formation of ε-martensite and reduce its critical resolved shear stress (CRSS), while it retards the evolution of dislocation pattern. The number of activated martensite variants in individual grain can be well predicted by its M value. With increasing strain amplitude, the fraction of ε-martensite increases in a manner of thinner but denser plates.

Cyclic strain amplitude-dependent fatigue mechanism of gradient nanograined Cu

Different grain coarsening behaviors (i.e. abnormal and homogeneous) are prevalently observed in gradient nanograined (GNG) Cu under stress controlled high-cycle and strain controlled low-cycle fatigue tests, respectively. In this paper, to comprehensively understand the intrinsic fatigue mechanism of gradient nanograined structures, both high and low cycle fatigue behaviors of GNG Cu are investigated under strain-controlled fatigue tests with a wide strain amplitude ranges. Cyclic behavior transition from abnormal grain coarsening at small strain amplitude to homogeneous grain coarsening at large strain amplitude is observd in GNG Cu. Microstrucural analysis reveals that the grain coarsening behavior in either abnormal or normal (homogeneous) mode is closely related to the spatial distribution of the cyclic plastic strain in the GNG layer (localized or delocalized) under cyclic loading. Such unique cyclic strain amplitude-dependent fatigue behavior is inherent to the gradient nanostructure, which fundamentally differs from the conventional strain localizing mechanism in metals with homogeneous structures under cyclic loading.

Size effect in cyclic torsion of micron-scale polycrystalline copper wires

Cyclic torsion of micron-scale polycrystalline copper wires was experimentally studied. It was found that cyclic hardening is more pronounced with larger strain amplitude under symmetric cyclic straining. The mean stress relaxation is accelerated with larger initial strain and smaller strain amplitude under asymmetric cyclic straining. Meanwhile, both sample size and grain size effects were observed. That is the mean stress relaxation increases with decreasing sample size and grain size. The grain size effect is caused by an elevated internal stress in wire with smaller grain size. The observed sample size effect is attributed to the internal stress induced by geometrically necessary dislocations.

Characterization of closed-die forged AZ31B under pure axial and pure shear loading

Extruded AZ31B was closed-die forged at a relatively low temperature of 250 °C. Quasi-static axial and shear tests in addition to cyclic pure axial and cyclic pure shear tests were performed to characterize the uniaxial response of the forged parts. To examine the effect of forging on the mechanical behavior of the material, quasi-static and fatigue response of the starting extruded AZ31B was also studied under axial loading. The forging process refined the grain structure and modified the crystallographic texture of the extruded AZ31B. The intensity of texture and the orientation of c-axis in the forged part were found to be controlled by the extent and the direction of plastic deformation, respectively. The modified microstructure resulted in insignificant effect on yield strength, slight decrease in ultimate strength, and enhanced failure strain of the forged AZ31B under axial loading. However, the forged AZ31B exhibited superior yield strength, similar ultimate strength, and lower failure strain under shear loading. The cyclic axial strength of the forging was similar to the starting extruded material under high strain amplitudes, but slightly superior under lower strain amplitudes, due to the development of a smaller tensile mean stress. The half-life hysteresis response for the forged material was asymmetric under large axial strain amplitudes, but it was symmetric under cyclic shear loading. This difference is originated from activation of twinning/ detwinning deformation under cyclic axial loading, while dislocation slip is the dominant deformation mechanism during cyclic shear loading. Fatigue fracture surface of forged AZ31B depicts that fatigue cracks were initiated from multiple locations under both cyclic axial and shear loadings.

Physical hydrogel with tunable flowability and self-recovery properties through introducing branched polymer and nanoparticle

To achieve injectability and printability of hydrogels, physical hydrogels with tunable flowability and self-recovery properties are reported in this article. Flowability of polyacrylamide (PAAm) physical hydrogel is adjusted by introducing branched polyethyleneimine (PEI) with a large number of –NH2 and –NH– groups. The AAm5 physical gel, which is generally solid-like and elastic (G' > G″), can transform to a shear-thinning and viscous fluid after introducing a certain amount of PEI. But following that transformation, its strength decreased. The strength of PEI/PAAm hydrogels can be improved by SiO2 nanoparticle. The G′ of PEI/PAAm/SiO2 physical gels increased with SiO2 mass concentration increasing, indicating that the strength and viscoelastic behavior of PEI/PAAm/SiO2 physical gels were dependent on SiO2 mass concentration. Moreover, the self-recovery property of PEI/PAAm/SiO2 physical gels was studied by three cycles of alternating strain and time sweeps. The results showed that AAm5-PEI0.02-TM500.08 and AAm5-PEI0.02-SM0.08 gels display a remarkable self-recovery property after three cycles of alternating strain sweep and time sweep. And strain thinning behavior of AAm5-PEI0.02-TM500.08 gel was observed at larger strain amplitude.

Modeling shear stress response of bituminous materials under small and large strains

The paper at hand focuses on modeling the stress response of different mastics and asphalt binders exposed to small and large shear strains using Bergström-Boyce (BB) constitutive model as well as Finite Element (FE) approach. In this paper, a set of experiments based on Large Amplitude Oscillatory Shear (LAOS) test were designed and conducted to capture the state of strain dependence of bituminous mastics and binders over a broad spectrum of strain domain (0.5%, 10%, 20%, 30%, and 40%) pertaining linear and nonlinear regimes of such materials. Using the experimental data, the BB constitutive model was utilized to describe the attained behavior at two temperatures (30 °C and 40 °C) and varied strain amplitudes. The material properties derived from the BB model were further implemented into a Finite Element Model (FEM) using the ABAQUS platform to simulate the stress response of bituminous materials for a wide range of strain amplitudes. It has been shown that the bituminous mastics and binders have strong nonlinearity at high strain amplitudes, depicted graphically based on the progressive distortion from the elliptical form of Lissajous-Bowditch (LB) plot. Based on the observed goodness of fitting, the BB model well-described the experimental results for linear and nonlinear behaviors. Using the optimized parameters, it was confirmed that the BB model is well suited to build a numerical model that could reproduce stress responses derived from the LAOS results for a wide range of strain levels. The advantage of the methodology presented herein allows adaptable model constants of the BB model depending on the imposed level of strain and temperature and hence, the FEM can describe both linear and nonlinear behaviors of bituminous mastics and binders. From this paper, researchers can take advantage of capturing the stress response of binders and mastics under small and large strain amplitudes to stimulate the research on better representation of the complex behavior of asphalt mixes based on the role of mastic and asphalt binder.

Scaling laws for frictional granular materials confined by constant pressure under oscillatory shear.

Herein we numerically study the rheology of a two-dimensional frictional granular system confined by constant pressure under oscillatory shear. Several scaling laws for the storage and loss moduli against the scaled strain amplitude have been found. The scaling laws in plastic regime for large strain amplitude can be understood by the angular distributions of the contact force. The scaling exponents are estimated by considering the physical mechanism.

Bauschinger Effect of Mn18Cr18N Austenitic Stainless Steel

The experimental study of Bauschinger effect in Mn18Cr18N austenitic stainless steel was presented by compression-tensile cyclic loading tests with the prestrains ranging from 0.005 to 0.1, which was illustrated utilizing stress-strain curves and analysed by TEM images from aspects of microstructural mechanisms. Moreover, the Bauschinger effect and its associated roundness phenomenon in reverse flow curve with respect to different cycles and cyclic strain amplitudes were evaluated in a quantitative manner. The experimental results indicate that Bauschinger effect is apparent during the test. At smaller cyclic strain amplitude, intergranular backstress is the main source of Bauschinger effect. With further increasing of cycles, dislocation density increases and dislocation movement is hindered in the reverse deformation. Therefore, Bauschinger effect is weakened to some extent. At large cyclic strain amplitude, backstress originating from the dislocation pile-up at grain boundaries and the continuous formation of deformation twins dominate the Bauschinger effect. In addition, the backstress results in the roundness of reverse curve during cyclic loading. The larger value of Δep*, the more obvious the roundness of the reverse curve, and the more significant the Bauschinger effect.

Extremely - low cycle fatigue fracture of Q235 steel at different stress triaxialities

This study presents an experimental and numerical investigation on the Extremely-Low Cycle Fatigue (ELCF) behavior of Q235 structural steel under different stress states and large strain amplitudes. A set of Q235 structural steel cylindrical specimens of different radii of curvature were selected to examine the effect of the triaxial state of stress on the fracture behavior. Cyclic axial tension-compression loading tests characterized by large strain amplitudes were conducted to obtain the hysteresis loops and the failure process by measuring both macroscopic and microscopic fracture morphologies. The results shows that, the failure behavior of Q235 steel in ELCF loading is a mixture of fatigue fracture and ductile fracture. Specimens with different stress triaxialities are characterized by different failure modes. A fracture criterion, namely the Combinatory Work Density Model (CWDM), was calibrated based on the test results. Furthermore, a cyclic plasticity constitutive model, i.e., the Chaboche model, was calibrated to describe the yield and cyclic hardening behaviors of the Q235 structural steel. Finite element (FE) simulations in the commercial software ABAQUS accounting the calibrated CWDM and Chaboche model were carried out to evaluate the fracture characteristics with different stress triaxialities and their stress-strain hysteretic curves under ELCF loading. The simulation results demonstrate that the developed FE model can reproduce the hysteretic characteristics and capture the failure process of Q235 structural steel. The proposed practical numerical tool can be used for the ELCF failure prediction in steel structures under complex stress state.

Pure elastic stiffness of sand represented by response envelopes derived from cyclic triaxial tests with local strain measurements

The elastic stiffness of a fine sand at small to moderate strains ( $$\varepsilon \le 2 \times 10^{-4}$$ ) has been studied based on cyclic triaxial tests on cube-shaped samples with local strain measurements. Three samples with different densities (between very loose and very dense) were tested at up to 21 average stresses in succession (variation of mean pressure and stress ratio). At each average stress cycles were applied in six different directions, as a result of a simultaneous sinusoidal oscillation of the axial and lateral effective stress. Ten preconditioning cycles with larger strain amplitudes $$\varepsilon ^{\mathrm{ampl}}= 3 \times 10^{-4}$$ per polarization were intended to induce a shakedown. An almost purely elastic response was then observed during the 5 subsequent cycles per polarization with lower strain amplitudes $$\varepsilon ^{\mathrm{ampl}}= 2 \times 10^{-4}$$ . The stress and strain paths measured during the latter ones were used to derive the components of the incremental elastic stiffness tensor $${\mathsf{E}}= \{E_{PP}, E_{PQ}, E_{QP}, E_{QQ}\}$$ at a given average stress. The analysis of $${\mathsf{E}}$$ is based on all 60 reversal points and the corresponding stress and strain points lying in a certain distance $$\Delta \varepsilon$$ (e.g. $$10^{-4}$$ ) from the reversals. A graphical presentation of $${\mathsf{E}}$$ by means of response envelopes is shown. They are used to calibrate the hyperelastic stiffness incorporated into a new hypoplastic constitutive model.