Low Strain Amplitudes Research Articles

On the low-cycle fatigue behavior of friction stir welded Al–Si12 parts produced by selective laser melting

The solid-state friction stir welding (FSW) process was used to join Al–Si12 parts fabricated via the selective laser melting (SLM) technique. The effect of the welding process on microstructural evolution and mechanical properties of the samples is investigated in present work. Microstructural studies demonstrate that FSW is capable of changing Si phase morphologies (i.e. shape and size) resulting in various mechanical properties. The stir zone of the welded joint shows significantly lower micro-hardness in comparison to the as-built SLM samples. Correspondingly, the friction stir welding process results in significant reduction of tensile strength, while ductility is strongly improved. The fully-reversed strain-controlled low-cycle fatigue (LCF) tests imply that at low strain amplitudes the FSW and SLM samples show almost the same fatigue life, while at the high strain amplitudes the SLM samples show superior LCF performance. Fracture analysis of fatigued samples reveals that the near-surface pores lead to the crack initiation in both SLM and FSW cases.

The distinct influences of pre-strain on low cycle fatigue behavior of CP-Ti along rolling direction at different strain amplitudes

In this paper, the distinct influences of pre-strain on low cycle fatigue (LCF) behavior of CP-Ti at different strain amplitudes are clarified from macroscopic and microscopic aspects. At low strain amplitude, the sample of as-received material (AR) shows pronounced secondary cyclic hardening, however, this phenomenon gradually disappears in pre-strained (PS) sample with the increase of pre-strain. As cyclic stress amplitude and mean stress of PS sample increase with the decrease of strain amplitude, the detrimental effect of pre-strain on LCF life becomes more significant at lower strain amplitude, indicating the pre-strain dependent LCF behavior. At high strain amplitude, due to the more significant cyclic softening and mean stress reduction behavior, cyclic stress amplitude and mean stress rapidly decay to the value of AR sample in the initial few cycles, indicating the pre-strain independent LCF behavior. As the reduction of LCF life is related to the increase of mean stress and stress amplitude, the asymmetry coefficient related model can be applied to predict LCF life of CP-Ti. Further TEM observation shows that at low strain amplitude, dislocation structures of AR sample are mainly composed of planar slip structures and the secondary cyclic hardening is caused by corduroy structure. After pre-strain, both planar slip and wavy slip structures are observed in PS sample, indicating that the irreversibility of the dislocation structures inherited from pre-strain causes the decrease of LCF life. At high strain amplitude, the dislocation structures introduced by pre-strain can be erased completely during subsequent cyclic deformation, consequently, dislocation configurations of AR and PS samples are composed of the same wavy slip structures.

Integrated manufacture of polymer and conductive tracks for real-world applications

The present study demonstrates for the first time a unique UK-designed and built Additive Manufacturing (AM) hybrid system that combines polymer based structural deposition with digital deposition of electrically conductive elements. This innovative manufacturing system is based on a multi-planar build approach to improve on many of the limitations associated with AM, such as poor surface finish, low geometric tolerance and poor robustness. Specifically, the approach involves a multi-planar Material Extrusion (ME) process in which separated build stations with up to 5 axes of motion replace traditional horizontally-sliced layer modelling. The construction of multi-material architectures also involved using multiple print systems in order to combine both ME and digital deposition of conductive material. To demonstrate multi-material 3D Printing (3DP) we used three thermoplastics to print specimens, on top of which a unique Ag nano-particulate ink was printed using a non-contact jetting process, during which drop characteristics such as shape, velocity, and volume were assessed using a bespoke drop watching system. Electrical analysis of printed conductive tracks on polymer surfaces was performed during mechanical testing (static tensile and flexural testing and dynamic fatigue testing) to assess robustness of the printed circuits. Both serpentine and straight line patterns were used in the testing of Ag particle loaded ink and they showed very similar resistance changes during mechanical exposure. Monitored resistance and stress changed as a function of strain exhibiting hysteresis with more prominent residual strain during stretching and compression cycles and 3-point bending flexural tests of PA and CoPA substrates. Bare and encapsulated tracks exhibited low electrical resistivity (1–3*10−6 Ω*m), and its change was more rapid on ABS and minor on PA and CoPA when increasing tensile and flexural strain up to 1.2% and 0.8%, respectively. Resistance of Ag tracks on ABS also increased rapidly during fatigue testing and the tracks easily fractured during repeated stretching-compression cycles at 1% and 1.2% strain. No resistance changes of Ag tracks printed on PA and CoPA were observed at lower strain amplitudes whereas at higher strain amplitudes these changes were the lowest for conductive tracks on CoPA. Thermal analyses were conducted to determine the printed material’s glass transition temperature (Tg), stability and degradation behavior to find the optimum annealing conditions post printing. The novel AM printer has the ability to fabricate fully functional objects in one build, including integrated printed circuitry and embedded electronics. It enables product designers and manufactures to produce functional saleable electronic products. This new technology also gives the opportunity for designers to improve existing products, as well as create new products with the added advantages of geometrically unconstrained 3DP.

Analysis of the Fatigue Damage Behavior of AW2099-T83 Al-Li Alloy under Strain-Controlled Fatigue

Microstructural characteristics, monotonic and strain-controlled cyclic axial behaviors of AW2099-T83 Aluminum-Lithium alloy were investigated. Grain sizes and structures are not uniform in the different orientations studied. High strength and low ductility characterize the tensile behavior of the alloy under static loading. Strain-controlled fatigue testing was conducted at strain amplitudes ranging from 0.3% to 0.7%. Over this range, macro plastic deformation was only observed at 0.7%. Cyclic stress evolution was found to be dependent on both the applied strain amplitude and the number of cycles. Limited strain hardening was observed at low number of cycles, followed by softening, due probably to damage initiation. With low plastic strain, analytical approach was adopted to profile the damaging mechanism for the different applied strain amplitude. Because of the absence of fatigue ductility parameters due to low plasticity, a three-parameter equation was used to correlate fatigue life. Fractured specimens were studied under SEM to characterize the fracture surface and determine the controlling fracture mechanisms. The fractography analysis revealed that fracture at low strain amplitudes was shear controlled while multiple secondary cracks were observed at high strain amplitude. Intergranular failure was found to be the dominant crack propagation mode.

Influence of loading amplitude on viscoelastic properties of bitumen, mastic and bituminous mixtures

Bituminous materials are considered as linear viscoelastic for a small number of applied cycles at low strain amplitudes. Their behaviour can be represented considering the complex modulus and the complex Poisson’s ratio (isotropic case), which are obtained for sinusoidal loading. These two properties are independent of strain/stress amplitude in the case of linear viscoelasticity (LVE). However, when increasing amplitude, nonlinearity induces a strain dependence of the measured complex modulus. This paper investigates the phenomenon of nonlinearity in bitumen, mastic and bituminous mixture (BM). Strain amplitude sweep (SAS) tests were performed at different temperatures and frequencies. From LVE characterisation results, it was possible to observe relationships between the rheological behaviours of bitumen, mastic and bituminous mixture. Nonlinearity results show that BM presents non-negligible nonlinearity even for very small strain (few tens of µm/m). Nonlinearity effect is temperature- and frequency- dependent. The LVE limit decreases with temperature for BM and increases for bitumen and mastic. LVE limit in terms of stress amplitude changes following the same factor for all materials, suggesting that the nonlinearity observed on bituminous mixtures is inherited from the bitumen.

Low‐cycle fatigue behavior of a newly developed cast aluminum alloy for automotive applications

AbstractThe drive for increasing fuel efficiency and decreasing anthropogenic greenhouse effect via lightweighting leads to the development of several new Al alloys. The effect of Mn and Fe addition on the microstructure of Al‐Mg‐Si alloy in as‐cast condition was investigated. The mechanical properties including strain‐controlled low‐cycle fatigue characteristics were evaluated. The microstructure of the as‐cast alloy consisted of globular primary α‐Al phase and characteristic Mg2Si‐containing eutectic structure, along with Al8(Fe,Mn)2Si particles randomly distributed in the matrix. Relative to several commercial alloys including A319 cast alloy, the present alloy exhibited superior tensile properties without trade‐off in elongation and improved fatigue life due to the unique microstructure with fine grains and random textures. The as‐cast alloy possessed yield stress, ultimate tensile strength, and elongation of about 185 MPa, 304 MPa, and 6.3%, respectively. The stress‐strain hysteresis loops were symmetrical and approximately followed Masing behavior. The fatigue life of the as‐cast alloy was attained to be higher than that of several commercial cast and wrought Al alloys. Cyclic hardening occurred at higher strain amplitudes from 0.3% to 0.8%, while cyclic stabilization sustained at lower strain amplitudes of ≤0.2%. Examination of fractured surfaces revealed that fatigue crack initiated from the specimen surface/near‐surface, and crack propagation occurred mainly in the formation of fatigue striations.

Strain controlled isothermal low cycle fatigue life, deformation and fracture characteristics of Superni 263 superalloy

The total axial strain controlled low-cycle fatigue (LCF) behaviour of a wrought nickel-base superalloy Superni 263 has been evaluated at 298 K, 673 K, and 923 K employing the strain amplitudes in the range ± 0.25% to ± 0.80%. All the tests were performed using a triangular wave form at a constant strain rate of 10−3 s−1. The Superni 263 alloy was subjected to a solutionizing treatment at 1373 K/1.5 h followed by water quenching. An ageing treatment of 1073 K/8 h was given to the solutionized samples. The microstructure of the alloy is composed of γʹ in the intragranular regions and discrete M23C6 precipitates on the grain boundaries. Few undissolved (Ti, Mo)C and TiN precipitates were also noticed in the matrix. The strain amplitude and temperature played a significant role in the evolution of macroscopic cyclic stress response and the development of deformation substructure. The alloy displayed serrated flow in the plastic portions of stress-strain hysteresis loops in the tests conducted at 673 K and 923 K, predominantly at strain amplitudes higher than ±0.40%. Several manifestations depicting the occurrence of dynamic strain ageing (DSA) were derived by analysing both the macroscopic and micro-mechanistic information generated. The comparative evaluation of monotonic and cyclic stress-strain curves was conducted and the factors responsible for rapid cyclic hardening during DSA were identified. The fatigue life decreased drastically with increasing temperature, particularly at low strain amplitudes. The strain-life data could be represented well by using Basquin and Coffin-Manson relationships. The slope in Coffin-Manson relationship revealed more negative values under the influence of DSA. The crack initiation and propagation modes at all the test conditions remained transgranular without the indications of interference from creep and oxidation effects. The deformation substructure at elevated temperatures was characterized by the occurrence of co-planar slip, stacking faults, micro twinning and high dislocation density in between the slip bands.

Microstructural evolution and mechanical behavior of copper processed by low strain amplitude multi-directional forging

Experiments were performed to analyze the microstructural evolution and mechanical behavior of commercial-purity copper (99.8%) processed by up to 48 cycles of multi-directional forging (MDF) using a low strain amplitude of ∼0.075 (total accumulated strain ε ≈ 10.8). Parabolic work-hardening concomitantly with increasing dislocation densities was observed up to ε ≈ 2, followed by a practically constant flow stress due to dynamic recovery. The average grain size was reduced from 30.5 μm in the annealed metal down to 4.1 μm for ε ≈ 7.2; the fraction of sub-micrometric grains reached ∼12% for ε ≈ 10.8. The microstructural changes were attributed to the fragmentation of the original grains by dislocation structures having low misorientation angles which gradually evolved into arrays of high-angle grain boundaries with increasing numbers of MDF cycles. The Cu samples subjected to 48 cycles of MDF displayed limited dynamic recrystallization, exhibiting basically dislocation cells and sub-grains with an average size of ∼0.6 μm. It is demonstrated that low strain amplitude MDF delays the kinetics of grain refinement in copper compared with MDF using higher strain amplitudes.

Improvement of low-cycle fatigue resistance in AISI 4140 steel by annealing treatment

The low-cycle fatigue (LCF) behaviour of AISI 4140 steel under annealed and as-received conditions was investigated at room temperature. The annealing treatment causes a marked decrease in mechanical strength but an increase in plastic energy and ductility. The annealing treatment of AISI 4140 steel significantly increases the LCF resistance of the material. In addition, the steel exhibits a transitional behaviour from initial cyclic softening to stable cyclic hardening with increasing strain amplitude. By contrast, the as-received AISI 4140 steel undergoes progressive cyclic softening until failure. Microstructural changes induced in the annealed steel cause near-Masing-type behaviour at low and high strain amplitudes. The enhancement of the LCF resistance of the annealed steel is attributed to the high magnitude of the compressive stress, which is dependent on the applied strain amplitude. A good correlation of the total failure cycles with plastic strain and elastic strain provides a precise equation model for predicting the LCF life of annealing-treated AISI 4140 steel.

Low Cycle Fatigue Properties of Extruded 6061-T6 Aluminum Alloy

This paper presents the low cycle fatigue properties of an extruded 6061 aluminum alloy. The cyclic strain-controlled fatigue tests were performed under fully reversed total strain amplitudes ranging from 0.5% to 1.3% at a fixed strain rate of 0.004 s−1 using smooth specimens cyclically loaded along with the extrusion directions. The fatigue test results represented by the hysteresis curves of stress-strain show slight Bauschinger effect at the total strain amplitudes (Δεat) ≤ 0.7 %. The corresponding cyclic strain response revealed that the alloy underwent cyclic softening particularly at the lower strain amplitude (Δεat ≤0.7%) and at the higher strain amplitudes, the alloy tended to undergo cyclic hardening. The strain-fatigue life models were empirically determined by the Coffin-Manson-Basquin relationships.

Effects of Thermal Aging on the Low Cycle Fatigue Behaviors of Cast Duplex Stainless Steels

The low cycle fatigue (LCF) behaviors of cast duplex stainless steel (CDSS) thermally aged at different times were investigated under different strain amplitudes. The effects of thermal aging on the LCF lives of CDSS are closely related to the strain amplitude. At a low strain amplitude, the fatigue life of the material increases significantly after thermal aging, while the LCF life decreases with an increasing aging time at a high strain amplitude. After thermal aging at 400 °C for 10,000 h, the fatigue fracture morphologies of CDSS change from fatigue fringes to mixture features including fatigue fringes in austenite and cleavage cracks in ferrite. Severe plastic deformation in ferrite of the aged CDSS under a high strain amplitude causes the cleavage cracking of ferrite. The premature failure of ferrite accelerates the propagation of fatigue crack and shortens the fatigue life at a high strain amplitude.

Fracture morphology and crack mechanism in pure polycrystalline magnesium under tension–compression fatigue testing

The fatigue fracture was characterized and the fracture behavior was analyzed, using scanning electron microscope (SEM) and electron back-scattered diffraction (EBSD), the fatigue tests of two strain amplitude at room temperature were 0.5% and 1.0% respectively, and the results showed that the fatigue deformation of different strain amplitude produced two typical fatigue fracture morphology, and when the strain amplitude was 1.0%, fatigue fracture mechanism of AZ31 magnesium alloy induced by $$\{ 10\bar{1}2\}$$ twins, when the strain amplitude is 0.5%, it was induced by $$\{ 10\bar{1}2\} - \{ 10\bar{1}2\}$$ double twins. In the present study, the average thickness of primary twin is ~ 20 μm at amplitude of 0.5% and ~ 80 μm at amplitude of 1.0%. The thickness of $$\{ 10\bar{1}2\}$$ primary twins was large enough to activate $$\{ 10\bar{1}2\} - \{ 10\bar{1}2\}$$ secondary twins at a high strain amplitude, while the thickness of $$\{ 10\bar{1}2\}$$ primary twins was too narrow to activate $$\{ 10\bar{1}2\} - \{ 10\bar{1}2\}$$ secondary twins at a low strain amplitude.

Material Characterizations of Gr-Based Magnetorheological Elastomer for Possible Sensor Applications: Rheological and Resistivity Properties.

Considering persistent years, many researchers continuously seek an optimum way to utilize the idea of magnetorheology (MR) materials to be practically used for everyday life, particularly concerning resistivity sensing application. The rheology and resistivity of a graphite (Gr)-based magnetorheological elastomer (Gr-MRE) were experimentally evaluated in the present research. Magnetorheological elastomer (MRE) samples were prepared by adding Gr as a new additive during MRE fabrication. The effect of additional Gr on the rheological and resistivity properties were investigated and compared with those of typical MREs without a Gr additive. Morphological aspects of Gr-MRE were characterized using field emission scanning electron microscopy (FESEM) and energy dispersive X-ray spectroscopy (EDX). Rheological properties under different magnetic fields were evaluated using a parallel-plate rheometer. Subsequently, the resistivity of all samples was measured under different applied forces and magnetic fields. From the resistivity evaluation, two relationship curves resistance (R) under different applied forces (F) and different magnetic fields (B) were established and plotted by using an empirical model. It was observed from the FESEM images that the presence of Gr fractions arrangement contributes to the conductivity of MRE. It was also observed that, with the addition of Gr, rheological properties such as the field-dependent modulus can be improved, particularly at low strain amplitudes. It is also demonstrated that the addition of Gr in MRE can contribute to the likely use of force detection in tactile sensing devices.

Effects of initial {10-12} twins on cyclic deformation and fatigue of magnesium alloy at low strain amplitudes

An extruded AZ31B (Mg-3Al-1Zn-0.5Mn) magnesium alloy with a twin volume fraction of 60% was subjected to fully reversed strain-controlled tension-compression along the extrusion direction at strain amplitudes ranging from 0.23% to 0.45%. Dislocation slips were the dominant plastic deformation mechanisms without involving persistent twinning-detwinning. At an identical strain amplitude, the fatigue life of the pre-twinned alloy was much lower than that of the as-extruded alloy. Fatigue cracks were mainly initiated on the prismatic or prismatic-basal slip bands in the parent grains. The material volume reduction of the parent grains in the pre-twinned alloy enhanced fatigue damage. Twin cracks were not observed.

Prevention of network destruction of partially hydrolyzed polyacrylamide (HPAM): Effects of salt, temperature, and fumed silica nanoparticles

Polymer flooding is one of the most effective enhanced oil recovery (EOR) methods. High temperature and a high salt content in oil reservoirs significantly decrease the performance of polymer flooding. In this work, the viscoelastic properties of a partially hydrolyzed polyacrylamide (HPAM) solution with and without salt (NaCl) and at two different temperatures (35 °C and 70 °C) were evaluated using rheological approaches. Two fumed silica nanoparticles (NPs) featuring different surface chemistries were used, and their ability to prevent destruction of the polymer network structure against salt addition and temperature increase was investigated. Linear rheological tests (frequency sweep, creep, and creep recovery) and nonlinear rheological tests (large amplitude oscillatory shear) were employed to evaluate the network structure of these systems. The results showed that either adding salt or increasing the temperature destroyed the mechanical integrity of the HPAM 3-dimensional elastic network. However, the introduction of both types of NPs at a sufficient concentration maintained the network structure of HPAM solutions in the small deformation region. In the large deformation region, it was shown that the extent of intra-cycle shear-thickening behavior in the HPAM solution (T = 35 °C and without any salt) decreased by incorporating salt or by increasing the temperature. Moreover, upon incorporating either of the NPs to the HPAM solution, the nonlinear viscoelastic behavior dramatically changed, and the critical strain (linear to nonlinear transition) decreased to a much lower strain amplitude. The outcomes of this study will help petroleum scientists to design more efficient EOR methods.

On the phase angle role in the shear response of ZK60 Mg alloys under multiaxial fatigue

Proportional and non-proportional multiaxial fatigue tests are conducted on the closed-die forged ZK60 extrusion. The shear strain amplitude was kept constant at 0.5% for all the tests, while two different axial strain amplitudes of 0.4% and 0.7% were considered. At the higher strain amplitude (0.7%) significant difference was observed between the torque amplitudes of proportional and non-proportional tests, whereas the axial load amplitude responses remained the same regardless of the phase angle shifts. It is likely that as the phase angle changes from 0-90, the twin volume fraction at the peak shear strain decreases resulting in higher torque responses. On the other hand, at the lower strain amplitude, i.e. 0.4%, where twinning is not active, phase angle does not show any effect on the shear response. An energy-based fatigue model is employed that effectively explains the different damage contributions by the axial and torsional loadings at different strain amplitudes, and accurately predicts the proportional and non-proportional multiaxial fatigue lives.

Cyclic damage behavior of Sanicro 25 alloy at 700 °C: Dispersed damage and concentrated damage

The damage evolution behavior of a novel Sanicro 25 alloy was investigated based on low-cycle fatigue tests at 700 °C. The results show that at relatively low total strain amplitude (Δεt/2), the dispersed damage was dominant, which led to prolonged fatigue life. However, at relatively high Δεt/2, the concentrated damage was dominant, which led to reduced fatigue life. Based on the damage characteristics, a modified Coffin-Manson equation that accounts for microporosity (f) was derived. The curved surface of plastic strain amplitude (Δεp/2) - f - number of reversals to failure (2Nf) shifts upward with increasing fatigue ductility exponent c. However, this curved surface shifts downward when the cyclic strength coefficient K′ increases. A new model of micro-crack initiation considering the precipitates at the grain boundary was derived. The Gibbs free energy change of crack nucleation (ΔG) decreased with decreasing Δεt/2. Finally, based on the prediction model of energy-based fatigue life, the theoretical formulas of the fatigue toughness Wf and the fatigue cracking exponent β were derived. Wf increases and β decreases with increasing Δεp/2.

Multiscale mechanical fatigue damage of stainless steel investigated by neutron diffraction and X-ray microdiffraction

Mechanical fatigue behavior of AL6XN stainless steel as a typical type of planar slip alloy was investigated by in situ neutron diffraction and synchrotron-based X-ray microdiffraction methods. Under cyclic loading at a high strain amplitude (±0.8%), the fatigue damage originated mainly from the accumulation of statistical stored dislocations, as clearly evidenced from a continuous increase in diffraction peak width with increasing the number of load cycles. However, under cyclic loading at a low strain amplitude (±0.3%), the density of statistical stored dislocations became saturated just after a hundred loading cycles and the fatigue damage was mainly dominated by the accumulation of persistent Lüders bands (PLBs) and the complex interactions among various PLBs as evidenced through X-ray microdiffraction measurements. It was further found that there exists obvious grain-orientation-dependent local damage in the low-strain-amplitude fatigued sample. In particular, fatigued grains orientated with [001] paralleling the loading direction are subjected to compressive stress and contain a large number of broad PLBs in boundaries arraying the edge dislocation pile-ups, which generate a large stress gradient leading to local plastic instability. The highly localized stress field at PLBs in the cyclically-deformed sample at a low strain amplitude may explain the obvious cyclic stress softening.

Microstructure analysis and low-cycle fatigue behavior of spray-formed Al–Li alloy 2195 extruded plate

Microstructure and low-cycle fatigue behavior of spray-formed Al–Li alloy 2195 extruded plate were investigated in this work. The spray-formed alloy after hot extrusion experiment was treated with solid solution treatment and artificial aging. Microstructure analysis indicated the aged plate was dominated by elongated unrecrystallized grains, and had a rolling-type texture along extrusion direction with the highest intensity at Brass component. The existence of T1 phase strengthened the alloy crucially, but δ′ phase was basically absent. Then, the fully-reversed strain-controlled low-cycle fatigue tests were conducted at total strain amplitudes ranging from 0.4% to 1.0% for samples along two orthogonal directions. The stress-strain hysteresis loops were acquired, and the cyclic stress response curves were derived. At low strain amplitudes (0.4–0.5%), the initial cyclic hardening was slight and followed by a cyclic stability, while at higher strain amplitudes (0.6–1.0%), the alloy merely presented a continuously increasing cycle hardening behavior. Moreover, the fatigue life model based on the total strain energy was built and found to be suitable to predict life. Finally, the fatigue fractography observation showed that the fatigue source is relatively concentrated and the fracture surface had typical fatigue striations at 0.5% strain amplitude, while multiple cracks originated on the sample surface and the final fracture zone showed a ductile characteristic at 1.0%. The deformed microstructure near fracture surfaces were observed, and it was found that the cyclic hardening and stability were closely associated with the interaction between moving dislocations and obstacles including (sub)grain boundaries and secondary phase particles against them.

Fourier-transform rheology of unvulcanized styrene butadiene rubber filled with increasingly silanized silica

ABSTRACTSilica as one the most important fillers for rubber material is routinely modified by silane to improve its compatibility with the rubber matrix. Silanization of the silica particle affects both the linear and nonlinear rheological behaviors of the compounds. Their rheological nonlinearity, however, is mostly analyzed in an indirect way from linear rheological parameters, e.g. G′(ω1, γ0) and G″(ω1, γ0), which lose their physical meaning in the nonlinear viscoelastic regime. In the present work, the nonlinearity is directly quantified by the Fourier-transform rheology (FT-Rheology) technique in terms of I3/1(ω1, γ0), the third relative higher harmonic, for unvulcanized styrene butadiene rubber compounds filled with a fixed amount of silica, but varying dosages of silane. With the proposed model for I3/1(γ0), the contributions toward nonlinearity from the filler networks at a low strain amplitude and the one from the polymer networks at high strain amplitude can be successfully separated for filled systems. The utmost nonlinearity contribution from the filler networks decreases with the silane content, which is assigned to the weakening interparticle interaction of the filler. With increasing silanization of silica, the utmost nonlinearity contribution from the polymer networks is found to increase. This nonlinear mechanical response is attributed to the enhanced interfacial interaction between the filler and polymer.