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The Mechanical Properties of Solid Polymers
... where ε 0 is the initial strain, ε ve (t) is the viscoelastic creep strain, ε pl (t) is the viscoplastic creep strain. The constitutive modelling begins with the linear viscoelastic framework, incorporating the Boltzmann superposition principle, Prony series, and TTSP [42]. Subsequently, to model the non-linear viscoelastic behavior, the linear model is extended with the Free Volume Model. ...
... Each Voigt element consisting of a spring with modulus E j and a damper with viscosity η j in parallel, models the viscoelastic response which corresponds to the creep compliances in the Prony series. Ward described [42] that the summation in Eq. (5) can be written as an integral: ...
... where T is temperature, t(T) is the real-time scale at a temperature, tʹ(T 0 ) is known as the reduced time at a chosen reference temperature, and a(T) is the shift factor with a(T 0 ) = 1. The conventional empirical equation for the shift factor is the WLF equation [47] describes the TTSP of amorphous polymers around ±50K at the glass transition temperature for polymers [42]. In Section 1. it was mentioned that the average glass transition temperature for ETFE is around 80-150 C • , which region is almost irrelevant for the usage of ETFE foils in civil engineering approach, as it is between − 20 • C and 80 • C [20]. ...
Ethylene-Tetrafluoroethylene (ETFE) is gaining prominence in the building industry as a thin transparent membrane foil in tensile membrane structures. When installed on façades or roofs in inflated cushions, these thermoelastic foils, which exhibit time-, temperature-and direction-dependent behavior, are subjected to significant mechanical forces over extended periods. Recent research suggests an emerging focus on modelling the nonlinear thermoviscoelastic plastic behavior of the material. The formulation of a reliable constitutive model below the material glass transition temperature that captures the shift from linear to nonlinear elastic behavior is of significant importance for economical engineering design. This paper presents a thermomechanical characterization of ETFE foils through a viscoelastic plastic model up to yielding above its first yielding point until its second yield point around 20 % strains. This was achieved through uniaxial tensile and creep tests, which were performed at temperatures between 16 • C and 32 • C, in the material directions 0 • ; 45 • ; 90 • , at a strain rate of 0.166 %/s and load level from 4 MPa on a 50 mm width specimen. The study derives a comprehensive set of material parameters for linear viscoelastic and nonlinear viscoelasto-plastic models, using the Boltzmann su-perposition law with Time-Temperature Superposition Free Volume Model to capture nonlinearity, Perzyna law to capture viscoplastic behavior. For an engineering approach, an isotropic material model is assumed. The model validation of the viscoelastic model through independent creep on a load level 8 MPa and 16 MPa and uniaxial tensile tests at different strain rate from 0.0083 %/s to 0.83 %/s shows promising results for engineering applications across linear, nonlinear and plastic regimes, with physically reasonable material parameters.
... In a recent paper [2], we have studied the onset of shear yielding of amorphous polymer glasses under multiaxial loading conditions. A pressure-modified von Mises criterion [8] accurately describes the maximum shear yield stress as a function of the applied stress for different temperatures. However, in these simulations the bulk polymer was deformed at a single constant strain rate. ...
... Eq. (2) contains only a single relaxation time scale and predicts an apparent yield stress that varies logarithmically with the strain rate and a prefactor that depends linearly on temperature. Despite its simplicity, experimental results [8] are often fitted to Eq. (2), and the value of V * is associated with a typical volume required for a molecular shear rearrangement. ...
... It would be interesting to extend these measurements to very low temperatures and to higher shear rates. Note that typical room temperature experimental values for V ⋆ in polymers correspond to 3 or 4 repeat units [8], which is of the same order as the values we find at T = 0.1 or 0.2u 0 /k B . ...
We study shear yielding and steady state flow of glassy materials with molecular dynamics simulations of two standard models: amorphous polymers and bidisperse Lennard-Jones glasses. For a fixed strain rate, the maximum shear yield stress and the steady state flow stress in simple shear both drop linearly with increasing temperature. The dependence on strain rate can be described by a either a logarithm or a power-law added to a constant. In marked contrast to predictions of traditional thermal activation models, the rate dependence is nearly independent of temperature. The relation to more recent models of plastic deformation and glassy rheology is discussed, and the dynamics of particles and stress in small regions is examined in light of these findings.
... During start-up flow with a constant applied shear rate, the accumulation of elastic strain reduces as the plastic shear rate increases. In the solidstate polymer plasticity literature, the yield stress in case of ideal plasticity (no strain hardening or strain softening) is then defined as the stress at which the elastic shear rate becomes zero and the applied shear rate equals the plastic shear rate [44]. During plastic flow, the stress is then per definition equal to the yield stress, which might be pressure, temperature, and strain-rate dependent, see, for example, Bauwens-Crowet et al. [45]. ...
... According to the elastoviscoplastic model discussed in the Theory section, at the yield point, the elastic shear rate becomes zero and the plastic shear rate equals the total applied shear rate. Therefore, after reaching a steady-state flow stress σ during a start-up experiment at constant applied shear rate _ γ, a steady-state viscosity η can be calculated as η ¼ σ= _ γ [44]. In addition, flow-stress values were determined from steady-state flow derived from the plateau-creep rate during creep experiments (see Sec. IV B). ...
... First, by depicting the steady-state flow stress as a function of the applied shear rate (Fig. 4); second, by plotting the steady-state viscosity as a function of applied shear rate [ Fig. 5(a)]; and third, by plotting the same viscosity as a function of the measured steady-state flow stress [ Fig. 5(b)]. From Fig. 4, it is immediately clear that the Eyring model will not be able to describe these data as it is well known that the Eyring model appears as a straight line on a semilogarithmic plot of the flow stress versus strain rate [44]. ...
An elastoviscoplastic constitutive equation is proposed to describe both the elastic and rate-dependent plastic deformation behavior of Carbopol ® dispersions, commonly used to study yield-stress fluids. The model, a variant of the nonlinear Maxwell model with stress-dependent relaxation time, eliminates the need for a separate Herschel-Bulkley yield stress. The stress dependence of the viscosity was determined experimentally by evaluating the steady-state flow stress at a constant applied shear rate and by measuring the steady-state creep rate at constant applied shear stress. Experimentally, the viscosity's stress-dependence was confirmed to follow the Ree-Eyring model. Furthermore, it is shown that the Carbopol ® dispersions used here obey time-stress superposition, indicating that all relaxation times experience the same stress dependence. This was demonstrated by building a compliance mastercurve using horizontal shifting on a logarithmic time axis of creep curves measured at different stress levels and by constructing mastercurves of the storage-and loss-modulus curves determined independently by orthogonal superposition measurements at different applied constant shear stresses. Overall, the key feature of the proposed constitutive equation is its incorporation of a nonlinear stress-activated change in relaxation time, which enables a smooth transition from elastic to viscous behavior during start-up flow experiments. This approach bypasses the need for a distinct Herschel-Bulkley yield stress as a separate material characteristic. Additionally, the model successfully replicates the observed steady-state flow stress in transient-flow scenarios and the steady-state flow rate in creep experiments, underlining its effectiveness in capturing the material's dynamic response. Finally, the one-dimensional description is readily extended to a full three-dimensional finite-strain elastoviscoplastic constitutive equation.
... Therefore, the smaller the activation volume of the composite, the greater the restriction on the mobility of chain segments at the polymer-filler interface, indicating stronger interaction. This model is represented in Equation 1 [32] . ...
... Where σ is the tensile strength (ε max ), A is the activation energy, V is the activation volume, T is the temperature, R is the universal gas constant (8.31 J.mol -1 .K -1 ). The correlation between σ and the logarithm of the Deformation Speed is linear, whose slope of the generated line, can be represented by Equation 2 [32] . The tensile strength (σ) was determined at three different deformation speeds (20, 50 and 100 mm/ min) at temperature of 25 ºC. ...
Composite based on PP/CaCO3 contained micro and nanoparticles were investigated in relation its activation volume, mechanical, thermal and transport properties. The additives were initially dispersed in homopolymer polypropylene (hPP) blended with compatibilizer maleic anhydride grafted polypropylene (PP-g-MA) in twin-screw extruder, producing CaCO3 masterbatches, that were subsequently diluted in hPP. To optimize fillers dispersion in the polymer matrix, a Design of Experiment (DOE) was used, that combined Extruder screw rotation (N: 250 and 500 rpm); Extruder feed flow (Q:10 and 15 kg/h) and Average particle size (ϕ: 40 nm and 1.7 μm) at four different filler concentrations. Based on mechanical characterization results, the best process found was 500 rpm@10 kg/h, which provided suitable Specific Mechanical Energy (SME), increasing the nanocomposites strength. Finally, improvements of Impact Resistance up to 7.8% and Young's Modulus up to 9.3% related to microcomposite and Tensile Strength (Fmax), up to 7.9%, related to hPP, with higher strain.
... The failure of glassy polymers such as polystyrene (PS) or polymethylmethacrylate (PMMA) under external stresses occurs either through shear deformation or through crazing [1,2]. While shear yielding occurs essentially at constant volume, crazing has a strong dilational component, and the volume of the material increases to several times its original value before catastrophic fracture occurs. ...
... Despite the frequent appearance of crazes, there is still comparatively little theoretical understanding about the conditions and mechanisms of craze nucleation, growth and ultimate breakdown [1,2,3,4,7,15]. In this paper, we present an extensive set of nonequilibrium molecular dynamics (MD) simulations that address these various phenomena. In this approach, polymers are modeled on a coarse-grained scale that takes into account van-der-Waals (vdW) and covalent interactions without specific reference to chemical detail. ...
We report on an extensive study of craze formation in glassy polymers. Molecular dynamics simulations of a coarse-grained bead-spring model were employed to investigate the molecular level processes during craze nucleation, widening, and breakdown for a wide range of temperature, polymer chain length N, entanglement length and strength of adhesive interactions between polymer chains. Craze widening proceeds via a fibril-drawing process at constant drawing stress. The extension ratio is determined by the entanglement length, and the characteristic length of stretched chain segments in the polymer craze is . In the craze, tension is mostly carried by the covalent backbone bonds, and the force distribution develops an exponential tail at large tensile forces. The failure mode of crazes changes from disentanglement to scission for , and breakdown through scission is governed by large stress fluctuations. The simulations also reveal inconsistencies with previous theoretical models of craze widening that were based on continuum level hydrodynamics.
... The ability to predict the conditions under which a material will yield is of great fundamental interest and technological importance [1][2][3][4]. Over the past three centuries, a number of yield criteria have been formulated that predict whether a combination of stresses on a solid will produce irreversible deformation. ...
... Using values of u 0 and d from Ref. [17] our values of τ 0 correspond to 1 to 50 MPa. This coincides well with the experimental range [3,12] of 5-100 MPa, but quantitative comparisons for specific polymers are not possible without more detailed models of atomic interactions. ...
Shear yielding of glassy polymers is usually described in terms of the pressure-dependent Tresca or von Mises yield criteria. We test these criteria against molecular dynamics simulations of deformation in amorphous polymer glasses under triaxial loading conditions that are difficult to realize in experiments. Difficulties and ambiguities in extending several standard definitions of the yield point to triaxial loads are described. Two definitions, the maximum and offset octahedral stresses, are then used to evaluate the yield stress for a wide range of model parameters. In all cases, the onset of shear is consistent with the pressure-modified von Mises criterion, and the pressure coefficient is nearly independent of many parameters. Under triaxial tensile loading, the mode of failure changes to cavitation.
... The course of the tensile curves depends on both the proportion of filler and plasticiser. For plasticised poly(vinyl chloride) (P40, Figure 1a), the course of the relationship is characteristic of highly elastic materials: there is a gradual increase in stress with increasing strain, without a clearly defined c point [35,39]. The plasticiser present in the material significantly reduces intermolecular interactions by facilitating the orientation of polymer chains during progressive deformation [24,32,40]. ...
... At the same time, the value of the tanδ maximum decreases with increasing proportions of both plasticiser and wood flour. The tanδ value determines the energy damping and dissipation capacity due to viscoelastic interactions in the material [39]. An increase in the proportion of rigid filler particles at the expense of plasticised poly(vinyl chloride) reduces the dispersion and energy-dissipation capacity, which is associated with a reduction in damping properties at this temperature value. ...
The paper presents the results of testing the properties of wood–polymer composites (WPC) based on plasticised poly(vinyl chloride) (PVC-P). Materials with variable contents of wood filler (Arbocel C 320) or plasticiser (di-isononyl phthalate) were produced and then analysed. The share of wood flour in the material was up to 50 phr, and the plasticiser content was up to 40 phr. Functional properties, such as tensile properties, mechanical properties at variable temperature (DMTA), and water absorption, as well as processing properties such as rheological properties and analysis of the fusion process, were analysed. The influences of wood flour and plasticiser on the composites’ properties in the solid and melted state were found. For example, with 40 phr of plasticiser, increasing the filler share from 0 phr to 50 phr resulted in an increased tensile modulus from 18 MPa to 274 MPa and viscosity at a share rate of 20 s⁻¹, from 721 Pa·s to 1581 Pa·s. However, increasing the share of plasticiser from 20 phr to 40 phr with 30 phr of filler reduces the value of these properties from 1760 MPa to 112 MPa and from 2768 Pa·s to 1151 Pa·s, respectively. It was also found that increasing the share of wood flour in the composite noticeably reduces the effectiveness of the plasticiser.
... Furthermore, this analogy can be confirmed in view of the fact that the loss modulus E ′′ (ω) or the loss compliance J ′′ (ω) are related to the relaxation time spectrum H(τ), or the retardation time spectrum L(τ), which according to the Alfrey's approximation, are given by the following equations [41,42]: ...
... Based on these results, the attempt rate value at room temperature was found, on average, to be equal to 8.2 10 −4 s −1 . The temperature dependence of parameter γ T may follow an Arrhenius or Vogel-Fulcher [41] formula, and in order to study this dependence, a set of experimental data at various temperatures would be necessary. What is important to be mentioned is that all creep-recovery curves ( Figure 3) could be simulated with the same set of parameters, as shown in Table 4, in a quite satisfactory manner. ...
The description of various loading types within the frame of viscoelasticity, such as creep–recovery and stress relaxation in a wide time scale, by means of the same model and similar model parameters is always an interesting topic. In the present work, a viscoelastic model that was analyzed in previous works has been utilized to describe the main standard loading types of viscoelasticity with the same set of model parameters. The relaxation function of this model includes a distribution function followed by the energy barriers that need to be overcome by the molecular domains when a stress field is applied. This distribution function attains a decisive role in the analysis and it was shown that it can be determined on the basis of the loss modulus master curve experimental results. Thereafter, requiring no additional parameters, the creep compliance, the relaxation modulus of poly-lactic acid (PLA) in a wide time scale, as well as creep–recovery at various stresses could be predicted. It was also found that by employing the distribution function associated with the PLA matrix, the creep–recovery experimental data of PLA/hybrid nanocomposites could subsequently be predicted. Therefore, the proposed analysis was shown to be a useful method to predict the material’s viscoelastic response.
... Polymeric materials found applications in several engineering domains due to their exceptional properties and versatility [1,2]. These materials do indeed find widespread applications in various industrial sectors such as the medical sector, industrial machinery, aerospace, and, automotive sectors for the realization of seals and o-ring, vibration isolators, and tires [3,4]. ...
... where are the material constants,̄1 and̄2 are the first and second invariant of the left Cauchy-Green deformation tensor, is the compressibility parameters and is the determinant of the deformation gradient. The indices , and in Eq. (2) identify the order of the Mooney-Rivlin model [1]. For example, the easiest Mooney-Rivlin material model is the two parameters model which takes the form: ...
Polymeric materials find extensive applications across various engineering sectors. Among these, a particularly critical application for these materials is in the field of roller coasters. The wheels are typically made with an aluminum hub and a dense polyurethane coating, which, being in contact with the track, endures dynamic loads at high speeds. Due to the viscoelastic behavior typical of polymeric materials, these loads induce overheating of the coating leading to rapid degradation of the wheel. This results in machine downtime and a significant waste of time and money. In this manuscript, a methodology for finite element thermal-structural analysis has been developed. This method allows for the rapid evaluation of temperatures reached during operational cycles if compared to classical coupled-field thermal-structural analysis. The proposed methodology proves to be useful in selecting the appropriate type of wheels during the design phase requiring short computational time. The study first involved the development of the methodology, followed by validation through a comparison of analysis results with data obtained from experimental tests conducted by the manufacturer.
... CB. It is known that the process of orientation of macromolecular chains of polymeric materials results in an increase in the mechanical properties of the polymer in the direction of orientation [28]. According to the data of XRD analysis (Figure 3 and Figure 4) and mechanical tests ( Figure 5), the orientational strengthening of UHMWPE governs the mechanical properties of the composite material independently of the amount of modifying filler and is determined purely by the degree of polymer orientation. ...
In this study, oriented nanocomposite gel-spun fibers and solid-state-processed tapes were manufactured and analyzed. The fibers and tapes were produced using a specific type of nascent disentangled ultra-high molecular weight polyethylene (UHMWPE) reactor powder. As the filler, commercially available electrically conductive carbon black (CB) was used. The ultra-high filler content values up to 75 wt.% were achieved for the UHMWPE/CB gel-spun fibers, while the degree of filling was limited (up to 30 wt.%) in the case of the solid-state processing approach. This was attributed to the type of the filler distribution achieved with both processing methods. The influence of the filler distribution on the composite characteristics in case of the homogeneous filler distribution in the gel-spun fibers and extremely segregated filler distribution in the solid-state tapes was studied. To this end, the resulting composite UHMWPE/CB gel-spun fibers and solid-state processed tapes were characterized using a combination of research techniques, including X-ray diffraction, scanning electron microscopy, mechanical testing, and conductivity measurements. A comparative study of the electrical conductivity of the gel-spun and solid-state-processed UHMWPE/CB composites was conducted for both the unoriented and oriented states of the composite materials. The obtained solid-state processed UHMWPE/CB tapes were characterized by a low filler percolation threshold value of 2.5 wt.%, while the percolation threshold for the composite gel-spun fibers exceeded 15 wt.%. Regardless of the filler distribution type, a notable reduction in electrical conductivity was observed following the orientation drawing of the composites. At the same time, while a notable reduction in the maximum achievable orientation deformation ratio and subsequent tensile strength decline was observed in the case of gel-spun fibers, no impact of the filling on orientation strengthening was detected in the case of solid-state processed tapes.
... The supermolecular structure of semicrystalline polymers determines the properties predominantly [1][2][3][4]. The primary process of crystallization is a first-order thermodynamic phase transformation, which has been studied extensively in the past decades [5][6][7]. ...
This work introduces a probabilistic numerical simulation method to describe or predict the spherulitic morphology of semicrystalline polymer formed during non-isothermal crystallization process. The numerical simulation is based on the general crystallization theory, which consists of random nucleation and subsequent growth of supermolecular formations. The model is capable for prediction of morphology from the conversion curve of crystallization recorded by calorimetry during crystallization at a constant cooling rate. Samples made of polypropylene nucleated by different nucleating agents were used as a model material for testing the simulation approach. The results indicated that valuable structural information can be predicted from the conversion curve, like nucleus density, average spherulite size and size distribution as well. In addition, the simulation method also capable to predict the mechanism of nucleation during the crystallization process, namely, whether the number of nuclei is constant or continuously changing. The results also indicated that nucleus density increases significantly as a consequence of heterogeneous nucleation, which indicates that the simulation results in realistic and reliable structural data both in nucleated and non-nucleated samples.
... Regarding the rubber elasticity theory for incompressible material, the crosslinking density, n, can be determined from the storage moduli, E′ in the rubbery state according to [38,39] as Equation (1). ...
The mechanical properties of silicone‐rubber composites filled with nano‐ or micro‐silica‐particles are discussed experimentally and theoretically. The matrix rubbers cured under various ratios of the main component to the curing agent are prepared to change the crosslinking density of the matrix rubber. Because the interphase layer made of the matrix rubber in the glassy state is formed around the nano‐particle, the nano‐particle behaves as an apparent single particle together with the interphase layer and the interphase layers apparently increase the nano‐particle volume fraction. The Young's moduli of the nano‐ and micro‐composites with a larger (apparent) particle volume fraction are greater than that of the matrix rubber. However, the proportional limit strains are smaller, although the fracture strains are slightly smaller. The Young's modulus and proportional limit strain can be analyzed theoretically with the (apparent) volume fraction. The fracture toughness of the composites increases as the (apparent) volume fraction increases, but it increases little at the (apparent) volume fraction above 0.2. However, the fracture toughness monotonically increases for the nano‐composites with low crosslinking density of the matrix rubber. Finally, the mechanical properties can be designed by using the matrix rubber with the different crosslinking density and the interphase layer.
... In addition to Y (t) , another interesting quantity is the mechanical relaxation form, namely the complex dynamic modulus G * (ω), or equivalently, its real G ′ (ω) and imaginary G ′′ (ω) components, which are known as the storage and the loss moduli 41,42 . For very dilute solutions and for ω > 0, G ′ (ω) and G ′′ (ω) for the Rouse model are given by ...
A central issue in the study of polymer physics is to understand the relation between the geometrical properties of macromolecules and various dynamics, most of which are encoded in the Laplacian spectra of a related graph describing the macrostructural structure. In this paper, we introduce a family of treelike polymer networks with a parameter, which has the same size as the Vicsek fractals modeling regular hyperbranched polymers. We study some relevant properties of the networks and show that they have an exponentially decaying degree distribution and exhibit the small-world behavior. We then study the Laplacian eigenvalues and their corresponding eigenvectors of the networks under consideration, with both quantities being determined through the recursive relations deduced from the network structure. Using the obtained recursive relations we can find all the eigenvalues and eigenvectors for the networks with any size. Finally, as some applications, we use the eigenvalues to study analytically or semi-analytically three dynamical processes occurring in the networks, including random walks, relaxation dynamics in the framework of generalized Gaussian structure, as well as the fluorescence depolarization under quasiresonant energy transfer. Moreover, we compare the results with those corresponding to Vicsek fractals, and show that the dynamics differ greatly for the two network families, which thus enables us to distinguish between them.
... 22−24 Of particular interest is necking, which is a phenomenon that can be observed as a reduction in stress after the yield point in the engineering stress−strain graphs (Figures 4a and S3−S5). Necking is a consequence of plastic instability and a nonuniform deformation of the material, 9,50,51 and in polymers, the phenomenon indicates the presence of regions of mechanical weakness or heterogeneous structures at all scales. Thus, fibers that do not display necking are in principle more uniform with respect to fibers that display necking. ...
Recent biotechnological advancements in protein production and development of biomimetic spinning procedures make artificial spider silk a promising alternative to petroleum-based fibers. To enhance the competitiveness of artificial silk in terms of mechanical properties, refining the spinning techniques is imperative. One potential strategy involves the integration of post-spin stretching, known to improve fiber strength and stiffness while potentially offering additional advantages. Here, we demonstrate that post-spin stretching not only enhances the mechanical properties of artificial silk fibers but also restores a higher and more uniform alignment of the protein chains, leading to a higher fiber toughness. Additionally, fiber properties may be reduced by processes, such as aging, that cause increased network entropy. Post-spin stretching was found to partially restore the initial properties of fibers exposed aging. Finally, we propose to use the degree of necking as a simple measure of fiber quality in the development of spinning procedures for biobased fibers.
... Activation energy is the energy barrier that molecules need to surpass in order to start flowing. Its calculation method is based on the Arrhenius Equation as described in the relative literature [9]. Lower activation energy values result in a lower temperature sensitivity. ...
The main objective of this study was the investigation of the characteristic properties of lignin-modified bitumen with different lignin contents. Three (3) blends with different lignin contents (5%, 10% and 15% by weight of bitumen) were produced. Characteristic properties such as penetration, ring & ball, elastic recovery, force ductility, dynamic viscosity and storage stability were determined for the reference bitumen and the three lignin blends. Furthermore, the results of the tests were utilized to calculate the Penetration Index (PI), Activation Energy (Ea), Viscosity-Temperature Susceptibility (VTS) Index and Mixing Temperature (Tmixing) along with their respective Pearson's Correlation Coefficient (PCC), R 2 and p-values. The main conclusion was that Kraft lignin powder hardens the conventional bitumen. Specifically, the addition of 15% lignin to the bitumen hardened the blend to such a degree that the bitumen changed category from 50/70 to 35/50 with respect to EN 12591. Additionally, a strong linear statistical correlation was observed between Ea and VTS Index suggesting that these values should be taken into consideration when characterizing the temperature susceptibility of bio-modified bitumen.
... The rLDPE granules were analysed from the point of view of physical-mechanical properties and the results obtained are presented in Table 3. The results obtained for the characterization of mechanically recycled polyethylene waste -rLDPE, according to data from the literature [19][20][21] are close in value to those of virgin polymers. ...
The paper presents our studies regarding the superior valorization of recycled low-density polyethylene (rLDPE) by compounding with thermoplastic starch (TPS) and ethylene propylene terpolymer elastomer (EPDM). Low-density polyethylene post-consumer waste from foil packaging was used for the experiments. The waste was mechanically recycled and the rLDPE granules obtained were characterized both from a physical-mechanical and structural point of view. In order to obtain new sustainable materials, rLDPE granules were mixed with TPS, EPDM, compatibilizers and crosslinking agents. The mixtures were obtained in a PlastiCorder Brabender mixer at 140�C, 30-80 rpm, working time 7 minutes. The samples made show very good resistance to bending and abrasion, they have very good values of Charpy impact resistance and tear strenght, they show very good behavior to accelerated aging and to the action of some liquids, they have high hardness (51-53) �ShD and a Vicat softening point of 93-96�C. The new materials can be processed by methods specific to plastic materials (extrusion, injection, compression) in order to obtain finished products, and their field of applications can include: the footwear industry, the automotive industry, construction, packaging, agriculture, etc. The LCA analysis of the composites show a low environment impact. The values of the carbon footprint range between 0.58 Kg CO2 eq/kg and 0.75 Kg CO2 eq /kg due to the use of recycle low-density polyethylene and optimised efficient production process.
... [6][7][8][9] In addition to experiments, the mechanical properties of glassy polymer nanocomposites have been studied by molecular dynamics (MD) simulations in the linear elastic regime, [10][11][12][13][14][15] as well as under large deformation. [16][17][18] Glassy PNC exhibit a maximum in the stress-strain curves (yielding point) at a strain value of a few percent and a typical yield stress value of a few GPa, [19] followed by the so-called stress softening regime corresponding to a decrease of stress, depending on the thermomechanical history of the structures. [20] This regime is followed by a stress plateau corresponding to plastic flow or perfectly plastic behavior. ...
Polymer nanocomposites have found ubiquitous use across diverse industries, attributable to their distinctive properties and enhanced mechanical performance compared to conventional materials. Elucidating the elastic‐to‐plastic transition in polymer nanocomposites under diverse mechanical loads is paramount for the bespoke design of materials with desired mechanical attributes. In the current work, the elastic‐to‐plastic transition is probed in model systems of polyethylene oxide (PEO) and silica, SiO 2 , nanoparticles, through detailed atomistic molecular dynamics simulations. This comprehensive, multi‐scale analysis unveils pivotal markers of the elastic‐to‐plastic transition, highlighting the quintessential role of microstructural and regional heterogeneities in density, strain, and stress fields, featuring the polymer‐nanoparticle interphase region. At the atomic level, the behavior of polymer chains interacting with nanoparticle surfaces is traced, differentiating between free and adsorbed chains, and identifying the microscopic origins of the linear‐to‐plastic transition. The mechanical behavior of subregions are characterized within the PEO/SiO 2 nanocomposites, focusing on the interphase and bulk‐like polymer areas, probing stress heterogeneities and their decomposition into various force contributions. At the inception of plasticity, a disruption is discerned in isotropy of the polymeric density field, the emergence of low‐density regions, and microscopic voids/cavities within the polymer matrix concomitant with a transition of adsorbed chains to free. The yield strain also emerges as an inflection point in the local versus global strain diagram, demarcating the elastic limit, and the plastic regime shows pronounced strain heterogeneities. The decomposition of the atomic Virial stress into bonded and non‐bonded interactions indicates that the rigidity of the material is primarily governed by non‐bonded interactions, significantly influenced by the volume fraction of the nanoparticle. These findings emphasize the importance of the microstructural and micromechanical environment at the polymer‐nanoparticle interface on the linear‐to‐plastic transition, which is of great importance in the design of nanocomposite materials with advanced mechanical properties.
... The reference temperature for the TTSP was chosen as T ref = 20 • C as the midspan of the temperature range considered and similar to ambient temperature. A horizontal shift of all curves, except from the one at the reference temperature, was performed, aiming to create a smooth experimental master curve by means of aligning the starting point of each sample's compliance to the neighbour curve (Ward 2013). Data from tests performed (Schapery 1969). ...
Ethylene-tetra-fluoroethylene (ETFE) is a polymer employed in tension membrane structures with mechanical properties that strongly depend on time and temperature effects. A comprehensive understanding of the mutual influence of these variables and a unified viscoelastic constitutive model design can enable wider exploitation of ETFE in sustainable lightweight construction. This study presents a thermomechanical characterisation of ETFE foils through quasi-static tensile experiments spanning two orders of magnitude of strain rates, creep, relaxation, shear and dynamic cyclic tests in a wide range of temperatures suitable for building applications, from −20∘ C to 60∘ C. The experimental results in different material orientations are used to identify the limits of the linear viscoelastic domain, define the direction-dependent creep compliance master curves and calibrate the parameters of a plane stress orthotropic linear viscoelastic model, employing the Boltzmann superposition and the time-temperature superposition principles. The model has been numerically implemented using a recursive integration algorithm and its code is provided open source. A validation on independently acquired data shows the accuracy of the constitutive model in predicting ETFE behaviour within the linear viscoelastic regime usually adopted during structural design, with excellent extrapolation capabilities outside the range of the calibration data.
... Two rheological models are commonly proposed to represent the viscoelasticity of polymers: Kelvin and Maxwell models. Kelvin model is generally used to study the creep phenomenon and Maxwell model is applied for relaxation experience [35,36]. In these models, springs and dashpots are used to represent the stiffness and viscous behavior of materials, respectively. ...
The mechanical properties of BaTiO3 filled HDPE nanocomposites are studied by experimental and numerical approaches. First, the viscoelastic behavior of neat HDPE is highlighted experimentally in tensile and relaxation tests. A method is then proposed to define a constitutive viscoelastic law representative of this behavior at
different tensile crosshead speeds at room temperature. Afterward, this law is implemented in a finite-elementbased
micromechanical model representing the BaTiO3 filled HDPE nanocomposites with different filler amounts. The experimental and numerical results are further compared. Both the experiments and numerical simulations confirm the viscoelastic behavior of the polymer nanocomposite. For nanocomposites with filler
concentrations up to 20 %, the error between the experimental and numerical findings remains less than 8 %, confirming that the model represents well the composite behavior for low and moderate filler amounts. The proposed strategy can be applied to other polymer composites in order to predict the complete mechanical behavior of viscoelastic composite materials.
... Silicone rubbers are polymers belonging to the category of elastomers. They are highly deformable materials with a great capacity of recovery of their mechanical characteristics if the time between two consecutive loads is sufficient [25]. Their behaviour is then viscoelastic with the particularity of having an elastic modulus and a recovery modulus strongly depending on the temperature and the strain level [26]. ...
In situ characterization of structural behaviour under seismic hazard provides an opportunity to acquire experimental data that improve our understanding of soil-structure interaction (SSI). Experimental programs such as Lotung and Hualien in Taiwan, EuroProteas in Greece and NUPEC in Japan, are amongst the most known. Such investigations aim at studying a structure with a rigid shallow raft and measuring the seismic impedance functions at soil-foundation interface. Indeed, impedance functions are by far the most widely used tools to study SSI. In this paper, considering feedbacks from these in situ tests, we aim at assessing the feasibility to acquire measurements of the seismic impedance functions for any structure with a rigid shallow foundation. To test the proposed methodology, we carry out a laboratory test with a small-scale device: the soil is represented by a model material (silicon rubber block) and the foundation by a cylindrical shaker inducing monitored harmonic vertical forces on the silicon rubber block. Experimental tests are paired with numerical simulations to identify, by inverse analysis, unknown parameters and to compute the order of magnitude of displacements and forces within the system. This paper presents the laboratory test setup, the experimental design, and the results of the associated simulations.
... It is known that the highest Poisson's ratio for isotropic amorphous polymers is 0.5 for natural rubbers. [107] The values of ν 31 higher than 0.5 for uniaxially stretched PVDF [104,105] and LDPE [106] are interesting observations. If we use ν 31 = 0.3 for unstretched PVDF, d 31 should only bẽ 10 pC/N. ...
Despite extensive research on piezoelectric polymers since the discovery of piezoelectric poly(vinylidene fluoride) (PVDF) in 1969, the fundamental physics of polymer piezoelectricity has remained elusive. Based on the classic principle of piezoelectricity, polymer piezoelectricity should originate from the polar crystalline phase. Surprisingly, the crystal contribution to the piezoelectric strain coefficient d31 is determined to be less than 10%, primarily owing to the difficulty in changing the molecular bond lengths and bond angles. Instead, >85% contribution is from Poisson's ratio, which is closely related to the oriented amorphous fraction (OAF) in uniaxially stretched films of semicrystalline ferroelectric (FE) polymers. In this perspective, the semicrystalline structure–piezoelectric property relationship is revealed using PVDF‐based FE polymers as a model system. In melt‐processed FE polymers, the OAF is often present and links the crystalline lamellae to the isotropic amorphous fraction. Molecular dynamics simulations demonstrate that the electrostrictive conformation transformation of the OAF chains induces a polarization change upon the application of either a stress (the direct piezoelectric effect) or an electric field (the converse piezoelectric effect). Meanwhile, relaxor‐like secondary crystals in OAF (SCOAF), which are favored to grow in the extended‐chain crystal (ECC) structure, can further enhance the piezoelectricity. However, the ECC structure is difficult to achieve in PVDF homopolymers without high‐pressure crystallization. We have discovered that high‐power ultrasonication can effectively induce SCOAF in PVDF homopolymers to improve its piezoelectric performance. Finally, we envision that the electrostrictive OAF mechanism should also be applicable for other FE polymers such as odd‐numbered nylons and piezoelectric biopolymers.
... The activation energy is the energy barrier that the molecules of bitumen need to overcome to start moving and thus for the bitumen to start flowing [29]. In order to further investigate the rheological properties of the blends, the activation energy was calculated according to the Arrhenius equation (Equation (1)) [30,31]: ...
The main aim of this study was to identify and evaluate the characteristic properties of bitumen modified with algae. Two types of algae, each with distinct gradation and origin, were employed for this investigation. For each type of algae (noted as chlorella and microchlorella), three blends were created with varying algae contents (5%, 10%, and 15% by weight of bitumen), utilizing a 70/100 reference bitumen as the virgin material and a basis for comparison. The properties of the blends were investigated using the Penetration, Softening Point, Elastic Recovery, Force Ductility, Dynamic Viscosity, and Storage Stability tests, both before and after short-term ageing (TFOT). The test results were then used to calculate the Activation Energy (Ea), Viscosity-Temperature Susceptibility (VTS) Index, and Mixing Temperature (Tmixing), along with their respective Pearson Correlation Coefficient (PCC) and R² and p-values. The main finding of the study was that the addition of a low algae content of 5% caused a change in the classification of the unaged bitumen from 70/100 to 50/70 according to EN 12591 and thus hardened the reference bitumen. Additionally, a strong linear statistical correlation was observed between Ea and the VTS index, suggesting that these values should be considered when characterizing the temperature susceptibility of algae-modified bitumen.
... [Color figure can be viewed at wileyonlinelibrary.com] linear slope with an offset difference of 2% and measuring the value of the intercept point between the lines. 27 Five samples were tested, and the average values and the confidence interval were calculated using Excel with a 95% confidence. ...
Polyamide 11 (PA11) is a polymer used in flexible lines for oil prospection due to its properties. After the decommissioning of the lines, the materials used are discarded in landfills or left in the ocean. As developing a sustainable economy is of utmost importance, reusing these discarded materials would be a step in the right direction. This research focused on examining two kinds of PA11 previously used in flexible lines to see their properties changed compared to virgin PA11 and to infer if they can still be reused. Chemical, thermal, and mechanical analysis were employed to analyze the PA11 that came from the two oilfields and recycled ones that were hot pressed with an unused PA11 in a 50/50 wt% proportion. Results indicate that one of the oilfield samples was less degraded than the other one, which provided better mechanical properties, and the same pattern happened with the recycled samples, indicating that some properties such as viscosity, plasticizer content, and crystallinity need to be evaluated before taking in consideration the reuse (be it recycling or repurposing) of this type of polymers in consideration.
... Thus, the behavior law is sometimes defined in quasi-static mode or the dynamic mode. In quasi-static mode, these materials can undergo large deformations and return to their initial form without permanent deformation [13][14][15][16]. In dynamics, elastomeric materials exhibit a frequency and time behavior having the characteristics of a spring [17]. ...
This paper proposes the study of the visco-hyperelastic behavior of a rubber sample. This rubber, coded as the BX rubber sample, is simultaneously loaded and subjected to linear vibrations.
A multiplicative non-separable variables law of the Nashif has been used to model the behavior that depends on both stretch and frequency. This method allows splitting the intricately combined test performed jointly on both stretch and frequency. On the one hand, we use Young’s complex modulus calculated from the experimental data, and on the other hand, the hyperelastic characteristics of the same material obtained from the experimental tensile curve. The hyperelastic phenomenological Gent–Thomas model and the hyperelastic molecular Flory–Erman model are used to evaluate the combined complex modulus .
We obtain results that go in the physical sense, i.e, Young’s modulus increases when the material is stretched, while the damping decreases.
... The intrinsic properties of crystalline and amorphous structures are often very different. These structures affect the macroscopic behaviour of the material [42][43][44]. Rapid cooling of the molten polymer in the mould causes the degree of crystallization to be lower than the maximum crystallization value in polymer materials with low crystallization kinetics. Low crystallisation kinetics implies that there should be sufficient temperature and time for nucleation and growth of nuclei in the polymer melt. ...
Polyamide polymers are widely used in tribological areas in a wide range of industries. The purpose of this study is to extend the tribological life of this material. For this purpose, composite materials were produced by adding solid lubricants such as graphite and wax to the polyamide 6 (PA6) matrix at different rates, and the synergistic effect of these composites on tribological behavior was investigated. Tribological experiments were carried out under dry sliding conditions and on themselves. The polyamide 6/graphite/wax composites were first produced in the form of granules in a twin‐screw extruder, and then test samples were molded using the injection molding technique. Wear tests were performed using a pin‐on‐disc wear device. Tribological tests were carried out at a sliding speed of 0.5 m s⁻¹ and under loads ranging from 10 N to 250 N. Following the experiments, the friction coefficient, specific wear rate, and surface wear were determined under the condition of the materials working on each other. The results showed that the lowest specific wear rate and friction coefficient were obtained for the polyamide 6 composites containing 6 % wax and 15 % glass fiber working on each other.
Ultra-thin stacked chip scale packaging (UT-SCSP) technology has been widely used to package many non-CPU products, such as wireless and communication devices. In this package, multiple thin silicon dice are stacked on top of each other, and a thin layer of die-attach adhesive is applied between two adjacent Si dice. Consequently, the thermal expansion and viscoelastic properties of the die-attach material have an important effect on package thermal stress and warpage development. In this study, the thermal expansion behavior of a thin film die-attach material used for UT-SCSP applications was determined by thermomechanical analyzer (TMA), whereas the viscoelastic behavior was characterized by conducting time–temperature superposition (TTS) experiments using dynamic mechanical analyzer (DMA). From the TTS results, master curves were constructed for both the storage (), the loss moduli (), and the loss factor ( as a function of frequency at a preselected reference temperature. Shift factors were obtained by fitting the experimental data to the Williams–Landel–Ferry (WLF) equation. Knowing the shift factors and the frequency and temperature dependences of and , one can obtain the time dependence of the relaxation modulus E(T, t) for various temperatures. The obtained master curves were analyzed using the Havriliak–Negami relaxation model, from which the four temperature-independent relaxation parameters (, , , and ) and one temperature-dependent average relaxation time can be extracted. These results characterized the relaxation behavior of the die-attach material and provided key material properties for modeling package stress development.
Hydrogels comprised of natural and synthetic polymers are widely used in the biomedical field due to their distinguishing properties, such as softness, flexibility, swelling, and biocompatibility. In this study, we obtained and characterized hydrogel materials based on chitosan/acrylamide copolymer as potential matrices for biomedical applications. FTIR studies confirmed the formation of chitosan/polyacrylamide graft copolymer. Kinetics of gel formation was investigated with the rheological tests and the change of reaction mixture viscosity in the shear mode was measured. Scanning electron microscopy revealed a porous surface with micron- and submicron-sized gels. The kinetics of swelling/drying processes in the obtained hydrogels were studied at varying pH values. A significant decrease in the equilibrium swelling degree in an alkaline medium was observed, dropping from 50 g/g in the first cycle to 36 g/g in the second cycle. Mechanical characteristics of the chitosan/polyacrylamide hydrogel-shaped samples were tested both in compression and tension modes. It was found that for the samples swollen at pH 6.8, the tensile and compression strengths were 37 kPa and 19 kPa, respectively. The biological activity of the obtained hydrogels was evaluated by the MTT test. The Kinetics of drug release from hydrogels in phosphate buffer was studied using lidocaine hydrochloride as a model compound.
The scope of the present work is to study, experimentally and theoretically, the temperature and strain rate effect on the yielding and postyielding tensile behavior of an epoxy resin. Regarding the theoretical study, a three-dimensional viscoplastic model, namely a Zener B model, associated with the decomposition of the total strain into elastic and viscoplastic part was employed. To have an integrated aspect regarding the various models potentiality, a fractional Zener B viscoelastic model was comparatively utilized. Due to the limited capability of the two well-known models to describe the strain softening, exhibited by the polymeric material, apart from a stress-dependent viscosity related to a nonlinear Eyring-type dashpot, a strain-dependent activation volume was considered to be developed by a distribution function. The strain hardening hereafter was simulated by a back stress, associated with a hyperelastic spring. The strain rate effect could be successfully predicted by the scaling rule valid in viscoelasticity. No essential superior capability simulation was deduced from the comparative study between the two models.
Wood as an elastic anisotropic solid can be characterized with mechanical vibrations in the acoustic frequency range. For this purpose, resonance methods are employed for the determination of the elastic constants of wood.
Poly(ethylene terephthalate) (PET) films are widely used in flexible electronics and optoelectronics, where their mechanical durability and optical performance under strain are essential for device reliability. This study investigates the impact of applied mechanical strain on the optical and molecular properties of PET at room temperature,using UV-Vis absorption and Raman spectroscopy. The work explores how varying strain levels, from 0% (unstretched) to 30%, affect the transparency, vibrational modes, and molecular reorganization within PET films. UV-Vis absorbance measurements reveal that strain induces significant changes in the light transmission properties of PET, particularly in the visible range, and increases absorption in the UVA and visible region by up to 100%. Raman spectra indicate that strain levels higher than 5% lead to irreversible shifts of vibrational lines, accompanied by an increase of their full width at half maximum (FWHM), suggesting molecular reorientation and crystallinity changes. The phonon mode coupled with C-O stretching [O-CH2] shows the strongest response to applied mechanical stress. This study provides a comprehensive understanding of strain-induced optical and structural alterations in PET, with implications for improving the mechanical and optical performance of PET-based devices in strainsensitive applications, such as organic solar cells (OSCs), organic light-emitting diodes (OLEDs), and flexible sensors.
Abstract
Biodegradability, biocompatibility, non-toxicity, eco-friendly, and renewability make biopolymers as excellent and safe fillers for biopolymer matrices to fabricate nano-composites. However, most of biopolymers are hydrophilic and possess inadequate mechanical properties, thus uses of biopolymers in food coating and packaging are limited. There is a particular solution as follows: some particular biopolymers (cellulose, chitin, and starch) are good candidates as fillers to improve oxygen, moisture, and gas barrier and mechanical properties of hydrophilic natural polymers as continuous phases. Literature reports have shown that the above-mentioned biopolymers and their derivatives as nano-fillers improved mechanical and barrier properties of hydrophilic biopolymer matrices. The following conclusions were derived from some literature reports; (i) the advantages of bio-nanocomposites made from bio-fillers and biopolymers matrices over other bio-nanocomposites are: these nanomaterials are 100% biodegradable and recyclable, i.e., both continuous and discontinuous phases (matrix and filler) are safe for human and environment. The resulting nanocomposites are green nanomaterials; (ii) nano-bio-fillers have potential to improve gas and WVB properties of biomacromolecule continuous phases; (iii) use of nano-bio-fillers reduces cost for fabrication of desirable nanocomposites and reduce dependency to other types of fillers such as metal oxides; and (iv) use of nano-bio-fillers and biopolymer matrices in food packaging systems will certainly protect food from deterioration attacks, prolong shelf-life of food, and maintain the quality and safety of foodstuffs.
The influence on the mobility of polypeptide chains caused by strain misfit due to molecular electric dipole distortions under applied electric fields up to 769 kV m-1, in cow cortical femur samples annealed at 373 K, 423 K, and 530 K, is determined. The behaviour of strain misfit as a function of the electric field strength is determined from a mean-field model based on the Eshelby theory. In addition, Friedel's model for describing the mobility of dislocations in continuum media has been modified to determine the interaction energy between electrically generated obstacles and the polypeptide chains. Depending on the denaturation states from the bones due to the annealing treatments, the different locations of the activated dipoles and their effects on the mobility of the polypeptide chains were determined. Furthermore, it was also determined that dahllite does not affect the degree of chain mobility under an applied electric field. Dynamic mechanical analysis measurements conducted under a high electric field, differential thermal analysis and thermogravimetry are used in the present work. To our knowledge, this is the first time dynamic mechanical analysis studies have been carried out on bones subjected to high electric fields.
Bolted flange joints are the most common type of connection in various piping systems. However, few studies have focused on the influence of flexible joints on the vibration characteristics of fluid-conveying pipes. In this work, stability and nonlinear dynamic behavior of a jointed pipe are investigated, with the main aim of revealing the near-resonant response driven by the transverse harmonic excitation. By combining the nonlinear transmitted torque equation and the boundary conditions at the joints, the global modes and their orthogonality relations are determined and then used to transform the continuous model into a reduced-order one via the Galerkin method. Numerical results show that the variations in joint stiffness and pipe length induce different asymmetric equilibrium configurations. In the free vibration analysis, buckling and combined buckling-flutter behaviors can occur under varying linear and nonlinear joint stiffness. A nonlinear dynamic analysis is performed using the pseudo-arclength continuation method and a variable step-size Gear technique to study the nonlinear response. It is found that the pipe exhibits quasi-periodic behavior with increasing flow velocity and excitation amplitude. In the near-internal-resonance region, the dual-peak responses become complex with the breaking of the hardening and softening characteristics. The linear joint stiffness at the left and middle boundaries only affects the hardening and softening behaviors of the first or second primary resonance, but the nonlinear ones can change the first and second primary resonance responses simultaneously.
Helix formation has been of ongoing interest because of its role in both natural and synthetic materials systems. It has been extensively studied in gel-based ribbons where swelling anisotropies drive...
In four-dimensional additive manufacturing (4DAM), specific external stimuli are applied in conjunction with additive manufacturing technologies. This combination allows the development of tailored stimuli-responsive properties in various materials, structures, or components. For shape-changing functionalities, the programming step plays a crucial role in recovery after exposure to a stimulus. Furthermore, precise tuning of the 4DAM process parameters is essential to achieve shape-change specifications. Within this context, this study investigated how the structural arrangement of infill patterns (criss-cross and concentric) affects the shape memory effect (SME) of compression cold-programmed PLA under a thermal stimulus. The stress–strain curves reveal a higher yield stress for the criss-cross infill pattern. Interestingly, the shape recovery ratio shows a similar trend across both patterns at different displacements with shallower slopes compared to a higher shape fixity ratio. This suggests that the infill pattern primarily affects the mechanical strength (yield stress) and not the recovery. Finally, the recovery force increases proportionally with displacement. These findings suggest a consistent SME under the explored interval (15–45% compression) despite the infill pattern; however, the variations in the mechanical properties shown by the stress–strain curves appear more pronounced, particularly the yield stress.
Necking localization under quasi-static uniaxial tension is experimentally observed in ductile thin-walled cylindrical tubes, made of soft polypropylene. Necking nucleates at multiple locations along the tube and spreads throughout, involving the occurrence of higher-order modes, evidencing trefoil and fourth-foiled (but rarely even fifth-foiled) shaped cross-sections. No evidence of such a complicated necking occurrence and growth was found in other ductile materials for thin-walled cylinders under quasi-static loading. With the aim of modelling this phenomenon, as well as all other possible bifurcations, a two-dimensional formulation is introduced, in which only the mean surface of the tube is considered, paralleling the celebrated Flügge 's treatment of axially-compressed cylindrical shells. This treatment is extended to include tension and a broad class of nonlinear-hyperelastic constitutive law for the material, which is also assumed to be incompressible. The theoretical framework leads to a number of new results, not only for tensile axial force (where necking is modelled and, as a particular case, the classic Considère formula is shown to represent the limit of very thin tubes), but also for compressive force, providing closed-form formulae for wrinkling (showing that a direct application of the Flügge equation can be incorrect) and for Euler buckling. It is shown that the J2-deformation theory of plasticity (the simplest constitutive assumption to mimic through nonlinear elasticity the plastic branch of a material) captures multiple necking and occurrence of higher-order modes, so that experiments are explained. The presented results are important for several applications, ranging from aerospace and automotive engineering to the vascular mechanobiology, where a thin-walled tube (for instance an artery, or a catheter, or a stent) may become unstable not only in compression, but also in tension.
Hybrid nanocomposite materials based on polyethylene terephthalate and inorganic flame-retardant diammonium phosphate were prepared according to the fundamental strategy of environmental crazing of polymers. Structural-mechanical modification of the initial amorphous polyethylene terephthalate and the resultant nanocomposite polyethylene terephthalate-based was carried out by rolling at room temperature. The effect of preliminary rolling on the deformation behavior of polyethylene terephthalate during subsequent stretching in air and in physically active liquid media was established.
The earliest approaches to non-linear viscoelasticity (simplified generalizations of Boltzmann’s superposition principle, direct treatment of experimental creep data and semi-empirical correlations) are followed by the description of the first attempts at viewing the molecular scale processes as thermally activated. A series combination of an activated “dashpot” was the model chosen to describe non-linearity and, despite its simplicity, basic agreement was obtained with experiments on specific polymer systems. It is then argued that what the field of non-linear viscoelasticity still lacks is (1) an effective account for a range of molecular structures taking part in materials’ responses and the resulting spectra of characteristic times, and (2) a general mechanistic and dynamic description of the processes at the molecular scale. With those objectives, it seemed important to illustrate how one might devise insightful physical models and formulations of the process of non-linear creep. The example given is too specific, with excessive microscopic detail, thus restricting its applicability, but its application to polymer creep data suggested a strong connection of the range of retardation times to a range of “relaxor” sizes, indicating that cooperativity and clustering will hold the key for successful and desirably universal formulations of the behavior of amorphous condensed matter.
From the 1st-order ordinary differential equations of the Maxwell and Voigt–Kelvin model units and modified versions, formulations are obtained and physically discussed of the simplest forms of linear viscoelastic behavior under uniaxial tensile stress relaxation, creep and sinusoidal stressing. The physical and mathematical equivalence of the modified Maxwell and Voigt–Kelvin models is shown and used to define a standard linear solid, the paradigm of the linear viscoelastic behavior, with one single characteristic response (relaxation or retardation) time—different but directly related to each other via the elastic constants of the system. Irreversible viscous flow is then combined with the viscoelastic response of a standard linear solid to obtain the stress relaxation, creep and storage and loss behavior of what many be called a standard linear liquid; the effects of viscous flow are analytically formulated and graphed, and physically discussed. The conventional presentation of linear viscoelasticity ends with the physical justification and formulation of the spectra of relaxation and retardation times that characterize the behavior of real materials, one of the major subjects of Part II of the book.
Following basic definitions of tensile and shear stresses and strains, the range of materials’ mechanical behavior (elastic, viscoelastic and viscous) is illustrated with examples and graphs, including how it changes with temperature and the timescale or speed of testing. The time-dependent behavior of viscoelastic materials is then qualitatively presented and physically justified in uniaxial tensile stress relaxation and creep (with full descriptions of both types of excitations), for amorphous and semi-crystalline polymers, with graphical reference to the effects of crosslinking and crystallinity, respectively. The classical phenomenological representations are recalled of the elastic (spring) and viscous (Newtonian damper or “dashpot”) components of the mechanical behavior (to be combined in Chap. 3 in simple models of linear, constant-parameter, viscoelasticity, namely the standard linear solid and liquid) and the Boltzmann’s superposition principle justified in that linear domain. The formulation and physical analysis are then presented of the response of elastic and viscoelastic materials to cyclic (sinusoidal) strain and stress excitations, with reference to its storage and loss or dissipative components and including qualitative plots of their variation with frequency and with the crosslinks’ density and crystallinity, for amorphous and semi-crystalline polymers, respectively. The chapter ends with the formal interrelationships of the various linear viscoelastic functions.
Shape-shifting helical gels have been created by various routes, notably by photolithography. We explore electron-beam lithography as an alternative to prescribe microhelix formation in tethered patterns of pure poly(acrylic acid)....
The influence of different types of deformation of the metal matrix on mechanical behavior of the amorphous PET film upon its transverse compression in the ductile metal matrix has been investigated. Three deformation modes have been probed. In the first case, a disc-shaped polymer specimen has been put between two 5 mm thick discs of the lead–tin alloy and squeezed in the press. In the second and the third cases, planar elongation has been performed in the so called “dead channel”, i.e., the channel with fixed side walls, the film being elongated due to decrease in the width or thickness, respectively. The plots of true yield stress at different draw ratios have formed a common master curve. At high total draw ratio Λ, the true yield stresses have been close for the considered three types of drawing in the metal. At the draw ratio Λ 2.6, the neck has not appeared, and the specimen has been deformed uniformly. When the film in the channel is elongated due to the decrease in thickness at constant width, the specimen width has been mainly decreased during subsequent elongation in the testing machine. When the film in the channel is elongated due to the decrease in width at constant thickness, further elongation has mainly led to the decrease in the specimen thickness. The true stress Σ has been expressed as Σ = Σ0 + KΛ3, with K being a constant. Deformation of the polymer in the channel occurred with the formation of shear bands. At the preliminary draw ratio Λ = 1.82, the bands have been oriented at the angle 21.5° with respect to the stretching axis. The planar elongation has led to abnormally strong deformation softening of the polymer. The drawing has been accompanied by an increase in the elasticity modulus of the polymer. The obtained results have suggested that the macromolecules orientation is the main reason for strain hardening of the polymer.
Two thermoplastic polycarbonate bisphenol A types were exposed to the influence of natural weathering at continental location and at marine location for a period of 8 years (96 months). Every six months the specimens of medium molecular weight polycarbonate and high molecular weight polycarbonate were taken from mentioned locations and tested. Seven characteristics were chosen for determination of quality before exposition and during the process of degradation of two mentioned polycarbonate types (tensile strength, elongation to break, Shore hardness, Vicat softening point, water absorption, density and Charpy impact resistance). Changes of these seven properties at continental location are similar to the changes of mentioned characteristics at marine location during specified period of time. Data obtained by testing specimens of medium molecular weight polycarbonate pointed out that there were two important changes of quality regarding elongation to break and Charpy impact resistance (first after 36 months and second after 54 months of exposure). After 96 months of natural weathering of the above-mentioned material at both locations meaningful drop of tensile strength, moderate change of water absorption and negligible changes of Shore hardness, Vicat softening point and density were recorded. The influence of molecular weight is very apparent because high molecular weight polycarbonate exhibited higher resistance to the degradation process in natural conditions. Two very important characteristics of this polycarbonate material (tensile strength and Charpy impact resistance) practically did not change during 96 months of exposition in an open air, while drop of elongation to break is meaningful, diminution of water absorption is moderate and changes of Shore hardness, Vicat softening point and density are very small.
Due to the widespread use of carbon nanotube (CNT)‐reinforced polymers in various industries, investigating the dynamic mechanical response of these materials under impact loading is of significant importance. A three‐dimensional viscoelastic (VE)–viscoplastic (VP) constitutive model for CNT/epoxy nanocomposites is developed. A proper rheological model is established using the generalized Maxwell model to represent the VE behavior and propose an exponential function to express the elasto‐VP response. Employing an empirical logarithmic relationship to estimate material properties at different strain rates, the VP behavior is modeled based on the overstress concept. The 3D numerical discretization of the proposed rate‐dependent material model is also carried out to develop a user‐defined material model (UMAT) for the commercial finite element (FE) software of Abaqus. The performed FE simulations based on the proposed rate‐dependent constitutive material can properly capture stress relaxation and hysteresis behaviors of the nanocomposites. Comparing the estimated tensile and shear stress–strain curves through developed material models with experimental measurements, an excellent agreement is observed.
Highlights
Tensile/shear properties of CNT/epoxy are measured at three strain rates.
An empirical constitutive model is proposed for any arbitrary strain rates
Viscoplastic behavior is captured based on over‐stress concept
A 3D incremental form of a viscoelastic–viscoplastic material model is developed.
This paper concerns the development of a constitutive model of Polyvinylidene fluoride (PVDF), a piezoelectric polymer. Suitable assumptions are made based on experimental data available in literature. The model is proposed for Form II of the PVDF material. Mooney-Rivlin and Neo-Hookean models are assumed to predict the finite elastic deformation characteristics of the material and experimental data are fitted to test the range of validity of the model. Predictions based on the Mooney-Rivlin and the Neo-Hookean models show that the Mooney-Rivlin model correlates very well with the experimental data within reasonably finite strain ranges (deviation upto 3-5Vo) whereas the Neo-Hookean model deviates largely from the experimental (about 50Vo).
This study investigates the mode-II delamination performance of filament-wound unidirectional composites with different types of epoxies as their matrix phase under room and cryogenic temperatures. A typical vacuum infusion resin, an aerospace-grade cold-curing resin and crack-resistant toughened resin systems were wet-wound with 12K carbon fiber tows to manufacture the composite samples. Test samples with a (0)16 ply sequence were tested according to ASTM D7905-19. The tested samples were investigated via microscopic analysis to assess the failure mechanisms associated with varying the matrix material and temperature. ENF tests at room temperature were found to be susceptible to the inherent variance in the fiber architectures along with resin-viscosity-driven fiber wetting. Cryogenic conditions induce a shift in the mode-II delamination behavior from a rather complex failure mechanism to a consistent fiber/matrix debonding mode with diminishing GIIc values except for the toughened resin system. The provided comprehensive fractographic analysis enables an understanding of the various causes of fracture, which determines the laminate performance. The combined evaluation of the distinctive damage modes reported in this study provides guidance on the conventional wet-winding process, which still remains a volumetrically dominant and viable option for cryogenic applications, particularly for vessels with limited operational durations like sounding rockets.
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