A theory of finite tensile deformation of double-network hydrogels

A continuum damage model was developed to describe the finite tensile deformation of tough double-network (DN) hydrogels synthesized by polymerization of a water-soluble monomer inside a highly crosslinked rigid polyelectrolyte network. Damage evolution in DN hydrogels was characterized by performing loading-unloading tensile tests and oscillatory shear rheometry on DN hydrogels synthesized from 3-sulfopropyl acrylate potassium salt (SAPS) and acrylamide (AAm). The model can explain all the mechanical features of finite tensile deformation of DN hydrogels, including idealized Mullins effect and permanent set observed after unloading, qualitatively and quantitatively. The constitutive equation can describe the finite elasto-plastic tensile behavior of DN hydrogels without resorting to a yield function. It was showed that tensile mechanics of DN hydrogels in the model is controlled by two material parameters which are related to the elastic moduli of first and second networks. In effect, the ratio of these two parameters is a dimensionless number that controls the behavior of material. The model can capture the stable branch of material response during neck propagation where engineering stress becomes constant. Consistent with experimental data, by increasing the elastic modulus of the second network the finite tensile behavior of the DN hydrogel changes from necking to strain hardening.     

A study of the yield and post‐yield behavior of syndiotactic polypropylene

The strain recovery of three syndiotactic polypropylenes (s‐PPs) differing in the percentage of [rrrr] pentad is investigated. A suitable method based on loading–unloading tests at constant displacement rate in tensile loading conditions is adopted to measure the residual and recovered strain components of the applied strain. The method allows to obtain a large amount of data from few tests and to explore a wide strain range. The dependence of the material's strain recovery on the applied strain is analyzed in relation to s‐PP strain‐induced microstructural changes and crystalline form transitions, which are reported in literature. © 2014 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2014 , 52, 1276–1282     

Characterization of nonlinear response in quasi-unidirectional E-glass fabric reinforced polypropylene composites under off-axis tensile loading

The present paper addressed the nonlinear stress-strain response in quasi-unidirectional E-glass fabric reinforced polypropylene composites under off-axis tensile loading. A series of monotonic and cyclic loading-unloading tensile tests were carried out. Both irreversible strains and stiffness degradation were observed in cyclic loading-unloading tests, which indicate that the nonlinear response of composites was induced by a combination of damage and plasticity. A coupled damage-plasticity model was employed to describe the nonlinear off-axis tensile stress-strain relation of materials. In this model, a plastic potential function together with associated plastic flow rule were adopted to assess the evolution of plastic strains. The damage variables in forms of stiffness degradation were expressed as a Weibull function of the effective stress. A full suite of model parameters was experimentally determined from cyclic loading-unloading tensile tests. The stress-strain curves predicted by this model agreed well with experimental results.     

Dynamic uniaxial extension of elastomers at constant true strain rate

Elastomers are widely used for damping components in various industrial contexts because of their remarkable dissipative properties: they can bear severe mechanical loading conditions, i.e., high strain rates and large strains. Depending on the strain rate, the mechanical response of these materials can vary from purely rubber-like to glassy. In the intermediate strain rate range (1-100/s), uniaxial extension experiments are classically conducted at constant nominal strain rate. We present here a new experimental methodology to investigate the mechanical response of soft materials at constant true strain rate in the intermediate strain rate range. For this purpose, the displacement imposed on the specimen by the tensile machine is an exponential function of time. A high speed servo-hydraulic machine is used to perform experiments at strain rates ranging from 0.01 to 100/s. A specific specimen is designed in order to achieve a uniform strain field (and thus a uniform stress field). Furthermore, an instrumented aluminium bar is used to measure the applied force; which overcomes the difficulties due to dynamic effects. Simultaneously, a high speed camera enables the measurement of strain in the sample using a point tracking technique. Finally, the method is applied to determine the stress-strain curve of an elastomer for both loading and unloading responses up to a stretch ratio λ = 2.5; the influence of the true strain rate on both stiffness and dissipation of the material is then discussed.     

Effect of strain rate on the dynamic tensile behaviour of UHMWPE fibre laminates

Ultra-high molecular weight polyethylene (UHMWPE) fibre has great potential for strengthening structures against impact or blast loads. A quantitative characterization of the mechanical properties of UHMWPE fibres at varying strain rates is necessary to achieve reliable structural design. Quasi-static and high-speed tensile tests were performed to investigate the unidirectional tensile properties of UHMWPE fibre laminates over a wide range of strain rates from 0.0013 to 163.78 s⁻¹. Quasi-static tensile tests of UHMWPE fibre laminates were conducted at thicknesses ranging from 1.76 mm to 5.19 mm. Weibull analysis was conducted to investigate the scatter of the test data. The failure mechanism and modes of the UHMWPE fibre laminates observed during the test are discussed. The test results indicate that the mechanical properties of the UHMWPE fibre laminate are not sensitive to thickness, whereas the strength and the modulus of elasticity increase with strain rate. It is concluded that the distinct failure modes at low and high strain rates partially contribute to the tensile strength of the UHMWPE fibre laminates. A series of empirical formulae for the dynamic increase factor (DIF) of the material strength and modulus of elasticity are also derived for better representation of the effect of strain rate on the mechanical properties of UHMWPE fibre laminates.     

Experimental and numerical investigation of yielding phenomena in a shape memory polymer subjected to cyclic tension at various strain rates

This paper presents experimental and numerical results of a polyurethane shape memory polymer (SMP) subjected to cyclic tensile loading. The goal was to investigate the polymer yielding phenomena based on the effects of thermomechanical coupling. Mechanical characteristics were obtained with a testing machine, whereas the SMP temperature accompanying its deformation process was simultaneously measured in a contactless manner with an infrared camera. The SMP glass transition temperature was approximately 45 °C; therefore, when tested at room temperature, the polymer is rigid and behaves as solid material. The stress and related temperature changes at various strain rates showed how the SMP yield limit evolved in subsequent loading-unloading cycles under various strain rates. A two-phase model of the SMP was applied to describe its mechanical response in cyclic tension. The 3D Finite Element model of a tested specimen was used in simulations. Good agreement between the model predictions and experimental results was observed for the first tension cycle.     

Microstructure evolution during tensile loading histories of a polyurea

The evolution in the hard/soft domain microstructure of an elastomeric‐like polyurea during different tensile loading histories was studied using in situ small‐ and wide‐angle X‐ray scattering (SAXS/WAXS). The nonlinear stress–strain behavior is initially stiff with a rollover yield to a more compliant response; unloading is highly nonlinear showing substantial hysteresis while also exhibiting significant recovery. Reloading reveals a substantially more compliant “softened” behavior and dramatically reduced hysteresis. WAXS peaks monitor characteristic dimensions of regular features within the hard domains; the peak location remains unchanged with tensile deformation indicating no separation of the internal structure within a domain, but the peak intensity becomes anisotropic with deformation evolving in a reversible manner consistent with orientation due to stretch. The SAXS profiles provide information between major hard domains. SAXS peaks are found to shift with tensile loading in a relatively affine manner up to a tensile true strain of ～0.4, which, using a Bragg reduction to aid interpretation, reveals an axial increase and a transverse decrease in interdomain spacings; this evolution is reversible for strains less than ～0.4. Increasing axial strain beyond a true strain of ～0.4 is accompanied by a dramatic, progressive, and irreversible reduction in axial Bragg spacing, indicating a breakdown in the hard domain aggregate network structure. A four‐point pattern is seen to develop during stretching. The breakdown in networked structure during a first load cycle gives a new structure for subsequent load cycles, which is seen to evolve in a reversible manner for strains less than or equal to the prior maximum strain. However, for strains exceeding the prior maximum strain excursion, additional breakdown is found. These SAXS results show that a breakdown in the hard domain aggregate network structure is a governing mechanism for the large dissipation (hysteresis) loops of the first load cycle and are also responsible for the softened reloading response. The absence of structure breakdown during subsequent load cycles corresponds to the substantially reduced hysteresis loops as well as the stable softened behavior. DMA data on pristine and previously deformed samples show a more compliant storage modulus in the predeformed sample, supporting the softened cyclic stress–strain data and the structural breakdown observed in the SAXS; the loss modulus was unchanged with deformation, which correlates with the lossy features measured in DMA with time‐dependent viscosity rather than losses due to structural breakdown. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Irreversible deformation of isotactic polypropylene in the pre-yield regime

In the modeling of the mechanical response of a polymer over a large strain range, the nonlinear viscoelastic and viscoplastic behavior must be considered. For many polymers, nonlinear behavior is observed at low loads, e.g. by a stress-dependence of the creep compliance for stresses above 2 MPa in case of the polypropylene used in this study. Additionally, plastic deformation has been observed at strains below the yield point for several polymers. In this study, the irreversible deformation by cavitation and shear yielding of polypropylene are characterized in the pre-yield regime in uniaxial tensile tests using digital image correlation. The recovery of strain after unloading at a prescribed strain level is measured and used to identify the evolution of the plastic strain during uniaxial tension. An experimental technique for simultaneous determination of the true stress–true strain curve and the degree of stress whitening, which relates to the amount of cavitation, is introduced and the initiation of cavitation is compared to the plastic deformation detected in strain recovery at various temperatures.     

Tensile mechanical properties of basalt fiber reinforced polymer composite under varying strain rates and temperatures

High-strength woven fabrics and polymers are ideal materials for use in structural and aerospace systems. It is very important to characterize their mechanical properties under extreme conditions such as varying temperatures, impact and ballistic loadings. In this present work, the effects of strain rate and temperature on the tensile properties of basalt fiber reinforced polymer (BFRP) were investigated. These composites were fabricated using vacuum assisted resin infusion (VARI). Dynamic tensile tests of BFRP coupons were conducted at strain rates ranging from 19 to 133 s⁻¹ using a servo-hydraulic high-rate testing system. Additionally, effect of temperature ranging from −25 to 100 °C was studied at the strain rate of 19 s⁻¹. The failure behaviors of BFRP were recorded by a Phantom v7.3 high speed camera and analyzed using digital image correlation (DIC). The results showed that tensile strength, toughness and maximum strain increased 45.5%, 17.3% and 12.9%, respectively, as strain rate increased from 19 to 133 s⁻¹. Moreover, tensile strength was independent of varying temperature up to 50 °C but decreased at 100 °C, which may be caused by the softening of epoxy matrix and weakening of interfaces between fibers and matrix when the glass transition temperature was exceeded.     

The effect of annealing on the elastoplastic response of isotactic polypropylene

Four series of tensile loading-unloading tests are performed on isotactic polypropylene in the sub-yield domain of deformations at room temperature. In the first series, injection-molded specimens are used as produced, whereas in the other series the samples are annealed for 24 h at 120, 140 and 160 °C, which covers the low-temperature region and an initial part of the high-temperature region of annealing temperatures. A constitutive model is developed for the elastoplastic behavior of a semicrystalline polymer. The stress-strain relations are determined by five adjustable parameters that are found by fitting the experimental data. The effect of annealing is analyzed on the material constants.     

The Nonlinear Time‐Dependent Response of Semicrystalline Polymers: Correlations Between the Configurational Entropy and the Rate of Rearrangement of Chains

Two series of tensile creep tests are performed on isotactic poly(propylene) in the sub‐yield region of deformations at room temperature. In the first series, injection‐molded specimens are used as produced, whereas in the other series the samples are preloaded (five loading–unloading cycles with the maximal strain 0.01). A constitutive model is derived for the viscoelastic and elastoplastic behavior of semicrystalline polymers. A polymer is treated as an equivalent transient network of chains bridged by junctions. Active chains separate from their junctions and dangling chains merge with the network at random times when they are thermally activated. The network is modelled as an ensemble of meso‐regions (MRs) with various activation energies for detachment of chains from temporary nodes (a distribution function for the activation energies entirely determines the configurational entropy of the ensemble). Rearrangement of chains in the network reflects the viscoelastic response. The elastoplastic behavior is attributed to sliding of junctions with respect to their reference positions and to changes in the distribution of activation energies (driven by fine and coarse slip of lamellar blocks). Stress–strain relations for a semicrystalline polymer are determined by four adjustable parameters that are found by fitting the experimental data. It is demonstrated that the attempt rate for detachment of active chains from their nodes is proportional to the configurational entropy of the ensemble of MRs.     

Studies of craze fibril deformation during fatigue in polystyrene

Small-angle scattering of synchrotron x-ray radiation has been used to study the effects of fatigue on craze fibril microstructure. The results obtained during unloading and reloading during a single cycle have been compared with those predicted by a model of sinusoidally bent fibrils. In addition the total displacement of the craze boundaries was found from the change in the invariant on unloading. The mean fibril diameter D was measured at the maximum tensile strain in each cycle. Over 250 cycles, D increased by at least a factor of 2 from an initial value of 6.5 nm, with most of this change happening in the first few cycles. The increase in D must occur by fibril coalescence, a mechanism that requires that the material in craze fibrils have considerable molecular mobility, even at room temperature, 70°C below the glass transition temperature.     

Loading-unloading of an elastic-plastic adhesive spherical microcontact

A numerical solution is presented for a single load-unload cycle of an adhesive contact between an elastic-plastic sphere and a rigid flat. The interacting forces between the sphere and the flat are obtained through connecting nonlinear spring elements having force-displacement behavior that obeys the Lennard-Jones potential. Kinematic, rather than isotropic, hardening is assumed for the sphere material to account for possible secondary plastification during the unloading. The well-known Tabor parameter and a plasticity parameter are shown to be the two main dimensionless parameters governing the problem. The effects of these two parameters on the load-approach curves, on the plastically deformed sphere profiles, and on the plastic strain fields inside the sphere are presented, showing different modes of separation during the unloading.     

Electrical and mechanical behavior of filled elastomers. I. The effect of strain

Electrical and mechanical property tests have been used to examine the changes in the carbon black network structure that occur in a filled elastomer at large strains in tension and compression. These changes have been examined both in materials that have no previous loading history and in test pieces that have been subjected to a specific known prestrain. When a previously unstrained, filled elastomer specimen is stretched to moderate extensions, the electrical resistivity increases. This is ascribed to the breakdown of the carbon black network structure. At higher tensile extensions, the resistivity decreases. This reduction in the electrical resistivity is attributed to the alignment of the shaped carbon black aggregates under strain. During unloading, the resistivity behavior is different from that during loading, with the final unloaded electrical resistivity being significantly higher than that measured in the unstrained elastomer. This dramatic change in the electrical properties after unloading is in marked contrast to the relatively modest changes observed in the mechanical behavior. After the first cycle, the electrical behavior becomes much more reversible, and this indicates that the bulk of the damage experienced by the carbon black network is developed during the first cycle. After unloading from a large strain, the electrical anisotropy is small, whereas the mechanical anisotropy is more marked. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 2079–2089, 2003     

Effect of strain rate on the mechanical properties of Staphylococcus epidermidis biofilms

The quantification of biofilm mechanical properties can serve as a basis for understanding biofilm resilience and for developing biofilm control strategies. One aspect of tensile testing that is likely to be important for a viscoelastic material such as bacterial biofilm, but unfortunately is often overlooked (i.e., not controlled or reported), is the strain rate used during testing. Thus, we performed tensile testing on intact S. epidermidis biofilms using the microcantilever method at 12 strain rate values ranging over approximately 3 orders of magnitude (0.013-9.07 s(-1)). Ultimate or cohesive strength, elastic modulus, and toughness increased with increasing strain rate and approached a plateau at approximately 1.3 s(-1). Failure strain, on the other hand, did not exhibit any trend with strain rate. Given that the mean values of some parameters increased by as much as 1 order of magnitude over the strain rate range used in this work, we suggest that the strain rate during tensile testing should be carefully controlled and reported to facilitate comparisons among different studies. Furthermore, the quantitative expressions developed in this work that relate mechanical property values with strain rate may be useful for modeling the deformation of bacterial biofilms under applied loads.     

Cyclic stress–strain behavior of the dry polycarbonate craze

Equipment and methods have been developed which allow photomicrographic determination of the stress–strain properties of the individual craze. Serial cyclic tensile tests on polycarbonate crazes are described. Under stress the typical dry polycarbonate craze thickens solely by straining; no adjacent polymer of normal density is converted to craze material. The craze exhibits a yield stress followed by a recoverable flow to roughly 40–50% strain at 6000–8000 psi. On return to zero stress the craze exhibits creep recovery at a decelerating rate. The yield stress and loss factor of each cycle decrease with increasing initial strain and cycles initiating at 50% strain or more show completely Hookean behavior. Creep recovery results in recovery of yield stress and loss factor also. Craze tensile behavior is suggested to be essentially an extension of the craze formation process. Decrease in elastic modulus and yield stress with increasing strain are rationalized in terms of strain-produced decrease in density and resultant increase in stress concentration factor on the microscopic polymer elements of the craze. Polymer surface tension and the large internal specific surface area of the craze are suggested to be important factors in the large creep recovery rates of the craze.     

Tension testing of polycarbonate at high strain rates

Dynamic tensile tests were performed on polycarbonate using a split Hopkinson tension bar (SHTB) system. A prefixed short metal bar was used to generate the incident stress pulse. The shape of the incident pulse was controlled to meet the requirement of the one-dimensional experimental principle of SHTB. The dynamic tensile stress–strain responses of polycarbonate at high strain rates up to a rate of 1750 s⁻¹ were obtained. Experimental results indicate that the tensile behavior of polycarbonate is dependent on the strain rate. Its yield stress and unstable strain all increase with the increased strain rate. The yield behavior was modeled for a wide range of strain rates based on the thermally activated theory. The correlation between the experimental data and the model is good.     

Fatigue fracture of a highly stretchable acrylic elastomer

Dielectric elastomer has been extensively explored in various applications as soft active material. In most applications, dielectric elastomer is subjected to cyclic loading-unloading condition. As a result, a small initial defect in a dielectric elastomer may finally grow to a critical size to induce catastrophic rupture. In this article, we carried out an experimental study of the crack growth in an acrylic dielectric elastomer under cyclic loading-unloading. Pure-shear test specimens were used to measure the relationship between crack growth rate and energy release rate. Such relationship can be simply fit to a power-law. We further used the measured power-law to successfully predict the fatigue lifetime of the acrylic elastomer with an edge crack and subject to simple extension cyclic loading-unloading test.     

Deformation and adhesion of elastomer poly(dimethylsiloxane) colloidal AFM probes

We report on the synthesis and characterization of elastomer colloidal AFM probes. Poly(dimethylsiloxane) microparticles, obtained by water emulsification and cross-linking of viscous prepolymers, are glued to AFM cantilevers and used for contact mechanics investigations on smooth substrates: in detail cyclic loading-unloading experiments are carried on ion-sputtered mica, the deformation rate and dwell time being separately controlled. We analyze load-penetration curves and pull-off forces with models due respectively to Zener; Maugis and Barquins; and Greenwood and Johnson and account for bulk creep, interfacial viscoelasticity, and structural rearrangements at the polymer-substrate interface. A good agreement is found between experiments and theory, with a straightforward estimation of colloidal probes' material parameters. We suggest the use of such probes for novel contact mechanics experiments involving fully reversible deformations at the submicrometer scale.