Strain-hardening modulus of cross-linked glassy poly(methyl methacrylate)

The strain hardening modulus, defined as the slope of the increasing stress with strain during large strain uniaxial plastic deformation, was extracted from a recently proposed constitutive model for the finite nonlinear viscoelastic deformation of polymer glasses, and compared to previously published experimental compressive true stress versus true strain data of glassy crosslinked poly(methyl methacrylate) (PMMA). The model, which treats strain hardening predominantly as a viscous process, with only a minor elastic contribution, agrees well with the experimentally observed dependence of the strain hardening modulus on strain rate and crosslink density in PMMA, and, in addition, predicts the well-known decrease of the strain hardening modulus in polymer glasses with temperature. General scaling aspects of continuum modeling of strain hardening behavior in polymer materials are also presented. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1464–1472, 2010     

Latent energy of deformation of bisphenol A polycarbonate

The thermodynamic behavior of poly(bisphenol A carbonate) (PC) during uniaxial cold drawing and the properties of the drawn polymer were examined. Isothermal deformation calorimetric measurements were made during the drawing process. The deformation calorimeter measures heat, work, and internal energy changes for deformation. It was found that PC exhibited nonideal plasticity with approximately 50–80% of the work of deformation dissipated as heat. The remainder of the work of deformation was stored as a latent internal energy change. The value of the internal energy change was dependent on strain rate at 20°C but was not strongly dependent on temperature in the range 20–65°C. Thermomechanical measurements on cold-drawn PC samples demonstrated striking behavior at temperatures far below the glass transition temperature T_g. Stress-temperature experiments showed that the stress increased for uniaxially constrained samples, and this stress increase began at temperatures just above the deformation temperature. Additional experiments indicated that the changes which took place during cold drawing were physical in nature and were thermoreversible. These changes in physical properties are related to those which occur due to physical aging below T_g.     

Athermal simulation of plastic deformation in amorphous solids at constant pressure

An algorithm is introduced for the molecular simulation of constant-pressure plastic deformation in amorphous solids at zero temperature. This allows to directly study the volume changes associated with plastic deformation (dilatancy) in glassy solids. In particular, the dilatancy of polymer glasses is an important aspect of their mechanical behavior. The new method is closely related to Berendsen's barostat, which is widely used for molecular dynamics simulations at constant pressure. The new algorithm is applied to plane strain compression of a binary Lennard-Jones glass. Conditions of constant volume lead to an increase of pressure with strain, and to a concommitant increase in shear stress. At constant (zero) pressure, by contrast, the shear stress remains constant up to the largest strains investigated (ε = 1), while the system density decreases linearly with strain. The linearity of this decrease suggests that each elementary shear relaxation event brings about an increase in volume which is proportional to the amount of shear. In contrast to the stress–strain behavior, the strain-induced structural relaxation, as measured by the self-part of the intermediate structure factor, was found to be the same in both cases. This suggests that the energy barriers that must be overcome for their nucleation continually grow in the case of constant-volume deformation, but remain the same if the deformation is carried out at constant pressure. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2057–2065, 2004     

Effect of morphology on the mechanical and rheo-optical properties of a styrene–butadiene–styrene block copolymer

The mechanical and rheo-optical properties of a styrene–butadiene–styrene block copolymer of a given chemical composition are dependent upon the morphology of the polymer as affected by the solvent system from which a polymer film is cast. Films cast from methyl ethyl ketone and from toluene are compared. Properties found to differ are the stress–strain curve, the birefringence–strain curve, stress relaxation birefringence relaxation, and the dynamic mechanical spectra.     

Anisotropic plasticity and chain orientation in polymer glasses

The anisotropic mechanical response of oriented polymer glasses is studied through simulations with a coarse-grained model. Systems are first oriented by uniaxial compression or tension along an axis. Then the mechanical response to subsequent deformation along the same axis or along a perpendicular axis is measured. As in experiments, the flow stress and strain hardening modulus are both larger when deformation increases the degree of molecular orientation produced by prestrain, and smaller when deformation reduces the degree of orientation. All stress curves for parallel prestrains collapse when plotted against either the total integrated strain or the degree of molecular orientation. Stress curves for perpendicular prestrains can also be collapsed. The stress depends on the degree of strain or molecular orientation along the final deformation axis and is independent of the degree of orientation in the perpendicular plane. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1473–1482, 2010     

Visualization of deformation-induced structural rearrangements in amorphous polymers

A technique is proposed for decorating amorphous polymers: Before the deformation (shrinkage) of an amorphous polymer, its surface is decorated with a thin metal coating. The subsequent deformation is accompanied by surface structure formation, which makes the processes that occur in the polymer visible. The proposed technique makes it possible to visualize and describe the mechanism of transfer of the polymer from the surface into the bulk and vice versa and to obtain direct information about the direction of the actual local stress. The technique makes it possible to obtain information about the topological heterogeneity of rubber networks, to reveal the features of structural rearrangements that occur during the cold rolling of amorphous polymers, and to describe the phenomenon of self-elongation during annealing of the oriented PET. These microscopic data explain the following features of the structural and mechanical behavior of glassy polymers from a unified viewpoint: stress relaxation in a polymer in the elastic (Hookean) region of the stress-strain curve, an increase in stress in a deformed glassy polymer during its isometric annealing below T _g, the low-temperature shrinkage of a deformed polymer glass in the strain range below its yield point, the storage of internal energy in a deformed glassy polymer in the strain range below the yield point, some anomalies of thermophysical properties, and some other features.     

Tensile behavior of Nafion and sulfonated poly(arylene ether sulfone) copolymer membranes and its morphological correlations

The tensile stress–strain behavior of Nafion 117 and sulfonated poly(arylene ether sulfone) copolymer (BPSH35) membranes were explored with respect to the effects of the strain rate, counterion type, molecular weight, and presence of inorganic fillers. The yielding properties of the two films were most affected by the change in the strain rate. The stress–strain curves of Nafion films in acid and salt forms exhibited larger deviations at strains above the yield strain. As the molecular weight of the BPSH35 samples increased, the elongation at break improved significantly. Enhanced mechanical properties were observed for the composite membrane of BPSH35 and zirconium phenylphosphonate (2% w/w) in comparison with its matrix BPSH35 film. The stress‐relaxation behavior of Nafion and BPSH35 membranes was measured at different strain levels and different strain rates. Master curves were constructed in terms of plots of the stress‐relaxation modulus and time on a double‐logarithm scale. A three‐dimensional bundle‐cluster model was proposed to interpret these observations, combining the concepts of elongated polymer aggregates, proton‐conduction channels, and states of water. The rationale focused on the polymer bundle rotation/interphase chain readjustment before yielding and polymer aggregate disentanglements and reorientation after yielding. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 1453–1465, 2006     

Mechanistic model for deformation of polymer nanocomposite melts under large amplitude shear

We report the mechanical response of a model nanocomposite system of poly(styrene) (PS)-silica to large-amplitude oscillatory shear deformations. Nonlinear behavior of PS nanocomposites is discussed with the changes in particle dispersion upon deformation to provide a complete physical picture of their mechanical properties. The elastic stresses for the particle and polymer are resolved by decomposing the total stress into its purely elastic and viscous components for composites at different strain levels within a cycle of deformation. We propose a mechanistic model which captures the deformation of particles and polymer networks at small and large strains, respectively. We show, for the first time, that chain stretching in a polymer nanocomposite obtained in large amplitude oscillatory deformation is in good agreement with the nonlinear chain deformation theory of polymeric networks. © 2013 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2013     

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.     

Structure and properties of nanosized coatings deposited onto polymers

Results of studies aimed at developing a new approach to measuring stress-strain properties of nanosized solids (strength, yield stress, and the value of plastic deformation at uniaxial tension) are generalized. This approach is based on the analysis of the parameters of microrelief arising upon the deformation of polymer films with thin coatings. It is demonstrated for the first time that the stress-strain properties of aluminum coatings deposited onto Lavsan substrates depend on the level of stresses in the substrate, the value of its deformation, and the thickness of the coating. The evolution of these parameters is related to the strain hardening of metal and the effect of nanostructuring of crystalline materials in the range of small thicknesses. When precious metal (Au, Pt) nanosized films are deposited onto polymers by ion-plasma sputtering, in the course of metal deposition, polymer surface layers interact with cold plasma. Stress-strain properties of polymer surface layers modified by plasma are quantitatively estimated for the first time. The model is proposed that makes it possible to take into account the contribution of the properties of precious metal and plasma-modified polymer surface layer to the strength of the coating.     

Strain-Controlled Tensile Deformation Behavior and Relaxation Properties of Isotactic Poly(1-butene) and Its Ethylene Copolymers

The tensile deformation behaviour of poly(1-butene) and two of its ethylene copoloymers was studied at room temperature. This was done by investigating true stress-strain curves at constant strain rates, elastic recovery and stress relaxation properties and in-situ WAXS patterns during the deformation process. As for a series of semicrystalline polymers in previous studies, a strain-controlled deformation behaviour was found. The differential compliance, the recovery properties and the stress relaxation curves changed simultaneously at well-defined points. The strains at which these points occurred along the true stress-strain remained constant for the different samples despite their different percentage crystallinities. The well-defined way in which the different samples respond to external stresses complies with the granular substructure of the crystalline lamellae in a semicrystalline polymer.     

Effects of graded porous structure on local strain distribution under compression in silicone rubber

Silicone rubber samples with gradually changing pore sizes within the range of 70–610 μm are produced using an improved spacer method. The samples are scanned using an X‐ray computed tomography to evaluate their graded structure as compared to uniform rubber. A compressive test reveals that graded porous silicone rubber has characteristic stress–strain curves whose slope changes within a specific strain range depending on the porous structure. Analysis results of local strain based on a digital image correlation of the graded porous silicone rubber under compression demonstrate that the characteristic stress–strain properties are caused by shifts in the main deformation region in the graded structure. © 2019 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2019 , 57, 1033–1042     

Tensile strength of Iβ crystalline cellulose predicted by molecular dynamics simulation

The mechanical properties of Iβ crystalline cellulose are studied using molecular dynamics simulation. A model Iβ crystal is deformed in the three orthogonal directions at three different strain rates. The stress–strain behaviors for each case are analyzed and then used to calculate mechanical properties. The results show that the elastic modulus, Poisson’s ratio, yield stress and strain, and ultimate stress and strain are highly anisotropic. In addition, while the properties that describe the elastic behavior of the material are independent of strain rate, the yield and ultimate properties increase with increasing strain rate. The deformation and failure modes associated with these properties and the relationships between the material’s response to tension and the evolution of the crystal structure are analyzed.     

Comparison of mechanical and molecular measures of mobility during constant strain rate deformation of a PMMA glass

We performed constant strain rate deformation and stress relaxation on a poly(methyl methacrylate) glass at T_g – 19 K, utilizing three strain rates and initiating the stress relaxation over a large range of strain values. Following previous workers, we interpret the initial rate of decay of the stress during the relaxation experiment as a purely mechanical measure of mobility for the system. In our experiments, the mechanical mobility obtained in this manner changes by less than a factor of 3 prior to yield. During these mechanical experiments, we also performed an optical measurement of segmental mobility based on the reorientation of a molecular probe; we observe that the probe mobility increases up to a factor of 100 prior to yield. In the post‐yield regime, in contrast, the mobilities determined mechanically and by probe reorientation are quite similar and show a similar dependence on the strain rate. Dynamic heterogeneity is found to initially decrease during constant strain rate deformation and then remain constant in the post‐yield regime. These combined observations of mechanical mobility, probe mobility, and dynamic heterogeneity present a challenge for theoretical modeling of polymer glass deformation. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 1957–1967     

Analysis of the cyclic tensile behaviour of an elasto-viscoplastic polyamide

The present paper is concerned with the experimental and theoretical investigation of the progressive accumulation of inelastic deformation observed in cyclic tension tests performed on a particular polyamide. The elastic properties are not strongly affected by the strain rate, but the strain hardening induced by the plastic deformation is rate-dependent. Thus, the material behaviour is elasto-viscoplastic rather than viscoelastic or elasto-plastic. For the polymer studied in this paper, the kinematic hardening is much more significant than the isotropic hardening, and a negative plastic strain rate may occur even with a positive stress. The kinematic hardening is strongly dependent, not only on the accumulated plastic strain, but also on the loading rate. An elasto-viscoplastic mechanical model able to describe the cyclic inelastic behaviour for an arbitrary loading history is proposed. All parameters that arise in the theory are identified experimentally. The preliminary theoretical results concerning the modelling of cyclic load-unload tests are in good agreement with the experiments.     

A theory for the drawing of oriented crystalline polymers

The load-elongation behavior during the postneck drawing stage in the deformation of crystalline polymers is shown to be modeled quantitatively by an aligned short-fiber composite in which crystalline fibrils form the reinforcing phase in a matrix of less well-ordered material. Three modes of deformation are distinguished in the model and are shown to correspond to the observed loadelongation relations in polyethylene and polypropylene. The regions are (I) elastic–plastic crystals in an elastic matrix, (II) elastic–plastic crystals in an elastic–plastic matrix, (III) elastic crystals in an elastic–plastic matrix. A requirement of the theory is that the flow stress in the crystals is little affected by temperature whereas that in the matrix falls as the temperature rises. Expressions are given for stress in terms of the applied strain and the relevant parameters of the system: concentration of fibrils, length and diameter of fibrils, and elastic and yield properties of fibrils and matrix.     

Effect of the comonomer content on the mechanical parameters and microhardness values in poly(ethylene‐co‐1‐octadecene) synthesized by a metallocene catalyst

Stress–strain and microhardness measurements were carried out on a series of copolymers of ethylene and 1‐octadecene with different comonomer contents in the corresponding homopolymer of ethylene, synthesized with a metallocene catalyst. The different mechanical properties, deduced from the stress–strain curves (Young's modulus, yield stress, deformation at break, and energy to break) are interpreted in terms of the crystallinity and molecular weight of the samples because these two characteristics show considerable variations with the comonomer content. The microhardness values are explained in terms of these properties, and they are also correlated with Young's moduli and yield stresses deduced from the stress–strain curves. Linear relations are found between microhardness and yield stress and between the logarithm of the microhardness and the logarithm of the elastic modulus. The properties deduced from these lines are compared with literature values. © 2000 John Wiley & Sons, Inc. J Polym Sci B: Polym Phys 39: 277–285, 2001     

Stress–strain behavior in extension of elastomer networks with crosslinks of different lenghts

Stress–strain behavior in extension and the swelling of polymer networks with different lenghts of crosslinks is reported. These networks were prepared by copolymerization of butyl acrylate with different amounts of various difunctional comonomers which yield crosslinks of 4, 7, 10, and 16 bonds in length. The efficiency of the comonomers in crosslinking is low, improving with increasing length of the chain between their unsaturated endgroups. Analysis of a large number of stress–strain data obtained at elongations between 2 and 8% elongation showed that in this deformation range the stress–strain relation based on the statistical theory of elasticity represents the data better than does Hooke's law or the Mooney-Rivlin relation. It was found that the relation between the modulus at small deformations and the swelling ratio of the various samples inindependent of the length of the crosslinks. Also the shapes of the Mooney-Rivlin curves are the same for all networks. Furthermore, the creep behavior of various networks with different crosslink lengths is the same for networks compared at the same elastically effective chain concentration. It is concluded that the lenght of the crosslinks, at least up to 16 bonds, does not affect the elastic response of polymer networks.     

Characterization of the compressive deformation behavior with strain rate effect of low-density polymeric foams

This study investigates the compressive deformation behavior of a low-density polymeric foam at different strain rates. The material tested has micron-sized pores with a closed cell structure. The porosity is about 94%. During a uni-axial compressive test, the macroscopic stress–strain curve indicates a plateau region during plastic deformation. Finite Element Method (FEM) simulation was carried out, in which the yield criterion considered both components of Mises stress and hydrostatic stress. By using the present FEM and experimental data, we established a computational model for the plastic deformation behavior of porous material. To verify our model, several indentation experiments with different indenters (spherical indentation and wedge indentation) were carried out to generate various tri-axial stress states. From the series of experiments and computations, we observed good agreement between the experimental data and that generated by the computational model. In addition, the strain rate effect is examined for a more reliable prediction of plastic deformation. Therefore, the present computational model can predict the plastic deformation behavior (including time-dependent properties) of porous material subjected to uni-axial compression and indentation loadings.