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     

Does the strain hardening modulus of glassy polymers scale with the flow stress?

Using a generic coarse‐grained bead‐spring model, Hoy and Robbins reproduced important experimental observations on strain hardening, specifically the generally observed Gaussian strain hardening response and its dependence on network density and temperature. Moreover, their simulation results showed that the strain hardening response at different strain rates collapses to a single curve when scaled to the value of the flow stress, a phenomenon that has not yet been verified experimentally. In the present study, the proposed scaling law is experimentally investigated on a variety of polymer glasses: poly(methyl methacrylate), poly(phenylene ether), polycarbonate, polystyrene, and poly(ethylene terephthalate)‐glycol. For these polymers, true stress–strain curves in uniaxial compression were collected over a range of strain rates and temperatures and scaled to the flow stress. It was found that, generally, the curves do not collapse on a mastercurve. In all cases, the strain hardening modulus is observed to increase linearly, but not proportionally to the flow stress. The experimental data, therefore, unambiguously demonstrate that the proposed scaling law does not apply within the range of temperature and strain rate covered in this study. © 2008 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 46: 2475–2481, 2008     

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     

Effect of homopolymer solubilization on triblock gel structure and mechanical response

The linear modulus, swelling behavior, and high strain response of a set of well-characterized model triblock gels were investigated to understand the effect of homopolymer solubilized within the micelle core on gel structure and mechanical properties. Structural parameters were obtained from small-angle X-ray scattering (SAXS) as well as from self-consistent field theory (SCFT) calculations. Experimental results are compared with Neo-Hookean and exponentially strain hardening models for gel behavior and rigid filler effects are discussed. The main conclusion is that the addition of homopolymer to the micelle core increases the chain stretching in both the core and coronal blocks. The total extension of a chain for a given external load is fixed by its length; however, the initial prestretch imparted to the chain due to micellization changes with the size of the micelle core and can greatly reduce the amount of extension observed for a given external force. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1395–1408, 2010     

Effect of chain entanglements on plastic deformation behavior of ultra‐high molecular weight polyethylene

Samples of ultra‐high molecular weight polyethylene, in which the chain topology within the amorphous component was altered using two‐stage processing, including crystallization at high pressure in the first step, were produced and their deformation behavior in the plane‐strain compression was studied. Deformation and recovery experiments demonstrated that the state of the molecular network governed by entanglement density is one of the primary parameters controlling the response of the material on the imposed strain, especially at moderate and high strains. Any change in the concentration of entanglements markedly influences the shape of the true stress–true strain curve. The strain hardening modulus decreases while the onset of strain hardening increases with a decrease of the entanglement density within the amorphous component. Density of entanglements also influences the amount of rubber‐like recoverable deformation and permanent plastic flow. In material of the reduced concentration of entanglements permanent flow appears easier and sets in earlier than in the material with a higher entanglement density, becoming a favorable deformation mechanism at moderate strains. As a result, strong strain hardening is postponed to higher strain when compared with the samples of equilibrium entanglement density. In the samples of an increased entanglement density the molecular network becomes stiffer, with a reduced ability of strain induced disentangling of chains. Consequently, there is a less permanent flow and strain hardening begins earlier than in the reference material of an unaltered chain topology. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 276–285, 2010     

Effect of nanoscale diamondoids on the thermomechanical and morphological behaviors of polypropylene and polycarbonate

Nanoscale MolecularDiamond products (various diamondoid materials), obtained from petrochemical feedstocks, have been investigated as additives for polypropylene and polycarbonate. Three of the homologues of this family (diamantane, triamantane, and the [121]tetramantane isomer) have marginal effects on the thermal and mechanical properties of nonpolar/semicrystalline polypropylene. Mixtures of methylated tetramantane nanofillers also increase the stress–strain behavior of polypropylene composites without significantly impacting their glass transition temperatures. The addition of the selected diamondoids to amorphous/moderately polar polycarbonate increases the polymer tensile modulus significantly with marginal increases in the yield stress. The effects of the selected diamondoids on the thermal stability, crystallinity, and optical properties of polypropylene and polycarbonate are also reported. The results for the mechanical properties show that the selected diamondoids behave as plasticizers in polypropylene, whereas in polycarbonate, they act as antiplasticizers without adversely affecting the optical clarity. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1077–1089, 2007     

Deformation induced evolution of mobility in PMMA

The stress relaxation response in the glassy state just below T_g was measured for poly(methylmethacrylate) following application of constant strain rate uniaxial tensile deformation at various locations on the stress–strain curve, including the yield and post‐yield region. The macroscopic mobility was determined from analysis of the relaxation response. Up to a factor of 3 decrease in relaxation time was observed with the fastest relaxation occurring in the post‐yield softening region. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2010     

Strain hardening of high density polyethylene

The introduction of true stress strain measurements, at constant strain rate, has promoted the development of empirical or semiempirical models for large deformations in thermoplastics. One such theory, which proposes that the post yield deformation process can be represented by equations derived from the theories of rubber elasticity, has been successfully applied to several glassy polymers. Unexpectedly, it can also model the post yield deformation of many different grades of polyethylene, even when rubber theory is employed in the simplest Gaussian form. Strain hardening is then represented by the single strain hardening coefficient Gp. Examples are given of this equation, which can be modified to give the true engineering or nominal stress σ_n and then be differentiated to give dσ_n/dλ = Gp ? Y₀ / λ² + 2Gp / λ³, where Y₀ is the yield stress and λ the extension ratio. Negative values of this differential then predict the onset of necking in tension and positive values stabilization of the neck. The relation of Gp to molecular weight is then discussed using literature measurements for polyethylenes of differing molecular weight and similar molecular weight distributions. When these results are then plotted, a strong dependency of Gp on molecular weight is observed. Some implications of these measurements are then considered. © 2007 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 45: 1090–1099, 2007     

Effect of ionic additives on deformation behavior of bisphenol a polycarbonate

The deformation behavior of bisphenol A polycarbonate containing only a small amount of oligoionomeric additives in the range of a few parts per hundred parts of resin was examined. The impact strength of polycarbonate markedly decreased as the content of additive increased, and brittle fracture of polycarbonate was observed in tensile tests when the concentration of additive was above 2.5 phr. The ductile‐to‐brittle transition that was determined using a comparison of the critical shear yield stress and the critical craze stress appeared to exist in the range of 2.5–3.5 phr of additive. The measured entanglement density was also found to decrease significantly with the addition of a few parts per hundred parts of resin of additives, and the change of the dominant deformation mechanism from ductile to brittle failure was recognized as a result of the change of the entanglement density of polycarbonate. Therefore, it was concluded that the presence of a small amount of ionomeric additives caused the loss of entanglement density that induced transition of the deformation mechanism of polycarbonate from ductile to brittle failure and led to the corresponding deterioration of impact strength. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 39: 2635–2643, 2001     

Relationship between fracture toughness and intrinsic deformation parameters in isotropic and flow‐oriented linear low‐density polyethylene

The fracture toughness of isotropic and flow‐oriented linear low‐density polyethylene (LLDPE) is evaluated by the Essential Work of Fracture (EWF) concept, with a special setup of CCD camera to monitor the process of deformation. Allowing for the molecular orientation, flow‐oriented sample, prepared via melt extrusion drawing, is stretched parallel (oriented‐0°) and perpendicular (oriented‐90°) to its original melt extrusion drawing direction, respectively. The obtained values of specific EFW w_e are 34.6, 10.2, and 4.2 N/mm for the oriented‐0°, isotropic and oriented‐90° sample, respectively. With knowledge of intrinsic deformation parameters deduced from uniaxial tensile tests, moreover, a relationship between specific EFW w_e the ratio of true yield stress to strain hardening modulus σ_ty/G is well established. It means that the fracture toughness of polyethylene is determined by both crystalline and amorphous parts, rather than by one of them. Moreover, the true yield stress seems to be nondecisive factors determining the fracture toughness of polyethylene. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 2880–2887, 2006     

Shear band formation and mode II fracture of polymeric glasses

Mode I and II fracture studies were performed from quasistatic to low velocity impact rates on polymethyl methacrylate (PMMA) and polycarbonate (PC). Mode II tests used an angled double‐edge notched specimen loaded in compression. The shear banding response of PMMA is shown to be highly sensitive to rate, with diffuse shear bands forming at low rates and sharp distinct shear bands forming at high rates. As the rate increases, shear deformation becomes more localized to the point where Mode II fracture occurs. PC is much less rate dependent and stable shear band propagation is observed over the range of rates studied with lesser amounts of localization. A new theory is formulated relating orientation in a shear band to intrinsic material properties obtained from true‐stress true‐strain tests. In a qualitative sense the theory predicts the high rate sensitivity of PMMA. A kinematic limit for orientation within a shear band is also derived based on entanglement network parameters. Mode II fracture in PMMA is shown to occur at this kinematic limit. For the case of PC, the maximum impact rates were not high enough to reach the kinematic limit. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2011     

Cross deformation and stress relaxation of biaxially oriented polystyrene films

When a biaxially oriented polystyrene film was stretched along one direction and subsequently stretched along the perpendicular direction, the film showed enhanced ductility with pronounced yield softening and extended strain hardening. In the forward deformation, at least two types of shear bands were observed. The bands at the early stages of yielding did not seem to contribute to the reduction of thickness. They were approximately 200 μm thick and had an intersection angle of approximately 120°. The bands developed in the later stages contributed to the thickness reduction. These bands were smaller and possessed an intersection of approximately 90°. In the cross deformation, new shear bands developed that were likely related to the reverse shearing of the existing bands. Stress relaxation showed a power‐law relationship between the stress rate and relaxation time. The internal stress of the cross deformation was significantly (ca. 3 times) lower than that of the forward deformation at the same strain. The enhancement in ductility may be attributed to the lowering of internal stress during the cross deformation. The internal stress increased with the applied stress and strain. Fracture occurred when the internal stress reached a certain level, about 57–68 MPa for deformation along both directions and approximately 44–47% of the final applied stress. © 2003 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 41: 687–700, 2003     

Strain hardening of polymer glasses: Effect of entanglement density,temperature, and rate

The strain hardening behavior of model polymer glasses is studied with simulations over a wide range of entanglement densities, temperatures, strain rates, and chain lengths. Entangled polymers deform affinely at scales larger than the entanglement length as assumed in entropic network models of strain hardening. The dependence of strain hardening on strain and entanglement density is also consistent with these models, but the temperature dependence has the opposite trend. The dependence on temperature, rate, and interaction strength can instead be understood as reflecting changes in the flow stress. Microscopic analysis of local rearrangements and the primitive paths between entanglements is used to test models of strain hardening. © 2006 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 44: 3487–3500, 2006     

Neck propagation in polyethylene

Intrinsic true stress–true strain response was evaluated at room temperature for three linear polyethylene samples deformed in conventional tensile tests. It was observed that high crystallinity is associated with a low rate of strain hardening that results in a sharp neck and a large drop in nominal stress. The maximum and minimum deformation loads are accounted for by Considère's analysis of neck initiation and stabilization, respectively. Following stabilization, neck propagation occurs at a load or nominal stress that is lower than the yield stress. The jump analysis of Ericksen and Hutchinson/Neale predicts steady state neck propagation stresses that are in very good (ca. 10%) agreement with experiment. Although the jump analysis is done in terms of uniaxial stress, the actual value of the propagation stress is established by the triaxial stress state in the neck shoulders. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2081–2091, 2004     

Theoretical implications of the elastic modulus discontinuity in rubber networks

The existence of a discontinuity in the modulus of rubber as the strain transitions from compression to extension is strongly suggested by multiple experiments. Classical rubber elasticity theories, however, do not admit such behavior. Here, we investigate a modification of the assumptions of classical elasticity theory to reconcile this discrepancy. We present an analysis of the consequences of assuming that chain forces are nonzero only for chain extension relative to the unstrained state, in contrast to the classical elasticity theory, which assumes that the chain force is directly proportional to the chain end‐to‐end distance (an entropic spring). Assuming an affine transformation of the network node coordinates, we derive two modulus discontinuity factors between compression and extension: D₁, based on the differing number of network chains being extended and D₂, based on the average differential chain extension. The discontinuities arise due to geometric effects, inherent in the affine transformation between compressive and extensive strains. We find that D₁, the ratio of the numbers of participating chains (compressive/extensive = 1.37), suffices to account for the experimentally observed modulus discontinuity in natural rubber of 1.34. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1795–1798, 2010     

Physical aging and deformation kinetics of polycarbonate

Considering the current view that physical aging of glasses results in an increase of activation barriers to plastic deformation, it is surprising that, until now, no influence of physical aging was observed experimentally on the temperature dependence of plastic deformation in polymeric glasses. This study evaluates why such an influence has not been found, and it is shown that detailed analysis of a set of uniaxial compression data on polycarbonate (PC) at different strain rates and temperatures leads to the conclusion that a significant influence indeed exists. As a consequence, the Eyring activation energy depends on the aging history of the material. These experimental observations are rationalized in terms of a simple physical interpretation of the aging phenomenon. The article also contains a discussion of the apparent deaging of amorphous polymers induced by large‐strain plastic deformation. This discussion is of key importance here, because this study compares yield stresses of aged PC with those of mechanically deaged, or rejuvenated, PC. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012     

Prediction of yield and long‐term failure of oriented polypropylene: Kinetics and anisotropy

The time‐dependent yield and failure behavior of off‐axis loaded uniaxially oriented polypropylene tape is investigated. The yield and failure behavior is described with an anisotropic viscoplastic model. A viscoplastic flow rule is used with an equivalent stress, based on Hill's anisotropic yield criterion, and the Eyring flow theory combined with a critical equivalent strain definition. This model is based on factorization of the rate and draw ratio dependence and is capable of quantitatively predicting the rate, angle and draw ratio dependence of the yield stress as well as time‐to‐failure in various off‐axis tensile loading conditions characterized solely from the transverse direction. © 2009 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 47: 2026–2035, 2009     

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.     

Rejuvenation of PLLA: Effect of plastic deformation and orientation on physical ageing in poly(l‐lactic acid) films

Poly(l ‐lactic acid) (PLLA) is a bio‐degradable polyester which exhibits brittle behaviour due to relatively fast physical ageing of the amorphous phase. This work describes the effects of thermal rejuvenation and molecular orientation of the amorphous phase on this physical ageing process. Uniaxial compression testing showed that physical ageing of the amorphous phase increases the yield stress and the associated strain softening response, both contributing to the observed embrittlement of PLLA in tension. Molecular orientation at constant crystallinity was applied by uniaxial and biaxial plastic deformation just above the glass transition temperature, up to plastic strains of 200% to avoid strain‐induced crystallisation. Using stress‐relaxation experiments combined with tensile testing, both as a function of ageing time, it is shown that both uniaxial and biaxial plastic deformation in excess of 150% plastic strain, decelerates and possibly prohibits the physical ageing process. The oriented monofilaments and films have improved mechanical properties such as stiffness, strength and strain‐to‐break, which were not affected by physical ageing during the whole testing period (40 days). In addition, plastic deformation to higher draw ratios and/or higher temperatures strongly enhanced crystallinity and resulted in PLLA monofilaments and films that also exhibited tough behaviour, not affected by physical ageing. © 2016 Wiley Periodicals, Inc. J. Polym. Sci., Part B: Polym. Phys. 2016 , 54, 2233–2244