Yield conditions for deformation of amorphous polymer glasses

Tensile Properties and Fracture Mechanism of Thermal Spraying Polyurea

In this study, polyurea was experimentally tested under various spraying temperatures and pressures. The number of holes and the pore size produced after the tensile fracture of the polyurea were counted to illustrate the effect of the various spraying temperatures and pressures on the performance of the polyurea. The tensile characteristics of polyurea were greatly influenced by the spraying temperatures and pressures, according to the experimental findings and statistical analysis. The polyurea tensile performance was best when the spraying pressure was 17.25 MPa with a spraying temperature of 70 °C. The fracture mechanism was illustrated by the silver streaking phenomenon generated during the tensile stretching process. The fracture energy was absorbed by the fracture holes and pores during silver streaking, thus creating the huge gap in tensile properties.

Universal Strain Energy-Mediated Dynamic Porosity in Physically Networked Elastomers and Their Applications

Mechanical and physical properties of porous polymers are highly dependent on the arrangement of their internal pores, which once synthesized are widely considered static. However, here we introduce an unconventional dynamic porosity strategy in physically networked elastomer polymers, irrespective of their chemistry. This strategy allows for an omnidirectional and reversible reconfiguration of porosity in response to applied mechanical deformations, even at ambient conditions. In particular, the normal contact pressure between human fingers (just 0.62 MPa) applied on thin elastomer films results in a permanent reversion of the pores to a denser and more solid state. The porous-to-solid transition leads to a 3 order of magnitude reduction in pore density and up to a 22% relative volumetric shrinkage of the films, resulting in an opaque-to-transparent transition (OTT) that acts as a visual indication of porosity state (porous vs nonporous). It is shown that the pore reversion pressure onset is dependent on the average pore-to-pore distance that is controllable through process-specific parameters. Furthermore, the porosity transition is reversible for multiple cycles when the through-plane compression activation is coupled with an in-plane stretch (ε = 700%). A strain energy-mediated thermodynamic model is successfully implemented to confirm the effects of mechanical deformations on pore reversion and generation. Finally, applications of the newfound dynamic porosity concept are exploited for pressure indication, on-demand modulation of materials' mechanical and thermal characteristics, and flexible photomasks.

Development of dissociative force field for all-atomistic molecular dynamics calculation of fracture of polymers

A dissociative force field for all-atomistic molecular dynamics calculations has been developed to investigate impact fracture of polymers accompanying dissociation of chemical bonds of polymer main chain. Energy of dimer molecules was evaluated as a function of both bond-length b and bond-angle θ by CASPT2 calculations, whose quality is enough to describe dissociation of chemical bonds. Because we found that the bond dissociation energy D decreases with increasing bond-angle, we employed the Morse-type function V_Bond (b, θ) = {D - V_Angle (θ)}[1 - exp{-α(b - b₀ ) - β(b - b₀ )² }] where a quartic function V_Angle (θ) = k₁ (θ - θ₀ ) + k₂ (θ - θ₀ )²  + k₃ (θ - θ₀ )³  + k₄ (θ - θ₀ )⁴ . This function reproduced well the CASPT2 potential energy surface in a wide range of b and θ. The parameters have been obtained for four popular glassy polymers, polyethylene, poly(methyl methacrylate), poly(styrene), and polycarbonate. © 2019 Wiley Periodicals, Inc.

Tuning cavitation and crazing in polymer nanocomposite glasses containing bimodal grafted nanoparticles at the nanoparticle/polymer interface

The mechanical properties of polymer nanocomposites containing bimodal grafted nanoparticles can be tuned at the nanoparticle/polymer interface using different graft chain types.

Nonmonotonic dependence of polymer-glass mechanical response on chain bending stiffness

We investigate the mechanical properties of amorphous polymers by means of coarse-grained simulations and nonaffine lattice dynamics theory. A small increase of polymer chain bending stiffness leads first to softening of the material, while hardening happens only upon further strengthening of the backbones. This nonmonotonic variation of the storage modulus G^{'} with bending stiffness is caused by a competition between additional resistance to deformation offered by stiffer backbones and decreased density of the material due to a necessary decrease in monomer-monomer coordination. This counterintuitive finding suggests that the strength of polymer glasses may in some circumstances be enhanced by softening the bending of constituent chains.

Mechanical properties and state of miscibility in poly(racD,L-lactide-co-glycolide)/(L-lactide-co-ε-caprolactone) blends

Polymers based on lactic acid (PLA) are a very promising category of biopolymers. As they are multi-stimuli responsive, can, in many ways, positively interact with the host, stimulating the innate reparative machinery of the human body. Since biopolymers for medical applications are subject to restrictive regulations, blending stands out as an effective method for obtaining tailored properties within a reduced time to market if compared to synthesis. Hence, in this study a set of PDLGA/PLCL blends was obtained by means of thermoplastic techniques and then further characterized. Evaluation techniques include GPC, NMR, DSC, tensile testing and SEM. Although mixtures proved to be immiscible, a full range of tensile properties was achieved. Observation of the surfaces of fracture provided visual evidence of the deformation mechanisms that occurred during the tensile tests which in the end led to failure. Interpretation of the thermal events based on molecular characterization parameters revealed phase separation, crystallization and plasticisation mechanisms that are relevant to any potential applications based on mechanical performance and shape memory behaviour.

Mechanisms of Contact, Adhesion, and Failure of Metallic Nanoasperities in the Presence of Adsorbates: Toward Conductive Contact Design

The properties of contacting interfaces are strongly affected not only by the bulk and surface properties of contacting materials but also by the ubiquitous presence of adsorbed contaminants. Here, we focus on the properties of single asperity contacts in the presence of adsorbates within a molecular dynamics description of metallic asperity normal contact and a parametric description of adsorbate properties. A platinum-platinum asperity contact is modeled with adsorbed oligomers with variable properties. This system is particularly tailored to the context of nanoelectromechanical system (NEMS) contact switches, but the results are generally relevant to metal-metal asperity contacts in nonpristine conditions. Even though mechanical forces can displace adsorbate out of the contact region, increasing the adsorbate layer thickness and/or adsorbate/metal adhesion makes it more difficult for metal asperity/metal surface contact to occur, thereby lowering the electrical contact conductance. Contact separation is a competition between plastic necking in the asperity or decohesion at the asperity/substrate interface. The mechanism which operates at a lower tensile stress dominates. Necking dominates when the adsorbate/metal adhesion is strong and/or the adsorbate layer thickness is small. In broad terms, necking implies larger asperity deformation and mechanical work, as compared with decohesion. Optimal NEMS switch performance requires substantial contact conductance and minimal asperity deformation; these results indicate that these goals can be achieved by balancing the quantity of adsorbates and their adhesion to the metal surface.

Physical modelling of failure in composites

Structural integrity of composite materials is governed by failure mechanisms that initiate at the scale of the microstructure. The local stress fields evolve with the progression of the failure mechanisms. Within the full span from initiation to criticality of the failure mechanisms, the governing length scales in a fibre-reinforced composite change from the fibre size to the characteristic fibre-architecture sizes, and eventually to a structural size, depending on the composite configuration and structural geometry as well as the imposed loading environment. Thus, a physical modelling of failure in composites must necessarily be of multi-scale nature, although not always with the same hierarchy for each failure mode. With this background, the paper examines the currently available main composite failure theories to assess their ability to capture the essential features of failure. A case is made for an alternative in the form of physical modelling and its skeleton is constructed based on physical observations and systematic analysis of the basic failure modes and associated stress fields and energy balances. This article is part of the themed issue 'Multiscale modelling of the structural integrity of composite materials'.

Strain localization in glassy polymers under cylindrical confinement

Although the origin of ductility in crystalline materials is well understood through the motion of dislocations and defects, a similar framework for understanding deformation in amorphous materials remains elusive. In particular, the difference in the mechanical response for small-molecule amorphous solids, such as organic glasses that are typically brittle, and polymer glasses, which are frequently very tough, has not been systematically explored. Here, we employ molecular dynamics simulations to investigate the mechanical response of model glassy polymers confined to a nanoscopic pillar under tensile deformation. We vary the chain length, cooling rate for forming the glass, and the deformation rate and investigate the changes in the mechanical response. We find that samples that are cooled at a slower rate and deformed at a slower rate are more prone to localization of the strain response, or shear banding. Interestingly, this effect is independent of chain length over the range of parameters we have investigated so far, and we believe this is the first direct observation of shear banding in deformed polymer glasses under cylindrical confinement. Finally, by using the isoconfigurational ensemble approach, we provide evidence that the location where the shear band forms is due to structural features that are frozen in place during sample preparation.

Coarse-grained molecular dynamics simulations of the tensile behavior of a thermosetting polymer

Using a previously developed coarse-grained model, we conducted large-scale (∼ 85 × 85 × 85 nm(3)) molecular dynamics simulations of uniaxial-strain deformation to study the tensile behavior of an epoxy molding compound, epoxy phenol novolacs (EPN) bisphenol A (BPA). Under the uniaxial-strain deformation, the material is found to exhibit cavity nucleation and growth, followed by stretching of the ligaments separated by the cavities, until the ultimate failure through ligament scissions. The nucleation sites of cavities are rather random and the subsequent cavity growth accounts for much (87%) of the volumetric change during the uniaxial-strain deformation. Ultimate failure of the materials occurs when the cavity volume fraction reaches ∼ 60%. During the entire deformation process, polymer strands in the network are continuously extended to their linear states and broken in the postyielding strain hardening stage. When most of the strands are stretched to their taut configurations, rapid scission of a large number of strands occurs within a small strain increment, which eventually leads to fracture. Finally, through extensive numerical simulations of various loading conditions in addition to uniaxial strain, we find that yielding of the EPN-BPA can be described by the pressure-modified von Mises yield criterion.

Capillary adhesion at the nanometer scale

Molecular dynamics simulations are used to study the capillary adhesion from a nonvolatile liquid meniscus between a spherical tip and a flat substrate. The atomic structure of the tip, the tip radius, the contact angles of the liquid on the two surfaces, and the volume of the liquid bridge are varied. The capillary force between the tip and substrate is calculated as a function of their separation h. The force agrees with continuum predictions based on macroscopic theory for h down to ∼5 to 10 nm. At smaller h, the force tends to be less attractive than predicted and has strong oscillations. This oscillatory component of the capillary force is completely missed in the macroscopic theory, which only includes contributions from the surface tension around the circumference of the meniscus and the pressure difference over the cross section of the meniscus. The oscillation is found to be due to molecular layering of the liquid confined in the narrow gap between the tip and substrate. This effect is most pronounced for large tip radii and/or smooth surfaces. The other two components considered by the macroscopic theory are also identified. The surface tension term, as well as the meniscus shape, is accurately described by the macroscopic theory for h down to ∼1 nm, but the capillary pressure term is always more positive than the corresponding continuum result. This shift in the capillary pressure reduces the average adhesion by a factor as large as 2 from its continuum value and is found to be due to an anisotropy in the pressure tensor. The component in the plane of the substrate is consistent with the capillary pressure predicted by the macroscopic theory (i.e., the Young-Laplace equation), but the normal pressure that determines the capillary force is always more positive than the continuum counterpart.

Biaxial normal strength behavior in the axial-transverse plane for human trabecular bone--effects of bone volume fraction, microarchitecture, and anisotropy

The biaxial failure behavior of the human trabecular bone, which has potential relevance both for fall and gait loading conditions, is not well understood, particularly for low-density bone, which can display considerable mechanical anisotropy. Addressing this issue, we investigated the biaxial normal strength behavior and the underlying failure mechanisms for human trabecular bone displaying a wide range of bone volume fraction (0.06-0.34) and elastic anisotropy. Micro-computed tomography (CT)-based nonlinear finite element analysis was used to simulate biaxial failure in 15 specimens (5 mm cubes), spanning the complete biaxial normal stress failure space in the axial-transverse plane. The specimens, treated as approximately transversely isotropic, were loaded in the principal material orientation. We found that the biaxial stress yield surface was well characterized by the superposition of two ellipses--one each for yield failure in the longitudinal and transverse loading directions--and the size, shape, and orientation of which depended on bone volume fraction and elastic anisotropy. However, when normalized by the uniaxial tensile and compressive strengths in the longitudinal and transverse directions, all of which depended on bone volume fraction, microarchitecture, and mechanical anisotropy, the resulting normalized biaxial strength behavior was well described by a single pair of (longitudinal and transverse) ellipses, with little interspecimen variation. Taken together, these results indicate that the role of bone volume fraction, microarchitecture, and mechanical anisotropy is mostly accounted for in determining the uniaxial strength behavior and the effect of these parameters on the axial-transverse biaxial normal strength behavior per se is minor.

Analysis of local properties during a scratch test on a polymeric surface using molecular dynamics simulations

This work demonstrates a possible route to connect a particle (chain) based understanding with continuum mechanical questions about contact mechanics. The bond orientation, chain conformation and stress field of a polymer film were analyzed during scratch tests (tangential contact) using a molecular dynamics (MD) simulation approach. Scratch tests with a conical tip at constant scratching velocity were simulated on linear amorphous polymer surfaces at various temperatures and roughnesses of the tip and for various interactions between the tip and the particles of the polymer chains. The second Legendre polynomial (computed for small domains around the tip) gave the bond orientation inside the polymer film during sliding of the tip. The gyration tensor (layer-resolved in the direction of the polymer film thickness) provided information about the conformation of the polymer chains. These results allowed us to argue in favor of Briscoe's hypothesis (thin film sheared vs. "bulk" compressive behavior) concerning the friction properties of the polymer surfaces. Finally, the first stress measurements of the virial stress tensor (in sub-boxes placed in the MD cell) revealed a complex combination between compressive hydrostatic pressure and shear stress, which may be interpreted as a complex sheared domain at the interface.

Mechanisms of crazing in glassy polymers revealed by molecular dynamics simulations

Mechanisms leading to initiation of crazing type failure in a glassy polymer are not clearly understood. This is mainly due to the difficulty in characterizing the stress state and polymer configuration sufficiently locally at the craze initiation site. Using molecular dynamics simulations, we have now been able to access this information and have shown that the local heterogeneous deformation leads to craze initiation in glassy polymers. We found that zones of high plastic activity are constrained by their neighborhood and become unstable, initiating crazing from these sites. Furthermore, based on the constant flow stresses observed in the unstable zones, we conclude that microcavitation is the essential local deformation mode to trigger crazing in glassy polymers. Our results demonstrate the basic difference in the local deformation mode as well as the conditions that lead to either shear-yielding or crazing type failures in glassy polymers. We anticipate our paper to help in devising a new criterion for craze initiation that not only considers the stress state, but also considers local deformation heterogeneities that form the necessary condition for crazing in glassy polymers.

Mechanical behavior of linear amorphous polymers: comparison between molecular dynamics and finite-element simulations

This paper studies the rheology of weakly entangled polymer melts and films in the glassy domain and near the rubbery domain using two different methods: molecular dynamics (MD) and finite element (FE) simulations. In a first step, the uniaxial mechanical behavior of a bulk polymer sample is studied by means of particle-based MD simulations. The results are in good agreement with experimental data, and mechanical properties may be computed from the simulations. This uniaxial mechanical behavior is then implemented in FE simulations using an elasto-viscoelasto-viscoplastic constitutive law in a continuum mechanics (CM) approach. In a second step, the mechanical response of a polymer film during an indentation test is modeled with the MD method and with the FE simulations using the same constitutive law. Good agreement is found between the MD and CM results. This work provides evidence in favor of using MD simulations to investigate the local physics of contact mechanics, since the volume elements studied are representative and thus contain enough information about the microstructure of the polymer model, while surface phenomena (adhesion and surface tension) are naturally included in the MD approach.

Molecular simulation of the frictional behavior of polymer-on-polymer sliding

Molecular simulations of the sliding processes of polymer-on-polymer systems were performed to investigate the surface and subsurface deformations and how these affect tribological characteristics of nanometer-scale polymer films. It is shown that a very severe deformation is localized to a band of material about 2.5 nm thick at the interface of the polymer surfaces. Outside of this band, the polymer films experience a uniform shear strain that reaches a finite steady-state value of close to 100%. Only after the polymer films have achieved this steady-state shear strain do the contacting surfaces of the films show significant relative slippage over each other. Because severe deformation is limited to a localized band much thinner than the polymeric films, the thickness of the deformation band is envisaged to be independent of the film thickness and hence frictional forces are expected to be independent of the thickness of the polymer films. A strong dependency of friction on interfacial adhesion, surface roughness, and the shear modulus of the sliding system was observed. Although the simulations showed that frictional forces increase linearly with contact pressure, adhesive forces contribute significantly to the overall friction and must therefore be accounted for in nanometer-scale friction. It is also shown that the coefficient of friction is lower for lower-density polymers as well as for polymers with higher molecular weights.

Contact and friction of nanoasperities: effects of adsorbed monolayers

Molecular dynamics simulations are used to study contact between a rigid, nonadhesive, and spherical tip with radius of order 30 nm and a flat elastic substrate covered with a fluid monolayer of adsorbed chain molecules. Previous studies of bare surfaces showed that the atomic scale deviations from a sphere that are present on any tip constructed from discrete atoms lead to significant deviations from continuum theory and dramatic variability in friction forces. Introducing an adsorbed monolayer leads to larger deviations from continuum theory but decreases the variations between tips with different atomic structure. Although the film is fluid, it remains in the contact and behaves qualitatively like a thin elastic coating except for certain tips at high loads. Measures of the contact area based on the moments or outer limits of the pressure distribution and on counting contacting atoms are compared. The number of tip atoms making contact during a time interval Deltat grows as a power of Deltat when the film is present and as the logarithm of Deltat for bare surfaces. Friction is measured by displacing the tip at a constant velocity or pulling the tip with a spring. Both static and kinetic friction rise linearly with load at small loads. Transitions in the state of the film lead to nonlinear behavior at large loads. The friction is less clearly correlated with contact area than load.

From macroscopic yield criteria to atomic stresses in polymer glasses

The relationship between macroscopic shear yield criteria and local stress distributions in deformed polymer glasses is investigated via molecular dynamics simulations on different scales of coarse-graining. Macroscopic shear stresses at the yield point obey a pressure-modified von Mises (pmvM) criterion for many different loading conditions and strain rates. Average local stresses in small volume elements obey the same yield criterion for volumes containing approx. 100 atoms or more. Qualitatively different behavior is observed on smaller scales: the average octahedral atomic shear stress has a simple linear relationship to hydrostatic pressure regardless of macroscopic stress state and failure mode. Local plastic events are identified through a threshold in the mean-squared nonaffine displacement and compared to the local stress state. We find that the pmvM criterion only predicts local yield events when stress and displacements are averaged over at least 100 atoms. By contrast, macroscopic shear yield criteria appear to lose their ability to predict plastic activity on the atomic scale.

Fracture in glassy polymers: a molecular modeling perspective

Over the past 25 years, molecular modeling and simulations have provided important insights into the physics of deformation and fracture of glassy polymers. This review presents an overview of key results discussed in the context of experimentally observed polymer behavior. Both atomistic and coarse-grained polymer models have been used in different deformation protocols to study elastic properties, shear yielding, creep, physical aging, strain hardening and crazing. Simulations reproduce most of the macroscopic features of plasticity in polymer glasses such as stress-strain relations and creep response, and reveal information about the underlying atomistic processes. Trends of the shear yield stress with loading conditions, temperature and strain rate, and the atomistic dynamics under load have been systematically explored. Most polymers undergo physical aging, which leads to a history-dependent mechanical response. Simulations of strain hardening and crazing demonstrate the nature of polymer entanglements in the glassy state and the role of local plasticity and provide insight into the origin of fracture toughness of amorphous polymers.

Local elasticity map and plasticity in a model Lennard-Jones glass

In this work we calculate the local elastic moduli in a weakly polydispersed two-dimensional Lennard-Jones glass undergoing a quasistatic shear deformation at zero temperature. The numerical method uses coarse-grained microscopic expressions for the strain, displacement, and stress fields. This method allows us to calculate the local elasticity tensor and to quantify the deviation from linear elasticity (local Hooke's law) at different coarse-graining scales. From the results a clear picture emerges of an amorphous material with strongly spatially heterogeneous elastic moduli that simultaneously satisfies Hooke's law at scales larger than a characteristic length scale of the order of five interatomic distances. At this scale, the glass appears as a composite material composed of a rigid scaffolding and of soft zones. Only recently calculated in nonhomogeneous materials, the local elastic structure plays a crucial role in the elastoplastic response of the amorphous material. For a small macroscopic shear strain, the structures associated with the nonaffine displacement field appear directly related to the spatial structure of the elastic moduli. Moreover, for a larger macroscopic shear strain we show that zones of low shear modulus concentrate most of the strain in the form of plastic rearrangements. The spatiotemporal evolution of this local elasticity map and its connection with long term dynamical heterogeneity as well as with the plasticity in the material is quantified. The possibility to use this local parameter as a predictor of subsequent local plastic activity is also discussed.

Mechanical rejuvenation and overaging in the soft glassy rheology model

Mechanical rejuvenation and overaging of glasses is investigated through stochastic simulations of the soft glassy rheology (SGR) model. Strain- and stress-controlled deformation cycles for a wide range of loading conditions are analyzed and compared to molecular dynamics simulations of a model polymer glass. Results indicate that deformation causes predominantly rejuvenation, whereas overaging occurs only at very low temperatures, small strains, and for high initial energy states. Although the creep compliance in the SGR model exhibits full aging independent of applied load, large stresses in the nonlinear creep regime cause configurational changes leading to rejuvenation of the relaxation time spectrum probed after a stress cycle. During recovery, however, the rejuvenated state rapidly returns to the original aging trajectory due to collective relaxations of the internal strain.

Strain hardening of polymer glasses: entanglements, energetics, and plasticity

Simulations are used to examine the microscopic origins of strain hardening in polymer glasses. While stress-strain curves for a wide range of temperature can be fit to the functional form predicted by entropic network models, many other results are fundamentally inconsistent with the physical picture underlying these models. Stresses are too large to be entropic and have the wrong trend with temperature. The most dramatic hardening at large strains reflects increases in energy as chains are pulled taut between entanglements rather than a change in entropy. A weak entropic stress is only observed in shape recovery of deformed samples when heated above the glass transition. While short chains do not form an entangled network, they exhibit partial shape recovery, orientation, and strain hardening. Stresses for all chain lengths collapse when plotted against a microscopic measure of chain stretching rather than the macroscopic stretch. The thermal contribution to the stress is directly proportional to the rate of plasticity as measured by breaking and reforming of interchain bonds. These observations suggest that the correct microscopic theory of strain hardening should be based on glassy state physics rather than rubber elasticity.

Simulations of aging and plastic deformation in polymer glasses

We study the effect of physical aging on the mechanical properties of a model polymer glass using molecular dynamics simulations. The creep compliance is determined simultaneously with the structural relaxation under a constant uniaxial load below yield at constant temperature. The model successfully captures universal features found experimentally in polymer glasses, including signatures of mechanical rejuvenation. We analyze microscopic relaxation time scales and show that they exhibit the same aging characteristics as the macroscopic creep compliance. In addition, our model indicates that the entire distribution of relaxation times scales identically with age. Despite large changes in mobility, we observe comparatively little structural change except for a weak logarithmic increase in the degree of short-range order that may be correlated with an observed decrease in aging with increasing load.