Mechanical Behavior Of Semi-crystalline Polymers Research Articles

Building a phenomenological chain-level understanding of mechanics of semicrystalline polymers: 2. Conceptual

To rationalize the comprehensive phenomenology in Paper 1 (this volume, p. 125878), we present a qualitative description for the mechanical behavior of semicrystalline polymers (SCPs) through a synthesis of prior understandings about the mechanical characteristics of glassy and semicrystalline polymers. Based on the central idea to regard an SCP as a crystalline chain network (CCN), in which a test chain can have crystalline and amorphous strands, we emphasize several key concepts: (a) crystallization determines the structure of the CCN, which is generally weaker than the pre-crystallization chain network in the molten state formed by interchain uncrossability, (b) ductility in SCPs is afforded by a sufficiently robust CCN, and (c) yielding and plastic deformation of SCPs require a successful structural transformation involving shape-change of crystalline phases through appreciable chain pull-out from the crystalline phases without breakdown of the CCN. In other words, it is the CCN that drives ductile SCPs to undergo yielding and subsequent large deformation through massive pull-out of load bearing strands (LBSs), which are the tie and entangling strands. Brittle fracture and lack of drawability occur in those SCPs where the CCN is too weak (due to a sparse population of LBSs) to cause sufficient meltdown of crystalline phases: There are not enough LBSs to undergo pull-out that is necessary for yielding and crystal transformation. Based on these concepts we can explore the processing-structure-property (P–S–P) relationship by demonstrating how pre-deformation in either crystalline or molten state produces more favorable structures for stronger mechanical characteristics.

Building a phenomenological chain-level understanding of mechanics of semicrystalline polymers: 1. Experimental

The current understanding of mechanical behavior of semicrystalline polymers (SCPs) is insufficient even at a qualitative level. Since a disproportional extent of efforts have been made to describe yielding rather than brittle fracture or lack of drawability in SCPs, we have avoided basic questions such as when and why tensile extension of SCPs result in brittle failure. Consequently, it has remained ambiguous just exactly what crystallization does, e.g., whether crystallization favors ductile or brittle mechanical response, what polymer entanglement does in the crystalline state, and exactly how and why tie-strands play an essential role to bring about yielding and ductility in SCPs. The present work (in a sequence of two papers) builds a coherent phenomenological basis to propose a chain-level qualitative framework where answers to these questions start to emerge. We first present extensive data in Paper 1 to (a) show how ductility depends on the state of crystallization, (b) describe a ductile-to-brittle (non-drawable) transition as a function of temperature and drawing rate, including the anomalous temperature and rate dependences, and (c) demonstrate how the structures of SCPs may be affected by pre-deformation to improve ductility and increase tensile strength. While some observations appear familiar, the total phenomenology has never been holistically compiled to depict a comprehensive (qualitative) molecular picture in Paper 2 that elucidates the effect of crystallization and the roles of chain entanglement and tie-strands regarding drawability.

Simultaneous SAXS-WAXS Experiments on Semi-Crystalline Polymers: Example of PA11 and Its Brill Transition

This manuscript of the special issue “Microstructural Evolution and Mechanical Behavior of Semi-Crystalline Polymers” aims to show that Small Angle X-ray Scattering (SAXS) and Wide Angle X-ray Scattering (WAXS) experiments performed simultaneously constitute a unique tool to obtain valuable information on the hierarchical structure of semi-crystalline polymers. These structural quantitative data are needed to model macroscopic properties of polymeric materials, for example their mechanical properties. To illustrate our point, we focus our study on the structure and morphology of polyamide 11. Through a simultaneous SAXS-WAXS experiment, we show that the absence of enthalpic signal in Differential Scanning Calorimetry (DSC) is not synonymous with the absence of structural and morphological evolution with temperature. The case of a thermally activated crystal–crystal transition, the Brill transition, is particularly detailed. Through this SAXS-WAXS study, we show, among other points, and for the first time, that the periodicity of crystalline lamellae (LP) changes at the transition, probably due to a modification of the amorphous phase’s free volume at the Brill transition. We also explain the crucial role of annealing to stabilize polymeric materials that may experience temperature changes over their lifetime. The influence of the annealing on the perfection of crystalline structure, morphology and mechanical behavior is more particularly studied.

The Continuum Approach to the Description of Semi-Crystalline Polymers Deformation Regimes: The Role of Dynamic and Translational Defects.

This paper presents a new approach to describe the mechanical behavior of semi-crystalline polymers, the plastic deformation of which is determined by their two-phase structure. To describe the plastic behavior of semi-crystalline polymers, a two-phase model is used. In the framework of this model, one phase is in a hard (crystalline) state, and the other in a soft (amorphous) state. The two-phase material is modeled by a single-phase homogeneous continuum based on the approximation of the effective medium. It is assumed that two infinitely close material points of the continuum are connected in series by elastic and viscous bonds, which corresponds to the Maxwell model. It is shown that, in this case, the Maxwell continuum is a pseudo-Euclidean space. Generalizing the definition of defects from a three-dimensional space to a four-dimensional pseudo-Euclidean space, we obtained a dynamic system of nonlinear, interrelated equations to describe the behavior of translational-type defects in the solid phase and dynamic defects in the amorphous phase. As an example of an application for these equations, the phenomenon of creep under uniaxial loading is considered. It is shown that the formalism of the proposed two-phase model makes it possible to describe creep phenomenon regularities, which correspond to both the aging theory and the flow theory.

Micro/macro-stress relationship and local stress distribution in polyethylene spherulites upon uniaxial stretching in the small strain domain

Local stress of polyethylene spherulites under uniaxial stretching in small strain domain has been investigated by in-situ wide angle X-ray diffraction (WAXD) in comparison with macroscopic stress. Particular attention is paid to the elastic strain range. The local stress in equatorial and polar regions both increase in absolute value and follow a linear relation versus macroscopic stress. However, local stress turns out to be heterogeneous over the whole spherulites volume. The polar region shows higher local stress than equatorial region. Moreover, local stress along the a and b crystallographic axes in the crystalline lamellae enable determining the local stress triaxiality which is heterogenous. The increase of crystallinity promotes stress distribution heterogeneity throughout the spherulites. The origin of these phenomenon are discussed in terms of crystalline network percolation and effect of amorphous layer that modifies the local mechanical behavior. The present study provides a useful means for achieving the scale transition between the micro and the macro structural levels that is necessary for the modeling of the mechanical behavior of semi-crystalline polymers via micromechanical approaches.

Role of the Intercrystalline Tie Chains Network in the Mechanical Response of Semicrystalline Polymers.

We examine the microscopic origin of the tensile response in semicrystalline polymers by performing large-scale molecular dynamics simulations of various chain lengths. We investigate the microscopic rearrangements of the polymers during tensile deformation and show that the intercrystalline chain connections known as tie chains contribute significantly to the elastic and plastic response. These results suggest that the mechanical behavior of semicrystalline polymers is controlled by two interpenetrated networks of entanglements and tie chains.

A hyperelastic-thermoviscoplastic constitutive model for semi-crystalline polymers: Application to PEEK under dynamic loading conditions

In this work, a hyperelastic-thermoviscoplastic constitutive model including thermomechanical coupling is presented to predict the mechanical behavior of semi-crystalline polymers. The constitutive model is based on the original approach developed by Polanco-Loria and coauthors (2010) and it accounts for: material hardening due to strain rate sensitivity, temperature evolution during the deformation process due to heat generation induced by plastic dissipation, thermal softening and thermal expansion of the material. The parameters of the constitutive model have been identified for polyether-ether-ketone (PEEK) from experimental data published by Rae and coauthors (2007). In order to analyze the predictive capacity of the model under dynamic conditions, the constitutive model has been implemented in a FE code within a large deformation framework to study two different problems: low velocity impact test on PEEK thin plates and dynamic necking on PEEK slender bar. These problems involve large and irreversible deformations, high strain rates and temperature increment due to plastic dissipation. The analysis determines the interplay between strain rate and thermal effects in the material behavior. The constitutive model presented herein reproduces adequately the mechanical behavior of PEEK under different thermal and loading conditions, demonstrating the importance of considering the coupling between temperature and strain rate.

Towards the size estimation of a Representative Elementary Domain in semi-crystalline polymers

Like in any heterogeneous material, predicting the macroscopic mechanical behavior of semi-crystalline polymers from scale transition approaches requires to estimate the size of a Representative Volume Element (RVE). However, no quantitative estimation has been reported so far in the literature for these materials. This study is a step forward, by estimating the minimal domain over which the microscopic strain must be spatially averaged to match the macroscopic strain, in a stretched linear low-density polyethylene. A statistical RVE determination method inspired from the work by Kanit et al. (2006) was applied to strain fields acquired at the spherulitic scale from in-situ Digital Image Correlation in a Scanning Electron Microscope. Results show that the size of a representative domain significantly exceeds the size of a single spherulite. Several spherulites are actually contained, depending on the wanted estimation accuracy and on the number of realizations one is ready to generate.

Modeling of spherulite microstructures in semicrystalline polymers

Semicrystalline polymers are composed of crystalline structures together with amorphous polymer chain networks and therefore they exhibit deformation mechanisms of both crystalline materials and amorphous polymers. One of the most common microstructures observed in semicrystalline polymers is the spherulite microstructure in which crystalline lamellae are embedded in a matrix of amorphous material and grow out from a common central nucleus in radial directions. The mechanical behavior of semicrystalline polymers is strongly dependent on the underlying spherulite microstructure. Therefore, characterization of the deformation of spherulites is very important to understand the mechanical behavior of semicrystalline polymers. In this work, we propose a new FEM-based model for semicrystalline polymers which explicitly discretizes the spherulite microstructure consisting of crystalline and amorphous phases. In the model, a viscoplastic crystal plasticity model is employed for the crystalline phase, whereas 8-chain model is employed for the amorphous phase. The model captures the evolution of inhomogeneous plastic deformation activity in a spherulite microstructure, as well as the important features of the spherulite deformation reported in the literature.

Formulation and implementation of a constitutive model for semicrystalline polymers

The paper outlines a new constitutive model and its numerical implementation for the mechanical behaviour of semicrystalline polymers. Essential for the constitutive model is a homogenization approach that makes use of a representative mesostructure (RMS) and of the micromechanical description of the two characteristic phases of semicrystalline polymers, the amorphous and the crystalline phase. A homogenization approach is used to characterise the macroscopic element by extracting the macroscale characteristics of the material from the results of a microscale boundary value problem. For the microscopic amorphous constitutive model, a new evolution law is introduced for the athermal shear stress to the constitutive model proposed by Miehe et al. (2009), who developed a constitutive formulation for amorphous polymers in the logarithmic strain space. For the microscopic crystalline model, the approach proposed by Simo (1988a), who numerically implemented an algorithm for plasticity for crystalline materials, is transformed into a logarithmic kinematical framework. The modelling capability of the proposed formulation is verified by comparison of numerical simulations to experimental investigations carried out by the Leibniz-Institut für Polymerforschung (IPF) Dresden. The experiments were performed on isotactic polypropylene (iPP) and the mechanical tensile and compression tests were carried out at different temperatures. The model is also used for quasi-static (QS) and dynamic (DY) simulations of an iPP car bumper.

Micromechanical modeling of the deformation kinetics of semicrystalline polymers

AbstractThe mechanical behavior of semicrystalline polymers is strongly dependent on their crystallinity level, the initial underlying microstructure, and the evolution of this structure during deformation. A previously developed micromechanical constitutive model is used to capture the elasto‐viscoplastic deformation and texture evolution in semicrystalline polymers. The model represents the material as an aggregate of two‐phase layered composite inclusions, consisting of crystalline lamellae and amorphous layers. This work focuses on adding quantitative abilities to the multiscale constitutive model, in particular for the stress‐dependence of the rate of plastic deformation, referred to as the slip kinetics. To do that, the previously used viscoplastic power law relation is replaced with an Eyring flow rule. The slip kinetics are then re‐evaluated and characterized using a hybrid numerical/experimental procedure, and the results are validated for uniaxial compression data of HDPE, at various strain rates. A double yield phenomenon is observed in the model prediction. Texture analysis shows that the double yield point in the model is due to morphological changes during deformation, that induce a change of deformation mechanism. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1297–1310, 2011

Characterisation of the mechanical behaviour of semicrystalline polymers under multiaxial loading

Characterisation of the mechanical behaviour of semicrystalline polymers under multiaxial loading

High-temperature mechanical behavior of semi-crystalline polymers and relationship to a rubber-like “relaxed” state

This work addresses the general issue of the mechanical behavior of the confined amorphous phase in rubbery semi-crystalline polymers. The tensile behavior of four semi-crystalline polymers (with various degrees of crystallinity and transition temperatures) was characterized and analyzed at high-temperature (i.e. a few tens degrees below the melting point) and at low strain-rates to try to approach a “relaxed” mechanical behavior. Monotonic loadings followed by different unloading/relaxation/creep stages, and strain-rate jumps experiments were performed on two testing machines equipped with different extensometers. Despite significant differences of micro-structure between the tested materials, a general phenomenon was observed: a non strain-rate sensitive regime was reached both at loading and unloading. However, a “relaxed” equilibrium response cannot account for this regime because of concomitant contradictory features among which (i) the creep and relaxation kinetics which involve the same strain-rates as observed in the non strain-rate sensitive loading regime or (ii) the unusual strain-rate sensitivity observed in strain-rate jump tests. The whole set of experiments has consequences for mechanical modeling. They are discussed as a conclusion of this experimental mechanics work.

A two-phase model for the mechanical behaviour of semicrystalline polymers. Part I: Large strains multiaxial validation on HDPE

Due to their microstructural properties, semicrystalline polymers (SCPs) generally present the ability to undergo large plastic strains. In structure with plastic components, large strains can thus be locally reached, during creep or in crack tip for examples. On the other hand, the stresses state is generally tridimensional. It is consequently important to develop mechanical models able to predict the tridimensional and large strains behaviour of SCPs, in order to design structures. The proposed model consists of an extension to large strains of a model previously proposed for moderate strains [Cangémi, L., Meimon, Y., 2001. A two-phase model for the mechanical behaviour of semicrystalline polymers. Oil Gas Sci. Technol. – Rev. IFP 56 (6), 555–580]. The model is based on a two-phase representation of SCPs at a mesoscopic level. The thermodynamics of porous media permits to introduce a mechanical coupling between the two phases. The main features of SCPs (mean stress dependence, volume change, viscosity, hardening) are described from a specific yield surface and a viscoplastic formalism. A cavities nucleation criterion is also included to predict the dilatant volume strain of SCPs obtained under specific loading conditions. The large strains model is validated for HDPE under uniaxial tension, simple shear, uniaxial compression and plane strain compression conditions, from literature data and experimental data performed in the study.

A two-phase model for the mechanical behaviour of semicrystalline polymers. Part II – Modelling of the time-dependent mechanical behaviour of an isotropic and a highly oriented HDPE grade

This paper presents an application of the model presented in Part I for the prediction of the mechanical response of two semicrystalline polymers. This Part II particularly emphasises the capacity of the model to predict the time-dependent behaviour of semicrystalline polymers, whereas Part I illustrates the potentiality of the model to predict their multiaxial and large strains behaviour. The two studied materials consist of an initially isotropic HDPE, studied up to the beginning of the tensile hardening, and of any highly oriented HDPE bands, so that their mesostructure state can be considered constant in the studied strains domains. This paper shows that the large strains model can be simplify to predict the mechanical behaviour of SCPs, as well isotropic as anisotropic. The model is validated for the two studied HDPE materials under uniaxial tension on the basis of experimental data, which evidence the sensitivity to the strain rate, and the short-time and long-time viscous behaviour.

Modelling effects of degree of crystallinity on mechanical behavior of semicrystalline polymers

Viscoplasticity theory based on overstress (VBO) which is one of the unified state variable theories is extended to account for crystallinity ratio ( ϕ) on mechanical behavior of semicrystalline polymers. The modifications on VBO are done considering the semicrystalline polymeric materials somewhat as a composite material since it consists of amorphous and crystalline phases. Amorphous and crystalline phase resistances are arranged in two different analog models: amorphous stiffness and flow are in parallel and series with crystalline phase. Apart from many existing work in the literature, not only uniaxial loading are modeled but also creep and relaxation behaviors are simulated for a hypothetical material. It is shown that when amorphous and crystalline phase resistances acting in parallel are considered in the model, creep, relaxation and uniaxial loading and unloading behaviors can be simulated well using the modified VBO. In addition, uniaxial compression loading and unloading behavior of highly crosslinked ultra-high molecular weight polyethylene (UHMWPE) and creep behavior of polytetrafluoroethylene (PTFE) with different crystallinity ratios are simulated using the proposed VBO model where amorphous and crystalline phases are parallel. Simulation results are compared to the experimental data by Kurtz et al. (2002) and Sun et al. (2005) [Kurtz, S.M., Villarragaa, M.L., Herra, M.P., Bergström, J.S., Rimnacc, C.M., Edidin, A.A., 2002. Thermomechanical behavior of virgin and highly crosslinked ultra-high molecular weight polyethylene used in total joint replacements. Biomaterials 23, 3681–3697; Sun, H., Cooke, R. S., Bates, W. D., Wynne, K.J., 2005. Supercritical CO 2 processing and annealing of polytetrafluoroethylene (PTFE) and modified PTFE for enhancement of crystallinity and creep resistance. Polymer 46, 8872–8882] respectively and good match with experimental data is obtained.

Extensibility of the Inter-Lamellar Amorphous Layer and the Mechanical Behaviour of Polyethylene

The mechanical behaviour of semicrystalline polymers is dependent upon the property of both the amorphous and crystalline phases and their eventual interactions. In this context, heat shrinkable films have been evidenced as an interesting material model to investigate the influence of the amorphous phase on the mechanical behaviour of semicrystalline polymers, as upon heating these materials only show changes on the extensibility of the amorphous phase (macromolecular conformational state). The effect of the amorphous phase on the mechanical behaviour can therefore be studied independently. In this work are investigated the mechanical properties of a heat shrinkable polyethylene films as processed and after annealing at 60 °C (for 15 min). The morphology of the film before and after the annealing treatment was characterised by 2D-SAXS patterns. The tensile tests were performed at 50 mm/min and room temperature (23 °C) in different directions respectively to the longitudinal film direction, LD (0, 30, 45, 60 and 90º). The results show that the conformational state of the amorphous phase affects the tensile modulus and the deformation capabilities of the films, namely in the transverse machine direction. No influence on the sustained stress level was observed. Furthermore, the essential work of fracture is determined at large extent by the conformational state of the amorphous phase. This study suggests the high importance of the amorphous network on the initial strain levels and on deformation capabilities of the lamellar structure loaded transversely to the crystalline phase orientation.

Modeling morphology evolution and mechanical behavior during thermo-mechanical processing of semi-crystalline polymers

A new model is proposed that combines statistical mechanics and thermodynamic aspects to characterize orientation development, nucleation and growth of crystallites, and chain entanglement slippage with interdependent relationships necessary to accurately correlate and in some cases predict the morphology and mechanical behavior of semi-crystalline polymers during various thermo-mechanical processes in the rubbery state, close to the glass transition temperature. Internal state variables (ISVs) that directly represent the underlying microstructure state are used to characterize polymer morphology and the resulting properties throughout deformation. The model uses fundamental thermodynamic coefficients for polyethylene terephthalate (PET) and is correlated to experimental data at various strain rates and temperatures just above the glass transition temperature. Experimental data are used that measure the stress, amorphous orientation, and crystallinity during uniaxial deformation of PET. The model is found to correlate well to these experimental data.

The use of synchrotron X-ray scattering coupled with in situ mechanical testing for studying deformation and structural change in isotactic polypropylene

The mechanical behaviour of semi-crystalline polymers is greatly influenced by the properties of the crystalline and the amorphous phases. As a result this topic has been the subject of extensive research. However, to date, a comprehensive relationship between the structure and mechanical properties for semi-crystalline polymers has yet to be established. This present study concerns the commissioning of a novel method for in situ data collection during the deformation of polymers. This involves the combination of three different techniques into a single experiment, namely tensile testing, synchrotron radiation wide angle X-ray scattering, and optical microscopy. For this current investigation, three isotactic polypropylene samples have been studied, produced using different thermal treatments. This enables the influence of thermal treatment on the mechanical properties and crystallographic structure to be assessed. The results indicate that tensile properties are influenced by thermal treatment via the relative fraction of β-phase material in the sample. As the temperature increases at which thermal treatment takes place, iPP ductility decreases due to the greater rigidity of the increasing α-phase content. Differences in crystal strain between the different iPP crystal phases are also observed although the reasons for such differences remain unclear.

Stability analysis of the permanent shiplock slopes of the Three Gorges Project

The paper outlines a new constitutive model and its numerical implementation for the mechanical behaviour of semicrystalline polymers. Essential for the constitutive model is a homogenization approach that makes use of a representative mesostructure (RMS) and of the micromechanical description of the two characteristic phases of semicrystalline polymers, the amorphous and the crystalline phase. A homogenization approach is used to characterise the macroscopic element by extracting the macroscale characteristics of the material from the results of a microscale boundary value problem. For the microscopic amorphous constitutive model, a new evolution law is introduced for the athermal shear stress to the constitutive model proposed by Miehe et al. (2009), who developed a constitutive formulation for amorphous polymers in the logarithmic strain space. For the microscopic crystalline model, the approach proposed by Simo (1988a), who numerically implemented an algorithm for plasticity for crystalline materials, is transformed into a logarithmic kinematical framework. The modelling capability of the proposed formulation is verified by comparison of numerical simulations to experimental investigations carried out by the Leibniz-Institut für Polymerforschung (IPF) Dresden. The experiments were performed on isotactic polypropylene (iPP) and the mechanical tensile and compression tests were carried out at different temperatures. The model is also used for quasi-static (QS) and dynamic (DY) simulations of an iPP car bumper.