Micromechanical modeling of the deformation kinetics of semicrystalline polymers

The process of plastic deformation in semicrystalline polymers is complicated due to the operation of a variety of mechanisms at different levels and is strongly dependent on their crystallinity level, the initial underlying microstructure, and the evolution of this structure during deformation. Any macroscopically homogeneous deformation is accommodated by various deformation mechanisms in the heterogeneous microstructure. The objective of this work is to establish a quantitative relation between the microstructure and the mechanical performance of semicrystalline polymers, as characterized by elasto-viscoplastic deformation. In order to do that, a micromechanically based constitutive model is used. The model represents the microstructure as an aggregate of layered composite inclusions, each consisting of a crystalline lamella, which is mechanically coupled to its adjacent amorphous layer. The crystalline phase is modeled as anisotropic elastic with plastic flow governed by crystallographic slip. The amorphous phase is assumed to be isotropic elastic with a rate dependent plastic flow and strain hardening resulting from molecular orientation. To relate the volume-averaged mechanical behavior of each layered composite inclusion to the aggregate of composite inclusions, a hybrid local-global interaction law is used. The concept of a layered composite inclusion as a representative element is extended with a third phase, which is also referred to as the interphase or the rigid-amorphous phase. This phase represents the region between crystalline and amorphous domains, having a somewhat ordered structure and a fixed thickness. The incorporation of the interphase in the composite inclusion model naturally leads to a dependence on the lamellar thickness, i.e. on an internal length scale. This rigid-amorphous phase is particularly relevant for quantitative modeling of the behavior of oriented semicrystalline structures. A comparison with experimental data shows a good prediction with the two-phase model for isotropic material. A critical factor for adding quantitative predictive abilities to the micromechanical model for prediction of the elasto-viscoplastic behavior in semicrystalline polymers is the stress-dependence of the rate of plastic deformation, the slip kinetics, which is the mechanism underlying time-dependent, macroscopic failure. The kinetics of the macroscopic plastic flow strongly depend on the slip kinetics of the individual crystallographic slip systems, accompanied by the yield kinetics of the amorphous domain. To obtain an accurate quantitative prediction, the viscoplastic power law relation, normally used in micromechanical modeling, 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. A double yield phenomenon is observed in the model prediction, and is found to be related to morphological changes during deformation, which induce a change of deformation mechanism. Experimental data on the yield kinetics of polyethylene at different temperatures and strain rates reveals the contribution of two relaxation processes. Further experimental observations on the stress dependence of the time-to-failure show a linear relation in semi-logarithmic plots, with the same slope as that of the yield kinetics. This indicates that the kinetics of failure under applied strain-rate and applied stress are strongly related. To predict failure under both conditions and for different temperatures, the crystallographic slip kinetics and the amorphous yield kinetics were further refined, and the Eyring flow rule was modified by adding a temperature shift function. The creep behavior of polyethylene was then simulated directly using the multi-scale, micromechanical model, predicting the time-to-failure without any additional fitting parameter. To enable the prediction of both tension and compression, a non-Schmid effect is added to the constitutive relation of each slip system. Injection molded or extruded polymers possess a different morphology than isotropic polymers, due to the subjection to shear and elongational flow during processing. Therefore, their plastic deformation and failure behavior are anisotropic. The relation between the initially oriented microstructure and the deformation kinetics of oriented polyethylene tapes is investigated using the multi-scale micromechanical model. The initial orientation distribution for the model is obtained based on wide angle X-ray scattering experiments. Due to the presence of oriented amorphous domains in the drawn samples, the macroscopic plastic flow is predominantly governed by the yield kinetics of the amorphous phase. The necessity of modeling the load angle dependence of the properties of the oriented amorphous domain for an accurate quantitative prediction is discussed. Furthermore, the possibilities for identifying the properties of distinct crystallographic slip systems are investigated

Micromechanical modeling of the deformation kinetics of semicrystalline polymers

The process of plastic deformation in semicrystalline polymers is complicated due to the operation of a variety of mechanisms at different levels and is strongly dependent on their crystallinity level, the initial underlying microstructure, and the evolution of this structure during deformation. Any macroscopically homogeneous deformation is accommodated by various deformation mechanisms in the heterogeneous microstructure. The objective of this work is to establish a quantitative relation between the microstructure and the mechanical performance of semicrystalline polymers, as characterized by elasto-viscoplastic deformation. In order to do that, a micromechanically based constitutive model is used. The model represents the microstructure as an aggregate of layered composite inclusions, each consisting of a crystalline lamella, which is mechanically coupled to its adjacent amorphous layer. The crystalline phase is modeled as anisotropic elastic with plastic flow governed by crystallographic slip. The amorphous phase is assumed to be isotropic elastic with a rate dependent plastic flow and strain hardening resulting from molecular orientation. To relate the volume-averaged mechanical behavior of each layered composite inclusion to the aggregate of composite inclusions, a hybrid local-global interaction law is used. The concept of a layered composite inclusion as a representative element is extended with a third phase, which is also referred to as the interphase or the rigid-amorphous phase. This phase represents the region between crystalline and amorphous domains, having a somewhat ordered structure and a fixed thickness. The incorporation of the interphase in the composite inclusion model naturally leads to a dependence on the lamellar thickness, i.e. on an internal length scale. This rigid-amorphous phase is particularly relevant for quantitative modeling of the behavior of oriented semicrystalline structures. A comparison with experimental data shows a good prediction with the two-phase model for isotropic material. A critical factor for adding quantitative predictive abilities to the micromechanical model for prediction of the elasto-viscoplastic behavior in semicrystalline polymers is the stress-dependence of the rate of plastic deformation, the slip kinetics, which is the mechanism underlying time-dependent, macroscopic failure. The kinetics of the macroscopic plastic flow strongly depend on the slip kinetics of the individual crystallographic slip systems, accompanied by the yield kinetics of the amorphous domain. To obtain an accurate quantitative prediction, the viscoplastic power law relation, normally used in micromechanical modeling, 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. A double yield phenomenon is observed in the model prediction, and is found to be related to morphological changes during deformation, which induce a change of deformation mechanism. Experimental data on the yield kinetics of polyethylene at different temperatures and strain rates reveals the contribution of two relaxation processes. Further experimental observations on the stress dependence of the time-to-failure show a linear relation in semi-logarithmic plots, with the same slope as that of the yield kinetics. This indicates that the kinetics of failure under applied strain-rate and applied stress are strongly related. To predict failure under both conditions and for different temperatures, the crystallographic slip kinetics and the amorphous yield kinetics were further refined, and the Eyring flow rule was modified by adding a temperature shift function. The creep behavior of polyethylene was then simulated directly using the multi-scale, micromechanical model, predicting the time-to-failure without any additional fitting parameter. To enable the prediction of both tension and compression, a non-Schmid effect is added to the constitutive relation of each slip system. Injection molded or extruded polymers possess a different morphology than isotropic polymers, due to the subjection to shear and elongational flow during processing. Therefore, their plastic deformation and failure behavior are anisotropic. The relation between the initially oriented microstructure and the deformation kinetics of oriented polyethylene tapes is investigated using the multi-scale micromechanical model. The initial orientation distribution for the model is obtained based on wide angle X-ray scattering experiments. Due to the presence of oriented amorphous domains in the drawn samples, the macroscopic plastic flow is predominantly governed by the yield kinetics of the amorphous phase. The necessity of modeling the load angle dependence of the properties of the oriented amorphous domain for an accurate quantitative prediction is discussed. Furthermore, the possibilities for identifying the properties of distinct crystallographic slip systems are investigated

Micromechanics of the deformation and failure kinetics of semicrystalline polymers

An elasto-viscoplastic two-phase composite inclusion-based model for the mechanical performance of semicrystalline materials has previously been developed. This research focuses on adding quantitative abilities to the model, in particular for the stress-dependence of the rate of plastic deformation, referred to as the yield kinetics. A key issue in achieving that goal is the description of the rate-dependence of slip along crystallographic planes. The model is used to predict time-to-failure for a range of static loads and temperatures. Application to oriented materials shows a distinct influence of individual slip systems.</p

A micromechanical study on the deformation kinetics of oriented semicrystalline polymers

The mechanical response of extruded and injection molded semicrystalline materials, in which an oriented microstructure is commonly observed, depends on the direction of loading. Plastic deformation and failure are, therefore, both anisotropic. The ability of a micromechanical model, including the characterization of the kinetics of crystallographic slip and amorphous yield, to describe the yield kinetics of oriented high-density polyethylene tapes with different draw ratios is evaluated here. The initial morphology of the material is characterized with wide-angle X-ray diffraction experiments, which evidence a strong alignment of molecular chains with the drawing direction for specimens produced with a large draw ratio. Anisotropic crystal plasticity alone in a two-phase framework proves not able to quantitatively describe the macroscopic mechanical response in the solid state hot drawn samples. Most likely, these deviations are related to process-induced orientation within the amorphous domains. Therefore, the influence of loading angle dependent yield kinetics for the amorphous phase is evaluated, and indeed the description improves considerably. Finally, the possibilities for characterizing the properties of different crystallographic slip systems are discussed

Micromechanical modeling of the elastic properties of semicrystalline polymers: a three-phase approach

The mechanical performance of semicrystalline polymers is strongly dependent on their underlying microstructure, consisting of crystallographic lamellae and amorphous layers.In line with that, semicrystalline polymers have previously been modeled as two and three-phase composites, consisting of a crystalline and amorphous phase and, in case of the three-phase composite, a rigid-amorphous phase between the other two, having a somewhat ordered structure and a constant thickness. In this work, the ability of two-phase and three-phase composite models to predict the elastic modulus of semicrystalline polymers is investigated.The three-phase model incorporates an internal length scale through crystalline lamellar and interphase thicknesses, whereas no length scales are included in the two-phase model. Using linear elastic behavior for the constituent phases, a closed form solution for the average stiffness of the inclusion is obtained. A hybrid inclusion interaction model has been used to compute the effective elastic properties of polyethylene. The model results are compared to experimental data to assess the capabilities of the two- or three-phase composite inclusion model

Micromechanics of semicrystalline polymers: towards quantitative predictions

\u3cp\u3eAn initially qualitative two-phase elasto-viscoplastic micromechanical model for the mechanical performance of semicrystalline materials has previously been developed. In the last decade, a series of extensions to this model have been aimed towards quantitative predictions of the response of semi-crystalline polymers based on their microstructure. These developments included extensive experimental characterization and modelling of the yield kinetics, time-to-failure, creep and thermal shrinkage and expansion. This paper gives an overview of the route from the initially qualitative model to a model that quantitatively captures these complex aspects of the mechanical response of a semicrystalline polymer.\u3c/p\u3