Deformation Of Semicrystalline Polymers Research Articles

Micromechanical modeling of the effects of crystal content on the visco-hyperelastic-viscoplastic behavior and fracture of semi-crystalline polymers

In this work, we present a novel physically based visco-hyperelastic-viscoplastic micromechanical constitutive model, which establishes a link between the evolution of the macromolecular network properties to the mechanical and fracture behavior of variable-crystallinity semi-crystalline polymers. Unlike previous micromechanical constitutive models that were only time independent, we propose a time-dependent scheme. It employs the computational effective eight-chain model for micro-macro transition while assuming a composite structure for the polymer. Thus, an innovative approach that couples the deformation and damage of individual polymer chains is developed. The proposed constitutive framework assumes that the stress developed through the deformation of semi-crystalline polymers is the sum of a macromolecular network and an intermolecular part. The macromolecular part accounts for the conformational change associated with Kuhn segments reorientation and the bond potential associated with the deformation of the bonds between Kuhn segments. Meanwhile, the intermolecular part accounts for the deformation of the crystalline and the amorphous phases. The constitutive equations are integrated using a mixed explicit/implicit integration algorithm. To validate and calibrate our model, we utilize uniaxial tensile experimental data obtained from three different polyethylene materials with varying crystallinity levels and different strain rates. We propose a robust calibration procedure, ensuring the identification of a single set of parameters that remain independent of crystal content and strain rate. Finally, we assess the model's predictive capabilities in predicting the mechanical behavior and fracture at different strain rates for variable-crystallinity polyethylene is evaluated. This comprehensive approach enhances our understanding and predictive capacity in modeling the intricate mechanical response up to fracture of semi-crystalline polymers under diverse conditions.

The retardation effects of lamellar slip or/and chain slip on void initiation during uniaxial stretching of oriented iPP

Cavitation is frequently encountered during the deformation of semi-crystalline polymers. Although abundant works have been performed to reveal the cavitation behavior in detail, the relationship between void formation and the plastic deformation of crystalline phase is still unclear. In this work, by in-situ synchrotron X-ray scattering, the void formation and the slip process in crystalline phase during uniaxial stretching of oriented isotactic polypropylene (iPP) were investigated. Results proved clearly that lamellae slip or/and chain slip presents a retardation effect on void formation. As the Deviation Angle (DA, defined as the angle between stretching direction and lamellae normal) was 0°, voids were initiated at a Hencky strain (εH) of 0.04 and the longitude direction of voids was perpendicular to lamellae normal. Meanwhile, no slip process happened when voids were induced. As DA was 15°, lamellae slip took place once the stretching was started and voids were formed at εH of 0.09. When DA was further enlarged to 30° and 45°, both lamellae slip and chain slip could be found as voids were induced. The εH of voids formation were 0.29 and 0.31, respectively. Interestingly, it is worth noting that as DA was increased from 0° to 45°, although the orientation degree of voids was decreased, the longitude direction of voids stayed perpendicular to the normal of lamellae. When DA was enlarged further to 90°, voids were formed at εH of 0.1 and the longitude direction of voids coincided with lamellae normal. Additionally, neither lamellae slip nor chain slip existed once voids appeared. Combining the value of micro-strain of lamellae stacks and crystal lattice, it is proposed that voids were formed either in the amorphous phase on the normal side of lamellae (0° ≤ DA ≤ 45°) or in the amorphous phase on the lateral side of lamellae (DA = 90°).

Double Yielding in Deformation of Semicrystalline Polymers

Double Yielding in Deformation of Semicrystalline Polymers

Microbuckling Instability and the Second Yield during the Deformation of Semicrystalline Polyethylene.

Deformation instabilities, such as microbuckling or lamellar fragmentation due to slip localization, play a very important role in the deformation of semicrystalline polymers, although it still not well explored. Such instabilities often appear necessary to modify the deformation path and facilitate strain accommodation in an energy-minimizing manner. In this work, microbuckling instability was investigated using partially oriented, injection-molded (IM) samples of high-density polyethylene, deformed by a plane-strain compression. Deformed samples were probed by SEM, X-ray (small- and wide-angle X-ray scattering: SAXS, WAXS), and differential scanning calorimetry (DSC). It was found that microbuckling instability, followed quickly by the formation of lamellar kinks, occurred in high-density polyethylene (HDPE) at a true strain of about e = 0.3–0.4, mainly in those lamellar stacks which were initially oriented parallel to the compression direction. This phenomenon was observed with scanning electron microscopy, especially in the oriented skin layers of IM specimens, where a chevron morphology resulting from lamellae microbuckling/kinking was evidenced. Macroscopically, this instability manifested as the so-called “second macroscopic yield” in the form of a hump in the true stress–true strain curve. Microbuckling instability can have a profound effect on the subsequent stages of the deformation process, as well as the resulting structure. This is particularly important in deforming well-oriented lamellar structures—e.g., in drawing pre-oriented films of a semicrystalline polymer, a process commonly used in many technologies.

Double Yielding in Deformation of Semicrystalline Polymers

AbstractDifferent semicrystalline polymers including poly(l‐lactic acid), poly(ethylene terephthalate), syndiotactic polystyrene, and polyamide 12 are studied in terms of their mechanical response to uniaxial compression deformation. Apparent decoupling of yielding of amorphous and crystalline phases is identified as separate peaks in the stress–strain curve in the vicinity of the glass transition temperature. The same feature is also observed for the uniaxial extension of predrawn semicrystalline poly(ethylene terephthalate). It is indicated that in absence of a strong amorphous phase a semicrystalline polymer is unable to yield and undergo plastic deformation and it fails in a brittle manner in the uniaxial compression. Treating a semicrystalline polymer as a composite of amorphous and crystalline phases, putting emphasis on the crucial role of amorphous phase in acting as connectors between crystalline domains and indicating that the yielding of amorphous phase is a prerequisite for yielding of crystalline phase, work toward a better understanding of the mechanical properties of semicrystalline polymers at the molecular level is done.

Analysis of Mullins effect in polyethylene using ultrasonic guided waves

Abstarct Small strain deformations below yielding can cause plastic deformation in semicrystalline polymers by a process similar to what is described for filled rubber-like materials known as the Mullins effect. Inter-lamellae chains contribute predominantly in deformations at this level, and the residual plastic strain can be attributed to permanent damage to the tie chains, affecting the long-term mechanical resistance of a molded part. With little detectable alteration of the polymer crystallinity at this early onset of plastic deformation, the primary characterization method applied to date is cyclic tensile loading, which provides information of stress-softening by monitoring the unloading path or relaxed stress behavior. An alternative method for monitoring the development of Mullins effect is proposed that can examine a molded part by using selected modes based on ultrasonic guided waves analysis. The technique was examined to determine if it could follow this effect induced by cyclic strain-controlled tensile deformations since it does not require sample preparation and could ultimately be applied while a part was in-service. Results for different polyethylene grades agree in trend with relaxed stress values over four cycles for tests of increasing applied tensile strain, demonstrated by an increase in the attenuation of ultrasonic guided waves. The correlation reveals a good promise in applying this method to structural health monitoring of plastic parts, while in use, to follow the initiation and progress of early service damage.

Deformation of semicrystalline polymers – the contribution of crystalline and amorphous phases

The plastic deformation process of semicrystalline polymers and the micromechanisms involved are discussed. The particular attention is paid to the dependence of deformation on structure and mutual influence of deformation of crystalline and amorphous components. Deformation of a semicrystalline polymer appears a complex series of continuous processes, involving mostly crystallographic deformation mechanisms operating in the crystalline phase. However, a very important role in that sequence is played by the deformation of amorphous interlamellar layers, partially reversible on unloading, which produces not only the high orientation of amorphous component but also influences deeply and supports the deformation of crystalline phase since crystalline lamellae and amorphous interlamellar layers, intimately connected through covalent bonds of chains crossing the interface, can deform only simultaneously and consistently. In particular, an influence of the topology of the amorphous phase, including the density of the molecular network of entangled chains and number of chains connecting adjacent crystalline and amorphous layers, on deformation instabilities of crystalline component in polyethylene are discussed. The induced instabilities of crystallographic slip lead to formation of lamellar kinks and frequently to an extensive fragmentation of lamellae. These transformations of crystalline structure together with restructurization of amorphous phase at high strains influence deeply the formation of the final highly oriented structure of the deformed semicrystalline polymer.

Study on Modeling of Inelastic Deformation of Semi-crystalline Polymer based on Kinetics of Molecular Chain

Study on Modeling of Inelastic Deformation of Semi-crystalline Polymer based on Kinetics of Molecular Chain

Micromechanics of semicrystalline polymers: Yield kinetics and long‐term failure

AbstractThe 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 underlying 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. To do that, a micromechanically based constitutive model is used. The model describes the material as an aggregate of two‐phase layered composite inclusions, consisting of crystalline lamellae and amorphous layers. The starting point for adding quantitative abilities to the model, in particular for the yield kinetics, is formed by experimental observations on both the yield kinetics and the time‐to‐failure of polyethylene at different temperatures, which reveal the contribution of two relaxation processes. To predict the thermo‐rheologically complex short‐term and long‐term failure behavior, the crystallographic slip kinetics and the amorphous yield kinetics are re‐evaluated, and the Eyring flow rule is modified by adding a temperature shift function. To enable the prediction of both tension and compression, a non‐Schmid effect is added to the constitutive relation of each slip system. The creep behavior of polyethylene is then simulated directly using the multiscale, micromechanical model, predicting the time‐to‐failure, controlled by plastic deformation. © 2012 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys, 2012

Plasticity/damage coupling in semi-crystalline polymers prior to yielding: Micromechanisms and damage law identification

Abstract This work addresses the question of the intimate coupling of plastic and damaging processes during the deformation of semi-crystalline polymers at small strains. The evolution of the spherulitic structure in the pre-yield strain range under tensile testing is investigated by atomic force microscopy for three semi-crystalline polymers, namely polycaprolactone, poly(1-butene) and polyamide 6. These materials have different spherulite size, crystallinity index and lamella thickness, and different glass transition temperature of the amorphous phase. Strain-induced damage is clearly evidenced through the gradual loss of elastic properties upon cyclic tensile tests, since the early stage of stretching. In parallel, volume strain appears to be about nil up to the yield point for the three polymers. AFM reveals that fragmentation of the crystalline lamellae occurs well before the yield strain at room temperature, starting about the core region of the spherulites and extending towards the periphery, for all polymers. This is claimed as evidence that lamella fragmentation is a basic mechanism of damage without significant cavitation at low strain. An approach of damage modeling is carried out via preliminary assessment of the viscoelastic contribution from low strain dynamic mechanical analysis using a generalized Maxwell model. It is shown that computing the viscoelastic contribution in the strain range up to yielding, in the assumption of linearity, fairly account for the loading-unloading hysteresis of the tensile cycles. A phenomenological plasticity/damage coupling law is established from the elastic modulus drop with increasing plastic strain, both assessed from the “relaxed” tensile cycles. The same kind of law is shown to apply for the three polymers. A physical meaning to the phenomenological law is proposed via a simple model of fiber rupture in single-fiber-reinforced composite.

312 デジタル画像相関法を用いた微小領域における結晶性高分子材料の不均一変形の評価(OS3.計算力学に貢献する実験的アプローチ(3),OS・一般セッション講演)

312 デジタル画像相関法を用いた微小領域における結晶性高分子材料の不均一変形の評価(OS3.計算力学に貢献する実験的アプローチ(3),OS・一般セッション講演)

Computational Evaluation of Elasto-Viscoplastic Deformation and Strength of Rubber Blended Semi-crystalline Polymer

In order to clarify the elasto-viscoplastic deformation behavior and strength of rubber blended semi-crystalline polymer, micro- to mesoscopic mechanical behavior was modeled by using large deformation finite element homogenization method. In this model, dimension of mesostructure is identified by the volume fraction of interface region around the rubber particles. The effects of strain rate and the size of rubber particles on the mesoscopic true stress—strain relation, strain rate distribution in mesoscopic area, and change in mesoscopic morphology with deformation are investigated by numerical simulation of uniaxial tensile deformation of semi-crystalline polymer with nonuniformly distributed rubber particles. A series of computational simulations clarified that mechanical behavior of blend polymer is strongly affected by the size of rubber particles. Mesoscopic true stress—strain relationship shows softening for blend polymer with large rubber particles, which is closely related to the distribution of strain rate on mesoscopic scale. When the rubber particles are large, local strain rate is highly concentrated in the ligament area between adjacent rubber particles, while it distributes in larger area of semi-crystalline polymer matrix in case of small rubber particles. The difference in these localized deformation leads to characteristic change in the size and shape of rubber particles with straining. Nonuniform deformation in mesoscopic area caused by heterogeneous rubber particle distribution is emphasized by high strain rate and large rubber particles. Furthermore, maximum mean stress generated in semi-crystalline polymer matrix is very high when the size of rubber particles is smaller than or ligament thickness is larger than a specific value. The specific thickness corresponds to the critical value for brittle-ductile transition of rubber blended semi-crystalline polymer obtained by impact test.

A07 結晶性高分子材料の引張り試験における局所変形分布の連続評価(OS5 材料の変形・破壊の計測・解析と損傷評価II)

A07 結晶性高分子材料の引張り試験における局所変形分布の連続評価(OS5 材料の変形・破壊の計測・解析と損傷評価II)

Deformation of the lamellar structure in semi-crystalline polymers studied by computer simulations

Abstract Yield in a semi-crystalline polymer involves the disruption of the crystalline phase in an irreversible deformation process. In a semi-crystalline polymer, the crystalline lamellar regions are bridged together by inter-lamellar amorphous layers, which act as a loading transfer medium. The deformation of both phases is, therefore, to some extent inter-related. In this work we adopted a continuous mechanic approach (neglecting atomic/molecular interactions) of the lamellar deformation of semi-crystalline polymers in the sense that we simulated the mechanical response of a lamellar structure (two lamellae interconnected by amorphous regions) in a finite element analysis. The use of computer simulations allows studying independently the effect of each relevant morphological parameter on the mechanical response. Several simulations were performed considering isolated variations of the following morphological parameters: i) mechanical behaviour of the amorphous material; ii) thickness of the crystalline regions; iii) length of the amorphous regions; iv) number of amorphous regions connected with a crystalline lamella; v) relative angle between the crystalline and the amorphous regions; vi) mode of loading (tension and compression). The thickness of the crystalline lamellae is evidenced as the most significant factor affecting the tensile response of the lamellar structure, followed by the mechanical behaviour of the amorphous phase. The connection angle between amorphous and crystalline regions and the number of amorphous regions bridging adjacent crystalline lamellae play only a minor role. The length of the amorphous regions has a negligible influence. As expected, the lamellar structure shows also distinct behaviours under distinct loading modes, tensile loading showing the highest stresses.

Deformation of lamellar structures: Simultaneous small‐ and wide‐angle X‐ray scattering studies of polyamide‐6

AbstractStructural changes during tensile deformation in semicrystalline polymers are studied by the analysis of both small‐ and wide‐angle X‐ray scattering data from polyamide‐6 fibers. The strain in the lamellar spacing is about the same as or higher than the fiber strain, suggesting that fiber elongation occurs by the deformation of the lamellar stack rather than slippage of the fibrils, especially during initial stages of elongation. The modulus of the lamellar structure is approximately 5 GN/m2, and this is close to the fiber modulus, which is only 2–3% of the crystal modulus. Fiber modulus is, therefore, determined by the lamellar structure as much as by the interfibrillar oriented chain segments. The four‐point small‐angle X‐ray scattering pattern in the relaxed fiber transforms reversibly into a two‐point pattern under strain. The structures that correspond to these two patterns, the bistable states of the lamellae, coexist until fiber breakage. The structure that gives rise to the two‐point pattern determines the ultimate strength of the fiber. Despite the small crystalline strain in the fiber direction, it is possible to follow the almost fully reversible changes in the orientation, size, and unit cell of the lamellar crystals. It is proposed that the appearance of the two‐point pattern, the decrease in the lateral crystallite size, and the increase in the stack diameter are due to tilting of the lamellar surface caused by large‐scale reversible strain in the interlamellar amorphous regions. This tilt is accomplished by slippage of the hydrogen‐bonded sheets along the chain axis. © 2002 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 40: 691–705, 2002

On the micromechanisms of plastic deformation in semicrystalline polymers

Many different molecular processes that cause plastic deformation in polymers can be investigated by transmission electron microscopy (TEM). A short review of those deformation mechanisms is given in this paper using model morphologies and correlating them to the corresponding mechanical behavior.

Rate Dependent Deformation of Semi-Crystalline Polypropylene Near Room Temperature

We examine the strain rate dependent, large plastic deformation in isotropic semi-crystalline polypropylene at room temperature. Constant strain rate uniaxial compression tests on cylindrical polypropylene specimens show very little true strain softening under quasi-static conditions. At high strain rates very large amounts (38 percent) of apparent strain softening accompanied by temperature rises are recorded. We examine the capability of a recently proposed constitutive model of plastic deformation in semi-crystalline polymers to predict this behavior. We neglect the contribution of the amorphous phase to the plastic deformation response and include the effects of adiabatic heating at high strain rates. Attention is focused on the ability to predict rate dependent yielding, strain softening, strain hardening, and adiabatic temperature rises with this approach. Comparison of simulations and experimental results show good agreement and provide insight into the merits of using a polycrystalline modeling assumption versus incorporating the amorphous contribution. Discrepancies between experiments and model predictions are explained in terms of expectations associated with neglecting the amorphous deformation.

Twinning as a Fundamental Process in Polymer Crystal Orientation

Abstract During a deformation experiment the chain molecules are orientated. The mechanisms of chains orientating producing the crystal orientation differ from orientating of chains within the amorphous phase. Some of them may be active. Twinning processes changing the c-axis direction within the crystallites are possible. They rotate the crystal lattice and change the shape of crystals. This explains easily numerous observed properties previously described in literature. Twinning modes of the orthorhombic and the monoclinic crystal modification of polyethylene, which are believed to be involved, are discussed. Twinning processes observed macroscopically by deforming single crystals of poly(diacetylene), will be of universal importance during the deformation of semicrystalline polymers.

Relationships between mechanical properties and microhardness of polyethylenes

AbstractThe values of the elastic modulus (E) and the yield stress (Y) and the shape of the strain‐stress curves of different polyethylenes have been related to the microhardness (MH) of these materials, considering the roles that the crystalline, amorphous, and interfacial regions play in the deformation of semicrystalline polymers. Linear relations between microhardness and degree of crystallinity, (1 – λ)d, and between the logarithms of E and MH have been found. The variations of the parameters 100Y/E and σmin/Y (σmin is the relative minimum value of the nominal stress for elongations above the yield point) as a function of (1–λ)d follow different trends for linear and branched polyethylenes. Moreover, it has been found that the ratio MH/Y is smaller than three for these materials, approaching this theoretical value (Tabor relation) only for the highest crystallinity levels.

On the plastic deformation of fibre self-reinforced polymers

The plastic deformation of semi-crystalline polymers containing needle crystals has been investigated. Stress-strain curves exhibit two linear regions, the elastic (Hookeian) range and a second linear plastic part. The onset of the plastic part depends on pre-straining and the slopeα = dσ/de of the plastic part is dependent on the morphology of the samples. An interpretation is given in terms of the shear-lag theory of discontinuous uniaxially oriented fibres.