The mechanical properties of semi-crystalline polymers are dictated by the individual characteristics of crystalline and amorphous phases and the complex interplay between them. Processing conditions can strongly influence micro-structural features such as crystallinity and orientation of crystalline structures, thereby changing the polymer behavior. In the present study, we employ a micromechanical composite inclusion model to obtain a direct relation between the microstructure and the resulting properties for alpha isotactic polypropylene (alpha-iPP). The model uses a dedicated constitutive law for each constituent phase, thus capturing the elasto-viscoplastic phenomena of both the isotropic amorphous and anisotropic crystalline phases. As such, it is intrinsically capable of covering the macro-mechanical effects of texture evolution caused by crystalline slip. The model parameters for crystalline and amorphous phases of isotropic alpha-iPP are identified by comparing the model output with experimental results of uniaxial compression and tension tests at different strain rates and temperatures. Finally, the long-term response of alpha-iPP in uniaxial creep loading is predicted and compared to experimental results.

Identifying and predicting the performance of process-induced defects, such as weld lines in injection-moulded thermoplastic components, is critical for failure assessment. While previous studies have addressed various weld line phenomena, accurately predicting their instantaneous and long-term strength remains a challenge. This study investigates the thermo-mechanical performance of unreinforced, and 30 % glass fiber-reinforced isotactic polypropylene (iPP) processed by injection moulding into specimens containing a central weld line due to a stagnating flow. Short-term experiments on smooth tensile bars at various strain rates (from 10-6 to 10- 2 s- 1) and temperatures (-20 degrees C, 23 degrees C and 80 degrees C) identify plasticity driven failure kinetics with a transition towards brittle crack-growth driven failure at high temperatures and low strain rates. Long-term plasticity driven performance is assessed through creep-to-rupture and cyclic fatigue tests on tensile bars and identify the same transition from ductile-to-brittle failure, as well as a clear discrepancy in perceived plasticity-governed strength when comparing short- and long-term experiments. The key novelty of the work is found in the demonstration that stress rate-controlled tensile experiments rationalise this observed discrepancy in strength that is explained by strain localisation. We therefore propose the stress rate-controlled tensile test to be more suitable to assess the strength of a weld line compared to the traditional strain-rate controlled tensile test. All observations are accurately captured using Ree-Eyring flow theory. The crack-growth governed failure of the weld line is explored by including fatigue crack growth experiments on CT specimens on both unreinforced and reinforced materials and general findings are presented.

In this study, an experimental approach is presented to determine strain-based failure envelopes for short-fiber reinforced thermoplastics under multiaxial loading conditions. The multiaxial failure behavior is experimentally investigated by Nakajima puncture tests that, via geometrical variations, allow the change of the stress state from uniaxial to biaxial. Local failure initiation can be mostly not identified by the macroscopic force-displacement curve. Instead, failure is assessed using 3D digital image correlation (3D DIC), which is used to measure the local strain and determine local failure. The methodology is demonstrated for systems with a ductile (polypropylene), pseudo-ductile (polycarbonate), and brittle (polyphenylene sulfide) matrix. The shape of the failure envelopes is found to be very similar for most of the systems and shown to be governed by a critical strain parallel and perpendicular to the main fiber direction. The magnitude of the critical strains varies widely between the various systems and depends on the reinforcing constituent (e.g., fiber volume fraction), matrix characteristics (e.g., yield stress), and the addition of impact modifiers, as illustrated for the reinforced thermoplastics studied. The determined critical strain can be straightforwardly used to predict failure for complex products under multiaxial loading conditions.

Upon their cooling and solidification, significant thermal residual stresses can develop in short-fiber reinforced thermoplastics due to the mismatch in coefficient of thermal expansion between fiber and matrix. In this study we set out to investigate this effect numerically. The build-up of thermal residual stresses is modeled by expanding a well-established constitutive model, the Eindhoven glassy polymer (EGP) model, with thermal expansion. The experimentally measured thermal residual stresses can be described using an effective glass-transition temperature and a constant coefficient of thermal expansion without the need for complex equilibrium kinetics associated with the glass transition itself. Subsequently, the influence of thermal residual stress on the deformation behavior for a short-fiber reinforced thermoplastic is studied employing multi-fiber representative volume elements (RVEs) for different fiber-weight fractions. The micromechanical models are evaluated on the importance of thermal residual stresses on the local and nominal stress state. From these analyses it can be concluded that the thermal residual stresses should be accounted for when assessing the quantitative local stress state and are therefore essential when local mechanisms are studied. In contrast, thermal residual stresses are not required to capture the nominal transient stress–strain response.

The rate- and temperature-dependent mechanical behavior of unidirectional carbon fiber-reinforced polyvinylidene fluoride (PVDF) is investigated through uniaxial tension and compression experiments under various off-axis loading conditions. To improve the understanding of the behavior of the composite, a 3D micromechanical model is developed. Microscopic analyses are used to characterize the geometrical properties of the UD composite at the fiber length-scale. These properties are used to construct a periodic 3D representative volume element (RVE). In combination with periodic boundary conditions, uniaxial macroscopic deformation (in any possible direction) is applied to the RVE to accurately and efficiently model off-axis loading. The rate- and temperature-dependent behavior of the PVDF matrix is accurately described using an elasto-viscoplastic constitutive model. The finite element simulations of uniaxial tension and compression tests are compared to the experimental data and the micromechanical response is analyzed. The micromechanical model accurately describes the rate-dependent macroscopic behavior of unidirectional carbon fiber-reinforced PVDF for various off-axis loading directions at different temperatures. Analysis of the local matrix response in the RVE reveals the influence of the matrix on the macroscopic behavior of the composite.

To model the engineering performance of components made of polyvinylidene fluoride (PVDF), the 3D elasto-viscoplastic Eindhoven glassy polymer (EGP) model is extended to describe the rate-dependent behavior of PVDF. Careful analysis of the intrinsic behavior of PVDF revealed that the postyield compressive response shows a strain rate-dependence that evolves with increasing deformation. The extension of the constitutive model captures the deformation-dependent evolution of the activation volume and the rate-factor, which describes the driving stress. Given the significant temperature-dependent behavior, the model has been characterized for different temperatures (23, 55 and 75 degrees C). The accuracy of the model has been validated by means of tension and creep experiments at these temperatures. The constitutive model is implemented in finite element simulations and the results are compared with the experiments. It is shown that the proposed model allows for an accurate prediction of the short- and long-term rate-dependent behavior of PVDF.

In this study, we demonstrate that the strength of a short-fiber reinforced polymer as measured in uniaxial tension is not a good indicator for its strength under multiaxial loading conditions. To illustrate this fact, the influence of physical aging on the strength of a 20 wt% short-fiber reinforced polycarbonate is studied for a uniaxial and biaxial loading condition. Results demonstrate that aging strongly reduces the strength in multiaxial loading, whereas, it increases in uniaxial loading. To rationalize these observations, a micromechanical analysis of the local stress state is performed using three-dimensional (3D) representative volume elements (RVE) in combination with a constitutive model that adequately describes the intrinsic deformation response of the matrix. RVE simulations demonstrate that biaxial loading results in higher local hydrostatic stresses and triaxiality than the uniaxial loadcase for the composite system considered, and aging results in a shift towards higher values. The high triaxiality, the magnitude of the hydrostatic stress, and the shift in hydrostatic stress upon aging, presents a clear rationalization why physical aging induces a strength reduction in biaxial loading and not in uniaxial loading. These results highlight that care should be taken when predicting strength under complex loading conditions with only uniaxial data available.

In our previous study, we demonstrated that the time-dependent failure of transversely loaded UD (unidirectional) glass/iPP is fully plasticity-controlled and proposed a lifetime prediction method based on plasticity to predict transverse failure. In the present work, extending our previous study to other off-axis angles, we aim to investigate the effect of the off-axis angle on the time-dependent failure of UD glass/iPP, and to propose a lifetime prediction method for the off-axis failure. Glass/iPP specimens with different off-axis angles are tested at various strain rates, creep, and fatigue loads to characterize the anisotropic, time-dependent mechanical response. It is demonstrated that the influences of strain rate and fiber orientation angle on tensile strength are multiplicatively separable; also referred to as factorizable, enabling one to characterize the angle dependence at a single strain rate and the strain rate dependence at a single angle. Moreover, similar to transverse loading, off-axis failure is also observed to be plasticity-controlled. Based on these observations, the lifetime prediction method for the plasticity-controlled transverse failure is extended to off-axis loading using the aforementioned factorazibility, which resulted in lifetime predictions in agreement with the experimental creep and fatigue data.

In the present study, the influence of electron-beam irradiation on plasticity-controlled and crack-growth-controlled failure in high-density polyethylene (HDPE) is investigated and the effect of both molecular weight distribution (MWD) and short chain branching (SCB) content are taken into account. Size exclusion chromatography (SEC) is used to study the evolution of the MWD of the sol fraction as a function of irradiation dose. Here, it is seen that chains shorter than the percolation threshold (5 kDa) are largely unaffected by electron beam radiation, while the fraction of longest chains (M > 300 kDa) is nearly entirely incorporated into the cross-linked network. Both yield stress and Young's modulus increased with irradiation dose, where the magnitude of the increase appears to be connected to the gel fraction. The (fatigue) crack growth kinetics of the grades changed relatively little with irradiation dose, which is unexpected. Furthermore, convergence of the crack growth kinetics parameter to a narrow range of values could be observed for the investigated grades at relatively high gel fractions. This would imply that the crack growth kinetics become increasingly independent of the MWD upon irradiation cross-linking, which could be attributed to a shift in the underlying crack growth mechanism from chain slip to chain scission.

Researchers have long sought to predict the mechanical behavior of polyethylene from its microstructure. In particular, the yield strength and yield kinetics have been reported to be dependent on crystallinity and crystal thickness, but the relative importance of these two microstructural attributes has not been shown. In the present work, a series of microstructures was obtained through a combination of controlled quench rates from the melt and inclusion of various amounts of hexene comonomer. The yield strength for a wide range of strain-rates was linearly dependent on the crystallinity, and independent of crystal thickness (chain stem length), both measured by Raman spectroscopy. Similarly, yield kinetics described by a Ree-Eyring two-process stress activated model showed linear dependence on crystallinity and no dependence on crystal thickness. The results of the present work call into question models of yield kinetics dependent on screw dislocation nucleation, which depend on crystal thickness.

The anisotropy and strain rate dependence of the mechanical response of short-fiber-reinforced thermoplastics was studied using a straightforward micromechanical finite element analysis of representative volume elements (RVEs). RVEs are created based on the fiber orientation tensor, which quantifies the processing-induced fiber orientation distribution. The matrix is described by a strain rate-dependent constitutive model (the Eindhoven glassy polymer (EGP) model), which accurately captures the intrinsic response of amorphous polymers. The micromechanical results indicate that the influence of strain rate and that of the loading direction on the yield stress are multiplicatively decouplable, which confirms previous experimental observations. Moreover, it is demonstrated that the yield stress, to a good approximation, can be directly linked to the fiber orientation in the direction of loading. This leads to a new relation that uniquely links the rate dependence of the yield stress to the fiber orientation in loading direction.

Herein, temperature-dependent long-term behavior of polypropylene and its transversely loaded unidirectional glass fiber reinforced composite is investigated and a lifetime prediction method is proposed, which is based on the observed long-term failure mechanisms. Furthermore, the effect of cooling rate during processing on the time-dependent behavior is addressed. The composite is revealed to exhibit multiple molecular deformation mechanisms, similar to neat polypropylene, which is modeled using the Ree-Eyring approach. Failure kinetics under constant-strain-rate and creep tests are found to be identical and switching from creep to cyclic loading decelerates the failure, which are signs of plasticity-controlled failure. Hence, lifetime is predicted well by using a lifetime prediction methodology for the plasticity-controlled failure which combines the Ree-Eyring approach and the concept of critical strain. A change in the cooling rate alters the deformation and failure kinetics: lower cooling rates promote embrittlement.

The conditions to which fiber reinforced plastics (FRPs) are exposed in state of the art applications are becoming more extreme, for example in the offshore oil and gas industry. Therefore, the ability to predict the long-term behaviour, and thereby identifying the failure mechanisms, of fiber reinforced plastics is of great importance. Especially under these extreme conditions, the contribution of the matrix plays an important role and a detailed description of its behaviour is required. In oil and gas applications, polyvinylidene fluoride (PVDF) is used because of its excellent gas barrier properties. In this work the rate-and temperature-dependent micro-mechanical behaviour of carbon fiber reinforced polyvinylidene fluoride is studied. The behaviour of the composite is studied by using a micro-mechanical model that is composed of individually modelled carbon fibers embedded in a PVDF matrix. The time-and temperature-dependent behaviour of PVDF is captured by the Eindhoven Glassy Polymer (EGP) constitutive model [1]. This model enables the description of the intrinsic behaviour of the semi-crystalline matrix over a range of applied strain rates and temperatures using a single set of material parameters. The characterization of these material parameters, requires a set of experimental data obtained from uniaxial compression and tensile tests performed at different temperatures and applied strain rates. To describe the material behaviour of the individually modelled carbon fibers, an elastic orthotropic material model is employed. Off-axis tensile tests of the composite led to the observation that the interface behaviour between matrix and fiber must be incorporated in the micro-mechanical model as well. Subsequently, an interface between the matrix and fiber is added to the model by using cohesive zone interface elements. The behaviour of these interface elements is described by an appropriate constitutive

Flow-induced fibre orientation generally causes anisotropy in the mechanical response of short fibre reinforced thermoplastics. In this manuscript, this anisotropy is studied for a wide selection of fibre-reinforced thermoplastics, focusing on the strain-rate dependence of the strength, and its relation to the stress-dependence of the lifespan under static load (creep rupture). It is demonstrated that, for short- as well as long-fibre reinforced thermoplastics, the influence of fibre-orientation and applied strain-rate on the tensile strength can be multiplicatively decomposed; the response is factorizable in load-angle and strain-rate. This factorizability appears to be generic to fibre-reinforced systems, since it is observed regardless of fibre type, fibre length, fibre weight fraction, matrix type and level of interfacial fibre-matrix interaction. The apparent factorisation of fibre-orientation and strain-rate dependence of the fracture stress opens up a possibility to considerably reduce experimental efforts required for composite characterisation. Subsequently, an anisotropic viscoplastic model previously developed by van Erp et al. (2009), is analysed for its capability describe the observed factorizability. This model is expressed in a form of an associated flow rule, which combines the Eyring flow equation, required to describe the strain rate dependence at a reference orientation, with the Hill equivalent stress formulation to capture the load-angle dependence. The model not only describes the load-angle and strain-rate dependence of the tensile strength accurately, but, in combination with a critical strain concept, it also provides accurate predictions of the creep lifetime for different loading angles.

In continuous fiber-reinforced thermoplastics, the macroscopic failure mode in transverse long-term failure is dominated by a brittle crack-growth mechanism. Neat thermoplastic matrices, on the other hand, generally display also a plasticity-controlled mechanism in long-term loading at elevated stress levels and/or temperature. This failure mechanism requires a different approach to lifetime prediction than crack growth; hence, it is important to identify it in the long-term performance of composites. In this study, we demonstrate the presence of the plasticity-controlled failure mechanism in long-term failure of transversely loaded unidirectional (UD) thermoplastic composites made of glass/iPP, carbon/PEEK and carbon/PEKK. The main method used is to compare the lifetime in cyclic loading to that in static loading at the same level of maximum stress, where an increase in lifetime is characteristic for plasticity controlled failure, and, vice versa, a decrease is indicative for fatigue crack growth. In addition, the applicability of a lifetime prediction method common to plasticity-controlled failure of neat thermoplastics is evaluated for the composites investigated. The results of this study indicate that the plasticity-controlled failure was present in composites, although the extent to which the effects are present varied depending on the materials investigated. Glass/iPP showed the most explicit evidence of the plasticity-controlled failure over the entire load range experimentally covered. Its long-term failure was delayed with a decrease in the stress ratio and lifetime was predicted well using the principles of plasticity-controlled failure.

An elasto-viscoplastic constitutive model was previously developed and successfully used to describe the anisotropic time-dependent response of short fiber reinforced thermoplastics. It is demonstrated that when it is applied to systems with a higher level of anisotropy, the apparent anisotropy of the rate-dependent yield stress deviates from the Hill parameters that are used to define it. This becomes more apparent if the level of anisotropy is increased. The origin of this discrepancy is mathematically investigated and shown to be related to the viscoplastic multiplier of the associated flow rule employed. A solution is proposed that completely restores consistency and extends the applicability of the model to systems with high anisotropy.

The present study focuses on the influence of the molecular weight distribution (MWD) on the crack-growth kinetics of fatigue-crack propagation in high-density polyethylene (HDPE) homopolymers. Compact-tension specimens of HDPE homopolymer grades, with polydispersities ranging from 2 to 45 and weight-averaged molar mass ranging from 49 to 450 kg/mol, are tested in cyclic loading at temperatures ranging between 23 and 92 degrees C. Through a variation of sample thickness, linear elastic-fracture mechanics is shown to apply for the chosen geometry (compact tension). It was found that the crack-propagation kinetics obey the Paris-Erdogan law, for which the Paris-Erdogan exponent m is (highly) similar for all grades tested (m = 3.9), implying that the Paris-Erdogan prefactor A is the governing parameter for the crack-growth kinetics. Relatively poor correlations are observed when the prefactor A is plotted as a function of both the tie-molecule fraction derived from the theoretical model by Huang and Brown, J. Mater. Sci. 1988, 23, 3648, and the average number of effective physical cross-links per chain as derived by Tervoort et al., Macromolecules 2002, 35, 8467. A far better correlation is observed between prefactor A and the weight-average molecular weight (M-w), which improved further when M-w is corrected for the width of the MWD, taking into account the z-average molecular weight M-v through the ratio M-z/M-w. A power-law correlation of prefactor A with M-w and the width-corrected M-w reveals slopes of -3.4 and -3.3, respectively. Because a molecular slip within the fibrils would require chain transport through the crystalline blocks, the temperature dependence of the fatigue-crack-growth kinetics is investigated to identify the underlying molecular processes. This investigation reveals the existence of a high-temperature and a low-temperature deformation process, both of which can be related to chain-slip mechanisms through their respective activation energies (125 and 50 kJ/mole), as their activation energies are considerably lower than that required for chain scission (430 kJ/mol). This, combined with the power-law exponent of -3.4, would suggest a possible connection between the underlying failure mechanisms of craze fibrils and reptation-like dynamics. Furthermore, experiments at elevated temperatures on a selection of homopolymer grades suggest that the MWD has no influence on the temperature dependence of fatigue-crack propagation for HDPE homopolymers.

The present study investigates the effect of processing conditions on the yield kinetics, such as rate dependence of the yield stress and creep rupture, of polyvinilidene fluoride. Samples were compression molded with cooling rates varying from 100 degrees C/s to 0.5 degrees C/min, or isothermally crystallized at temperatures varying from 20 to 120 degrees C. Deformation kinetics were studied over a wide range of strain rates and temperatures. It is shown that for all conditions the yield response is well represented by the Ree-Eyring model. Moreover, the activation volumes and activation energies are independent from the processing conditions. The effect of processing is fully covered by a simple relationship between the rate factors and the degree of crystallinity. Subsequently, the versatility of this relationship is demonstrated by experimental validation.

The effect of flow-induced fibre orientation on the fatigue performance of short fibre reinforced thermoplastics is investigated. Relative contributions of creep (static, time-dependent) and fatigue (cycle dependent) components are studied extensively by performing tests at different frequencies and load ratios for different fibre orientations and fibre weight fractions. An anisotropic, phenomenological model of crack growth controlled failure is proposed that relates creep/fatigue contributions to the lifetime in the crack growth controlled failure region for different fibre orientations and allows to extrapolate and estimate time-to-failure under a static load using shortterm cyclic tests.

ABSTRACTThe influence of stress, temperature, and relative humidity on plasticity‐controlled failure of molded and laser‐sintered polyamide 12 (PA12) has been investigated. Ree–Eyring's flow theory is employed and modified to take into account the effect of relative humidity on the deformation kinetics. By introducing the concept of critical strain, time to failure in plasticity‐controlled regime is predicted starting from the yield kinetics. Creep test is performed to estimate the critical strain and to validate model predictions. The model predictions are in good agreement with the experimental results, showing that the model is a suitable and reliable tool to evaluate mechanical response as function of temperature and relative humidity. We demonstrate that, while, at high applied strain rates, a significant difference is found, the mechanical response under constant strain rate as well as the failure kinetics in plasticity‐controlled regime of the sintered PA12 are comparable with those of the molded material. © 2019 The Authors. Journal of Applied Polymer Science published by Wiley Periodicals, Inc. J. Appl. Polym. Sci. 2020, 137, 48525.