Short Fiber-reinforced Thermoplastics Research Articles

On the effectiveness of deep material networks for the multi-scale virtual characterization of short fiber-reinforced thermoplastics under highly nonlinear load cases

A key challenge for the virtual characterization of components manufactured using short fiber-reinforced thermoplastics (SFRTs) is the inherent anisotropy which stems from the manufacturing process. To address this, a multi-scale approach is necessary, leveraging deep material networks (DMNs) as a micromechanical surrogate, for a one-stop solution when simulating SFRTs under highly nonlinear long-term load cases like creep and fatigue. Therefore, we extend the a priori fiber orientation tensor interpolation for quasi-static loading (Liu et al. in Intelligent multi-scale simulation based on process-guided composite database. arXiv:2003.09491, 2020; Gajek et al. in Comput Methods Appl Mech Eng 384:113,952, 2021; Meyer et al. in Compos Part B Eng 110,380, 2022) using DMNs with a posteriori approach. We also use the trained DMN framework to simulate the stiffness degradation under fatigue loading with a linear fatigue-damage law for the matrix. We evaluate the effectiveness of the interpolation approach for a variety of load classes using a dedicated fully coupled plasticity and creep model for the polymer matrix. The proposed methodology is validated through comparison with composite experiments, revealing the limitations of the linear fatigue-damage law. Therefore, we introduce a new power-law fatigue-damage model for the matrix in the micro-scale, leveraging the quasi-model-free nature of the DMN, i.e., it models the microstructure independent of the material models attached to the constituents of the microstructure. The DMN framework is shown to effectively extend material models and inversely identify model parameters based on composite experiments for all possible orientation states and variety of material models.

The Effect of Thermal Residual Stress on the Stress State in a Short-Fiber Reinforced Thermoplastic

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.

Fatigue Damage of Short Fibre-Reinforced Thermoplastics in Crashworthiness Simulation

Service loads repeatedly stress components on a regular basis and lead to fatigue damage in the material. In the case of components made of short fibre-reinforced thermoplastics, which are also crash-relevant in addition to only bearing service loads, however, a significant deterioration in mechanical properties can be observed after fatigue damage has been introduced. This is where the approach presented in this paper comes in: in order to enable a realistic simulation of such components in their used conditions, the material data are assigned depending on previously determined damage. The approach, which combines the domains of highly dynamic and cyclic experiments as well as different types of numerical simulations, is tested for its performance in the present paper. For this purpose, component tests are carried out on cross-rib beams, which serve to validate the method. The novelty and uniqueness of this paper lies in the linking of fatigue life and crashworthiness considerations for short fibre-reinforced thermoplastics, which, in this case, is raised to a new level by considering the component level for the first time.

Impact Energy Dissipation and Quantitative Models of Injection Molded Short Fiber-Reinforced Thermoplastics

Glass short fiber-reinforced thermoplastics (SGFRTP) are used to reduce carbon dioxide emissions from transportation equipment, especially household vehicles. The mechanical properties required for SGFRTP include flexural strength, impact resistance, etc. In particular, impact resistance is an important indicator of the use of SGFRTP. For this study, a mechanical model was developed to explain the notched impact strength of SGFRTP injection molded products in terms of their interfacial shear strength. The values obtained from the model show good agreement with the experimentally obtained results (R2 > 0.95). Results also suggest that the model applies to different fiber orientation angle and a range of fiber lengths in the molded product that are sufficiently shorter than the critical fiber length.

Full Field Solution for Remotely Loaded One Side Completely Debonded Short Rigid Line Inclusion Embedded in Soft Matrix: Two-Dimensional Analytical and Experimental Insights

Abstract The problem of a completely debonded short fiber (rigid line inclusion/anticrack) embedded in a 2D isotropic elastic soft matrix subjected to the remote loading condition is of fundamental interest. The current work investigates completely debonded anticrack embedded in a soft (isotropic) matrix using Kolosov Muskhelisvili's complex potential framework. Here two configurations are studied: debonded inclusion oriented (i) parallel and (ii) perpendicular to the loading direction. In particular, the potentials take the form of a non-homogeneous Riemann—Hilbert equation for the given problem. Upon solving analytical forms of potentials, the stress fields were obtained. The stress field for the fully debonded anticrack exhibited oscillatory singular behavior between r−3/4 and r−1/4 with the dependence on the oscillatory index ε and material constants. The correctness of the analytical solution was validated using numerical simulation and experiments based on the digital photoelasticity technique. The analytical results were in good agreement with the experimental and numerically obtained stress fields confirming the accuracy of it. The magnitude of singularity is quantified by defining a complex stress intensity factor at the tip of the discontinuity and compared with the experimentally estimated value. So far in the literature, no full-field analytical solution exists for the completely debonded rigid inclusion embedded in an isotropic soft matrix. The solution obtained in the present work is of fundamental importance in developing the constitutive properties of short fiber reinforced thermoplastic (SFRT) composites.

Role of confinement in the shear banding and shear jamming in noncolloidal fiber suspensions.

The jamming effect is critical in processing short fiber-reinforced thermoplastics (FRTs). Fiber jamming can induce discontinuous shear thickening (DST) in simple shear and result in fiber-matrix separation in more complex flows such as injection molding and compression molding of FRTs. The confinement effect commonly induces local jams and strongly enhances fiber jamming. However, the transient evolution of local fiber jams under confinement and its correlation with the tumbling of fibers are still elusive. In this study, we adopted rheo-PIV (particle image velocity) techniques to study this effect for glass fiber-reinforced thermoplastics (FRTs). The translational and tumbling motion of fiber were determined during rheological measurements, and the distribution of fiber orientation was determined by X-ray CT. Three shear banding regions appeared after the viscosity overshoot under high shear stress in suspensions with high fiber content, which was associated with the three regions of fiber orientation across the gap due to confinement. Shear banding was ascribed to the different tumbling speeds across the gap because of the different initial orientations and different wall confinements near and far from the wall. The local shear thickening and jamming behavior became most significant under intermediate confinement, and were affected by shear strain, shear stress, and fiber contents. 3D state diagrams were constructed to show the confinement effect on the evolution of shear banding and jamming.

Rapid inverse calibration of a multiscale model for the viscoplastic and creep behavior of short fiber-reinforced thermoplastics based on Deep Material Networks

In this work, we propose to use deep material networks (DMNs) as a surrogate model for full-field computational homogenization to inversely identify material parameters of constitutive inelastic models for short fiber-reinforced thermoplastics (SFRTs).Micromechanics offers an elegant way to obtain constitutive models of materials with complex microstructure, as these emerge naturally once an accurate geometrical representation of the microstructure and expressive material models of the constituents forming the material are known. Unfortunately, obtaining the latter is non-trivial, essentially for two reasons. For a start, experiments on pure samples may not accurately represent the conditions present in the composite. Moreover, the manufacturing process may alter the material behavior, and a subsequent modification is necessary. To avoid modeling the physics of the manufacturing process, one may identify the material models of the individual phases of the composite based on experiments on the composite. Unfortunately, this procedure requires conducting time-consuming simulations.In the work at hand, we use Deep Material Networks to replace full-field simulations, and to carry out an inverse parameter optimization of the matrix model in a SFRT. We are specifically concerned with the long-term creep response of SFRTs, which is particularly challenging to both experimental and simulation-based approaches due to the strong anisotropy and the long time scales involved. We propose a dedicated fully coupled plasticity and creep model for the polymer matrix and provide details on the experimental procedures.

In situ micromechanical analysis of discontinuous fiber-reinforced composite material based on DVC strain and fiber orientation fields

The influence of fiber orientation and its distribution on the global and local mechanical behavior of a short fiber-reinforced thermoplastic (SFT) composite is studied based on an in situ tensile test using synchrotron X-ray tomography. The in situ test data are utilized to compute three-dimensional (3D) strain fields inside the material at various loading steps through an in-house digital volume correlation (DVC) code. The DVC analysis finds that, although the global strain fields seem relatively uniform, the internal strain fields are locally non-uniform because of the complex reinforcement architecture. The local non-uniformity is further investigated at a single fiber level to find a correlation between the orientation of fibers, fiber volume fraction, and strain field. The investigation is performed on micro-scale subvolumes, in which all the fibers are individually segmented from the 3D tomographic data. It is found that the fibers aligned in the direction transverse to loading impede transversal shrinkage, resulting in a locally small compressive strain in that direction. The in situ test has revealed that the average fiber orientation does not change noticeably even after the global strain reaches 18%. This small change implies that initially-determined fiber orientation is crucial to the locally anisotropic mechanical behavior of a SFT-like material even undergoing large deformation. On the other hand, the loading-directional strain is more affected by the local volume fraction than the fiber orientation. The local volume fraction also mainly determines the stiffness of the subvolume that can be estimated from an analytical homogenization model. The effect of the local volume fraction on the subvolume stiffness is identified from multivariate analysis.

Effect of severe thermo-oxidative aging on the mechanical behavior and fatigue durability of short glass fiber reinforced PA6/6.6

The work deals with the fatigue lifetime estimation of Short Fiber Reinforced Thermoplastics (SFRP), with a focus on conjugated effects of thermal aging. Two materials containing 35% (V35) and 50% (V50) weight ratio of short glass fibers were aged for 500 h at 200°C in air and compared to the same materials in a Dry-As-Molded (DAM) state. Monotonic and fatigue tests were performed in samples machined out of injected plates and cut along three different orientations to the injection one (0°, 45°, 90°) in order to capture the anisotropy of the skin-core microstructure, classical in injected SFRP.Monotonic tensile tests evidenced the stiffening and embrittlement of the Polyamide matrix reported in the literature, nevertheless with an acuity depending on the matrix ratio and fiber orientation. Stress-controlled fatigue tests were performed at constant amplitude, frequency (10 Hz), temperature (200°C) and stress ratio R = 0.1. The fatigue curves of V35 are more affected by aging than those of the V50 material. The combined results from the mean strain evolutions and SEM observations confirmed that the initiation approach for fatigue lifetime estimation was still valid in aged composites. Several fatigue criteria, among the most recently reported in the literature, were evaluated from this database. The effect of aging on the cyclic evolution of the different Fatigue Indicator Parameters (FIP) involved in the criteria was analyzed preliminarily. For the present fatigue conditions, the best criteria for unaged materials (i.e cyclic creep energy-based ones) were shown to still be the best for aged materials. Finally, the ability to predict fatigue lifetime for aged composites from the identification of the fatigue criterion in the unaged state was evaluated.

Solidification Temperature of Short Fiber-Reinforced Thermoplastics: Identification and Cooling Rate Correlation in Injection Molding using Differential Scanning Calorimetry

Solidification Temperature of Short Fiber-Reinforced Thermoplastics: Identification and Cooling Rate Correlation in Injection Molding using Differential Scanning Calorimetry

Training deep material networks to reproduce creep loading of short fiber-reinforced thermoplastics with an inelastically-informed strategy

Deep material networks (DMNs) are a recent multiscale technology which enable running concurrent multiscale simulations on industrial scale with the help of powerful surrogate models for the micromechanical problem. Classically, the parameters of the DMNs are identified based on linear elastic precomputations. Once the parameters are identified, DMNs may process inelastic material models and were shown to reproduce micromechanical full-field simulations with the original microstructure to high accuracy. The work at hand was motivated by creep loading of thermoplastic components with fiber reinforcement. In this context, multiple scales appear, both in space (due to the reinforcements) and in time (short- and long-term effects). We demonstrate by computational examples that the classical training strategy based on linear elastic precomputations is not guaranteed to produce DMNs whose long-term creep response accurately matches high-fidelity computations. As a remedy, we propose an inelastically informed early stopping strategy for the offline training of the DMNs. Moreover, we introduce a novel strategy based on a surrogate material model, which shares the principal nonlinear effects with the true model but is significantly less expensive to evaluate. For the problem at hand, this strategy enables saving significant time during the parameter identification process. We demonstrate that the novel strategy provides DMNs which reliably generalize to creep loading.

FE-based damage modeling approach for short fiber reinforced thermoplastics under quasi-static load coupling anisotropic viscoplasticity and matrix degradation

It is challenging to predict the material degradation and crack initiation of short fiber reinforced thermoplastics (SFRT) components with high computation efficiency and low parameter identification effort. To achieve that, this work utilizes a hybrid method combining micro- and macro-mechanical approaches to describe the damage-coupled material behavior of SFRT. The Mori-Tanaka mean-field homogenization method is used to determine the effective linear elastic properties of SFRT, whereas the consideration of plasticity is based on a macro-mechanical anisotropic viscoplastic model. The effect of micro-damage in the matrix material on the macroscopic behaviors of SFRT is considered within the Continuum Damage Mechanics (CDM) framework. A nonlinear damage evolution law is implemented to account for the nonlinearity in the damage evolution. Targeting industrial applications, the proposed damage-coupled material model is implemented into the commercial FE software ANSYS with a novel stepwise damage updating process, requiring no user-defined subroutine. The model is calibrated with experimental data on flat specimens under monotonic and cyclic tensile loading. The FE simulation with the calibrated material model accurately describes the anisotropic deformation and crack initiation of the investigated SFRT material observed in experiments.

Data enriched lubrication force modeling for a mechanistic fiber simulation of short fiber-reinforced thermoplastics

The simulative prediction of fiber orientation for injection-molded short fiber-reinforced thermoplastics is an important step in prediction warpage and failure of injection molded parts. There exists a variety of phenomenological macroscopic fiber orientation models, which are computationally very efficient but strongly dependent on phenomenological parameters. This research focuses on a mechanistic fiber orientation model for concentrated short fiber-reinforced thermoplastics. A fully coupled computational fluid dynamics particle simulation is used to estimate the lubrication forces between two fibers in different configurations (angles between fibers, velocities) with varying fiber length and surrounding fluid viscosity. Based on these data, a calibrated lubrication model is developed and implemented in a mechanistic fiber orientation simulation. In addition, the fiber orientation estimated by the enhanced mechanistic fiber model is compared to experimental fiber orientation data obtained with a glass fiber-reinforced thermoplastic industrial grade, which showed an improvement over a simulation that did not include the lubrication force.

A Pragmatic Approach for Modelling the Viscoelastic-Viscoplastic Behaviour of Short-Fibre Reinforced Thermoplastics Coupled with Anisotropic Damage

In this paper, a previously developed viscoelastic-viscoplastic behaviour model for short-fibre-reinforced thermoplastics (SFRT) is enriched with matrix ductile damage and fibre/matrix interfacial debonding constitutive laws. Aiming at industrial applications, model development takes special care to ensure a relatively easy characterisation of material parameters, as illustrated with case of a short-glass-fibre-reinforced polypropylene. Numerical simulations are done to assess the capability of the model to account for all specificities of SFRT behaviour with a particular attention paid on the coupled influence of strain rate and microstructure configuration on the initiation and development of matrix damage and fibre/matrix debonding.

Modelling the influence of the microstructure on the high cycle fatigue crack initiation in short fibre reinforced thermoplastics

In this work, a new criterion to predict fatigue crack initiation in plain Short Fibre Reinforced Thermoplastics is proposed. Several experimental observations in the literature showed that the initiation of a macro crack results from the accumulation of damage in the matrix at the micro-scale. Accordingly, in the proposed criterion the life to crack initiation is predicted through an effective stress acting in the most critical regions in the matrix (close to the fibre ends and lateral surfaces). More precisely, the effective stress is evaluated within a control volume defined as a certain percentage of the matrix volume subjected to the highest stresses. A multi-scale (macro-meso-micro) procedure is adopted for estimating the local stress fields in the polymer. The criterion was proved to successfully predict the influence of the material microstructure (fibre content and orientation distribution) and load orientation.

Calibration of Fiber Orientation Simulations for LFT—A New Approach

Short fiber reinforced thermoplastics (SFT) are extensively used due to their excellent mechanical properties and low processing costs. Long fiber reinforced thermoplastics (LFT) show an even more interesting property profile and are increasingly used for structural parts. However, their processing by injection molding is not as simple as for SFT, and their anisotropic properties resulting from the fiber microstructure (fiber orientation, length, and concentration) pose a challenge with regard to the engineering design process. To reliably predict the structural mechanical properties of fiber reinforced thermoplastics by means of micromechanical models, it is also necessary to reliable predict the fiber microstructure. Therefore, it is crucial to calibrate the underlying prediction models, such as the fiber orientation model, within the process simulation. In general, these models may be adjusted manually, but this is usually ineffective and time-consuming. To overcome this challenge, a new calibration method was developed to automatically calibrate the fiber orientation model parameters of the injection molding simulation by means of optimization methods. This optimization routine is based on experimentally determined fiber orientation distributions and leads to optimized parameters for the fiber orientation prediction model within a few minutes. To better understand the influence of the model parameters, different versions of the fiber orientation model, as well as process and material influences on the resulting fiber orientation distribution, were investigated. Finally, the developed approach to calibrate the fiber orientation model was compared with a classical approach, a direct optimization of the whole process simulation. Thereby, the new optimization approach shows a calculation time reduced by the factor 15 with comparable error variance.

Arbitrary-Reconsidered-Double-Inclusion (ARDI) Model to Describe the Anisotropic, Viscoelastic Stiffness and Damping of Short Fiber-Reinforced Thermoplastics

Current state of the art, simulation methods to determine the frequency-, temperature- and humidity-depending stiffness and damping do not show an accurate prediction of the structural dynamics of short-fiber-reinforced thermoplastics. Thus, in the current work the new developed Arbitrary-Reconsidered-Double-Inclusion (ARDI) model has been used to describe the stiffness and damping. Thereby, a homogenization equation has been used to derive the transversal-isotropic stiffness and damping tensors. By rotating and weighting these tensors using orientation distribution functions (ODF), it is possible to create a material database. A validation of the developed ARDI model was performed on bending vibration specimens under variation of the fiber direction, temperature and humidity, to investigate the structural dynamics. In general, the comparison of the results of the simulation and experiments shows a good correlation of the eigenfrequencies and the amplitudes. The main differences in the simulation can be traced back to the used modelling of the damping behavior.

A model to describe the cyclic anisotropic mechanical behavior of short fiber-reinforced thermoplastics

Due to the injection molding process, short fiber-reinforced thermoplastic composites show a complex fiber orientation distribution and, as a consequence, an overall anisotropic mechanical behavior. The monotonic and cyclic mechanical behavior of PolyEtherEtherKetone thermoplastic reinforced with 30 wt.% of short carbon fibers was characterized through a series of tests generating various complex loading histories (loading–unloading with creep or recovery steps, cyclic loading with various stress amplitudes) performed at room temperature on samples with various homogeneous and heterogeneous fiber orientation distributions. A three-dimensional model relying on a thermodynamic framework was then developed to represent the anisotropic mechanical behavior of the material, including elastic, viscoelastic, and plastic phenomena. Relevant constitutive laws were defined to describe the phenomena within wide ranges of loading rates and levels, with a limited number of parameters. Elastic anisotropy and plastic anisotropy were naturally described by using a two-step homogenization method and a Hill-like equivalent stress taking into account the fiber orientation distribution. The model was implemented into a finite element code to be able to simulate the response of complex parts with a heterogeneous fiber orientation distribution subjected to a heterogeneous loading. Model parameters were identified by applying a robust and original approach relying on a limited number of relevant experiments. The prediction capability of the model was demonstrated by simulating several types of tests not used for the identification, covering a wide range of monotonic and cyclic, homogeneous and heterogeneous, loading conditions, for various simple and complex fiber orientation distributions. In particular, the model is shown to be able to predict the energy dissipated in the material when subjected to cyclic loading.

Effect of Fiber Length on Mechanical Properties of Injection Molded Long-Fiber-Reinforced Thermoplastics

Fibers of long-fiber-reinforced thermoplastic (LFT) pellets are longer than those of short-fiber-reinforced thermoplastic (SFT) pellets produced by extrusion. To overcome the fiber length limitations of the SFT pellets, LFT pellets were prepared by a pultrusion process using continuous fibers, which afforded longer fibers. Currently, long glass-fiber-reinforced polypropylene (LGF-PP) materials, which are one of the growing markets of the plastics industry, are typically used, particularly for applications in the automotive industry where lightweight performance and cost savings are required. The LFT pellets are primarily converted into the final product by injection molding. During the injection molding process, the LFT pellets are broken and the fiber length decreases as a consequence. In this study, glass and carbon-fiber-reinforced polypropylene of various pellet lengths (3-16 mm) were prepared by impregnating pultrusion process to evaluate the effect of mechanical properties according to fiber length. The length of the residual fibers recorded after injection molding were observed to decrease in proportion to the pellet length. Even with LFTs having the same material composition, the mechanical properties was different after injection molding according to the residual fiber length. In this injection molded LFT, the flexural modulus was higher as the residual fiber length was shorter. The impact strength was larger in samples without adhesive resin and the observed differences were larger for longer fiber lengths. From these results, the mechanical properties of LFT can be improved by understanding the properties of long fibers.

Fatigue life assessment of a Short Fibre Reinforced Thermoplastic at high temperature using a Through Process Modelling in a viscoelastic framework

A Through Process Modelling (TPM) fatigue life assessment methodology – previously validated in an elastic framework for Short Fibre Reinforced Thermoplastics at room temperature – was extended to high temperature. The viscoelasticity of the matrix was taken into account to estimate the local effective mechanical properties at any point, from the knowledge of local fibre orientation provided by the simulation of injection-moulding. Lifetime estimation was obtained from an energetic fatigue criterion applied in the stationary regime. The approach was validated from uniaxial fatigue tests conducted at 110 °C in tension, on PA66GF30 samples cut out from injected plates with three different orientations to the injection direction, at two stress ratios (0.1 and −1).