Tensile creep of a long‐fibre glass mat thermoplastic (GMT) composite. II. Viscoelastic‐viscoplastic constitutive modeling

In Part I of this article, the short‐term tensile creep of a 3‐mm‐thick continuous long‐fibre glass mat thermoplastic composite was characterized and found to be linear viscoelastic up to 20 MPa. Subsequently, a nonlinear viscoelastic model has been developed for stresses up to 60 MPa for relatively short creep durations. The creep response was also compared with the same composite material having twice the thickness for a lower stress range. Here in Part II, the work has been extended to characterize and model longer term creep and recovery in the 3‐mm composite for stresses up to near failure. Long‐term creep tests consisting of 1‐day loading followed by recovery were carried out in the nonlinear viscoelastic stress range of the material, i.e., 20–80 MPa in increments of 10 MPa. The material exhibited tertiary creep at 80 MPa and hence data up‐to 70 MPa has been used for model development. It was found that viscoplastic strains of about 10% of the instantaneous strains were developed under load. Hence, a non‐linear viscoelastic–viscoplastic constitutive model has been developed to represent the considerable plastic strains for the long‐term tests. Findley's model which is the reduced form of the Schapery non‐linear viscoelastic model was found to be sufficient to model the viscoelastic behavior. The viscoplastic strains were modeled using the Zapas and Crissman viscoplastic model. A parameter estimation method which isolates the viscoelastic component from the viscoplastic part of the nonlinear model has been developed. The model predictions were found to be in good agreement with the average experimental curves. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers     

Nonlinear mechanical response of high density polyethylene. Part I: Experimental investigation and model evaluation

The nonlinear behavior of high density polyethylene (HDPE) is investigated for samples cut from thick-walled HDPE pipe. Extensive experimental work has been performed to characterize the non-linear time-dependent response of the material tested under uniaxial compression. Tests were conducted under conditions of constant strain rate, creep, stress relaxation, constant loading rate, abrupt change of strain rate, creep-recovery, cyclic strain rate, and various combinations of these loading conditions. Creep and stress relaxation response after strain reversal and the effect of the transient response on the following stress-strain behavior is examined. Permanent strains for the test specimens and their dependence on loading histories are investigated. Specimens cut at various orientations from the pipe are used to quantify the small amounts of local anisotropy in the pipe specimen. The experimental work has been used to develop both nonlinear viscoelastic (NVE) and viscoplastic (VP) constitutive models in a companion paper. Both the test results and the corresponding model predictions are reported in this paper. It is found that the VP model reproduces the nonlinear viscoelastic-viscoplastic behavior of HDPE very well provided that the current strain is not below the maximum strain imposed (there is no strain reversal). The NVE model predicts the material behavior reasonably well for some loading conditions, but inadequately for others.     

Tensile creep of a long‐fiber glass mat thermoplastic composite. I. Short‐term tests

This work is part of a larger experimental program aimed at developing a semi‐empirical constitutive model for predicting creep in random glass mat thermoplastic (GMT) composites. The tensile creep response of a long‐fiber GMT material has been characterized for 3‐ and 6‐mm thick material. Tensile tests showed that the variability within and between plaques are comparable with an overall variability of about 6% and 8% for the 3‐ and 6‐mm thick materials, respectively. The thicker material exhibited slightly higher variability and directional dependence due to greater flow during molding of the plaques. Short‐term creep tests consisting of 30 min creep and recovery, respectively, were performed over the stress range between 5 and 60 MPa. Three tests for determining the linear viscoelastic region were considered which showed that the 3‐ and 6‐mm thick GMT are linear viscoelastic up to 20 and 25 MPa respectively. The 6‐mm thick GMT consisting of a higher fiber weight fraction was linear over wider stress range. Furthermore, it was found that plastic strains were accumulated during creep, which suggests that a nonlinear viscoelastic–viscoplastic model would be more appropriate for long‐term creep at relatively high stresses, which will be presented in our companion paper. The magnitude of the plastic strains developed in the creep tests presented here was lower because a single specimen was loaded at multiple stress level over short durations. Hence, a nonlinear viscoelastic constitutive model has been developed for the two thickness materials. POLYM. COMPOS., 2009. © 2008 Society of Plastics Engineers     

A rate‐type nonlinear viscoelastic–viscoplastic cyclic constitutive model for polymers: Theory and application

A thermodynamically consistent rate‐type viscoelastic–viscoplastic constitutive model is developed in the framework of isothermal and small deformation to describe the nonlinear and time‐dependent deformation behaviors of polymers, e.g., ratchetting, creep, and stress relaxation. The model is proposed on the base of a one‐dimensional rheological model with several springs and dashpot elements. The strain is divided into viscoelastic and viscoplastic parts, and the stress is also decomposed into two components. Each stress component is further divided into elastic and viscoelastic sub‐components. The viscoelasticity is described by introducing pseudo potentials, and the ratchetting is considered by the viscoplastic flow which is derived by the codirectionality hypotheses. The capability of the proposed model to describe the nonlinear and time‐dependent deformation of polymers is then verified by comparing the simulations with the corresponding experimental results of polycarbonate (PC) polymer. It is shown that the nonlinear and time‐dependent stress–strain responses of the PC can be reasonably predicted by the proposed model. POLYM. ENG. SCI., 56:1375–1381, 2016. © 2016 Society of Plastics Engineers     

Nonlinear mechanical response of high density polyethylene. Part II: Uniaxial constitutive modeling

Based on the experimental data presented in Part I, two uniaxial constitutive models are constructed. The first, a nonlinear viscoelastic (NVE) model, is formulated using the mechanical analogy consisting of one independent spring and six Kelvin elements in series. Creep data are used to determine the model parameters. The second model, a viscoplastic (VP) formulation, is developed using the viscoplastic theory proposed by Bodner to characterize the uniaxial viscoplastic behavior of metals. Inelastic strain rate is introduced into the state variable in addition to inelastic work to depict the strong rate dependent behavior of HDPE. Experimental data from constant strain rate tests are employed to construct the material functions of the model. Limitations in the application of each model are discussed in conjunction with possibilities for future work.     

Finite element modeling of the time-dependent behavior of nonlinear ductile polymers

A finite element algorithm developed previously has been successfully extended to the study of nonlinear time-dependent problems. Nonlinear viscoelastic and viscoplastic models have been used to study the time-dependent deformation and failure of high density polyethylene (HDPE). Two classes of nonlinear models have been identified; those that allow stress redistribution with time under specified traction boundary conditions, and those that do not. The implications of using viscoelastic vs. viscoplastic models, as well as the specific mathematical form of the constitutive equations selected for use, have been studied. Strains predicted using the FE algorithm have been compared with experimental measurements for (i) a HDPE plate with a hole and (ii) a double edge notch HDPE specimen, both under remote tension. Excellent agreement was obtained between numerical predictions and the experimental values.     

Tensile creep behavior of unidirectional glass‐fiber polymer composites

The tensile creep behavior of unidirectional glass‐fiber polymer composites was studied at three different temperatures, namely 298, 333, and 353 K. Testing was performed on the pure epoxy matrix, the 0° specimens as well as off‐axis at 15, 30, and 60 degrees in respect to the axis of tension. The creep strain rate was negligible at room temperature, while it was considerable at the higher temperatures examined. The materials exhibit nonlinear viscoelastic behavior, and the creep response of the composites was treated as a thermally activated rate process. The creep strain was considered to include an elastic, a viscoelastic and a viscoplastic part. The viscoplastic part was calculated through a functional form, developed in a previous work, assuming that viscoplastic response of polymer composites arises mainly from the matrix viscoplasticity. The model predictions in terms of creep compliances were found to be satisfactory, compared with the experimental results. POLYM. COMPOS. 26:287–292, 2005. © 2005 Society of Plastics Engineers.     

AC-13级配钢渣沥青混合料粘弹塑本构模型研究

为了研究钢渣沥青混合料非线性粘弹塑性变形特性,提出Schapery模型与改进Swchartz模型组合的积分型粘弹塑本构模型。采用钢渣替换AC-13级配中粒径2.36 mm以上的石灰石粗骨料,制作得到钢渣沥青混合料试件。设计并开展一系列的单轴压缩蠕变实验,通过应力递增蠕变回复实验,获得不同应力条件下材料的弹性、粘弹性应变和粘塑性应变,进而拟合确定本构模型参数。利用0.4 MPa、1.0 MPa下的蠕变回复实验验证模型有效性。结果表明,模型不仅能准确刻画钢渣沥青混合料蠕变过程中的弹性、粘弹性与粘塑性变形,还可用于预测不同应力水平下钢渣沥青混合料蠕变变形规律。     

A Mathematical Model for Amorphous Polymers Based on Concepts of Reptation Theory

Mechanical behaviors of amorphous polymers have been investigated in all aspects from macroscopic thermodynamics to molecular dynamics in past five decades. Most models either have too complex mathematics or can only explain mechanical behaviors of specific materials under certain defined conditions. In this article, a mathematical model is proposed to understand mechanical behaviors of amorphous polymers with aid of the concepts of reptation theory. This new model is capable to match most experimental results of different amorphous polymers for a wide range of time and temperature effect from rubber zone to glassy zone. Above glass transitional temperature, the model shows hyperelastic behavior. Below glass transitional temperature, elastic–viscoplastic properties can be obtained. In the proposed model, no yielding surface is assumed. Hyperelasticity and Mullin's effect are illustrated in a different way without assuming strain energy function in advance. Yielding stress is controlled by Young's moduli, defect density, and defect velocity of molecular chains. Anisotropic plasticity is simply controlled by anisotropic Young's moduli. Therefore, no additional anisotropic parameters are needed to define anisotropic yielding surface. Strain rate, temperature, and hydrostatic pressure effects on yielding stress are through their effect on Young's moduli. Linear elastic, hyperelastic, viscoelastic, and viscoplastic models are put into one single equation, which makes the mathematical structure very easy to understand and easy to use. This model is validated by comparing with five existed experimental data. Proposed model also shares some features similar to the old well‐known large deformation models for amorphous polymers. POLYM. ENG. SCI., 59:2335–2346, 2019. © 2019 Society of Plastics Engineers     

Viscoelastic behavior of polymer tape in a wound roll

A viscoelastic computational model is developed that uses experimentally determined viscoelastic material properties as input and can be used to predict the behavior of a tape material in a wound roll as stresses relax over time. Experimental creep test results are used to find best‐fit creep‐compliance parameters to describe two high density data storage tape media. The two tapes used in the analysis are a developmental tape with a poly(ethylenenaphthalate) (PEN) substrate and metal particle (MP) front coat similar to linear tape open (LTO4) (referred to in this work as “Tape C”), and LTO3, a commercially available tape with a PEN substrate and MP front coat. Sets of best‐fit creep‐compliance parameters are determined for both tapes. The differences between the predicted behavior using three‐, five‐, and seven‐parameter Kelvin–Voigt models are evaluated, both for a benchmark case and in a viscoelastic wound roll model. The choice of material model is found to significantly influence the predictions of the wound roll model. The differences between different material models for the same material are on the order of the differences found between the two different materials. A material model with a higher number of creep‐compliance parameters, although more computationally expensive, produces better results, particularly over long spans of time. The relative differences between the three‐, five‐, and seven‐parameter models are shown to be qualitatively consistent for several variations in the computational model setup, allowing predictions to be made based on simple benchmarks. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Analytical approach of creep behavior of carpet yarn

Based on mechanical models, the creep behavior of carpet yarns after dynamic loading was investigated. For prediction the creep elongation, the frequently used mechanical models reported in the literature were analyzed. The mechanical models which were used in this article were: standard linear model, four‐element model, two‐component Kelvin's model, and Eyring's model. The obtained creep formulas were fitted to experimental creep data, and the parameters of the model can be obtained using the Marquardt algorithm for nonlinear regression. When comparing the experimental creep curve with the fitted curve from the mechanical model, it is clear that the four‐element model explain the experimental creep curve better. During tufting machine stops, the carpet yarns were undergone constant load. The confirmed viscoelastic model will be used to calculate total creep elongation during carpet machine stoppage. Thus, the start‐up marks which occurred at carpet machine restarts can be exactly eliminated by adjusting the feeding length according to the creep elongation. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2012     

Mechanical Response of Thermoset Polymers under High Compressive Loads, 2

Summary: A nonlinear viscoelastic material model was used to describe the experimental behaviour of thin vinyl ester specimens subjected to compression in thickness direction. The stress‐dependent material functions in the model were found in creep and strain recovery tests on thick cylindrical specimens. The elastic and creep response of thin thermoset polymer specimens subjected to compressive loads was simulated while varying the geometry of the test set samples. The calculated increase in the apparent elastic modulus and decrease of the creep‐strain rate due to reduced thickness‐to‐width ratio is in a good qualitative correlation with experimental results for corresponding geometries. The constraint due to friction and interaction with the material outside the loaded surface area were identified as the cause for high apparent stiffness, which converges with decreasing thickness to an asymptotic value dependent on the modulus and Poisson's ratio of the material.

The shape of a 2 mm‐thick specimen under compression.     

Nonlinear viscoelastic and viscoplastic response of glassy polymers

The main features of inelastic mechanical behavior of glassy state were studied theoretically and experimentally in terms of tensile stress‐strain and tensile creep experiments. A theoretical treatment introduced in earlier work, which takes into account the viscoelastic path at small strains and the viscoplastic one at higher stresses, proved to be capable of describing the main aspects of mechanical response of glassy polymers, i.e. nonlinear viscoelasticity during creep procedure, and yield stress, yield strain, strain softening and rate effect in a constant crosshead speed test.     

Time–temperature superposition principle applied to a kenaf‐fiber/high‐density polyethylene composite

The time–temperature superposition principle was applied to the viscoelastic properties of a kenaf‐fiber/high‐density polyethylene (HDPE) composite, and its validity was tested. With a composite of 50% kenaf fibers, 48% HDPE, and 2% compatibilizer, frequency scans from a dynamic mechanical analyzer were performed in the range of 0.1–10 Hz at five different temperatures. Twelve‐minute creep tests were also performed at the same temperatures. Creep data were modeled with a simple two‐parameter power‐law model. Frequency isotherms were shifted horizontally and vertically along the frequency axis, and master curves were constructed. The resulting master curves were compared with an extrapolated creep model and a 24‐h creep test. The results indicated that the composite material was thermorheologically complex, and a single horizontal shift was not adequate to predict the long‐term performance of the material. This information will be useful for the eventual development of an engineering methodology for creep necessary for the design of structural building products from these composites. © 2005 Wiley Periodicals, Inc. J Appl Polym Sci 97: 1995–2004, 2005     

A comprehensive study on frictional dependence and predictive accuracy of viscoelastic model for optical glass using compression creep test

Compression creep tests (CCTs) have been widely used in phenomenological characterization of viscoelastic materials such as glasses. However, disturbed by specimen-tool interface friction, the real stress-strain data regarding the pure viscoelastic deformation are frequently misestimated in conventional CCTs, causing decreased accuracies of the derived viscoelastic parameters. This study proposes a comprehensive CCT-based approach to develop a viscoelastic model with weakened frictional disturbance and enhanced predictive accuracy. An integrated calculation procedure is first built to mathematically characterize the frictional and viscoelastic behaviors of glass during compression. Uniaxial CCTs of a typical borosilicate glass (L-BAL42) are then performed at varied frictional conditions. The quantified coefficients of interface friction indicate that a minor frictional disturbance is achieved when Nickel foils are used as interfacial layers, whereby a more realistic viscoelastic constitutive relation of the glass is derived. The obtained frictional and viscoelastic constants are further incorporated into computational modeling of the CCT and precision molding processes. The demonstrated consistencies between the simulated and measured results (creep displacement and molding force) suggest that, by technically slashing the interface friction and theoretically correcting the friction-involved stress in CCTs, the frictional disturbance to experimental stress-strain data can be effectively weakened, and a viscoelastic model of enhanced predictive accuracy can be thus developed.     

On the nonlinear characterization of the long term behavior of polymeric materials

In the linear viscoelastic range the long term behavior of viscoelastic materials—such as polymers—can be described by using exponential series with a limited number of terms for the approximation of the relaxation modulus or of the creep compliance. This procedure can be extended to the nonlinear viscoelastic range by multiplying the linear parameters of the material by certain nonlinearity factors, which depend upon the level of the applied loading. Application of this method to stress relaxation data of several polymers has shown that nonlinearity factors can be approximated as linear functions of the applied constant strain. From creep tests, on the other hand, one can observe that the immediate strain response to the suddenly applied stress is linear elastic even in the nonlinear viscoelastic range of the investigated polymer. The computation of the linear viscoelastic material parameters as well as of the nonlinearity factors is conducted numerically by using least squares techniques. Good agreement between computed results and experimental data can be observed in the presented examples.     

Critical stress of high‐density polyethylene during stress and photo‐oxidative aging

The long‐term photo‐oxidative aging behavior of high‐density polyethylene (HDPE) under different tensile stress was studied using a stress‐aging apparatus. The aging behavior was investigated through the methods of the surface morphology observation, gel content measurement, Fourier transform infrared spectroscopy, and creep behavior. It was found that stress has influence on the development of cracks and stress induces cracking through creep deformation. With increasing stress, the cracking time decreases in a reversed S‐shape curve way, and there is a critical stress near 7 MPa where the cracking time has a maximum decreasing rate. Meanwhile, the creep deformation increases rapidly when the stress exceeds the critical stress. The critical stress of HDPE is about 20–25% of breaking strength, and HDPE with low comonomer content has good dimensional stability when the stress is less than the critical stress, while HDPE with high comonomer content has a good performance when the stress exceeds the critical stress. This study may be useful for the rational selection of HDPE for the sheath material of bridge cable. POLYM. ENG. SCI., 55:2277–2284, 2015. © 2015 Society of Plastics Engineers     

Time dependent response of polycarbonate and microcellular polycarbonate

Microcellular polycarbonate is a novel cellular material with cells on the order of 10 μm in diameter and a cell density on the order of 10⁹ cells per cm³. In this study the room temperature creep response of microcellular polycarbonate is experimentally determined and compared with the creep behavior of polycarbonate. The viscoelastic response of polycarbonate and microcellular polycarbonate is characterized using Schapery's theory of nonlinear viscoelasticity. Polycarbonate exhibited a nonlinear creep response at stress levels above 24.13 MPa, while the nonlinear behavior in microcellular polycarbonate was initiated at lower stress levels. Creep strains of microcellular polycarbonate contain a significantly higher viscoplastic component compared with the unfoamed material.     

Investigation of the viscoelastic response of high temperature AS4‐12K/RP46 composites using a micromechanical approach

The viscoelastic behavior of a RP46 polyimide resin is characterized at high temperature and the results are used within a micromechanical model to predict the viscoelastic response of a RP46 based carbon fiber composite. The creep master curve of the neat resin is obtained using the time temperature superposition principle (TTSP) from creep tests at three different temperatures, namely 180, 220, and 270°C. The viscoelastic behavior of RP46 is modeled based on Schapery's single integral constitutive equation whose Prony Series coefficients are obtained from the master curve. The acquired properties are then incorporated into a Simplified Unit Cell Micromechanical model to study the creep response of a RP46 resin based composite system. The advantage of this particular micromechanical model lies in its ability to give closed form expressions for the effective viscoelastic response of unidirectional composites as well as each of their constituents. Two types of nonlinearities were observed, one due to stress and the other due to temperature. Both of these nonlinearities can be modeled through the use of proper coefficients in the constitutive equation of the matrix material. The model predictions are found to be in good agreement with experimental results obtained from tests conducted on the RP46 resin based composite system. POLYM. COMPOS., 37:1407–1414, 2016. © 2014 Society of Plastics Engineers