A uniform phenomenological constitutive model for glassy and semicrystalline polymers

A phenomenological constitutive model is proposed on the basis of four models: the Johnson‐Cook model, the G'Sell‐Jonas model, the Matsuoka model, and the Brooks model. The proposed constitutive model has a concise expression of stress dependence on strain, strain rate and temperature. It is capable of uniformly describing the entire range of deformation behavior of glassy and semicrystalline polymers, especially the intrinsic strain softening and subsequent orientation hardening of glassy polymers. At least three experimental stress‐strain curves including variation with strain rate and temperature are needed to calibrate the eight material coefficients. Sequential calibration procedures of the eight material coefficients are given in detail. Predictions from the proposed constitutive model are compared with experimental data of two glassy polymers, polymethyl‐methacrylate and polycarbonate under various deformation conditions, and with that of the G'Sell‐Jonas model for polyamide 12, a semicrystalline polymer.     

Plastic deformation of low‐density polyethylene reinforced with biodegradable polylactide,Part 2: Creep characterization and modeling

The behavior of low‐density polyethylene (LDPE) and two blends prepared with polylactide (PLA) was determined by means of a novel video‐controlled testing method under stretching at constant true strain rate, under creep at constant true stress, and under creep at constant nominal stress. Most tests were performed at 23°C and 50°C. In this second part, the experimental data are modeled with the G'Sell‐Jonas phenomenological law expressing the axial true stress versus axial true strain and axial true strain rate. This model describes correctly the various deformation stages: (i) initial viscoelasticity, (ii) plastic yielding, and (iii) strain hardening up to rupture. It shows clearly the reinforcing effect of the PLA particles that increases the yield stress in stretching experiments and slows down the deformation kinetics under creep. It is shown how the local stress/strain behavior is related to the standard force/extension curves. Consequently, it is proposed that tensile tests at constant true strain rates should be systematically preferred to creep tests for the characterization of constitutive relations because they take much less time to be performed. POLYM. ENG. SCI., 2011. © 2010 Society of Plastics Engineers.     

Analysis of multiaxial impact behavior of polymers

Impact performance is a primary concern in many applications of polymers. In this paper, finite element analysis (FEA) and ABAQUS/Explicit are used to simulate the deformation and failure of polymers in the standard ASTM D3763 multiaxial impact test. The specimen geometry and loading mode in this multiaxial impact test provides a close correlation with practical impact conditions. A previously developed constitutive model (“DSGZ” model) for polymers under monotonic compressive loading is generalized and extended for any loading mode and takes into account the different behavior of polymers in uniaxial tensile and compression tests. The phenomenon of thermomechanical coupling during plastic deformation is also included in the analysis. This generalized DSGZ model, along with thermomechanical coupling and a failure criterion based on maximum plastic strain, is incorporated in the FEA model as a coupled‐field user material subroutine to produce a unique tool for the prediction of the impact behavior of polymeric materials. Load‐displacement curves from FEA simulations are compared with experimental data for two glassy polymers, ABS‐1 and ABS‐2. The simulations and experimental data are in excellent agreement up to the maximum impact load. It is shown that not accounting for the different behavior of the polymer in uniaxial tensile and compression tests and thermomechanical coupling effects leads to an overestimation of the load and impact energy, especially at large displacements and plastic deformations. Friction also plays an important role in the impact behavior. If one neglects the friction between the striker and polymer disk, the predicted impact loads are lower as compared with experimental data at large displacements.     

Evaluation of the material constants of nitrile butadiene rubbers (NBRs) with different carbon black loading (CB): FE-simulation and experimental

In this paper, the experimental data of the mechanical properties of NBR with different carbon black loading (CB) have been determined through tension, compression and relaxation tests. Nonlinear mechanical behaviors of the rubbers are described by strain energy functions in order to guarantee that rigid body motions play no role in the constitutive law. The mathematical models are based on the existence of strain energy density functions, W, to be the scalar potential that depends on the component of the right Cauchy–Green deformation tensor or Green’s strain tensor. The experimental data are fitted to these models in order to find the rubber material constants. Visco-hyperelasticity behavior is generated by fitting the experimental data provided from standard quasi-static tests (tensile, compression) and will be applied to determine the material constants. While standard relaxation tests are used for obtaining the scalar multipliers and relaxation time constants. A comparison between the experimental load/displacement response and finite element (FE)-analysis of a uniaxial compression test at different CB loading is presented.     

Experimental and numerical study on the performance of hollow and concrete‐filled elliptical steel columns subjected to severe fire

This paper presents the results of an experimental and validated theoretical study to investigate the performance of steel columns with hollow and concrete‐filled elliptical sections subjected to hydrocarbon fire. The test programme involved 18 columns with 200 × 100 × 8‐mm, 300 × 150 × 8‐mm and 400 × 200 × 8‐mm elliptical sections representing slenderness of 50, 33 and 24, respectively. The 1800‐mm columns were subjected to the severe hydrocarbon fire curve and tested under loadings ratios of 20%, 40% and 60% of the EC3 ultimate strength. The paper presents the obtained experimental results including measured axial and lateral displacements, failure temperatures and failure time. A three‐dimensional model was built using the finite element method (FEM) and was validated using the obtained tests results. The finite element model showed an excellent agreement with tests results of failure temperatures, failure modes, and axial and lateral displacements. However, because of restrictions in the software capabilities, the mechanical–thermal behaviour of concrete including spalling was not considered in the model. The verified finite element model was used to conduct a parametric analysis involving a range of parameters of loading level and slenderness. The study has shown that the concrete‐filled sections have demonstrated an improved fire resistance when compared with the hollow sections under the low loading ratios. The FEM model has successfully predicted the unique thermal profile of elliptical section under fire, which was observed during the tests. Copyright © 2015 John Wiley & Sons, Ltd.     

Modeling of visco‐hyperelastic behavior of transversely isotropic functionally graded rubbers

In this article, visco‐hyperelastic constitutive model is developed to describe the rate‐dependent behavior of transversely isotropic functionally graded rubber‐like materials at finite deformations. Zener model that consists of Maxwell element parallel to a hyperelastic equilibrium spring is used in this article. Steady state response is described by equilibrium hyperelastic spring and rate‐dependence behavior is modeled by Maxwell element that consists of a hyperelastic intermediate spring and a nonlinear viscous damper. Modified and reinforced neo‐Hookean strain energy function is proposed for the two hyperelastic springs. The mechanical properties and material constants of strain energy function are graded along the axial direction based on exponential function. A history‐integral method has been used to develop a constitutive equation for modeling the behavior of the model. The applied history integral method is based on the Kaye‐BKZ theory. The material constant parameters appeared in the formulation have been determined with the aid of available uniaxial tensile experimental tests for a specific material and the results are compared to experimental results. It is then concluded that, the proposed constitutive equation is quite proficient in forecasting the behavior of rubber‐like materials in different deformation and wide ranges of strain rate. POLYM. ENG. SCI., 56:342–347, 2016. © 2016 Society of Plastics Engineers     

Viscoelastic constitutive model for uniaxial time‐dependent ratcheting of polyetherimide polymer

Based on the experimental observations, a cyclic nonlinear viscoelastic constitutive model was proposed to describe the uniaxial time‐dependent ratcheting of polyetherimide (PEI) polymer under tension–compression and tension–tension cyclic loading. The model was constructed by extending the nonlinear viscoelastic Schapery model (Schapery, Polym. Eng. Sci., 9, 295 (1969)). The extension emphasized the changes of parameter functions used in the original model, which enabled the model to describe the ratcheting of polymer material. Comparing the simulations with corresponding experimental results, the capability of the extended model to predict the uniaxial time‐dependent ratcheting of PEI was verified. It is shown that the extended model can reasonably describe the uniaxial time‐dependent ratcheting of the polymer under the tension–compression and tension–tension cyclic loading with different peak‐holdings, stress rates, and stress levels. POLYM. ENG. SCI., 52:1874–1881, 2012. © 2012 Society of Plastics Engineers     

Assessment of hyperelastic material models for the application of adhesive point-fixings between glass and metal

For the investigation of adhesive point-fixings a computationally demanding finite element model is required. The accuracy of the numerical results depends highly on the validity of the used material models, which describe the deformation behaviour of the adhesive. The material models are derived from curve-fitting the mathematical expressions to experimental data mostly derived from uniaxial and equibiaxial experiments. In literature the suitability of the used material models is determined by comparing the numerical results from the same uniaxial and equibiaxial experiments to the experimental results. In contrast, in this contribution, the material models are validated by two additional validation experiments, i.e. an adhesive point-fixing loaded in uniaxial tension and an adhesive point-fixing loaded in a combination of tension and shear.After comparison of the numerical and experimental displacements, it appears that the material models that are calibrated by shear tests or by a combination of shear tests yield the best results. In addition, most numerical load-displacement curves have an almost linear gradient at small strains. Such behaviour is also demonstrated in the experimental measurements of the deformation.     

Impact behavior and modeling of engineering polymers

Because of their many unique and desirable properties, engineering polymers have increasingly been applied in applications where impact behavior is of primary concern. In this paper, the impact behavior of a glassy polymer acrylonitrile‐butadiene‐styrene (ABS) and a semicrystalline polymer alloy of polycarbonate and polybutylene‐terephthalates (PBT) are obtained as a function of impact velocity and temperature from the standard ASTM D3763 multiaxial impact test. As computer simulation of destructive impact events requires two material models, a constitutive model and a failure model, uniaxial mechanical tests of the two polymers are carried out to obtain true stress vs, true strain curves at various temperatures and strain rates. The generalized DSGZ constitutive model, previously developed by the authors to uniformly describe the entire range of deformation behavior of glassy and semicrystalline polymers for any monotonic loading modes, is calibrated and applied. The thermomechanical coupling phenomenon of polymers during high strain rate plastic deformation is considered and modeled. A failure criterion based on maximum plastic strain is proposed. Finally, the generalized DSGZ model, the thermomechanical coupling model, and the failure criterion are integrated into the commercial finite element analysis package ABAQUS/Explicit through a user material subroutine to simulate the multiaxial impact behavior of the two polymers ABS and PBT. Impact load vs. striker displacement curves and impact energy vs. striker displacement curves from computer simulation are compared with multiaxial impact test data and were found to be in good agreement.     

Three‐dimensional imaging of large compressive deformations in elastomeric foams

Specimens of silica‐reinforced polysiloxane foam pads were three‐dimensionally imaged during axial compressive loading to densification. The foams' behavior was highly nonlinear and showed the three characteristic regions of linear elastic, elastic buckling, and densification. A finite‐element technique, based upon conversion of the image voxels to finite elements, was used to calculate the mechanical properties of the foams. The results were compared with conventional mechanical testing and theory. The finite‐element calculations were in excellent agreement with experimental stress–strain data over the entire range of compressive loading. Theoretical models, on the other hand, overestimated the stiffness of the foam above the elastic buckling stress by not correctly predicting the abruptness of the transition from elastic buckling to densification. Three‐dimensional analysis of the deformed microstructures indicated that there was a critical foam density beyond which the cell morphology suddenly changed from open‐celled to closed‐celled and that this “phase”‐like transition was responsible for the abrupt increase in stiffness near densification. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 80: 1746–1755, 2001     

Effect of high‐temperature annealing on the elastoplastic response of isotactic polypropylene in loading–unloading tests

A series of uniaxial tensile loading–unloading tests is performed on isotactic polypropylene at room temperature. Prior to mechanical testing, injection‐molded specimens are annealed for 24 h at temperatures T = 145, 150, 155, 158, 160, 163, and 165°C, which cover the entire region of high‐temperature annealing temperatures. A constitutive model is developed for the elastoplastic behavior of a semicrystalline polymer at small strains. The stress–strain relations are determined by six adjustable parameters that are found by matching observations in cyclic tests. Fair agreement is demonstrated between the experimental data and the results of numerical simulation. It is shown that all material constants are affected by the annealing temperature, which is explained by changes in the crystalline morphology driven by thermal treatment. Some of the adjustable parameters experience finite jumps in the vicinity of the critical temperature T_c = 159°C. These jumps are attributed to the α₂ → α₂′ phase transformation. © 2003 Wiley Periodicals, Inc. J Appl Polym Sci 90: 186–196, 2003     

A procedure for modeling the nonlinear viscoelastoplastic creep of HDPE at small strains

HDPE pipes are frequently laid in buried or submerged conditions and are often subjected to considerable internal pressure. This context requires the consideration of HDPE as a structural material and demands constitutive models to predict failure possibilities in short and long terms. This article presents an approximate procedure to simulate the viscoelastoplastic nature of HDPE's material behavior under creep conditions. While a generalized Kelvin‐Voigt model based on Prony series is used to model viscoelasticity, the power law of Zapas‐Crissman is adopted to account for viscoplastic effects. The associated material parameters are obtained from experimental creep‐recovery tests evaluated at different stress levels and constant temperature. As this type of test allows an uncoupled procedure for identifying the viscoelastic and viscoplastic material parameters, this task is divided into two stages: (i) a constrained nonsmooth optimization problem is defined and solved for the viscoelastic parameters, and (ii) the viscoplastic parameters are determined by linear regression. Thereafter, the viscoelastic and viscoplastic parameters obtained for each experimental stress level are interpolated linearly for intermediate stress conditions. Finally, a numerical‐experimental example is presented, showing that the proposed procedure is able to reproduce adequately more complex loading conditions. POLYM. ENG. SCI., 57:144–152, 2017. © 2016 Society of Plastics Engineers     

On the application of a damped model to the falling weight impact characterization of glass beads–polystyrene composites

Instrumented falling weight impact tests were carried out to characterize the mechanical behavior of a material pattern formed by polystyrene and different amounts of glass beads. This characterization was performed at high strain rate using two different impact arrangements: the first uses high impact energy at the striker, whereas the second uses a low‐impact energy. Starting from a conservative model, a nonconservative one has been proposed for the low‐energy impact configuration as a better approach to the material behavior. In this latter model, the energy losses were quantified through the restitution coefficient. Two alternative methods for its calculation are described. The results shows good agreement between the flexural modulus and break stresses calculated in either the low‐ or the high‐energy arrangement; however, the low‐energy impact method yields more confidence results. Using the proposed model, the composites' fracture onset was determined, and also in the samples with low content of glass beads, it was possible to assess the micromechanism of failure, given the estimation for the stress to produce crazing. © 2004 Wiley Periodicals, Inc. J Appl Polym Sci 93: 1271–1284, 2004     

Rubber modeling using uniaxial test data

Accurate modeling of large rubber deformations is now possible with finite‐element codes. Many of these codes have certain strain‐energy functions built‐in, but it can be difficult to get the relevant material parameters and the behavior of the different built‐in functions have not been seriously evaluated. In this article, we show the benefits of assuming a Valanis–Landel (VL) form for the strain‐energy function and demonstrate how this function can be used to enlarge the data set available to fit a polynomial expansion of the strain‐energy function. Specifically, we show that in the ABAQUS finite‐element code the Ogden strain‐energy density function, which is a special form of the VL function, can be used to provide a planar stress–strain data set even though the underlying data used to determine the constants in the strain‐energy function include only uniaxial data. Importantly, the polynomial strain‐energy density function, when fit to the uniaxial data set alone, does not give the same planar stress–strain behavior as that predicted from the VL or Ogden models. However, the polynomial form does give the same planar response when the VL‐generated planar data are added to the uniaxial data set and fit with the polynomial strain‐energy function. This shows how the VL function can provide a reasonable means of estimating the three‐dimensional strain‐energy density function when only uniaxial data are available. © 2001 John Wiley & Sons, Inc. J Appl Polym Sci 81: 837–848, 2001     

The dynamic response and failure of Polycarbonate plate by soft body impact

This article is mainly to experimentally and numerically investigate the dynamic response and failure of Polycarbonate (PC) plate against strike by soft body. The experimental results show that high speed soft body impact leads to a large global displacement for PC sheet, though, the obtained strain data shows deformation of PC material are still small. This evidence allows us to employ a thermo‐viscoelastic constitutive model we proposed in our previous work, where the model parameters are determined based on the uniaxial tension test data of PC materials, to describe the PC plate. Then, the simulation is made in finite element (FE) software LS‐DYNA and computational results get a fair agreement with experiments including displacement, strain, and the crack propagations at high velocity impact. The temperature effect on mechanical behavior of PC sheet under impact is numerically studied as well. It is found that the effect gets more significant with the increase of impact velocity, and the higher temperature of PC sheet would lead to its larger deflection but smaller maximum resistance force and principal stress. POLYM. ENG. SCI., 56:1160–1168, 2016. © 2016 Society of Plastics Engineers     

Fracture behavior of sisal fiber–reinforced starch‐based composites

The fracture behavior of biodegradable fiber–reinforced composites as a function of fiber content under different loading conditions was investigated. Composites with different fiber content, ranging from 5 to 20 wt%, were prepared using commercial starch‐based polymer and short sisal fibers. Quasistatic fracture studies as well as instrumented falling weight impact tests were performed on the composites and the plain matrix. Results showed a significant increase in the crack initiation resistance under quasistatic loading. This was caused by the incorporation of sisal fibers to the matrix and the development of failure mechanisms induced by the presence of the fibers. On the other hand, a modest increasing trend of the resistance to crack initiation with fiber loading was detected. An improved fracture behavior was also observed when the impact loading was parallel to the thickness direction. Under these experimental conditions, the composites exhibited higher values of ductility index, energy at initiation and total fracture energy than the plain matrix. Furthermore, an increasing trend of these parameters with fiber content was detected in the biocomposites. Overall, the addition of sisal fibers to the biodegradable matrix appears to be an efficient mean of improving fracture behavior under both quasistatic and impact loading conditions. POLYM. COMPOS. 26:316–323, 2005. © 2005 Society of Plastics Engineers     

Viscoplastic parameter identification of temperature‐dependent mechanical behavior of modified polyphenylene oxide polymers

Modified polyphenylene oxide (MPPO) is a widely known thermoplastic polymer and is extensively utilized for weight reduction of automobiles since it possesses outstanding mechanical properties, such as resistance and toughness. In this study, the viscoplastic behaviors of MPPO with respect to changes in temperature were identified through an approximate optimization method. For this work, parameter studies were conducted with a tensile simulation of the MPPO polymer, in accordance with the modified two‐layer viscoplastic material parameters and the suggested shift parameter. The sensitivity tendency of the force‐displacement curves was captured in accordance with the material parameters. Computational experiments for obtaining calibration error data were performed using the material parameters based on interior central composite design. Surrogate models of root mean square error relative to force and displacement were generated using the response surface method. The accuracy of the surrogate models was evaluated with R‐square. Optimization for obtaining the material parameters was performed using the non‐dominant sorting genetic algorithm‐II. The results showed that the calibration error from the finite element analysis was minimized and agreed with experimental data. POLYM. ENG. SCI., 59:E200–E211, 2019. © 2018 Society of Plastics Engineers     

Finite element modeling of curing of epoxy matrix composites

A two‐dimensional finite element model is developed to simulate and analyze the mechanisms pertaining to resin flow, heat transfer, and consolidation of laminated composites during autoclave processing. The model, which incorporates some of the best features of models already in existence, is based on Darcy's law, the convection–diffusion heat equation, and appropriate constitutive relations. By using a weighted residual method, a two‐dimensional finite element formulation for the model is presented and a finite element code is developed. Numerical examples, including a comparison of the present numerical results with one‐dimensional and two‐dimensional analytical solutions, are given to indicate the accuracy the finite element formulation. Moreover, using the finite element code, the one‐dimensional cure process of a laminate made of 228 and 380 plies of AS4/3501‐6 unidirectional tape is simulated and numerical results are compared with available experimental results. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 103: 2310–2319, 2007     

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