FEM simulation of polymeric foam with random pore structure: Uniaxial compression with loading rate effect

This study establishes FEM modeling for compressive deformation behavior of polymeric foams with different loading rates. The polymeric foam used in this study was made from polypropylene (the base matrix of the polymer) with porosity of about 95%. The pore size and shape were randomly distributed in the foam. The X-ray CT method was first conducted to observe the microstructure, the geometric feature of which was reproduced in the FEM model. Uniaxial compression tests with different loading speeds were carried out to investigate an effect of loading rate (strain rate) dependency on the deformation behavior. By using the X-ray CT method, in situ observation of microscopic deformation was carried out. Furthermore, FEM computations were carried out to simulate macroscopic and microscopic deformation behaviors. The random porous structure was modeled using Surface Evolver. The elastoplastic property with strain rate dependency was used in this model. The established FEM framework may be useful for a porous polymer with a random pore structure and for deformation modeling with strain rate effect.     

Experimental and numerical investigations of the anisotropic deformation behavior of low-density polymeric foams

Low-density porous materials and foams have been widely used for a variety of applications, such as light structural components, impact energy absorption, thermal insulation and sound absorption. The macroscopic deformation of such materials is strongly dependent on their inherent micro-cellular structure. This study investigated the compressive anisotropic deformation behavior of low-density polymeric foam by using X-ray computed tomography (CT) and the finite element method (FEM) in order to understand both the microscopic and macroscopic deformation behavior. The foams used in this study have a closed cell structure, with pores that are elliptical in shape. Three different types of expansion ratios were employed. The porosities of these materials were 93.5, 95, and 96%. From the observations using the X-ray CT method, the averaged pore heights were 1 mm and the aspect ratios were 2, 2.5, and 2.25, respectively. The foam demonstrated anisotropic deformation, dependent on the uni-axial compression direction. It was found that the deformation rigidity in the longitudinal direction was larger than that in the transverse direction. By using the X-ray CT method in situ, the microscopic deformation behavior when subjected to compressive loading was observed. Deformation and collapse of pores was observed for both directions during the loading. In conjunction with this, FEM computations were carried out to elucidate how such pore geometry undergoes elastoplastic deformation and leads to macroscopic deformation behavior. The FEM-created three-dimensional spatial structures were based on elongated rhombic dodecahedrons. It is revealed that the FEM computation shows relatively good agreement with the experimental results. Thus, our experimental and computational models may be useful for microstructural design using anisotropic cellular materials.     

Constitutive model and failure locus of a polypropylene grade used in offshore intake pipes

BorECO^®™ BA212E is a polypropylene block co-polymer which has become a common material in the manufacturing of large diameter non-pressurized gravity offshore intake pipelines. These lines are used for transportation of sea water for cooling of petrochemical process plants. The pipe sections are joined by butt heat fusion welding to create the pipeline. Recently a few premature failures of such pipelines have been reported in the field. Hence, there is a need to characterize the constitutive behavior of the pipe and weld material in order to properly design these pipes. The aim of this work is to determine the material constitutive behaviors of the pipe material and the welded joint material. Uniaxial tensile tests of both the pipe and weld joint material are conducted at various strain rates. Both the pipe and weld material show a rather high strain rate dependency, with the weld material having about half the yield strength than that of the pipe material. An analytical constitutive material model is developed for both the pipe and weld material, incorporating the effect of strain rate. The failure locus, expressed in terms of the equivalent plastic strain at failure vs. the stress triaxiality, for both materials is also determined as part of the constitutive model using notched dumbbell specimens. The constitutive model and failure loci for the pipe and weld material are implemented in a finite element model (FEM) and are validated by conducting a series of independent four-point bend experiments on both material types. The validation is carried out by comparing the FEM results of the four-point bend model with the experimental results, which show a rather good agreement.     

Strain-hardening modulus of cross-linked glassy poly(methyl methacrylate)

The strain hardening modulus, defined as the slope of the increasing stress with strain during large strain uniaxial plastic deformation, was extracted from a recently proposed constitutive model for the finite nonlinear viscoelastic deformation of polymer glasses, and compared to previously published experimental compressive true stress versus true strain data of glassy crosslinked poly(methyl methacrylate) (PMMA). The model, which treats strain hardening predominantly as a viscous process, with only a minor elastic contribution, agrees well with the experimentally observed dependence of the strain hardening modulus on strain rate and crosslink density in PMMA, and, in addition, predicts the well-known decrease of the strain hardening modulus in polymer glasses with temperature. General scaling aspects of continuum modeling of strain hardening behavior in polymer materials are also presented. © 2010 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 48: 1464–1472, 2010     

Analysis of the cyclic tensile behaviour of an elasto-viscoplastic polyamide

The present paper is concerned with the experimental and theoretical investigation of the progressive accumulation of inelastic deformation observed in cyclic tension tests performed on a particular polyamide. The elastic properties are not strongly affected by the strain rate, but the strain hardening induced by the plastic deformation is rate-dependent. Thus, the material behaviour is elasto-viscoplastic rather than viscoelastic or elasto-plastic. For the polymer studied in this paper, the kinematic hardening is much more significant than the isotropic hardening, and a negative plastic strain rate may occur even with a positive stress. The kinematic hardening is strongly dependent, not only on the accumulated plastic strain, but also on the loading rate. An elasto-viscoplastic mechanical model able to describe the cyclic inelastic behaviour for an arbitrary loading history is proposed. All parameters that arise in the theory are identified experimentally. The preliminary theoretical results concerning the modelling of cyclic load-unload tests are in good agreement with the experiments.     

Dynamic property and constitutive model of polyvinyl butaral material at high strain rates

The polyvinyl butaral (PVB) interlayer of automotive windshield plays an important role in the protection of both pedestrian and passenger, the mechanical property of PVB material should be in‐depth studied. In this article, the systematical uniaxial tensile experiments of PVB material under high strain rates are conducted, the strain rates range from 125.6 to 3768 s^?1. The results of experiments show that there exists a phenomenon of stress spurt caused by the stress hardening in the final stage of tension, and the strain rate exerts great influence on mechanical property of PVB material. Further, the data fitting basing on Mooney–Rivlin model is carried out, it is found that the fitting results are consistent with the experiment data, which means that the Mooney–Rivlin constitution model can describe the large deformation behavior of PVB material. At last, the rate‐dependent mechanical behavior of the PVB material is further investigated in this article. On the basis of the experiment results and Johnson–Cook model, a rate‐dependent constitutive model is proposed to describe the tensile mechanical property of PVB material under high strain rates. This work will be beneficial to the simulation and analysis of automotive collision safety and pedestrian safety protection, which are related to damage of automotive windshield. Copyright © 2014 John Wiley & Sons, Ltd.     

On the time and indentation depth dependence of hardness,dissipation and stiffness in polydimethylsiloxane

Nanoindentation tests were performed on polydimethylsiloxane to characterize its mechanical behavior at different indentation depths and loading times. Astonishing indentation size effects have been observed in these experiments where the universal hardness increases by about 15 times from indentation depths of 5000 down to 100 nm. The hardness was found to depend on the loading time at small indentations, while at larger indentation depths the hardness hardly changed with loading time. In an attempt to unveil the underlying deformation mechanisms, an in-depth experimental study is pursued in this article with detailed analysis of the experimental data. Applying different loading times, the indentation experiments were evaluated at indentation depths from 100 to 5000 nm with respect to (a) universal hardness, (b) ratio of remaining indentation depth after unloading to maximum indentation depth, (c) ratio between elastic and total indentation works, and (d) indentation stiffness at maximum applied force. All these characteristics are found to be significantly different compared to a reference material that does not exhibit indentation size effects. The corresponding experimental data has been analyzed with an existing indentation depth dependent hardness model for polymers that has been motivated by a Frank elasticity related theory incorporating rotation gradients.     

Anisotropic compressive behavior of rigid PVC foam at strain rates up to 200 s−1

The elevated strain rate compressive response of closed-cell polyvinyl chloride (PVC) foam at various densities is investigated. Two loading directions, (i.e., parallel and perpendicular to foam rise direction) were considered to investigate structural anisotropy. The elevated strain rates tests (up to 200 s⁻¹) were performed using a customized drop tower device. Engineering stress/strain behavior, energy dissipation, and maximum stress capacity were obtained for each density and compared against each other. Except for the lowest density of 45 kg/m³, strain rate effects were clearly observed through increased compressive strength and plateau stress when loading in the foam rise direction. The strain rate effect is more evident at higher densities. However, no significant strain rate effect was observed when loading perpendicular to the foam rise direction. Scanning electron microscopy (SEM) analysis showed that plastic hinges are the primary deformation mechanism for PVC foam cells. An analytical model has been calibrated using the experimental results and successfully predicted the mechanical response of the foam. Shape anisotropy has been measured employing the SEM images. The analytical approach was also able to predict the foam's anisotropic mechanical response.     

Investigation for impact behavior of acrylonitrile-butadiene-styrene amorphous thermoplastic

Acrylonitrile-Butadiene-Styrene (ABS) is an important terpolymer that find applications in numerous engineering fields due to its high impact resistance. Thereby, the experimental characterzation and numerical validation of its impact behavior is the main focus of this investigation. Impact tests were carried out using hemi-spherical impactor at three velocities of 4.43 m/s, 5.775 m/s and 6.264 m/s, respectively. The localized material change caused by microvoids was noticed near the impact zone on non-impacted surfaces for all impact velocities. The damage morphologies on the non-impacted surface for 4.43 m/s includes plastic deformation and crazes without any microvoids, whereas a combination of crazes and microvoids were discovered for other two velocities. Tensile tests at various strain rates, compression and shear tests were performed on ABS material at quasi-static conditions to utilize as an input to the SAMP-1 material model in impact simulations. The predicted impact histories and damage morphologies were compared with the experimental results.     

The deformation and failure response of closed-cell PMDI foams subjected to dynamic impact loading

The present work aims to investigate the bulk deformation and failure response of closed-cell Polymeric Methylene Diphenyl Diisocyanate (PMDI) foams subjected to dynamic impact loading. First, foam specimens of different initial densities are examined and characterized in quasi-static loading conditions, where the deformation behavior of the samples is quantified in terms of the compressive elastic modulus and effective plastic Poisson's ratio. Then, the deformation response of the foam specimens subjected to direct impact loading is examined by taking into account the effects of material compressibility and inertia stresses developed during deformation, using high speed imaging in conjunction with 3D digital image correlation. The stress-strain response and the energy absorption as a function of strain rate and initial density are presented and the bulk failure mechanisms are discussed. It is observed that the initial density of the foam and the applied strain rates have a substantial influence on the strength, bulk failure mechanism and the energy dissipation characteristics of the foam specimens.     

Misorientation mapping for visualization of plastic deformation via electron back-scattered diffraction.

The ability to map plastic deformation around high strain gradient microstructural features is central in studying phenomena such as fatigue and stress corrosion cracking. A method for the visualization of plastic deformation in electron back-scattered diffraction (EBSD) data has been developed and is described in this article. This technique is based on mapping the intragrain misorientation in polycrystalline metals. The algorithm maps the scalar misorientation between a local minimum misorientation reference pixel and every other pixel within an individual grain. A map around the corner of a Vickers indentation in 304 stainless steel was used as a test case. Several algorithms for EBSD mapping were then applied to the deformation distributions around air fatigue and stress corrosion cracks in 304 stainless steel. Using this technique, clear visualization of a deformation zone around high strain gradient microstructural features (crack tips, indentations, etc.) is possible with standard EBSD data.     

Relationship between compressive yield and tensile behavior in glassy thermoplastics

The effect of temperature and strain rate on the compressive yield behavior of polystyrene is compared with the effect of the same variables on crazing in tension. The results support the conclusion of other, more extensive work, which shows that crazing involves the same types of molecular processes as those which occur during deformation under compression and shear. An improved method of measuring compressive stress–strain curves is then described, and the compressive yield stress is also compared with an extrapolated tensile yield stress. The difference between the two is in line with concepts which assume a dependence of yield stress on the state of hydrostatic tension (or compression). It can be adequately described by the Mohr-Coulomb yield criterion. Application of this criterion also enables a theoretical stress strain curve in tension to be derived from other results in compression. Comparison of the tensile stress–strain curve so obtained with those which can be directly measured with other plastics, supports the hypothesis that crazing is favored by a marked decline in engineering stress during tensile elongation (plastic instability).     

Athermal simulation of plastic deformation in amorphous solids at constant pressure

An algorithm is introduced for the molecular simulation of constant-pressure plastic deformation in amorphous solids at zero temperature. This allows to directly study the volume changes associated with plastic deformation (dilatancy) in glassy solids. In particular, the dilatancy of polymer glasses is an important aspect of their mechanical behavior. The new method is closely related to Berendsen's barostat, which is widely used for molecular dynamics simulations at constant pressure. The new algorithm is applied to plane strain compression of a binary Lennard-Jones glass. Conditions of constant volume lead to an increase of pressure with strain, and to a concommitant increase in shear stress. At constant (zero) pressure, by contrast, the shear stress remains constant up to the largest strains investigated (ε = 1), while the system density decreases linearly with strain. The linearity of this decrease suggests that each elementary shear relaxation event brings about an increase in volume which is proportional to the amount of shear. In contrast to the stress–strain behavior, the strain-induced structural relaxation, as measured by the self-part of the intermediate structure factor, was found to be the same in both cases. This suggests that the energy barriers that must be overcome for their nucleation continually grow in the case of constant-volume deformation, but remain the same if the deformation is carried out at constant pressure. © 2004 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 42: 2057–2065, 2004     

A theory for the drawing of oriented crystalline polymers

The load-elongation behavior during the postneck drawing stage in the deformation of crystalline polymers is shown to be modeled quantitatively by an aligned short-fiber composite in which crystalline fibrils form the reinforcing phase in a matrix of less well-ordered material. Three modes of deformation are distinguished in the model and are shown to correspond to the observed loadelongation relations in polyethylene and polypropylene. The regions are (I) elastic–plastic crystals in an elastic matrix, (II) elastic–plastic crystals in an elastic–plastic matrix, (III) elastic crystals in an elastic–plastic matrix. A requirement of the theory is that the flow stress in the crystals is little affected by temperature whereas that in the matrix falls as the temperature rises. Expressions are given for stress in terms of the applied strain and the relevant parameters of the system: concentration of fibrils, length and diameter of fibrils, and elastic and yield properties of fibrils and matrix.     

Uniaxial ratcheting behavior of polytetrafluoroethylene at elevated temperature

A series of uniaxial ratcheting experiments has been carried out on cold compaction polytetrafluoroethylene (PTFE) specimens. All the tests were performed under stress control at elevated temperature. The effects of mean stress, stress amplitude, applied temperature and their histories on the ratcheting behavior of PTFE were studied. It is shown that, as the applied temperature was raised, the elastic modulus of PTFE declined rapidly. The ratcheting strain increased as the mean stress, stress amplitude and temperature increased. Especially, when the temperature was over 100 °C, the ratcheting strain accumulated rapidly. Furthermore, the loading histories also play an important role in the progress of ratcheting. Previous cycling with higher mean stress and stress amplitude greatly restrains ratcheting strain of subsequent cycling at lower ones. Such a phenomenon is due to the enhancement of the material deformation resistance caused by the previous loadings. As the applied temperature changes, the ratcheting strain still accumulates along the direction of mean stress.     

Continuous stiffness mode nanoindentation response of poly(methyl methacrylate) surfaces

Indentation is a comparatively simple and virtually nondestructive method of determining mechanical properties of material surfaces by means of an indenter inducing a localized deformation. The paper present experimental results of the load-displacement curves, the hardness and the elastic modulus data, and associated analysis for poly(methyl methacrylate) (PMMA) surfaces as a function of contact displacement. The experimental results include continuous stiffness indentations performed using constant loading rate and constant displacement rate experiments. The continuous stiffness indentation involves continuous calculation of a material stiffness, and hence hardness and elastic modulus of surfaces, during discrete loading-unloading cycles, as in a conventional indentation routine, and in a comparatively smaller time constant. The dependence of the compliance curves, the hardness, the elastic modulus and the plasticity index upon the imposed penetration depth, the applied normal load and the deformation rate are described. Tip area and load frame calibrations for the continuous stiffness indentation are also reported. The paper includes practical considerations encountered during indentation of polymers specifically at low penetration depths. The experimental results show a peculiarly harder response of PMMA surfaces at the submicron (near to surface) layers.     

Experimental investigation and modeling of the mechanical behavior of PC/ABS during monotonic and cyclic loading

The purpose of this work is to characterize the mechanical behavior of blends of polycarbonate (PC) and acrylonitrile-butadiene-styrene (ABS) during monotonic and cyclic loading. Compression experiments were performed using a SHIMADZU universal testing machine (10⁻⁴ to 10⁻² s⁻¹) and a split Hopkinson pressure bar (1600–5000 s⁻¹), with, the test temperatures ranging from 293 to 353 K. The influence of the rate and temperature on the deformation of PC/ABS is discussed in detail. Based on the investigation of numerous constitutive models, a phenomenological model called DSGZ was chosen to describe the compression behavior of PC/ABS. This model could not accurately reproduce the deformation of polymers at high strain rates when utilizing the same material coefficients for the low and high strain–rate deformations. In addition, this model was unable to capture the deformation features during unloading and subsequent reloading when adopting the original stress–strain updating algorithm. Hence, some improvements to the model have been implemented to better predict the deformation. Finally, the model predictions are shown to be consistent with the experimental results.     

Irreversible deformation of isotactic polypropylene in the pre-yield regime

In the modeling of the mechanical response of a polymer over a large strain range, the nonlinear viscoelastic and viscoplastic behavior must be considered. For many polymers, nonlinear behavior is observed at low loads, e.g. by a stress-dependence of the creep compliance for stresses above 2 MPa in case of the polypropylene used in this study. Additionally, plastic deformation has been observed at strains below the yield point for several polymers. In this study, the irreversible deformation by cavitation and shear yielding of polypropylene are characterized in the pre-yield regime in uniaxial tensile tests using digital image correlation. The recovery of strain after unloading at a prescribed strain level is measured and used to identify the evolution of the plastic strain during uniaxial tension. An experimental technique for simultaneous determination of the true stress–true strain curve and the degree of stress whitening, which relates to the amount of cavitation, is introduced and the initiation of cavitation is compared to the plastic deformation detected in strain recovery at various temperatures.     

Relationship of deformation behavior to thermal transitions of ethylene/styrene and ethylene/octene copolymers

The stress‐strain response of low‐crystallinity ethylene‐octene (EO) and ethylene‐styrene (ES) copolymers with 7–20 mol % comonomer was compared over a temperature range that spanned the glass‐transition and crystal melting regions. Above the onset temperature of the glass transition, the copolymers exhibited elastomeric behavior with low initial modulus, uniform deformation to high strains, and high recovery after the stress was released. In the glass‐transition range, an initial low‐stress elastomeric response was followed by a distinct “bump” in the stress‐strain curve. On the basis of the temperature and rate dependence of the stress‐strain curve, local strain‐rate measurements, local temperature changes, and recovery characteristics, the “bump” was identified as high strain yielding. Hence, the stress‐strain curve sequentially exhibited the features of elastomeric and plastic deformation. Following high strain yielding, strain hardening dramatically increased the fracture strength. This behavior was defined as elastomeric‐plastic. Elastomeric‐plastic behavior in the broad glass‐transition range constituted a gradual transition from elastomeric behavior at higher temperatures to low‐temperature plastic behavior with high modulus and macroscopic necking. Because of the lower glass‐transition temperature of EO, ?40 °C as compared with ?10 °C for ES, the onset of elastomeric‐plastic behavior occurred at a significantly lower temperature. The concept of a network of flexible chains with fringed micellar crystals serving as the multifunctional junctions that provides the structural basis for elastomeric behavior of low‐crystallinity ethylene copolymers was extended to elastomeric‐plastic behavior by considering a network with a fraction of rigid, glassy chains. © 2001 John Wiley & Sons, Inc. J Polym Sci Part B: Polym Phys 40: 142–152, 2002     

Micromechanical modeling of the deformation kinetics of semicrystalline polymers

The mechanical behavior of semicrystalline polymers is strongly dependent on their crystallinity level, the initial underlying microstructure, and the evolution of this structure during deformation. A previously developed micromechanical constitutive model is used to capture the elasto‐viscoplastic deformation and texture evolution in semicrystalline polymers. The model represents the material as an aggregate of two‐phase layered composite inclusions, consisting of crystalline lamellae and amorphous layers. This work focuses on adding quantitative abilities to the multiscale constitutive model, in particular for the stress‐dependence of the rate of plastic deformation, referred to as the slip kinetics. To do that, the previously used viscoplastic power law relation is replaced with an Eyring flow rule. The slip kinetics are then re‐evaluated and characterized using a hybrid numerical/experimental procedure, and the results are validated for uniaxial compression data of HDPE, at various strain rates. A double yield phenomenon is observed in the model prediction. Texture analysis shows that the double yield point in the model is due to morphological changes during deformation, that induce a change of deformation mechanism. © 2011 Wiley Periodicals, Inc. J Polym Sci Part B: Polym Phys 49: 1297–1310, 2011