Numerical implementation of strain rate dependent thermo viscoelastic constitutive relation to simulate the mechanical behavior of PMMA

In this work, a nonlinear viscoelastic constitutive relation was implemented to describe the mechanical behavior of a transparent thermoplastic polymer polymethyl methacrylate (PMMA). The quasi-static and dynamic response of the polymer was studied under different temperatures and strain rates. The effect of temperature was incorporated in elastic and relaxation constants of the constitutive equation. The incremental form of constitutive model was developed by using Poila–Kirchhoff stress and Green strain tensors theory. The model was implemented numerically by establishing a user defined material subroutine in explicit finite element (FE) solver LS-DYNA. Finite element models for uniaxial quasi-static compressive test and high strain rate split Hopkinson pressure bar compression test were built to verify the accuracy of material subroutine. Numerical results were validated with experimental stress strain curves and the results showed that the model successfully predicted the mechanical behavior of PMMA at different temperatures for low and high strain rates. The material model was further engaged to ascertain the dynamic behavior of PMMA based aircraft windshield structure against bird impact. A good agreement between experimental and FE results showed that the suggested model can successfully be employed to assess the mechanical response of polymeric structures at different temperature and loading rates.     

Models of thermomechanical behavior of polymeric materials undergoing glass transition

The phenomenological models of the thermomechanical behavior of polymeric materials in a temperature range including the relaxation transition from the highly elastic to the glassy state (vitrification) and the reverse transition (softening) are considered. A model based on the interpretation of the glass transition as a process of gradual increase in intermolecular bonds in the polymer network, “freezing” the current strain with decreasing temperature is developed. A scalar parameter is introduced—the “degree of vitrification,” to establish the quantitative dependence of the relaxation transition completion by temperature. Constitutive relations of thermomechanical behavior of vitrifying polymers in uniaxial and complicated stress states in the “elastic approximation” simplification are obtained. A system of experiments for the identification of the proposed model material functions and constants is formulated and implemented. Analytical model problems are solved, clearly illustrating the mechanism for generation of technological and residual stresses in glass polymers in non-uniform cooling.     

Isothermal physical aging characterization of Polyether-ether-ketone (PEEK) and Polyphenylene sulfide (PPS) films by creep and stress relaxation

This paper considers the experimental characterization of isothermal physical aging of PEEK and PPS films using a dynamic mechanical analyzer. Using the short-term test method established by Struik, momentary creep and stress relaxation curves were measured at several temperatures within 15–35°C below the glass transition temperature (T _g ) at various aging times. Stress and strain levels were such that the materials remained in the linear viscoelastic regime. These curves were then shifted together to determine momentary master curves and shift rates using the PHYAGE program. In order to validate the obtained isothermal physical aging behavior, the results of creep and stress relaxation testing were compared and shown to be consistent with one another using appropriate interconversion of the viscoelastic material functions. Time–temperature superposition of the master curves was also performed. The temperature shift factors and aging shift rates for both PEEK and PPS were consistent for both creep and stress relaxation test results.     

Damage characterization in non-isothermal stretching of acrylics. Part II: Experimental validation

Influence of temperature and strain rate on damage accumulation and large deformation behavior of acrylics was investigated under conditions similar to actual polymer processing. Poly(methyl methacrylate) (PMMA) samples were stretched to large strains at different rates under transient thermal conditions. During testing, specimens were cooled down from temperatures above glass transition temperature (θ_g) to temperatures well-below θ_g inducing a transition from rubbery state to solid state. Contrary to common practice of studying thermo-mechanical coupling in terms of adiabatic heating; in proposed experimental study, temperature effect on mechanical response of material was emphasized by externally intervening temperature variation within specimen. An improved version of dual-mechanism constitutive model presented in Part I [Gunel, E.M., Basaran, C., 2010. Damage characterization in non-isothermal stretching of acrylics. Part I: Theory. Mechanics of Materials] was proposed to predict thermo-mechanical response of amorphous polymer below and above θ_g. Applicability of proposed constitutive model for the specific case of non-isothermal stretching of PMMA at different test conditions was demonstrated by incorporating it into a finite element scheme. Constitutive model was reasonably accurate to capture observed temperature-displacement-force history in experimental study. Damage evolution under different testing conditions was studied in terms of irreversible thermal and mechanical entropy production.     

Fabrication of a microfluidic system for capillary electrophoresis using a two-stage embossing technique and solvent welding on poly(methyl methacrylate) with water as a sacrificial layer

Methods for fabricating poly(methyl methacrylate) microchips using a novel two-stage embossing technique and solvent welding to form microchannels in microfluidic devices are presented. The hot embossing method involves a two-stage process to create the final microchip design. In its simplest form, a mold made of aluminum is fabricated using CNC machining to create the desired microchannel design. In this work, two polymer substrates with different glass transition temperatures (Tg), polyetherimide (PEI) and poly(methyl methacrylate) (PMMA), were used to make the reusable secondary master and the final chip. First, the aluminum mold was used to emboss the PEI, a polymeric substrate with Tg approximately 216 degrees C. The embossed PEI was then used as a secondary mold for embossing PMMA, a polymeric substrate with a lower Tg ( approximately 105 degrees C). The resulting PMMA substrate possessed the same features as those of the aluminum mold. Successful feature transfer from the aluminum mold to the PMMA substrate was verified by profilometry. Bonding of the embossed layer and a blank PMMA layer to generate the microchip was achieved by solvent welding. The embossed piece was first filled with water that formed a solid sacrificial layer when frozen. The ice layer prevented channel deformation when the welding solvent (dichloroethane) was applied between the two chips during bonding. Electrophoretic separations of fluorescent dyes, rhodamine B (Rh B) and fluorescein (FL), were performed on PMMA microchips to demonstrate the feasibility of the fabrication process for microreplication of useful devices for separations. The PMMA micro-chip was tested under an electric field strength of 705 V cm-1. Separations of the test mixture of Rh B and FL generated 55 500 and 66 300 theoretical plates/meter, respectively.     

High-temperature deformation behavior of Cu–6.0Ni–1.0Si–0.5Al–0.15?Mg–0.1Cr alloy

The hot compression deformation behavior of Cu–6.0Ni–1.0Si–0.5Al–0.15?Mg–0.1Cr alloy with high strength, high stress relaxation resistance and good electrical conductivity was investigated using a Gleeble1500 thermal–mechanical simulator at temperatures ranging from 700 to 900?°C and strain rates ranging from 0.001?to 1?s^?1. Working hardening, dynamic recovery and dynamic recrystallization play important roles to affect the plastic deformation behavior of the alloy. According to the stress–strain data, constitutive equation has been carried out and the hot compression deformation activation energy is 854.73?kJ/mol. Hot processing map was established on the basis of dynamic material model theories, and Prasad instability criterion indicates that the appropriate hot processing temperature range and strain rate range for hot deformation were 850~875?°C and 0.001~0.01?s^?1, which agreed well with the hot rolling experimentation results.     

Modeling of deformation behavior and strain-induced crystallization in poly(ethylene terephthalate) above the glass transition temperature

A constitutive model for large deformation stress–strain behavior and strain-induced crystallization in poly(ethylene terephthalate), at temperatures above the glass transition temperature, is proposed. In this model, the intermolecular resistance is treated in a composite framework where the crystalline and amorphous phases are considered as two separate resistances coupled through two different analog representations leading to the upper and the lower bound approaches. The crystallization rate is expressed following a non-isothermal phenomenological expression based on the modified Avrami equation. Our predicted results are compared to existing experimental results and good agreement is found.     

不同温度下MDYB-3有机玻璃的棘轮效应

对在不同温度和应力状态下, MDYB-3有机玻璃的棘轮效应进行了实验和分析.运用棘轮应变与应力-应变滞回环能量的对应关系和高聚物塑性变形的应力促进热激活理论,建立了一种新的适用于高聚物材料的稳态棘轮应变增长率的计算模型,揭示了温度、载荷频率、平均应力和应力幅值对棘轮应变演化的影响.将该模型应用于不同温度下MDYB-3有机玻璃疲劳过程中的棘轮变形增长行为的描述,理论预测结果与试验结果吻合良好.     

Synthesis and mechanical properties of cardanol-formaldehyde (CF) resins and CF-poly(methylmethacrylate) semi-interpenetrating polymer networks

Cardanol-formaldehyde (CF) resins (both novolac and resol) and CF-poly(methylmethacrylate) (PMMA) semi-interpenetrating polymer networks were synthesized and their mechanical properties and thermal transitions were evaluated. The lower tensile strength of CF resins compared to phenol-formaldehyde (PF) resins may be understood on the basis of the structure of the C₁₅ side chain imparting steric hindrance and reduction in intermolecular interactions. Interpenetration of CF with PMMA increased the mechanical properties only marginally. Scanning electron micrographs of the semi-IPNs showed two distinct phases. Thermomechanical analysis gave two glass transition temperatures,T _g, for the IPNs, the lowerT _g corresponding to the PMMA phase and the higherT _g to the CF phase. However, the unusual increase inT _g of the CF from 128°C to 144°C suggests restrictions in the segmental motion of the CF phase brought about by mixing with another rigid polymer such as PMMA.     

温度、应变率对航空PMMA压缩力学性能的影响研究

本文利用INSTRON试验机和分离式Hopkinson压杆测试了航空有机玻璃在试验温度为299K～373K之间,两种准静态应变率(10-3,10-1 1/s)和一种动态应变率(550 1/s)下的压缩力学行为.试验结果表明:在准静态载荷下,随着温度的升高,材料的弹性模量和流动应力减小,在应变率为10-1 1/s时表现出明显的应变软化行为;在高应变率(550 1/s)下,随着温度的升高,材料的流动应力逐渐减小而破坏应变增大,当温度超过333K时也有应变软化现象发生;在相同温度下,随着应变率的升高,材料的流动应力增大,但破坏应变减小.通过观察变形后试样的形貌,可以认为试样内部的微裂纹是应变软化的主要原因.最后,ZWT粘弹性本构模型被用来对试验数据进行拟合,结果表明该模型能够较好地预测这种材料在应变8%以内的力学行为.     

Modeling hot deformation behavior of low-cost Ti-2Al-9.2Mo-2Fe beta titanium alloy using a deep neural network

Ti-2Al-9.2Mo-2Fe is a low-cost β titanium alloy with well-balanced strength and ductility, but hot working of this alloy is complex and unfamiliar. Understanding the nonlinear relationships among the strain, strain rate, temperature, and flow stress of this alloy is essential to optimize the hot working process. In this study, a deep neural network (DNN) model was developed to correlate flow stress with a wide range of strains (0.025–0.6), strain rates (0.01–10 s⁻¹) and temperatures (750–1000 °C). The model, which was tested with 96 unseen datasets, showed better performance than existing models, with a correlation coefficient of 0.999. The processing map constructed using the DNN model was effective in predicting the microstructural evolution of the alloy. Moreover, it led to the optimization of hot-working conditions to avoid the formation of brittle precipitates (temperatures of 820–1000 °C and strain rates of 0.01–0.1 s⁻¹).     

Steady ratcheting strains accumulation in varying temperature fatigue tests of PMMA

The evolutions of ratcheting strains of polymethyl methacrylate (PMMA) at different temperatures and stress levels were experimentally investigated. A steady ratcheting strain growth region with a constant rate was observed in all specimens, which occupied significant part of total fatigue failure life. Experimental results also showed that the steady ratcheting growth rate varied with applied temperatures and loading. In this paper, theory of thermally activated process for glassy polymers was used to describe the plastic deformations during the cycle. Based on the correlations between ratcheting strains per cycle and hysteresis loop energy, a new ratcheting strains accumulative model for polymer materials was developed, which quantificationally elucidated the effects of temperature, loading frequency, mean stress and stress amplitude on the accumulative rate of ratcheting strains. Comparing the predications from the proposed model with experimental ratcheting strain data of PMMA, it was found that the model could describe the steady ratcheting strain accumulative behaviors under arbitrary temperatures and loading conditions exactly.     

A time and hydration dependent viscoplastic model for polyelectrolyte membranes in fuel cells

Ionomers are co-polymers with ionic groups. One of the interesting applications of ionomer membranes is as electrolytes in proton exchange membrane (PEM) fuel cells. The most commonly used membranes in PEM fuel cells are perfluorosulfonic acid (PFSA) membranes, e.g., Nafion^® from DuPont^TM. Besides its dependency on temperature and hydration due to phase inversion and cluster formation, Nafion^® as a polymer, exhibits strong time and rate effects. In this work, the stress–strain behavior of Nafion^® at different strain rates has been obtained in an environmental chamber for various temperatures and hydrations. After a certain strain was reached in each test, stress relaxation was performed for an hour to observe the relaxation behavior of Nafion^®. We attempted to use a nonlinear, time-dependent constitutive model to predict the hygro-thermomechanical behavior of Nafion^®. Because a substantial component of the response is unrecoverable, a viscoplastic model was employed. The proposed two-layer viscoplasticity model consisted of an elastoplastic network that was in parallel with an elastic-viscous network (Maxwell model) which separates the rate-dependent and rate-independent behavior of the material. After obtaining the necessary parameters for different hydrations, this model showed reasonably accurate success in predicting the stress–strain behavior at different strain rates, and matched the relaxation test results. Finite element simulations based on the proposed two-layer viscoplasticity model were in good agreement with test results and can be used to study the stress–strain state of the ionomer membranes in fuel cell configurations.     

Effect of norbornene content on deformation properties and hot embossing of cyclic olefin copolymers

The dynamic mechanical behaviour of a series of cyclic olefin copolymers (COCs) with varying norbornene content has been examined in the vicinity of the glass transition temperature, T _g. Using dynamic mechanical thermal analysis (DMTA), the temperature of the glass transition in COC increased linearly with increase in % norbornene. Above T _g, the magnitude of the elastic storage modulus, E′, decreased exponentially with rise in temperature for all of the copolymers. The loss modulus, E″, has also sharply decreased at temperatures above the transition with a levelling-off in E″ at ≥20 °C above T _g for all grades. The results of DMTA have been used in the identification of the optimum conditions for hot embossing experiments. Hot embossing of COC at ≥20 °C above the transition temperature in a region of viscous liquid flow has resulted in a full replication of channel depth without cracking or distortion.     

Tensile behaviour of blends of poly(vinylidene fluoride) with poly(methyl methacrylate)

Blends of poly(vinylidene fluoride) (PVF₂) and poly(methyl methacrylate) (PMMA) were prepared over a wide concentration range and tested in tension at the same relative temperature below the glass transition. Testing was performed at strain rates ranging from 10 to 0.01 min^–1 at test temperatures fromT _g-40 toT _g-10. By normalizing the test temperature to fixed increments belowT _g, blends and homopolymers can be compared on the basis of PVF₂ and PMMA composition and crystallinity. In nearly all blends, under conditions favouring disentanglement, (decrease in strain rate, or increase in test temperature), the yield stress and drawing stress decreased while the breaking strain increased. For materials with about the same degree of crystallinity, those with a higher proportion of amorphous PVF₂ exhibited brittle-like behaviour as a result of interlamellar tie molecules. In the semicrystalline blends, yield stress remains high as the test temperature approachesT _g, whereas in the amorphous blends the yield stress falls to zero nearT _g. Results of physical ageing support the role of interlamellar ties which cause semicrystalline blends to exhibit ageing at temperatures aboveT _g.     

Modelling flow stress behaviour of aluminium alloys during hot rolling

Abstract

A mathematical model is proposed to predict the flow stress behaviour of aluminium alloys under hot rolling conditions. To do so, a dislocation model for evaluating flow stress during deformation is coupled with a finite element analysis to access metal behaviour under non-isothermal and variable strain rate conditions. Then, with the aid of the proposed model, a hot strip rolling process was simulated. In order to verify modelling results, flow stress behaviour of an aluminium alloy is studied employing hot compression tests in various temperatures and strain rates and the model was examined on this material. Non-isothermal hot rolling experiments were carried out and good agreement was found between predictions and experiments.     

Prediction of flow stress in dynamic strain aging regime of austenitic stainless steel 316 using artificial neural network

Flow stress during hot deformation depends mainly on the strain, strain rate and temperature, and shows a complex nonlinear relationship with them. A number of semi empirical models were reported by others to predict the flow stress during deformation. In this work, an artificial neural network is used for the estimation of flow stress of austenitic stainless steel 316 particularly in dynamic strain aging regime that occurs at certain strain rates and certain temperatures and varies flow stress behavior of metal being deformed. Based on the input variables strain, strain rate and temperature, this work attempts to develop a back propagation neural network model to predict the flow stress as output. In the first stage, the appearance and terminal of dynamic strain aging are determined with the aid of tensile testing at various temperatures and strain rates and subsequently for the serrated flow domain an artificial neural network is constructed. The whole experimental data is randomly divided in two parts: 90% data as training data and 10% data as testing data. The artificial neural network is successfully trained based on the training data and employed to predict the flow stress values for the testing data, which were compared with the experimental values. It was found that the maximum percentage error between predicted and experimental data is less than 8.67% and the correlation coefficient between them is 0.9955, which shows that predicted flow stress by artificial neural network is in good agreement with experimental results. The comparison between the two sets of results indicates the reliability of the predictions.     

High ductility in poly(methyl methacrylate) induced by absorption and desorption of an acetonitrile aqueous solution

Tension tests were conducted in air at room temperature on PMMA sheet specimens which had been previously soaked in a 40 vol % acetonitrile aqueous solution at 20 °C for 24 h and then dried in air at room temperature for 480 h. In contrast with an untreated specimen which fractured at a stress of 84 MPa and a strain of 9 %, shear yielding clearly took place at 42 MPa and the elongational fracture strain increased to about 148 %. No crazes were observed on the specimen surface and as a result the transparency of the PMMA was thoroughly maintained until fracture. Thus this soaking treatment may change PMMA to a completely ductile polymer without a crazing mechanism. The results of the dynamic viscoelastic measurements at 1 Hz show that the glass transition temperature was lowered to about 80 °C (as compared to about 110 °C), and the relaxation became much sharper with a higher peak value of 20 °C (as compared to a broad curve with a peak at 50 °C). This clear relaxation at room temperature may contribute to shear yielding and large plastic elongation of the treated PMMA.     

Static and dynamic mechanical properties of poly(vinyl chloride) loaded with aluminum oxide nanopowder

A series of nanocomposites from poly(vinyl chloride) loaded with different concentrations of Al₂O₃ nanopowder was prepared. The tensile mechanical properties of these composites were studied at different temperatures namely; stress–strain curves. The elastic modulus was calculated and found to decrease with increasing both filler loading and temperature. The strain at a certain stress at different temperatures was studied and the thermal activation energy for polymer chains was calculated. The complex viscosity as well as the storage modulus was found to decrease with increasing the filler loadings at different frequencies. The relaxation time of the polymer matrix was calculated and found to independent on the concentration of the filler but it decreased linearly with increasing frequency. The glass transition temperature was found to increase with increasing both filler loading and frequency.     

微流控芯片制作及电特性研究

采用热压和键合的方法制作玻璃和有机聚合物(PMMA)芯片,对玻璃和PMMA芯片在高压直流电场作用下的伏安特性进行了研究和分析。实验表明,玻璃芯片的伏安线性区域为1100V,PMMA芯片为700V,由于玻璃的导热性能优于PMMA,所以玻璃芯片的伏安线性区域大于PMMA芯片。在此线性段内,根据基尔霍夫电流定律将芯片简化为等效电阻模型,研究了分离电压以及分离焦耳热对芯片分离效果的影响因素,为微流控芯片的优化设计提供了理论依据。