Prediction of residual stress and viscoelastic deformation of film insert molded parts

Film insert molding (FIM) has been modeled numerically to predict residual stress and viscoelastic deformation of the part. Nonisothermal three dimensional flow analysis for filling, packing, and cooling stages was carried out by using a commercial software. It was assumed that the inserted film was solid throughout the entire molding procedure although remelting could occur at the interface with the substrate. The flow analysis results, e.g., temperature, stress, and density distribution in the substrate domain, were transported to a finite element stress analysis program for viscoelastic stress analysis. Deflection of the FIM part was obtained as soon as the part was ejected from the mold by assuming isotropic elastic material. The residual stress distribution in the FIM part was acquired by removing the constraints along the boundary of the molded part. Viscoelastic deformation of the FIM part was predicted by performing viscoelastic stress analysis in order to understand long term behavior of the FIM part when exposed to room temperature. Durability of automotive and electronic parts produced by the film injection molding can be predicted by the procedure adopted in this study. POLYM. ENG. SCI., 2008. © 2008 Society of Plastics Engineers     

Molded geometry and viscoelastic behavior of film insert molded parts

Virgin injection‐molded tensile specimens without any inserted film and four kinds of film insert molded (FIM) tensile specimens were prepared. They were annealed at 80°C to investigate the effect of residual stresses and thermal shrinkage of the inserted film on thermal deformation of tensile specimens. The FIM specimens with the unannealed film were bent after ejection in such a way that the film side was protruded and the warpage was reversed gradually during annealing and the film side was intruded. Warpage of the FIM specimen with the film annealed at 80°C for 20 days was not reversed during annealing. Processing of the FIM specimens have been modeled numerically to predict thermoviscoelastic deformation of the part and to understand the warpage reversal phenomenon (WRP). Nonisothermal three‐dimensional flow analysis was carried out for filling, packing, and cooling stages. The flow analysis results were transported to a finite element stress analysis program for prediction of deformation of the FIM part. The WRP was caused by the combined effect of thermal shrinkage of the inserted film and relaxation of residual stresses in the FIM specimen during annealing. It is expected that this study will contribute towards the improvement of the FIM product quality and prevention of large viscoelastic deformation of the molded part. © 2008 Wiley Periodicals, Inc. J Appl Polym Sci, 2009     

Effects of film and substrate dimensions on warpage of film insert molded parts

Three‐dimensional flow and structural analyses were carried out for film insert injection molding to investigate warpage of film insert molded (FIM) parts with respect to variation of film and substrate thickness. Asymmetry of temperature distribution in the thickness direction was increased with increasing film thickness but decreased with increasing substrate thickness. Asymmetry of the in‐mold residual stress distribution in the FIM specimen was generated by the nonuniform temperature distribution, and it was increased with increasing film thickness but reduced with increasing substrate thickness. Warpage of the ejected FIM specimen was determined by relaxation of the asymmetric in‐mold residual stress distribution, and it was increased with increasing film thickness but reduced with increasing substrate thickness. Warpage of FIM specimens annealed at 80°C for 30 min showed complex behavior, and the behavior was understood by using factors such as degree of warpage of the ejected part, thermal shrinkage of the inserted film, and retardation of heat transfer. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers     

Viscoelastic flow analysis of surface morphology on injection‐molded polypropylene

The molecular orientation of a frozen layer in an injection‐molded specimen of a polypropylene–rubber blend was investigated. A typical V‐shaped pattern of birefringence was observed from the surface to the core in a crosscut section. From the comparison of the V‐patterns near the gate to the flow end, it was assumed that a frozen layer formed from the surface to a depth of 0.06 mm in a plaque (3 mm thickness) during the injection molding filling process. Numerical viscoelastic analysis of the fountain flow was carried out using an original 2D unsteady flow simulation program and ignored crystallization. A large extensional deformation formed just when the molten polymer contacted the cavity wall and the deformation immediately froze. A layer with a small birefringence between the surface and the shear‐oriented layer was divided into two parts. The depth profile of birefringence was compared to the principal stress difference calculated by numerical analysis. POLYM. ENG. SCI., 2010. © 2010 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     

Numerical prediction of residual stresses and birefringence in injection/compression molded center‐gated disk. Part I: Basic modeling and results for injection molding

The present study attempted to numerically predict both the flow‐induced and thermally‐induced residual stresses and birefringence in injection or injection/compression molded center‐gated disks. A numerical analysis system has been developed to simulate the entire process based on a physical modeling including a nonlinear viscoelastic fluid model, stress‐optical law, a linear viscoelastic solid model, free volume theory for density relaxation phenomena and a photoviscoelasticity and so on. Part I presents physical modeling and typical numerical analysis results of residual stresses and birefringence in the injection molded center‐gated disk. Typical distribution of thermal residual stresses indicates a tensile stress in the core and a compressive stress near the surface. However, depending on the processing condition and material properties, the residual stress sometimes becomes tensile on the surface, especially when fast cooling takes place near the mold surface, preventing the shrinkage from occurring. The birefringence distribution shows a double‐hump profile across the thickness with nonzero value at the center: the nonzero birefringence is found to be thermally induced, the outer peak due to the shear flow and subsequent stress relaxation during the filling stage and the inner peak due to the additional shear flow and stress relaxation during the packing stage. The combination of the flow‐induced and thermally‐induced birefringence makes the shape of predicted birefringence distribution quite similar to the experimental one.     

Development of warpage and residual stresses in film insert molded parts

Residual stresses, bending moments, and warpage of film insert molded (FIM) parts were investigated by experimental and numerical analyses. Thermally induced residual stresses in FIM parts were predicted by numerical simulations with both commercial and house codes. Bending moments and warpage of FIM tensile specimens were calculated numerically and compared with experimental results. Thermally induced residual stresses were predicted by utilizing a one‐dimensional thermoelastic model where constant material properties are assumed. The residual stress distribution depended remarkably on the Biot number and the heat was removed rapidly through the surface resulting in high residual stresses. Asymmetric residual stresses generated by nonuniform cooling of the part provoked nonuniform shrinkage and warpage of the molded tensile specimen. It was found that the numerically calculated bending moment is in good agreement with the experimental results. POLYM. ENG. SCI., 2009. © 2009 Society of Plastics Engineers     

粘弹性流体在微孔道中流动的受力分析

针对亲油岩石水驱后残余油膜的存在形式及聚合物溶液的粘弹特性,选取粘弹性流体中的上随体Maxwell本构方程并使用计算流体软件Polyflow对模型进行数值分析。对比研究了在不同的松弛时间,不同的孔道宽度下,聚合物溶液作用于残余油膜上的应力T11的变化趋势,并且将水与聚合物溶液的驱替结果进行了比较。结果表明:随着聚合物溶液弹性的增强,对油膜的作用力T11就越强;孔道宽度与油膜高度越接近,对油膜的作用力就越强;聚合物溶液对油膜的作用力较水溶液强。     

橡胶材料非线性高弹-粘弹性本构模型

本文提出的修正Zener模型,即以非线性弹簧与粘壶代替原来的线性弹簧与粘壶,得到一种适合橡胶材料在单轴作用下的非线性高弹-粘弹性本构模型。该模型可同时描述加载、卸载及应力松弛行为。模型将应力分解为弹性应力与粘性应力。弹性应力由Yeoh高弹性模型得到;粘性应力由加载及卸载过程的瞬时应力通过积分变换得到。此外考虑到应力松弛的作用,因此将粘性应力分解成两部分：一是在加载、卸载过程所用时间内由应变的改变所导致的粘性力;二是在该时间内由应力松弛所产生的反作用力。最后,将实验结果与该模型的计算结果进行对比,结果表明计算结果与实验结果具有良好的一致性,说明该本构模型可靠、合理。     

Analytical estimate for curing‐induced stress and warpage in coating layers

A thermoset coating that is applied to an elastic substrate will develop residual stresses during curing because of polymerization shrinkage of the resin. This shrinkage only partly contributes to the residual stresses because, before gelation, the stresses relax completely. In this study, we developed explicit analytical expressions for the curing efficiency factor, the residual stresses, and the resulting warpage. We did this by assuming that after gelation, the material was in its rubbery state and that viscoelastic effects were absent. A difference between the free and constrained warpages during curing was made. The analytical warpage models were shown to give results comparable to those of the numerical calculations with a fully curing‐dependent viscoelastic material model. Furthermore, for the first time, accurate analytical expressions for the stress‐free temperature and stress‐free strain were obtained. With these expressions, the effect of curing shrinkage on the residual stresses could easily be incorporated into existing (numerical) stress analysis without the need for extensive curing‐dependent viscoelastic material models. © 2012 Wiley Periodicals, Inc. J. Appl. Polym. Sci., 2012     

Linear and nonlinear melt rheology and extrudate swell of acrylonitrile‐butadiene‐styrene and organoclay‐filled acrylonitrile‐butadiene‐styrene nanocomposite

Melt viscoelastic behavior and the die swell of Acrylonitrile‐Butadiene‐Styrene (ABS) and ABS/clay nanocomposites varying in organoclay loading were studied. A pronounced low‐frequency nonterminal behavior exhibited in linear viscoelastic experiments along with an apparent yield stress in transient startup flow tests suggested the existence of a network type, because of interconnection of rubber particles in ABS matrix. From the results of linear and nonlinear viscoelastic measurements, it was found that the incorporation of organoclay can lead to the formation of an additional network formed between organoclay tactoids that caused reduced temperature dependency of linear viscoelastic properties of the nanocomposite samples compared with ABS matrix. The swelling behavior of samples was interpreted using the results of stress relaxation experiments after cessation of steady shear flow. The great reduction in the die swell of nanocomposite samples could be explained in terms of great surface area and anisometric nature of organoclay tactoids and/or platelets, which promote energy consumption and less energy to be stored in chains. POLYM. ENG. SCI., 2010. © 2010 Society of Plastics Engineers     

A unified K-BKZ model for residual stress analysis of injection molded three-dimensional thin shapes

The flow-induced and thermally induced residual stresses during injection molding of a thin part with complex geometries are predicted. The injection molding precess was considered to consist of a filling and a post-filling stage (packing coupled with cooling). Additionally, the analysis were applied to successive stages of the process. The model takes into account the viscoelasticity of the molding polymer, which has been neglected in most previous works, because of the complexity of its inclusion. A unified K-BKZ viscoelastic constitutive model, capable of modeling both the fluid-rubbery state and the glass state of amorphous polymers, was employed for simulating this problem. For the flow-induced residual stress predictions of the filling stage, a quasi-steady state approximation was employed for each element of the part, for the calculation of stress profile and subsequent stress relaxation after cessation of flowf. Stress calculations were provided for the thermally induced residual stress predictions of the post-filling stage. These explicit calculations led to the results of pressure and temperature distributions of the part during the post-filling stage into the viscoelastic constitutive model. Additionally, the pressure and asymmetric temeprature profiles of the post-filling stage were based on finite element packing analysis coupled with a boundary element cooling analysis of the molding process. Finally, the total residual stress in the part was obtained via superposition of the flow-induced and thermally induced residual stresses. An example is provided to demonstrate the entire concept. The results indicate that thermally induced residual stress is higher than the flow-induced residual stress by one to two orders of magnitude.     

Residual stresses and thermoviscoelastic deformation of laminated film prepared for film insert molding

Residual stresses and thermoviscoelastic deformation of a laminated film utilized for film insert molding was investigated through measurement of thermal expansion coefficient (CTE) and relaxation modulus. Thermoviscoelastic deformation of the film was also analyzed with numerical analysis by applying measured relaxation modulus, CTE, and residual stress to finite element method (FEM). Stress relaxation of the pristine film showed significantly different behavior from that of the unannealed film during annealing. Effects of the CTE and relaxation modulus on the thermoviscoelastic deformation were predicted by considering thermal shrinkage and structural relaxation. Moreover, numerical results on thermoviscoelastic deformation were in good agreement with experiments when initial stress distribution in the solid specimen was applied to the numerical analysis. POLYM. ENG. SCI., 2012. © 2011 Society of Plastics Engineers     

A neck‐in model in extrusion lamination process

In this study, the experiment of the extrusion lamination process using high‐pressure process low‐density polyethylene (LDPE) was performed. The nonisothermal viscoelastic simulation of the extrusion lamination experiment was also carried out. The simulation results were in good agreement with the experimental data within wide range of take up velocity and air gap length. We developed the theoretical model based on force balance and deformation type of a film to predict the neck‐in behavior in the extrusion lamination or cast film process. It was suggested from the neck‐in model that the neck‐in correlates with the ratio of planar to uniaxial elongational viscosity. It was confirmed that the neck‐in model could predict the film edge shape and neck‐in properly for conventional LDPE. POLYM. ENG. SCI., 2010. © 2009 Society of Plastics Engineers     

Numerical simulation of three‐dimensional fiber orientation in injection molding including fountain flow effect

It is essential to predict the nature of flow field inside mold and flow‐induced variation of fiber orientation for effective design of short fiber reinforced plastic parts. In this investigation, numerical simulations of flow field and three‐dimensional fiber orientation were carried out in special consideration of fountain flow effect. Fiber orientation distribution was described using the second‐order orientation tensor. Fiber interaction was modeled using the interaction coefficient C_I. Three closure approximations, hybrid, modified hybrid, and closure equation for C_I=0, were selected for determination of the fiber orientation. The fiber orientation routine was incorporated into a previously developed program of injection mold filling (CAMPmold), which was based on the fixed‐grid finite element/finite difference method assuming the Hele‐Shaw flow. For consideration of the fountain flow effect, simplified deformation behavior of fountain flow was employed to obtain the initial condition for fiber orientation in the flow front region. Comparisons with experimental results available in the literature were made for film‐gated strip and centergated disk cavities. It was found that the orientation components near the wall were were accurately predicted by considering the fountain flow effect. Test simulations were also carried out for the filling analysis of a practical part, and it was shown that the currently developed numerical algorithm can be effectively used for the prediction of fiber orientation distribution in complex parts.     

Separating stress and time dependent effects in the temperature dependent creep of polyethylene nanocomposites

The nonlinear time dependent creep of linear‐low density polyethylene (LLDPE) reinforced with montmorillonite layered silicate was investigated. A previous study related the time/stress dependence of creep compliance of the material at room temperature using the Burger and Kohlrausch‐Williams‐Watts models. Using both the creep and recovery compliance curves, we employ the Schapery formulation to study the relationship between deformation, time, stress, and temperature of LLDPE nanocomposites. Smooth mastercurves are constructed using time–temperature–stress superposition principles. The stress and temperature‐related creep constants and shift factors were determined for the material using the Schapery nonlinear viscoelastic equation. The prediction results confirm the enhanced creep resistance of nanofillers even at extended time scales and low temperatures. POLYM. ENG. SCI., 50:1646–1657, 2010. © 2010 Society of Plastics Engineers     

黏弹特性对模内微装配成型热流固耦合变形的影响

建立了综合考虑二次成型黏弹性熔体充填流动约束环境影响的模内微装配成型过程黏弹性热流固耦合变形机理的理论模型,并通过有限元数值模拟,研究了二次成型熔体黏度对模内微装配成型过程黏弹性热流固耦合变形的影响规律。结果表明,黏弹性热流固耦合作用诱导的预成型微型轴变形的驱动力来源于微装配界面形成的热流固耦合压力和黏性拖曳剪应力,而二次成型熔体流动的弹性正应力对耦合变形具有抑制作用,微装配界面的热流固耦合载荷和微型轴的变形均随着二次充填熔体的黏度增大而增大,减小二次成型熔体黏度有利于提高其微装配加工精度。     

Birefringence and interface in sequential co‐injection molding of amorphous polymers: Simulation and experiment

Modelings of the interface distribution and flow‐induced residual stresses and birefringence in the sequential co‐injection molding (CIM) of a center‐gated disk were carried out using a numerical scheme based on a hybrid finite element/finite difference/control volume method. A nonlinear viscoelastic constitutive equation and stress‐optical rule were used to model the frozen‐in flow stresses in disks. The compressibility of melts is included in modeling of the packing and cooling stages and not in the filling stage. The thermally induced residual birefringence was calculated using the linear viscoelastic and photoviscoelastic constitutive equations combined with the first‐order rate equation for volume relaxation and the master curves for the relaxation modulus and strain‐optical coefficient functions of each polymer. The influence of the processing variables including melt and mold temperatures and volume of skin melt on the birefringence and interface distribution was analyzed for multilayered PS‐PC‐PS, PS‐PMMA‐PS, and PMMA–PC–PMMA molded disks obtained by CIM. The interface distribution and residual birefringence in the molded disks were measured. The measured interface distributions and the gapwise birefringence distributions in CIM disks were found to be in a fair agreement with the predicted interface distributions and the total residual birefringence obtained by the summation of the predicted frozen‐in flow and thermal birefringence. POLYM. ENG. SCI., 55:88–106, 2015. © 2014 Society of Plastics Engineers     

Indentation Creep of Hydrated Soda–Lime Silicate Glass Determined by Nanoindentation

Time-dependent deformation behavior was investigated for soda–lime silicate glass with various water contents, using a nanoindentation technique. The complete indentation curve, loading and unloading part, is analyzed. It is shown that this deformation behavior may be represented in terms of a simple mechanical model analogous to a viscoelastic system. Values for Young's modulus were derived, a retardation spectrum was deduced, and apparent viscosity values were calculated. Structural rearrangements of the glass appear to be responsible for the observed changes of the viscoelastic properties. Water in the glass reduces Young's modulus and yield stress and thus promotes viscous flow.     

Simulation of nonisothermal flow of melt during melting process of vibration‐induced polymer extruder

A simplified 2D melt film model was established to simulate the nonisothermal melt flow during the melting process of the vibration‐induced polymer extruder of which the screw can vibrate axially. Since polymer has time‐dependent nonlinear viscoelastic characteristic with vibration force filed (VFF), a self‐amended nonisothermal Maxwell constitutive equation that can reflect the relaxation time spectrum of polymer was adopted. Using the 2D melt film model, melt films of two kinds of thickness representing different melting stages were simulated to investigate the influence tendency of the same VFF on the different melting stage. Special flow patterns and temperature distribution of melt in the melt film between the driving wall and the solid/melt interface with various vibration force fields were systematically simulated. It is found out that within a certain range of vibration strength, the application of vibration can optimize the time‐averaged shear‐rate distribution, improve the utilization efficiency of energy, and promote melting process; and the thinner the melt film is, the more intense the nonlinear viscoelastic response becomes with the same VFF; moreover, there exists optimum vibration strength to make the melting process fastest, which is in accord with the visualization experimental results. © 2006 Wiley Periodicals, Inc. J Appl Polym Sci 102: 5825–5840, 2006