Modeling of curing processes based on a multi-field potential. Single- and multiscale aspects

This paper provides a continuum mechanical model for the curing of polymers, including the incompressibility effects arising at the late stages of the process. For this purpose, the free energy density functional is split into a deviatoric and a volumetric part, and a multifield formulation is inserted. An integral formulation of the functional is used to depict the time-dependent material behavior. The model is also coupled with the multiscale finite element method, a numerical approach serving for the modeling of heterogeneous materials with a highly oscillatory microstructure. The effects of the proposed extensions are illustrated on the basis of several numerical examples concerned with the study of the influence of Poisson’s ratio on the curing process and the behavior of the microheterogeneous polymers.     

A micromechanical study of residual stress and its effect on transverse failure in polymer–matrix composites

Cure residual stress and its effect on damage in unidirectional fibre-reinforced polymer–matrix composites under transverse loading were studied using a micromechanical unit cell model and the finite element method. The overall residual stress introduced from curing was determined by considering two contributions: volume shrinkage of matrix resin from the crosslink polymerization during isothermal curing and thermal contraction of both resin and fibre as a result of cooling from the curing temperature to room temperature. To examine the effect of residual stress on failure, a model based on the Maximum Principal Stress criterion and stiffness degradation technique was used for damage analysis of the unit cell subjected to mechanical loading after curing. Predicted damage initiation and evolution are clearly influenced by the inclusion of residual stress. Residual stress is always detrimental for transverse compressive loading and pure shear loading. For transverse tensile loading, residual stress is detrimental for relatively low resin strength and beneficial for relatively high resin strength. Failure envelopes were obtained for both biaxial normal loading and combined shear and normal loading and the results show that residual stress results in a shifting and contraction of the failure envelopes.     

Analysis of Composite Molding Using the Homogenization Method

In this paper, we present an application of the homogenization method to the analysis of Resin Transfer Molding (RTM) and Structural Reaction Injection Molding (SRIM). RTM and SRIM are relatively new molding processes for manufacturing continuous fiber reinforced polymer composites. First, the mold flow is analyzed. In the molding process, the resin experiences significant temperature changes as it fills the mold and forms a free boundary with air as it pushes out the air. In addition, the flow domain is the mold cavity packed with fiber perform, which is a porous medium. Here, the homogenization method is used to model the non-isothermal flow through porous media with free boundaries. A computer program is developed which is capable of simulating a three-dimensional mold flow using the finite element approximation. An example is provided for a three-dimensional part. Then, an analysis of the residual stress developed in the curing stage is given. The curing stage starts when the mold is completely filled and it involves chemical reaction and large temperature variation. In curing, the resin part undergoes larger volume shrinkage than the fiber part, and the residual stresses are developed due to this volume mismatch. In some cases, these stresses are large enough to cause micro-cracking and to exhaust the strength of the material. Here, a brief discussion of the application of the homogenization method to a residual stress analysis is given and one example is provided.     

固化温度对碳纤维/环氧基体界面行为影响的分析

对界面粘结性能及热残余应力影响下的单纤维复合材料的界面行为进行了分析。采用界面的弹性-软化内聚力模型,用解析法对单纤维复合材料由固化引起的热残余应力、以及单纤维碎断过程纤维的轴向应力分布进行了模拟,得到了碳纤维/环氧树脂在常温和高温固化两种情况的界面粘结性能。结果表明：与常温固化相比,高温固化后,界面的剪切强度增幅不大,界面的断裂韧性显著增加;高温固化后形成的界面,使界面的软化提前、界面的脱粘延迟;高温固化产生的纤维轴向和界面径向热残余应力对界面的软化均有延迟作用;界面径向热残余应力还对界面的脱粘有延迟作用。     

考虑强度与固化变形的复合材料加筋壁板铺层优化方法

加筋壁板是复合材料飞行器主承力构件的主要结构形式,通过复合材料铺层参数设计可以有效优化壁板的强度,但铺层参数的变化也会影响壁板的固化变形.因此,复合材料加筋壁板铺层设计过程中需要综合考虑整体强度和固化变形.本文针对复合材料加筋壁板结构,建立了失效分析模型和固化变形分析模型;基于实验设计方法、NSGA-Ⅱ遗传算法以及上述分析模型,建立了综合考虑强度与固化变形的加筋壁板铺层优化方法.优化结果显示复合材料加筋壁板在强度提高的同时,固化变形显著降低.     

Z-pin复合材料细观模型固化残余应力研究

针对植入Z-pin后碳纤维增强复合材料的微观结构，通过施加Z-pin周期性边界约束条件，建立了Z-pin复合材料单层板单胞细观模型．考虑固化过程中树脂体积收缩、弹性模量随固化度变化和纤维因Z-pin进入偏转因素，运用有限单元法计算了单胞结构在固化成型工艺过程中树脂和纤维应力发展和分布，并研究了Z-pin直径和分布密度对单层板面内残余应力的影响．结果表明：凝胶点之前，树脂模量和残余应力很小，凝胶点之后，树脂模量和残余应力增加较快；残余应力分布与纤维偏转有关；Z-pin直径和分布密度增加会使固化残余应力增大．     

Experimental investigation of interface curing stresses between PMMA and composite using digital speckle correlation method

This paper studies the interface curing stresses between polymethyl methacrylate (PMMA) and composite by means of digital speckle correlation method (DSCM). A new method by combining DSCM with the marker points is developed to measure the interface curing stresses, and the measurement principle is introduced. The interface curing stresses between PMMA and composite with different curing bonding conditions are measured and analyzed, this indicates that the residual stress for furnace heating and furnace cooling is the smallest. Finally, the measurement error is discussed by means of finite element method, the influences of glass microsphere between adhesive and PMMA can be ignored.     

Modelling the curing process in magneto-sensitive polymers: Rate-dependence and shrinkage

This paper deals with a phenomenologically motivated magneto-viscoelastic coupled finite strain framework for simulating the curing process of polymers under the application of a coupled magneto-mechanical load. Magneto-sensitive polymers are prepared by mixing micron-sized ferromagnetic particles in uncured polymers. Application of a magnetic field during the curing process causes the particles to align and form chain-like structures lending an overall anisotropy to the material. The polymer curing is a viscoelastic complex process where a transformation from fluid to solid occurs in the course of time. During curing, volume shrinkage also occurs due to the packing of polymer chains by chemical reactions. Such reactions impart a continuous change of magneto-mechanical properties that can be modelled by an appropriate constitutive relation where the temporal evolution of material parameters is considered. To model the shrinkage during curing, a magnetic-induction-dependent approach is proposed which is based on a multiplicative decomposition of the deformation gradient into a mechanical and a magnetic-induction-dependent volume shrinkage part. The proposed model obeys the relevant laws of thermodynamics. Numerical examples, based on a generalised Mooney–Rivlin energy function, are presented to demonstrate the model capacity in the case of a magneto-viscoelastically coupled load.     

Cures for expansion shock and shock instability of Roe scheme based on momentum interpolation mechanism

The common defects of the Roe scheme are the non-physical expansion shock and shock instability. By removing the momentum interpolation mechanism (MIM), an improved method with several advantages has been presented to suppress the shock instability. However, it cannot prevent the expansion shock and is incompatible with the traditional curing method for expansion shock. To solve the problem, the traditional curing mechanism is analyzed. Effectiveness of the traditional curing method is discussed, and several defects are identified, one of which leads to incompatibility between curing shock instability and expansion shock. Consequently, an improved Roe scheme is proposed, which is with low computational costs, concise, easy to implement, and robust. More importantly, the proposed scheme can simultaneously solve the problem of shock instability and expansion shock without additional costs.     

Numerical and Experimental Evaluation of Dispersion Coefficient for Resin Transfer Modeling

Resin transfer molding (RTM) is a composite manufacturing process. A preformed fiber is placed in a closed mold and a viscous resin is injected into the mold. In this article, a model is developed to predict the flow pattern, extent of reaction, and temperature change during the filling and curing in a thin rectangular mold. A numerical simulation is presented to predict the free surface and its interactions with heat transfer and cure for flow of a shear-thinning resin through the preformed fiber.To simulate this process, using local thermal equilibrium assumption, it is essential to include the thermal dispersion term in energy equation. The best method to achieve this result is experimental simulation and preparing proportionate system at simple conditions without curing. By comparison of recorded temperature values (using installed instruments at various locations), and the corresponding results from numerical solution for different estimated values of dispersion coefficient, this coefficient has been evaluated based on the best matching estimate. The results show that, to simulate composite manufacturing process by RTM method, the effect of dispersion term in energy equation shall not be neglected.     

New method to determine restrained-shrinkage stresses in propellant-grain models

This paper deals with the photoelastic determination of restrained-shrinkage stresses which may be produced by curing or by thermal effects in models of solid propellant grains bonded to the case. Use is made of the birefringence exhibited in the curing process of a restrained polyurethane rubber. The techniques developed to take advantage of this property are shown in detail. The method can also be applied to the determination of the residual stresses produced in the curing process of a propellant cast around a rigid insert. An example of this application is also given. The extension of the method, using epoxies, to three-dimensional analyses is pointed out.     

Evolution of viscoelastic properties of polyurethane in the course of curing

Simultaneous measurements of the components of dynamic modulus at the set of frequencies were made by Fourier-Transform Mechanical Spectroscopy (FTMS) to investigate the curing process of a segmented polyurethane.The whole process of curing is treated as consisting of three stages. In the first stage, the material can flow and this stage is complete at the gel-point. In the second stage, the curing proceeds in the network and ends with phase separation of aggregating segments (blocks) of polymeric chains. In the third stage, the curing continues in the two-phase system. The object of investigation was the transition from the second to the third stage. It was shown that the position of the maximum of loss tangent depends on frequency and does not coincide with different characteristic points marking the time dependencies of G and G. This is due to the formation of micro-particles of the newly formed phase. The FTMS method is used for separation of the modulus changes into parts related to formation of chemical and physical networks.Special means of treating calorimetric measurements identified a weak maximum heat output at the moment corresponding to the transition point.     

Simulation of curing-induced viscoplastic deformation: a new approach considering chemo-thermomechanical coupling

A modelling and simulation approach for plastic deformation effects in curing resins is presented. For this purpose known rheological models of viscoelasticity and viscoplasticity are combined and a thermochemical element is added to account for chemical shrinkage and thermal expansion. The degree of cure of the resin has a major influence on the behaviour of the curing material, and therefore, the material model is formulated depending on the degree of cure. It affects the viscoelastic behaviour as well as the chemical shrinkage and the yield function of the viscoplastic part of the model. For the yield function a von Mises approach with isotropic hardening is chosen, where the initial yield stress as well as the yield surface depends on the degree of cure and the temperature.     

用Hamilton半解析法分析固化降温过程中的层间热应力

推导了增量形式Ｈａｍｉｌｔｏｎ半解析法公式；给出了层合板瞬态热弹性问题的求解过程；对复合材料层合板在固化降温过程中的热应力进行了分析。结果表明，在降温过程中层合板内将会出现较大的应力峰值，这些应力峰值将是导致层合板在固化工艺过程中出现破坏的原因。本文的工作将对固化工艺研究具有参考价值。     

Shrinkage Measurement in Concrete Materials using Cure Reference Method

This paper describes the details of using Cure Reference Method (CRM) to determine the shrinkage that develops in concrete materials. The technique involves the replication of diffraction grating on the concrete specimen during curing. After demolded, the specimen is stored in a chamber where a specific drying condition is maintained for 6 days. Every day in this period, the specimen is removed from the chamber and a set of the consecutive moiré fringe patterns are recorded with the help of a specially-designed stage. An automated fringe analysis program is developed to obtain the full-field displacement and strain information. Shrinkage as a function of location, time, and drying conditions is measured. A numerical method is developed in order to obtain material properties from the complex geometry used in the tests. The test in different drying condition and the ring test are performed, and their results are compared with FEA to validate the constructed model.     

光纤模斑谱传感器复合材料固化监测研究

提出利用一种新型光纤传感器，通过测量光纤末端近场模斑谱反映光纤埋置周围树脂折射率的变化．计算了随着树脂固化过程中折射率变化的功率谱密度分布，给出截止频率与折射率的近似关系．给出了利用这种传感器进行复合材料树脂固化监测的实验结果．发现这种光纤传感器的信号可以用来反映固化凝胶点和固化结束点．由于固化后光纤仍保持光波导特性，该光纤还可以用来监测结构受环境的扰动如温度变化、振动等．     

充-岩界面耦合体爆破动力响应机理

充填采矿法的充填体与矿岩体构成的界面耦合结构体,受采矿爆破影响会持续受到动力扰动,在充-岩界面耦合处易产生脱粘、裂隙扩展等行为,为井下生产带来安全隐患。采用ANSYS/LS-DYNA建立了充-岩界面耦合体模型,分析了爆破作用对界面耦合体结构的力学影响,获取了不同界面粗糙度、充填体养护龄期和起爆方式等因素对爆破裂隙扩展及应力波峰值应力的影响,探讨了爆破动力作用机理。结果表明:（1）爆破冲击在界面耦合体中存在拉、压和剪3种力学作用,且随着界面粗糙度的提高,界面受力呈先上升后下降趋势;（2）随着充填体养护时间增长,界面破坏逐步从受拉转化成剪切损伤;（3）同时起爆对耦合界面的损伤比逐孔起爆的小。     

基于Box-Behnken法的合肥湖积软土固化配方优化的试验研究

选择CaO和纯碱作为激发剂掺入GGBS(粒化高炉矿渣微粉)制备GGBS+CaO+纯碱固化合肥湖积软土,通过无侧限抗压强度试验研究固化黏土的强度变化规律。以GGBS、CaO和纯碱的掺量作为影响因子,以7d和28d固化土的无侧限抗压强度作为响应值,基于Box-Behnken法确定3种外添剂的最佳配合比。研究表明:GGBS掺量的变化对强度响应影响最大,且其敏感程度随龄期的增大而增大;而对于CaO和纯碱,情况则相反。养护7d后,各因素对强度的线性效应和曲面效应均显著,CaO与纯碱的交互作用显著;养护28d后,GGBS与纯碱的交互作用显著。最终得出:GGBS、CaO和纯碱三掺量固化黏土最佳配比分别为13.08%、4.89%和1.25%;在最佳配合比下,7d和28d的预测强度分别达到550.904kPa和665.953kPa。最后对实测值与预测值进行了对比分析。研究成果可为在合肥滨湖地区应用矿渣类软土固化剂提供理论依据。     

On the simulation of panel distortions due to hot curing adhesives

Hot curing one-part adhesives are often used to bond car body shells. The cure process of the adhesive, however, can lead to distortions, i.e. unwanted, visible deformations of the adherends. In case of outer car panels, these distortions are considered as visual defects, even though the structural integrity might not be affected. In order to avoid distortions by a proper control of the bonding process, a thorough understanding of the development of distortions is necessary. Finite element simulations can help to gain insight into this development. In this work, a simulation model is proposed and used to study the appearance of distortions in a steel sheet over different temperature cycles. The model takes chemical shrinkage and thermal deformation as well as gelation and stress relaxation into account. It was found that the heating rate can affect distortions. Lowering the cure temperature only lowers distortions for high temperature rates. Low heating rates can reduce distortions.