Modeling of the influence of fibers on creep of fiber reinforced cementitious composite

An analytical model has been developed to study the influence of fibers on creep of fiber reinforced cementitious composites. The model is based on the assumption that shear stress is produced between fiber and surrounding matrix as the matrix deforms. This shear stress in turn influences the matrix creep behavior resulting in macroscopic creep strain lower than that of pure cement-based matrix. In the present paper, a creep strain expression in the form of matrix creep strain multiplying by a fiber influence factor, which reflects the influences of matrix and fiber properties as well as fiber orientation characteristics, is presented. A parametric study, including the influence of elastic moduli of fiber and matrix, fiber dimension and fiber content is carried out. The modeling results indicate that creep strain of fiber reinforced cement-based composite is significantly influenced by the elastic moduli of fiber and matrix as well as fiber length and thickness (i.e. diameter for fiber with circular cross-section). Model predictions compare favorably with experimental measurements of creep strain of fiber reinforced mortar and concrete under compressive load.     

Creep behavior of unidirectional composites

The creep behavior of the continuous fiber reinforced unidirectional composites due to the viscoelasticity of the resin matrix is investigated assuming that the constituent matrix obeys the nonlinear creep law and the fiber is the linear elastic materials. Utilizing a quasi three-dimensional finite element method, the macroscopic creep behavior of the composites with regular fiber packing is obtained, giving the orthotropic creep law for the composites. Then, the creep of the composites with random fiber packing is estimated applying the random model proposed by Kondo and Saito in which the neat matrix cylinders are embedded in the regular array composites. The theoretical predictions for the creep behavior are compared with the experimental results.     

Effect of interface diffusion on the strain and stress stability of particulate reinforced electrostrictive materials

This paper presents an analytical method to solve the creep rate and stress relaxation behaviors of particle reinforced electrostrictive composites induced by the interface diffusion between particle and electrostrictive matrix, subjected to external electric fields. Based on the microstructures evolution theory and electroelastic theory of electrostrictive materials, the thermodynamic equations of creep rate and stress relaxation induced by the interface diffusion are, respectively, deduced and solved. The investigation results show that the strain and stress stabilities of particle reinforced electrostrictive materials can be enhanced by optimizing the shape, stiffness and volume fraction of reinforced particles.     

应力水平和纤维角度对CGF/PP复合材料蠕变行为的影响及其Burgers模型参数的数值预测

采用DMA的Creep模式分别测试了短时间内（15 min）聚丙烯（PP）在不同应力水平和温度下的单向拉伸蠕变行为,长时间内（10 h）连续玻璃纤维增强聚丙烯（CGF/PP）复合材料单层板在不同应力水平和不同纤维角度上的拉伸蠕变行为。利用Burgers黏弹性模型拟合了蠕变测试数据,构建了相关参数与应力水平和纤维角度的依赖性。结果表明:PP和CGF/PP单层板的蠕变柔量均随应力增大而显著增加,稳态蠕变速率也随之增加,蠕变模量保留率明显下降,PP基体的黏弹性主要决定了CGF/PP单层板在低应力水平下的蠕变行为; 30%应力水平下,偏轴拉伸的纤维角度在0°~90°范围内存在拉-剪耦合效应,在45°时最为显著,此时稳态蠕变速率和蠕变变形量最大;利用四元件Burgers黏弹性模型拟合各条件下蠕变曲线得到的数值模型与实验数据具有较好的相关性,相关系数达到0.99,从得到的数值模型可知相关模型参数存在明显的应力和角度依赖关系;利用模型参数的数值拟合公式分别预测10 MPa应力下0°纤维方向的蠕变曲线及45°纤维方向上30%应力水平的偏轴蠕变曲线均与实验曲线一致,表明本文得到的数值模型的可靠性。      

界面对硅酸铝短纤维增强AZ91D镁基复合材料蠕变性能的影响

界面对复合材料蠕变性能的影响很大。在试验分析的基础上建立了硅酸铝短纤维增强AZ91D镁基复合材料理论分析模型,利用三维有限元分析方法,系统研究了界面特性、界面上应力应变分布和短纤维位向变化对硅酸铝短纤维增强AZ91D镁基复合材料蠕变性能的影响。研究表明：界面特性,如厚度、模量,均对纤维最大轴应力和稳态蠕变速率有影响,当界面厚度增加,纤维最大轴应力减小而稳态蠕变速率增大;当界面模量增大,纤维最大轴应力增大而稳态蠕变速率减小,但当界面模量高于基体模量时,纤维最大轴应力和稳态蠕变速率均保持不变;纤维位向也影响轴应力分布和稳态蠕变速率,纤维在其末端界面上存在较大的应力和应变,此处容易产生微裂纹而使材料抗蠕变能力下降;界面对硅酸铝短纤维增强AZ91D镁基复合材料的蠕变曲线和蠕变断裂机制也有影响,其影响程度还与纤维位向有关。     

碳纤维增强树脂复合材料细观蠕变性能

碳纤维增强树脂复合材料以其优异的性能,在各领域得到广泛应用。由于树脂基体具有黏弹性,使其合成的复合材料也表现出黏弹性行为。蠕变是材料黏弹性行为中最典型的一类现象,因此对碳纤维增强树脂复合材料细观蠕变性能的研究具有重要意义。室温下利用纳米压痕技术对碳纤维增强树脂复合材料中的基体、界面及纤维相在不同峰值载荷下的细观蠕变行为进行分析。结果表明:在相同的蠕变时间下,最大载荷为2 mN和10 mN的纤维蠕变位移约为基体蠕变位移的1/3和1/2,界面的蠕变位移介于两者之间;稳态蠕变阶段的蠕变速率小于0.1%;基体、界面、纤维的蠕变应力指数分别为3.6、2.9和2.1。同时根据Kelvin-Voigt模型得到了基体、界面及纤维的第一、第二复数模量、黏度系数及蠕变柔量。      

氧化铝短纤维增强铝基复合材料的蠕变破坏行为

研究了挤压铸造Al₂O₃短纤维增强铝基复合材料在350℃恒应力条件下的蠕变行为。蠕变试验过程中采用中断实验的方法对复合材料的显微组织进行观察,发现复合材料在蠕变过程中纤维发生断裂,弱界面发生破坏以及基体合金在应力作用下发生变形。根据复合材料在蠕变三个阶段中显微组织的变化情况,对其宏观蠕变行为进行了分析,认为位错在复合材料中滑移和攀移控制整个蠕变过程,并提出了短纤维增强金属基复合材料的蠕变断裂机理,合理地解释了复合材料的蠕变过程。      

Dynamic compressive behavior of unidirectional E-glass/vinylester composites

Results from an experimental investigation on the mechanical behavior of unidirectional fiber reinforced polymer composites (E-glass/vinylester) with 30%, 50% fiber volume fraction under dynamic uniaxial compression are presented. Specimens are loaded in the fiber direction using a servo-hydraulic material testing system for low strain rates and a Kolsky (split Hopkinson) pressure bar for high strain rates, up to 3000/s. The results indicate that the compressive strength of the composite increases with increasing strain rate. Post-test scanning electron microscopy is used to identify the failure modes. In uniaxial compression the specimens are split axially (followed by fiber kink band formation). Based on the experimental results and observations, an energy-based analytic model for studying axial splitting phenomenon in unidirectional fiber reinforced composites is extended to predict the compressive strength of these composites under dynamic uniaxial loading condition.     

Semi-analytically presenting the creep strain rate and quasi shear-lag model as well as finite element method prediction of creep debonding in short fiber composites

In this research work, semi-analytical method (SAM) is presented to predict composite creep strain rate and quasi shear-lag (QSL) formulation directly, as well as, finite element method (FEM) is employed for predicting partial creep debonding at the interface in steady state creep of short fiber composites under tensile axial stress. Also, new formulation QSL is introduced to obtain the average axial stress in fiber which its results are similar to the results of shear lag (SL) model. Then, it is shown that FEM can approximately predict the partial debonding in some regions of the interface. As a result, interfacial debonding can be caused by high tensile axial and circumferential stresses, high shear and equivalent stresses, and low compressive radial stresses with considering stress concentration. The results obtained from SAM are in good agreement with the available experimental results. Finally, it is concluded that FEM simulation can be useful for predicting some defects such as interfacial debonding and also better designing the fibrous composites.     

Creep of fibrous composite materials

Models are presented for the creep behaviour of fibrous composite materials with aligned fibres. The models comprise both cases where the fibres remain rigid in a creeping matrix and cases where the fibres are creeping in a creeping matrix. The treatment allows for several contributions to the creep strength of composites. The advantage of combined analyses of several data sets is emphasized and illustrated for some experimental data. The analyses show that it is possible to derive creep equations for the (in situ) properties of the fibres. The experiments treated include model systems such as Ni + W-fibres, high temperature materials such as Ni + Ni₃Al + Cr₃C₂-fibres, and medium temperature materials such as Al + SiC-fibres. For the first two systems reasonable consistency is found for the models and the experiments, while for the third system too many unquantified parameters exist and further studies seem necessary.     

考虑界面效应的GFRP复合材料蠕变模型

建立了包含界面的玻璃纤维增强树脂复合材料(GFRP)蠕变混合率单胞模型,对GFRP的蠕变性能进行分析;并与GFRP在应力水平为初始弯曲强度的20%所对应的载荷下的弯曲蠕变实验结果进行对比。分析了界面模量、界面厚度、纤维连续性与形态以及位向等因素对复合材料蠕变性能的影响。结果表明:相较于不考虑界面效应的混合率模型,本模型具有更高的准确性,与实验结果更为吻合;界面模量反应了纤维与基体的结合程度,对复合材料的蠕变性能产生影响,其蠕变柔量随着界面模量的增大而减小;界面厚度的增大会导致复合材料的蠕变柔量略微增大;相较于连续纤维增强树脂复合材料,短切纤维毡增强树脂复合材料的蠕变性能更易受到界面效应的影响;纤维方向对复合材料蠕变性能有显著影响,随着纤维方向角的增大,复合材料蠕变柔量增大,但当纤维方向角达到60°后,纤维已基本失去载荷传递和增强能力,复合材料蠕变柔量不再继续随着纤维方向角的增大而增大。      

Simulation of creep crack growth in ceramic composites

The elevated temperature response resulting from tensile creep of fiber reinforced ceramic composites was modeled using Monte Carlo simulation. The model consisted of a uniaxially loaded fiber tow aligned with the direction of applied load, and modeled the growth of matrix cracks resulting from creep failure of bridging fibers. A creep strain rate consisting of primary and steady state components was assumed, and each component was modeled by a power law relationship. Power law creep exponents in the range of 2.0–2.5 for a selected SiC/SiC system at stress levels ranging from 60 MPa to 200 MPa were evaluated. Fatigue-like behavior was predicted as a result of tensile creep, and a fatigue exponent of 3.03 ± 0.07 was predicted for nominal stress levels less than 200 GPa. The influence of initial crack length on failure lifetime was also studied, but was found to have little influence on the predicted lifetime. The predicted failure response suggested a stress dependent creep process could be used to model experimental data and evaluate the failure mechanism of reinforced composites.     

Intra/inter-ply shear behaviors of continuous fiber reinforced thermoplastic composites in thermoforming processes

The thermoforming of continuous fiber reinforced thermoplastic (CFRTP) composite panels generally involves significant in-plane shear deformation. In the present work, the in-plane shear behavior of woven thermoplastic composites (Carbon/Polyphenylene Sulfide) over a range of processing temperatures is studied by bias-test experiments at different velocities. The experimental data of force versus displacement and force versus shear strain are presented for different extension velocities and temperatures. A thermo-visco-elastic model for numerical simulations of woven thermoplastic composite forming is proposed considering the influences of temperature and of strain rate. We applied a large displacement three-dimensional cohesive element with eight nodes which has been used for crack analysis in fracture mechanics by other authors, to investigate the inter-ply shear mechanism of woven thermoplastic composites. Applying three-dimensional cohesive elements, multi-plies forming simulations are performed to show inter-ply slip behaviors at different temperatures. The proposed models can be useful to predict from the properties of reinforcement and resin the intra/inter-ply shear behaviors of woven thermoplastic composites at high temperatures if experimental characterization of composite laminate behaviors is difficult to conduct.     

Finite difference solution of steady state creep deformations in a short fiber composite in presence of fiber/matrix debonding

A finite difference technique is developed to predict the second stage creep displacement rates and stress analysis of a short fiber metal matrix composite subjecting to a constant axial load through a micromechanical approach. The technique is capable to take into account the presence of interfacial debonding as one of the main factors affecting the creep performance of short fiber composites. The exponential law is adopted to describe the matrix creep behavior. Also, a model for prediction of interfacial debonding at fiber/matrix interface is developed using a stress based method. The obtained results could greatly help to better understand the flow pattern of matrix material and the load transfer mechanism between fiber and matrix with and without the presence of interfacial debond. The predicted strain rate by the proposed approach exhibits good agreement with the experimental results.     

Creep failure time prediction of polymers and polymer composites

A theoretical approach for the prediction of creep rupture time of polymers and polymer composites is analyzed in the present work. This analysis takes into account the viscoelastic path at small strains and the viscoplastic path at higher stresses. The calculation of the rate of creep strain is based on a thermally activated rate process, while the emergence and growth of plastic strain, with increasing creep time, is also taken into account. When the accumulated strain attains values, high enough to lead to failure, its slope versus time exhibits an abrupt change. At this specific time, the creep rate function in respect to time appears a minimum. The creep failure time is defined as the time where the creep rate takes its minimum value. The model has been tested for various types of polymeric materials, as well as for polymer composites. Once the model parameters are estimated from short time creep strain data, then it was proved to successfully predict the creep failure time at a variety of stress levels, for all material types examined.     

Flexural creep behavior of discontinuous thermoplastic composites: Non-linear viscoelastic modeling and time–temperature–stress superposition

Flexural creep behavior of nylon 6/6, polypropylene and high-density polyethylene long fiber thermoplastic (LFT) composites was studied according to ASTM D-2990. Neat polymers were tested for baseline data and compared with the 40 wt.% E-glass reinforced LFTs, all processed by compression molding. All materials exhibited non-linear viscoelasticity and showed a succession in creep resistance consistent with static flexural yield strength. A four parameter empirical model used for short fiber thermoplastics (SFT), proposed by Hadid et al., was found to provide an excellent fit to the experimental data. Time-compliance data from flexural creep and dynamic mechanical analysis (DMA) were combined to utilize short-term flexural creep tests to predict lifetime of the composites. A time–temperature–stress superposition (TTSSP) procedure was used, where stress-based vertical shifts were applied in addition to horizontal shifts used in a traditional time–temperature superposition (TTSP). Master curves obtained by this method projected the long-term creep properties, the order of creep resistance being consistent with the flexural creep data.     

基于分数阶黏弹性模型的木塑复合材料蠕变/回复性能分析

木塑复合材料(WPC)是一种木质纤维增强聚合物的新型环保复合材料,为分析WPC在非恒定荷载下的变形行为,进行结构的长期变形设计,对WPC的蠕变/回复变形进行计算分析。采用叠加原理对比分析既有蠕变计算模型对WPC蠕变/回复的整体预测效果。结果表明,现有模型均不能良好预测其蠕变/回复行为。采用基于分数阶微积分的黏弹性模型对其蠕变/回复行为进行预测,提出一种双参数法的修正分数阶黏弹性模型。通过与已有实测数据对比表明,该模型能够准确反映WPC的静态黏弹性行为。结合实验数据,给出了不同WPC蠕变/回复模型的参数取值。      

FRP约束混凝土的应力-应变关系

通过修正已有文献中提供的约束混凝土体积应变计算模型,并基于受定侧压力作用下混凝土的应力-应变关系模型,采用数值方法,全过程计算了具有被动约束特征的圆形截面纤维增强塑料(FRP)约束混凝土的应力-应变关系。结果表明,无论是对于具有强化特征还是具有软化特征的FRP约束混凝土,计算结果和实验结果及其他文献报道的实验结果均吻合良好。     

Modeling and simulation of the effect of fiber breakage on creep behavior of fiber-reinforced metal matrix composites

A theoretical model and computer simulation methodology was developed to predict the effect of fiber fracture on creep behavior of continuous fiber-reinforced metal matrix composites. Initially, a single fiber model was developed based upon the fiber statistical characteristics and a shear-lag analysis to establish the computation simulation route. Then, the methodology was extended to predict the creep behavior of a multiple fiber composite. A failure criterion was also incorporated in the model to predict the rupture life of the composite. A parametric study was also conducted to investigate the effects of properties of the constituents on the longitudinal creep behavior of the SCS-6/Ti composite.