Statistical Assessment of Tensile Static,Creep and Fatigue Strengths for Unidirectional CFRP

Background

The tensile strength along the longitudinal direction of unidirectional carbon fiber reinforced plastics (CFRPs) constitutes important data for the reliable design of CFRP structures. Our earlier reports proposed the formulations for the statistical static, creep, and fatigue strengths of CFRP based on Christensen’s model of the viscoelastic crack kinetics.

Objective

This study is concerned with the statistical assessment of the tensile static, creep, and fatigue strengths of unidirectional CFRPs by using the proposed formulations and the characterization of the long-term strengths of unidirectional CFRPs.

Method

First, the proposed formulations for the time-dependent and temperature-dependent statistical static, creep, and fatigue strengths of CFRP are introduced. Second, the tensile static, creep and fatigue strengths of unidirectional CFRP are measured statistically at various temperatures using resin-impregnated CFRP strands as tensile test specimens by measuring the viscoelasticity of the matrix resin. Finally, the master curves showing the long-term life of these strengths are constructed by substituting these measured data into the formulations.

Results

The results clarify that the formulations are applicable with high reliability over wide ranges of time and temperature for the statistical tensile static, creep and fatigue strengths of unidirectional CFRP except above the glass transition temperature of the matrix resin. Therefore, the fatigue strength degradation phenomena of unidirectional CFRPs can be expressed by the time- and temperature-dependent part due to the viscoelastic behavior of the matrix resin and the number of load cycle-dependent parts.

Conclusions

The long-term life prediction of unidirectional CFRPs under static, creep and fatigue tension loadings can be determined by ascertaining the mechanical properties of the CFRP and matrix resin in the proposed formulations.

     

Dynamic tensile strength of composite laminate joints fastened mechanically

The tensile strength of composite joints is determined under dynamic loading conditions. The composites are laminates made from hybrid fiber reinforced plastic (HFRP) and carbon fiber reinforced plastic (CFRP). Three different mechanically fastened joint configurations are considered: they are the pin-connected, single-lap and double-lap type. The joint strength under dynamic load is found to be lower than that under quasi-static load. The pin-connected joint was the weakest. Investigated also are the influence of geometric parameters for pin-connected HFRP laminate joints. The results shed light on how to improve the bearing strength of mechanical joints when encountering dynamic loads.     

ARALL 材料拉伸力学性能的试验研究

利用自行研制的旋转盘式间接杆杆型冲击拉伸试验装置对ＡＲＡＬＬ材料以及施加预应力的ＡＲＡＬＬ材料进行了３个应变率（２００、５００、１３００ｓ－１）的冲击拉伸试验，得到了两种材料在不同应变率下的完整的应力应变曲线。结果表明ＡＲＡＬＬ材料在高速加载条件下的变形可以分为弹性变形、塑性变形和材料失稳后的残余变形三个部分，每个部分都有不同的变形机理。结果还表明，随着应变率的增加两种材料的屈服应力、失稳应力以及失稳应变均相应增加，表现出明显的应变率强化和动态韧性现象。最后根据材料在不同应变率下的试验结果，建立了ＡＲＡＬＬ材料计及应变率影响的三段线性本构模型。     

Dynamic stability analysis of shear-flexible composite beams

Dynamic stability behavior of the shear-flexible composite beams subjected to the nonconservative force is intensively investigated based on the finite element model using the Hermitian beam elements. For this, a formal engineering approach of the mechanics of the laminated composite beam is presented based on kinematic assumptions consistent with the Timoshenko beam theory, and the shear stiffness of the thin-walled composite beam is explicitly derived from the energy equivalence. An extended Hamilton’s principle is employed to evaluate the mass-, elastic stiffness-, geometric stiffness-, damping-, and load correction stiffness matrices. Evaluation procedures for the critical values of divergence and flutter loads of the nonconservative system with and without damping effects are then briefly introduced. In order to verify the validity and the accuracy of this study, the divergence and flutter loads are presented and compared with the results from other references, and the influence of various parameters on the divergence and flutter behavior of the laminated composite beams is newly addressed: (1) variation of the divergence and flutter loads with or without the effects of shear deformation and rotary inertia with respect to the nonconservativeness parameter and the fiber angle change, (2) influence of the internal and external damping on flutter loads whether to consider the shear deformation or not.     

Load-Deformation Behavior of Nitinol Stents

The rate of fracture of Nitinol stents in the superficial femoral artery (SFA) is higher than desirable. Development of more fracture-resistant stents requires a better understanding of in-vivo loads, how stents deform under these loads, and the influence of the artery on stent deformation. In the work reported here, testing devices were designed and constructed to measure loads in stents undergoing tensile, bending, and torsional deformations. Tests to measure mechanical stiffnesses were performed on stents, mock arteries, and stents emplaced in mock arteries. Significant stent/artery interaction was observed under tension and bending; little interaction occurred under torsion loads. The results are explained by changes in stent geometry under load. The deformation, load, and stent/artery interaction information will be useful in validating finite element codes for designing and analyzing stents.     

FATIGUE LIFE PREDICTION OF RC BEAMS STRENGTHENED WITH PRESTRESSED CFRP UNDER CYCLIC BENDING LOADS

The application of prestressed carbon reinforced polymer(prestressed CFRP)in reinforced concrete(RC)members can improve the mechanical properties of strengthened structures and strengthening efficiency.This paper proposed a semi-empirical prediction formula of fatigue lives of the RC beams strengthened with prestressed CFRP under bending loads.The formula is established based on the fatigue life prediction method of RC beams and fatigue experimental data of non-prestressed CFRP reinforced beams done before.Fatigue effect coefficient of the formula was confirmed by the fatigue experiments of the RC beams strengthened with prestressed carbon fiber laminate(prestressed CFL)under cyclic bending loads.Fatigue lives of the strengthened beams predicted using the formula agreed well with the experimental data.     

热载荷作用下梯度多孔材料梁弯曲及过屈曲力学行为的研究

基于Bernoulli-Euler梁理论,引入物理中面解耦了复合材料结构的面内变形与横向弯曲特性,研究了梯度多孔材料矩形截面梁在热载荷作用下的弯曲及过屈曲力学行为．假设沿梁厚度方向材料的性质是连续变化的,利用能量法推导了矩形截面梁的控制微分方程和边界条件,并用打靶法对无量纲化的控制方程进行数值求解．利用计算得到的结果分析了材料的性质、热载荷、边界条件对矩形截面梁非线性力学行为的影响．结果表明,对称材料模型下,固支梁与简支梁均显示出了典型的分支屈曲行为特征,而其临界屈曲热载荷值均会随着孔隙率系数的增加而单调增加．非对称材料模型下,固支梁仍显示出分支屈曲行为特征,但其临界屈曲热载荷不再随着孔隙率系数的变化而单调变化;而对于两端简支梁,发生了弯曲变形,弯曲挠度随载荷的增大而增大．     

Dynamics of hybrid shafts

In this paper the dynamic performance and cross-section deformation of shafts made of metals (steel and aluminum), composites (CFRP and GFRP) and hybrids of metals and composites have been studied. A layered finite degenerated shell element with transverse shear deformation and dynamic behavior is employed. Results obtained show that improvements in dynamic performance and reduction of cross-section deformation of hybrid shafts over metallic and composite shafts are possible.     

The effect of the irregular interface geometry in deformation and fracture of a steel substrate–boride coating composite

Presented in this paper is a computational analysis of the mechanisms involved in plastic deformation and fracture of a composite with coating under compressive and tensile loading. Using a steel specimen surface-hardened by diffusion borating, a role of the irregular geometry of the interface between the base material and hardened surface layer is investigated. In order to describe the mechanical behavior of the steel substrate and brittle coating, use is made of a plastic flow model including isotropic strain hardening and a fracture model, respectively. Using the Huber fracture criterion, the model takes into account the difference in the critical strength values for different types of local compressive and tensile states. It is shown that the irregular, serrated shape of the substrate–coating interface retards propagation of a longitudinal crack into this coating and prevents it from spalling under external compression of this composite. It is found out that even in the case of a simple uniaxial compression of the mesovolumes of this composite the boride “teeth” are subjected to tensile stresses, whose values are comparable with those of the external compressive load, and the direction of crack propagation and the general fracture behavior largely depend on the external loading conditions.     

Micromechanics and macromechanics of carbon nanotube-enhanced elastomers

The effects of carbon nanotubes on the mechanical behavior of elastomeric materials is investigated. The large deformation uniaxial tension and uniaxial compression stress-strain behaviors of a representative elastomer are first presented. This elastomer is then reinforced with multi-wall carbon nanotubes (MWNTs) and the influence of weight fraction of MWNTs on the large deformation behavior of the resulting composite is quantified. The initial stiffness and subsequent strain-induced stiffening at large strains are both found to increase with MWNT content. The MWNTs are also found to increase both the tensile strength and the tensile stretch at break. A systematic approach for reducing the experimental data to isolate the MWNT contribution to the strain energy of the composite is presented. A constitutive model for the large strain deformation behavior of MWNT-elastomer composites is then developed. The effects of carbon nanotubes are modeled via a constitutive element which tracks the stretching and rotation of a distribution of wavy carbon nanotubes. The MWNT strain energy contribution is due to the bending/unbending of the initial waviness and provides the increase in initial stiffness as well as the retention and further enhancement of the increase in stiffness with large strains. The model is shown to track the stretching and rotation of the CNTs with macroscopic strain as well as predict the dependence of the macroscopic stress-strain behavior on the MWNT content for both uniaxial tension and uniaxial compression.     

Control of mechanical deformation of a laminate by piezoelectric actuator taking into account the transverse shear

Summary The control of dynamic deformation of a laminate plate is conducted by applying electrical load to a piezoelectric actuator integrated into the laminate. The dynamic behavior of the laminate is analyzed in the paper taking into account the effect of transverse shear. The analytical model of the laminate is composed of fiber-reinforced laminae and piezoelectric layers constituting a symmetric cross-ply laminate rectangular plate with simply-supported egdes. It is subjected to mechanical and electrical loads acting on the piezoelectric actuator in order to compensate the effect of the mechanical loads. The behavior of the laminate is analyzed based on the first-order shear deformation theory. Closed-form solutions are obtained for the following quantities: (1) natural frequencies of the laminate plate, (2) weight functions for the deflections and rotations and (3) transient deflections due to loads varying arbitrarily with time. Illustrative examples are shown for the control of deflections caused by the mechanical loads by means of electrical voltage applied to the piezoelectric actuators.     

Geometrically nonlinear large deformation analysis of triangular CNT-reinforced composite plates

A first known investigation on the geometrically nonlinear large deformation behavior of triangular carbon nanotube (CNT) reinforced functionally graded composite plates under transversely distributed loads is investigated. The analysis is carried out using the element-free IMLS-Ritz method. In this study, the first-order shear deformation theory (FSDT) and von Kármán assumption are employed to account for transverse shear strains, rotary inertia and moderate rotations. A convergence study is conducted by varying the supporting size and number of nodes. The effects of transverse shear deformation, CNT distribution and CNT volume fraction on the nonlinear bending characteristics under different boundary conditions are examined.     

Experimental analysis and modeling of biaxial mechanical behavior of woven composite reinforcements

This paper presents experimental studies on the mechanical behavior of fiber fabrics using a biaxial tensile device based on two deformable parallelograms. The cross-shaped specimens are well adapted to fabrics because of their lack of shear stiffness. Tension versus deformation curves, for different strain ratios, are obtained in the case of composite woven reinforcements used in aeronautic applications. It is shown that the tensile behavior of the fabric is strongly nonlinear due to the weaving undulations and the yarn contraction, and that the phenomenon is clearly biaxial. A constitutive model is described and identified from the experimental data. The essential role played by the yarn crushing will be pointed out.     

激光冲击喷丸与激光辐照LY12铝合金材料拉伸力学行为的实验研究

为了研究激光冲击喷丸与激光辐照处理后LY12铝合金材料的微尺度变形特点和失效机理,对经过不同激光功率密度处理后的LY12铝合金材料,在扫描电镜下进行了原位拉伸力学行为和失效机理研究。在扫描电子显微镜（SEM）下,得到各组试件的拉伸载荷曲线和不同载荷下的微观区域图像,并利用数字图像相关技术进行不同载荷下的微观区域全场变形分析,并对拉伸断口形貌也进行了分析。研究表明：激光处理的功率大小对LY12铝合金拉伸最大载荷有明显的影响,激光处理的交界处有较强的应变集中。     

Cyclic deformation of ternary nanocomposites: Experiments and modeling

Observations are reported on the mechanical response of a ternary composite (blend of polypropylene and a thermoplastic elastomer reinforced with montmorilonite nanoclay) at cyclic tensile deformations with relatively large amplitudes (up to the necking point). Constitutive equations for the viscoplastic behavior of hybrid nanocomposites are derived by using the laws of thermodynamics. Adjustable parameters in the stress–strain relations are found by fitting the experimental data. It is demonstrated that the model adequately predicts stress–strain diagrams of the nanocomposite under cyclic loading.     

Numerical study of strength properties for a composite material with short reinforcing fibers

A numerical approach to the determination of strength properties for concrete with short reinforcing fibers on the basis of the finite element method is proposed. The mathematical model takes into account various processes of nonlinear deformation of the concrete matrix under compressive and tensile loads, the possibility of developing the inelastic strains in the concrete matrix and reinforcing fibers and the nonlinear interaction between them. The effect of fiber concentration, various loading surfaces for the material matrix, and the bonding type on the deformation of a composite material is analyzed. Numerical examples of strength analysis are given.     

Prediction of bond failure and deflection of carbon fiber-reinforced plastic reinforced concrete beams

Carbon fiber-reinforced plastic (CFRP) reinforced concrete beams can fail due to interface debonding, due to the high tensile strength of such rebars. A set of 16 concrete beams reinforced with different amounts of CFRP reinforcement was subject to static three-point bending. The beam dimensions and CFRP reinforcements used were selected to demonstrate a transition from compression failure to bond failure with decreasing reinforcement ratio. It is shown that accurate bond strength data to predict such failures can be obtained from a “hinged-beam” test configuration, rather than the conventional direct “pull-out” tests. Deflection under service loads can also be predicted more accurately using a proposed equation that includes the reinforcement ratio and the elastic modulus of the reinforcement.     

橡胶粘结颗粒材料粘弹性性能的试验研究与离散元模拟

制备了颗粒规则四方排列和六方排列的橡胶粘接颗粒材料试样,实验测试了所制备试样在单向拉伸载荷下的应力松弛曲线和不同应变率时的应力应变曲线。基于所测试的应力松弛曲线,采用曲线拟合方法得到了所测试材料的宏观Burger’s粘弹性本构模型参数。采用离散元模型中单元间连结模型代表颗粒间橡胶粘接剂的作用,并基于试样的宏观Burger’s模型参数与离散元模型中细观Burger’s连结模型参数间的关系,建立了橡胶粘接颗粒材料的无厚度胶结离散元分析模型。最后采用所建立的离散元模型计算了所测试试样的松弛和拉伸力学性能。离散元预测结果与实验结果的对比表明,采用无厚度胶结离散元模型能较好的计算颗粒规则排列的橡胶粘接颗粒材料松弛和拉伸力学性能,但基于应力松弛实验拟合而来参数不能准确反应橡胶粘接剂在高应变率条件下其力学性能的应变率相关性。     

Homogenization method for strength and inelastic behavior of nanocrystalline materials

Homogenization techniques are used for modeling the so-called “breakdown” of the Hall–Petch law in the case of nanocrystalline (NC) materials. In this paper, the NC material is modeled as a composite material composed of two phases: the grain core (inclusion) and the grain boundaries (matrix). The deformation of the inclusion phase has a viscoplastic component that takes into account the dislocation glide mechanism as well as Coble creep. The boundary phase is modeled as an amorphous material with a perfect elastic–plastic behavior. An application of the model is developed on pure copper under tensile load. The results are compared with various experimental data.     

Features of plane wave propagation along the layers of a prestrained nanocomposite

Features of the propagation of longitudinal and transverse plane waves along the layers of nanocomposites with process-induced initial stresses are studied. The composite has a periodic structure: it is made by repeating two highly dissimilar layers. The layers exhibit nonlinear elastic behavior in the range of loads under consideration. A Murnaghan-type elastic potential dependent on the three invariants of the strain tensor is used to describe the mechanical behavior of the composite constituents. To simulate the propagation of waves, finite-strain theory is used for developing a problem statement within the framework of the three-dimensional linearized theory of elasticity assuming finite initial strains. The dependence of the relative velocities of longitudinal and transverse waves on two components of small initial stresses in each layer and on the volume fraction of the constituents is studied. It is established that there are thickness ratios of layers in some nanocomposites such that the wave velocities are independent of the initial stresses and equal to the respective wave velocities in composites without initial stresses __________ Translated from Prikladnaya Mekhanika, Vol. 43, No. 4, pp. 3–26, April 2007.