Residual Strains using Integrated Continuous Fiber Optic Sensing in Thermoplastic Composites and Structural Health Monitoring

The evolution of spatially resolved internal strain/stress during the manufacturing of thermoplastic composites and subsequent relaxation from water intake are evaluated using an in-situ fiber optic sensor corresponding to a coated optical glass fiber with a nominal diameter of 160 μm. Unidirectional carbon fiber-polyamide 6 composites are produced using compression molding with an embedded fiber optic for strain measurement. The distributed fiber optic based strain sensor is placed in an arrangement to capture 0, 45, and 90° strains in the composite to resolve in-plane strain tensor. Strains are monitored in the direction of fiber optic sensor along its length at high resolution during the various stages of compression molding process. Results indicate considerable internal strains leading to residual stress at the end of processing step along the off-axis (45°) and transverse (90°) directions, and small strains in the carbon fiber pre-preg (0°) direction. At the end of compression molding process, an average of 7000 and 10,000 compressive micro-strains are obtained for residual state of strain in the off-axis and transverse direction. Since water/moisture infusion affects the mechanical properties of polyamide-6 matrix resin, these composite panels with embedded sensors targeted for marine applications are monitored in a water bath at 40 °C simulating accelerated testing conditions. Using the same fiber optic sensor based technique, the strain relaxation was observed during water uptake demonstrating in-situ strain monitoring during both manufacturing and subsequent composite implementation/application environment. The technique presented in this paper shows the potential of optimizing time-temperature-pressure protocols typically utilized in thermoplastic manufacturing, and continuous life-cycle monitoring of composite materials using a small diameter and inexpensive distributed fiber optic sensing.     

短纤维复合材料的压缩强度

细观力学理论得到的复合材料内应力是均值应力,在进行破坏和强度预报前,必须转化到真实值.对于短纤维复合材料,除了轴向压缩真实应力外,基体其它方向真实应力计算已得到解决,等于其均值应力乘以基体应力集中系数.论文基于弹性力学方法得到了短纤维复合材料轴向压缩下基体的应力场,并据此定义基体的轴向压缩应力集中系数.与基体其它方向应...     

Strain-space plasticity analysis of fibrous composites

A strain-space formulation of plasticity theory for metal matrix fibrous composites is discussed. Specific results are obtained for a composite system in which the fibers are elastic until failure, while the matrix is of the Mises type, with kinematic hardening. The material model of the composite is based on the assumption that the fiber diameter is vanishingly small, and the fiber volume fraction is finite. Explicit expressions are obtained for instantaneous strain concentration factors in the phases, for the instantaneous overall stiffness, and for the overall loading surface and hardening rule during mechanical straining along a prescribed path.     

Macroscopic constitutive relations for elastomers reinforced with short aligned fibers: Instabilities and post-bifurcation response

This paper is concerned with the characterization of the macroscopic response and possible development of instabilities in a certain class of anisotropic composite materials consisting of random distributions of aligned rigid fibers of elliptical cross section in a soft elastomeric matrix, which are subjected to general plane strain loading conditions. For this purpose, use is made of an estimate for the stored-energy function that was derived by Lopez-Pamies and Ponte Castañeda (2006b) for this class of reinforced elastomers by means of the second-order linear comparison homogenization method. This homogenization estimate has been shown to lose strong ellipticity by the development of shear localization bands, when the composite is loaded in compression along the (in-plane) long axes of the fibers. The instability is produced by the sudden, collective rotation of a band of fibers to partially release the high stresses that develop in the elastomer matrix when the composite is compressed along the stiff, long-fiber direction. Consistent with the mode of the impending instability, a lower-energy, post-bifurcation solution is constructed where “striped domain” microstructures consisting of layers with alternating fiber orientations develop in the composite. The volume fractions of the layers and the fiber orientations within the layers adjust themselves to satisfy equilibrium and compatibility across the layers, while remaining compatible with the imposed overall deformation. Mathematically, this construction is shown to correspond to the rank-one convex envelope of the original estimate for the energy, and is further shown to be polyconvex and therefore quasiconvex. Thus, it corresponds to the “relaxation” of the stored-energy function of the composite, and can in turn be viewed as a stress-driven “phase transition,” where the symmetry of the fiber microstructures changes from nematic to smectic.     

An asymmetrical dynamic model for bridging fiber pull-out of unidirectional composite materials

An elastic analysis of an internal crack with bridging fibers parallel to the free surface in an infinite orthotropic elastic plane is studied. An asymmetrical dynamic model for bridging fiber pull-out of unidirectional composite materials is presented for analyzing the distributions of stress and displacement with the internal asymmetrical crack under the loading conditions of an applied non-homogenous stress and the traction forces on crack faces yielded by the bridging fiber pull-out model. Thus the fiber failure is determined by maximum tensile stress, resulting in fiber rupture and hence the crack propagation would occur in a self-similarity manner. The formulation involves the development of a Riemann-Hilbert problem. Analytical solution of an asymmetrical propagation crack of unidirectional composite materials under the conditions of two moving loads given is obtained, respectively. After those analytical solutions were utilized by superposition theorem, the solutions of arbitrary complex problems could be obtained.     

Effect of modulus ratio on stress near a discontinuous fiber

The effect of the fiber to matrix modulus of elasticity ratio varying from 1.0 to 200 was investigated for a two-dimensional plane-stress composite configuration having a simulated fiber volume fraction of 0.45 and containing a discontinuous fiber. Uniaxial loading parallel to the fibers was considered. Two independent techniques were used: moiré strain analysis and finite-element analysis. Displacements were measured from four experimental models by utilizing optical fringe-multiplication techniques. The finite-element method yielded stresses which agreed closely with those obtained from the experimental analysis. Matrix stress-concentration factor near the discontinuous fiber was found to increase rapidly with increasing modulus ratio, reaching a value of 20 for a modulus ratio of 200. The finite-element method was shown to be a valuable tool for micromechanical stress analysis of composite materials, and the accuracy of strain analysis by moiré-fringemultiplication techniques was demonstrated for problems containing sever strain gradients.     

Asymmetrical dynamic fracture model of bridging fiber pull-out of unidirectional composite materials

An elastic analysis of an internal crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane is studied, and asymmetrical dynamic fracture model of bridging fiber pull-out of unidirectional composite materials is presented for analyzing the distributions of stress and displacement with the internal asymmetrical crack under the loading conditions of an applied non-homogenous stress and the traction forces on crack faces yielded by the bridging fiber pull-out model. Thus the fiber failure is ascertained by maximum tensile stress, the fiber ruptures and hence the crack propagation should also appear in the modality of self-similarity. The formulation involves the development of a Riemann-Hilbert problem. Analytical solution of an asymmetrical propagation crack of unidirectional composite materials under the conditions of two increasing loads given is obtained, respectively. In terms of correlative material properties, the variable rule of dynamic stress intensity factor was depicted very well. After those analytical solutions were utilized by superposition theorem, the solutions of arbitrary complex problems could be gained.     

Onset of failure in finitely strained layered composites subjected to combined normal and shear loading

A limiting factor in the design of fiber-reinforced composites is their failure under axial compression along the fiber direction. These critical axial stresses are significantly reduced in the presence of shear stresses. This investigation is motivated by the desire to study the onset of failure in fiber-reinforced composites under arbitrary multi-axial loading and in the absence of the experimentally inevitable imperfections and finite boundaries.By using a finite strain continuum mechanics formulation for the bifurcation (buckling) problem of a rate-independent, perfectly periodic (layered) solid of infinite extent, we are able to study the influence of load orientation, material properties and fiber volume fraction on the onset of instability in fiber-reinforced composites. Two applications of the general theory are presented in detail, one for a finitely strained elastic rubber composite and another for a graphite-epoxy composite, whose constitutive properties have been determined experimentally. For the latter case, extensive comparisons are made between the predictions of our general theory and the available experimental results as well as to the existing approximate structural theories. It is found that the load orientation, material properties and fiber volume fraction have substantial effects on the onset of failure stresses as well as on the type of the corresponding mode (local or global).     

Experimental research on pre-cracked marble under compression

An experimental approach on propagation and coalescence of pre-existing cracks (fractures) in marble samples under compression is carried out. Two types of newborn cracks are observed: wing (tensile) cracks and secondary (shear) cracks. Both types of cracks initiate from the tips of the fractures and propagate in a stable manner. Wing cracks initiate at an angle with the fractures and tend to propagate towards the direction of the most compressive stress. Secondary cracks, however, initiate in a direction quasi-coplanar to the fractures and also parallel to the wing cracks but in the opposite direction. The orientations and geometries of fractures can decide which kind of wing cracks and secondary cracks will be produced. The interactions between fractures strongly affect the initiation and propagation of wing cracks and secondary cracks, and make examples’ failure patterns thoroughly different. The initial fracture angles of wing cracks range among 52°–68°, which are lower than the results (about 77°) of previous experiments on molding materials. In addition, the characters of acoustic emission (AE) of pre-cracked marble samples are also studied. For some rock samples, a secondary peak value phenomenon of AE counts is observed. For the samples with zigzag fractures, the accumulated AE counts at the moment of failure occupy almost half of the summation of whole load processes. This reveals that the failure of materials with zigzag fractures is more unexpected.     

Elastic response of water-filled fiber composite tubes under shock wave loading

We experimentally and numerically investigate the response of fluid-filled filament-wound composite tubes subjected to axial shock wave loading in water. Our study focuses on the fluid–structure interaction occurring when the shock wave in the fluid propagates parallel to the axis of the tube, creating pressure waves in the fluid coupled to flexural waves in the shell. The in-house-developed computational scheme couples an Eulerian fluid solver with a Lagrangian shell solver, which includes a new and simple material model to capture the response of fiber composites in finite kinematics. In the experiments and simulations we examine tubes with fiber winding angles equal to 45° and 60°, and we measure the precursor and primary wave speeds, hoop and longitudinal strains, and pressure. The experimental and computational results are in agreement, showing the validity of the computational scheme in complex fluid–structure interaction problems involving fiber composite materials subjected to shock waves. The analyses of the measured quantities show the strong coupling of axial and hoop deformations and the significant effect of fiber winding angle on the composite tube response, which differs substantially from that of a metal tube in the same configuration.     

二维编织陶瓷基复合材料应力-应变行为

对二维编织陶瓷基复合材料拉伸应力-应变行为进行了试验研究和理论模拟. 将二维 编织结构简化为：正交铺层结构和纤维束波动结构. 基于基体随机开裂、纤维随机断裂分布 理论,得到正交铺层结构的应力-应变关系;基于体积平均方法,将纤维束波动部分进行分割, 引入强度分析模型,得到纤维束波动部分的应力-应变关系. 结合正交铺层部分和纤维束波动 部分的应力-应变关系,得到二维编织结构的应力-应变行为,理论与试验吻合较好.     

An experimental investigation on the tensile moduli and strengths of graphite/epoxy laminates

The results of a series of tensile tests on graphite/epoxy [0°]_8S and [0°/±30°/0°]_2S laminates at rates varying from 0.002 in/min to 2 in./min are reported. The loads are applied at various angles to the fiber directions in each case. The rate-dependent behavior of the stress-strain response is assessed. Evidence is presented to indicate that failure first occurs on inner plies. Also, evidence is presented to indicate that, in some cases, moduli increase with increased stress or strain level. Lamination theory is used to predict moduli and comparisons with experiment are given. This theory is also used in conjunction with three failure theories to predict ultimate strengths with varying degrees of success. Further, two approaches to ply unloading after first-ply failure are used and discussed. One is a standard method found in the literature while the other is a proposed ‘strength-of-materials’ type of technique which is computationally much simpler.     

Behavior of Pin-loaded Laminated Composites

In this study, an investigation was carried out to determine the effects of joint geometry and fiber orientation on the failure strength and failure mode in a pinned joint laminated composite plate. Behavior of pin-loaded laminated composites with different stacking sequence and different dimensions has been observed experimentally. E/glass–epoxy composites were manufactured to fabricate the specimens. Mechanical properties of the composites were characterized under tension, compression and in-plane shear in static loading conditions. Laminated composites were loaded through pins. Single-hole pin-loaded specimens were tested for their tensile response and width-to-hole diameter (W/D) and edge distance-to-hole diameter (E/D) ratios evaluated. A series of experiments was performed with six different material configurations ([0/±45]_s–[90/±45]_s, [0/90/0]_s–[90/0/90]_s and [90/0]_2s–[±45]_2s), in all, over 120 specimens. E/D ratios and W/D ratios of plates were changed from 1 to 5 and 2 to 5, respectively. Failure propagation and failure type were observed on the specimens. The influence of the joint geometry on the strength of the pin-loaded composites was assessed. When laminated composite plates were loaded to final failure, three basic failure modes consisting of net-tension, shear out and bearing failure were observed for the different geometric dimensions. All the connections tested showed that the fiber orientations have a definite influence on the position around hole circumference at which failure initiated. Net-tension failure occurred for specimens that had small width and large end distance. When the width was increased, the specimens which had small end distances failed in the shear-out modes. When the end distance was increased, bearing failure developed in addition to shear-out failure. The experimental results showed that the ultimate load capacities of E/glass–epoxy laminate plates with pin connection were increased by increasing W and E. However, increasing the E/D and W/D ratios beyond a critical value has an insignificant effect on the ultimate load capacity of the connection.     

Strain-Rate-Dependent Failure of a Toughened Matrix Composite

The strain-rate-dependent behavior of a toughened matrix composite (IM7/8552) was characterized under quasi-static and dynamic loading conditions. Unidirectional and off-axis composite specimens were tested at strain rates ranging from 10^?4 to 10³ s^?1 using a servo-hydraulic testing machine and split Hopkinson pressure bar apparatus. The nonlinear response and failure were analyzed and evaluated based on classical failure criteria and the Northwestern (NU) failure theory. The predictive NU theory was shown to be in excellent agreement with experimental results and to accurately predict the strain-rate-dependent failure of the composite system based on measured average lamina properties.     

A maximum shear stress theory of plastic failure of fiber-reinforced materials

A theory of plastic behavior of fiber-reinforced composite materials is presented. The theory allows for several failure modes of the composite material, including plastic failure of the matrix material alone and the combined ductile failure of the fibers and the matrix. The latter mode may be readily modified to allow for brittle behavior of the fiber material.     

复合材料层合板壳非线性力学的研究进展

复合材料层合板壳是由多种组分材料组合而成.与单一材料的板壳结构相比,它无明确的材料主方向,各层间材料间断和不连续,具有明显的几何非线性和材料非线性等新的特点.其失效模式也远比单一材料的情况复杂,具有如基体开裂、脱胶、分层、分层裂纹偏转、多分层以及分层传播等多种模式.各国学者基于不同的考虑,提出了多种方法研究复合材料层合板壳的失效.首先,在简要介绍了层合板壳线性力学基本理论的基础上,重点回顾了层合板壳结构非线性力学几种基本理论发展的过程,主要阐述了经典大挠度非线性理论、一阶剪切变形理论、高阶剪切变形理论、锯齿理论、广义分层理论的理论体系及基本公式,并对几种理论之间的联系和差异进行了总结;其次,介绍了当前层合结构非线性领域的研究进展,综述了典型复合材料板壳结构的失效机理及优化设计、复合材料板壳结构在复杂环境下的破坏机理、复合材料板壳结构的物理非线性、含脱层纤维增强复合材料板壳结构的破坏机理等各研究热点的最新研究成果;最后,对该领域未来的研究方向进行了展望.     

Instabilities and loss of ellipticity in fiber-reinforced compressible non-linearly elastic solids under plane deformation

In a recent paper we examined the loss of ellipticity and its interpretation in terms of fiber kinking and other instability phenomena in respect of a fiber-reinforced incompressible elastic material. Here we provide a corresponding analysis for fiber-reinforced compressible elastic materials. The analysis concerns a material model which consists of an isotropic base material augmented by a reinforcement dependent on the fiber direction. The assessment of loss of ellipticity can be cast in terms of the eigenvalues of the acoustic tensors associated with the isotropic and anisotropic parts of the strain-energy function. For the anisotropic part, two different reinforcing models are examined and it is shown that, depending on the choice of model and whether the fiber is under compression or extension, loss of ellipticity may be associated with, in particular, a weak surface of discontinuity normal to or parallel to the deformed fiber direction or at an intermediate angle. Under compression the associated failure interpretations include fiber kinking and fiber splitting, while under extension fiber de-bonding and matrix failure are included.     

Experimental and analytical characterization of multidimensionally braided graphite/epoxy composites

This paper presents results of an investigation of a novel, through-the-thickness fiber-reinforced composite material. The generic name for this composite technology is multidimensional (X-D) braiding. X-D braided composites consist of a net-shaped, densely braided fiber skeleton which is rigidized with a structural epoxy-resin system. This material is an alternative to the conventional laminated composite and has the potential for being more resistant to delamination and matrix cracking. This paper describes results of the mechanical characterization of one graphite fiber system which was braided into panels in which two braid parameters could be investigated. The variables investigated included the effect of edge condition and braid pattern on the tensile, compressive and flexural properties of the braided panels. These properties were obtained in the braid direction only. The cutting of the specimen edges substantially reduced both tensile and flexural strengths and moduli. Of the three braid patterns investigated, 1×1, 3×1, and 1×1×1/2 F, the 3×1 braid pattern showed superior tensile performance, while the 1×1×1/2 F braid pattern exhibited superior flexural properties. The development of an analytical method for modeling the tensile performance of the multidimensionally (X-D) braided composite is also presented. The fiber geometry in X-D braids was modeled based on the braid parameters used in the construction of these composites. By the nature of the symmetry of the resulting braided structure, an analytical model based on classical lamination theory was used to determine the extensional stiffness in the three principal geometric directions of a braided composite. These analytical results are shown to compare favorably with those obtained experimentally. Finally, to further validate the ability of this material to contain damage, multidimensionally braided and conventionally laminated panels were impacted and the resulting damage was nondestructively determined. The multidimensionally braided material was shown to reduce the area of damage caused by impact by a factor of three for the energy levels tested.