Debonding and fiber pull-out in reinforced composites

In order to evaluate the strength of fiber-reinforced composites, there is first the need to investigate the interfacial debonding and the pull-out of fibers in a fractured composite with intact fibers. This type of problem in crack bridging has been investigated by several authors based on different models and assumptions [1–7]. In this study, we will consider a three-dimensional model of a single fiber of finite length bonded by a finite cylindrical matrix with an initial crack existing in a portion of the interface. In the model, one end of the cylinder is so constrained that the axial component of displacement vanishes. A tensile stress is applied to the fiber at the other end. The aim is to determine the pull-out of the fiber and the critical condition for interfacial debonding. Both the fiber and the matrix are treated as elastic materials. Analysis is made based on a method using Papkovich-Neuber displacement potential functions for the problem of an elastic solid subjected to axisymmetrical boundary conditions. Solutions are found by means of the technique of trigonometrical series. Effects of initial misfit strains and frictional sliding between the fiber and the matrix over the interfacial crack are also included in the study.     

A dynamic model of bridging fiber pull-out of composite materials

An elastic analysis of an internal central crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane is carried out. In this paper a dynamic model of bridging fiber pull-out is presented for analyzing the distributions stress and displacement of composite materials with the internal central crack under the loading conditions of an applied non-uniform stress and the traction forces on crack faces yielded by the fiber pull-out model. Thus the fiber failure is determined by maximum tensile stress, the fiber breaks and hence the crack propagation should occur in self-similar fashion. By reducing the dynamic model to the Keldysh–Sedov mixed boundary value problem, a straightforward and easy analytical solution can be attained. When the crack extends, its fibers continue to break. Analytical study on the crack extension under the action of an inhomogeneous point force Px/t, Pt is obtained for orthotropic anisotropic body, respectively; and it can be utilized to attain the concrete solutions of the model by the ways of superposition.     

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.     

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.     

Axisymmetric micromechanics of elasticity-perfectly plastic fibrous composites under uniaxial tension loading

The uniaxial response of a continuous fiber elastic-perfectly plastic composite is modelled herein as a two-element composite cylinder. An axisymmetric analytical micromechanics solution is obtained for the rate-independent elastic-plastic response of the two-element composite cylinder subjected to tensile loading in the fiber direction for the case wherein the core fiber is assumed to be a transversely isotropic elastic-plastic material obeying Tsai-Hill's yield criterion, with yielding simulating fiber failure. The matrix is assumed to be an isotropic elastic-plastic material obeying Tresca's yield criterion. It is found that there are three different circumstances that depend on the fiber and matrix properties: (1) fiber yield, followed by matrix yielding; (2) complete matrix yield, followed by fiber yielding; and (3) partial matrix yield, followed by fiber yielding, followed by complete matrix yield. The order in which these phenomena occur is shown to have a pronounced effect on the predicted uniaxial effective composite response.     

A variational method for unidirectional fiber-reinforced composites with matrix creep

A variational method is developed for analyzing the matrix creep induced time-dependent change in fiber stress profiles in unidirectional composites. A functional of admissible profiles of fiber stress rate is presented by supposing a fiber broken in matrix as well as a fiber pulled out from matrix. The functional is shown to have the stationary function satisfying an incremental differential equation based on the shear lag assumption. Then, the stationary function is approximately determined by assuming bilinear profiles of fiber stress and a power law of matrix creep, leading to analytical solutions for the time-dependent change in fiber stress profiles. The solutions are verified on the basis of an energy balance equation and a finite difference computation. Moreover, it is shown that the solution for the fiber pull-out model agrees well with an experiment on a single carbon fiber/acrylic model composite if the initial slip at fiber/matrix interface is taken into account. In addition, the solution for the fiber breakage model is used for evaluating the characteristic time in long-term creep rupture of unidirectional composite.     

DYNAMIC CRACK MODELS ON PROBLEM OF BRIDGING FIBER PULL-OUT OF COMPOSITE MATERIALS

An elastic analysis of an internal central crack with bridging fibers parallel to the free surface in an infinite orthotropic anisotropic elastic plane was performed. A dynamic model of bridging fiber pull-out of composite materials was presented. Resultingly the fiber failure is governed by maximum tensile stress, the fiber breaks and hence the crack extension should occur in self-similar fashion. By the methods of complex functions, the problem studied can be transformed into the dynamic model to the Reimann-Hilbert mixed boundary value problem, and a straightforward and easy analytical solution is presented. Analytical study on the crack propagation subjected to a ladder load and an instantaneous pulse loading is obtained respectively for orthotropic anisotropic body. By utilizing the solution, the concrete solutions of this model are attained by ways of superposition.     

End-shaped copper fibers in an epoxy matrix—predicted versus actual fracture toughening

End-shaped copper fibers are placed in a brittle thermoset epoxy matrix at 10 vol% and tested in four-point bending to determine the fracture toughness of the composite. Results from four-point bend tests agree well with the theoretical predictions of the fracture toughness increment ‘ΔG’ of a metal fiber/brittle thermoset matrix composite based on single fiber pullout (SFP) tests. This close agreement demonstrates that SFP testing, along with the theoretical model, can be used as an effective end-shape screening tool for ductile fibers before full scale composite testing. The model predicts that the composite’s fracture toughness will be 46% higher with flat end-impacted fibers and 4% lower with rippled fibers compared to straight fibers at a 0° orientation. Four-point bend results show the actual composite’s fracture toughness is 49% higher with flat end-impacted fibers and 5% lower with rippled fibers compared to straight fibers. Further, four-point bend results show that end-shaped copper fibers improve both the flexural strength and modulus of the composite, demonstrating that end-shaped ductile fibers provide a good stress transfer to the fibers by anchoring the fibers into the matrix. Lastly, experimental validation of the model also indicates that at low fiber volume fractions, fiber–fiber interaction has only a minor influence on the fracture toughness for the tested ductile fiber/brittle matrix composite.     

共晶基陶瓷复合材料的断裂韧性

应用细观力学方法研究了由具有随机尺寸和方位的棒体共晶体构成的共晶基陶瓷复合材料的断裂韧性.首先根据棒状共晶体的细观结构特性,考虑共晶体边界处的微观滑移确定共晶陶瓷复合材料的开裂应力,当外载荷达到开裂应力时,裂纹开始扩展.然后分析裂纹表面处的棒状共晶体桥联力使裂纹产生闭合效应,减小裂纹尖端的应力集中,建立棒状共晶体桥联增韧机制;再依据棒状共晶体拔出过程中摩擦力做功,建立棒状共晶体拔出增韧机制.最后在棒状共晶体的桥联与拔出增韧机制的基础上,得到了共晶基陶瓷复合材料断裂韧性的理论表达式.结果表明共晶基陶瓷复合材料的断裂韧性与棒状共晶体的长径比密切相关.     

Fiber fracture and strength degradation in unidirectional graphite/epoxy composite materials

An experimental study was conducted to determine the influence of load factor on fiber fracture development and residual strength of fatigue loaded unidirectional graphite/epoxy composite laminated. 8-phy composite laminates with a layer of release cloth imbedded at the middle ply were fatigued at different load levels and were examined for fiber fracture and residual strength at several stages of life based on the average number of cycles to failure (according to S-N data). From the experimental results, it is evident that the number of fiber fractures is nearly constant after the first few percent of the life. It is also suggested that the load level is much more important than the number of cycles of loading in the determination of the state of fiber fracture. This behavior was interrupted at high load levels (S60% S_u where the final fracture was highly affected by the longitudinal matrix splittings. Residual strength is found to be independent of the global fiber fracture density, and to be controlled by local behavior such as matrix cracking, local clustering of fiber fractures, and other local stress concentrations.     

An elastic–plastic crack bridging model for brittle-matrix fibrous composite beams under cyclic loading

A fibrous composite beam with an edge crack is submitted to a cyclic bending moment and the crack bridging actions due to the fibers. Assuming a general elastic-linearly hardening crack bridging model for the fibers and a linear-elastic law for the matrix, the statically indeterminate bridging actions are obtained from compatibility conditions. The elastic and plastic shake-down phenomena are examined in terms of generalised cross-sectional quantities and, by employing a fatigue crack growth law, the mechanical behaviour up to failure is captured. Within the framework of the proposed fracture mechanics-based model, the cyclic crack bridging due to debonding at fiber–matrix interface of short fibers is analysed in depth. By means of some simplifying assumptions, such a phenomenon can be described by a linear isotropic tensile softening/compressive hardening law. Finally, numerical examples are presented for fibrous composite beams with randomly distributed short fibers.     

Strength probability of unidirectional hybrid composites

A probability strength analysis of an unidirectional three-component hybrid composite (HC) is carried out for the cases of high modulus (HM) fibres and low modulus (LM) elastic fibers regularly embedded in a low elastic modulus matrix. Both single layer intraply and multilayer HC are considered. The fiber strength is assumed to be a random variable with a Weibull distribution. Breaking of the HM fibers are accumulated initially while probability of LM fiber failure is low. Failure modes tend to be covered by the two extreme cases of alternative failure of HM and LM fibers only. These modes can be categorized by using graph technique. Developed are the algorithm for finding the most probable pattern of fiber breaking and method for estimating the strength and fiber damage of a HC. The stress level at which the LM fibers are found to break represents a lower bound of the HC strength. Damage of HM fibers in a three-component HC is much higher than in a two-component HM fibre composite. Negative ‘hybrid effect’ for strength is obtained.     

Prediction of overall tension behavior of short fiber-reinforced composites

The bridging stress of fibers along the crack surface plays an important role in analyzing the tension behavior of short or long fiber-reinforced composites. This paper uses the inclusion theory to obtain the expression of bridging stress for short fiber reinforced composite (SFRC) . A simplified model with periodically distributed fibers is proposed to estimate the average fiber spacings. The total fracture resistance is calculated as an energy summation including interface debonding energy dissipation, frictional sliding work between fibers and matrix, strain energy increment of fibers and matrix. The bend over point (BOP) stress is calculated by this fracture resistance. The necessary conditions of the fibers and matrix for the multiple cracking in SFRCs are discussed and the expression of ultimate external stress is derived. The critical fiber volume fraction for the strain hardening response is determined by an iteration method. In the meanwhile, the average spacing between two short fibers is proposed by a periodical distribution assumption. The theoretical prediction is compared with experimental data.     

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.     

结构增韧材料在裂纹扩展中的韧度增值

本文分析了由裂纹扩展过程中形成的耗能尾区和桥联段所产生的增韧效应。根据对扩展裂纹的能量积分的贡献,结构增韧材料在裂纹扩展中的韧度增值机制可分解为:尾区体膨胀塑性增韧;尾区剪切屈服带增韧;裂纹面夹杂第二相桥联;未贯穿裂纹的基体桥联。本文结合结构高分子材料和短纤维复合材料等材料体系进行了具体的增韧分析计算。     

A double inclusion model for microcrack arrest in fibre reinforced brittle materials

A model for the prediction of microcrack growth in a fibre reinforced brittle matrix composite material is suggested. The model is based on composite material theory and linear elastic fracture mechanics. The microcracks in question are so-called large microcracks, i.e. microcracks which are bridged by the reinforcing fibres. The crack bridging fibres are “smeared” out to form a homogeneous medium. This homogeneous medium constitutes together with the matrix crack an ellipsoidal so-called “double inclusion.” Matrix cracking as well as interfacial debonding can be analysed and this analysis can be synthesized and interpreted as a determination of the strength of the reinforced matrix. The model is compared with some experimental results, and good agreement is found. The model can serve as a tool for the design of brittle matrix composite materials because it identifies the significance of fibre geometry, volume fraction of fibres, and adhesion between fibres and matrix.     

极端环境下连续碳纤维增韧的陶瓷基复合材料的力学行为

连续纤维增韧的碳化硅复合材料(以下简称C/SiC),作为超高速飞行器热结构使用时,有可能在高温环境下受到高速撞击的作用,因此,掌握其在极端环境(高温、高应变率)下的力学性能是进行结构安全设计的基础。本文采用具有高温实验能力的分离式Hopkinson杆,在293~1273K温度范围内进行了动态压缩力学性能测试,研究了环境温度和加载速率对材料力学性能的影响。结果表明:C/SiC复合材料的高温压缩力学性能主要受应力氧化损伤和残余应力的共同影响。实验温度低于873K时,应力氧化损伤的影响很小,而由于增强纤维和基体界面残余应力的释放使界面结合强度增大,复合材料的压缩强度随温度的升高而增大;当实验温度高于873K时,应力氧化损伤加剧,其对压缩强度的削弱超过残余应力释放对强度的贡献,材料的压缩强度随温度的升高逐渐降低。由于应力氧化损伤受应变率的影响很大,当温度由873K升高至1273K时,高应变率下压缩强度降低的程度要比应变率为0.0001/s时低得多。     

Interaction of fiber and transformation toughening

B small scale bridging (SSB) assumption, a theoretical study is made of the interaction between the fracture toughening effects of transforming particles and crack bridging fibers which are aligned in the direction perpendicular to the crack surfaces. The fibers bridging the crack are assumed to undergo large amounts of slipping inside the matrix. It is found that the interaction can be synergistic over a parametric range of material properties of the ceramic composite system. The Mode-1 plane-strain fracture toughness of the ceramic composite system is determined in terms of fiber strength, transformation toughening parameters and interaction parameters. The results obtained here are qualitatively similar to those for the interaction between the fracture toughening effects of transforming particles and crack-bridging ductile particles by A and B (1988a, J. Mech. Phys. Solids 36, 581).     

Assessment of composite failure and ultimate strength without experiment on composite

This paper attempts to estimate the ultimate strength of a laminated composite only based on its con- stituent properties measured independently. Three important issues involved have been systematically addressed, i.e., stress calculation for the constituent fiber and matrix materials, failure detection for the lamina and laminate upon the internal stresses in their constituents, and input data determination of the constituents from monolithic measurements. There are three important factors to influence the accuracy of the strength prediction. One is the stress concentration factor （SCF） in the matrix. Another is matrix plasticity. The third is thermal residual stresses in the constituents. It is these three factors, however, that have not been sufficiently well realized in the composite community. One can easily find out the elastic and strength parameters of a great many laminae and laminates in the current literature. Unfortunately, necessary information to determine the SCF, the matrix plasticity, and the thermal residual stresses of the composites is rare or incomplete. A useful design methodology is demonstrated in the paper.