界面脱粘对正交铺设SiC/CAS复合材料基体开裂的影响

采用细观力学方法研究了正交铺设SiC/CAS复合材料在单轴拉伸载荷作用下界面脱粘对基体开裂的影响。采用断裂力学界面脱粘准则确定了0°铺层纤维/基体界面脱粘长度, 结合能量平衡法得到了主裂纹且纤维/基体界面发生脱粘(即模式3)和次裂纹且纤维/基体界面发生脱粘(即模式5)的临界开裂应力, 讨论了纤维/基体界面剪应力、 界面脱粘能对基体开裂应力的影响。结果表明, 模式3和模式5的基体开裂应力随纤维/基体界面剪应力、 界面脱粘能的增加而增加。将这一结果与Chiang考虑界面脱粘对单向纤维增强陶瓷基复合材料初始基体开裂影响的试验研究结果进行对比表明, 该变化趋势与单向SiC增强玻璃陶瓷基复合材料的试验研究结果一致。     

正交铺设陶瓷基复合材料单轴拉伸行为

采用细观力学方法对正交铺设陶瓷基复合材料单轴拉伸应力-应变行为进行了研究。采用剪滞模型分析了复合材料出现损伤时的细观应力场。采用断裂力学方法、 临界基体应变能准则、 应变能释放率准则及Curtin统计模型4种单一失效模型确定了90°铺层横向裂纹间距、 0°铺层基体裂纹间距、 纤维/基体界面脱粘长度和纤维失效体积分数。将剪滞模型与4种单一损伤模型结合, 对各损伤阶段应力-应变曲线进行了模拟, 建立了复合材料强韧性预测模型。与室温下正交铺设陶瓷基复合材料单轴拉伸应力-应变曲线进行了对比, 各个损伤阶段的应力-应变、 失效强度及应变与试验数据吻合较好。分析了90°铺层横向断裂能、 0°铺层纤维/基体界面剪应力、 界面脱粘能、 纤维Weibull模量对复合材料损伤及拉伸应力-应变曲线的影响。      

Modeling Loading/Unloading Hysteresis Behavior of Unidirectional C/SiC Ceramic Matrix Composites

The loading/unloading tensile behavior of unidirectional C/SiC ceramic matrix composites at room temperature has been investigated. The loading/unloading stress–strain curve exhibits obvious hysteresis behavior. An approach to model the hysteresis loops of ceramic matrix composites including the effect of fiber failure during tensile loading has been developed. By adopting a shear-lag model which includes the matrix shear deformation in the bonded region and friction in the debonded region, the matrix cracking space and interface debonded length are obtained by matrix statistical cracking model and fracture mechanics interface debonded criterion. The two-parameter Weibull model is used to describe the fiber strength distribution. The stress carried by the intact and fracture fibers on the matrix crack plane during unloading and subsequent reloading is determined by the Global Load Sharing criterion. Based on the damage mechanisms of fiber sliding relative to matrix during unloading and subsequent reloading, the unloading interface reverse slip length and reloading interface new slip length are obtained by the fracture mechanics approach. The hysteresis loops of unidirectional C/SiC ceramic matrix composites corresponding to different stress have been predicted.     

Non-Axisymmetric Matrix Cracking and Interface Debonding with Friction in Ceramic Composites

A three-dimensional analytical model based on the principle of minimum potential energy is developed and applied to determine the stress state in a discrete fiber/matrix composite cylinder subjected to axial tensile loading in the fiber direction and containing a non-axisymmetric transverse matrix crack and an interface debond. The friction over the debonded interface is incorporated into the analysis. The strain energy release rates associated with the matrix crack and the interface debonding under the combination of the applied load and the interface frictional force are computed. The strain energy release rate criterion has been employed to evaluate the critical applied loads for the two fracture modes and to assess the competition between propagation of a matrix crack and growth of interface debonding. A parametric study has been carried out. The computed results show that the interface friction plays an important role in the failure of brittle matrix composites.     

Fracture mechanics of single-fibre pull-out test

Pull-out of an elastic fibre from an elastic matrix was investigated. A simple pull-out mechanics has been developed, based on the fracture energy criterion, to describe the debonding process, including friction. Experiments were carried out using polytetrafluoroethylene (PTFE) fibres embedded in a polypropylene (PP) matrix. It was found that growth of an interfacial crack was stable after the initiation of a debond at the loaded fibre end. At first, the debonding force increased linearly with the crack length due to friction in the debonded region. However, the crack accelerated after reaching a critical length, dependent on the embedded fibre length. At this point, the force required to propagate the debond levelled off. Thus, further increase in the debonding force was not necessary to further complete the debonding process. The debonding force was found to be in good agreement with that predicted by the present theory. Techniques for determining the interfacial properties, including adhesive fracture energy, compressive residual stress and coefficient of friction, were considered. In addition, a simple criterion has been derived to predict which fibre end, either embedded end or loaded end, will debond first when the specimen is subjected to an axial load.     

Mathematical modeling of damage in unidirectional composites

Solutions are developed for the two-dimensional region containing unidirectional fibers embedded in an elastic matrix with an initial flaw in the form of a transverse notch, a rectangular cut-out, and a circular hole. Subsequent damage due to the presence of the flaw is generated by remote stresses acting parallel to the fibers. This work is an extension of the paper by Goree and Gross [1] in which the flaw was taken in the form of a notch (crack) and the subsequent damage, due to loading, consisted of longitudinal matrix yielding and splitting at the end of the notch. The present study accounts for longitudinal matrix damage as in [1] and, in addition, includes transverse matrix and fiber damage in the vicinity of the flaw for the above three initial shapes. The fibers are taken as linearly elastic, the matrix material as elasticperfectly plastic and the classical shear-lag stress displacement assumptions are used. An ultimate stress failure criterion is used for both the fibers and the matrix; simple tension for the fibers and shear failure for the matrix.

For ductile matrix composites (boron/aluminum) the present results indicate that both longitudinal matrix yielding and transverse notch extension must be included in order for the model to agree with experimental results. Interestingly, the extent of the transverse damage region at failure is shown to be approximately constant, independent of the initial flaw shape or length.

Very little difference is found between the results for the three types of initial damage, i.e. the notch, rectangular cut-out and circular hole. In all cases, the presence of additional damage changes the nature of the stress distribution in the unbroken fibers. For the original Hedgepeth[2] problem of a notched laminate the stresses decay as the square root of the distance from the notch tip. Inclusion of longitudinal or transverse damage significantly reduces the maximum stress concentration in the unbroken fibers and gives a much more uniform stress state. It is shown that this behavior cannot be accounted for by introducing an effective notch length or crack tip damage zone with a square root behavior.     

An Investigation of Interfacial Fatigue in Fiber Reinforced Composites

Based on the shear-lag model and the modified degradation formula for coefficient of friction, the interfacial fatigue and debonding for fiber reinforced composites under cyclic loading are studied. The loading condition is chosen as the kind that is the most frequently used in fiber-pull-out experiments. The stress components in the debonded and bonded regions are obtained according to the maximum and minimum applied loading. By the aid of theory of fracture mechanics and Paris formula, the governing equation is solved numerically and the interfacial debonding is simulated. The relationships between the parameters (such as the debond rate, debond length, debond force) and the number of cycles are obtained.     

Interface debond crack growth in tension–tension cyclic loading of single fiber polymer composites

Fiber/matrix interface debond crack growth from a fiber break is defined as one of the key mechanisms of fatigue damage in unidirectional composites. Considering debond as an interface crack its growth in cyclic loading is analyzed utilizing a power law, where the debond growth rate is a power function of the change of the strain energy release rate in the cycle. To obtain values of two parameters in the power law cyclic loading of fragmented single fiber specimen is suggested. Measurements of the debond length increase with the number of load cycles in tension–tension fatigue are performed for glass fiber/epoxy single fiber composites. Analytical method in the steady-state growth region and FEM for short debonds are combined for calculating the strain energy release rate of the growing debond crack. Interface failure parameters in fatigue are determined by fitting the modeling and experimental results. The determined parameters for interface fatigue are validated at different stress levels.     

Fracture behavior of notched unidirectional Si-Ti-C-O/BMAS composite

Experimental and modeling studies on tensile fracture behavior of notched unidirectional Si-Ti-C-O (Tyranno fiber) reinforced BMAS (barium magnesium aluminosilicate) glass matrix composite were carried out. The longitudinal crack arose at the tip of the transverse notch before overall fracture. The critical energy release rate around at initiation of the longitudinal cracking was estimated to be nearly 100 J/m² by application of the present model to the experimentally observed relation between the stress of the composite in the very early stage of longitudinal cracking and the notch size. The notched strength was higher than that predicted by the fracture mechanical criterion due to the blunting arising from the premature longitudinal cracking, but it was lower than that predicted by the net stress criterion due to the constraint effect arising from the bridging of the fibers and the spalling of the segmented matrix into the longitudinal crack.     

Debonding of circular second phase particles

The plastic relaxation of a shear crack situated normal to the interface of a second phase particle of circular cross section is quantitatively analyzed. The ratio of applied stress to yield stress and the relative displacement of crack faces at the tips in the matrix and at the interface of the second phase particle are related to the crack parameters—namely the length of the crack, the width of the plastic zone along the interface and the width of the plastic zone in the matrix. The effect of the shear modulus and size of the second phase particle on the behavior of the plastic zones is determined. A critical value of the relative displacement of the crack faces at the tip is used as the criterion to determine the tendency to brittle extension of the crack into the matrix or along the interface. Conclusions are made on the debonding of the second phase particle from the matrix.     

Transverse stiffness properties of unidirectional fiber composites containing debonded fibers

First-principles micromechanics modeling for the determination of transverse stiffness properties of a unidirectional fiber composite with fiber–matrix interfacial debonding is presented. The composite has a packing arrangement of a periodic square array of fibers, but contains randomly distributed debonded fibers. The finite element method is employed for the exact treatment of local microscopic stress and strain fields in a representative volume element of the composite material, and of the nonlinear problem of separation and contact of fiber and matrix at debonded interface. The randomness of the distribution of debonded fibers is dealt with by means of the Monte Carlo method, and the composite stiffness properties are found as ensemble average properties over a large number of representative volume elements. Bimodular behavior of the composite under transverse loading, i.e., different stiffnesses in tension and compression, is accurately captured.     

An Approach to Estimate Interface Shear Stress of Ceramic Matrix Composites from Hysteresis Loops

An approach to estimate interface shear stress of ceramic matrix composites during fatigue loading has been developed in this paper. By adopting a shear-lag model which includes the matrix shear deformation in the bonded region and friction in the debonded region, the matrix crack space and interface debonding length are obtained by matrix statistical cracking model and fracture mechanics interface debonding criterion. Based on the damage mechanisms of fiber sliding relative to matrix in the interface debonded region upon unloading and subsequent reloading, the unloading counter slip length and reloading new slip length are determined by the fracture mechanics method. The hysteresis loops of four different cases have been derived. The hysteresis loss energy for the strain energy lost per volume during corresponding cycle is formulated in terms of interface shear stress. By comparing the experimental hysteresis loss energy with computational values, the interface shear stress corresponding to different cycles can then be derived. The theoretical results have been compared with experimental data of three different ceramic composites.     

Crack bridging and fibre pull-out in polyethylene fibre reinforced epoxy resins

An investigation has been undertaken of the stress distributions in high-performance polyethylene fibres bridging cracks in model epoxy composites. The axial fibre stress has been determined from stress-induced Raman band shifts and the effect of fibre surface treatment has been followed using untreated and plasma-treated polyethylene fibres. It is found that when the specimen is cracked, the fibres do not break and stress is transmitted from the matrix to the fibre across the fibre/matrix interface. A debond propagates along the fibre/matrix interface accompanied by friction along the debonded interface. The axial stress distributions in the fibres can be analysed using a partial-debonding model based upon shear-lag theory and it is found that the maximum interfacial shear stress at the bond/debond transition is a function of the debond length. The debonding process has been modelled successfully in terms of the interfacial fracture energy-based criterion developed by Hsueh for the propagation of a debond along a fibre/matrix interface accompanied by constant friction along the interface.     

An efficient BEM to calculate weight functions and its application to bridging analysis in an orthotropic medium

An efficient boundary element method to calculate crack weight functions is developed. The weight function method is applied to bridging effect analysis in a single-edge notched composite specimen by using a bridging law which includes both interfacial debonding and sliding properties between fiber and matrix in ceramic matrix composites. A numerical method to solve the distributed spring model treating bridging fibers as stress distribution to close the crack surface is provided to determine the bridging stress, debond length, crack opening displacement and stress intensity factor.     

Micromechanics characterization of sublaminate damage

A micromechanics analytical model is developed for characterizing the fracture behaviour of a fibre reinforced composite laminate containing a transverse matrix crack and longitudinal debonding along 0/90 interface. Both the matrix and the fibres are considered as linear elastic. A consistent shear lag theory is used to represent the stress-displacement relations. The governing equations, a set of differential-difference equations, are solved satisfying the boundary conditions appropriate to the damage configuration by making use of an eigenvalue technique. The properties of the constituents appear in the model explicitly. Displacements and stresses in the fibres and the matrix are obtained, and the growth of damage is investigated by using the point stress criterion. The investigation includes fibre stress distribution in zero degree plies, transverse crack and debonding intitiation as functions of laminate geometry, and the effect of fibre breaks in the zero degree ply on damage growth. The predicted damage growth patterns and the corresponding critical strains agree with the finite element and experimental results.     

Some aspects of crack growth and failure in fibre reinforced composites

A theoretical analysis, previously developed to deal with the machanics of matrix cracking in unidirectional composites and with transverse ply cracking in cross ply laminates, has been developed further to deal with the tensile failure of unidirectional fibrous composites in with the fibres have a known distribution of strengths. It is proposed that, under the application of a tensile load, stable transverse cracks are formed which originate from regions of initial damage and which become unstable at some critical strain value. The model takes account of various parameters including the interfacial fibre/matrix debonding energy, the residual frictional shear strength of the debonded interface and the elastic properties of fibres and matrix. Comparisons are made between the predictions of the model and the observed failing strains of the 0° plies in carbon fibre polymer matrix laminates. The relevance of the model to the study of delayed fracture in fibrous composites is discussed. The modification of this model, previously developed to describe crack growth in the transverse plies of 0°/90° laminates, is used to predict the initial cracking strains for a wide range of CFRP laminate geometries and initial crack sizes. Some aspects of the mechanics of crack extension across interply interfaces are discussed.     

Characterization and modeling of stiffness reduction in SCS-6-Ti composites under low cycle fatigue loading

The stiffness reduction and evolution of microstructural damage of a unidirectional silicon carbide fiber reinforced titanium matrix composite under tension-tension fatigue were investigated. Tests were conducted under load control with maximum applied stresses ranging from 750 to 945 MPa. The crack density of the interfacial reaction layer and matrix, matrix crack length, and interfacial debonding length as a function of fatigue cycles and applied stress levels were measured. The results showed that the composites exhibited an initial regime with slow stiffness reduction, followed by a rapid stiffness drop regime and a plateau regime with minimal change in stiffness for the applied stress levels used in this study. The residual stiffness at N = 10⁶ cycles is independent of the applied stress levels, while the microstructural damage accumulation varied with the applied stresses. A partial crack shear-lag model was also developed to predict the residual stiffness as a function of fatigue damage accumulation. Analytical simulation indicated that the profile of the stiffness reduction curves was dominated by the matrix crack density, while the extent of stiffness reduction was dominated by the matrix crack length.     

Fatigue crack growth with fiber failure in metal-matrix composites

Crack growth during the fatigue of fiber-reinforced metal-matrix composites can be predicted analytically by determining the reduction in the crack tip stress intensity range resulting from fiber bridging. Various canonical functions exist that relate the crack tip stress intensity range to bridged crack geometries and loading for both infinite and finite width specimens; however, comprehensive crack growth predictions incorporating fiber failure require knowledge of the maximum fiber stress in the bridged zone for all notch sizes and crack lengths. Previous modeling efforts have been extended to predict complete growth curves with fiber failure for specimens of finite width. Functions for maximum fiber stresses in the bridged zone are presented here for a center crack in tension and edge cracks in tension and bending. The rapid increase in crack growth when fibers fail emphasizes the importance of determining the loads and notch sizes that mark the beginning of fiber failure. Critical loads for given notch sizes and fiber strengths are easily determined for finite width specimens using the functions presented in this work.     

Analysis of first ply failure in composite laminates

The mechanics of transverse cracking in an elastic fibrous composite ply is explored for the case of low crack density. Cracks are assumed to initiate from a nucleus created by localized fiber debonding and matrix cracking. It is found that cracks may propagate in two directions on planes which are parallel to the fiber axis and perpendicular to the midplane of the ply. In general, crack propagation in the direction of the fiber axis controls the strength of thin plies, while cracking in the direction perpendicular to the fiber axis determines the strength of thick plies. The theory relates ply thickness, crack geometry and ply toughness to ply strength. It predicts a significant increase in strength with decreasing ply thickness in constrained thin plies. The strength of thick plies is found to be constant, but it may be reduced by preexisting damage. Results are illustrated by comparison with experimental data.     

Progressive failure analysis of unidirectional fiber-reinforced polymers with inhomogeneous interphase and randomly distributed fibers under transverse tensile loading

The effect of damage due to interfacial debonding on the post initial failure behavior of unidirectional fiber-reinforced polymers subjected to transverse tension was investigated using numerical homogenization techniques based on the finite element method. Calculations were performed for unit cells containing fibers distributed at random over the transverse cross-section with inhomogeneous interphase layers. The mechanism of progressive failure was examined at both a global and a local level. A detailed analysis of the proposed micromechanics model revealed that it is able correctly to simulate the evolution of damage and to explain the softening mechanism. It was found that the post initial failure behavior of unidirectional lamina under transverse tension is mainly controlled by the interface strength and the interphase stiffness. The present study showed that local fiber array irregularities are a significant contributor to matrix cracking through local stress concentrations and the occurrence of localization.