Residual strength of metal particulate reinforced ceramics with parallel cracks

This work investigates the residual strength of metal particulate reinforced ceramic matrix composites with periodically spaced, parallel cracks. A Fourier transform/integral equation method is used to obtain the stress intensity factor at the tips of the cracks bridged by the plastically stretched metal particulates. The crack bridging of metal particulates is described by a linear softening bridging law that relates the bridging stress and crack opening. The residual strength of the cracked composites is calculated using a stress intensity factor criterion with consideration of crack bridging. Numerical results are presented for three composite systems, i.e., WC/Co, Al₂O₃/Ni, and glass/Al composites to illustrate the effects of interactions between multiple cracks/bridging zones on the residual strength behavior of the reinforced ceramics with parallel cracks. It is found that for given volume fraction of metal particulate and debonding length of the particulate–matrix interface the residual strength increases with decreasing crack spacing. For a given crack spacing, the residual strength initially decreases dramatically with an increase in initial crack length and levels off for long initial cracks.     

金属裂纹板复合材料胶接修补强度的弹塑性有限元预测

金属裂纹板经复合材料补片胶接修补后,其结构强度明显提高,但裂纹板中的裂纹会导致严重的应力集中现象,并易产生塑性变形,呈现强烈的材料物理非线性特性,需要采用弹塑性力学原理,进行复合材料胶接修复结构的静强度预测。为此,考虑金属板材料的非线性特性,建立了金属裂纹板复合材料胶接修补结构的弹塑性有限元模型,并通过试验验证了模型的有效性。在此基础上,提出了基于裂纹尖端的张开位移(COD)判据的拉伸强度预测方法,分析了修复结构的塑性应变、COD以及静拉伸强度。结果表明:相对于应力强度因子K判据, COD判据能更有效地预测修复试件的静拉伸强度。      

FRACTURE MODELLING OF BRITTLE-MATRIX COMPOSITES WITH SPATIALLY DEPENDENT CRACK BRIDGING

Abstract In brittle-matrix composites cracking of the matrix is often accompanied by bridging of the crack surfaces. The bridging will reduce the net stress intensity factor at the crack tip and consequently increase the toughness of the composite material. The bridging mechanism is due to for example unbroken whiskers, fibres, ductile particles or interlocking grains. Analysis of the bridging mechanism in cracked structures is conveniently carried out using the concept of cohesive zone modelling. In this case the action of the bridging elements is replaced by a distribution of forces, so called cohesive forces trying to close the crack. The commonly used approach in such modelling has been to replace the action from individual bridging elements by a continuous spatially independent distribution of closing tractions whose magnitude is a function of the crack opening displacement only. In this paper the influence of the spatial distribution of bridging elements is considered for plane crack problems. The cross section of the bridging elements is assumed to be circular and the distance between the different bridging elements is determined by the volume fraction, the radius and the geometrical distribution of the bridging elements. Damage resistance curves have been calculated for typical whiskers-reinforced ceramic composites, and the results from the present spatially dependent models are compared with results from calculations with spatially independent models. The influence of the radius of the bridging element, the volume fraction of whiskers and the material properties are illustrated and the use of spatially independent models is discussed.     

Analysis of the distribution of thermal residual stresses in bonded composite repair of metallic aircraft structures

In this study, the distribution of the thermal residual stresses due to the adhesive curing in bonded composite repair is analysed using the finite element method. The computation of these stresses comprises all components of the structures: cracked plate, composite patch and adhesive layer. In addition, the influence of these residual stresses on the repair performance is highlighted by analysing their effect on the stress intensity factor at the crack tip. The obtained results show that the normal thermal stresses in the plate and the patch are important and the shear stresses are less significant. The level of the adhesive thermal stresses is relatively high. The presence of the thermal stresses increases the stress intensity factor at the crack tip, what reduce the repair performance.     

Experimental evidence of crack tip shielding mechanisms in quasi-brittle materials

To gain insight into the shielding processes in quasi-brittle materials, in situ crack propagation and crack profile measurements were performed inside the scanning electron microscope (SEM). Crack tip shielding phenomena were studied in monolithic alumina and in SiC fibre-reinforced alumina matrix composites as a function of fibre coatings. The crack in the fibre-reinforced composite samples is bridged by a row of fibres which contains a fibre area fraction of 10%. The applied stress intensity factor necessary to extend the crack in the composite materials increased 25% for the gold coated fibre-reinforced alumina matrix composites and 13% for the polymer-coated fibre-reinforced composites, compared to the monolithic samples. Crack extension in the monolithic samples and in the fibre-reinforced composites occurred after the crack opening displacements close to the crack tip approached the critical crack tip profile corresponding to the intrinsic toughness of alumina. A hypothesis on the effect of closure stresses on crack profile shape and net toughness has been developed. Furthermore, crack profiles revealed that grain bridging in the vicinity of the fibres was operative in the fibre-reinforced composites at stress intensity factors far exceeding the critical stress intensity factor of the monolithic matrix material. The additional grain bridging in the vicinity of the fibres has never been reported and can only be revealed through crack profile measurements. This revised version was published online in November 2006 with corrections to the Cover Date.     

The mechanics of matrix cracking in fiber reinforced ceramic composites containing a viscous interface

A detailed fracture mechanics analysis of matrix cracking in a fiber reinforced ceramic composite is presented for the case where the fiber—matrix interface exhibits viscous flow as can be the case when ceramic composites containing amorphous interfacial layers are subjected to loads at elevated temperatures. The analysis considers the case where matrix cracks are fully bridged by fibers, and the role of the viscous interface is to introduce a time dependence into the stress-intensity formulations. Such time-dependence arises because the bridging fibers are able to pull out of the matrix by viscous interfacial flow, with the result that the crack opening, as well as the actual (or shielded) matrix crack-tip stress-intensity factor, increase with time under the action of a constant externally applied load to the composite. The differential equation governing the mechanics of the fiber pull-out is derived. This is then applied to obtain expressions for the time-dependence of the crack opening and the effective crack-tip stress-intensity factor in terms of material and microstructural factors. These expressions predict that the matrix crack will exhibit stable crack growth, with the crack growth rate being essentially crack length (and time) independent and a function only of the applied stress and of material and microstructural factors. It is also shown that the composite lifetime is independent of the sizes of pre-existing cracks and is dependent only on a critical microstructure dependent flaw size, applied stress and microstructural factors.     

Numerical analysis of fibre bridging and fatigue crack growth in metal matrix composite materials

The analysis of bridged crack configurations in unidirectional fibre-reinforced composites is relevant to a variety of crack growth problems, including the fatigue of metal matrix composites and the study of fibre failure in the wake of a bridged matrix crack. Details of numerical procedures for predicting fibre stresses and their effect on crack tip stress intensity factors are presented here to provide a useful overview of how standard bridging calculations are done. Results are presented and discussed in the context of predicting fatigue crack growth with fibre failure in metal matrix composites.     

Micromechanical modelling of strain hardening and tension softening in cementitious composites

This paper will describe a procedure for modelling the complete macroscopic response (including strain hardening and tension softening) of two short fibre reinforced cementitious composites and show how their microstructural parameters influence this response. From a mathematical point of view it is necessary to examine how bridging forces imposed by the fibres alter the opening of multiple cracks in elastic solids under unidirectional tensile loading. The strain hardening is essentially due to elastic bridging forces which are proportional to crack opening displacements. After a certain critical crack opening displacement is reached, some fibres progressively debond from the elastic matrix and thereafter provide a residual bridging force by frictional pull-out, while others continue to provide full bridging. This results in a kind of elasto-plastic bridging law which governs the initial tension softening response of the composite. Besides the usual square-root singularity at crack tips, the elasto-plastic bridging law introduces a logarithmic singularity at the point of discontinuity in the bridging force. These singularities have been analytically isolated, so that only regular functions are subjected to numerical integration. Unbridged multiple crack problems have in the past been solved using double infinite series which have been found to be divergent. In this paper a superposition procedure will be described that eliminates the use of double infinite series and thus the problem of divergence. It is applicable to both unbridged and bridged multiple cracks. The paper will end by showing how the model of multiple bridged cracks can accurately predict the prolonged nonlinear strain hardening and the initial tension softening response of two cementitious composites.     

Crack growth induced delamination on steel members reinforced by prestressed composite patch

ABSTRACT Prestressed composite patch bonded on cracked steel section is a promising technique to reinforce cracked details or to prevent fatigue cracking on steel structural elements. It introduces compressive stresses that produce a crack closure effect. Moreover, it modifies the crack geometry by bridging the crack faces and so reduces the stress intensity range at the crack tip. Fatigue tests were performed on notched steel plate reinforced by CFRP strips as a step toward the validation of crack patching for fatigue life extension of riveted steel bridges. A crack growth induced debonded region in the adhesive‐plate interface was observed using an optical technique. Moreover, the size of the debonded region significantly influences the efficiency of the crack repair. Debond crack total strain energy release rate is computed by the modified virtual crack closure technique (MVCCT). A parametric analysis is performed to investigate the influence of some design parameters such as the composite patch Young's modulus, the adhesive thickness and the pretension level on the adhesive‐plate interface debond.     

Modelling fatigue crack propagation of a cracked metallic member reinforced by composite patches

The concept of fracture for material elements at front of a crack for fatigue crack propagation was extended to the fatigue crack propagation of a cracked metallic member reinforced with a composite patch in this paper. From static mechanics and linear elastic fracture mechanics, force transfer on a cracked member through a composite patch was analyzed and a formula connecting the stress intensity factor with crack length was obtained. Thereafter, a fracture model for fatigue crack propagation of a repaired cracked metallic member was proposed. A new expression for the fatigue crack propagation rate has thus been derived. The expression was verified objectively by the test data. It is in good agreement with the test results.     

Determination of Crack Bridging Stresses from Crack Opening Displacement Profiles

This paper discusses the development of an optimization procedure to deduce the bridging stress from the crack opening displacements (COD) measured during fatigue crack growth. Finite element analysis was conducted using the center-cracked geometry to verify the optimization procedure. The proposed procedure successfully predicted the bridging stress distributions with zero stresses at the crack tip and the bridging stress distributions with non-zero stresses at the crack tip. The results also showed that COD measurements spaced at ≈ 0.8-1.0 mm are sufficient for reliable prediction of bridging stresses. Accurate prediction of bridging stresses near the crack tip required COD data within ≈ 0.1 mm from the crack tip. The application of the proposed procedure to a metal matrix composite (SCS-6/TIMETAL®21S) is also discussed.     

复合材料补片止裂性能的方法研究

含裂纹金属板经复合材料补片胶接修补后的应力强度因子计算可分为两个阶段：首先假设复合材料补片胶接到一块没有裂纹的金属板上,根据广义平面应力的弹性包容理论计算胶接修补区内金属板上的应力值;其次在金属板上引入一条长度为2c的裂纹,并用近似方法估算裂纹尖端的应力强度因子和疲劳寿命。所得结果与有限元计算结果和疲劳寿命试验结果吻合较好。     

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.     

On the fatigue response of bridging ductile fibers in an MoSi2 intermetallic composite

The fatigue response of bridging molybdenum fibers in an MoSi₂ matrix has been investigated. The composite consists of a MoSi₂-40% SiC matrix reinforced with alumina coated Mo fibers. Previous work demonstrated that the ductility and interfacial debonding of coated Mo fibers promoted high monotonic fracture resistance based on a bridging mechanism. The current study shows that debonding ductile fibers have also the potential to give adequate fatigue crack growth resistance. A tensile test was devised to measure the opening of a bridged crack as a function of number of cycles. The results suggest that if the applied stress is below a threshold stress governed by the flow stress of the ductile fibers, then the crack opening remains constant after a large number of cycles. This information can be used, in principle, to predict the crack growth rate in composites.     

Fracture Analysis of Double-Side Adhesively Bonded Composite Repairs to Cracked Aluminium Plate Using Line Spring Model

A line spring model is developed for analyzing the fracture problem of cracked metallic plate repaired with the double-sided adhesively bonded composite patch. The restraining action of the bonded patch is modeled as continuous distributed linear springs bridging the crack faces provided that the cracked plate is subjected to extensional load. The effective spring constant is determined from 1-D bonded joint theory. The hyper-singular integral equation (HSIE), which can be solved using the second kind Chebyshev polynomial expansion method, is applied to determine the crack opening displacements (COD) and the crack tip stress intensity factors (SIF) of the repaired cracked plate. The numerical result of SIF for the crack-tip correlates very well with the finite element (FE) computations based on the virtual crack closure technique (VCCT). The present analysis approaches and mathematical techniques are critical to the successful design, analysis and implementation of crack patching.     

On the Mode I stress intensity factor for an external circular crack with fibre bridging

This paper presents a theoretical analysis of an external matrix crack located in a unidirectional fibre-reinforced elastic solid modelled as a transversely isotropic material. The presence of matrix cracking with fibre continuity introduces bridging action that has an influence on the stress intensity factors at the crack tip of the external crack. This paper presents a model for the bridged crack, where the fibre ligaments induce a constant displacement-dependent traction constraint over the external crack. This gives rise to a Fredholm integral equation of the second kind, which can be solved in an approximate fashion. We examine the specific problem where the bridged external circular crack is loaded by a doublet of concentrated forces. Numerical results are presented to illustrate the influence of the fibre–matrix modular ratio and the location of the loading on the bridged-crack opening mode stress intensity factor.     

Evaluation of fracture parameters of composites subjected to thermal shock using the boundary element method and sensitivity analysis techniques

Quasi-static crack extension in fiber-reinforced composites subjected to thermal shock is analyzed using the boundary integral equation method, in combination with sensitivity analysis techniques. Buekner's formulation is employed to evaluate the stress intensity factor in a cracked body. This method eliminates the need for special element types to model the crack tip, as well as the use of a large number of elements near the cracked zone of interest. A numerical procedure involving sensitivity analysis techniques based on the adjoint structure approach has been developed to evaluate the energy integrals in the cracked body. Gradients of the functionals of response quantities with respect to variables such as the crack length, necessary for the evaluation of fracture parameters, are determined directly by this method. The numerical differentiation used in other numerical methods, such as the finite element method, which requires the repeated solution of the equations for different crack sizes is avoided. Results for stress intensity factors as a function of crack length are presented for various composite systems. These results are in good agreement with analytical results and results from the finite element method. The present approach results in significantly improved computational efficiency.     

Coupled transient thermoelastic contact problems for axial cracks in hollow cylinders

A coupled transient thermoelastic behaviour of an axial-cracked hollow circular cylinder subjected to a sudden heating is investigated in this study. It is shown that surface heating may induce the compressive thermal stress near the inner surface of the cylinder which in turn may force the cracked surfaces to close together. Assuming that the existence of the crack does not alter the temperature distribution, we can divide this problem into two parts and solve it by the principle of superposition. First, the temperature and transient thermal stress distributions along the axisymmetric surface of the imaginary cylinder without crack are obtained by finite element implicit time integration method Secondly, the opposite sense of the stress distributions along the cracked surfaces, which is obtained previously, is treated as the traction boundary conditions; the contact length and contact pressure of the real cracked cylinder are obtained by modified elimination finite element scheme. Finally, we also obtained the normalized stress intensity factor for the crack tip of the cylinder. It is concluded that the effect due to thermoelastic coupling term on stress intensity factor becomes more important for higher coupling coefficient, and this coupling term also results in a small time lag in temperature, thermal stress and stress intensity factor.     

Stress states and growth behavior of bridged cracks at creep regime

In this study growth behavior of bridged cracks, resulting from the growth of pre-nucleated creep cavities with diffusional and dislocation-assisted mechanisms, is investigated numerically. The elements bridging the crack are assumed to be elastic; the bridging behavior ranges from full development of the bridging zones to failure of the bridging elements during the course of crack growth. The results indicate that the bridging traction significantly relaxes even with the overall creep deformation alone. The rate of this relaxation is not influenced by the rate of crack growth. However, the rate of change in the bridging zone length or the density of the bridging elements in the bridging zone strongly affects both the maximum value and the distribution of the traction in the bridging zone. A much weaker stress singularity than the ones described by K or C^* was found ahead of the bridged cracks in the creep regime. In this weak singularity region the cavities, located at increasing distance from the crack tip, grow at similar high rates to each other.     

Progressive edge cracked aluminium plate repaired with adhesively bonded composite patch under full width disbond

In this study, the crack growth behaviour of an aluminium plate cracked at the tip and repaired with a bonded boron/epoxy composite patch in the case of full-width disbond was investigated. This effect is the imperfection which could result during the bonded patch of the repaired structure. Disbonds of various sizes and situated at different positions with respect to the crack tip as well as the effect of adhesive and patch thickness on repair performance were examined. An analysis procedure involving the efficient finite element modelling applied to cracked plate, adhesive and composite patch was used to compute the stress intensity factors. The crack growth rate is dominated by the stress intensity factor near the location and size of the pre-existing disbonds. The cracked plate and disbond propagation result in an increase in the patch deformation. The patch does not have an influence on the crack growth when the ratio 2a/d_R exceeds 0.8.