Effect of microstructure on elevated-temperature fracture behaviour of two-dimensional carbon/carbon composites

The fracture behaviour of two-dimensional carbon/carbon composites has been studied at temperatures upto 1650°C, using both chevron-and straight-notch single-edge notch beam (SENB) specimens. In all cases, the R-curve behaviour and fracture toughness variations with specimen orientation and temperature are characterized and correlated with the specific microstructure and failure micromechanisms. Higher crack growth resistance and fracture toughness of the longer fibre composite are attributed to the enhanced fibre pull-out and fibre bridging in the following wake region. The relative contribution from the frontal and following wake zone is determined experimentally by the use of renotching methods which demonstrate the effectiveness of the traction zone behind the crack tip. The temperature effects on the toughening mechanisms are examined in terms of crystal structure and fibre matrix interfacial characteristics.     

Bifurcation and stability of structures with interacting propagating cracks

A general method to calculate the tangential stiffness matrix of a structure with a system of interacting propagating cracks is presented. With the help of this matrix, the conditions of bifurcation, stability of state and stability of post-bifurcation path are formulated and the need to distinguish between stability of state and stability path is emphasized. The formulation is applied to symmetric bodies with interacting cracks and to a halfspace with parallel equidistant cooling cracks or shrinkage cracks. As examples, specimens with two interacting crack tips are solved numerically. It is found that in all the specimens that exhibit a softening load-displacement diagram and have a constant fracture toughness, the response path corresponding to symmetric propagation of both cracks is unstable and the propagation tends to localize into a single crack tip. This is also true for hardening response if the fracture toughness increases as described by an R-curve. For hardening response and constant fracture toughness, on the other hand, the response path with both cracks propagating symmetrically is stable up to a certain critical crack length, after which snapback occurs. A system of parallel cooling cracks in a halfspace is found to exhibit a bifurcation similar to that in plastic column buckling.     

R-curve behavior in notched beam tests of rocks

The R-curve for sandstone is obtained from the load-crack mouth opening response of notched specimens subjected to three-point-bending. This approach is used to analyze the fracture behavior under monotonic and cyclic loading. The asymptotic limit of the R-curve compares well with the fracture toughness determined through an effective crack model. The analysis of the relaxation observed before the unloading-reloading cycles in the cyclic tests leads to the conclusion that the fracture toughness remains practically constant while the crack propagates slightly during the load drop.     

Effect of ion exchange on <Emphasis Type="Italic">R</Emphasis>-curve behavior of a dental porcelain

The objective of this study was to evaluate the effect of the ion exchange treatment on the R-curve behavior of a leucite-reinforced dental porcelain, testing the hypothesis that the ion exchange is able to improve the R-curve behavior of the porcelain studied. Porcelain disks were sintered, finely polished, and submitted to an ion exchange treatment with a KNO₃ paste. The R-curve behavior was assessed by fracturing the specimens in a biaxial flexure design after making Vickers indentations in the center of the polished surface with loads of 1.8, 3.1, 4.9, 9.8, 31.4, and 49.0 N. The results showed that the ion exchange process resulted in significant improvements in terms of fracture toughness and flexural strength as compared to the untreated material. Nevertheless, the rising R-curve behavior previously observed in the control group disappeared after the ion exchange treatment, i.e., fracture toughness did not increase with the increase in crack size for the treated group.     

Prediction of the fracture toughness of fibrous composites

A statistical/micromechanical model is developed for the prediction of the fracture toughness of fibrous composites. The fracture resistance of the material is assumed to be related to the statistical distribution of the fiber pull-out length. The distribution of the fiber pull-out length is derived from the fiber strength distribution. The R-curve behavior of the fibrous composite is predicted and interpreted based on the present model. The limiting fracture toughness is predicted to be proportional to the square root of the ineffective length, or proportional to the square root of the fiber length if the fiber length is less than the ineffective length.     

FATIGUE CRACK GROWTH BEHAVIOUR AND FRACTURE RESISTANCE IN CERAMICS

Fatigue crack growth and the fracture resistance curve (R-curve) were investigated in a polycrystalline alumina (AD90) and a silicon carbide whisker-reinforced alumina composite (Al₂O₃-SiC_w) at room temperature in air using a combined loading technique for stabilizing crack growth, and a surface film technique for monitoring crack length. Fatigue crack growth was evaluated successfully with those experimental techniques. Load shedding tests were performed until the crack became dormant, in order to determine the threshold stress intensity factor K_th. Subsequently, the specimens were used for quasi-static crack growth tests under a monotonic loading condition. The R-curves were determined in this experiment; however, fracture resistance did not increase markedly with crack growth. Detailed observations of the crack growth behaviour revealed that the flat R-curve was attributed to the shielding effect of the fatigue crack tip wake. Thus, the fatigue precrack introduced by the load shedding test was not regarded as an ideal crack for determining the R-curve. Fractographic observations were performed to investigate the mechanistic difference between fatigue and quasi-static crack growth. It was found that the cyclic loading produced fretting damage in the wake region and it reduced the shielding effect of the fatigue cracks. Based on the experimental results, the relationship between the fatigue crack growth and the R-curve is discussed as is the significance of K_th as a material parameter.     

Combined effect of fiber content and microstructure on the fracture toughness of SGF and SCF reinforced polypropylene composites

Composites of polypropylene (PP) reinforced with short glass fibers (SGF) and short carbon fibers (SCF) were prepared with extrusion compounding and injection moulding techniques. The fracture behavior of the two types of composites was studied. The fracture toughness (K _c of the composites was measured in the T-direction [main crack transverse to mould flow direction (MFD)] and in the L-direction (main crack parallel to the MFD) using compact tension (CT) specimens made from the plaques manufactured. The study was focused on the combined effect of fiber volume fraction and microstructure (fiber length and alignment) on the fracture toughness of short fiber composites. It was observed that the addition of fibers effectively enhanced the fracture toughness for both SGF/PP and SCF/PP systems in the T-direction but only improved the composite toughness in the L-direction for the case of a low fiber volume fraction (8%). The composite fracture toughness kept almost unchanged in the T-direction and decreased in the L-direction with increasing fiber volume fraction. These were explained using the combined effect of fiber volume fraction and microstructure.     

PROCESSING AND FRACTURE TOUGHNESS OF SINTERED FIBER REINFORCED CERAMIC MATRIX COMPOSITES

ABSTRACT

The paper discusses the processing and the resulting mechanical properties of sintered fiber reinforced ceramic matrix composites. In situ observations of the sintering process revealed that stresses which develop due to the differential shrinkage between the fibers and the matrix initiate already during the heating cycle and are of sufficient magnitude and duration that crack like damage forms. Successful methods were employed for reducing and avoiding these stresses during the sintering process. Coarse grained alumina coatings deposited onto the fibers with a coating thickness of up to 10 µm delayed and reduced the stress development. Polymer coated fibers produced fully dense composites on which fracture toughness measurements were performed. Crack propagation and crack/fiber interaction was observed in situ inside a scanning electron microscope. The importance of studying both the crack front and the crack wake phenomena in fiber reinforced composites is illustrated. In specimens where the cracks are already bridged by 10% area fraction of fibers a toughness of 7 MPa √m was obtained. However, in samples where the cracks are not bridged yet by fibers, the crack becomes unstable before reaching the fiber positions and the fibers had no effect in resisting the crack propagation.     

Evaluation of the electrical potential drop technique in the determination of crack growth resistance-curves of Carbon/Carbon composites and carbon bonded refractories

Electrical potential drop (EPD) and compliance techniques are compared as techniques for crack length measurement in determining the crack growth resistance-curve (R-curve) of two Carbon/Carbon (C/C) composites and two carbon-bonded oxide-graphite refractories. The two C/C composites differ in the strength of the fibre/matrix interaction, resulting from the use of untreated and surface treated carbon fibres. The refractories differ in the volume fraction of graphite flakes. R-curve measurements on the C/C composites were made on specimens with chevron notches whilst straight-through notches were used for carbon bonded refractories. In the EPD method, the instantaneous crack length was determined from the instantaneous electrical potential across the notch plane, which was recorded in line with load and displacement data, and experimental calibration data. In the compliance method, the instantaneous crack length was determined analytically using the instantaneous load and displacement data. From the EPD technique smaller crack lengths were calculated than from the compliance technique in the regions of fracture where the composites had well developed process zones, and for the whole region in the refractories. The EPD technique underestimates the actual crack length, due to current conduction in the wake zone by bridging fibres/grains, and as a result the R-curves are different from those reported by the compliance technique, which are considered to be more reliable. The compliance-based results are used to establish the effects of fibre surface functionality and graphite flake content on crack growth resistance in the two systems.     

Cohesive models for quasistatic cracking in inelastic solids

In has been shown that slow stable cracking process can be sustained by strain-softening materials such as cementitious composites, e.g., rock, concrete, mortars, ceramics and others. A mathematical model is proposed based on the theory of quasi-static crack extension governed by Wnuk's criterion of final stretch (equivalent to the CTOA condition). Requirement of self-similarity of the crack opening profile, maintained during the quasistatic growth phase, leads to a differential equation defining the material resistance to sustained crack extension, as a function of crack growth increment, material properties such as tearing modulus, strain-softening parameter, and the size of the process zone.The equations derived on the basis of the step-like distribution of the restraining stress which operates within a structured end zone associated with a moving crack, are compared against the Wnuk-Rice-Sorensen equation to ran R-curve in an ideal elasto-plastic material, and with the more recent results of Wnuk and Hunsacharoonroj [1] pertaining to strain-hardening materials which obey the Ramberg-Osgood power law.Present results suggest that the nature of constitutive equations substantially influence composite fracture resistance as measured by the R-curve. Ability to absorb energy and the ensuing resistance to crack growth can be significantly enhanced when the mechanisms of energy dissipation within the matrix are properly understood. This work establishes a bridge between the continuum mechanics and micromechanics of deformation and meture processes by providing a relation between material fracture toughness and its constitutive equations supplemented by certain microstructural characteristics.     

Evaluation of the fracture toughness of Nb-40Al-8Cr-1W-1Y-0.05B intermetallic material by indentation techniques

The fracture toughness of an Nb-40Al-8Cr-1W-1Y-0.05B intermetallic material was evaluated by indentation techniques at room temperature. Two widely used indentation methods, crack size measurement and indent strength, yielded excellent agreement with a conventional fracture toughness technique using straight-through precracked specimens, despite the occasional formation of poorly configured cracks. However, the modified indentation technique, using dummy indent flaws, resulted in a low fracture toughness compared to that evaluated by the other methods. The material did not exhibit rising R-curve behaviour, as evaluated from the indentation strength data. These results indicate that indentation fracture principles are applicable to this brittle intermetallic material without modification of the residual contact stress term originally calibrated for ceramic materials.     

The resistance to crack growth of asbestos cement

The crack resistance of sheet asbestos cement has been characterized in terms of anR-curve which can accomodate effects which often influence the measurement of the critical stress intensity factorK _c. The detection and location of the acoustic emission (AE) obtained from the asbestos cement has shown that it originates from microcracks in a zone just in front of the crack. The size of this zone increases to a maximum during slow propagation of the major crack and afterwards remains of constant size during the final crack growth. The form of theR-curve has been explained in terms of the mechanisms of fracture with the aid of AE and fractography studies. An analytical study has related the experimentalR-curve to a theoreticalR-curve and, hence, to the volume fraction, fibre aspect ratio and the strength of the fibre—matrix interface. It has been shown that the microcracking zone can be considered as a theoretical extension, of about one third of the zone length, to the real crack length.     

Evaluation of R-curve behavior of ceramic-metal functionally graded materials by stable crack growth

This paper deals with the fracture toughness and R-curve behavior of ceramic-metal functionally graded materials (FGMs). A possibility of stable crack growth in a three-point-bending specimen is examined based on the driving force and resistance for crack growth in FGMs, and the distribution of fracture toughness or R-curve behavior is evaluated on FGMs fabricated by powder metallurgy using partially stabilized zirconia (PSZ) and stainless steel (SUS 304). The materials have a functionally graded surface layer (FGM layer) with a thickness of 1 mm or 2 mm on a SUS 304 substrate. Three-point-bending tests are carried out on a rectangular specimen with a very short crack in the ceramics surface. On the three-point-bending test, a crack is initiated from a short pre-crack in unstable manner, and then it propagates in stable manner through the FGM layer with an increase in the applied load. From the relationship between applied load and crack length during the stable crack growth in the FGM layer, the fracture toughness is evaluated. The fracture toughness increases with an increase in a volume fraction of SUS 304 phase.     

PROCESSING AND FRACTURE TOUGHNESS OF SINTERED FIBER REINFORCED CERAMIC MATRIX COMPOSITES

The paper discusses the processing and the resulting mechanical properties of sintered fiber reinforced ceramic matrix composites. In situ observations of the sintering process revealed that stresses which develop due to the differential shrinkage between the fibers and the matrix initiate already during the heating cycle and are of sufficient magnitude and duration that crack like damage forms. Successful methods were employed for reducing and avoiding these stresses during the sintering process. Coarse grained alumina coatings deposited onto the fibers with a coating thickness of up to 10 µm delayed and reduced the stress development. Polymer coated fibers produced fully dense composites on which fracture toughness measurements were performed. Crack propagation and crack/fiber interaction was observed in situ inside a scanning electron microscope. The importance of studying both the crack front and the crack wake phenomena in fiber reinforced composites is illustrated. In specimens where the cracks are already bridged by 10% area fraction of fibers a toughness of 7 MPa √m was obtained. However, in samples where the cracks are not bridged yet by fibers, the crack becomes unstable before reaching the fiber positions and the fibers had no effect in resisting the crack propagation.     

Size effects in concrete fracture – Part II: Analysis of test results

This paper presents an analysis of the extensive experimental program aimed at assessing the influence of maximum aggregate size and specimen size on the fracture properties of concrete. Concrete specimens used were prepared with varying aggregate sizes of 4.75, 9.5, 19, 38, and 76mm. Approximately 250 specimens varying in dimension and maximum aggregate size were tested to accomplish the objectives of the study. Every specimen was subjected to the quasi-static cyclic loading at a rate of 0.125mm/min (0.005in./min) leading to a controlled crack growth. The test results were presented in the form of load-crack mouth opening displacement curves, compliance data, surface measured crack length and crack trajectories as well as calculated crack length, critical energy release rate, and fracture toughness (G ₁). There is a well pronounced general trend observed: G ₁ increases with crack length (R-curve behavior). For geometrically similar specimens, where the shape and all dimensionless parameters are the same, the R-curve for the larger specimens is noticeably higher than that for the smaller ones. For a fixed specimen size, G ₁ increases with an increase in the aggregate size (fracture surface roughness). For the same maximum aggregate size specimens, the apparent toughness increases with specimen size. It was clear that the rate of increase in G ₁, with respect to an increase of the dimensionless crack length (the crack length normalized by the specimen width), increases with both specimen size and maximum aggregate size increase. The crack trajectory deviates from the rectilinear path more in the specimens with larger aggregate sizes. Fracture surfaces in concrete with larger aggregate size exhibit higher roughness than that for smaller aggregate sizes. For completely similar specimens, the crack tortuosity is greater for the larger size specimens. The crack path is random, i.e., there are no two identical specimens that exhibit the same fracture path, however, there are distinct and well reproducible statistical features of crack trajectories in similar specimens. Bridging and other forms of crack face interactions that are the most probable causes of high toughness, were more pronounced in the specimens with larger maximum size aggregates.     

Interlaminar fracture (model II) of commingled yarn-based GF/PP composites

A 5050 wt % mixture of commingled glass/polypropylene fibre system was selected to study the correlations between the morphological details, mode II interlaminar fracture toughness and corresponding failure mechanisms. Mode II interlaminar fracture tests were performed by using the end-notched flexure test procedure. Compared to conventional composite laminates, mode II interlaminar crack extension in these commingled yarn-based composites was very stable, and extensive fibre nesting occurred along the main crack plane. Crack jumping and non-broken matrix links were observed.R-curve behaviour for these materials was identified and the toughness for initiation was much lower than that for propagation. Compared to mode I interlaminar fracture toughness, similar trends in effects of cooling rates and isothermal crystallizations on mode II interlaminar fracture toughness were observed. However, the effects were not as significant as those found for mode I interlaminar fracture toughness.Alexander von Humboldt Fellow.     

Crack growth resistance (R-curve) behaviour and thermo-physical properties of Al2O3 particle-reinforced AlN/Al matrix composites

Crack growth resistance behaviour and thermo-physical properties of Al₂O₃ particle-reinforced AlN/Al matrix composites have been studied as a function of AlN volume fraction as well as Al₂O₃ particle size. The fracture toughness of the composites decreased with increase in vol% AlN and decrease in Al₂O₃ particle size. All the composites exhibited R-curve behaviour which has been attributed to crack bridging by the intact metal ligaments behind the crack tip. The Young’s modulus of the composites increased with the vol% of AlN whereas the thermal diffusivity and coefficient of thermal expansion followed a reverse trend. The composites exhibited hysteresis in thermal expansion as a function of temperature and the hysteresis decreased with decrease in metal content of the composite.     

A shear lip analysis of concave R-curves for an AlMgZn alloy

A concave R-curve for an AlMgZn alloy covers the transition from fully flat to fully slant fracture in 25 mm thick specimens of varying geometry. The transition is associated with the onset of plane stress conditions near the crack front. The concave R-curve is analysed using the increasing width of the shear lips, as in the Krafft et al. model, which increased the plastic work parabolically. The elastic and plastic work rates are evaluated using parabolic curve fits to the R-curve data. The present study showed that the plastic work rate scales with the crack extension from fully flat to fully slant fracture, which is geometry dependent     

Fracture toughness of 2-D carbon fibre reinforced carbon composites

The fracture toughness of 2-D woven carbon fibre reinforced carbon laminate has been evaluated by linear elastic fracture mechanics (LEFM),R-curve andJ-integral analysis using the single edge-notched bending (SENB) specimen of edge and flatwise geometries. The edgewise specimens failed by a small extension of the self similar crack whereas the flatwise specimens failed by delamination. The surface damage developing from the tip of the initial crack was revealed by the brittle lacquer coating technique and the zone shape varied with the specimen geometry, i.e. the loading axis relative to the woven layers. Acoustic emission (AE) was also used to monitor crack growth, and the total ring down count of AE was observed to increase as the initial crack length was decreased. Both the damage zone size and total AE counts were found to increase in two linear stages as a function of the square of the stress intensity factor,K.