Determination of fracture toughness and bridging tractions from crack-opening displacement measurements in particulate composites of diamond in zinc sulfide

The fracture toughness of zinc sulfide ceramic and a series of ZnS diamond particle composites was studied through measurements of crack opening displacement profiles. Five composites were fabricated using weight fractions of 10, 20 and 30% of 0–1 μm diamond particles, and 10 and 20% of 1–3 μm particles in a ZnS matrix. The cracks were grown using a novel specimen geometry and a loading technique that permitted stable crack growth even in small specimens. The fracture toughness of each material was calculated on the basis of the displacement profiles and the material properties, as opposed to the applied loads and the specimen geometry. The pure zinc sulfide material exhibited nearly ideal brittle behavior, and the toughness measurements agreed closely with other methods. The greatest toughening occurred in the 1–3 μm particle size composites, in which weak bridging tractions (⩽ 100 MPa) over a short distance along the crack (50–100 μm) could explain the reduced displacements near the crack tip. Even smaller size bridging zones (5–10 μm) may have been present in the 0–1 μm particle size composites, but elastic shielding alone can explain the observed toughening. The specimen geometry used here permitted toughness measurements using small specimens (< 5 mm) but is limited to materials having bridging zones that are less than about 250 μm.     

Effects of temperature,rate, and cyclic loading on the strength and toughness of monolithic ceramics

The concept of grain bridging and pullout is applied to monolithic ceramics to understand the effects of temperature, displacement rate, and load cycling on crack wake shielding. At low temperature, the pullout of completely debonded grains accounts for all the toughening. The importance of this process diminishes with temperature. This is because of the more uniform stress distribution along the crack plane and the softening of grain boundary glassy phases, both of which tend to reduce the incidence of complete grain boundary decohesion. At sufficiently high temperature, however, the softening of grain boundary phases may allow the sliding zone to extend to the grain's end, increasing the incidence of intergranular fracture. This “high temperature” pullout triggers a sudden increase in toughness. Our pullout model successfully explains the high temperature peak and the dependence of peak position on displacement rate in fracture toughness and strength observations for some monolithic and whisker-reinforced ceramics. Degradation of interfacial friction, as by cyclic loading, is seen to decrease the frictional work for low temperature pullout but increases the frictional work for high temperature pullout. Thus, this model also provides a rationale for the opposite effect of stress cycling on crack resistance at low and high temperatures reported recently for ceramics.     

On the strength of ductile particle reinforced brittle matrix composites

This study examines theoretically the strength characteristics of ductile particle reinforced brittle materials in which the strength enhancement is derived from the crack bridging process. The crack bridging is characterized by rectilinear and linear softening bridging laws that relate the crack surface traction to the crack opening displacement. The composite strength is expressed in terms of two non-dimensional parameters that combine the effects of the flaw size, elastic modulus, matrix toughness, and the bridging-law parameters. It is shown that such composites can be substantially more flaw tolerant than the monolithic matrices owing to a narrowing of the strength distribution. The role of interface debond length is also examined. It is shown that there exists optimal debond lengths of which the composite strength is maximized. In contrast, the steady state toughness increases monotonically with debond length. The implications of these results on the design of composite microstructures are briefly described.     

Crack Growth Resistance of Hybrid Fiber-Reinforced Cement Matrix Composites

The effect of hybrid fiber reinforcement on fracture energy and crack propagation in cement matrix composites is examined. The crack in cement matrix composites is allowed to fracture under mode-I loading with three-point bending beam specimens. The influence of fiber types and their combination is quantified by using the toughness index and fracture energy. A proper hybrid combination of steel fibers and polyvinyl alcohol microfibers enhances the resistance to both the nucleation and growth of the crack. The micromechanical model of hybrid composites by using a fiber bridging law is emphasized, and the numerical model prediction closely matches the behavior obtained from the experiment. The influencing role of the material parameters in the fracture tests (e.g., the fracture toughness index and fracture energy) becomes more apparent than ones used in some conventional strength-based or fiber pullout tests, and these fracture parameters could screen the effect of fiber/microfiber reinforcement in enhancing the crack growth resistance of cementitious composites. This study demonstrates that fundamental fracture tests are effective to characterize and develop high-performance hybrid fiber–reinforced cement matrix composites.     

The mechanics of toughness development in ductile phase reinforced brittle matrix composites

This study is a numerical exercise to theoretically analyze toughening in brittle materials consisting of ductile reinforcements, on the basis of crack bridging by ductile particles. The effects of the particle constitute behavior, the shape of the stress-displacement law, the matrix fracture toughness and the overall elastic modulus of the composite on toughness have been illustrated by simple fracture mechanics calculations of self-consistent crack opening displacement profiles and crack bridging stress distributions. An approach to calculate the crack surface displacements, crack bridging stresses and stress intensity factors in any specimen geometry, using weight functions, is presented. Different types of idealized particle stress-displacement responses were used in the calculations. The opening characteristics of a bridge crack and the evolution of toughness for these types have been examined. The conditions for maximum bridging and toughness as well as the conditions at which a fully bridged crack transforms to a partially bridged one have been identified. The role of individual parameters used in constructing the stress-displacement law on composite toughness has been assessed. The toughness has been found to manifest from a complex interaction of the matrix fracture toughness, the composite modulus and the flow behavior of the ductile particle.     

Analytical Method for Pullout of Anchor from Anchor–Mortar–Concrete Anchorage System due to Shear Failure of Mortar

Depending on the relevant material properties, failure of grouted anchors can take forms of pullout of concrete cones, debonding at either anchor–grout or grout–concrete interface, fracture of anchor and combination of some of these failure modes. Further, if the thickness of the grout layer is thin enough, the shear strength of the grout is relatively low or the anchor is in the form of a steel bar with ribs or spirals, the grout would be sheared off so that the anchor is pulled out. The present study presents an analytical method for the last scenario, i.e., anchor pullout from an anchor–mortar–concrete anchorage due to shear failure of mortar. Two different boundary conditions are considered: fixed bottom surface of concrete as Boundary 1, and top surface of concrete with uniform distributed force as Boundary 2. A shear-lag model was introduced to analyze the behaviors of the mortar and the interfacial properties of both the anchor–mortar and the mortar–concrete interfaces were also considered. Based on the deformation compatibilities of the interfaces and the mortar layer, the distributions of the tensile stresses in the anchor and shear stresses in the mortar along the embedment length were obtained analytically during different loading stages for both Boundaries 1 and 2. Moreover, the probabilities and sequences of shear cracks induced by the mortar failure were determined according to the boundary conditions and the comparison between the shear stresses at the loading and nonloading ends. Double shear crack propagation from both ends with different crack lengths was then investigated. Besides, the pullout load was expressed as a function of the shear crack lengths. Then the maximum load and the corresponding critical crack lengths were obtained by using the theories of extremum. Finally, a series of material, structural, and interfacial parameters were adopted to study their influences on the calculated results using the proposed method, including the critical crack lengths, initial cracking load and maximum pullout load. It was found that the initial cracking and maximum loads in Boundary 1 are larger than those in Boundary 2. However, as the longitudinal rigidity of the concrete increases, the values of the maximum pullout loads in both of the boundary conditions approach each other. It was also found that there exists an effective bonding length, beyond which the critical crack length and maximum pullout load are no longer increased.     

Experimental Investigation and Fracture Analysis of Debonding between Concrete and FRP Sheets

The last few years have witnessed a wide use of externally bonded fiber reinforced polymer (FRP) sheets for strengthening existing reinforced and prestressed concrete structures. The success of this strengthening method relies on the effectiveness of the load-transfer between the concrete and the FRP. Understanding the stress transfer and the failure of the concrete–FRP interface is essential for assessing the structural performance of strengthened beams and for evaluating the strength gain. This paper describes an experimental investigation of the interfacial bond behavior between concrete and FRP. The strain distributions in concrete and FRP are determined using an optical technique known as digital image correlation. The results confirm that the debonding process can be described in terms of crack propagation through the interface between concrete and FRP. The data obtained from the analysis of digital images was used to determine the interfacial material behavior for the concrete–FRP interface (stress versus relative displacement response) and the fracture parameter GF (fracture energy). The instability in the test response at failure is shown to be the result of snapback, which corresponds with the elastic unloading of the FRP as the load carrying ability of the interface decreases with increasing slip.     

Effect of Fiber Strength and Fiber-Matrix Interface on Crack Bridging in Cement Composites

This article proposes a new theory for predicting the crack-bridging performance of random short fibers involved in cementitious composites. The current theoretical model for estimating crack bridging performance of random short fiber reinforced cement composites under tension is limited to specific constituent properties: friction-dominant fiber-matrix interface and complete fiber pull-out from matrix without rupture. The new theory extends this model by accounting for two often-encountered features in practice: fiber strength reduction and rupture in composites, and chemical bond–dominant fiber-matrix interface. The new theory was verified to capture important characteristics in bridging performance in comparison with composite tensile test data. As a result, the new theory forms an important foundation for developing high-performance random short fiber reinforced cement composites.     

Failure diagrams for unidirectional

Pertinent failure processes in unidirectional fiber metal-matrix composites (MMCs) have been identified and analyzed. The critical conditions for interface delamination in several composites are compared with the theoretical delamination diagram proposed by He and Hutchinson, in which interface delamination and fiber fracture are delineated on the basis of their relative tough-ness values. It is shown that the delamination diagram does not provide information about the extent of interface cracking or the onset of fiber bridging. An alternative failure diagram that depicts composite fracture processes, such as matrix yielding followed by fiber fracture, inter-face cracking, and fiber bridging, is proposed. Development of the composite failure diagramvia micromechanical modeling of individual mechanisms is presented together with experimental results from the literature. Good correlation between theory and experiment suggests that the composite failure diagram might be used for tailoring composite properties through control of the dominant fracture mechanism.     

Investigation of Bond between Fiber Reinforced Polymer and Concrete Undergoing Global Mixed Mode I∕II Loading

A novel experimental method using modified double cantilever beam specimens and a customized test frame are introduced to evaluate bond characteristics and toughness of fiber reinforced polymer (FRP) composite overlays and a concrete substrate under mixed mode loading. A computer vision system is used to measure the crack location, near-tip deformations and crack opening displacement during the crack growth process. Digital image correlation is used to determine the crack opening displacement (COD) for flaws growing in the vicinity of the FRP–concrete interface. Results from this study indicate that during crack growth, (1) the Mode I component of COD is dominant for all angles of specimen loading, (2), the magnitude of the local Mode I component of COD is maximized when good bond quality is present and crack extension occurs within the mortar∕concrete near the FRP–concrete interface and (3) good agreement exists between independent energy release rate estimates based upon both an approximate elastic double cantilever beam formulation and also use of the measured components of COD in a classical linear elastic expression.     

Moiré Interferometry Analysis of Fiber Debonding

Progressive fiber debonding in steel fiber∕cementitious matrix composites has been studied using a single fiber pullout test that permits simultaneous measurements of the load versus crack opening displacement relationship and Moiré interferometry fringe patterns. Analysis of Moiré interferometry patterns allows the fiber axial and interfacial shear stresses to be calculated along the entire fiber length. The interfacial shear stress distribution along the debonded length of the fiber indicates a steep decrease in shear stress with interfacial slip, from 6 to 1 MPa for 7 μm of fiber slip and a crack opening displacement of 22 μm. These results suggest that improvements in the toughness of cement-based composites could be achieved by developing materials in which the decrease in shear stress is less severe.     

Processing,microstructure, and mechanical behavior of cast magnesium metal matrix composites

Magnesium metal matrix composites (MMCs) have been receiving attention in recent years as an attractive choice for aerospace and automotive applications because of their low density and superior specific properties. This article presents a liquid mixing and casting process that can be used to produce SiC particulate-reinforced magnesium metal matrix composites via conventional foundry processes. Microstructural features, such as SiC particle distribution, grain refinement, and particle/matrix interfacial reactions of the cast magnesium matrix composites, are investigated, and the effects of solidification-process parameters and matrix alloys (pure Mg and Mg-9 pct Al-1 pct Zn alloy AZ91) on the microstructure are established. The results of this work suggest that in the solidification processing of MMCs, it is important to optimize the process parameters both to avoid excessive interfacial reactions and simultaneously achieve wetting, so that a good particle distribution and interfacial bonding are obtained. The tensile properties, strain hardening, and fracture behavior of the AZ91/SiC composites are also studied and the results are compared with those of the unreinforced AZ91 alloy. The strengthening mechanisms for AZ91/SiC composite, based on the proposed SiC particle/matrix interaction during deformation, are used to explain the increased yield strength and elastic modulus of the composite over the magnesium matrix alloy. The low ductility found in the composites is due to the early appearance of localized damages, such as particle cracking, matrix cracking, and occasionally interface debonding, in the fracture process of the composite.     

Enhanced Electrical and Mechanical Properties of Alumina-Based TiC Composites by Spark Plasma Sintering

Alumina composites incorporating with 0, 5, 10 15, 20, and 25 vol pct of TiC were consolidated by the spark plasma sintering at 1673 K (1400 °C). The effects of increasing TiC compositions on electrical and mechanical properties of the composites were investigated at room temperature. The dc electrical conductivity behavior demonstrates a transition from insulator to conductor around 12.5 vol pct of TiC in the framework of percolation theory. The conductivity attains a maximum value of ≈230 S/m at 25 vol pct of TiC sufficient to machine the composite by electro discharging machining. The Vickers hardness and fracture toughness of the composites increase with the addition of TiC vol pct, whereas elastic modulus decreases. The results indicate that crack deflection, crack bridging, and crack branching by the TiC particles are responsible for the significantly improved fracture toughness of the composites.     

Analytical Solution for Fracture Analysis of CFRP Sheet–Strengthened Cracked Concrete Beams

Fiber-reinforced polymer (FRP) composite materials have been widely used in the field of retrofitting. Theoretical analysis of FRP plate- or sheet-strengthened cracked concrete beams is necessary for estimating service reliability of the structural members. In previous studies, the effect of a perfectly bonded FRP plate or sheet was equivalent to a cohesive force acting at the bottom of crack to delay the crack propagation in concrete and reduce the crack width. However, delamination between FRP and cracked beam is inevitable due to interfacial shear stress concentration at the bottom of crack. The intention of this paper is to present an analytical solution for fracture analysis of carbon FRP (CFRP) sheet–strengthened cracked concrete beams by considering both vertical crack propagation in concrete and interfacial debonding at CFRP-concrete interface. The interfacial debonding is modeled as the interfacial shear crack propagation in this paper. Four different stages are discussed after initial cracking state of the concrete. At the first stage, only fictitious crack propagation occurs in the concrete. At the second stage, macrocrack propagates in the concrete without interfacial debonding. At the third stage, both vertical macrocrack propagation in the concrete and horizontal shear crack propagation at the CFRP-concrete interface occur in the strengthened beam. The tensile stress in the CFRP sheet and interfacial shear stress along the span are formulated based on the deformation compatibility condition at the CFRP-concrete interface at this stage. Finally, macroshear crack propagates at the interface until the CFRP sheet is completely peeled out from the beam, and then the member is fractured. The applied load is determined as a function of the referred two crack lengths at different stages. At the beginning, the applied load increases to one peak value with the full propagation of fictitious crack at the first stage. At the third stage, the applied load is improved to another peak value due to the relatively high cohesive effect of the CFRP sheet. Then the two peak values are determined by the Lagrange multiplier method. The validity of the proposed analytical solution is verified with the experimental results and numerical simulations. It can be concluded that the proposed analytical solution can predict the load-bearing capacity of CFRP sheet-strengthened cracked concrete beams with reasonable accuracy.     

Fatigue crack growth of SM-1240/TIMETAL-21S metal matrix composites at elevated temperatures

A series of high-temperature fatigue crack growth experiments was conducted on a continuous-fiberreinforced SM1240/TIMETAL-21S composite using three different temperatures, room temperature (24 °C), 500 °C, and 650 °C, and three loading frequencies, 10, 0.1, and 0.02 Hz. In all the tests, the cracking process concentrated along a single mode I crack for which the principal damage mechanism was crack bridging and fiber/matrix debonding. The matrix transgranular fracture mode was not significantly influenced by temperature or loading frequency. The fiber debonding length in the crack bridging region was estimated based on the knowledge of the fiber pullout lengths measured along the fracture surfaces of the test specimens. The average pullout length was correlated with both temperature and loading frequency. Furthermore, the increase in the temperature was found to lead to a decrease in the crack growth rate. The mechanism responsible for this behavior is discussed in relation to the interaction of a number of temperature-dependent factors acting along the bridged fiber/matrix debonded zone. These factors include the frictional stress, the radial stress, and the debonding length of the fiber/matrix interface. In addition, the crack growth speed was found to depend proportionally on the loading frequency. This relationship, particularly at low frequencies, is interpreted in terms of the development of a crack tip closure induced by the relaxation of the compressive residual stresses developed in the matrix phase in regions ahead of the crack tip during the time-dependent loading process.     

界面改性对SiCp/Cu复合材料力学性能的影响

研究了界面改性对SiC颗粒增强Cu基复合材料力学性能和断裂机制的影响。结果表明：经过SiC颗粒表面涂层处理后，可在复合材料中获得干净、紧密的界面结合。通过复合材料界面优化，可在基体和增强物之间有效传递载荷，减少了拉伸变形时的界面脱粘，从而提高了复合材料的屈服强度、抗拉强度和断裂延伸率。     

Fatigue crack growth in Ti-matrix composites with spatially varied interfaces

Spatially varied interfaces (SVIs) is a design concept for composite materials where the interface mechanical properties are varied along the length and circumference of the fiber/matrix interface. These engineered interfaces can be used to modify critical titanium matrix composite properties such as transverse tensile strength and fatigue crack growth resistance in ways that produce a balanced set of properties. The SVI approach may also be used to probe interface failure mechanisms for the purpose of understanding complex mechanical phenomena. Single lamina Ti-6Al-4V matrix composites containing strongly bonded SiC fibers were fabricated both in the as-received condition and with a weak longitudinal stripe along the sides of the fibers. The striped SVI composites exhibited an increase in the overall fatigue crack growth life of the specimens compared to the unmodified specimens. This improvement was caused by an increased extent of debonding and crack bridging in SVI composites. This article is based on a presentation made in the symposium “Fatigue and Creep of Composite Materials” presented at the TMS Fall Meeting in Indianapolis, Indiana, September 14–18, 1997, under the auspices of the TMS/ASM Composite Materials Committee.     

Role of matrix/reinforcement interfaces in the fracture toughness of brittle materials toughened by ductile reinforcements

Crack interactions with ductile reinforcements, especially behavior of a crack tip at the interface, have been studied using MoSi₂ composites reinforced with Nb foils. Effects of fracture energy of interfaces on toughness of the composites have also been investigated. Variation of interfacial bonding was achieved by depositing an oxide coating or by the development of a reaction prod- uct layer between the reinforcement and matrix. Toughness was measured using bend tests on chevron-notched specimens. It has been established that as a crack interacts with a ductile re- inforcement, three mechanisms compcte: interfacial debonding, multiple matrix fracture, and direct crack propagation through the reinforcement. Decohesion length at the matrix/reinforcement interface depends on the predominant mechanism. Furthermore, the results add to the evidence that the extent to which interfacial bonding is conducive to toughness of the composites depends on the criterion used to describe the toughness and that ductility of the ductile reinforcement is also an important factor in controlling toughness of the composites. Loss of ductility of the ductile reinforcement due to inappropriate processing could result in little improvement in tough- ness of the composites.     

On the tensile properties of a fiber reinforced titanium matrix composite—II. Influence of notches and holes

The effects of holes and notches on the ultimate tensile strength of a unidirectionally reinforced titanium matrix composite have been examined. During tensile loading, a narrow plastic strip forms ahead of the notch or hole prior to fracture, similar to that observed in thin sheets of ductile metals. Examination of the fibers following dissolution of the matrix indicates that essentially all the fibers within such a strip are broken prior to catastrophic fracture of the composite. The trends in notch-strength have been rationalized using a fracture mechanics-based model, treating the plastic strip as a bridged crack. The observations suggest that the bridging traction law appropriate to this class of composite is comprised of two parts. In the first, the majority of fibers are unbroken and the bridging stress corresponds to the unnotched tensile strength of the composite; in the second, the fibers are broken and the bridging stress is governed by the yield stress of the matrix, with some contribution derived from fiber pullout. This behavior has been modeled by a two-level rectilinear bridging law. The parameters characterizing the bridging law have been measured and used to predict the notch strength of the composite. A variation on this scheme in which the fracture resistance is characterized by an intrinsic toughness in combination with a rectilinear bridging traction law has also been considered and found to be consistent with the predictions based on the two-level traction law.     

氧化铝基氧化物/氧化物复合材料的合成与评价

Al2O3 matrix oxide/oxide composites containing rod-like Ba-β-Al2O3 and equiaxed ZrO2 particles have been successfully synthesized by an in-situ process from a mixture of Al2O3 and BaZrO3 powders.The long-axis direction of rod-like Ba-β-Al2O3 phase is parallel to ,while the longitudinal interface between Ba-β-Al2O3 phase and Al2O3 matrix is parallel to(0001) of the Ba-β-Al2O3 phase.The mechanical properties of the composites,such as Vickers hardness and fracture toughness,are enhanced with increasing the sintering temperature.Furthermore,the presence of rod-like Ba-β-Al2O3 particles results in enhancement of fracture toughness of the in-situ synthesized composites due to crack deflection and crack bridging.