Mixed-Mode Fracture Toughness of Ceramic Materials

An experimental technique whereby pure mode I, mode II, and combined mode I-mode II fracture toughness values of ceramic materials can be determined using four-point bend specimens containing sharp, through-thickness precracks is discussed. In this method, notched and fatigue-precracked specimens of brittle solids are subjected to combined mode I-mode II and pure mode II fracture under asymmetric four-point bend loading and to pure mode I under symmetric bend loading. A detailed finite element analysis of the test specimen is performed to obtain stress intensity factor calibrations for a wide range of loading states. The effectiveness of this method to provide reproducible combined mode I-mode II fracture toughness values is demonstrated with experimental results obtained for a polycrystalline Al₂O₃. Multiaxial fracture mechanics of the Al₂O₃ ceramic in combined modes I, II, and III are also described in conjunction with the recent experimental study of Suresh and Tschegg (1987). While the mode II fracture toughness of the alumina ceramic is comparable to the mode I fracture toughness K _Ic, the mode III fracture initiation toughness is 2.3 times higher than K _Ic. The predictions of fracture toughness and crack path based on various mixed-mode fracture theories are critically examined in the context of experimental observations, and possible effects of fracture abrasion on the apparent mixed-mode fracture resistance are highlighted. The significance and implications of the experimental methods used in this study are evaluated in the light of available techniques for multiaxial fracture testing of brittle solids.     

Experimental and numerical investigation of fracture of ABS polymeric material for different sample's thickness using a new loading device

The fracture behavior of ABS (acrylonitrile butadiene styrene) polymeric material has been investigated under the full range of in‐plane loading conditions using a new loading device to obtain more reliable results. Loading conditions from pure mode‐I through various mixed‐mode I/II ratios up to pure mode‐II have been generated using the proposed new loading device for the same specimen geometry. From the experimentally measured critical loads, the mode‐I, mode‐II, and the various mixed‐mode I/II critical energy release rates have been determined at different loading angles from 0° to 90°. Using the FE results, nondimensional stress intensity factors were applied to the specimen. The primary objectives of this study were to develop a new loading device to determine the mixed‐mode fracture toughness K_IC and K_IIC of ABS polymeric material. Another goal was to obtain stress intensity and strain energy release rates solutions associated with the crack, and to examine effects of thickness and geometric variables, particularly under mixed‐mode loading conditions. It was found that the thickness of the 10 mm specimen satisfied the plane strain condition with average fracture toughness ≈4.32 MPa·m^1/2 under pure mode‐I loading and ≈1.42 MPa·m^1/2 for pure mode‐II loading. POLYM. ENG. SCI., 54:2086–2096, 2014. © 2013 Society of Plastics Engineers     

Crack Path Selection in Adhesively-Bonded Joints: The Role of Material Properties

This paper investigates the role of material properties on crack path selection in adhesively bonded joints. First, a parametric study of directionally unstable crack propagation in adhesively-bonded double cantilever beam specimens (DCB) is presented. The results indicate that the characteristic length of directionally unstable cracks varies with the Dundurs' parameters characterizing the material mismatch. Second, the effect of interface properties on crack path selection is investigated. DCB specimens with substrates treated using various surface preparation methods are tested under mixed mode fracture loading to determine the effect of interface properties on the locus of failure. As indicated by the post-failure analyses, debonding tends to be more interfacial as the mode II fracture component in the loading increases. On the other hand, failures in specimens prepared with more advanced surface preparation techniques appear more cohesive for given loading conditions. Using a high-speed camera to monitor the fracture sequence, DCB specimens are tested quasi-statically and the XPS analyses conducted on the failure surfaces indicate that the effect of crack propagation rate on the locus of failure is less significant when more advanced surface preparation techniques are used. The effect of asymmetric interface property on the behavior of directionally unstable crack propagation in adhesive bonds is also investigated. Geometrically-symmetric DCB specimens with asymmetric surface pretreatments are prepared and tested under low-speed impact. As indicated by Auger depth profile results, the centerline of the crack trajectory shifts slightly toward the interface with poor adhesion due to the asymmetric interface properties. Third, through varying the rubber content in the adhesive, DCB specimens with various fracture toughnesses are prepared and tested. An examination of the failure surfaces reveals that directionally unstable crack propagation is more unlikely to occur as the toughness of the adhesive increases, which is consistent with the analytical predictions that were discussed using an energy balance model.     

Crack Path Selection in Adhesively-Bonded Joints: The Role of Material Properties

This paper investigates the role of material properties on crack path selection in adhesively bonded joints. First, a parametric study of directionally unstable crack propagation in adhesively-bonded double cantilever beam specimens (DCB) is presented. The results indicate that the characteristic length of directionally unstable cracks varies with the Dundurs' parameters characterizing the material mismatch. Second, the effect of interface properties on crack path selection is investigated. DCB specimens with substrates treated using various surface preparation methods are tested under mixed mode fracture loading to determine the effect of interface properties on the locus of failure. As indicated by the post-failure analyses, debonding tends to be more interfacial as the mode II fracture component in the loading increases. On the other hand, failures in specimens prepared with more advanced surface preparation techniques appear more cohesive for given loading conditions. Using a high-speed camera to monitor the fracture sequence, DCB specimens are tested quasi-statically and the XPS analyses conducted on the failure surfaces indicate that the effect of crack propagation rate on the locus of failure is less significant when more advanced surface preparation techniques are used. The effect of asymmetric interface property on the behavior of directionally unstable crack propagation in adhesive bonds is also investigated. Geometrically-symmetric DCB specimens with asymmetric surface pretreatments are prepared and tested under low-speed impact. As indicated by Auger depth profile results, the centerline of the crack trajectory shifts slightly toward the interface with poor adhesion due to the asymmetric interface properties. Third, through varying the rubber content in the adhesive, DCB specimens with various fracture toughnesses are prepared and tested. An examination of the failure surfaces reveals that directionally unstable crack propagation is more unlikely to occur as the toughness of the adhesive increases, which is consistent with the analytical predictions that were discussed using an energy balance model.     

Measurement of Mode I and Mode II Fracture Properties of Wood-Bonded Joints

In this work, the fracture characterisation of wood-bonded joints under pure mode I and mode II loading was performed. The tested material was maritime pine (Pinus pinaster Ait.) bonded with an epoxy adhesive. Two fracture mechanical tests were chosen: the double cantilever beam (DCB) for opening mode I loading, and the end-notched flexure (ENF) for sliding mode II loading. The compliance-based beam method (CBBM) was used for both mode I and mode II fracture, since the Resistance-curves can be obtained directly from the global mechanical response of the specimens (load–displacement curve), without crack monitoring during propagation. This data reduction scheme was validated by direct comparison with the modified experimental compliance method (MECM).     

Fracture Toughness of Polycrystalline Ceramics in Combined Mode I and Mode II Loading

Fracture of Polycrystalline alumina and zirconia ceramics in combined mode I and mode II loading was studied using precracked disk specimens in diametral compression. Fracture toughness was assessed in different stress states (including pure mode I, combined mode I and mode II, and pure mode II) by aligning the center crack at specific angles relative to the loading diameter. The resulting mixed-mode fracture-toughness envelope showed significant deviation to higher fracture toughness in mode II relative to the predictions of the linear elastic fracture mechanics theory. Critical comparison with corresponding results on soda–lime glass and fracture-surface observations showed that crack-surface resistances arising from grain interlocking and abrasion were the main sources of the increased fracture resistance in mode II loading of the polycrystalline ceramics. Quantitative fractography confirmed an increased percentage of transgranular fracture of the grains in mode II loading.     

Crack propagation analysis in composite bonded joints under mixed-mode (I+II) static and fatigue loading: experimental investigation and phenomenological modelling

This paper illustrates the results of an extensive experimental investigation on composite bonded joints under mixed-mode (I+II) static and cyclic loading conditions oriented to understand the influence of the mode mixity condition on the crack propagation resistance at the bondline. The double cantilever beam (DCB), end notch flexure (ENF) and mixed-mode bending (MMB) tests were conducted on pre-cracked samples and both fracture toughness and crack propagation resistance were seen to increase, both for static and fatigue loading, respectively, as the mode II contribution increases. The crack propagation and damage evolution were carefully investigated and documented, and a strong dependence of the propagation mode on the mode mixity was found. Fatigue data under the different loading conditions are then described by a phenomenological model based on the strain energy release rate contributions, which represents a useful engineering tool for preliminary design. After that a damage-based model, developed on the basis of the actual damage mechanisms, is presented in a companion paper.     

Temperature dependence and fracture criterion of mixed mode I/II fracture toughness of phenolic resin for friction material

In this study, the temperature dependence of the mixed‐mode fracture toughness of the phenolic resin for friction materials is investigated. For pure mode I, the fracture toughness decreases as the temperature increases, and it increases again after showing its minimum value. For pure mode II, the fracture toughness shows a similar trend but has its minimum value at a higher temperature. The temperature dependence of the mixed‐mode fracture toughness varies depending on the mode mixity, which is attributed to the different sensitivity to the relaxation phenomenon. At room temperature, as the fracture toughness for pure mode I and II are almost the same, the fracture locus shows a circular arc. At elevated temperatures, the locus becomes smaller and noncircular. At high temperature, the fracture locus shows an elliptical arc, where the fracture toughness for pure mode II is smaller than that for mode I. An empirical fracture criterion based on the time‐temperature dependence of the resin is proposed, and the proposed method successfully predicts the fracture toughness under various conditions of the temperature, time, and mode mixity. The crack initiation angles, on the other hand, are almost consistent regardless of the temperature, which agree with the maximum hoop stress theory. © 2011 Wiley Periodicals, Inc. J Appl Polym Sci, 2011     

Fracture and Subcritical Crack Growth in Soda-Lime Glass under Combined Modes I and II Loading

Fracture and subcritical crack growth characteristics under combined modes I and II loading were studied using the compact tension shear specimens of soda–lime glass. The maximum normal stress criterion gives a good agreement with the experimental mode I–mode II fracture toughness envelope for initially straight cracks and kinked cracks. Subcritical crack growth characteristics were determined under sustained modes I and II loading in water. The values of K _I and K _II were calculated approximately by replacing the subcritical kinked crack with an assumed straight crack ā, and the K _Imax value based on the maximum normal stress criterion was used to describe this subcritical kinked crack growth. The experimental results show that subcritical crack growth under pure mode I, pure mode II, and various combined modes I and II loading can be well described by the K _Imax value based on the approximate maximum normal stress criterion.     

Comparison of fracture behavior between acrylic and epoxy adhesives

An experimental study was conducted on the strength of adhesively bonded steel joints, prepared epoxy and acrylic adhesives. At first, to obtain strength characteristics of these adhesives under uniform stress distributions in the adhesive layer, tensile tests for butt, scarf and torsional test for butt joints with thin-wall tube were conducted. Based on the above strength data, the fracture envelope in the normal stress-shear stress plane for the acrylic adhesive was compared with that for the epoxy adhesive. Furthermore, for the epoxy and acrylic adhesives, the effect of stress triaxiality parameter on the failure stress was also investigated. From those comparison, it was found that the effect of stress tri-axiality in the adhesive layer on the joint strength with the epoxy adhesive differed from that with the acrylic adhesive. Fracture toughness tests were then conducted under mode l loading using double cantilever beam (DCB) specimens with the epoxy and acrylic adhesives. The results of the fracture toughness tests revealed continuous crack propagation for the acrylic adhesive, whereas stick-slip type propagation for the epoxy one. Finally, lap shear tests were conducted using lap joints bonded by the epoxy and acrylic adhesives with several lap lengths. The results of the lap shear tests indicated that the shear strength with the epoxy adhesive rapidly decreases with increasing lap length, whereas the shear strength with the acrylic adhesive decreases gently with increasing the lap length.     

Fatigue delamination,initiation, and growth,under mode I and II of fracture in a carbon‐fiber epoxy composite

In this article, interlaminar crack initiation and propagation under mode I and II dynamic loading of an epoxy matrix reinforced with unidirectional carbon fibers were evaluated. Delamination in mode I was carried out employing the DCB test (Double Cantilever Beam). In mode II, the ENF test (End Notched Flexure) was used. The fracture toughness in mode I was obtained using the methods of the ASTM D5528 Standard, whereas in mode II, the methods were applied in accordance with the ESIS (European Structural Integrity Society) Protocol. Employing this experimental program, the fatigue curves (ΔG,N) and growth rate curves (ΔG, da/dN) in both fracture modes were determined for an asymmetry ratio R = 0.2. The influence of the manufacturing process of the material on its behavior with respect to crack growth onset may be deduced from the experimental results, mainly the presence of resin bags. Moreover, as the crack growth rate decreases for large crack lengths, crack growth may even cease if the critical fracture energy does not increase above the values obtained in the static characterization of the material. POLYM. COMPOS., 2010. © 2009 Society of Plastics Engineers     

Subcritical Crack Growth in Soda-Lime Glass in Combined Mode I and Mode II Loading

Subcritical crack growth under mixed-mode loading was studied in soda-lime glass. Pure mode I, combined mode I and mode II, and pure mode II loadings were achieved in precracked disk specimens by loading in diametral compression at selected angles with respect to the symmetric radial crack. Crack growth was monitored by measuring the resistance changes in a microcircuit grid consisting of parallel, electrically conducting grid lines deposited on the surface of the disk specimens by photolithography. Subcritical crack growth rates in pure mode I, pure mode II, and combined mode I and mode II loading could be described by an exponential relationship between crack growth rate and an effective crack driving force derived from a mode I-mode II fracture toughness envelope. The effective crack driving force was based on an empirical representation of the non-coplanar strain energy release rate. Stress intensities for kinked cracks were assessed using the method of caustics and an initial decrease and a subsequent increase in the subcritical crack growth rates of kinked cracks were shown to correlate with the variations of the mode I and the mode II stress intensities.     

Temperature and Loading Rate Effects on the Fracture Behaviour of Adhesively Bonded GFRP Nylon-6,6

The combined effect of varying test temperature and loading rate on the Mode II fracture toughness of plasma-treated GFRP Nylon-6,6 composites bonded using a silica-reinforced epoxy adhesive has been studied. End notch flexure tests have shown that the adhesive system used in this study offers a wide range of fracture energies that are extremely sensitive to changes in temperature and loading rate. Increasing the test temperature resulted in a substantial reduction in the Mode II fracture toughness of the adhesive, with the value of G_IIc at 60°C being approximately one-half of the room temperature value. In contrast, increasing the crosshead displacement rate at a given temperature has been shown to increase the value of G_IIc by up to 250%. Compression tests performed on bulk adhesive specimens revealed similar trends in the value of [sgrave]_y with temperature and loading rate. In addition, it was found that the plasma treatment employed in this study resulted in stable crack propagation through the adhesive layer under all testing conditions.

A more detailed understanding of the effect of varying temperature and loading rate on the failure mechanisms occurring at the crack tip was achieved using the double end notch flexure (DENF) geometry, which was considered in tandem with the fracture surface morphologies. Here, changes in the degree of matrix shear yielding and particle-matrix debonding were used to explain the trends in [sgrave]_y and G_IIc.     

Controlled energy dissipation in fibrous composites. II: Microscopic failure mechanisms

Mechanical properties and microscopic fracture mechanisms of continuous fiber reinforced polymer composites were investigated. Perforated polyimide films (e.g. Kapton®) were added between composite prepreg layers to modify the interlaminar bonding strength. Addition of highly perforated films can increase the toughness of unidirectional glass/epoxy composites without an appreciable reduction in strength. The fibrous composites studied exhibit two fracture modes (compressive and tensile) when failed by three-point bending. In general, the compressive failure mode preceded the tensile failure mode. Real-time acoustic emission (AE) analysis was found to provide more fracture information which is otherwise not discernible from mechanical testing alone. The crack initiation stress level and the subsequent crack propagation mode were identified by real-time AE during deformation and by post-failure scanning electron microscopy fracture surface analysis.     

Analysis of cohesive failure in adhesively bonded joints with the SSPH meshless method

Adhesives have become the method of choice for many structural joining applications. Therefore, there is a need for improved understanding of adhesive joint performance, especially their failure, under a variety of loading conditions. Various numerical methods have been proposed to predict the failure of adhesive bonded material systems. These methods generally use a cohesive zone model (CZM) to analyze crack initiation and failure loci. The CZM incorporates a traction–separation law which relates the jump in surface tractions with the jump in displacements of abutting nodes of the cohesive segment; the area under the curve relating these jumps equals the energy release rate which is determined from experimental data. Values of parameters in the CZM are usually obtained through the comparison of results of numerical simulations with the experimental data for pure mode I and mode II deformations. Here a numerical approach to simulate crack initiation and propagation has been developed by implementing CZM in the meshless method using the symmetric smoothed particle hydrodynamics (SSPH) basis functions, and using the design of experiments technique to find optimal values of CZM parameters for mode I failure. Unlike in the finite element method where a crack generally follows a path between element boundaries, in the meshless method a crack can follow the path dictated by the physics of the problem. The numerical technique has been used to study the initiation and propagation of a crack in a double cantilever beam under mode I and mixed mode in-plane loadings. Computed results are found to agree well with the corresponding experimental findings. Significant contributions of the work include the determination of optimum values of CZM parameters, and simulating mode I, mode II and mixed mode failures using a meshless method with the SSPH basis functions.     

Interlaminar fracture toughness of a plain weave flax/epoxy composite

ABSTRACT

In recent decades, flax fibre has become a popular natural resource as reinforcement in polymeric composites. However, the pure mode characterisation of flax fibre composites is rather limited. Furthermore, the mixed-mode delamination is not yet available. Nevertheless, delamination behaviour is important to be characterised as it is a major problem in composite laminates. This study examined the delamination behaviour of a woven flax/epoxy composite. Specimens were tested using mode I double cantilever beam, mode II end-notched flexure and mixed-mode I+II single leg bending tests. Results showed that the mode I, mode II and mixed-mode I+II fracture toughness were 363.23, 962.17 and 649.06?N?m^?1, respectively. When the fracture toughness values were fitted using Benzeggagh–Kenane criterion, it was found that the best-fit material parameter η was attained at 0.88. This information is useful to estimate the variation of fracture toughness with the mode ratio. Finally, through scanning electron micrographs, it was noticed that fibre/matrix debonding was the major fracture mechanism in all loading modes. In conclusion, the findings from this study suggested that the composite was suitable to be used for structural applications under mixed-mode loading.     

Temperature and loading rate effects in the mode II interlaminar fracture behavior of carbon fiber reinforced PEEK

The combined effect of varying loading rate and test temperature on the mode II interlaminar fracture properties of AS4/carbon fiber reinforced PEEK has been investigated. End notch flexure tests have shown that this thermoplastic‐based composite system offers a very high value of interlaminar fracture toughness at room temperature. Increasing the test temperature leads to a reduction in the mode II interlaminar fracture toughness of the composite, with the value at 150°C being approximately one half of the room temperature value. In contrast, increasing the crosshead displacement rate has been shown to increase the value of G_IIc by up to 25%. A more detailed understanding of the effect of varying temperature and loading rate on the failure mechanisms occurring at the crack tip of these interlaminar fracture specimens has been achieved using the double end notch flexure (DENF) geometry. Here, extensive plastic flow within the crack tip region was observed in all specimens. It is believed that the rate sensitivity of G_IIc reflects the rate‐dependent characteristics of the thermoplastic resin.     

Fracture toughness characterization of phenolic resin and its composite

The aim of this study is to determine the fracture toughness of phenolic resin and its composite. Fracture tests on phenolic resin resulted in a fracture toughness close to values quoted for unmodified epoxy resins. Composite specimens of glass fiber reinforced phenolic were also tested. The interlaminar fracture toughness in both mode I and mode II failures was determined. The mode I initiation values were lower than the neat resin's toughness. Mode I propagation values were strongly influenced by fiber bridging. The mechanism of fiber bridging was found to be sensitive to specimen dimensions. The effect of fiber bridging on the mode I analysis is discussed. Fiber bridging was also evident in mode II failures. Two different geometries were used for the mode II tests (end loaded split and end notched flexure); a correlation between the results from the two geometries is made.     

Effects of carbon nanofiller functionalization and distribution on interlaminar fracture toughness of multi-scale reinforced polymer composites

Carbon nanofillers with different surface functional groups and aspect ratios, including carboxyl carbon nanotubes, un-functionalized carbon nanofibers (CNFs), glycidyloxypropyl-trimethoxysilane carbon nanotubes (GPS-CNTs) and nanofibers were evaluated for their potential for increasing the interlaminar fracture toughness of an S2-glass fiber/epoxy composite. The fillers were added in the matrix of the fiber reinforced plies, in the resin interlayer between plies, or in both regions. Comparisons were made based on mode I and mode II interlaminar fracture toughness. For composites made with CNTs dispersed in the matrix, fracture toughness was largely unaffected except for a slight increase seen with long GPS-CNTs. However, adding a CNF or CNT modified resin interlayer significantly increased the fracture toughness, with the highest improvement over the baseline material achieved by adding long GPS-CNTs in the interlayer (79% and 91% for mode I and mode II onset toughness, respectively). Important material parameters identified for improving interlaminar fracture toughness are the nanofiller aspect ratio and concentration at the fracture plane. Based on microscopic evaluations of the fracture surfaces, a high density of high aspect ratio nanofillers causes the best entanglement between the filler and glass fibers and effectively obstructs interlaminar crack propagation.     

Effects of rubber‐rich domains and the rubber‐plasticized matrix on the fracture behavior of liquid rubber‐modified araldite‐F epoxies

The fracture behavior of a bisphenol A diglycidylether (DGEBA) epoxy, Araldite F, modified using carboxyl‐terminated copolymer of butadiene and acrylonitrile (CTBN) rubber up to 30 wt%, is studied at various crosshead rates. Fracture toughness, K_IC, measured using compact tension (CT) specimens, is significantly improved by adding rubber to the pure epoxy. Dynamic mechanical analysis (DMA) was applied to analyze dissolution behavior of the epoxy resin and rubber, and their effects on the fracture toughness and toughening mechanisms of the modified epoxies were investigated. Scanning electron microscopy (SEM) observation and DMA results show that epoxy resides in rubber‐rich domains and the structure of the rubber‐rich domains changes with variation of the rubber content. Existence of an optimum rubber content for toughening the epoxy resin is ascribed to coherent contributions from the epoxy‐residing dispersed rubber phase and the rubber‐dissolved epoxy continuous phase. No rubber cavitation in the fracture process is found, the absence of which is explained as a result of dissolution of the epoxy resin into the rubber phase domains, which has a negative effect on the improvement of fracture toughness of the materials. Plastic deformation banding at the front of precrack tip, formed as a result of stable crack propagation, is identified as the major toughening process.