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.     

Combined Mode I–Mode II Fracture of 12-mol%-Ceria-Doped Tetragonal Zirconia Polycrystalline Ceramic

The mode I, mode II, and combined mode Imode II fracture behavior of ceria-doped tetragonal zirconia polycrystalline (Ce-TZP) ceramic was studied. The single-edge-precracked-beam (SEPB) samples were fractured using the asymmetric four-point-bend geometry. The ratio of mode I to mode II loading was varied by varying the degree of asymmetry in the four-point-bend geometry. The minimum strain energy density theory best described the mixed-mode fracture behavior of Ce-TZP with the mode I fracture toughness, K _IC= 8.2 ± 0.6 MPa·m^1/2, and the mode II fracture toughness, K_IIC= 8.6± 1.3 MPa·m^1/2.     

Mode II fracture mechanisms of PBT-modified brittle epoxies

Mode II fracture behavior of poly(butylene terephthalate) (PBT)-modified epoxy systems are studied. Two different types of testing for mode II fracture are conducted. One was to investigate the fracture behavior of bulk epoxy systems, in comparison with mode I fracture, using single-edge notched specimens under skew symmetric four-point loading. The other was to investigate the fracture behavior of epoxy layers sandwiched between aluminium adherends using compact shear specimens. The mode II fracture toughness obtained from the former for modified systems has been found to increase significantly over the control, although the increase of mode I fracture toughness for modified systems over the control is moderate. This finding is discussed in relation with cavitation and equivalent mode I stress intensity factor and also in comparison with rubber-modified epoxy systems in the literature to account for the increase. In addition, the difference in fracture morphology between mode I and II is discussed. Mode II fracture toughness obtained from the latter for modified systems has also been found to increase significantly over the control. Morphology of fracture surfaces relating to this finding is discussed. © 1998 John Wiley & Sons, Inc. J Appl Polym Sci 69: 405–415, 1998     

Mode I and mode II delamination of a chopped strand mat E-glass reinforced vinyl ester composite

The objective of the present work is to investigate mode I and mode II delamination behaviour of chopped strand mat (CSM) E-glass reinforced vinyl ester (VE) composite. Double cantilever beam and end notched flexure tests were carried out to evaluate the mode I and mode II delamination, respectively. The fracture toughnesses were calculated using the experimental calibration method. Results showed that the average mode I and mode II fracture toughnesses were 185 and 2386?N?m^?1, respectively. Furthermore, the mode II–mode I ratio for this material was 12.9. This value was the highest when compared with other composite materials from the literature. Finally, through scanning electron micrographs, the dominant failure mechanisms were found to be matrix cracking, fibre debonding and fibre breakage. In addition, shear cusps were observed in mode II specimen, which signified the shearing between the layers.     

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.     

Fracture toughness of polymers in shear mode

This paper presents a new test method that measures fracture toughness of polymeric materials when subjected to in-plane shear loading (mode II), and compares the toughness with that in tension mode (mode I). The new test method uses an Iosipescu device to apply the shear load, and determines the toughness based on the concept of essential work of fracture (EWF). Three physical-based criteria were used to verify the occurrence of mode II fracture. The new test method was then used to evaluate toughness of poly(acrylonitrile–butadiene–styrene) (ABS). The results suggest that for the ABS, the ratio of toughness in mode II to mode I is about 2.5 which leads to the dominance of mode I fracture in most loading conditions. The results also showed that for ABS in mode I fracture, the specific work of fracture (defined as the absorbed energy for fracture divided by the cross sectional area of the ligament between the notch tips) depends on ligament length; while in mode II fracture, it depends on ligament thickness. The study concludes that the new test method has a good potential for evaluation of mode II fracture toughness of polymers, though further study using polymers of different characteristics will be needed to confirm universality of the test method in the measurement of mode II fracture toughness.     

Interlaminar fracture toughness testing of composite mode I and mode II DCB specimens

A computer controlled test procedure for evaluating mode I and mode II interlaminar fracture behavior was used in experiments with eight different resin matrix/graphite fiber composites. Four analytical methods for calculating fracture toughness were compared. These included an energy rate determination of the J-integral, a compliance calibration procedure, equations based on linear beam bending, and an Area method calculation. Methods that account for nonlinear material behavior, such as the J-integral, were needed for characterizing the systems with high fracture toughness. The ratio of mode II to mode I fracture toughness ranged from 1.5 to 8.0, depending on the material system. Finally, preliminary work with a technique for constant strain rate testing of mode I DCB specimens is presented.     

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     

Effect of moisture on pure mode I and II fracture behaviour of composite bonded joints

The effect of moisture on the fracture properties of composite bonded joints under pure mode I and pure mode II was analysed in this work. The double cantilever beam and end notched flexure tests were used for mode I and mode II fracture characterisation, respectively. Three different moisture conditions (55% and 75% of relative humidity (RH) and immersion in distilled water (IW)) were tested to assess its influence on the fracture behaviour under both pure loading modes. It was verified that fracture energy is drastically affected for the immersion in water in both loading modes. A cohesive zone model was also used to estimate the influence of RH on the cohesive parameters defining the law that mimics accurately the fracture process for each case. It was concluded that alterations on the cohesive laws reflect an increase of material brittle behaviour with the increase of the moisture uptake.     

Fracture behavior of coated/uncoated graphite-epoxy composites

The static delamination behavior of graphite/epoxy composite specimens subjected to mode I tensile opening (using UDCB

1 Uniform double cantilever beam.

specimens), and pure mode II shear loading (using ENF

2 End-notched flexural.

specimens) were studied. The graphite epoxy composites for the study were made from commercially treated fibers, with and without an electropolymerized interlayer. The mode I fracture energy (G_IC) was found to be significantly higher (more than 50 percent) for the coated fibers. However, this improvement was accompanied by a high reduction (more than 3 times) in the mode II fracture energy (G_IIC). This effect is apparently related to poor adhesion between the interlayer and the epoxy resin, which may be corrected by use of a “top layer” of appropriate composition to form chemical bonds between the phases. The fracture toughness (K_IC) of composites made with commercially treated fibers was also evaluated, using double side-notched specimens.     

Fracture characterization of bonded joints using the dual actuator load apparatus

Mixed-mode I?+?II fracture characterization tests of steel-bonded joints were carried out with the dual actuator load apparatus using a previously developed data reduction scheme in order to obtain the fracture envelope. This test involves independent loading of the specimen arms of a clamped double cantilever beam, which allows for easy variation of the I?+?II mode mixity in fracture characterization through altering the applied displacement rates. Difficulties inherent to crack monitoring during its propagation and imperfections of initial crack manufacture are well managed with the proposed method. Three different cases corresponding to different mode mixities were tested. The experimental results revealed that a linear energetic criterion performs well in describing the fracture envelope of these bonded joints.     

An End-Loaded Shear Joint (ELSJ) Specimen to Measure the Critical Energy Release Rate in Mode II of Tough,Structural Adhesive Joints

This paper introduces a newly developed specimen type, which is used to measure the critical energy release rate of tough, structural adhesives loaded in shear. This End-Loaded Shear Joint (ELSJ) specimen is loaded until a shear crack propagates through the adhesive layer. When the crack propagation is stopped, by unloading the specimen, the critical energy release rate in mode II, G _IIc, can be obtained by correlating the energy dissipated during the test and the measured crack area on the fracture surface of the specimen. The paper presents the dimensions of the ELSJ specimen, the corresponding test setup and the evaluation method used to obtain G _IIc. An overview of the advantages and the limitations of the new specimen type shows the need for its development and improvement when compared to some state of the art experiments. The first results of ELSJ tests are shown and discussed, using the crash-optimized structural adhesive — Henkel Terokal 5077. The experimental results presented, focus on thin adhesive layers and quasi-static test velocities.     

Mode I and Mode II delamination resistance and mechanical properties of woven glass/epoxy–PU IPN composites

The effect of polyurethane on the mechanical properties and Mode I and Mode II interlaminar fracture toughness of glass/epoxy composites were studied. Polyurethanes (PU) synthesized using polyols and toluene diisocyanate were employed as modifier for epoxy resin by forming interpenetrating polymer network. The PU/Epoxy IPN was used as matrix material for GFRP. PU modified epoxy composite laminates having varying PU contents were prepared. The effect of PU content on the mechanical properties like interlaminar fracture toughness (Mode I, G_1c and Mode II, G_IIc), tensile strength, flexural strength, and Izod impact strength were studied. The morphological studies were conducted on the fractured surface of the composite specimen by scanning electron microscopy (SEM). Tensile strength, flexural strength, and impact strength of PU‐modified epoxy composite laminates were found to increase inline with interlaminar fracture toughness (G_1c and G_IIc) with increasing PU content to a certain limit and then it was found to decrease with increase in PU content. It was observed that toughening of epoxy with PU increases the Mode I and Mode II delamination toughness up to 17 and 120% higher than that of untoughened composite specimen, respectively. POLYM. COMPOS., 2008. © 2008 Society of Plastics Engineers     

A Rate-Dependent Cohesive Zone Model for Adhesively Bonded Joints Loaded in Mode I

The present work investigates the rate-dependent failure behaviour of structural adhesive joints loaded in mode I. Butt joint and tapered double cantilever beam (TDCB) specimens were tested at velocities ranging over more than six orders of magnitude. A rate-dependent extension of the bi-linear cohesive zone model is proposed and implemented into the finite element code LS-DYNA via an user-defined subroutine. The parameters for the implemented cohesive zone model are found directly by evaluation of experimental data. The comparison of simulations with experimental results for different specimen types and test velocities validates the proposed model. The critical energy release rate of adhesively bonded joints is usually measured in (tapered) double cantilever beam tests, and evaluated using the Irwin–Kies equation. In this paper a different evaluation method is proposed, which provides additional information on the energy dissipated during crack initiation. The results of this method agree with the results obtained using the Irwin–Kies equation. The investigations have focussed on thin adhesive layers. Parameter identification and validation have been performed using the crash-optimized adhesive Terokal 5077 from Henkel.     

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.     

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     

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.     

On the Use of Laminated Beams for the Determination of Pure and Mixed-Mode Fracture Properties of Structural Adhesives

The use of cracked laminated beam specimens is proposed for determining fracture properties of structural adhesives. Slight variations in specimen geometry and loading are used to produce pure mode I and II conditions as well as an intermediate mode-mix. Bounds are established for proper use of the specimens and mixed-mode fracture criteria are examined.     

On the effect of pulsed laser ablation on shear strength and mode I fracture toughness of Al/epoxy adhesive joints

The present work describes an experimental study about the shear strength and the mode I fracture toughness of adhesive joints with substrates pre-treated by pulsed laser ablation. An ytterbium-doped pulsed fiber laser was employed to perform laser irradiation on AA6082-T4 alloy. Morphological and chemical modifications were evaluated by means of surface profilometry, scanning electron microscopy (SEM) and X-ray photoelectron spectroscopy (XPS). Thick adherend shear tests were carried out in order to assess the shear strength while the mode I fracture toughness was determined using the double cantilever beam. For comparison, control samples were prepared using classical surface degreasing. The results indicated that laser ablation has a favorable effect on the mechanical behavior of epoxy bonded joints; however, while a + 20% increase was recorded for shear strength, a remarkable threefold enhancement of fracture toughness was observed with respect to control samples. XPS analyses of treated substrates and SEM observations of the fracture surfaces indicated that laser pre-treatment promoted chemical and morphological modifications able to sustain energy dissipation through mechanical interlocking. As a result cohesive failure within the adhesive bond-line was enabled under predominant peel loading.     

On the Use of Laminated Beams for the Determination of Pure and Mixed-Mode Fracture Properties of Structural Adhesives

The use of cracked laminated beam specimens is proposed for determining fracture properties of structural adhesives. Slight variations in specimen geometry and loading are used to produce pure mode I and II conditions as well as an intermediate mode-mix. Bounds are established for proper use of the specimens and mixed-mode fracture criteria are examined.