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.     

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.     

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

Fracture and subcritical crack-growth characteristics under combined Modes I and III loading were studied using the modified compact tension (CT) specimens of soda-lime glass. The combined mode load was applied to the specimen in the direction β with respect to the initial crack. By superposition of Mode III, the advancing crack begins to rotate at an angle Ψ to the initial crack plane, which nearly maximizes the Mode I stress intensity factor K _I(Ψ), and the crack continues to propagate in the same direction. In this case, unlike combined Modes I and II, the crack breaks into multiple partial fronts, and ligamentary bridging forms fracture lances when these segmented cracks are held together. The crack velocity d a /d t was plotted versus the maximum Mode I stress intensity factor K _I(Ψ) for combined Modes I and III loading. The d a /d t values are initially high, and the crack growth tends to be discontinuous compared with the result for pure Mode I. The subcritical crack growth seems to occur when the K _I value for the initial crack reaches a certain value. The d a /d t - K _I(Ψ) curves for combined Modes I and III lie roughly on the same curve as that for pure Mode I as the crack growth increases.     

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).     

Combined Mode I-Mode III Fracture of Fatigue-Precracked Alumina

The mixed-mode fracture behavior of (cyclic) fatigue pre-cracked ceramic specimens was studied in combined tension-torsion loading. Circumferentially notched cylindrical rods of polycrystalline alumina were precracked in uniaxiai cyclic compression to introduce a concentric mode I fatigue crack. Subsequently, the rods were quasi-statically fractured in pure tension, pure torsion, and various combinations of tensile and torsional stresses to obtain the mode I-mode III fracture envelope. The introduction of torsional loads promotes severe abrasion between the crack faces. The critical stress intensity factor for fracture initiation increases by a factor of °2.3 as the loading mode is changed from pure tension to pure torsion. Fracture surface tortuosity and abrasion "shield" the crack-tip from the far-field tensile and torsional loads to cause an apparent toughening effect. The mechanisms of mixed-mode fracture in alumina are examined and consequences of the breakdown of the similitude concept implicit in the nominal use of fracture mechanics are discussed.     

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.     

Subcritical Crack Growth in Soda–Lime Glass under Mixed-Mode Loading

Subcritical crack growth in glasses and ceramics has been studied extensively under Mode I loading. In this study, subcritical crack growth in soda–lime glass under mixed-mode loading has been determined, using the double cleavage drilled compression (DCDC) specimens with a hole offset from the center line. With this test configuration, cracks are nucleated at the pole of the hole and propagated parallel to the centerline of the specimen under mixed-mode loading. Under mixed-mode loading, subcritical-crack-growth rates are significantly less than those under Mode I loading at the same energy-release rates. Possible mechanisms for this increased resistance to subcritical crack growth under mixed-mode loading are discussed.     

Application of a new constant G load-jig to creep crack growth in adhesive joints

A novel constant energy release rate load-jig, capable of applying loads in the full range of mode mixes from pure mode I to pure mode II, was developed for studying creep crack growth in structural adhesive joints. Since the load-jig applies only pure bending moments to uniform double cantilever beam (DCB) specimens, the expressions for the energy release rate and mode ratio are both simple and accurate. The new load-jig was used to study mixed-mode creep crack growth in DCB specimens which had either an intact fillet or a steady-state failure zone. Both a rubber-toughened and a mineral-filled epoxy adhesive were tested at room temperature, which is far below the glass transition temperature for either structural adhesive. In all cases, crack speeds were observed to decelerate, indicating that the adhesive were self-toughening over time. In addition, crack growth was observed to propagate by the initiation and coalescence of microcracks, rather than by the continuous advancement of a crack tip.     

The mixed-mode fracture behavior of epoxy by the compact tension shear test

In this study, pure mode I, pure mode II and mixed mode fracture behavior of an epoxy were investigated. Specifically, the mixed mode values of fracture toughness and critical strain energy release rate (CSERR) were measured. Specimens were subjected to mixed mode loading using compact tension shear (CTS) test. Some experimental modifications were found to be necessary to eliminate rotation and ensure crack propagation at the notch when testing epoxy specimens at high mode II loading. A failure criterion for the mixed mode loading of polymer is developed and its predictions are compared with the experimental results. The crack propagation direction in epoxy was investigated in this research as well. A detailed study of failure mechanisms on the fracture surface was performed. The results indicate that the increase in the value of toughness can be directly related to the fracture morphology.     

Crack-Resistance Curves of Surface Cracks in Alumina

The resistance of coarse-grained alumina to stable crack growth, initiated from "naturally'occurring surface flaws, was studied in strength tests with a bend-bar technique. The surface cracks experienced R-curve behavior over the first few hundred micrometers; i.e., the applied crack driving force had to be increased with crack extension. Compared to R curves generated from long cracks in standard single-edge-notched-bend specimens, the surface-crack curves have lower initial values. The possible influence of localized residual stresses, counteracting the applied crack driving force, is discussed.     

Fracture Resistance and Stable Crack-Growth Behavior of 8-mol%-Yttria-Stabilized Zirconia

The crack-growth behavior of a yttria-stabilized zirconia ceramic (8 mol% of cubic-phase yttria) was studied at room temperature. Double-cantilever-beam specimens were loaded with pure bending moments in a specially designed loading fixture inside an environmental scanning electron microscope. Crack-growth data were obtained from truly sharp (arrested) cracks, bypassing interpretation problems that involve crack initiation from a machined notch. The crack-growth study was conducted over a range of applied energy-release rates that allowed crack arrest on one hand and fast fracture on the other. Three energy-release-rate values were relevant: initiation of crack growth (3.5 J/m²), crack arrest (2.8 J/m²), and fast fracture (8.0 J/m²). At the macroscopic scale, subcritical crack growth occurred as a continuous process. In situ observations revealed that, at the microscopic scale, crack growth occurred in small jumps. The fracture mode for stable crack growth was identified to be transgranular.     

Crack growth angle prediction of an internal crack under mixed mode load for unfilled elastomer using the strain energy density factor

This article investigates the prediction of the crack growth angle of an existing internal crack under mixed mode loading at the crack tip for an unfilled ethylene propylene diene terpolymer rubber (EPDM). For the realization of mixed mode loading, the cracks of the uniaxial loaded specimens were oriented with different angles to the loading direction. The energy density factor was used as a potential criterion for determining the crack growth angle. The determination of the strain energy density factor was carried out simulatively in Abaqus. The second-order Ogden model was used to describe the rubber-like material behavior. The relative local minimum of the strain energy density factor provides the possible growth angle. The experimental investigations show that the initial cracks grow orthogonally to the loading direction for the different crack orientation angles. For the crack orientation angle parallel to the load direction, the crack growth was observed because the strong stretching of the specimen caused strong necking in the crack region. The crack growth for the remaining crack orientation angles were induced due to shear loading at the crack tip. The predictive angle of different crack orientation angles shows very good accordance to the measured crack growth angles.     

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     

Mixed-Mode Fracture of Ceramics in Asymmetric Four-Point Bending: Effect of Crack-Face Grain Interlocking/Bridging

The mixed-mode fracture of a large-grain-size alumina ceramic and a soda-lime glass is investigated. These ceramics are tested using straight-through precracked or notched specimens. The straight-through precrack is introduced by the single-edge-precracked beam method. Precracked or notched specimens are subjected to combined mode I/II or pure mode II fracture, under asymmetric four-point bending, and pure mode I fracture, under symmetric four-point bending. A pure mode II fracture is never achieved in the precracked polycrystalline alumina by the crack-face friction inevitably induced by grain interlocking/bridging. The crack-face friction in sliding mode reduces the local mode II stress intensity factor in the crack-tip region and produces a sizable amount of mode I deformation. Accounting for the contribution of the crack-face friction to the crack-tip local stress intensity factors, K _I and K _II, in mixed-mode fracture tests, the experimental results of the K _I/ K _{I c} versus K _II/ K _{I c} envelope and the initial angle of noncoplanar crack extension are in good agreement with the theoretical predictions of the maximum hoop-stress theory.     

Cracking and Damage in a Notched Unidirectional Fiber-Reinforced Brittle Matrix Composite

Results of four-point bend tests on notched beams of a laminated unidirectional fiber-reinforced glass matrix composite are presented. The failure sequence has been established through in situ examination. The dominant damage mode is a mixed-mode, split crack that runs parallel to the predominant fiber directions. The crack interacts with and crosses over imperfectly aligned fibers. The resulting bridging tractions are sufficient to cause the critical strain energy release rate to increase substantially as the crack extends. Several other damage modes are also observed. These include mode I (tensile) matrix cracks bridged by fibers, mode II (shear) cracks, and compressive damage at the loading points.     

Mixed mode brittle fracture of sharp and blunt V-notches in polycrystalline graphite

Brittle fracture of polycrystalline graphite is studied experimentally and theoretically using Brazilian disk specimens containing sharp and rounded-tip V-notches subjected to different degrees of loading mixity, ranging from pure mode I to pure mode II. The main purpose is twofold. First, to provide a new set of experimental results on fracture of V-notched graphite samples, with different values of loading mixities, V-notch angles and notch radii, which may be helpful for researchers because enlarges the very scarce available data; and second, to provide a fracture criterion for polycrystalline graphite under the above-mentioned conditions. The averaged value of the strain energy density over a well-defined volume is used to predict the static strength of the considered specimens. Good agreement is found between the experimentally obtained fracture loads and the theoretical predictions based on the constancy of the mean strain energy density over the material volume.     

Crack Propagation in Polymer Adhesive/Glass Sandwich Specimens

Moisture-assisted crack growth in polymer adhesive/glass interfaces was measured as a function of the applied energy release rate, G, using a four-point flexure test coupled with an inverted microscope. The specimens consisted of two glass plates bonded together with an epoxy or an epoxy-acrylate adhesive. It was found that cracks formed and grew on both interfaces if the glass surfaces were both smooth; however, roughening the surface of one of the glass plates increased the fracture resistance of the interface sufficiently so that crack growth occurred only on the remaining “smooth” interface (top or bottom). Finite element analysis was used to determine the G and ψ (phase angle) appropriate for the different crack geometries. It was found experimentally that crack growth rates for all crack geometries depended on the applied G via a power law relationship and that for a given applied G, crack growth rates were sensitive to the crack geometry. The results indicate that the primary driving force for moisture-assisted crack growth at a polymer/glass interface is the applied G at the crack tip and that the effect of the phase angle for the different crack geometries (13° to 54°) is negligible.     

Experimental and numerical investigations of crack face adhesive bonding effect on the mixed-mode fracture strength of PMMA

Experimental and numerical investigations have been conducted to evaluate the effect of adhesive bonding of crack surfaces on the mixed-mode (I and II) fracture strength and effective stress intensity geometry/loading factor of a plate with an edge crack. The experimental tests were carried out on five batches of simple edge crack and specimens in which adhesive bonding was used on crack faces at different distances from the crack tip. The cracked specimens made from poly methyl-methacrylate rectangular plates. The specimens’ fracture strength was obtained by employing a tensile testing machine at different loading angles using a modified Arcan fixture. In the numerical part, finite element simulations were used to model the test specimens and thereby establishing their stress intensity geometry/loading factors. The results show that the adhesive bonding of the crack surfaces has a significant effect on reducing the equivalent mixed-mode stress intensity factor for all loading angles. The bonded specimens show considerable fracture force enhancement compared to the simple edge crack specimens.     

Quantitative fractography of mixed mode fracture in glass and ceramics

Many ceramic structural applications involve a combination of tensile (mode I) and shear (mode II) loading conditions. Quantitative fractography was performed on monolithic and R-curve materials. Soda-lime-silica glass was selected as the monolithic material. A mica glass ceramic was selected to represent R-curve materials. Mixed-mode fracture surfaces in both materials were characterized by an absence of the mist region. For the mica glass ceramic, crack-to-mirror size ratios were found to be a function of the crack length and mode mixity. Hackle markings on mixed-mode fracture surfaces appear as lances and differ from those observed on surfaces failed in pure Mode I. Atomic force microscopy showed that the features in different regions on the mixed-mode fracture surfaces are similar and differ only by scale. The practical implications of these observations are that forensic analyses can be used without a priori knowledge of the loading conditions.