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.     

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 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.     

Subcritical Crack-Growth Behavior of Borosilicate Glass under Cyclic Loads: Evidence of a Mechanical Fatigue Effect

Amorphous glasses are generally considered immune to mechanical fatigue effects associated with cyclic loading. In this study surprising new evidence is presented for a mechanical fatigue effect in borosilicate glass, in both moist air and dry nitrogen environments. The fatigue effect occurs at near threshold subcritical crack-growth rates (da/dt 3× 10^-8 m/s) as the crack extension per cycle approaches the dimensions of the borosilicate glass network. While subcritical crack growth under cyclic loads at higher load levels is entirely consistent with environmentally assisted crack growth, lower growth rates actually exceed those measured under monotonic loads. This suggests a mechanical fatigue effect which accelerates subcritical crack-growth rates. Likely mechanisms for the mechanical fatigue effect are presented.     

Fatigue Crack Propagation in Transformation-Toughened Zirconia Ceramic

Fatigue crack propagation under tension-tension loading is observed in a transformation-toughened partially stabilized zirconia (PSZ) ceramic containing 9 mol% MgO. Such subcritical crack growth behavior is demonstrated to be cyclically induced, based on a comparison with behavior under sustained loading (at the maximum load in the fatigue cycle) and at varying cyclic frequencies. Crack extension rates, which are measured as a function of the cyclic stress intensity range ΔK over the range 10^-10 to 10^-6 m/cycle, are found to be load ratio dependent and to show evidence of fatigue crack closure, similar to behavior in metals. Cyclic crack growth rates are observed at ΔK levels as low as 3 MPa m^1/2 and are typically many orders of magnitude faster than reported data on environmentally assisted, subcritical crack growth in PSZ under sustained-load conditions.     

Rate effects for mixed-mode fracture of plastically-deforming,adhesively-bonded structures

Mixed-mode fracture of an adhesively-bonded structure made from a commercial adhesive and a dual-phase steel has been studied under different rates. Since mixed-mode fracture occurs along the interface between the steel and the adhesive, the cohesive parameters for the interface were required. The mode-II interfacial properties were deduced in earlier work. In this paper the mode-I interfacial toughness and the mode-I interfacial strength were determined at different rates. The mode-I interfacial strength was not affected by rate up to crack velocities at levels associated with impact conditions, and was essentially identical to the cohesive strength appropriate for crack growth within the adhesive layer. The mode-I toughness was reduced by about 40% when the crack propagated along the interface rather than within the adhesive. Furthermore, transitions to a brittle mode of failure occurred in a stochastic fashion, and were associated with a drop in interfacial toughness by a factor of about five. The mode-I interfacial parameters were combined with the previously-determined mode-II interfacial parameters within a cohesive-zone model to analyze the mixed-mode fracture of the joints which exhibited both quasi-static and unstable fracture. The mixed-mode model and the associated cohesive parameters for both quasi-static and unstable crack propagation provide bounds for predicting the behavior of the bonded joints under various rates of loading, up to the impact conditions that could be appropriate for automotive design.     

High-Temperature Crack Growth in Monolithic and SiCw-Reinforced Silicon Nitride under Static and Cyclic Loads

Experimental results are presented on subcritical crack growth under sustained and cyclic loads in a HIPed Si₃N₄ at 1450°C and a hot–pressed Si₃N₄–10 vol% SiC_w composite in the temperature range 1300°–1400°C. Static and cyclic crack growth rates are obtained from the threshold for the onset of stable fracture with different cyclic frequencies and load ratios. Fatigue crack growth rates for both the monolithic and SiC_w-reinforced Si₃N₄ are generally higher than the crack growth velocities predicted using static crack growth data. However, the threshold stress intensity factor ranges for the onset of crack growth are always higher under cyclic loads than for sustained load fracture. Electron microscopy of crack wake contact and crack–tip damage illustrate the mechanisms of subcritical crack growth under static and cyclic loading. Critical experiments have been conducted systematically to measure the fracture initiation toughness at room temperature, after advancing the crack subcritically by a controlled amount under static or cyclic loads at elevated temperatures. Results of these experiments quantify the extent of degradation in crack–wake bridging due to cyclically varying loads. The effects of preexisting glass phase on elevated temperature fatigue and fracture are examined, and the creep crack growth behavior of Si₃N₄–based ceramics is compared with that of oxide-based ceramics.     

Mixed-mode fracture behaviour of refractories with asymmetric wedge splitting test. Part II: Experimental case study

The asymmetric wedge splitting test for performing mixed-mode loading and its numerical evaluation has been presented in a companion paper (Part I). In this work (Part II), the influences of various levels of mode II loading on damage behaviour of refractories with different brittleness were experimentally investigated by comparing mode I and mixed-mode fractures under symmetric and asymmetric wedge splitting loading with seven different wedge angles. The digital image correlation technique was also used for strain maps visualization as well as the deformation parameters acquisition.With the increase of asymmetric wedge angle, the fracture behaviour becomes unstable what is associated with steeper load-displacement curves, more instantaneous energy release and restrained fracture process zone development. The in-plane shear loading contributes to the accelerated extension of the crack tip and its deviation from central plane. Meanwhile, the co-existing local shear stresses caused by the refractory's heterogeneity lead to crack path deflection as well.     

Micromechanisms of interlaminar fracture and fatigue

The interlaminar fracture and fatigue properties of AS/3501-;6 graphite/epoxy are discussed from a mechanistic point of view. Particular emphasis is placed on the interaction between the loading mode and the local geometry of the interlaminar zone and on how this affects the stresses close to the crack tip and the resulting failure path. Delamination growth under Mode I loading is shown to depend on the likelihood of fiber bridging occurring and on how effective these bridged fibers are at diverting strain energy away from the crack tip. The Mode II behavior is controlled by both the work required to shear the fibers from the matrix and the ease with which tensile failure of the matrix between the fibers can occur.     

Improved Analytical Models for Mixed-Mode Bending Tests of Adhesively Bonded Joints

In this paper, improved analytical models have been developed for more accurate determination of mode I and mode II compliances and strain energy release rates of adhesively bonded Double Cantilever Beam (DCB) type specimens. In these models, the effects of adhesive layer, elastic foundation and shearing deformation ahead of the crack tip due to the Saint-Venant end effect were considered. The improved analytical models were verified using finite element analysis (FEA), and excellent agreements were found for a variety of crack lengths. The comparisons of the measured and predicted testing machine loading point compliances with crack length at three different mixed-mode loading conditions for the adhesive layer thickness of 0.254 mm were also performed for further validation. In addition, contributions to the total mode I strain energy release rate from each effect are summarized.     

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.     

Stress Corrosion Cracking in a Unidirectional Ceramic-Matrix Composite

A study of matrix cracking in a unidirectional ceramic-matrix composite under static loading conditions has been conducted. The evolution of crack density with time has been measured using both flexure and uniaxial tension tests. Subcritical cracking has been observed at stresses below that required to develop matrix cracks in short-duration, monotonic loading tests. Furthermore, a relatively high final crack density has been observed following extended periods (∼10⁶ s) under static load. A fracture mechanics analysis applicable to subcritical crack growth has been developed and used successfully to model the evolution of matrix cracking with time and applied stress. The model incorporates the properties of the matrix, fibers, and interfaces, as well as the residual stress and the initial flaw distribution in the matrix.     

Indentation Crack-Shape Evolution during Subcritical Crack Growth

Indentation crack-shape evolution during subcritical crack growth was examined in soda-lime glass. Crack-arrest markings were generated on the fracture surfaces by temporary unloading during subcritical crack growth. Crack shapes were determined from these crack-arrest markings by optical microscopy. The shapes were found to be semielliptical, but the ellipticity changed significantly with crack extension under an applied bending stress. Crack-shape evolution was predicted by using the stress intensity factor equation for a semielliptical crack for the applied stress distribution and the subcritical crack growth parameters for the material/environment system. Experimental results were found to be in excellent agreement with the predictions. The influence of the initial crack size and shape, the loading configuration, and the subcritical crack growth exponent n on crack-shape evolution was also investigated in the simulations. It was found that, for the particular loading configuration and material, there is an equilibrium shape associated with the subcritically growing crack. The variation in crack shape with its extension during subcritical crack growth was found to be an important factor in lifetime prediction.     

Analysis of an adhesively bonded single lap joint subjected to eccentric loading

A new experimental test is proposed, which allows the contribution of Mode I, II and III fracture modes to the failure of the adhesive layer of bonded joints aiming at achieving the realistic conditions often occurring during loading of practical joints. The main objective of this test is benchmarking of computational tools. The test is based on a Single Lap Joint subjected to Eccentric Loading (SLJ-EL). The basic concept that lies behind this configuration is that the applied in-plane tensile load leads the adhesive layer to develop normal stresses, in-plane and out-of-plane shear stresses, which correspond to Mode I, II and III loading and fracture. These tests were designed so that the metal substrates do not enter plasticity and the adhesive achieves a mode mixity ratio between Mode II and Mode III not lower than 0.5. The experiments were simulated in a 3-dimensional finite element space and a previously developed mixed-mode model is utilized for the adhesive layer, under the framework of Cohesive Zone Modeling (CZM) techniques. The numerical results are in very good agreement with the corresponding experimental measurements, as regards both the linear and non-linear region, and the attained strength. It is concluded that in the early stages of loading the contribution of Mode III is 150% higher than that of Mode II.     

Crack Propagation Behavior of Y-TZP Ceramics

Y-TZP ceramics present the twofold advantage of a very fine grain size and a phase transformation leading to some reinforcement, making them useful in hip joint head prostheses. The subcritical crack growth of such a material that mainly drives the lifetime of the components has been evaluated for wide crack velocity ranges down to 10^-11 m/s by using both double torsion and static fatigue tests. It appeared that subcritical crack growth was activated by H₂O. It is shown that two types of flaws should be considered: surface flaws caused by machining located in the compressive layer present at the surface, and so-called volume flaws. The subcritical crack growth and the toughness of both types of defects are different. The relevance of subcritical crack growth analysis for such surface cracks is discussed. The compressive layer at the surface leads to a threshold value below which no crack growth occurs.     

Environmentally Enhanced Fracture of Glass: A Historical Perspective

In this paper, we review the phenomenon of delayed failure, a life-limiting process for glasses that are subjected to tensile stresses. With the development of crack-weakening theories (Ingles and Griffith) and the observation that surface damage enhances delayed failure, the scientific community recognized that delayed failure in glass is caused by the growth of cracks that are subjected to tensile stresses. Fracture mechanics techniques were used to quantify crack growth rates in terms of applied stress, temperature, and the chemical environments that cause subcritical crack growth. We review the theories that have been developed to rationalize subcritical crack growth data, including theories based on plastic deformation at the crack tip, chemical adsorption of the reacting species, and direct chemical reaction of the environment with the strained bonds at the crack tip. The latter theory seems to be most consistent with the finding that water reacts directly with the strained Si–O bond because of the ability of water to donate both electrons and protons to the strained bond. Other chemicals having this characteristic also cause subcritical crack growth. Finally, we review the quantum mechanical calculations that have been used to quantify the chemical reactions involved in subcritical crack growth.     

Controlled Crack Growth Specimen for Brittle Systems

A pure Mode I fracture specimen and test procedure has been developed which provides extended, stable, through-thickness crack growth in ceramics and other brittle, nonmetallic materials. Fixed displacement loading, applied at the crack mouth, promotes stable crack extension by reducing the stored elastic strain energy. Extremely fine control of applied displacements is achieved by utilizing the Poisson expansion of a compressively loaded cylindrical pin. Stable cracks have been successfully grown in soda-lime glass and monolithic Al₂O₃ for lengths in excess of 20 mm without uncontrollable catastrophic failure.     

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.