Subcritical Crack Extension Research Articles

An Analytical Microcrack-Based Rock Model with Implications for Earthquake Mechanisms Induced by Stress Changes

Shear fracture triggered by subcritical crack extension in intact brittle rocks under long-term compressive loading plays a significant role in the evaluation of earthquake mechanisms. Changes in external loading strongly influence the subcritical crack growth of intact rocks during earthquake nucleation. An important conundrum is how to establish the relationship between shear fracture induced by subcritical crack growth and external loading path in brittle rocks under lithospheric conditions. A novel micromechanical method that introduces shear fracture behavior is proposed to predict the time-dependent shear properties induced by the subcritical cracking of brittle rocks when the initial state of rocks starts from the peak point of the stress–strain curve measured by the conventional triaxial compressive test. This approach is developed on the basis of the wing crack model, subcritical crack growth law, and Mohr–Coulomb strain-softening model. The effect of loading and unloading paths on the evolution of shear properties of rocks under lithospheric conditions is analyzed by drawing a function of historical stress. The corresponding evolution of strain, shear strength, cohesion, and internal friction angle caused by subcritical crack growth under different stress paths is studied. Cohesion and shear strength continuously undergo a weakening process, and the internal friction angle initially undergoes a strengthening and, finally, a weakening process during subcritical crack growth under constant compressive loadings. The effect of the sudden change in axial stress on shear strength is smaller than that of the sudden change in confining pressure. A sudden decrease in confining pressure causes a rapid drop in shear strength, leading to a dramatic rise and drop in the rate of shear strength. Implications for evaluating earthquake mechanisms triggered by stress changes from the evolution of shear properties caused by subcritical crack growth in brittle rocks are also proposed.

The impact of resin-coating on sub-critical crack extension in a porcelain laminate veneer material

ObjectivesCharacterisation of the interaction between crack extension, crack stabilisation and stress/strain relaxation in the polymeric matrix, the interplay between stress corrosion cracking and the mechanical response of a resin-based luting adhesive within a surface defect population could extend PLV restoration longevity by optimising cementation protocols. The aim was to investigate the influence of stress corrosion cracking and the viscoelastic behaviour of a resin-based luting adhesive independently by controlling the environmental conditions operative during test specimen fabrication. MethodsThe effects of stress corrosion at ceramic crack tips and potential viscoelastic responses to loading of the resin-coated impregnating cracks were isolated. Resin-coated feldspathic ceramic test specimens were fabricated in ambient humidity or following moisture exclusion. Bi-axial flexure strengths of groups (n = 20) were determined at constant loading rates of 2.5, 10, 40, 160 or 640 N/min and data was compared with uncoated controls. Fractographic analyses were performed on all fractured test specimens. ResultsResin-cement coating resulted in significant ceramic strengthening in all conditions tested (p < 0.01). A two-way ANOVA demonstrated that the exclusion of moisture during resin- coating significantly increased mean BFS (p<0.01) but post-hoc Tukey tests identified that moisture exclusion resulted in significant increases in BFS values only at intermediate loading rates with no significant differences observed at either the fastest or slowest loading rates (640 and 2.5 N/min, respectively). SignificanceMechanical reinforcement of PLV materials by resin-cement systems is yet to be optimized. The viscoelastic behavior of the resin-cement itself can influence the magnitude of reinforcement observed and sub-critical crack growth.

Microstructural effects on the R-curve behavior of WC-Co cemented carbides

The influence of microstructure on the R-curve behavior of hardmetals and its implication on their strength and reliability are studied. In doing so, an already validated model for R-curve description is implemented for rationalizing the fracture behavior of five microstructurally different WC-Co cemented carbides. Results indicate that hardmetals with R-curves developing smoothly over relatively long multiligament zones (i.e. lower slopes) exhibit reduced strength variability than those with steeper and shorter (i.e. higher slopes) ones. The reduced strength scatter associated with a low-slope R-curve behavior is discussed on the basis of the effectively developed toughness and the subcritical crack extension reached before unstable growth is triggered, both being dependent on microstructural length scale and initial flaw size. The results of this investigation highlight the relevance of an in-depth knowledge of R-curve characteristics of hardmetals in order to optimize the performance of engineering parts by means of microstructural design.

Nonlinear Load-Displacement Behavior Observed During Fracture Toughness Testing of Aluminum-Beryllium Material

Abstract In fracture toughness testing on beryllium and aluminum-beryllium materials, the load-displacement response exhibits a significant amount of nonlinearity that requires special, nontraditional methods for analysis. This work is directed toward determining what causes this nonlinearity, focusing on plasticity and subcritical crack extension. Plasticity was indirectly assessed by varying the size of the fracture toughness specimen, whereas crack advance was monitored with unloading compliance during the fracture toughness tests. Neither of these influences appears to be the primary contributor to the nonlinearity. Rather, the range of loading employed during precracking influences the load-displacement response of the material. The central, more linear portion of the load-displacement response appears bounded at the low end by the crack opening load and at the high end by the maximum load applied during the terminal stage of precracking. This region of the load-displacement curve represents an alternative to the standard 20 % to 80 % maximum load analysis region. Although using this region for analysis offers the advantage of representing the portion of the curve where the crack is fully open and behaving in an elastic manner, it will likely increase the number of invalid tests as a result of violation of the Pmax/PQ &amp;lt; 1.1 criterion.

Analysis of Axial Subcritical Crack Propagation in X80 Pipeline using Micro-Mechanical Model

This study provides an engineering application of a continuum damage model to analyze the ductile tearing of axial surface cracks in X80 pipelines. Compact tension experiments were conducted to examine the behavior of large crack extension of X80 pipeline steel. The test results were used to verify the optimized parameter set of the proposed damage model. In the numerical model, progressive damage was restricted within a predetermined fracture process zone (FPZ). The material’s damage behavior in FPZ was described in terms of the Gurson–Tvergaard-Needleman (GTN) micro-mechanical damage model. The measured load versus load line displacement curve of CT specimens was numerically predicted using the damage model developed. T* integral was calculated to determine the limiting crack size in X80 pipelines. The damage model was then used to analyze the axial subcritical crack extension. It can help Leak-Before-Break (LBB) assessment.

A probabilistic approach for thermal shock fatigue life of glass

ABSTRACTThis paper presents a probabilistic approach for predicting fatigue life of glass subjected to near‐ΔTC(critical temperature difference) thermal shock which exhibits little subcritical crack extension. First, thermal shock fatigue life Nf was derived as a function of temperature difference ΔT, fracture probability F and Biot's modulus β from the slow crack growth concept in conjunction with the Weibull distribution model. Next, thermal shock fatigue tests as well as flexural tests were performed for borosilicate glass to measure ΔTC and Nf versus ΔT. The parameters associated with slow crack growth were then determined from the experimental results while the heat transfer coefficient h or β was obtained with the aid of finite element analysis. Thirdly, the thermal shock fatigue diagram (ΔT−Nf curves) was depicted for various values of β. Finally, crack length was simulated on the basis of the present approach.

Boundary element analysis of cracked homogeneous or bi-material structures under thermo-mechanical cycling

We present a sub-domain boundary element procedure to evaluate the failure capacity of cracked homogeneous and bi-material media under cyclic thermo-mechanical loads. The boundary integral equations of uncoupled, time-dependent thermo-elasticity are employed to account for the time-varying nature of the thermal load. If crack closure due to thermal distortion takes place, then the displacement and traction field may affect the heat flux between the crack faces, and the thermal and mechanical parts of the problem will need to be solved repeatedly until thermo-mechanical convergence is achieved. We present results from cases of pure mode-I fracture in homogeneous materials and for interfacial fracture in bi-materials. Our study discusses the influence of crack closure on quasi-static, sub-critical crack extension. Especially in case of interfacial cracks the type of loading, the thermal resistance between the crack faces, and the coefficient of friction are also taken into account. The results suggest that the above parameters may have a severe impact on the predicted failure capacity of cracked structures and should be considered in the evaluation of fatigue life.

A Tensile-Load Relaxation Test for Measuring the Stress Enhanced Corrosion Exponent of Ceramics with Open Porosity

A tensile test is proposed for evaluating the stress enhanced corrosion-coefficient of ceramics with open porosity. The analysis of load at fixed grip conditions bases on the assumption that stress corrosion results in a spread of pre-existing generalised damage seen as micro-crack starter due to open porosity. Sub-critical crack extension of microcracks departs from pores and provokes a time dependant diminution of the Young’s modulus, and of the stiffness, of the tested sample. The description derives the number and the size of pre-existing micro-cracks with respect to time. The density of microcrack-nuclei results from the process and belongs to the microstructure, i.e., the number of channels or crack starters, and is considered to remain constant. The rate of diminution of the load is considered, either with respect to the initial one or to a deduced stress intensity factor. Simple relationships yield then an approximate diagram for stress enhanced corrosion. Samples resulting from sintering a mixture of alumina and titania powders were tested under tempered water flow. A stress corrosion exponent, n = 16, near to that of alumina was obtained.

Influence of Stress Parallel to Crack Plan on Subcritical Crack Propagation in Glass under Biaxial Stress

The aim of this study is to demonstrate the influence of the stress parallel to the crack plane on subcritical crack growth in brittle materials by using a numerical code MFPA2D. The mechanism of this influence is also discussed. The curves of subcritical crack extension vs. strain of brittle materials under uniaxial and biaxial stress were obtained through numerical tests with acoustic emission consideration. The results showed that the tensile stress parallel to the crack plane has the effect on crack arrest, while the compressive stress parallel to the crack plane plays important role in crack opening process. The numerical results were consistent with experimental observed result, which shows the reliability of the numerical method, and provides theoretic foundation for failure analysis and life estimation of brittle materials.

Interface crack extension at any constant speed in orthotropic or transversely isotropic bimaterials––II. Two important examples

Abstract Part I [Int. J. Solids Struct., 39, 1165–1182] gives exact general solutions for steady dynamic extension by a semi-infinite crack along the interface of dissimilar orthotropic/transversely isotropic half-spaces under in-plane loading. Crack speed is any constant value, and results are valid for all six possible relations between the four body wave speeds. These results are applied here to sub-critical interface crack extension, and to debonding from a rigid half-space at any constant speed. The former case demonstrates well-known phenomena––the minimum Rayleigh speed is critical, and complex conjugate eigenvalues cause the crack edge oscillatory/square-root singular behavior that implies interpenetration. Calculations for representative materials show that eigenvalue and stress intensity factor amplitude variation with crack speed is small except near the critical value. Results for the latter case complement those of other recent studies: Singular behavior vanishes for super-critical/sub-sonic crack speeds, although oscillations remain. For trans-sonic crack speeds, eigenvalues are real, singular behavior is no longer square-root, and interpenetration can still occur below a critical speed. Lines of displacement gradient discontinuity radiate from the crack edge, but can vanish at a critical speed. Calculations show that eigenvalue variation with crack speed is more pronounced than in the first case.

Initiation of stress-corrosion cracking in unidirectional glass/polymer composite materials

The purpose of this research is to determine the resistance to stress-corrosion cracking (SCC) of three unidirectional (pultruded) E-glass/polymer composites based on modified polyester, epoxy and vinyl ester resins. The composites have been subjected to a nitric acid solution of pH 1.2 in a newly designed four-point bend fixture. The stress-corrosion process was initiated on the as-supplied surfaces of the composites. The process has been monitored for acoustic emissions and the stress-corrosion surface damage in the specimens was investigated by the use of scanning electron microscopy. Experimental results indicate that the stress-corrosion cracks originate predominantly from exposed glass fibers on the surfaces of the composites. The process can be successfully monitored by means of acoustic emission equipment. Three stages of SCC, crack initiation, sub-critical crack extension and stable crack propagation, can be distinguished by carefully examining the curves of acoustic emission (number of events) versus time. For the first and second stages of SCC, the acoustic emission outputs are linear functions of time. The slopes of the first and second stages of the curves of acoustic emission versus time have been used to determine quantitatively both the resistance of the composites to crack initiation and sub-critical crack extension, respectively. It has been shown in this research that the resistance to the initiation of SCC in nitric acid of the E-glass/vinyl ester composite is approximately 10 times greater than the E-glass/epoxy composite. Furthermore, the E-glass/epoxy system exhibits approximately 5 times higher resistance to the initiation of SCC than the E-glass/modified polyester system. The sub-critical crack extension process is also significantly more rapid in the E-glass/modified polyester than in the E-glass/epoxy composite.

Fracture Resistance of Mullite Under Static and Cyclic Loads

The issue of whether ceramic materials might be sensitive to mechanical degradation by fluctuating loads has been addressed in many investigations in the last ten years. From these studies it is known that in many polycrystalline ceramics subcritical crack extension takes place under cyclic loads, leading to complete failure at stresses which are considerably smaller than their fracture resistance under monotonic loading. However, the question of how much of the observed crack growth under fluctuating loads is either just a consequence of slow crack growth induced by the influence of the environment or an intrinsic fatigue effect (cyclic fatigue) remains to be elucidated for some specific ceramic materials. Mullite (3Al{sub 2}O{sub 3}-2SiO{sub 2}) is one of the most common components of traditional ceramic materials. It is also considered an appealing material for high temperature applications because of its very good chemical, thermal and mechanical properties over a broad temperature range. However, mullite exhibits a relatively low fracture toughness at room temperature (about 2.3 MPa m{sup 1/2}) mainly because no significant toughening mechanism appears to be present in this material. In this investigation the mechanical behavior of mullite under static and cyclic loading for four different microstructures is studied, in termsmore » of grain size distribution, with specimens produced from two different commercial powders. The work was addressed to document the existence of cyclic fatigue by measuring fatigue life under static and cyclic loading, since no information was available on this topic for this particular material.« less

Strain energy density approach to stable crack extension under net section yielding of aircraft fuselage

In this paper, the incremental theory of plasticity is used in conjunction with the strain energy density criterion to determine the stress field in 4-in. wide test specimens containing 3 holes. These specimens, made from 0.04-in. thick sheets of 2024-T3 aluminum, also contained small collinear cracks emanating from the holes. The initial crack sizes varied from 0.15 to 0.26 in. Residual strength tests conducted with these specimens revealed that stable tearing occurred before failure. Analyses were performed to predict the stable crack extension and failure by plastic collapsed. Because of the complexities involved with nonlinear stress analysis combined with subcritical crack extension, the finite element method was used with the grid pattern adjusted for each increment of stable tearing. Reasonable correlation between the experimental data and predicted results was achieved.

Crack growth in elastically damaged materials

Brittle, polycrystalline and polyphase materials such as ceramics and fibre-reinforced brittle composites contain residual thermo-mechanical stresses from manufacturing. These stresses are concentrated at sites of microstructural inhomogeneities such as grain and phase boundaries. The nucleation and growth of microcracks can minimize the local micro-strain energy density; thus, the local, residual stresses can act as nuclei for microcracks. The density of nuclei, statistically distributed within the material, depends on grain size, i.e. the distance between nuclei, with defined values of micro-strain energy density, is material specific. Stress-induced microcracking can act as an attractor for elastic damage at the local scale to produce a process zone that acts as a sink of strain-energy release on a larger scale, for example, the process zone at a crack front. It can be shown that the stress-rate dependent growth of local damage follows a power law which quantifies strengthening and softening during slow crack growth, prior to catastrophic crack extension. The damage-induced zone, produced by the release of strain energy on the local scale, can shield the macrocrack and grow to a critical value at the failure load. The influence of the microstructure on damage will be quantified and related to sub-critical and critical crack extension in brittle materials.

Evaluation of strength, toughness and subcritical crack extension of a commercial HP-Si3N4 exposed to a sulphidizing environment

Structural ceramic materials, in particular silicon nitride, have attracted interest for coal gasification technology at temperatures in excess of 1200 °C. In this study, a commercially available hot pressed silicon nitride is exposed for 200 h in a 0.4% H2S + 0.75% H2O + H2 (balance) atmosphere, at 1200 and 1300 °C, simulating coal gasification environments. The crack growth behaviour of the as-received material is compared to that of the exposed condition. Measurements are carried out on specimens with small natural flaws (dynamic strength tests) and on specimens containing long cracks (chevron notch), both tested in four point bending. Results of strength tests (Modulus of rupture (MOR) and Weibull modulus) as well as toughness in both conditions are also presented. In view of the significant changes in the high temperature mechanical properties caused by crystallization of the intergranular glassy phase at triple points, further investigations of the effect of controlled devitrification seem surely worthwhile.

Some Microstructural Conditions for Evaluating Fracture Toughness and R-Curve Behavior in Platelet-Reinforced Composites

Abstract The validity of Kk determinations by various techniques usually employed and compared with each other is discussed in detail for two ceramic materials. They are a simple Si9N4 material fracturing with transgranular crack propagation and a Si9N4-25vol% SiC-platelet measured by four different methods: single-edge V-notched beam (SEVNB), single-edge precracked beam (SEPS), indentation fracture (IF), and chevron-notched beam (CNB). It is generally recognized that, in platelet composites, Kk values can be reliability obtained only by procedures adopting notched specimens in which the wake-zone of precracking is mechanically removed (SEVNB or renotched SEPB). In the present investigation the CNB method, in which the wake contribution to fracture resistance is generally small but not negligible, was also found to give stress-intensity factors at maximum load whose value was almost coincident with the KIc determined by SEVNB method. Using stereological concepts, fractographic observations, and acoustic emission (AE) experiments, the microstructural conditions for negligible wake-contribution during the subcritical stable crack extension in the CNB experiment were worked out and applied to rationalize the behavior of the present composite. Apparent toughness values markedly higher than the “true” Kk of the composite were measured both by the standard SEPB and IF method. Such a discrepancy is considered due, in the former case, mainly to traction forces between the precracked surfaces while, in the latter, to an insufficient account of the residual stress field associated with the indentation.

Evaluation of R-curve effects in ceramics

In coarse-grained alumina the crack growth resistance increases with increasing crack extension due to crack-border interactions. The crack shielding stress intensity factor can be calculated from the relation between the bridging stresses and the crack opening displacement. The parameters of this relation can be obtained from experimental results on stable or subcritical crack extension. Finally the effect of the R-curve on the behaviour of components with small cracks is discussed.

Determination of Fracture Toughness at High Temperatures after Subcritical Crack Extension

As a consequence of R‐curve behavior, ceramic materials may exhibit increased fracture toughness (KIc) following slow crack extention. In this investigation, the effect of crack propagation on fracture toughness is studied in static bending tests. For the calculation of stress intensity factors (KI) the stress distribution must be known at the moment of fracture. As a consequence of creep, this stress distribution must deviate from the linear distribution. The corresponding stress intensity factors are computed using the fracture mechanical weight function. Experimental results for fracture toughness are communicated for a 2.5%‐MgO‐doped hot‐pressed Si3N4 at 1300°.

Crack propagation in ceramic composites with layered granular structure

Fracture experiments under conditions of subcritical crack extension were performed with double torsion and single-edge notched bend specimens of different alumina-based ceramic composites having layered granular structure. It is shown that it is possible to increase significantly the work-of-fracture as a result of layered granular structure organization. The pecularities of structure influence on the crack propagation kinetics were investigated, and the possibilities of acceleration and deceleration of subcritical crack growth are reported.

Crack-tip strain fields and fracture microplasticity in hydrogen-induced cracking of Fe-3 wt% Si single crystals

Abstract The development of a sound physical view regarding crack quasi-stability during subcritical crack extension still remains challenging. It is evident that further progress requires exploration of the refined micromechanical processes of fracture. The present study emphasizes the experimental findings which indicate a crack arrest potential in terms of flexible dislocation activity available in semibrittle b.c.c. single crystals. This is particularly demonstrated in Fe-3 wt% Si single crystals with subcritical crack extension induced by sustained loading and external hydrogen interaction. Pre-fatigued crystals oriented in (001)[010] and loaded above 18 MPa m½ in 1 atm of gaseous hydrogen resulted in slow crack growth. Since a fine-scale localized approach was adopted, observations were conducted with the use of selected-area channelling patterns in a scanning electron microscope. This provided a 5 μm spatial resolution and a submicrometre depth resolution with regard to strain measurement. The curr...