Subcritical Crack Propagation Research Articles

Probabilistic fracture mechanics of irradiation assisted stress corrosion cracking in stainless steels

A probabilistic fracture mechanics model is applied to irradiation assisted stress corrosion cracking effect, assuming that the oxidized part of stainless steel sample plays an essential role in the crack propagation and sample failure. The Weibull statistical distribution of time-to-failures, estimated through the correlation with the statistical distribution of oxide strengths, fully accounts for the experimental results/scatter obtained in the constant load time-to-failure tests. Large failure uncertainties in these type of tests originate from intrinsic stochastic behavior of the oxide cracking due to subcritical crack propagation process.

Sub-critical cohesive crack propagation with hydro-mechanical coupling and friction

Looking at the long-time behaviour of a dam, it is necessary to assume that the water can penetrate a possible crack washing away some components of the concrete. This type of corrosion reduces the tensile strength and fracture energy of the concrete compared to the same parameters measured during a short-time laboratory test. This phenomenon causes the so called sub-critical crack propagation. That is the reason why the International Commission of Large Dams recommends to neglect the tensile strength of the joint between the dam and the foundation, which is the weakest point of a gravity dam. In these conditions a shear displacement discontinuity starts growing in a point, called Fictitious Crack Tip (shortened FCT), which is still subjected to a compression stress. In order to manage this problem, in this paper the cohesive crack model is re-formulated with the focus on the shear stress component. In this context, the classical Newton-Raphson method fails to converge to an equilibrium state. Therefore the approach used is based on two stages: (a) a global one in which the FCT is moved ahead of one increment; (b) a local one in which the non-linear conditions occurring in the Fracture Process Zone are taken into account. This two-stage approach, which is known in the literature as a Large Time Increment method, is able to model three different mechanical regimes occurring during the crack propagation between a dam and the foundation rock.

Experimental validation of inspection intervals for railway axles accompanying the engineering process

In the paper an example of successful cooperation between an operator, a vehicle manufacturer, a wheelset supplier and a research institute is presented demonstrating the current state of a design procedure which aims at meeting wheelset specification requirements recently adopted by the Deutsche Bahn (DB). Different from the conventional praxis, these requirements incorporate the fracture mechanics approach for determining inspection intervals of railway axles. The procedure includes the wheelset dimensioning based on current railway standards, fracture mechanics considerations to assess subcritical crack propagation starting from a crack size just below the detection limit, and crack propagation tests on full-scale axles under load spectrum representative of in-service conditions. The paper describes different steps of the procedure, while mainly focusing on fracture mechanics – both computational and experimental – issues.

Applications of lattice method in the simulation of crack path in heterogeneous materials

The simulation of critical and subcritical crack propagation in heterogeneous materials is not a simple problem in computational mechanics. These topics can be studied with different theoretical tools. In the crack propagation problem it is necessary to lead on the interface between the continuum and the discontinuity, and this region has different characteristics when we change the scale level point of view. In this context, this work applies a version of the lattice discrete element method (LDEM) in the study of such matters. This approach lets us to discretize the continuum with a regular tridimensional truss where the elements have an equivalent stiffness consistent with the material one wishes to model. The masses are lumped in the nodes and an uni-axial bilinear relation, inspired in the Hilleborg constitutive law, is assumed for the elements. The random characteristics of the material are introduced in the model considering the material toughness as a random field with defined statistical properties. It is important to highlight that the energy balance consistence is maintained during all the process. The spatial discretization lets us arrive to a motion equation that can be solved using an explicit scheme of integration on time. Two examples are shown in the present paper; one of them illustrates the possibilities of this method in simulating critical crack propagation in a solid mechanics problem: a simple geometry of grade material. In the second example, a simulation of subcritical crack growth is presented, when a pre-fissured quasi-brittle body is submitted to cyclic loading. In this second example, a strategy to measure crack advance in the model is proposed. Finally, obtained results and the performance of the model are discussed.

Critical issues in the design-by-testing of annealed glass components

To assess the reliability of glass components, a common practice is to test full-scale prototypes in the lab, and verify that the failure load is higher than that predicted from the design strength by means of structural calculations. However, any procedure of design-by-testing should be considered with great care because the gross strength of glass, being governed by the opening of pre-existing cracks on the material surface, strongly depends upon the type of defectiveness, the specimen size, the load history and the type of stress field (uniaxial, bi-axial). A model based upon an assumed law of subcritical crack propagation and a distribution à la Weibull of pre-existing flaws is considered for the body strength of annealed glass. This allows to correlate the expected macroscopic strength of glass, measured from testing the prototype, with the target probability of failure, for any type of size and load history. The discussion of paradigmatic examples confirms that appropriate theoretical considerations are needed for the correct interpretation of the experimental results.

Role of the pore fluid in crack propagation in glass

We investigate pore fluid effects due to surface energy variation or due to chemical corrosion in cracked glass. Both effects have been documented through experimental tests on cracked borosilicate glass samples. Creep tests have been performed to investigate the slow crack propagation behavior. We compared the dry case (saturated with argon gas), the nonreactive water saturated case (commercial mineralized water), and the distilled and deionized water saturated case (pure water). Chemical corrosion effects have been observed and evidenced from pH and water composition evolution of the pure water. Then, the comparison of the dry case, the mineral water saturated case, and the corrosion case allow to (i) evidence the mechanical effect of the presence of a pore fluid and (ii) show also the chemical effect of a glass dissolution. Both effects enhance subcritical crack propagation.

Brittle creep and subcritical crack propagation in glass submitted to triaxial conditions

AbstractAn experimental work is presented that aimed at improving our understanding of the mechanical evolution of cracks under brittle creep conditions. Brittle creep may be an important slow deformation process in the Earth's crust. Synthetic glass samples have been used to observe and document brittle creep due to slow crack‐propagation. A crack density of 0.05 was introduced in intact synthetic glass samples by thermal shock. Creep tests were performed at constant confining pressure (15 MPa) for water saturated conditions. Data were obtained by maintaining the differential‐stress constant in steps of 24 h duration. A set of sensors allowed us to record strains and acoustic emissions during creep. The effect of temperature on creep was investigated from ambient temperature to 70°C. The activation energy for crack growth was found to be 32 kJ/mol. In secondary creep, a large dilatancy was observed that did not occur in constant strain rate tests. This is correlated to acoustic emission activity associated with crack growth. As a consequence, slow crack growth has been evidenced in glass. Beyond secondary creep, failure in tertiary creep was found to be a progressive process. The data are interpreted through a previously developed micromechanical damage model that describes crack propagation. This model allows one to predict the secondary brittle creep phase and also to give an analytical expression for the time to rupture. Comparison between glass and crystalline rock indicates that the brittle creep behavior is probably controlled by the same process even if stress sensitivity for glass is lower than for rocks.

Subcritical crack growth in oxide and non-oxide ceramics using the constant stress rate test

Fracture toughness is one of the most important parameters for ceramics description. In some cases, material failure occurs at lower stresses than described by KIc parameter. In these terms, determination of fracture toughness only, proves to be insufficient. This may be due to environmental factors, such as humidity, which might cause subcritical crack propagation in a material. Therefore, it is very important to estimate crack growth velocities to predict lifetime of ceramics used under specific conditions. Constant Stress Rate Test is an indirect method of subcritical crack growth parameters estimation. Calculations are made by using strength data, thus avoiding crack measurement. The expansion of flaws causes reduction of material strength. If subcritical crack growth phenomenon occurs, critical value of crack lengths increases with decreasing stress rate due to longer time for flaw to grow before the critical crack propagation at KIc takes place. Subcritical crack growth phenomenon is particularly dangerous for oxide ceramics due to chemical interactions occurring as a result of exposure to humidity. This paper presents results of Constant Stress Rate Test performed for alumina, zirconia, silicon carbide and silicon nitride in order to demonstrate the differences in subcritical crack propagation phenomenon course.

Crescimento subcritico de trinca e previsão de vida em fadiga do compósito cerâmico ZrO2-Al2O3

Cerâmicas apresentam excelente durabilidade química, resistência ao desgaste, biocompatibilidade, respeito ao meio ambiente e estética. Uma das propriedades mais importantes a ser considerada em implantes dentários totalmente cerâmicos é a fadiga cíclica, devido às solicitações mecânicas cíclicas as quais os implantes estão subjugados durante processos de mastigação, que pode induzir milhares de ciclos de tensão por dia em uma restauração, com isso exibir significativo crescimento subcrítico de trinca e assim poder diminuir a resistência de componentes cerâmicos, ao longo do tempo. Nesse trabalho, a previsão de vida em fadiga cíclica do compósito ZrO2-Al2O3 foi investigada. Mistura de pós contendo 80% de ZrO2 e 20% de Al2O3 foi compactada e sinterizada a 1600 °C. As amostras sinterizadas foram caracterizadas por difração de raios X e microscopia eletrônica de varredura. Dureza, tenacidade e resistência à fratura por flexão foram determinadas, e os resultados utilizados na determinação dos parâmetros de fadiga. Os testes de fadiga foram realizados em dispositivo de flexão em 4 pontos, sob freqüência de 25 Hz e razão de tensão de 0,1. Um aumento do nível de tensão levou à redução do tempo de vida sob fadiga. Baseado nos parâmetros determinados pelos ensaios mecânicos e de fadiga, e utilizando-se a estatística de Weibull, associada a modelos de determinação de crescimento subcrítico de falha, a velocidade de propagação de trincas nesse compósito é determinada e relacionada com os mecanismos de transformação martensítica e tensão residual entre as fases. Os componentes submetidos ao carregamento cíclico exibiram propagação subcrítica de trinca, em níveis de tensão significativamente menores do que o KIC. Apesar desta susceptibilidade ao crescimento subcrítico de trinca, cálculos com base nos parâmetros de fadiga e nas tensões aplicadas indicam que os componentes com estruturas do compósito ZrO2-Al2O3 podem exibir vidas maiores que 20 anos, se o diâmetro do componente estrutural é adequadamente projetado.

Fracture Mechanics and Rockfill Dams

Rockfill behavior is dominated by particle breakage, a phenomenon which is analyzed from the perspective offered by the subcritical propagation of cracks within individual particles. Propagation velocity depends on stress concentration in particles as well as on the ambient Relative Humidity (RH). RH controlled oedometer and triaxial tests are reviewed and constitutive models reproducing the main features of observed behavior are outlined. The relevant issue of size effects is then introduced and some rules and possibilities to account for these effects in practice have been given. The Distinct Element Method is also a powerful tool to investigate rockfill behavior. Recent developments are described. The model developed incorporates particle breakage, delayed effects and the action of water. In the final part two real cases are presented: the response of a high rockfill embankment against a four year long rainfall regime and the analysis of Beliche dam. The lecture closes by a general discussion of partial saturation in granular materials ranging from coarse granular aggregates, such as rockfill, to clayey soils in an attempt to provide an integrated overview of water effects in soils.

Numerical Analysis of Sub-critical Crack Growth in Particulate Ceramic Composites

The strength of glass or ceramic containing materials can be affected by the environment (“stress corrosion”). Under applied stress, crack-like defects may grow (sub-critically) for stress intensity factors, KI, below the fracture toughness of the material, KIc. The aim of the present work was to develop a two-dimensional finite element model to analyze the subcritical crack growth behavior of ceramic-based particulate composites. The maximum tangential stress criterion (MTS) was used to predict the direction of the crack propagation, in the framework of linear elastic fracture mechanics. The modeled material was a Low Temperature Co-fired Ceramic (LTCC), containing alumina particles embedded in a glass matrix. The experimentally determined SCCG material behavior (i.e. v-KI data) was implemented in the numerical model. The effect of the elastic modulus of the particles on the subcritical crack propagation was investigated. The conclusions of this paper can contribute to a better understanding of the subcritical propagation of cracks in particulate composites.

Oil-Gas Transformation Induced Subcritical Crack Propagation and Coalescence in Petroleum Source Rocks

The present work describes a multi-physics model to investigate subcritical propagation of initially oil-filled, sub-horizontal collinear microcracks driven by the excess pressure induced by the conversion of oil to gas in a petroleum source rock under continuous burial. The crack propagation distance, propagation duration, crack coalescence and excess pressure in the crack are determined using a finite difference scheme that couples linear elastic fracture mechanics, oil-gas transformation kinetics and an equation of state for the gas. The numerical results for a shale source rock with typical properties show that when the crack spacing parameter b/a0 is greater than 3, where a0 is the half crack length and b the half distance between the crack centers, the cracks do not coalesce, and the duration of gas-driven crack propagation is governed by the transformation kinetics because the oil-gas conversion rate is much slower than the subcritical crack propagation rate. The collinear cracks coalesce for smaller crack spacing and the crack propagation duration may reduce significantly due to crack interactions. The multi-physics model presented in this work together with our previous model for crack propagation during the conversion of solid kerogen to oil indicates that self-propagating microcracks resulting from the buildup of excess fluid pressure during hydrocarbon generation may serve as effective pathways for primary migration of hydrocarbons.

Interlaminar Adhesive Strength of Nano-Reinforced Glass/Epoxy Laminates

Interlaminar fracture is significantly influenced by the adhesive strength of fiber/matrix interfaces. Critical strain energy release rate (GC) is the most common parameter used to quantify the interfacial strength. However, subcritical debonding can occur at lower mechanical loads than those required for interlaminar fracture toughness (IFT). This study was performed using nanoclay-reinforced epoxy/glass fiber laminates in order to analyze the influence of the addition of nanoclay and hydro aging on IFT and subcritical crack growth. Hydro aging was done immersinga batch of specimens in distilled water at 25°C for 30 days. Mode I IFT was significantly improved by the incorporation of nanoclays into the resin, the improvement reaching 31% for 3% of nanoclays content. The results of subcritical debonding were plotted in terms of da/dt versus G curves, for dry materials and long term hydro aged composites. Hydro aged composites exhibit not only a reduction of GIc, of about 14% for 3% of nanoclays, but also a higher subcritical crack propagation rate. The addition of nanoparticles reduces subcritical crack propagation rate.

A Study on the Evaluation of the Fracture Process Zone in CCNBD Rock Samples

The safety of many civil and mining concrete and rock structures including pre-existing crack networks is fundamentally affected by the mechanical behaviour of the material under static and cyclic loading. In cyclic loading case, cracks can grow at a lower load level compared to the monotonic case. This phenomenon is called fatigue due to subcritical crack propagation and depends on the behaviour of the fracture process zone (FPZ). This study presents the results of laboratory diametrical compression tests performed on Brisbane tuff disc specimens to investigate their mode-I (tensile) fracture toughness response to static and cyclic loading and relevant FPZ. The FPZ and fracture toughness response to cyclic loading was found to be different from that under static loading in terms of the ultimate load and the damage mechanisms in front of the chevron crack. A maximum reduction of the static fracture toughness (K IC ) of 42 % was obtained for the highest amplitude increasing cyclic loading test. Detailed scanning electron microscope (SEM) examinations were performed on the surfaces of the tips of the chevron notch cracks, revealing that both loading methods cause FPZ development in the CCNBD specimens. When compared with monotonic FPZ development, the main difference with the cyclically loaded specimens was that intergranular cracks were formed due to particle breakage under cyclic loading, while smooth and bright cracks along cleavage planes were formed under static loading. Further, the SEM images showed that fatigue damage in Brisbane tuff is strongly influenced by the failure of the matrix because of both intergranular and transgranular subcritical fracturing.

Flexural strength and defect behaviour of polygranular graphite under different states of stress

The effect of stress state on the fracture behaviour of Gilsocarbon, an isotropic nuclear grade polygranular graphite, has been studied by employing four-point bend and ring-on-ring loading configurations to achieve uniaxial and equi-biaxial flexural stress states, respectively. Optical images of the specimens’ tensile surface were analysed by digital image correlation to measure the full-field displacements: these were used to identify the fracture initiation sites, analyse crack geometry (surface length and opening displacements) and also to calculate the J-integral strain energy release rate associated with surface crack propagation. Surface cracks that did not propagate to failure were identified and subsequently examined by X-ray computed tomography combined with digital volume correlation: measurements were made of their three-dimensional displacement fields when subjected to an opening tensile stress using a modified (flat) Brazilian Disk test geometry. The crack opening behaviour is explained by an effect of stress state on the development of the crack tip fracture process zone, which is in agreement with the effect of stress state on the measured strain energy release rates of sub-critical crack propagation. Both are attributed to the plastic constraint effect, which varies with the stress state in materials that can undergo inelastic deformation.

Effect of fluid salinity on subcritical crack propagation in calcite

The slow propagation of cracks, also called subcritical crack growth, is a mechanism of fracturing responsible for a ductile deformation of rocks under crustal conditions. In the present study, the double-torsion technique was used to measure the effect of fluid chemistry on the slow propagation of cracks in calcite single crystals at room temperature. Time-lapse images and measurements of force and load-point displacement allowed accurate characterization of crack velocities in a range of 10−8 to 10−4m/s. Velocity curves as a function of energy-release rates were obtained for different fluid compositions, varying NH4Cl and NaCl concentrations. Our results show the presence of a threshold in fluid composition, separating two regimes: weakening conditions where the crack propagation is favored, and strengthening conditions where crack propagation slows down. We suggest that electrostatic surface forces that modify the repulsion forces between the two surfaces of the crack may be responsible for this behavior.

Influence of experimental variables on fracture toughness determined on SEVNB in three points bending. Mullite a case study

Abstract The effect of testing variables on toughness of single edge “V” notched beams (4 mm × 6 mm × 50 mm, α = 0.6) of a fine grained mullite (d50 = 0.7 ± 0.5 μm) in three points bending (span = 40 mm) is analysed. Mullite was selected as case material because it presents flat R-curve and subcritical crack propagation. Stable fracture was reached by using the CMOD as control variable (0.001 and 0.018 mm/min). Results for stable test and unstable displacement (0.05 mm/min) controlled tests are analysed. KIC has been calculated from maximum loads, KICp, and from the total fracture energy determined in stable tests, KICγ. The fact that for materials with flat R-curve both KIC values are coincident has been used as criterion for adequacy of the test. Stable fracture at high deformation rates is required to fulfil KICp = KICγ. Under such conditions, an intrinsic KIC = 0.86 ± 0.06 MPa m1/2, less than one half of those previously reported has been obtained.

Gas-driven subcritical crack propagation during the conversion of oil to gas

In this paper, we investigate subcritical propagation of an initially oil-filled, sub-horizontal microcrack driven by the excess fluid pressure associated with the conversion of oil to gas in a petroleum source rock under continuous burial. The crack propagation distance and propagation duration (the time required for the crack to propagate during conversion of all oil to gas), as well as the excess pressure inside the crack, are determined using a finite difference scheme that couples linear elastic fracture mechanics, oil–gas transformation kinetics and an equation of state for the gas. The effects of the source-rock temperature at the initial depth of the microcrack and fracture properties of the source rock are also considered. Our numerical results show that higher burial rates significantly reduce the crack propagation duration. However, the influence of the geothermal gradient on the propagation duration and distance is only marginal. Similar to the results for the oil-driven crack propagation during kerogen–oil conversion, the duration of gas-driven crack propagation is also governed by transformation kinetics because the subcritical crack propagation rate is much faster than the oil–gas conversion rate.

Describing fatigue crack growth and load ratio effects in Al 2524 T3 alloy with an enhanced exponential model

The fatigue crack behavior in metals and alloys under constant amplitude test conditions is usually described by relationships between the crack growth rate da/dN and the stress intensity factor range ΔK. In the present work, an enhanced two-parameter exponential equation of fatigue crack growth was introduced in order to describe sub-critical crack propagation behavior of Al 2524-T3 alloy, commonly used in aircraft engineering applications. It was demonstrated that besides adequately correlating the load ratio effects, the exponential model also accounts for the slight deviations from linearity shown by the experimental curves. A comparison with Elber, Kujawski and “Unified Approach” models allowed for verifying the better performance, when confronted to the other tested models, presented by the exponential model.

Crack Propagation in Honeycomb Cellular Materials: A Computational Approach

Computational models based on the finite element method and linear or nonlinear fracture mechanics are herein proposed to study the mechanical response of functionally designed cellular components. It is demonstrated that, via a suitable tailoring of the properties of interfaces present in the meso- and micro-structures, the tensile strength can be substantially increased as compared to that of a standard polycrystalline material. Moreover, numerical examples regarding the structural response of these components when subjected to loading conditions typical of cutting operations are provided. As a general trend, the occurrence of tortuous crack paths is highly favorable: stable crack propagation can be achieved in case of critical crack growth, whereas an increased fatigue life can be obtained for a sub-critical crack propagation.