Constant Crack Research Articles

Dissipation during crack growth in a viscoelastic material from a cohesive model for a finite specimen

AbstractIn the present paper, we extend results recently given by Ciavarella et al. (J Mech Phys Solids 169:105096, 2022) to show some actual calculations of the viscoelastic dissipation in a crack propagation at constant speed in a finite size specimen. It is usually believed that the cohesive models introduced by Knauss and Schapery and the dissipation-based theories introduced by de Gennes and Persson-Brener give very similar results for steady state crack propagation in viscoelastic materials, where usually only the asymptotic singular field is used for the stress. We show however that dissipation and the energy balance never reach a steady state, despite the constant propagation crack rate and stress intensity factor. Our loading protocol permits a rigorous solution, and implies a short phase with constant specimen elongation rate, but then possibly a very long phase of constant or decreasing elongation, which differs from typical experiments. For the external work we are therefore unable to use the de Gennes and Persson-Brener theories which suggested that the increase of effective fracture energy would go up to the ratio of instantaneous to relaxed modulus, at very fast rates. We show viscoelastic dissipation is in general a transient quantity, which can vary by orders of magnitude while the stress intensity factor is kept constant, and is largely affected by dissipation in the bulk rather than at the crack tip. The total work to break a specimen apart is found also to be possibly arbitrarily large for quite a large range of intermediate crack growth rates.

Using strain hardening to predict the stress crack resistance of unaged and aged smooth black HDPE geomembranes

The correlation between the single-point notched constant tensile load-stress crack resistance (SP-NCTL SCR) Test (ASTM D5397; Appendix) of smooth high density polyethylene (HDPE) geomembranes and their strain hardening modulus is investigated for both unaged and aged specimens. The strain hardening modulus was calculated based on the (force-elongation) raw data from the tensile strength test conducted at room temperature using Type IV and/or Type V specimens (as described in ASTM D638) at a test speed of 7 mm/min. Three different approaches are used to define the strain hardening modulus and to compare the representative strain hardening modulus with the SP-NCTL SCR. It is shown that the high test speed of 7 mm/min performed at room temperature provides a good correlation with the SP-NCTL SCR of different smooth black HDPE geomembranes. Additionally, the proposed method using Type V specimens predicts the SCR values during oxidative degradation close to those observed using the SP-NCTL SCR test. For the resins and conditions examined, the proposed method provides a quick assessment of the SP-NCTL SCR of unaged geomembranes when the SP-NCTL SCR takes long testing times (e.g., >1000 h) or in jurisdictions in which the use of surfactants becomes prohibited to allow conducting the SP-NCTL SCR tests.

Compressive Fracture Behavior and Acoustic Emission Characteristics of Sandstone under Constant Crack Water Pressure

Abstract Engineering rock containing flaws or defects under a large water source is frequently subject to the couple influence of constant crack water pressure and geostress. To investigate the fracture behavior of precracked rock under hydromechanical coupling with constant crack water pressure, compression tests were conducted on red sandstone specimens containing a single crack of different angles using a device to realize the constant crack water pressure during loading, and the failure process of rock specimens was monitored by acoustic emission (AE) technique. The results show that the presence of constant crack water pressure has a significant promotion effect on the development of shear wing cracks, and the promotion effect is influenced by the prefabricated crack angle and water pressure. As the constant crack water pressure increases, the failure mode of the 0° precrack specimen changes from “X”- shear failure to the single oblique shear failure along the shear wing crack direction, the main failure crack of the inclined precracked specimens (precrack angles of 15°, 45°, and 60°) changes from a small acute angle with the prefabricated crack to a direction along the shear wing crack, and irregular cracks occur at the chipped prefabricated crack in the 90° precracked specimen. With an increase in the constant crack water pressure, the average energy for a single hit, cumulative AE energy, and cumulative AE hits decrease, and the proportion of the tensile cracks increases and that of the shear cracks decreases.

Correlating stress ratio effects on the fatigue crack growth rate behavior of a nickel-based superalloy GTM718

Damage tolerance evaluation under service loads requires a unified constant amplitude fatigue crack growth law for the material which takes care of stress ratio effects. Several types of crack driving force parameters have been proposed in the past to correlate stress ratio effects on fatigue crack growth rates. In the present investigation, a unified crack growth law is derived for a nickel-based superalloy by considering various crack driving force parameters to eliminate stress ratio effects. Initially, the constant amplitude fatigue crack growth rate (FCGR) behavior of GTM718 alloy was experimentally determined at various stress ratios, R ranging from R = 0.1 to 0.7. As expected, increasing the stress ratio, increased crack growth rates, and decreased threshold stress intensity factor range, ΔKth. The conventional crack growth rate, da/dN vs stress intensity factor range, ΔK data was then modified and re-plotted as a function of different crack driving force parameters viz., (a) Elber’s parameter, ΔKeff, (b) Walkers’ parameter, Kw (c) Kujawski’s parameter, K*, (d) Forman’s parameter, Kf, and (e) Two-parameter crack driving force, ΔK*. It was observed that Kf and ΔK* crack driving force parameters were correlating stress ratio effects better than other models in all three regimes of crack growth rates. Further, a unified crack growth law was derived based on the Kf and ΔK* crack driving force parameters which is useful in predicting FCG behavior under service loads.

Determining SCC resistance of stainless steel claddings in high- temperature water by constant load crack growth tests and slow strain rate tests

Stress corrosion cracking (SCC) behaviors of 309 L and 308 L weld overlays are characterized in oxygen-free and oxygen-bearing high-temperature water using slow strain rate tests (SSRTs) and crack growth rate (CGR) tests with compact tension specimens. There is no apparent SCC indication on 308 L, while local SCC is observed on 309 L after SSRT in oxygen-free water. The SCC sensitivities of 308 L and 309 L increase with the increase of dissolved oxygen (DO) content, while 308 L shows relatively higher SCC resistance than 309 L in water with 200 ppb and 8000 ppb DO. SSRT and CGR test results show a similar effect of DO concentration on SCC of 309 L and 308 L. The fracture surface of 309 L exhibits extensive intergranular SCC, while 308 L shows only local interdendritic SCC after CGR tests. The crack tip blunting decreased the CGR in the low alloy steel. The highly island-shaped δ-ferrites and moderate strain hardening in 308 L contribute to its SCC resistance over 309 L.

Fatigue crack propagation behavior of the grain size transition zone in a dual microstructure turbine disc

Constant load amplitude andΔK fatigue crack propagation (FCP) tests have been carried out to investigateFCP behavior of grain size transition zone in a dual microstructure turbine disc. The results show grain size exerts more significant influence in the time-dependent FCP regime, but the effect of grain size is relatively limited in the cycle-dependent FCP regime.Larger local plastic deformation zone is found in fine-grained region,which is believed to be the reason that causes more significant grain boundary oxidation along with contribution from more grain boundaries acting as short-circuit diffusion paths of oxide-forming elements, resulting in accelerated FCP.

Self-Healing of Aged Concrete Containing Crystalline Admixture and Expansive Agent under Repeated Loading

While self-healing concrete has been increasingly studied this past decade, research on the self-healing of a crack after repeated loading is still scarce. Studying this topic is of utmost importance because structures in practice are subjected to repeated damage, causing a variety of crack openings. Hence, this paper presents an evaluation of the self-healing properties of aged concrete containing a combination of crystalline admixture (CA) and expansive agent (CSA), and submitted to repeated loading. Pre-cracked at 218 days old by means of a three-point bending test, the prisms were reloaded every three weeks and healed in wet/dry cycles in between. After two loadings, they were reloaded a third time until failure. Two types of reloading procedures were carried out: (1) reloading to the same residual crack width; and (2) reloading with increasing crack width. Self-healing was assessed with water permeability measures before and after each reloading, macroscopic observations of the cracks, and mechanical recovery. The results showed that two phenomena occurred with opposite effects: damage versus healing. The magnitude of both processes depends on the reloading procedure. When reloading to the same crack width, the damage effect was lower than the healing effect, indicating that the healing products provided sealing even after repeated loading. When reloading with an increasing crack width, the damage effect was greater than the healing effect, but the healing rates were higher than reloading to a constant crack width, because of the creation of new fresh crack surfaces that healed faster. In any case, multiple damage slows down healing but the self-healing process continues. This confirms the long-term healing potential of cracked structures made of, or repaired with, self-healing concrete.

Crack initiation in PMMA plates with circular holes considering kinetic energy and nonlinear elastic material behavior

The coupled criterion (CC) of finite fracture mechanics (FFM) is extended to assess crack initiation in PMMA specimens with holes under quasi-static loading considering nonlinear elastic (NLE) material model and considering the kinetic energy variation in the energy balance. If dynamic aspects are disregarded, the failure stress predicted using the CC for either linear elastic (LE) material model or NLE material model is underestimated compared to the one measured experimentally. A better representation of the failure stress variation as a function of the hole size is obtained considering constant crack velocity profiles and velocities in the range [550–900] m/s (LE material model) or [400–600] m/s (NLE material model). The predicted failure stresses also depend on the crack velocity profile.

Energy release rate and crack propagation rate behaviour of moisture-deteriorated epoxy adhesives through the double cantilever beam method

ABSTRACT In this study, the relationship between the energy release rate (G 1C), crack propagation rate (da/dN), and the fracture morphology of specimens with deteriorated adhesives after moisture absorption were investigated through the double cantilever beam (DCB) method. The specimens were prepared using a thermosetting epoxy adhesive based on compound carboxyl-terminated butadiene–nitrile rubber and Al 6061-T6 adherends. To accelerate the deterioration of the adhesives, open-faced specimens were immersed in water at 63°C at varying durations. Prior to the assembly of the DCB specimens, the adherends were either treated using acidic solutions or sand blasted. Consequently, the effect of the moisture deterioration of adhesive and the surface treatment performed on the adherend on the fracture morphology was studied. Furthermore, the relationship between G 1C and da/dN was systematically investigated. At a constant crack opening speed, the failure mode changed from cohesive to interfacial fracture, and then reverted back cohesive fracture as the deterioration of the specimens progressed due to increasing immersion time. Interfacial fracture was not observed for the specimens with sandblasted adherends. Lastly, a decrease in da/dN was not observed even with increasing G 1C values of the immersed specimens because interfacial fracture was easy to occur when the cyclic strains were applied.

Analysis of dynamic fracture propagation in steel pipes using a shell-based constant-CTOA fracture model

In this paper, a finite element (FE) model with shell elements using a constant crack tip opening angle (CTOA) as fracture criterion was implemented for the simulation of dynamic fracture propagation in steel pipes. The new model was developed to improve computational efficiency over current CTOA models while retaining a high level of numerical accuracy. The commercial FE code ABAQUS was used to generate the meshes and perform the analyses. The proposed model was first used to reproduce data from an existing CTOA model of an American Petroleum Institute (API) X65 steel, matching the steady-state fracture velocity within a maximum difference of 5% while drastically reducing the computational time required. The model was then used to analyze recent experimental data from a full-scale pipe burst test of a Japanese Industrial Standard (JIS) steel STPG370, matching the crack velocity data within 4%. It was thereby demonstrated that FE analysis using this shell-based constant-CTOA model is an efficient method for describing dynamic fracture propagation in steel pipes and can be used as an engineering tool to develop fracture driving force based on CTOA.

Prediction of fatigue crack growth under variable amplitude loading by artificial neural network-based Lagrange interpolation

Artificial neural network has been several applications on fatigue crack, with prediction on fatigue crack growth life often serving as milestones. A typical difficulty in predicting the life curve of fatigue crack growth is the retardation of crack growth caused by the overload effect. Overload retardation, resulting in the lack of experiment data points in the retardation interval, is a long-term challenge for predicting fatigue crack growth. We improve the ability of back-propagation neural network to predict fatigue crack growth life by Lagrange interpolation, an interpolation for local data points. It combines the trend of whole data point to deal with the retardation interval, and interpolates multiple data points in the retardation interval when there is a lack of local data, and uses a neural network to construct the prediction formula of crack growth through self-optimization. In the study involving constant and variable amplitude fatigue crack growth experiments, the proposed method is proved to improve, with statistical significance, the predictive ability on the whole range of experiment data. The method is simple and accurate. Consequently, it is helpful to solve the problem of fatigue crack growth life of engineering structure.

Crack propagation mechanism of rock-like specimens containing non-parallel flaws subjected to internal hydraulic pressure and shear loading

The rock masses with existing discontinuous joints are more prone to failure under the combination of fissure water and shear loading. Therefore, combining laboratory experiments with discrete element simulation, the mechanism of crack initiation, propagation, and coalescence in rock-like specimens (a type of high brittle cement mortar material) with non-parallel flaws under shear loading and internal water pressure is investigated. The results reveal that for specimens with various flaw dip angles the propagation direction of all newly generated cracks is basically parallel to the shearing loading. When the flaw inclination angle reaches −30°, the cracks initiated near pre-existing flaw tips are the result of the combined effects of fluid pressure and compressive stress fields. Compared with the hydraulic fracturing curve, both plateau period and water pressure fluctuations appear in the selected domain near the crack propagation paths, which can demonstrate that the evolution of water pressure is extremely complex due to the constant crack healing and opening. With the increase of water pressure, the global stress field becomes more uniform, and the stress concentration near pre-existing flaw tips is weakened, indicating that water pressure can lead to local stress redistribution. Ultimately, the work is expected to provide guidance to the safe construction of tunnel excavation under complex geological conditions.

Mode I creep fracture of rubber-like adhesive joints at constant crack driving force

This work contributes to the description of time-dependent mechanical mode I creep fracture of viscoelastic adhesive joints under pure peel loading at finite deformations. The focus is on the dependency of crack resistance and resulting crack propagation rate on the forming of minor cracks beside the macroscopic major crack tip. In this work, Double Cantilever Beam tests were carried out at polyurethane-based flexible adhesive joints. The experiments were externally controlled on a constant J-integral, which was calculated in-situ from measured data to obtain a constant crack driving force and a statically loaded crack tip, respectively. The resulting creep crack propagation was investigated using two cameras targeting both sides of the specimen. With help of image processing and the beam compliance method, crack extension and crack propagation rate were determined. The respective results were used to draw comparisons between these two methods. The slight difference between the methods was attributed to the appearance of minor cracks, which seemed to reduce the stress intensity at the macroscopic crack tip, yielding a lower crack propagation rate.

Predicting evaporation from moist, cracked soil, based on near‐surface wind speed, crack width and crack distance

AbstractEvaporation from both cracked and uncracked soil surfaces under moist conditions was measured as a function of near‐surface wind speed, with wind speeds ranging between 0 and 5 ms−1. Crack aperture width and distance between neighbouring cracks ranged from 2 to 20 mm and 40 to 120 mm, respectively, while crack depth was kept constant at 50 mm. Experiments were carried out in a wind tunnel with a 1 m × 1 m × 2.5 m test section, using large‐scale (50 cm diameter, 15 cm depth) soil samples. Sixty‐six combination of crack properties and wind speed were considered. Resulting evaporation data were used to assess the shape of the relationships between evaporation rate, wind speed conditions and crack properties. A semiempirical model for estimating evaporation from cracked soil, as a function of wind speed, crack width and crack distance, given evaporation as a function of wind speed from uncracked soil, was developed. Results showed that evaporation from cracked soil under moist conditions increased by 60%–65% compared to uncracked soil, for the wind speed and crack properties given above. Evaporation from crack apertures was up to eight times higher than from an uncracked surface under the same wind conditions. Results further indicated that for constant wind speed and crack distance, there exists a crack width at which evaporation from the soil is at maximum. The semiempirical model based on exponential and power function relationships, was able to very closely match the experimental data and is further expected to be able to approximate evaporation under natural conditions.Highlights Near‐surface wind speed is strongly affected by presence of cracks Cracking in moist soils can increase evaporation up to 65% over uncracked soil There exists an intermediate crack width at which evaporation is at a maximum Evaporation may be estimated based on wind speed and crack properties

On the effective elastic properties of a material with mutually perpendicular systems of parallel cracks

The effective properties of cracked solids are often expressed in terms of the crack density parameter or its tensor generalization, using the approximation of noninteracting cracks. This approximation remains accurate at sufficiently high crack densities, provided the location of cracks are random. The presented analysis confirms that the effective elastic moduli of a material with ordered fracture structures strongly depend on the linear dimensions of cracks and their mutual arrangement even at a constant crack density. A change in these parameters can cause a noticeable anisotropy of the effective properties of the material even when the eigenvalues of the crack density tensor are equal to each other. The effective elastic characteristics of a material with one doubly periodic system of parallel cracks are compared with those for a material with two mutually perpendicular systems of such cracks in a two-dimensional formulation. The calculations are carried out using the approximate method of M. Kachanov for determining the mean stresses at the cracks edges, applicable for large systems of interacting cracks. Analysis of the obtained results showed that the effective compliance of the material in a certain direction is largely determined by the effects of interaction (shielding and amplification) within a system of parallel cracks perpendicular to this direction. The interaction of this system of cracks with the perpendicular system has a weak effect on the indicated properties in the case of rectangular symmetry of the system. In this case, the interaction of mutually perpendicular systems of cracks leads to a violation of the symmetry of the tensor of effective elastic constants.

Subcritical Crack Growth Parameters for Glass under Different Environmental Conditions

In the present work, subcritical crack growth in soda‐lime silicate glass is investigated under different environmental conditions. Crack growth parameters as a function of temperature and humidity were determined by dynamic fatigue tests. The specimens were pre‐damaged for constant initial crack lengths in all specimens using the Vickers indenter. The initial flaw size induced by the Vickers indenter was obtained by a scanning electron microscope picture of the fracture surface, which could also show the initial flaw geometry. Furthermore, the influence of humidity and temperature on the failure stress of specimens with a constant initial crack length was simulated and the deviations are shown. A comprehensive version of this investigation is currently (16.03.2021) under review in the Journal for Glass Structures and Engineering.

The Crack Angle of 60° Is the Most Vulnerable Crack Front in Graphene According to MD Simulations

Graphene is a type of 2D material with unique properties and promising applications. Fracture toughness and the tensile strength of a material with cracks are the most important parameters, as micro-cracks are inevitable in the real world. In this paper, we investigated the mechanical properties of triangular-cracked single-layer graphene via molecular dynamics (MD) simulations. The effect of the crack angle, size, temperature, and strain rate on the Young’s modulus, tensile strength, fracture toughness, and fracture strain were examined. We demonstrated that the most vulnerable triangle crack front angle is about 60°. A monitored increase in the crack angle under constant simulation conditions resulted in an enhancement of the mechanical properties. Minor effects on the mechanical properties were obtained under a constant crack shape, constant crack size, and various system sizes. Moreover, the linear elastic characteristics, including fracture toughness, were found to be remarkably influenced by the strain rate variations.

Analytical model for rock effective elastic properties with aligned elliptical cracks embedded in transversely isotropic background

ABSTRACTSeismic methods are often used for fracture detection and characterization, for which many analytical rock physics models have been developed to link fracture parameters to rock elastic properties. However, most of these models are limited to isotropic background and circular (penny‐shaped) fractures. In this work, we derived a more general analytical model for effective elastic properties of rocks embedded with aligned elliptical cracks in transversely isotropic background. The solutions for the case with dry cracks parallel to isotropic plane of transversely isotropic background were first derived using the corresponding Eshelby's tensor. Then, the results were extended to the case with inclined and rotated cracks under the assumption of constant crack opening displacement tensor. Finally, to obtain the results for fluid‐filled crack case, the Brown–Korringa equation was applied. To investigate the controlling factors on rock elastic properties, we studied one fractured tight sandstone sample with transversely isotropic background. The results show that rock elastic properties are insensitive to crack spin angle, but sensitive to crack inclination angle. Depending on crack inclination angle and fluid saturation, background anisotropy can either amplify or reduce the anisotropy of seismic wave velocity. Crack density and aspect ratio are found to be controlling crack parameters for rock elastic properties. The crack plane shape has negligible direct influence on rock elastic properties, whereas it has indirect influence by affecting values of crack density and aspect ratio. Compared with the numerical model and the previous analytical model for the special case with circular cracks, our model agrees well with them, which validates the accuracy of our model.

Suitability of fatigue crack growth thresholds at negative stress ratios for ferritic steels and aluminum alloys in flaw evaluation procedures

Fatigue crack growth thresholds for ferritic steels and aluminum alloys in flaw evaluation documents are reviewed. The WRC (Welding Research Council) Bulletin, ASME (American Society of Mechanical Engineers) Code Section VIII, IIW (International Institute of Welding) and BS (British Standards) 7910 give constant fatigue crack growth threshold values at negative stress ratios. However, the definitions of the thresholds at negative stress ratios are different between these flaw evaluation documents. From fatigue crack growth tests and collection of fatigue crack growth threshold data, the thresholds are affected by compressive stresses. It can be said that the thresholds at negative stress ratios are not constant. Therefore, the thresholds given by the WRC Bulletin, ASME Section VIII and IIW are slightly un-conservative. The threshold given by BS 7910 is considerably conservative. A suitable definition of the threshold at negative stress ratios for application in flaw evaluation procedures is proposed as the variable threshold expressed by full range of stress intensity factors.

Fatigue Crack Growth Prediction under Spectrum Load in an Aluminium Alloy using Crack Driving Force K*eff Approach

Fatigue Crack Growth (FCG) behaviour in a Single-Edge-Notched Tension (SENT) specimen of 2024-T3 aluminium alloy under a standard mini-FALSTAFF spectrum load sequence was experimentally determined. Further, the FCG behaviour was predicted using cycle-by-cycle method and compared with experimental results. Prediction procedure involved are rain-flow counting of fatigue load cycles, estimation of crack driving force for each of the counted cycle and prediction of crack extension per cycle from constant amplitude crack growth rate equation. In the present work, a new crack driving force (CDF) K*eff involving Kujawski’s crack driving force K* in conjunction with Elber’s crack closure concept was used to account for load interaction effects. FCG prediction was also made using conventional CDF ΔKeff (Elber’s) approach. A good correlation was observed between experimental and predicted FCG behaviour under spectrum loads by the proposed K*eff approach. Also, this prediction was observed to be better than that predicted by conventional ΔKeff approach.