Size Of Fracture Process Zone Research Articles

A Review of the Hydraulic Fracturing in Ductile Reservoirs: Theory, Simulation, and Experiment

The bottom-hole pressure of hydraulic fracturing in ductile reservoirs is much higher than that of the hydraulic fracturing simulation, and the fracture toughness inferred from the field data is 1–3 orders of magnitude higher than that measured in the laboratory. The rock apparent fracture toughness increases with the increase in the confining pressure. Excluding the influence of the fluid viscosity and the fluid lag on the apparent fracture toughness, the fracture process zone (FPZ) at the fracture tip can explain the orders of magnitude of difference in the apparent fracture toughness between the laboratory and the field. The fracture tip is passivated by plastic deformation, forming a wide and short hydraulic fracture. However, the size of the FPZ obtained in the laboratory is in the order of centimeters to decimeters, while an FPZ of 10 m magnitude is speculated in the field. The FPZ size is affected by the rock property, grain size, pore fluid, temperature, loading rate, and loading configuration. It is found that the FPZ has a size effect that tends to disappear when the rock specimen size reaches the scale of meters. However, this cannot fully explain the experience of hydraulic fracturing practice. The hydraulic fracturing behavior is also affected by the relation between the fracture toughness and the fracture length. The fracture behavior of type II and mixed type for the ductile rock is poorly understood. At present, the apparent fracture toughness model and the cohesive zone model (CZM) are the most suitable criteria for the fracture propagation in ductile reservoirs, but they cannot fully characterize the influence of the rock plastic deformation on the hydraulic fracturing. The elastic-plastic constitutive model needs to be used to characterize the stress–strain behavior in the hydraulic fracturing simulation, and the fracture propagation criteria suitable for ductile reservoirs also need to be developed.

Crack face friction effects in the strength scaling of composites failing by kinked shear cracks under transverse compression

Recent research showed that the failure and strength scaling of composites under transverse compression exhibits a quasibrittle behavior, characterized by a non-negligible fracture process zone (FPZ). The present work is aimed at analyzing and quantifying the contributions of crack face friction towards this quasibrittleness, by focusing on fracture plane angles and the strength scaling. The failure, frictional effects, and strength scaling are numerically predicted via the fixed crack damage model, augmented with Puck’s friction-dependent damage initiation criterion and Ragueneau’s parallel coupling model for combined damage and friction evolution. The model is calibrated and verified using available test data and then used to analyze the transverse compressive failure in unnotched specimens and strength scaling in pre-cracked specimens, with and without friction. The analyses show that the friction-augmented model can accurately predict the fracture plane angle equal to 53 degrees in unnotched specimens, and can be tuned to reproduce other angles as well. Further, in all notched specimens failure occurs via a kinked shear crack propagating at an angle to the pre-crack, and having at its tip a large FPZ. The kink angle is observed to fall in the range of 44 to 47 degrees when friction is excluded, and 54 to 58 degrees when friction is included. The specimen strengths with or without friction, scale in accordance with the energetic type II size effect law. This finding is also supported analytically using energy balance-based arguments. The results reveal that the inclusion of friction can considerably increase the strength and enlarge the FPZ size (by nearly 90%), making the fracturing behavior significantly more quasibrittle. The strength increase is size dependent for smaller sizes, and appears to become roughly constant for larger specimen sizes. The FPZ of the kinked shear cracks is seen to embody a strongly multiaxial stress state. This makes the fracture energy associated with the kinked shear crack growth much higher than the pure mode II fracture energy. The frictional dissipation can further lead to an increase in this energy, which in the present case is found to be nearly 130%. These findings serve to emphasize the importance of considering and quantifying friction effects in the transverse compressive failure of composites.

Evolution trend and weakening mechanism of mode-I fracture characteristics of granite under coupled thermo-hydro-mechanical and thermal treatments

Understanding the fracture behavior and fracture-morphology evolution of granite after coupled thermo-hydro-mechanical (THM) environment is important for many geotechnical projects. Previous studies mostly focused on the fracture-response mechanism of rocks after a thermal treatment, whereas only a few studies were conducted on the fracture toughness, fracture-process-zone (FPZ) size, and fracture-morphology evolution of granite after the THM multifield coupling. Therefore, a coupled THM damage treatment (i.e., THM-induced damage) of granite was carried out using a self-developed, high-temperature, and high-pressure multifield coupling triaxial universal tester. Subsequently, a series of test methods was employed, which included the full-field 3D digital-image correlation technique (real-time tracking of the strain/displacement field on the specimen surface), X-ray computed tomography scanning technique (to obtain the microdamage structure inside the specimen), and 3D laser scanner (to obtain the section morphology of the specimen). These methods were employed to study the response mechanism of mode-I fracture of a granite specimen (fracture toughness, fracture trajectory, FPZ size, and fractal dimension of the section topography). Furthermore, to elucidate the correlation between the coupled THM induced damage and fracture characteristics of granite, the same experimental test was also carried out on the granite using a thermal treatment. The result show that the evolution pattern of the fracture and morphological parameters of granite after the coupled THM treatment was different from that using only the thermal treatment, and the value of these physical parameters fluctuated at approximately 400 °C–500 °C. This is due to the limitation of the triaxial stress on the thermal expansion (25 °C–300 °C), competitive effect of “opening” and “closing” of micropores/microcracks (400 °C–500 °C), and deterioration of the coupled THM field (600 °C–650 °C). The results provide insights and theoretical guidance for high-temperature underground rock-mass engineering such as deep nuclear-waste reservoir.

Transient and steady state viscoelastic crack propagation in a double cantilever beam specimen

Crack growth in viscoelastic materials is understood with the use of cohesive models, or steady state theories which focus on viscoelastic dissipation. We consider a double cantilever beam (DCB) specimen under a remote constant pure moment, which is initially suddenly applied to the beams. It is shown that the response to the applied moment rapidly reaches a steady state in terms of crack propagation speed. In contrast, it is shown that the external work rate, contributing to fracture energy, stored elastic energy and viscous dissipation, has a transient that possibly lasts a significantly longer time. The dissipation rate increases with speed for a standard material, reaching a limit governed by the ratio of instantaneous to relaxed modulus. However, the initial dissipation rate at low crack propagation speeds can be orders of magnitude larger than the latter limit, and depends on the ratio between the initial crack size and the fracture process zone size, a regime which we define ultratough. For thin beams, we do not find any evidence, even in the steady state, of the dissipation-based theories’ suggestion of a reduced maximum load and then of an unstable regime of decreasing load with speed.

Fracture and energetic strength scaling of epoxy-resins toughened with multi-walled carbon nanotubes

The paper studies the toughening effect of multi-walled carbon nanotubes (MWCNTs) as nanofiller on epoxy resins. We use the size-effect testing methodology to prepare geometrically similar epoxy specimens with varying MWCNT weight fractions. We tested 72 single-edge notched samples and 72 unnotched samples in tensile loading. The addition of MWCNTs resulted in a non-negligible fracture process zone (FPZ). A size-dependent strength is observed and is modeled using type-II energetic scaling law. The mode-I fracture toughness and the FPZ size increased with the MWCNT content, peaked at optimum weight fraction, and then decreased at higher weight fraction. Fractography showed the growth of nanoclusters with an increase in the MWCNT content. We speculate this reduction in the fracture toughness at higher weight fractions is due to failure occurring in the nanoclusters instead of the nanofiller-reinforced matrix.

Determination of mode I fracture toughness of rocks with field fitting and J-integral methods

Static fracture testing was performed on ISRM-suggested semi-circular bend (SCB) specimens with a constant CMOD increment rate of 0.0002 mm·s−1, and the digital image correlation (DIC) technique, as a practical and effective non-contact tool, was adopted for full-field deformation measurement and fracture process zone (FPZ) size determination. Two displacement-based methods, i.e. field fitting method and J-integral method, were employed to measure the fracture toughness of three types of rocks, i.e. red sandstone, marble, and granite. The effectiveness and robustness of two displacement-based methods were verified with synthetic images containing a mode I crack. Moreover, the sensitivity of the affecting factors in displacement-based methods, such as crack tip location, area for field fitting, the number of solution terms, and the integral paths were studied for more reliable fracture toughness of SCB specimens. Both displacement-based methods give the effective fracture toughness inherently considering the existence of the FPZ above the notch tip, without knowledge of the geometry of the specimen and applied loads. Experimental results indicated that the crack tip location estimated by the field fitting method is close to the merged point of the opening displacement contours, i.e. the tip of the FPZ. Both displacement-based methods generate comparable fracture toughness of three rocks, and an increase of 20%∼35% in fracture toughness is observed compared to the standard load-based method. Moreover, the effectiveness and applicability of the modified load-based method that takes the FPZ length into account are also verified with the two displacement-based methods.

Determining specimen thickness limit in fracture toughness tests applied to dental ceramics and metal alloy interfaces

The aims of the current study are to present computational simulations based on the finite element method in order to determine the lowest viable thickness of materials used to make ceramic samples based on the interface of groups of materials (Ni–Cr/ceramics, alumina/ceramics), and samples made of each of these materials, alone; as well as to report the effect of variation in the stress intensity factor of these interfaces (β). Test conditions were simulated in Abaqus CAE software and mesh features focused the crack tip. Fracture toughness analysis was carried out by simulating the three-point bending test (SEVNB specimen of the Fracture Mechanic standards). Based on the present results, the lowest material thickness necessary to meet the stress intensity requirement at the crack tip was 8 mm of each material, under symmetry condition, for sandwich composition. Such a thickness included fracture process zone (FPZ) size and plastic zone (PZ). Sandwich thickness was enough to maintain the test conditions established for the standards. Samples produced in the present study met the requirements of the fracture toughness test, based on the ASTM E−399 standard - specimens with the lowest possible sandwich thickness were obtained and they met the stress intensity requirements of the crack tip. This finding pointed towards a sample based on using a reduced amount of test materials - such as those used for dental restoration. The lowest material thickness in the sandwich was 8 mm, for all groups of materials, under symmetry conditions. This thickness includes fracture process zone size and plastic zone size. The herein proposed sandwich thickness was enough to maintain the test conditions established by fracture mechanic standards.

A modified G criterion considering T-stress and differentiating the separation and shear failure in crack propagation

In view of shear failure controlled by distortion and separation failure governed by dilation having different significance for the crack propagation, the traditional G criterion is modified by differentiating the volumetric and distortional parts in energy release rates which involve the influence of T-stress. The critical volumetric to distortional energy release rate ratio is introduced as an intrinsic material property. As the critical volumetric to distortional energy release rate ratio increases, the failure pattern for mode II crack gradually transits from separation dominant failure to shear dominant failure. The modified G criterion is theoretically investigated through discussing the influence of critical volumetric to distortional energy release rate ratio, T-stress and fracture process zone size on the crack propagation behavior (i.e., crack kinking angle and fracture resistances). The crack kinking angle is found to reduce as the critical volumetric to distortional energy release rate ratio increases, but enlarge as the T-stress or fracture process zone size increases. The fracture resistances are found to decrease as the critical volumetric to distortional energy release rate ratio, T-stress or fracture process zone size increases. The modified G criterion shows a superior predictability for the experimental results reported by Aliha et al. (2012, 2013), Williams and Ewing (1972) and Mousavi et al. (2020) over the maximum tensile stress criterion (MTS criterion) and traditional G criterion. The modified G criterion has the potential to predict the crack propagation behavior for a variety of materials.

Experimental study on fracture properties of concrete under cyclic loading using digital image correlation method

Three-point bending tests are performed on notched concrete beams under various cyclic loading regimes. Meanwhile, the digital image correlation (DIC) method is used to monitor the crack propagation. The fatigue fracture life decreases with the loading level increases for constant-amplitude cyclic loading. The residual crack mouth opening displacement (CMOD) accumulates and fracture stiffness degrades with the loading process. The size of fracture process zone (FPZ) can be determined based on the full displacement field monitored by DIC method. The length of FPZ increases linearly with the increasing of effective crack length before the crack tip opening displacement (CTOD) exceeds the critical value. When CTOD exceeds the critical value, a macroscopic crack formed in front of the initial crack tip. For cyclic envelope loading, the length of FPZ increases at beginning and then decreases with the increasing of effective crack length. For constant-amplitude loading, CTOD never reaches the critical value, and the macroscopic crack does not propagate forward. Finally, it is found that both the calculated effective crack lengths of concrete under constant-amplitude loading by two-parameter model (TPM) and DIC methods present three-stage feature, but the values calculated by TPM are smaller than those by DIC method.

Effect of microwave heating on fracture behavior of granite: An experimental investigation

Hard rock breaking is a great challenge for deep drilling and mining engineering, and the microwave-assisted rock breaking technique offers a promising solution. However, the lack of knowledge of the effects of microwave irradiation on hard rocks limits the further development of this technology. Laboratory tests have been conducted to investigate the variations of fracture properties of granite subjected to microwave heating. The semi-circular bend (SCB) specimens were prepared, and mode I fracture tests were conducted on the microwave treated granite specimens. The acoustic emission (AE) events was recorded and the strain field was calculated by the digital image correlation (DIC) technique. The test results demonstrated that the temperature of the sample surface increased linearly as the increasing heating time, and increasing microwave power contributes to enhancing the heating rate. According to the results of scanning electron microscope (SEM), intergranular cracks were the main form of cracks, and the transgranular cracks usually appeared in samples with high microwave power or longer heating time. The generation of micro-cracks can be attributed to the high temperature and the thermal shock. With the increasing heating time, the fracture toughness decreased exponentially, the AE active period prolonged, and the fractal dimension of the fracture surfaces (FSD) continuous increased. Compared to an untreated sample, the maximum principal strain and fracture process zone (FPZ) size of the microwave heated sample were larger at the same loading level, which indicated the enhancement of ductility. According to the experimental results, the relationships between FPZ size, fracture toughness and FSD were empirically regressed. Understanding the effects of microwave heating on the fracture properties is of significant to improve hard rock breaking efficiency.

Effect of the shape of the softening damage law on the predicted tensile fracturing and energy dissipation in textile composites

The fracturing behavior of fiber-reinforced composites is often modeled using continuum damage mechanics-based approaches which commonly assume a linear softening damage law, i.e. a linearly decreasing stress with increasing strain. The objective of this paper is to assess the suitability of this assumption for composites and to systematically analyze the effect of the assumed shape of the softening damage law at material point, on the predicted fracturing behavior of the structure. The material considered is an epoxy/carbon-fiber twill woven composite. Numerical evaluations are conducted by predicting the strength size effect and progressive accumulation of damage in a structure and comparing with experimental measurements. Damage models with a wide range of shapes of softening laws are considered. These include linear, bilinear, trilinear, exponential, power law and sigmoidal. The effect of introducing a sudden drop in the damage law is also evaluated. All modeling is conducted via the crack band model (CBM), to ensure the mesh objectivity of results. It is found that despite using the right strength and fracture energy as input at the material point level, not all softening law shapes can accurately predict the strength size effect and post-peak softening. Especially the sudden drop feature leads to severe underprediction of strength. Bilinear softening shows the best combination of simplicity and accuracy, especially if formulated via the R-curve approach. Further insights are obtained by assessing the predicted fracture process zone size and fracture energy via the size effect method. Finally structure level predictions are made by considering plug initiated axial crushing of a cylindrical crushcan. The close ties between the shape of the material softening law and predicted process zone, and structural fracturing are revealed, and shown to be an important consideration in formulating damage models.

An approximate method for evaluating the fracture process zone near mode II dynamic crack tip

Fracture process zone is the key for understanding the nonlinear fracture of quasi-brittle materials. Evaluation of the shape and size of fracture process zone near mode II dynamic crack tip is still a problem unsolved completely at present. The analytical methods for study on dynamic crack like integral transformation method and Wiener-hopf method are not easy to be used to calculate the stress fields near dynamic crack tip. So far the studies on fracture process zone near dynamic crack tip mostly focused on the experimental and numerical simulations. An approximate method for evaluating the shape and the size of fracture process zone is proposed and the feasibility of the new method is demonstrated by comparing with the results calculated based on the well-known stress fields. The shape and size of the fracture process zone near the mode II dynamic crack tip in dependence on crack propagation velocity are determined based on the approximate method. The results show that the areas of fracture process zone calculated based on the new method are nearly the same with the results calculated based on the well-known stress fields under plane stress condition and plane strain condition by the Von Mises criterion. The approximate method can provide a good reference for determination of the fracture process zone near mode II dynamic crack tip since no analytic method has been found for evaluating the fracture process zone near dynamic crack tip to the authors’ knowledge. The fracture process zone near mode II dynamic crack tip is distributed symmetrically with respect to crack plane and increases with the crack propagation velocity. The area of fracture process zone changes more rapidly when the Rayleigh wave velocity is approached. The areas of fracture process zone calculated under plane stress condition are bigger than these calculated under plane strain condition.

Induced anisotropy in the fracturing behavior of 3D printed parts analyzed by the size effect method

This paper analyzes via the size effect method, the induced anisotropy in the fracturing behavior of 3D printed parts made using Acrylonitrile Butadiene Styrene (commonly abbreviated as ABS). The aspects of fracturing behavior considered include the strength, fracture toughness, the nonlinear fracture process zone (FPZ) size, and the degree of quasibrittleness. 3D printed ABS specimens of various sizes and various relative orientations of the pre-crack and the 3D printed layers are considered. The fracture properties are measured via fracture tests on single edge notch bending specimens. The measurements are seen to conform to the well-known size effect laws for strength and fracture toughness. It is demonstrated that the 3D printed parts exhibit considerable anisotropy in their fracturing behavior, which would not occur in the monolithic counterparts. This occurs not only for the strength and fracture toughness, but also the FPZ size and therefore the degree of quasibrittleness. The anisotropy stems from the crack path direction relative to the stacking direction of macrolayers and microlayers within a layer. The results show that these effects must be given due consideration when developing reliable designs for additively manufactured parts.

Mixed mode fracture tests and inversion of FPZ at crack tip of overlying strata in underground coal gasification combustion cavity under real-time high temperature condition

Measuring the fracture parameters of rock materials under real-time high temperature is of great significance for accurately evaluating the stability and safety of high-temperature underground tunnels. At present, the related research is focused on the fracture properties of rocks after treatment with high temperature. To this end, we independently developed a set of testing apparatus with effect of THMC coupling of high temperature and high pressure. Using this equipment, a serious of mixed mode I ± II fracture experiments of overlying strata (red sandstone) in combustion cavity under real-time high temperature conditions (20–700 °C) are carried out. And, the variations of fracture toughness, fractal dimension of fracture trajectory and fracture initiation angle with respect to temperature and notch angle are clarified. In addition, in order to predict the fracture process and fracture behavior of red sandstone at real-time high temperature, the experimental fracture envelopes are compared with that predicted by traditional fracture criterion. It is concluded that the fracture process zone (FPZ) size at the crack tip plays a crucial role in the effectiveness of the fracture criterion, and it is temperature-dependent. Finally, based on the generalized tangential stress criterion (GMTS), the effective FPZ sizes of red sandstone under different high temperature conditions are determined by using particle swarm optimization (PSO) algorithm combined with least square method. The research results of this paper are of great significance for evaluating the stability and safety of overlying strata (red sandstone) in combustion cavity.

Mixed-Mode I-II Fracture Process Zone Characteristic of the Four-Point Shearing Concrete Beam.

The size of the fracture process zone (FPZ) has significance for studying the fracture mechanism and fracture characteristics of concrete. This paper presents the method of assessing the FPZ of Mixed-Mode I-II for quasi-static four-point shearing concrete beams with pre-notched by Lagrangian strain profiles from digital image correlation (DIC). Additionally, it explores the influences of volume rates of the coarse aggregate of 0%, 28%, 48%, and 68%, and the specific surface areas of 0.12 m2/kg, 0.15 m2/kg, and 0.26 m2/kg on the size of the FPZ. It shows that the size of FPZ in four-point shearing concrete beam can be characterized by the displacement field and strain field using DIC. The size of FPZ conforms to linear positive correlation with the volume rate of coarse aggregate, and linear negative correlation with the specific surface area of coarse aggregate. It presents that the crack initiation of the four-point shearing beam with the pre notch is dominated by mode I load, and the propagation and fracture of Mixed-Mode I-II cracks are caused by the combined effect of Mode I and Mode II loading.

A novel tearing residual strength model for architectural coated fabrics with central crack

This study concerns the tearing residual strength models of architectural woven coated fabrics. Firstly, central crack tearing tests were conducted, the evolution of tearing residual strength with the increase of initial crack length is investigated. Secondly, the commonly used tearing residual strength models, including linear elastic fracture mechanics (LEFM) models and stress field models, are summarized and analyzed. Due to their inherent defects in theoretical foundation, the prediction precision is merely determined by curve fitting, no physical meaning can be drawn from these models. Finally, an asymptotic model based on fracture mechanics theory is proposed. The relative size of fracture process zone (FPZ) is adopted to distinguish the transition from strength-controlled fracture to quasi-brittle fracture and finally to toughness-controlled fracture. The prediction results agree very well with the test data, and most of test data lies in nonlinear fracture range which has never been considered.

Use of DC voltage fluctuation method to investigate real-time Mode I and Mode II subcritical crack growth behavior in gypsum rock

Subcritical crack growth strongly influences the mechanical behavior of rock and the precursory phase of geohazards and catastrophic failure. In earlier studies, indirect measuring methods were used to investigate the subcritical crack growth behavior of rock materials. However, these methods cannot fully reflect the whole process of subcritical crack growth of geomaterials. Therefore, in this study, a new method (DC voltage fluctuation method) was developed which can monitor the whole process of crack growth and measure the crack growth rate in real time. This method is based on the monitoring principle of change in voltage caused by the change in resistance. Then, the whole processes of Mode I and Mode II subcritical crack growth of gypsum specimen were monitored in real time by the self-designed fracture strain gauge, which consists of 10 breakable resistance wires, and a DC voltage signal monitor. Furthermore, using the measured crack growth rates and the stress intensity factors of varying crack path lengths, the parameters of the modified Charles model were fitted. The results show that: (1) the subcritical crack growth process mainly includes three stages: cracking latent period (primary stage), steady-state crack growth stage (secondary stage), and accelerated crack growth stage (tertiary stage). The cracking latent period lasts for the largest proportion of the entire fracture process duration. The duration of each stage decreases gradually with increasing applied load. (2) In the steady-state crack growth stage, both Mode I and Mode II crack growth rates increase with increasing applied load. However, the crack growth rates in the accelerated stage are basically the same with increasing applied load. When a specimen is subjected to a given constant applied load, the subcritical crack growth rate of Mode II is higher than that of Mode I in the secondary and tertiary stages. (3) The parameters A and n of the subcritical crack growth model (modified Charles model) (secondary stage) increase with increasing external applied load. The parameters are closely associated with the size of fracture process zone at the crack tip. The results of this study can provide a deeper insight into the macroscopic failure of rock, and also provide the parameters for the time-dependent damage evolutional process of underground constructions.

On the effect of interfacial patterns on energy dissipation in plastically deforming adhesive bonded ductile sheets

Toughening of brittle adhesive joints is a topic of great interest for the fabrication of layered structures. Recent experimental work by the authors indicated that spatially varying interface properties (i.e., patterned interfaces obtained using laser irradiation) could tune energy dissipation in plastically deforming adhesive joints. In this study, we use a cohesive zone approach to ascertain the interplay between fracture process zone size and pattern geometry on the overall work of separation. The analysis is carried out in the context of the elasto-plastic peeling response of adhesive bonded ductile thin sheets. The mating surfaces of the adherents feature alternating strips with strong and weak cohesive properties. Our finite element study shows that a careful choice of pattern length-scales, which requires a small area fraction of surface pre-treatment, allows to achieve a step-like increase in peel load and absorbed energy in otherwise brittle adhesive joints.

Visualization of acoustic emission monitoring of fracture process zone evolution of mortar and concrete beams under three-point bending

By combining the b-value and acoustic emission (AE) event density, a parameter referred to as the T value was developed to construct a fracture process zone (FPZ) using AE data to study the fracture process of mortar and concrete beams under three-point bending tests. The FPZ is successfully constructed by using a T value contour map. The contour map shows that the FPZ evolved from the middle of the beam to the boundary for the mortar beam and that it evolved in the whole section of the beam at the beginning of the tests, localized in the middle of the beam and moved upward until the end of the test for the concrete beam. A quantitative analysis of the FPZ size shows that microcracks in the concrete beam are more developed and distributed in a wider range than those in the mortar beam. The mean T value in every contour map indicates that both the mortar beam and concrete beam show a decrease in the T value when reaching their peak load, which can be considered characteristic of the critical state of beams under three-point bending. When considering the use of coarse aggregate, note that the mesostructure formed by the coarse aggregate is responsible for the large-range FPZ region and the high load of the concrete beam. This method offers insight into the FPZ by AE and its successful reproduction. The T value contour map can also be applied for concrete structure damage monitoring.

Crack growth rate prediction based on damage accumulation functions for creep-fatigue interaction

The present study is concerned with formulation of a model for the creep–fatigue crack growth rate prediction on the base of fracture damage zone concepts. It is supposed that crack growth rate can be determined by integration of damage accumulation rate equations into the fracture process zone for low-cycle fatigue and creep loading independently. In the case of low-cycle fatigue loading the damage accumulation function proposed by Ye and Wang was used as well as a classical Kachanov-Rabotnov power law was employment for the creep damage accumulation characterization. Fracture process zone size is calculated on the base of the nonlinear stress intensity factors concept proposed by Shlyannikov. The background for the proposed general model of crack growth rate under creep and fatigue interaction is given in order to comparison with the experimental data. Experimental study of crack growth rate under creep and fatigue interaction is performed for compact tension specimen made from 20CrMoV5. Crack growth rate carried out at the elevated temperature of 550°C according to ASTM E2760 standard. The predictions of the crack growth rate were compared with the experimental data for the 20CrMoV5 steel obtained at an elevated temperature, and the agreement was found to be satisfactory.