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The fracture behavior of welding material at elevated temperatures can significantly affect the performance of steel welded connections in fires. Therefore, this paper investigates the fracture behavior and fracture model of welding material in steel welded connections exposed to elevated temperatures up to 700°C. Firstly, using the standard tension test data and numerical analysis method, the true stress–strain model of E7018 welding materials at elevated temperatures was derived for fracture prediction of steel welded connections. The fracture parameters of the welding materials at elevated temperatures in tension and shear were calibrated from the results of the standard tension test and longitudinal fillet-welded connection tension test, respectively. The 2D fracture models of welds at elevated temperatures were developed considering the relationship between stress triaxiality and equivalent plastic strain at fracture. The 3D fracture models of welds at elevated temperatures were then established from the 2D fracture model by considering the effect of Lode angle parameters in tension and shear. The 3D fracture models of welds were validated against the tension tests on the fillet welded connections at elevated temperatures under different load angles including 0°, 45°, and 90°. Finally, the fracture model as the function of temperature, stress triaxiality, Lode angle parameter, and plastic strain at fracture was proposed for E7018 welding material. According to the results, the welding material demonstrates ductile fracture behavior at elevated temperatures. The developed 3D fracture model can reasonably predict the fracture behavior of the welding material in steel welded connections at elevated temperatures. [ABSTRACT FROM AUTHOR]

Creep failure of hierarchical materials is investigated by simulation of beam network models. Such models are idealizations of hierarchical fibrous materials where bundles of load-carrying fibers are held together by multi-level (hierarchical) cross-links. Failure of individual beams is assumed to be governed by stress-assisted thermal activation over local barriers, and beam stresses are computed by solving the global balance equations of linear and angular momentum across the network. Disorder is mimicked by a statistical distribution of barrier heights. Both initially intact samples and samples containing side notches of various length are considered. Samples with hierarchical cross-link patterns are simulated alongside reference samples where cross-links are placed randomly without hierarchical organization. The results demonstrate that hierarchical patterning may strongly increase creep strain and creep lifetime while reducing the lifetime variation. This is due to the fact that hierarchical patterning induces a failure mode that differs significantly from the standard scenario of failure by nucleation and growth of a critical crack. Characterization of this failure mode demonstrates good agreement between the present simulations and experimental findings on hierarchically patterned paper sheets. [ABSTRACT FROM AUTHOR]

The method of backfill in underground mining is important for ground control as well as material recycling and energy efficiency. Even though extensive testing and field studies of backfill have been conducted, less is known about the detailed damage and fracturing that occurs directly at the rock/backfill interface. In this paper, cylindrical specimens containing an inner diameter of backfill and an outer diameter of rock (RB) were tested under triaxial compression. Acoustic emissions (AE) were used throughout testing, and X-ray computed tomography (CT) scanning was conducted before loading was applied and after the specimens had failed. The high-resolution CT images were then converted into point clouds to isolate the fractures and visualize them in three dimensions. The point clouds clearly show that fracturing occurred both in the rock and along with the contact between rock and backfill, while very little fracturing was found to occur in the backfill. Based on the point cloud and AE results, a unique evolution of fracturing is found to occur that includes two stages of shear fracturing in the rock, tensile fracturing along with the rock/backfill interface, and final tensile fracturing in the rock after delamination from the backfill, all of which contributed to the nonlinear stress–strain response. This paper presents a novel approach for investigating the initiation and propagation of 3D fractures in laboratory testing and can offer a useful reference for further studies on the mechanics of bi-material structures. [ABSTRACT FROM AUTHOR]

In solid mechanics, Maxwell stresses are known to be induced if a body is exposed to magnetic and, in the case of dielectrics, electric fields. Acting as tractions at outer or inner surfaces as well as volume forces, they are superimposed with tractions and stresses due to mechanical loads and provide a more or less significant contribution, depending on loading, material properties and geometric aspects. The Maxwell stress tensor, constituting the physical and mathematical basis, however, is controversially discussed to date. Several formulations are known, most of them having been suggested more than 100 years ago. Being equivalent in vacuum, they differ qualitatively just as quantitatively in solid or fluidic matter. In particular, the dissimilar effect of body forces, emanating from a choice of established Maxwell stress tensor approaches, on crack tip loading in dielectric solids is investigated theoretically in this paper. Due to the singularity of fields involved, their impact is basically non-negligible compared to external mechanical loading. The findings obtained indicate that fracture mechanics could be the basis of an experimental validation of Maxwell stress tensors. [ABSTRACT FROM AUTHOR]

When plates with edge cracks in the rolling process is straightened by cyclic tensile and compressive stress, the tip of edge crack always accompanied by stress concentration, which leads to crack propagation. In this paper, damage parameters are imported into the plate straightening model based on determining the GTN damage parameters of magnesium alloy materials by inverse finite element calibration method, the influence of different straightening process schemes and prefabricated V-shaped crack geometry on crack growth is analyzed through the way of the combination of simulation and straightening experiment. The results show that the peak values of equivalent stress and equivalent strain under each straightening roll appear at the crack tip. The value of longitudinal stress and equivalent stain decrease with the distance to crack tip becomes larger. The peak value of longitudinal stress appears when the crack circumferential angle is about 100°, and the crack tip is easy to form crack propagation; when the plate passes roll 2 and roll 4, the equivalent stress and strain concentration at the crack tip are most obvious; when the reduction reaches a certain degree, the void volume fraction (VVF) reaches the VVF of the material breaking; with the increase of the entrance reduction, the number of VVF at the crack tip which reaches the material fracture increases, and the length of crack propagation increases; the stress concentration at the tip of V-shaped crack with large length–width ratio is obvious, and the VVF is more likely to reach the VVF at the time of material fracture, crack initiates and propagates easily. [ABSTRACT FROM AUTHOR]

Frost crack evolution induced by cyclic freeze–thaw is responsible for rock deterioration in cold regions and poses major threats to public safety, engineering structures, and alpine slope stability. This paper presents experimental and numerical works aimed at investigating the frost crack evolution in fissured rock masses, as well as the interaction between frost cracks. A series of laboratory freezing experiments are conducted on rock-like specimens with various pre-existing fissures. Experimental results show that frost cracks initiate at the pre-existing fissure tips and propagate under the freeze–thaw treatment. Moreover, the frost crack evolution is significantly influenced by external stress conditions and frost crack interactions, forming several typical propagation patterns (e.g., deflection, coplanar and butterfly shape, etc.). Then, numerical simulations with a low-temperature thermal–mechanical coupled model, where the water/ice phase transition and hence volume expansion are explicitly simulated, are conducted to reproduce the experimental observation. The numerical results are consistent with the experimental observations and help to reveal the underlying mechanisms of the frost crack growth and frost crack interaction. This experimental and numerical investigation helps to improve the understanding of frost cracking mechanisms that can inform engineering design in cold regions with fissured rock masses. Highlights: Frost crack propagation and interaction under freeze-thaw cycles are investigated. Frost heaving pressure induced by ice expansion is large enough to drive crack propagation. Confining stresses alter the stress field around the crack tips, inducing crack orientation. Mutual interaction between adjacent frost cracks significantly affects the cracking pattern. Novel low-temperature thermal-mechanical coupling model is developed for frost cracking problems. [ABSTRACT FROM AUTHOR]

This paper describes the conditions leading to a sustained, low-rate, heave phenomenon affecting a building founded on hard Keuper anhydritic rock. The building was located in an abandoned gypsum quarry. Monitoring data as well as vertical profiles of gypsum and anhydrite content indicate that swelling was associated with the presence of a shallow level of anhydritic clay rock. This paper concludes that the initial quarry excavation as well as the additional building foundation work modified the original stress state and contributed to opening fractures at depth. It also resulted in a facilitated access of water to the upper rock levels, immediately under the foundation footings. Measured heave rates are substantially lower than other rates recorded in a few recent cases. An explanation is provided for the difference. This paper describes a comforting solution for the building. [ABSTRACT FROM AUTHOR]

Pipe bends, often referred to as 'elbows', are special pipeline components, widely used in onshore buried steel pipelines. They are sensitive to imposed deformations and their structural behavior is quite flexible and associated with the development of significant stress and strain, which may lead to failure. In the present paper, the mechanical performance of buried steel pipeline bends is investigated first, using rigorous finite element models that account for the pipe-soil interface. Three 36-inch-diameter pipe elbows are considered, subjected to pull-out force and embedded in cohesive soils. The elbows have bend angles equal to 90°, 60° and 30°, and bend radius-over-diameter ratio ( R/ D) equal to 5. The results show the increased flexibility of the pipeline bend with respect to the straight pipe, and are reported in the form of force-displacement diagrams. Furthermore the deformation limits of each elbow are identified in terms of appropriate performance criteria. The second part of the paper investigates the effect of pipe bends on the response of pipelines crossing active faults using a three-dimensional rigorous finite element model. The numerical results refer to a 36-inch-diameter pipeline crossing a strike-slip fault, and show that the unique mechanical response of pipe bends, in terms of their flexibility, may offer an efficient tool for reducing ground-induced deformations. The three-dimensional model employs the load-displacement curves of the first part of the paper as end conditions through nonlinear springs. Furthermore, the results show that there exist an optimum distance of the elbow from the fault plane, which corresponds to the maximum allowable ground displacement. Therefore, pipeline elbows, if appropriately placed, can be employed as 'mitigating devices', reducing ground-induced action on the pipeline at fault crossings. [ABSTRACT FROM AUTHOR]

Surface cracks are commonly observed in coatings and films. When structures with coatings are subject to stretching, opening mode cracks are likely to form on the surface, which may further lead to other forms of damage, such as interfacial delamination and substrate damage. Possible crack forms include cracks extending towards the interface and channeling across the film. In this paper, a two-dimensional numerical model is proposed to obtain the structural strain energy at arbitrary crack lengths for bilayer structures under uniaxial tension. The energy release rate and structural stress intensity factors can be obtained accordingly, and the effects of geometry and material features on fracture characteristics are investigated, with most crack patterns being confirmed as unstable. The proposed model can also facilitate the analysis of the stress distribution in periodic crack patterns of films. The results from the numerical model are compared with those obtained by the finite element method (FEM), and the accuracy of the theoretical results is demonstrated. [ABSTRACT FROM AUTHOR]

Large-size lump (e.g., coal reject or waste rocks) is one of the most popular backfill materials for underground mines attributed to its cost-effective and easy-to-obtain. The massive void between lumps, however, does generally affect the overall performance in eliminating the ground subsidence. This paper presents a conceptual backfill material, termed as lump-grout (LG) material, the attractive feature of which is that the voids between lumps are totally filled up with high-water content cementitious grout (CG) material. To explore the mechanical behaviour of LG material, a total of 36 LG specimens were prepared and tested under the uniaxial compression and the tensile loading. Other 20 CG specimens were tested in parallel for comparison. Key configurations investigated in the present research covered the particle size of lumps and the water-to-powder ratio of CG material. Test results indicated that the stress–strain behaviour of LG specimen is predominately affected by the strength of CG material. The failure of LG material generally occurred along the interface between lumps and the cementitious grout material rather than the lumps themselves. Compared to CG material, the axial deformation ability of LG material is slightly superior, when the utilization of CG material is significantly reduced. In addition to the backfill material, the proposed LG material can be also used as the infill material for the artificial standing supports for underground spaces. [ABSTRACT FROM AUTHOR]

The operation modes for the proposed FCC-ee collider foresee a very small beam spot size and stored beam energies of up to 20.6 MJ in Z production. This necessitates a dedicated beam dumping system. To reduce the complexity of the system as well as to minimize the required space, an optimized, semi-passive system has been designed and is presented here. The beam dilution is done with a defocusing triplet structure, followed by passive beam diluter elements (spoilers). This greatly reduces the risk of possible dilution failure scenarios compared to an active dilution kicker-magnet system. The dump core itself is located ∼ 70 m downstream of the spoilers and is designed following the experience gained from the LHC dump. The dilution performance as well as the interaction effects responsible for the energy deposited in the spoiler, are directly related to the radiation length and the dimension of the device in beam direction. Materials for these spoilers have been studied extensively and key requirements have been identified using both Monte Carlo shower simulations and thermo-mechanical Finite Element Analysis. Even though the maximum temperature reached in the spoilers is well within the working temperature range of the material, the induced mechanical stresses can lead to material failure. Thermo-mechanical simulations have shown that the transversal beam shape plays a key role in the magnitude of mechanical stresses as a result of the beam impact and the abrupt temperature change. This problem is addressed in this paper and an optimized solution is presented. [ABSTRACT FROM AUTHOR]

The creep-fatigue behaviors of P92 steel under strain range of 0.3 %–0.5 % and test temperature of 600–650 °C was studied carefully in this paper. With the increase of temperature, the creep-fatigue life is significantly reduced, and more vulnerable to temperature than strain amplitude. In addition, the dislocation density decreases with increasing creep fatigue, and the martensite laths become coarser. Furthermore, the increase of strain amplitude leads to more significant secondary cracks and fatigue striation. The higher temperature causes much deeper and larger dimples. During the test, the growth and accumulation of precipitates inevitably lead to stress concentration, resulting in material fracture and destruction. Finally, the linear cumulative damage (LCD), the modified ductility exhaustion (MDE) and the frequency separation life (FSL) model are used to predict the creep-fatigue life of P92 steel, and it is found that the frequency separation life model had the highest prediction accuracy among the threes. [ABSTRACT FROM AUTHOR]

Open circular holes are an important design feature, for instance in bolted joint connections. However, stress concentrations arise whose magnitude depends on the material anisotropy and on the defect size relative to the outer finite plate dimensions. To design both safe and light-weight optimal structures, precise means for the assessment are crucial. These can be based on analytical methods providing efficient computation. For this purpose, the focus of the present paper is to provide a comprehensive stress and failure analysis framework based on analytical methods, which is also suitable for use in industry contexts. The stress field for the orthotropic finite-width open-hole problem under uniform tension is derived using the complex potential method. The results are eventually validated against Finite-Element analyses revealing excellent agreement. Then, a failure analysis to predict brittle crack initiation is conducted by means of the Theory of Critical Distances and Finite Fracture Mechanics. These failure concepts of different modelling complexity are compared to each other and validated against experimental data. The size effect is captured, and in this context, the influence of finite width on the effective failure load reduction is investigated. [ABSTRACT FROM AUTHOR]

The ability of fracture propagation (fracability) is a key parameter of evaluating the fracture network generation during hydraulic fracturing. In order to consider the in situ conditions of the shale formation, four factors should be taken into consideration, which are brittleness, fracability, in situ stresses and natural fractures. The current shale brittleness and fracability evaluation methods rarely involve all the above factors. In this paper, coupling brittleness, stress-strain data and fracture morphology, a new shale fracability evaluation method is proposed. The brittleness is calculated by the mineral components and elastic parameters; the stress-strain data obtained by triaxial compression experiments are used to describe the shale breaking process; and the fracture morphology is evaluated by the fractal dimension method. This method is used to calculate the fracability index of the Longmaxi shale in Sichuan, China. The results show that: (1) the shale fracability under 5 MPa confining pressure is higher than that of under 20 MPa confining pressure; (2) the fracability in 7 coring angles shows a significant difference under the same confining pressure, the highest fracability is at 15∘ and the lowest is from 60∘ to 75∘. Compared with Jin and Rickman’s models, our model matches to the fracture morphologies and the fragments distribution closely. [ABSTRACT FROM AUTHOR]

The low-k/ultra-low-k (LK/ULK) dielectric materials are incorporated in the 40 nm technology node and beyond to reduce resistance and capacitance (RC) delays and improve chip performances. However, the LK/ULK integrity becomes critical in a flip-chip process because of the LK/ULK materials' higher porosity and fragility in mechanics. In this paper, we proposed a three-dimensional (3D) one-level global/local finite element model to study stresses and fracture behaviors in the chip with ULK dielectrics in the heating flip-chip process using SIMULIA ABAQUS software. The global model includes an effective thin layer that is equivalent to Cu/low-k multilayer interconnections. On the basis of stress analysis, the precracks at different locations of back-end of line (BEOL) were introduced to estimate the values of energy release rate (ERR) along the 3D crack fronts and the possible crack extension was discussed. Furthermore, the ERR affected by the ULK modulus, polyimide thickness and copper pillar diameter was investigated. The analysis reveals that the values of ERR are higher in upper layers of the BEOL and their values at interfaces of Cu/ULK are as much as two times than in ULK. The ERR reaches its maximum value under the edge of copper pillar with higher first principal stresses. The crack propagation becomes critical due to a quickly rising value of ERR when the polyimide (PI) thickness or the diameter of copper pillar is decreased. The study helps to understand the fracture behaviors in BEOL of an advanced chip during a packaging process. [ABSTRACT FROM AUTHOR]

The disposal of high-level radioactive waste (HLW) is one of the most challenging issues globally, and granite is considered an ideal host rock. In this paper, we present an experimental study on the transmissivity of fractured granite filled with different materials. A series of tests were carried out to study the effects of different factors (filling material, confining stress, and fracture roughness) on fracture transmissivity. Our results show that the properties of the filling material play a critical role in the transmissivity of fractured granite. Specifically, quartz sand significantly increases the transmissivity of the fractured granite, but the larger the sand particle size, the slower the transmissivity increases. Conversely, compared with fractured samples without any filling material, bentonite as a filling material decreases fracture transmissivity. Furthermore, confining stress also exhibits a great effect on transmissivity, and high stress compresses the filling material, resulting in a reduction in transmissivity. In addition, confining stress has a larger impact on the transmissivity of sand-filled fractured samples than others. We quantify the roughness of the fractures to examine its impact on the transmissivity. The results show that larger roughness reduces transmissivity for the unfilled fractures, but has an opposite effect on sand-filled fractures, while the results of bentonite-filled fractures are scattered. This study could provide an important guidance for evaluating the safety of HLW repositories. [ABSTRACT FROM AUTHOR]

The paper presents the results of the application of the refined calculation guidelines to the analysis of the stress-strain state and fracture resistance of the equipment elements of the NPP primary circuit system with WWER reactor, in particular, the cylindrical part and the zone of the reactor pressure vessel inlet nozzle, coolant collector welded joint in a steam generator, baffle, and reactor internals' shaft under the operating and emergency modes of thermomechanical loading. The calculation methodology is based on the use of the modern models and methods of solution to the nonlinear boundary tasks of non-isothermal thermal viscoplasticity and tasks of fracture mechanics using the refined mixed schemes of the finite element method with increased accuracy. They allow one to obtain reliable solutions to the tasks considering the deformation history of thermomechanical loading, modern concepts of fracture mechanics and approaches to the modeling of brittle-viscous fracture defects, irradiation swelling and creep of metal, as well as as the structural elements, under the conditions of elevated temperature, intensive neutron irradiation and nonstationary modes of thermomechanical loading. The authors obtained and analyzed the calculation results for the cylindrical part and zone of the inlet nozzle of the WWER-1000 reactor pressure vessel, coolant collector welded joint in a steam generator, baffle, and reactor internals' shaft using the proposed guidelines. The results imply the possibilities of the proposed recommendations and make it possible to analyze some general tendencies and features of the application of the refined calculation models to justify the strength and life extension of the NPP structural elements under investigation. [ABSTRACT FROM AUTHOR]

A masonry dome cracks when the tension stresses in the hoop rings near the springing reach the masonry's weak tensile strength. These meridional cracks arrive and spread along the dome. In this condition, the pressure surface with zero hoop stresses represents the extension to the three-dimensional case of the problem of the catenary. This analytical approach is adopted in the paper first to develop an accurate description of the minimum thrust state for the hemispherical masonry dome and the corresponding configuration of the pressure surface. Furthermore, the minimum thickness state is studied. Contributions of the paper are either an analytical formulation of the minimum thrust, depending on the geometrical thickness-radius ratio, or a modification of the minimum thickness-radius ratio with respect to the commonly accepted value. In this last geometrical configuration, the pressure surface has to touch the intrados of the dome at the crown, instead of passing through the extrados at the springing. [ABSTRACT FROM AUTHOR]

In this paper, the effect of creep-fatigue loading condition on crack tip deformation and stress fields of Grade 91 steel at 600 °C at crack initiation and growth is studied. By using finite element debond analysis method, creep-fatigue crack growth tests using C(T) specimens under various load ratios and hold times are simulated, and the effect of creep-fatigue load ratio and hold time on the crack opening profile, equivalent stress, crack-opening stress and triaxiality at crack initiation and growth is presented. It is found that the crack tip deformation and stress fields under tension–compression creep-fatigue loading are overall different from those under tension-tension creep-fatigue and pure creep loading, due to re-sharpening of the crack tip. [ABSTRACT FROM AUTHOR]

Crack growth leads to roller failure and damages other parts. The three-dimensional modeling of crack growth, the effect of different factors on the fatigue life of roller, and the effect of stress distribution are important factors that should be considered. The purpose of this paper is to investigate the failure and modeling of three-dimensional fatigue crack growth and fatigue life prediction of high chromium steel (HCS) rollers in hot rolling to minimize the failure of rollers by practical solutions. This article uses boundary element method for fatigue crack growth under the influence of stress field. The proposed method allows modeling each of the components involved separately in the contact area. As a result, this method is faster than finite element models with contact components. In this regard, the types and causes of cracks in the roller are analyzed with the effect of residual stresses on the roller. By selecting the HCS roller and sheet, modeling and stress analysis are performed by finite element method. This study includes the effect of crack growth factors such as load ratio, length, and initial crack angle. The results of the numerical model showed a good agreement with the results obtained in the field observations. [ABSTRACT FROM AUTHOR]

Connection (adhesive layer, welded seam, etc.) of solid bodies at the macro-level looks like a zero-thickness object (surface or line). At the micro-level, the connection is a three- or two-dimensional zone of complex geometry. Often it has no recognizable boundaries and/or inhomogeneous structure. Nevertheless [1-2], there exists a general relationship between the microscopic stress–strain state in the connecting zone and the stress–strain state at the macroscopic interface surfaces. It was demonstrated in [1-2] that independently of the specific form of this relationship, the microscopic stress–strain state does not influence the macroscopic interface conditions. It is the so-called erasing of the individual properties of the connection. In other words, the connection has no own properties and does not appear as an independent object in the interface elasticity theory problem. The opposite situation takes place if we address the strength properties of the connected bodies. Based on the same relationships [1-2], we demonstrate the interface surface demonstrates on the macro-level the own strength property. Namely, there exists a macroscopic strength criterion for the interface that differs from the strength criteria for the connected bodies. Thus, the interface is an independent object for the fracture mechanics. Both the features of the joint noted above are phenomena of asymptotic nature. In reality, the thickness of the joint is small but nonzero. In this case, the asymptotic provides us with the so-called leading terms. It means that in reality the microstructural properties of the connection slightly influence the macroscopic model and the macroscopic strength criterion may be used in practice as an approximation. Additional mathematical analysis is required to estimates of the accuracy of these approximations. It is impossible to obtain a simple relationship between the micro- and macroscopic stress–strain fields. However, the theoretical technique [1-2] can be implemented using the FEM software (with some additional programming). An example of the construction of the strength criterion of explosive welding seam is presented. [ABSTRACT FROM AUTHOR]

To study the anisotropic mechanical properties and energy evolution of layered rock masses under the action of cyclic loading, uniaxial graded cyclic loading and unloading tests under different upper and lower stress limits were carried out on samples with different bedding angles (0°, 22.5°, 45°, 67.5°, and 90°) to explore the deformation and mechanical response characteristics of bedded phyllite under cyclic loading and the mechanism controlling the evolution of the total absorption energy, elastic strain energy, and dissipated energy. The damage variable D and the damage increment ΔD were introduced to characterize the damage accumulation state inside the layered rock mass, and an instability criterion of bedded phyllite under mechanical cyclic loading was proposed. The results show that when the bedding angle increases from 0° to 90°, the failure types of the sample change from splitting shear failure to slipping shear failure and then to splitting tensile failure, and the corresponding irreversible strain and deformation modulus first decrease and then increase. With increasing stress level, the cumulative energy density increases in three stages, and the rate of increase presents a change in characteristic of "accelerating-steady-decelerating." The energy storage coefficient (Ke) decreases with increasing cycle number and stress level and first increases and then decreases with increasing bedding angle. Meanwhile, the energy dissipation coefficient (Kd) exhibits the opposite trend. The damage increment increases ΔD sharply after the first cycle in the nonfailure stage, drops sharply in the next cycle, and gradually decreases and stabilizes to near ΔD = 0.01 in the subsequent cycle. After entering the failure stage, the change in the damage increment of the variation in phyllite samples with different bedding angles is closely related to the stress level and number of cycles. The damage variable D can be used to describe the failure and instability of bedded phyllite under graded cyclic loading: when D ≤ 2 × 10–4, the rock is in the stage of compaction and steady crack growth; when D ≥ 2 × 10–4, the rock is at risk of failure and instability. Highlights: The changes in the irreversible strain and elastic modulus were analyzed based on the results of uniaxial graded cyclic loading and unloading testing. The evolution and distribution rules of various energy indicators under uniaxial graded cycle load are discussed from the perspective of energy. An instability judgment index based on energy dissipation theory is proposed, considering the relationship of layered millennium rock macro–micro deformation and energy evolution under the cyclic load. [ABSTRACT FROM AUTHOR]

The paper presents the results of experiments that were conducted to determine the influence of a triaxial stress state on the evolution of the permeability of an argillaceous limestone. The limestone rock is found in the Ordovician rock formations above the Precambrian basement located in southern Ontario, Canada, which is being considered as a potential host rock for the construction of a deep ground repository for storing low- and intermediate-level nuclear waste. The paper presents the results of an extensive series of hydraulic pulse tests and steady-state tests that were conducted to determine the permeability alterations in zones that can experience levels of damage that can be present in vicinity of an excavated underground opening. A 'state-space' relationship is developed to describe permeability evolution with the triaxial stress in the pre-failure regime. The permeability evolution in extensively damaged post-failure states of the rock is also investigated. It is shown that permeability alterations were four orders of magnitude higher as a result of significant damage to the material, which is an important consideration in establishing the efficiency of the host rock formation as a barrier for the long-term containment of radionuclide migration. [ABSTRACT FROM AUTHOR]

On the basis of Reissner's plate theory, the stress singularities at the tip of an arbitrarily inclined semiinfinite crack terminating at the interface of two dissimilar materials are investigated in the present paper. Using the eigenfunction expansion method, the eigenequation of the corresponding problem is derived explicitly by directly solving the governing equations of Reissner's plate theory in terms of three generalized displacement components. In this paper, the focus is on the calculation of the singularity order as a fundamental quantity in fracture mechanics. The singularity orders of the moments and shear force at the crack tip are determined by the dominant eigenvalues whose real parts lie between 0 and 1. The influences of the bi-material parameters and the crack inclination angle on the moment and shear force singularity orders are discussed in detail. Specifically, the variations of the shear force singularity order with the bi-material parameter and the crack inclination angle are examined in detail. It is proved that the shear force singularity order is a completely monotonic function of the bi-material parameter and the inclination angle. Some numerical results are given in order to prove the validity of the present study. [ABSTRACT FROM AUTHOR]

The scientific foundations for the development of a method for assessing the degree of danger of single crack-like defects found in thin-sheet metal structural elements are being investigated using AE testing using the low-temperature loading method. As a criterion, it is proposed to use the "critical activity" of the AE source, calculated using the equations of fracture mechanics and thermal conductivity. Loading is carried out via cooling the local ring-shaped zone by placing the carbon dioxide with a temperature of –78°C. At the same time, as a result of thermal contraction, tensile stresses arise that load the defect area during AE testing. The resulting temperature field and mechanical stresses are calculated by known theoretical methods using the heat and fracture mechanics equations. The annular appearance of the cooling zone determines the invariance of loading relative to the angle of the crack plane. Fracture mechanics criteria are employed that use the known power-law dependence of the number of acoustic emission acts on the stress intensity factor. Thus, the possibility of using the fracture mechanics criteria to assess the danger of crack-like defects by AE testing using the known power-law dependence of the number of acoustic emission acts on the stress intensity factor is shown. [ABSTRACT FROM AUTHOR]

The crack propagation behavior of rock during compression involves complex mechanisms. Describing the growth behavior of a large number of cracks with conventional mechanical models is a major challenge. Therefore, in this work, we propose a new method to describe crack growth behavior by considering crack bodies as free voxels that can expand and coalesce within a rock sample according to certain rules. Specifically, we first propose a crack growth model that quantitatively describes the crack growth ratio and crack growth rate, which are integrally related to the loading rate, internal friction angle, cohesion, initial porosity, and confining stress. Second, to avoid the complex analytical process of the traditional mechanical model in solving the propagation directions of multiple cracks, we introduce a method for determining the crack growth directions of shearing failure based on the colony growth assumption. This method defines the crack propagation direction as a synthetic vector of the inertial direction, the attractive direction, the Coulomb direction, and the edge direction. Moreover, a new mathematical description method of fracture energy and plastic energy is proposed to calculate the crack growth at each time step. The simulation results show that our crack growth model for shearing failure agrees well with the experimental results and explains the fracture behavior and transformation law of cracks to some extent. [ABSTRACT FROM AUTHOR]

The paper describes the computational aspects and numerical implementation of a two-scale cohesive surface methodology developed for analyzing fracture in heterogeneous materials with complex micro-structures. This approach can be categorized as a semi-concurrent model using the representative volume element concept. A variational multi-scale formulation of the methodology has been previously presented by the authors. Subsequently, the formulation has been generalized and improved in two aspects: (i) cohesive surfaces have been introduced at both scales of analysis, they are modeled with a strong discontinuity kinematics (new equations describing the insertion of the macro-scale strains, into the micro-scale and the posterior homogenization procedure have been considered); (ii) the computational procedure and numerical implementation have been adapted for this formulation. The first point has been presented elsewhere, and it is summarized here. Instead, the main objective of this paper is to address a rather detailed presentation of the second point. Finite element techniques for modeling cohesive surfaces at both scales of analysis (FE $$^2$$ approach) are described: (i) finite elements with embedded strong discontinuities are used for the macro-scale simulation, and (ii) continuum-type finite elements with high aspect ratios, mimicking cohesive surfaces, are adopted for simulating the failure mechanisms at the micro-scale. The methodology is validated through numerical simulation of a quasi-brittle concrete fracture problem. The proposed multi-scale model is capable of unveiling the mechanisms that lead from the material degradation phenomenon at the meso-structural level to the activation and propagation of cohesive surfaces at the structural scale. [ABSTRACT FROM AUTHOR]

This paper presents a combined continuous-discontinuous modeling technique for the dynamic ductile fracture analysis using an interactive particle enrichment algorithm and a strain-morphed nonlocal meshfree method. The strain-morphed nonlocal meshfree method is a nodel-integrated meshfree method which was recently proposed for the analysis of elastic-damage induced strain localization problems. In this paper, the strain-morphed nonlocal meshfree formulation is extended to the elastic-plastic-damage materials for the ductile fracture analysis. When the ductile material is fully degraded, the interactive particle enrichment scheme is introduced in the strain-morphed nonlocal meshfree formulation that permits a continuous-to-discontinuous failure modeling. The essence of the interactive particle enrichment algorithm is a particle insertion-deletion scheme that produces a visibility criterion for the description of a traction-free crack and leads to a better presentation of the ductile fracture process. Several numerical benchmarks are examined using the explicit dynamics analysis to demonstrate the effectiveness and accuracy of the proposed method. [ABSTRACT FROM AUTHOR]

Damage models are widely used to describe the ductile damage and fracture of metals. This paper proposes a new approach to determine the damage parameters of the Gurson-Tveergard-Needleman model, which uses a load-displacement curve coupled with finite element method. The load-displacement curve was obtained from a tensile test of a smooth tensile specimen and contained information about the damage and fracture behavior of the tested material. The principle of damage parameters identification is to minimize the deviation between experimental and simulated load-displacement curves by a hybrid particle swarm optimization. As a combination of particle swarm optimization and simulated annealing, the hybrid particle swarm optimization is an economical and effective algorithm to identify damage parameters. The identified damage parameters are also verified by testing and simulating deformation shapes of the smooth tensile specimen which is used for parameters determination. Tests and simulations of notched tensile specimens were carried out to discuss the transformability of the identified damage parameters. It is observed that the value of critical void volume fraction of the Gurson-Tveergard-Needleman model decreases with the increase of stress triaxiality. [ABSTRACT FROM AUTHOR]

Understanding the long-term behavior of brittle rocks requires fundamental consideration of time-dependent strain evolution and brittle creep processes. Previous studies have evaluated sub-critical crack growth during time-dependent deformation and damage evolution in brittle rocks; however, there is an incomplete knowledge of how damage evolves spatially and temporally within the body of intact rocks, where distributed regions of damage interact and coalesce during creep. This paper presents laboratory research focusing on evaluating brittle creep damage processes in Stanstead granite (SG) using 2-dimensional digital image correlation (2D-DIC). In the laboratory, the prismatic SG specimens were loaded beyond an estimated Crack Damage stress threshold (CD) level and then maintained a constant stress to initiate the creep process. DIC was used to characterize full-field spatiotemporal strain evolution, which was then interpreted in the context of local regions of “damage”, determined according to a strain-based criterion. A method was proposed for identifying “existing” and “new” damage regions over specified intervals during the test, followed by spatial clustering of these regions to assess their spatiotemporal evolution. The clustering analysis results demonstrated the extension of existing damage regions was the main damage process during brittle creep, which is consistent with existing models of sub-critical crack growth. In addition, temporal analysis of tensile and shear strains on a point-by-point basis revealed both new damage formation and the strain concentration within existing damaged regions significantly contribute to overall specimen strain during primary creep. In contrast, during secondary creep, increases in specimen deformation are influenced by the accumulation of strains within already damaged regions. [ABSTRACT FROM AUTHOR]

The paper proposes the model describing the initial stage of skin electrical explosion of cylindrical conductors. The model considers the magnetic field diffusion, skin effect, Joule heating, conducting material dynamics under the action of the Ampere force and thermoelastic stresses, material transition to the plastic state and plastic flow, phase transition from solid to liquid at the melting point, and transition from liquid to vapor (vaporization). The analysis is given to the nature of thermoelastic stresses and elastoplastic deformations of the material in states preceding its melting. Discussed is the probability of the material fracture and/or deformation of its surface. The dynamics of the outer boundary is calculated for both solid and liquid states of the material. The analysis is presented for the decrement of the perturbation growth on the molten surface, and ways of improving the stability of the external surface of exploding conductors are discussed. [ABSTRACT FROM AUTHOR]

The Callovo Oxfordian clay-rock (COx) is studied in France for the disposal of radioactive waste, because of its extremely low permeability. This host rock is governed by a hydromechanical coupling of high complexity. This paper presents an experimental study into the mechanisms of water uptake in small, unconfined, prismatic specimens of COx, motivated by the comprehension of cracking observed during concrete/COx interface sample preparation. Water uptake is monitored using both X-ray tomography and neutron radiography, the combination of these imaging techniques allowing material deformation and water arrival to be quantified, respectively. Given the speed of water entry and crack propagation, relatively fast imaging is required: 5-min X-ray tomographies and 10-s neutron radiographs are used. In this study, pairs of similar COx samples from the same core are tested separately with each imaging technique. Two different orientations with respect to the core are also investigated. Analysis of the resulting images yields with micro- and macro-scale insights into hydromechanical mechanisms to be obtained. This allows the cracking to be interpreted as a rapid breakdown in capillary suction (supposed large both to drying and rebound from in situ stress state) due to water arrival, which in turn causes a loss of effective stress, allowing cracks to propagate and deliver water further into the material. [ABSTRACT FROM AUTHOR]

Natural fractures in reservoirs can be the cause of many adverse effects during hydraulic fracturing treatment. In the present paper, hydraulic fracturing tests are used to investigate the interaction of a propagating hydraulic fracture with a natural fracture in the fractured blocks. Systematic experiments were designed and performed on the cement blocks with different pre-existing fracture strikes and dips (30°, 60° and 90°). The effect of horizontal stress difference on the propagation of hydraulic fractures was also determined through a series of experiments with different values for Δσ, which were 5 and 10 MPa, respectively. Propagation arrest of the hydraulic fracture and crossing the pre-existing fracture were two dominating fracture behaviors at horizontal stress differences of 5 and 10 MPa, respectively. It was observed that both the magnitude of differential stress and the pre-existing fracture geometry can magnify the effect of a pre-existing fracture on hydraulic fracture propagation. When the horizontal differential stress is low (5 MPa), the hydraulic fracture crosses the pre-existing fracture at a high pre-existing fracture dip (90°) and at an intermediate to high pre-existing fracture strike (60°-90°), while hydraulic fracture is arrested by the opening of the pre-existing fracture at a pre-existing fracture strike (30°). Meanwhile, when the pre-existing fracture dip is low to intermediate (30°-60°) and its strike is low to high (30°-90°), hydraulic fracture is arrested by the opening and shear slippage of the pre-existing fracture in this situation. However, at a high horizontal differential stress (10 MPa), when the pre-existing fracture dip is low to high (30°-90°), the hydraulic fracture crosses the pre-existing fracture at the strike of the pre-existing fracture of 60°-90°, and when it is decreased to 30°, the hydraulic fracture is arrested by th eopening and shear slippage of the pre-existing fracture. Therefore, the pre-existing fracture's strike and dip play a significant role in the propagation of hydraulic fracture at a low horizontal stress difference, while the role of the pre-existing fracture dip at a high horizontal stress difference is less than the pre-existing fracture strike on the propagation of hydraulic fracture. [ABSTRACT FROM AUTHOR]

In this paper, using a special class of nonlinear response relations between linearized strain and Cauchy stress tensors, we study a quasi-static mixed-mode (combination of mode-I and mode-II) fracture boundary value problem. A special subclass of such relations are strain-limiting in which the strains are guaranteed to be uniformly bounded in the neighborhood of crack-tip. In this article, we consider a finite element method based direct numerical simulation (DNS) of plane-strain mixed-mode fracture in a class of strain-limiting, transversely isotropic elastic bodies. We study the numerical solution of a nonlinear fracture boundary value problem with displacement as the primary unknown. The linearized version of the strong form was derived using damped Newton's method and the corresponding weak formulation was solved using a conforming finite element method. The results of this DNS indicate that even very near the crack tip, both stress and strain remain much smaller in magnitude than the corresponding predictions from the linearized elastic fracture mechanics (LEFM). While away from strain concentrating crack-tip region, the solution to the nonlinear, strain-limiting model agrees closely with the LEFM solution. This supports recent asymptotic theoretical studies of anti-plane and plane-strain fracture boundary value problems. Further, we also study the behavior of cleavage stress in the neighborhood of crack-tip. The numerical results indicate that the cleavage stress is largest along a line directly ahead of the crack-tip in agreement with the classical LEFM solution for pure mode I loading. [ABSTRACT FROM AUTHOR]

Brittle failure of adhesively bonded single lap joints is considered in this paper. A coupled stress and energy criterion in the framework of finite fracture mechanics is employed to study crack initiation by means of a numerical model presented by Hell et al. (Eng Fract Mech 117:112-126, ). Two different formulations of the coupled criterion are compared and the effect of geometrically nonlinear bending deformation of the adherends is analysed. A comparison to experimental results on the effect of the overlap length for single lap joints with composite adherends is given, showing a very good agreement of the failure load predictions. A detailed study of the effects of the geometrical and material parameters of a single lap joint configuration is given. As the energy release at crack formation is considered, the size effect of the adhesive layer thickness is covered correctly. The paper closes with an analysis of the effect of the unbonded adherend length. An approximate explicit expression for a minimum unbonded adherend length is given, which is required to optimize joint designs and to allow for the study of individual parameter effects in numerical and experimental studies. [ABSTRACT FROM AUTHOR]

This paper focuses on evaluating stress intensity factors (SIFs), for a curved beam of circular cross section with an external ring crack, applying an approach on the basis of estimating the strain energy release rate. The out of plane vibration of the beam is investigated. This approach requires an additional factor namely correction factor, on the basis of the energy release zone slope to approximate the SIFs. The initial curvature of the beam, however, adds some complication in using this factor. The second part of this study is investigating a numerical approach namely differential quadrature element method (DQEM) to gain the natural frequencies of the cracked beam. This method is applied to show the application of the SIFs to calculate the compliance of the cracked section for modeling the crack. The other method which is used to obtain the natural frequencies is the finite element method (FEM). The results of these two methods are found to be in good agreement, which shows the precision of the stress intensity factors of the cracked beam. [ABSTRACT FROM AUTHOR]

The unconventional fracture model can simulate complex fracture network propagation in a formation with pre-existing natural fractures. The interaction between hydraulic fracture branches, or stress shadowing effect, could be modeled by 2D or 3D displacement discontinuity method (DDM). In this paper, we concentrate on a hydraulic fracture model that integrates 3D DDM for computing the induced 3D stress field around the propagating hydraulic fractures and incorporates the changes in induced stress into the fracture height calculations and propagation criterion. Examples show that for parallel fractures, the height growth may be promoted or suppressed depending on the relative fracture height. For fractures initiated from different formation layers, the fracture growth into the layer occupied by the other fractures is reduced due to the vertical stress shadowing effect. [ABSTRACT FROM AUTHOR]

This paper considers the thermodynamically substantiated derivation of the scalar and vector forms of the J-integral for the Biot elastic porous medium model representing a permeable deformable matrix saturated with a fluid, which is described as a double continuum and whose behavior is determined by coupled equations of elasticity and filtration theory. [ABSTRACT FROM AUTHOR]

The Erdogan fundamental solutions are derived from an infinite plane containing a crack. When they are used in the formulation of the boundary element method (BEM), the stress boundary conditions on the crack surface are automatically satisfied and the singular behavior at the crack tip can be naturally reflected. Using the multi-domain technique, the multi-crack problem can be transformed into a series of single-crack problems involving displacement continuity conditions along common boundaries. In this paper, the displacements which are expressed in terms of the integral of a complex function in the Erdogan fundamental solutions are derived in closed-form expressions. Then, the multi-domain spline fictitious boundary element method (SFBEM) based on the above fundamental solutions is proposed and formulated for analyzing multi-crack problems. The computational accuracy and stability of the proposed method are verified by comparing the stress intensity factor (SIF) results of a double-inner crack problem with different inclined angles and crack lengths against those calculated by the finite element method. Also, the SIF results of a double-edge crack problem with different crack lengths are compared with those obtained from studies. Finally, the proposed method is applied to the analysis of the triple-crack problem, in which the shielding effects of multi-crack and stress contours are studied with different crack lengths and locations. [ABSTRACT FROM AUTHOR]

In this paper a new criterion for fracture investigation of orthotropic materials with cracks under mixed mode I/II loading is presented. In this fracture criterion, orthotropic material will be considered as a reinforced isotropic material. It is supposed that the crack will grow in the matrix of the orthotropic material. A new definition named here as “isotropic-orthotropic stress reduction factor” (IO-SRF) is utilized to consider the effects of the fracture process zone by a macro-mechanics approach. Also, the stress reduction factors will present a valuable relationship between the orthotropic and isotropic fracture toughness. Experimental and finite element methods will be introduced for computing the stress reduction factors. The SRFs are calculated for samples of glass-epoxy as an orthotropic material and samples of epoxy as a related isotropic one. Experimental tests under mixed mode I/II are performed on glass-epoxy composite samples to evaluate the validity of the presented mixed mode fracture criterion. The results of experimental tests on composite samples show a good agreement with the results of the presented criterion. Thus, the proposed criterion could be utilized as an efficient criterion for investigating the fracture of orthotropic materials under mixed mode I/II loading. [ABSTRACT FROM AUTHOR]

Calibration functions, used to determine crack extension from potential drop measurements, are not readily available for many common crack growth specimen types. This restricts testing to a limited number of specimen types, typically resulting in overly conservative material properties being used in residual life assessments. This paper presents a unified calibration function which can be applied to all common crack growth specimen types, mitigating this problem and avoiding the significant costs associated with the current conservative approach. Using finite element analysis, it has been demonstrated that Johnson’s calibration function can be applied to the seven most common crack growth specimen types: C(T), SEN(T), SEN(B), M(T), DEN(T), CS(T) and DC(T). A parametric study has been used to determine the optimum configuration of electrical current inputs and PD probes. Using the suggested configurations, the error in the measurement of crack extension is <6% for all specimen types, which is relatively small compared to other sources of error commonly associated with the potential drop technique. [ABSTRACT FROM AUTHOR]

The paper presents results from experimental studies on the influence of loading-unloading processes on the mechanical, linear, and nonlinear properties of the strain-hardening polycrystalline aluminum alloy AMg6 (Rus). The stress-strain curve is measured for AMg6 samples under high-cycle loading-unloading up to fracture of a sample. The microhardness of the sample is measured before and after its fracture. It has been found that the loading-unloading process leads to strain hardening of the AMg6 alloy. The influence of strain hardening of AMg6 on its linear and nonlinear elastic properties is studied by an ultrasonic method. To study the nonlinear elastic properties for different domains of the loading curve, we used the Thurston-Brugger method and spectral method by studying the efficiency of second acoustic harmonic generation. The experimental results are discussed. [ABSTRACT FROM AUTHOR]

Most of the engineering materials are faced with fracture phenomenon that needs to be controlled. There are several methods for controlling crack growth such as hole technique, using locks etc. In order to predict crack growth, stress intensity factor can be conducted as a useful tool. In this paper, the photoelasticity method is conducted as an experimental stress analysis tool in order to calculate the stress intensity factor (SIF). The investigations were conducted to find the effects of holes and locks on the fracture resistance and the SIF. This research is specially focused on the crack stitch as a unique technique to control crack propagation. In this technique, holes of locks are drilled close to each other in rows perpendicular to the crack then keys are inserted into the holes. Three batches including six different edge crack samples of polymethyl methacrylate rectangular plates were used for fracture tests. In the present study, the effects of locks in various geometries were investigated on the SIF. The results were obtained using a polariscope and the tensile load was applied to the specimens on the mode fracture (I) strength; then, the fracture forces were measured. The results showed that the samples with lock and hole have more fracture strength and thus their SIF decreases in comparison with the lock-less or hole-less samples. [ABSTRACT FROM AUTHOR]

Critical loads of columns under compressive follower forces have been widely discussed in the literature. By means of shape optimization, improvements by factors of more than eight could be achieved. However, the obtained solutions turn out to be not robust against perturbations of shape ormaterial parameters. The aim of this paper is to explain this sensitivity effect, basing on a study of eigenforms. Further, a robust alternative to the classical optimization approach is proposed. [ABSTRACT FROM AUTHOR]

The plastic zones of crack tips play a significant role in the fracture behavior of material. This paper proposes a semi-analytic solution for the plastic zones and stress distribution of an infinite space with multiple cracks and inhomogeneous inclusions under remote stress. In this solution, cracks can be treated as a distribution of edge dislocations with unknown densities according to the distributed dislocation technique, while inhomogeneous inclusions can be modeled as homogeneous inclusions with initial eigenstrain plus the unknown equivalent eigenstrain by using the equivalent inclusionmethod. These unknowns can be obtained by using the conjugate gradient method. The plastic zones ahead of crack tips are one-dimensional slender strips, and their sizes can be determined by canceling the stress intensity factor (SIF) due to the closure stress and that due to the applied load based on the Dugdale model of small-scale yielding. It is found that the plastic zones of crack tips are significantly affected by Young's modulus and the positions of inhomogeneous inclusions. [ABSTRACT FROM AUTHOR]

In this paper, an extension to a modified Gurson porous ductile material model, namely the Dung’s model, is introduced to investigate ductile fracture processes of AA6061-T6 aluminum alloy sheets. The combined Dung–Hill48 model accounts for anisotropic hardening effects of the matrix material. The constitutive model is implemented as a user-defined material subroutine in ABAQUS/Explicit to predict ductile fracture and formability of the aluminum alloy sheets. Ductile fracture predictability of the model comes from the description of void growth in an anisotropic strain hardening material. After being calibrated the model is applied to establish a fracture plastic strain–triaxiality relation using only tensile test data of smooth and R-notched specimens. Calculations of forming limits from seven deep drawing simulations with Nakajima specimens estimate the formability of the material. Influence of the material anisotropy on the obtained forming limit diagram is discussed. [ABSTRACT FROM AUTHOR]

Numerical simulations based on the bifurcation and imperfection versions of the strain localization theory are used in this paper to predict the failure loci of metals and applied to an advanced high strength steel subjected to proportional loading paths. The results are evaluated against the 3D unit cell analyses of Dunand and Mohr (J Mech Phys Solids 66(1):133–153, 2014. doi:10.1016/j.jmps.2014.01.008) available in the literature. The Gurson porous plasticity model (Gurson in J Eng Mater Technol 99(1):2–15, 1977. doi:10.1115/1.344340) is used to induce strain softening and drive the localization process. The effects of the void growth, void nucleation and void softening in shear are investigated over a large range of stress triaxialities and Lode parameters. A correlation between the imperfection and bifurcation results is established. [ABSTRACT FROM AUTHOR]

The goal of this paper is to predict how the properties of the constituent phases and microstructure of dual phase steels (consisting of ferrite and martensite) influence their fracture resistance. We focus on two commercial low-carbon dual-phase (DP) steels with different ferrite/martensite phase volume fractions and properties. These steels exhibit similar flow behavior and tensile strength but different ductility. Our experimental observations show that the mechanism of ductile fracture in these two DP steels involves nucleation, growth and coalescence of micron scale voids. We thus employ microstructure-based finite element simulations to analyze the ductile fracture of these dual-phase steels. In the microstructure-based simulations, the individual phases of the DP steels are discretely modeled using elastic-viscoplastic constitutive relations for progressively cavitating solids. The flow behavior of the individual phases in both the steels are determined by homogenizing the microscale calibrated crystal plasticity constitutive relations from a previous study (Chen et al. in Acta Mater 65:133–149, 2014) while the damage parameters are determined by void cell model calculations. We then determine microstructural effects on ductile fracture of these steels by analyzing a series of representative volume elements with varying volume fractions, flow and damage behaviors of the constituent phases. Our simulations predict qualitative features of the ductile fracture process in good agreement with experimental observations for both DP steels. A ‘virtual’ DP microstructure, constructed by varying the microstructural parameters in the commercial steels, is predicted to have strength and ductile fracture resistance that is superior to the two commercial DP steels. Our simulations provide guidelines for improving the ductile fracture resistance of DP steels. [ABSTRACT FROM AUTHOR]

In 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. [ABSTRACT FROM AUTHOR]

This paper describes the results of an experimental study on deformation and fracture of a Zr-1% Nb zirconium alloy in the case of multiple loads at low temperatures (-80°C). Samples cut out of pipes and applied as shells of nuclear fuel elements of fuel assemblies of nuclear reactors are used to conduct a series of experiments on low-cycle stretching and compression at low temperatures and study the effect of low temperature on stress relaxation in the material under different numbers of preliminary loads. [ABSTRACT FROM AUTHOR]