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• Low-cycle multiaxial fatigue experiments of Q355D notched specimens under different loadings were carried out. • The important factors affecting fatigue life of notched specimens were analyzed by three correlation analysis methods. • A modified MGM (1, N) model was established by fine-tuning the time series of the GM (1, N) model. • A new fatigue life prediction method for notched specimens was proposed. The paper aims to analyze the stress–strain response of building steel under low-cycle multiaxial fatigue and to accurately evaluate the fatigue life of specimens by selecting the more important relevant factors that affect fatigue behavior. Based on this, low-cycle multiaxial fatigue experiments of Q355D notched specimens under different multiaxial loading are carried out. Firstly, the fatigue behavior of notched specimens under different loadings and the relationship between the biaxial strain amplitude ratio and fatigue life are analyzed. Secondly, Grey correlation analysis, Pearson correlation analysis, and Random Forest importance analysis are used to screen out the important factors affecting fatigue life. Finally, the grey MGM (1, N) model is used to predict the fatigue life of notched specimens, and the results show that the predicted life based on Random Forest importance analysis is in good agreement with the experimental life. In this paper, the multiaxial fatigue problem is decoupled into two sub-problems, i.e. screening out related factors and life prediction based on the related factors, which can be used as a reference for life prediction in structural design. [ABSTRACT FROM AUTHOR]

• The behavior of low cycle fatigue at typical temperatures was comprehensively investigated. • The life prediction model based on entropy increase theory is in good agreement with the experimental data. • This paper offers a methodology for finite cycle prediction of overall fatigue life. Nickel-based single-crystal superalloys (Ni-SX) are prominently utilized in the fabrication of turbine blade materials for advanced aero-engines, owing to their commendable material characteristics. This paper delves into the low cycle fatigue (LCF) characteristics of a second-generation Nickel-based single-crystal superalloy across a temperature spectrum ranging from room temperature to 1000 °C. During this procedure, there is an escalation in the trend towards deformation homogenization, leading to a transition in fracture mode from shear fracture to normal fracture. A novel approach is introduced in the form of an entropy-based fatigue life prediction model, grounded in the correlation between cumulative plastic strain and entropy increase rate. Through a comparative examination with experimental data, the model demonstrates proficiency in precisely forecasting the fatigue life of Ni-SX under diverse strain amplitudes and temperature conditions. [ABSTRACT FROM AUTHOR]

• This paper presents a new damage-plasticity model that captures shear failure in concrete and reinforced concrete. • This paper presents a new damage-plasticity model that captures shear failure in concrete and reinforced concrete. • Both tension-shear coupling and compression-shear coupling effects are considered. • This paper presents a new damage-plasticity model that captures shear failure in concrete and reinforced concrete. Shear failure is an important design consideration for reinforced concrete structural components. Therefore much attention has been drawn to the development of theoretical and computational models for characterizing its complex and progressive nature. This paper establishes a damage-plasticity constitutive relationship for concrete through the introduction of a new stress decomposition procedure, referred to as shear-normal decomposition. The stress tensor is decomposed into a shear stress tensor representing the shear state and a normal stress tensor representing the tensile/compression state. The degradation of the mechanical performance of concrete is accounted for through shear, tension and compression damage variables. The shear stress-shear strain curve of concrete is calibrated by experiments and is rendered independent of the tensile and compressive stress–strain curves. The coupling between tension-shear and compression-shear are accounted for by the criterion for shear damage evolution. Several numerical examples are presented that illustrate the unique advantages of the proposed model. [ABSTRACT FROM AUTHOR]

• This paper presents the fracture model calibration of SS275 hot-rolled thin plates, which involved quasi-static tests and finite element analysis. • The hardening model parameters were determined using the Swift law, while the ductile fracture model parameters were calibrated using the Hosford-Coulomb model within the linear damage framework. • The accuracy of the model was validated by comparing the results with the test data, and it was found that the highest fracture strain occurred in the uniaxial tension state. • The calibrated model was then used to predict the cycle life to failure in an extreme low cycle fatigue test, which was found to be 70 cycles. • The results indicate that the ductile fracture model performed well in predicting extremely low-cycle fatigue. • The paper's findings can be useful in predicting the fracture initniaon of engineering structures and components under multiaxial stress states, which can ultimately lead to improved designs and increased safety. The complexity of the loading conditions makes it challenging to accurately predict the damage evolution and resulting ductile fracture in materials and structures. This paper presents an application method to predict fracture initiation for low cycle fatigue of 4-point bending in structural steel SS275. The swift isotropic hardening law was used in the numerical simulation to account for large strain deformation. The damage indicator framework with the Hosford-Coulomb (HC) model was adopted to characterize the damage accumulation and fracture behavior. Uniaxial tension tests on specimens with various fracture modes were conducted to determine the material properties required for calibration of the plasticity model and fracture model param1eters. Non-linear finite element analyses were performed to identify fracture model parameters based on the loading path of fracture initiation. The presented HC model was applied to an extremely low fatigue test (less than 100 cycles) and demonstrated good accuracy in predicting fracture initiation for complex loading scenarios. [ABSTRACT FROM AUTHOR]

• Experimental results of fracture test under biaxial loading tension with torsion (proportional mixed-mode I + III) on PMMA notched specimens. • Distinguishing critical load values, places and angles of crack initiation depending on the type of load being tested (mode I, mode III and mixed-mode I + III). • Nonlinear numerical analyses – FEM. • The stress–strain fracture criterion was formulated, which was then positively verified. This paper presents the results of experimental fracture test of flat PMMA specimens under biaxial loading condition tension with torsion (proportional). The specimens were made in two thicknesses: 5 and 15 mm and were weakened with V-type edge notches with different root radii: 0.5; 2 and 10 mm. Thanks to the ARAMIS 3D 4 M non-contact vision system, measurement of the elongation and twist angle were recorded. During experimental part all of the deformation processes were observed using PHANTOM cameras. Obtained records made it possible to precisely indicate the moment of crack initiation (tensile force and torsional moment values). Using the microscopic observations the location of crack initiations were determined. Results obtained for biaxial loading were compared with those obtained for uniaxial tension and torsion. Based on experimental data the numerical calculation with FEM were carried out. The principal stress and plastic strain distribution under critical load, were obtained. The points of occurrence of stress maxima and plastic strain were indicated, which were taken as potential crack initiation sites. On the basis of the stress and plastic strain values measured at the critical points, a stress–strain fracture criterion was formulated, which was then positively verified. Additionally, new form of stress–strain fracture criterion was proposed. The bilinear form of the fracture criterion can be successfully used to predict fracture in PMMA flat specimens, regardless of the notch root radius, type of load or element thickness. [ABSTRACT FROM AUTHOR]

• A micromechanical model was first established to study crack and fibers. • The isotropic, anisotropic and microscopic models were compared. • The impacts of crack size and location, fiber content on stress field were revealed. • The variations of various mechanical properties were discussed. Accurately clarifying the influence of cracks on the mechanical behaviors of unidirectional fiber-reinforced composites (UD FRCs) is of great significance for the structural integrity evaluation of UD FRCs with defects. Although several experiments and numerical analyses have explored the impact of cracks on stress field, satisfactory quantitative characterizations of crack size, a / W and location, Δ , fiber content, V f have not yet been obtained. In this paper, the accurate and detailed microscopic models containing crack were first established and thoroughly validated. Then, a parametric study was conducted using three-dimensional micromechanical analysis to investigate how the crack size and location, fiber content affect the von Mises, stress triaxiality, Lode angle and J -integral of UD FRCs. Results showed that homogeneous models, whether isotropic or anisotropic, cannot accurately describe the mechanical behavior of cracked UD FRCs. The von Mises stress and J -integral are greatly influenced by the crack and fiber content, while stress triaxiality and Lode angle are not sensitive to changes in these factors. Further, the von Mises and J -integral increase with the decrease of V f and the increase of a / W , but show a more complex trend in the variation of Δ. These findings will help clarify the failure mechanism of cracked UD FRCs and can be used for reliability evaluation. [ABSTRACT FROM AUTHOR]

This paper focuses on the development of the atomistic framework for determining the lower scale mechanical parameters of single components of a metal matrix composite for final application to a micromechanical damage model. Here, the deformation and failure behavior of NiAl–Al 2 O 3 interfaces and their components, metal and ceramic, are analyzed in depth using molecular statics calculations. A number of atomistic simulations of strength tests, uniaxial tensile, uniaxial compressive and simple shear, have been performed in order to obtain a set of stiffness tensors and strain–stress characteristics up to failure for 30 different crystalline and amorphous systems. Characteristic points on the strain–stress curves in the vicinity of failure are further analyzed at the atomistic level, using local measures of lattice disorder. Numerical results are discussed in the context of composite damage at upper microscopic scale based on images of the fracture surface of NiAl–Al 2 O 3 composites. • Atomistic study of fracture behavior of metal matrix composite has been performed • Deformation up to failure of matrix, reinforcement and interface has been simulated • NiAl–Al 2 O 3 interface has been revealed as the weakest element of the composite • Such conclusion has been confirmed by experimental SEM fractographic analysis • Lower-scale parameters have been successfully evaluated from atomistic simulations [ABSTRACT FROM AUTHOR]

• A numerical scheme to obtain C (t)-integral considering residual stress effect is given. • Eigenstrain and mechanical loading induced residual stress effects on C (t)-integral and transition time are computed and compared. • Tensile and compression residual stresses on C (t)-integral are studied. • Effects of nonproportional loading on C (t)-integral and transition time are confirmed and presented. Nonproportional loading and residual stresses effects on creep crack tip fields are important topics in fracture mechanics at elevated temperature. In this paper, nonproportional loading and residual stresses effects on creep crack tip fields are systematically investigated based on the novel interpretation of C (t)-integral considering residual stress. With the numerical implementation of the corrected C (t)-integral considering residual stress, the eigenstrain and mechanical induced residual stress effects on the creep crack tip fields are studied. We find that C (t)-integral level is affected remarkably in the presence of residual stress regardless of eigenstrain or mechanical induced residual stresses for creep crack tip under small scale creep. However, level of C *-integral is not significantly influenced under the effects of residual stresses in presence of large-scale creep although the transition creep time is remarkably changed. Otherwise, C (t)-integral is highly affected by loading path under small scale creep. However, C *-integral is independent of the loading path if the creep time is long enough. Nonproportional loading effect on C *-integral is very limited for creep crack tip field according to our study. The investigation given in this paper could deepen the understanding the effects of residual stress and nonproportional loading on the creep crack tip field. [ABSTRACT FROM AUTHOR]

This paper focuses on the numerical implementation of phase-field models of fracture using the Fast Fourier Transform based numerical method. Recent developments in that field rely on the separate solution of a coupled problem where the mechanical equilibrium problem is solved first, and then the phase-field evolution equation. The latter involves a diffusion term which has been simplified in previous works relying on the Fast Fourier Transform based numerical method. This simplification has theoretically no effect for homogeneous materials, but might influence predictions significantly for heterogeneous materials where fracture properties vary between the different components. In this paper, the influence of this simplification is assessed and a complete formulation is proposed as well as a novel implementation of this formulation using the Fast Fourier Transform based numerical method. The assessment relies on simulations with a material containing two components, one of them being defined as unbreakable by using higher fracture properties. Using the simplified formulation, the presence of an artificial diffusion of damage between the two components is evidenced, and non-zero damage values are observed in the unbreakable component. Although the complete formulation leads to an increase of the number of iterations to solve the phase-field evolution equation, it suppresses completely the diffusion of damage towards the unbreakable component. The two formulations, in fact, lead to identical results when the fracture properties are homogeneous, but the results diverge both in terms of local fracture patterns and global stress–strain relations when the fracture properties contrast increases. This difference is also more pronounced when the regularization length introduced by the phase-field model increases. • Phase-field modeling of fracture using the Fast Fourier Transform based numerical method. • Development of a new complete formulation of the phase-field equation. • Comparison with a simplified formulation previously proposed in the literature. • Complete formulation shown to eliminate unphysical damage diffusion between phases. [ABSTRACT FROM AUTHOR]

• This paper investigated the effects of large plastic deformation and residual stress on the Rice's J-integral and its path independence for a crack in ductile materials. • Considered the effect of plasticity theory, finite strain, and residual stresses on the J-integral and provided a mathematical equation of the modified J-integral. • Calculated and compared the Rice's J-integral and the residual stress modified J-integral based on the FEA calculations of J-integral for a notched beam. Large plastic deformation and residual stress exist in the oil and gas transmission pipelines with mechanical damages that often contain a gouge or crack. Residual stresses can alter the mechanics behavior of the crack, and cause the standard J-integral to become path-dependent and unable to describe the crack driving force. This paper investigated the effects of large plastic deformation and residual stress on the path independence of the J-integral for a crack in ductile materials. The basic conditions required for the path independence of the standard J-integral were first reviewed, and the major factors that affect the path independence were then analyzed. This includes the theory of plasticity, finite strain formulation, and residual stresses. Then, a residual stress modified J-integral was introduced for ensuring the path independence. After that, the elastic–plastic finite element analyses were performed for a notched beam in terms of the incremental plasticity to create residual stresses and to simulate a crack at the notch root subject to three-point bending. The path independence of the standard and modified J-integrals was numerically evaluated for each of the major factors. Results showed that the modified J-integral is path-independent and able to describe the crack driving force for a crack in a residual stress field, but the standard J-integral cannot do so because of its nature of path dependence when residual stresses are present. Thus, the modified J-integral can be used as an appropriate fracture parameter to assess the pipeline integrity for line pipes containing cracks and residual stresses. [ABSTRACT FROM AUTHOR]

• The stress and strain distribution on the critical plane is studied. • The concept of strain ratio is proposed. • The correlation degree analysis between relevant factors and fatigue life is carried out with gray theory. • A multidimensional gray Markov model is established by combining the advantages of the multidimensional gray GM(1, N) model and Markov theory. It is always a challenge to accurately predict the fatigue life of notched specimens under multiaxial loading, which is a guarantee of structural integrity. Therefore, in this paper, multiple factors affecting fatigue life are considered and a multidimensional grey Markov model is used for fatigue life prediction. Firstly, the plane of maximum shear strain amplitude is determined as the critical plane. Meanwhile, the stress–strain components on the critical plane are extracted, and the relevant parameters affecting the fatigue life are calculated. Secondly, due to the defects of the grey theory itself, the prediction error is larger. Therefore, the grey model is modified with Markov theory to get the grey Markov model. The correlation degree analysis between relevant factors and fatigue life is carried out with grey theory to analyze the degree of influence of different factors on fatigue life. Finally, the grey Markov model is analyzed and verified using experimental data from Q355(D), GH4169 and Al7050 notched specimens and the results show that the grey Markov model can provide an economical and effective method for multiaxial fatigue life prediction. [ABSTRACT FROM AUTHOR]

• Reveal the formation mechanism of complex non-plane fractures near the wellbore. • The fracture initiation and propagation mechanisms of multiple hydraulic fractures are investigated. • Hydraulic fracture propagation is affected not only by stress shadow but also by inclined well orientation. • Stress shadowing effect in staged fracturing results in a large deflection angle of fractures when the horizontal principal stress difference is small. Multi-cluster fracturing in horizontal wells is an important stimulation technology for unconventional tight reservoirs. The interference among multiple simultaneously growing hydraulic fractures results in a non-uniform fluid distribution into fractures and non-planar fracture geometries. In this paper, the competition mechanism between perforations under the stress shadow, the formation mechanism of complex non-plane fractures near the wellbore, and the initiation and propagation mechanism of multiple hydraulic fractures are investigated by using the 3D lattice method. Also, the effects of fracture geometry, fracture spacing and rock mechanics parameters on the stress interaction among fractures are analyzed by the dislocation theory. The results showed the complexity of fracture initiation near the wellbore and the low efficiency of the perforation initiation in the case of spiral perforation, due to a strong interaction between perforations. However, these initial micro-cracks will eventually coalesce to be a macroscopical fracture which perpendicular to the direction of minimum principal stress. The study indicated that stress interaction and fracture propagation is significantly affected by inclined well orientation. The hydraulic fracture is more likely to deflect and propagate non-uniformly with the increasing width of hydraulic fracture, the decreasing spacing between perforation clusters and the increasing rock modulus. When the horizontal principal stress difference is small, it is obvious to cause a large deflection angle and sometimes furcation of fractures. This study can provide a theoretical basis and technical guidance for hydraulic fracturing design in tight reservoirs. [ABSTRACT FROM AUTHOR]

• A PF model is developed for electromechanical fracture in flexoelectric solids. • The PF model is validated through benchmark numerical examples. • The flexoelectric effect can have great influences on the fracture behavior. • The PF model can simulate complex fracture behaviors of flexoelectric solids. Flexoelectricity describes the electromechanical coupling between the stain gradient and the electric polarization, which can play an important role in the fracture behavior of piezoelectrics since large strain gradients exist near the crack tip. In this paper, in order to investigate this effect, a phase field (PF) model is developed for electromechanical fracture in brittle flexoelectric solids, where the crack surfaces are assumed to be either electrically impermeable or electrically permeable. The damage driving force of the PF model is derived from the non-negative energy dissipation rate for both kinds of crack surface conditions, where the mechanical part is regarded as the driving force for the crack evolution. A decomposition method of the mechanical driving force is proposed to characterize the asymmetric fracture behavior under tension and compression. The governing equations are solved numerically with finite element method. The finite element formulation is implemented in Abaqus through the user defined subroutine UEL. The PF model and its numerical implementation are validated by studying benchmark problems. The simulation results indicate that the proposed PF model can well characterize the flexoelectric effect and predict complex crack propagation paths in flexoelectric solids. In addition, the numerical results show that whether a negative applied electric field promotes the crack propagation or retard the crack propagation is closely related to the electric field strength and the flexoelectric coefficients, which can reconcile the contradictory phenomena observed in previous experimental studies. The influences of the applied electric field and the length scale parameters on the electromechanical fracture behavior of flexoelectric solids as well as the size effect are discussed in detail in the paper. [ABSTRACT FROM AUTHOR]

The growth of short cracks in round bar specimens with a circumferential notch has been investigated by an extensive experimental study. This specific specimen geometry has been applied to determine notch support based on a reduced crack growth rate due to the induced stress gradient compared to situations without a notch. At the same time, this investigation of crack growth in low cycle creep-fatigue conditions reveals a significant influence of dwell times on crack closure, which is discussed in detail in this paper. Therefore, a fracture mechanical approach based on an elastic-(visco)plastic crack growth simulation is used to compute the cyclic effective fatigue and creep crack tip loading. The crack growth rates are then determined by a Paris and Nikbin–Smith–Webster model. All investigations are based on strain controlled conditions at different loading levels. The shape of the applied cycles is trapezoidal, having a dwell time of three minutes at maximum and minimum load, and is symmetric in tension and compression. It turns out that a separate consideration of crack opening and closure reveals an important difference in effective crack tip loading range and therefore has a significant impact on fatigue crack growth. Moreover, this paper shows that the effect of dwell times is linked to the influence on plasticity induced crack closure and to the stress relaxation during the dwell time in compression, yielding less crack closure. • Impact of creep in dwell times on plasticity induced crack closure. • Effectiveness of crack tip loading by cyclic J -Integral. • Crack growth simulation with elastic–viscoplastic behavior. • Analysis of contact stresses along crack flank. • Application and comparison of different crack closure criteria. [ABSTRACT FROM AUTHOR]

[Display omitted] • Adhesion strength of dental ceramic to milled and SLM Ti6Al4V alloy is studied. • The novelty is that experimental load–strain graphs are used in FEM simulations. • Normal, tangential and equivalent von Mises stresses are determined. • Greatest values of normal stresses perpendicular to porcelain/bond/metal interface. • They are primary reason for adhesive delamination of porcelain coating. The aim of the present paper is to investigate the adhesion strength of dental ceramic to milled and selective laser melted (SLM) Ti6Al4V alloy by experiment and finite element method (FEM). The experimental study was done by three-point bending test. Before applying the porcelain, the metal surface was treated by sandblasting, application of bonding agent and a combination of sandblasting and bonding layer. The novelty is that FEM simulations of individual samples from each group were conducted using the experimental load–strain graphs. The normal, tangential and equivalent von Mises stresses at endpoint of the edge of porcelain coating and bonding agent sublayer were determined. It was found that the distribution of the equivalent stresses along the porcelain edge on the porcelain/metal interface is uneven: low stresses at both ends and maximum value in the central part. The Y-axis normal stresses, acting perpendicular to the porcelain/metal, bond/metal, or porcelain/bond interface, have greatest values which is primary reason the coating to be adhesively delaminated by peeling the porcelain off the metal or bonding agent. For the milled specimens, the stress trend follows the adhesion strength trend. In the combined treatment, the highest equivalent and normal stresses are generated in the bond sublayer. If they are higher than the cohesive strength of the ceramic, the porcelain coating is destroyed cohesively by cracking. For the SLM fabricated specimens, the bond treatment increased the stresses at the bond/metal interface, and the stresses at the bond/porcelain interface were commensurate with the experimental adhesion strength. This causes the destruction of the coating to occur by peeling the porcelain off the bonding agent. [ABSTRACT FROM AUTHOR]

Biological materials depict an excellent combination of both strength and toughness, which is a vital requirement for most engineering materials. It provides motifs to revolutionize the techniques for producing novel materials with improved properties. However, there is still a lack of deep understanding regarding the toughening mechanisms in biological materials, in order to overcome the conflict between strength and toughness in synthetic materials. This paper establishes a microstructure-based fracture model to reveal the toughening effect of the microcrack zone near the crack tip. Firstly, the stress–strain relationship considering the initiation and saturation of microcracks is derived. Then, a fracture mechanics model incorporating the micro-mechanics of microcracks is established, based on the above nonlinear mechanical response. Finally, the model is used to investigate the influence of microstructural parameters on the fracture toughness considering microcracks. The results show that there are two nondimensional parameters that significantly influence the fracture toughness: the ratio between the gap and overlapped zone, ξ , and λ l a . In addition, the selection of the microstructural parameters not only needs to consider the balance between stiffness, strength, and toughness, but also achieve the optimal toughness by combining the effects of several different mechanisms. • The mechanical response considering microcracks in staggered composites is derived. • A fracture model is established to reveal the toughening effect of microcracks zone. • The micro-structural parameters need to be optimized to achieve excellent toughness. [ABSTRACT FROM AUTHOR]

• In this paper, the fatigue failure criterion of materials with static constitutive curve as the limit value is proposed, and the fatigue life is dominated by fatigue failure stress–strain in the fatigue envelope surface. • The fatigue state of materials can be described by extending the proposed criterion expression to fatigue state equation, and the analysis results show the monotonic trend. • The fatigue evaluation can be conducted through the value of fatigue state equation or the comparison of fatigue state and fatigue failure envelope surface. The fatigue failure problem actually can be explained by fatigue stress–strain envelope, and the fatigue evaluation based on fatigue stress–strain can avoid the uncertainty of selecting fatigue criteria in engineering applications. However, the application of experimental fatigue envelope criterion based on stress–strain curve is limited to concrete and rocks, and it also can not predict the fatigue failure time. To further develop the availability of fatigue stress–strain envelope criterion, the fatigue failure criterion of materials with static constitutive curve as the limit value is proposed to describe high-cycle and low-cycle fatigue failure through theoretical deduction of classic fatigue criteria and analysis of experimental results. The proposed criterion reveals the constraints mechanism that the fatigue life is dominated by fatigue failure stress–strain in the fatigue envelope surface. Finally, the comparison between calculated and experimental fatigue life indicates that the proposed criterion is suitable to. describe the fatigue failure well and has the comprehensive application prospect. [ABSTRACT FROM AUTHOR]

Due to the stress concentration and large strain gradient around the crack tip, strong flexoelectric effect would be produced there. Meanwhile, the flexoelectric effect could conversely affect the mechanical fields in materials, thus influence the fracture property of materials. To model the impact of flexoelectricity on crack tip fields and the electromechanical behaviors of materials, intensive mesh refinement is needed around the crack tip. Thus, an efficient numerical method is desired. In this paper, the flexoelectric effect around the tip of nano-cracks is simulated by using a collocation mixed finite element method (MFEM). Our collocation MFEM is based on C 0 continuous approximation and does not involve additional degrees of freedom (DOFs), so that it is quite efficient, which has been verified in our previous study (Tian et al., 2021). Using the collocation MFEM, we simulate the electric potential and field distributions around the crack tip in flexoelectric materials, and the influences of the direct flexoelectric effect on the crack tip opening displacement and J -integral are also studied. Numerical results indicate that the flexoelectric effect around the crack tip would be enhanced by increasing the tensile loading and crack length. Besides, the direct flexoelectric effect around the crack tip enhances the local strength of materials, and plays an important role in fracture mechanics of materials. [Display omitted] • The flexoelectric effect around the crack tip enhances the local strength. • Our collocation MFEM is based on C0 continuous approximation and efficient. • The existence of the direct flexoelectric effect decreases the J -integral. [ABSTRACT FROM AUTHOR]

[Display omitted] • 2D simulations of a hydraulic fracturing process are conducted. • A DEM/CFD-based pore-scale thermal-hydro-mechanical model is used. • Two-phase laminar fluid flow (water and gas) is taken. • Temperature difference between the rock matrix and fluid injection is assumed. • The impacts of the fluid's dynamic viscosity and gas phase content, are examined. In the paper, a two-dimensional (2D) numerical simulation of a small-scale hydraulic fracturing process in rock specimens possessing a single injection slot was conducted. A unique DEM/CFD-based pore-scale thermal-hydro-mechanical (THM) model was used to simulate two-phase laminar fluid flow (water and gas) with heat transfer in non-saturated porous materials with low porosity. Using a DEM fully coupled with CFD (based on a fluid flow network composed of channels in a continuous domain between discrete elements) and heat transfer at the mesoscale, a series of numerical calculations for small cohesive granular specimens of simplified spherical mesostructure with one injection slot were carried out. Plane strain compression conditions were assumed. Both the fluid (diffusion and advection) and bonded particles (conduction) were involved in heat transfer. The impacts of the fluid's dynamic viscosity, gas phase content, and temperature difference between the rock matrix and the fluid injection on the process of hydraulic fracture initiation and propagation were all examined in-depth. It was discovered that those effects were all of great significance to the behaviour of a single hydraulic fracture. [ABSTRACT FROM AUTHOR]

• The effect of three stress invariants on failure mechanism was investigated. • The effect of the parameters in the new failure criterion on the failure loci was analyzed. • The new failure criterion was calibrated with a set of test results on several materials. • Comparisons with KHPS2, Lou-Huh criterion and extended Mohr–Coulomb criterion were made. An accurate failure criterion is crucial for mechanical and structural design. In this paper, the effects of three stress invariants on material failure are studied based on microscopic mechanisms. A new ductile failure criterion that accounts for the influence of stress triaxiality and normalized third invariant of deviatoric stress tensor is proposed. The parameters in the new failure criterion are analyzed to determine their effects on the failure loci. The new proposed failure criterion is calibrated with a series of test results on 2024-T351 aluminum alloy, TRIP690 steel and additively manufactured Ti-6Al-4V. The results demonstrate that the new criterion can predict the failure loci of these materials with high accuracy. Comparisons with three criteria indicate that the new failure criterion has a broader application than Lou-Huh criterion and extended Mohr–Coulomb criterion for the above three materials. [ABSTRACT FROM AUTHOR]

• The interface crack between two dissimilar dielectric materials. • The gradient theory of elastodynamics. • Influence of flexoelectricity. • Influence of the micro-inertia length-scale parameter. • The mixed FEM formulation with C0 continuous finite elements for independent approximations of displacements and strains. In the present paper, the influence of flexoelectricity on behavior of the interface crack between two dissimilar dielectric materials under a dynamic mechanical load is investigated. The induced electric field affects the distribution and evolution of mechanical fields in dielectric materials. Large strain gradients induce the electric polarization in the direct flexoelectricity. Due to the large strain gradients at the crack tip vicinity it is needed to consider the strain gradient theory model. Governing equations in this theory contain higher-order derivatives than in the conventional continuum mechanics approach. The mixed finite element method (FEM) is developed here for a general boundary value problem, where the standard C0 continuous finite elements are applied for independent approximations of displacements and strains. The constraints between them are satisfied by collocation at appropriate internal points in elements. Interface cracks are observed in layered structures frequently due to a poor adhesion of layers. The incorporation of flexoelectricity and micro-inertial effects is needed into the failure analysis of interface cracks in nano-sized structures under dynamic loading. In numerical examples, we discuss the influence of flexoelectricity coefficients as well as the ratio of elastic coefficients and the geometrical size to microstructural (micro-stiffness and micro-inertia) length scale parameters of the bilayer composite on the crack opening displacement, stresses ahead the crack tip and induced electric intensity vector. [ABSTRACT FROM AUTHOR]

In this paper, the J -integral is derived for temperature-dependent elastic–plastic materials described by incremental plasticity. It is implemented using the equivalent domain integral method for assessment of three-dimensional cracks based on results of finite-element calculations. The J -integral considers contributions from inhomogeneous temperature fields and temperature-dependent elastic and plastic material properties as well as from gradients in the plastic strains and the hardening variables. Different energy densities are considered, the Helmholtz free energy and the stress-working density, providing a physical meaning of the J -integral as a fracture criteria for crack growth. Results obtained for a plate with two different crack configurations each loaded by a cool-down thermal shock show domain-independence of the incremental J -integral for different energy densities even for high temperature gradients and significant temperature-dependence of the yield stress and the hardening exponent in the presence of large scale yielding. Hence, the derived J -integral is an appropriate parameter for the assessment of cracks in thermomechanically loaded components. • J -integral for temperature-dependent incremental plasticity. • Plastic, thermal and material contributions to inhomogeneous field quantities. • Three-dimensional equivalent domain integral method implementation. • Domain-independency for the J -integral based on different energy contributions. • Post-processing routine suited for cracks in thermomechanically loaded components. [ABSTRACT FROM AUTHOR]

• A PF fracture model is developed based on the strain gradient elasticity theory. • An energy decomposition method is proposed for the new PF fracture model. • The PF model is numerically implemented through Abaqus subroutine UEL. • The proposed PF model can characterize the toughening effect of gradient elasticity. • The proposed PF model can well predict the curvilinear crack propagation path. In this paper, a novel phase field (PF) model for fracture is developed in the framework of strain gradient elasticity. The strain energy decomposition methods initially proposed for linear elastic fracture problems are extended to the gradient elasticity situation. The PF model is numerically implemented through Abaqus subroutine UEL (user defined element) with nine-node quatrilateral C1-continous element. The finite element implementation is validated by studying the stress field near the static crack tip. When the length-scale parameter of the gradient elasticity is zero, the stress field is consistent with the analytical solution predicted by linear elastic fracture mechanics (LEFM). For non-zero length-scale parameters, the Cauchy stress at the crack tip is found to be non-singular and the numerical results exhibit less mesh sensitivity in the crack tip region compared with the linear elastic case. After that, four different strain energy decomposition methods (Method I-IV) are compared and discussed by studying Mode I fracture behavior under tensile load. It is found that Method I can properly characterize the toughening effect of gradient elasticity. Based on Method I, the influences of the fracture length-scale parameter l c and the strain gradient length-scale parameter l on the characteristics of the smeared crack model and the load–displacement curves are systematically discussed. The specimen size effect of Mode I crack propagation is also investigated. It is found that the length-scale parameter l has a larger influence on the load–displacement curve as the specimen size decreases. Finally, crack propagation behavior in pure shear test, three point bending test and tensile test of a notched plate with hole is investigated. It is demonstrated that the proposed PF model can well predict the curvilinear crack propagation path and properly characterize the effect of gradient elasticity. Thus, the PF model developed in this paper can be applied to study complex fracture behaviors in the framework of gradient elasticity, where the effect of internal structure on the mechanical responses become significant. [ABSTRACT FROM AUTHOR]

• The paper focuses on FE modelling of the fracture process of porous 316L steel. • Modelling considers the 3D shape of the mesostructure using micro-CT. • Compensating method of the micro-CT inaccuracy was used. • The calculation models considers the effect of local fracture. • Influence of local fracture process on the macro behaviour was determined. This paper concerns numerical modelling of the deformation process, taking into account the local fracture of porous 316L sinters at the mesoscopic scale using the finite element method. Calculations are performed with the use of geometrical models, to map the realistic shape of the porous mesostructure of the material, obtained by means of computed microtomography. The microtomographic device has limited and insufficient measurement accuracy for materials such as the porous sinters studied. For this reason, a method to compensate the inaccuracy of mesostructure shape-mapping is used in the numerical modelling of the deformation and fracture process of the material. The normalised Cockroft-Latham ductile fracture criterion is used to model the local fracture process (at the mesostructure level) of porous metal sinters under tension. The paper describes the numerical modelling procedure and the results of the calculations. The influence of the material structure on the meso -scale fracture process is also discussed. The numerical nominal stress–strain curves are compared with the results of experimental testing. The analysis of stress and strain fields and their variability caused by local fracture in the investigated heterogeneous material is also carried out. [ABSTRACT FROM AUTHOR]

• Dynamic initiation and propagation of an internal crack in brittle material were observed. • The circumferential stress field at the pre-crack tip was obtained. • The effects of non-singular T stress and the friction were discussed. • The mode III fracture characteristics were observed in fracture morphology. Different defects are widely distributed inside natural rock masses, and the development of these defects poses a potentially severe threat to the entire structural stability and safety. Most studies at present are concentrated on the propagation of two-dimensional (2D) penetrated cracks under static loads. In this paper, a series of tests were carried out on cubic glass specimens containing a closed pre-crack using a split Hopkinson pressure bar (SHPB) system, aiming to investigate the internal three-dimensional (3D) crack growth under dynamic compression. The results indicate that the dynamic compressive strength of the cubic specimen is influenced by the inclination direction of the 3D pre-crack. Theoretical analysis of the circumferential stress field at the pre-crack tip reveals the mechanism behind dominant crack initiation and favorable direction, which are also affected by non-singular T stress along and perpendicular to the pre-crack plane, as well as friction between crack planes. Through the post-mortem examination, the mode III fracture characteristics, crack bifurcation and Wallner lines are observed in fracture morphology. The terminal length of wrapped wing cracks subjected to dynamic loads is sensitive to pre-crack inclination angle, while it is approximately 1–1.5 times the pre-crack radius under static compression. [ABSTRACT FROM AUTHOR]

• All crack-tip stress models are invalid within fracture process zone whose dimension is 2.5 Å away from crack tip. • Energy-based fracture criteria become invalid when crack length is less than 8 nm due to the nonlinear mechanical behavior. • Stress intensity factor criterion fails when crack length is less than 8 nm due to the decreasing K -dominant zone. • The critical distance theory and quantized fracture mechanics are applicable regardless of crack length and can be unified into a non-local stress criterion. Miniaturization of mechanical structures offers excellent performances of the device while has brought problems of fracture at nanoscale. However, whether the classical fracture theory is applicable at such a small scale and what is its low limit are still challenging problems. In this paper, by conducting atomistic simulation of graphene and compared with the reported in-situ experiments, the applicable range of distance from crack tip for crack-tip stress distribution models and the low limit of crack length for fracture criterion are investigated. It is found that all crack-tip stress models are invalid within fracture process zone whose dimension is 2.5 Å away from crack tip. The energy-based fracture criteria are not applicable when the crack length is less than 8 nm due to the nonlinear stress–strain relationship, while the modified Griffith criterion can be applied to low limit of crack length 5 Å. For the stress-based fracture criterion, the stress intensity factor criterion fails when the crack length is less than 8 nm due to the decreasing size of critical K -dominant zone Λ K , while the theory of critical distances and quantized fracture mechanics can accurately predict the critical fracture stress regardless of the crack length, which can be unified by a non-local stress criterion. This work will provide a mechanical basis for the reliable application of the microelectronic devices at nanoscale. [ABSTRACT FROM AUTHOR]

• A mechanism based multiaxial thermo-mechanical fatigue damage model is proposed. • The value of the scatter band of life prediction result is less than ± 2. • The mean relative error between predicted and experimental strain amplitudes is 6.54%. In this paper, a life prediction method based on damage mechanism for titanium alloy TC4 under multiaxial thermo-mechanical fatigue loading is proposed. Temperature and time dependent influence factors are proposed and introduced into the strain amplitude-life curve method to consider the temperature and time dependence of damage, respectively. The increase in fatigue and oxidation damages caused by tensile mean stress and non-proportional additional hardening is expressed by the mean stress in Macaulay brackets and by using a multiaxial damage parameter, respectively. A fast cracking influence factor is proposed to consider the influence of fast cracking of materials caused by the combined action of high temperature, tensile stress and shear stress on damage behavior. The material constants are identified by test data under uniaxial and proportional loadings, and are further used for prediction under non-proportional loading. The failure life results of uniaxial isothermal fatigue tests with and without dwell time, uniaxial and multiaxial thermo-mechanical fatigue tests are used to verify the proposed method. The value of the scatter band of life prediction result is less than ± 2, as well as the maximum and mean relative errors between predicted and experimental strain amplitudes are 18.49% and 6.54%, respectively. [ABSTRACT FROM AUTHOR]

• An improved method is proposed to compute the heat transfer coefficient on 3D airfoil. • The model of airfoil ice shape and crack growth was established by the self-developed C-DEICE program. • The 2D and 3D simulation calculation of crack propagation and the ice shape are achieved. • The fluid–solid coupling method is reliable for determining the initial crack location. For aircraft ice accumulation, this paper analyzed airfoil icing with OpenFOAM software, including the ice shape analysis, ice crack propagation analysis and ice stress intensity analysis. The direction of water overflow is divided along the chordwise and spanwise of the airfoil. And the heat and mass transfer process of icing is investigated by modifying the classical Messinger icing thermodynamic model. Based on the traditional calculation method of 2D surface heat transfer coefficient, an improved 3D airfoil surface heat transfer coefficient calculation method is proposed. And ice accretion is along the direction normal to the surface. The model of airfoil ice shape and crack growth was established by the self-developed C-DEICE program. The flow field of the 2D and 3D ice shape obtained by reverse modeling were calculated by the C-DEICE program. The crack propagation and ice shedding shape were simulated in 2D and 3D. Icing completely changes the pressure distribution on the airfoil surface, and the aerodynamic performance is decreased by 91.6%. The displacement of ice body above the crack increases significantly with the crack propagation, and the displacement increases with the distance from the crack tip, which is consistent with the 2D crack propagation simulation results. Furthermore, the self-developed C-DEICE program can better capture the trend of ice shape and the range of ice covering on the airfoil surface. It is found that the fluid–solid coupling method is reliable for determining the initial crack location. Meanwhile, it also lays a theoretical foundation for the follow-up study of ice shedding trajectory. [ABSTRACT FROM AUTHOR]

• Semi-empirical formula on notch stress field and SIF of orthotropic V-shaped thin plate with initial crack is presented. • The semi-empirical equation is verified with finite element method, traditional formula and various composite materials. • The proposed formula is extended to the solution of SIF for V-notch-cracked plate under tension-bending loads. For orthotropic materials, the solution of notch stress field and stress intensity factor (SIF) is not only related to crack opening angle, crack depth, notch length, geometric parameters, but also obviously influenced by material characteristics and constitutive relation. On the basis of isotropic notch stress field and SIF theoretical formula, a series of multi-parameter models of orthotropic materials were constructed and fitted. The effects of notch depth, crack length, the ratio of notch depth to plate width, opening angle and mechanical properties of composite materials on geometric correction coefficient Y I are systematically analyzed. On this basis, a semi-empirical formula of Y I is put forward by combining stress field analysis and multi-parameter fitting. The semi-empirical formula is further verified with finite element method, traditional formula and various composite materials. The numerical results show that the simple formula proposed in this paper has higher prediction accuracy. Finally, the proposed formula is extended to the solution of notch stress field and geometric correction coefficient for V-notch-cracked plate under bending load, tension-bending complex loads. [ABSTRACT FROM AUTHOR]

Twenty years in since its introduction, Peridynamics established by Silling provides an attractive theory for modeling deformation and fracturing in solid materials. The paper aims to revisit the well-established bond-based Peridynamic (BPD) and ordinary state-based Peridynamic (OSPD) models and attempts to provide new insights into them. To this aim, a novel decomposition of the Peridynamic bond length change is developed, and the bond length change components are used to define a new micro-potential function. The macroscopic nonlocal elastic strain energy density (NESED) is computed through the integral of the micro-potential over the horizon. The constitutive relation is obtained by the Frechet derivative of the NESED with respect to the deformation state. The NESEDs and constitutive bond force densities are discussed with specific influence functions. The main foundings of the present work are as follows: (1) An explicit expression of bond micro-potential is proposed, and the NESED obtained by the integral of the micro-potential over the horizon can retrieve the ad hoc NESED in the OSPD model. It could pave the way for the development of micro-potential based bond failure criterion for the OSPD model. (2) It is proven that the constitutive relation in the OSPD model can be recovered by the present constitutive relation with specific influence functions in the case where the deformation is small. (3) As the Poisson ratio is 1/3 in plane stress condition or 1/4 in plane strain condition, the present Peridynamic model with specific influence functions is reduced to the BPD model in the case of small deformation, and thus the BPD model can be considered as a reduced form of an OSPD model. Moreover, numerical investigations on a single edge-notched plate under mode II dominated loading and three-point bending tests are conducted to illustrate the descriptive and predictive capabilities of the present Peridynamic model. • A novel decomposition of the Peridynamic bond length change is developed. • An explicit expression of bond micro-potential is proposed, and the NESED obtained by the integral of the micro-potential over the horizon can retrieve the ad hoc NESED in the OSPD model. • The OSPD model can be recovered by the present Peridynamic model with specific influence functions in the case where the deformation is small. • The BPD model can be considered as a reduced form of an OSPD model. • A new mixed mode bond failure criterion is developed based on components of the micro-potential. [ABSTRACT FROM AUTHOR]

• The effect of build direction on tensile properties of LPBF samples at high temperature. • The variation of microstructure and tensile fracture surfaces of LPBF samples at high temperature. • The build direction has little effect on shape and envelope area of hysteresis loops of LPBF Ti6Al4V samples. • The build direction can affect the kinematic hardening of Ti6Al4V samples significantly, but it has little effect on isotropic hardening. Laser powder bed fusion (LPBF) Ti6Al4V has a great potential to be applied in high temperature vehicle structure. The columnar grains of the LPBF components grow along the build derection. Duo to the specific microstructures, the tensile and fatigue properties of LPBF components are anisotropic. So, the study on high temperature mechanical properties of LPBF Ti6Al4V need to be intestigated further. In this paper, high temperature tensile and fatigue samples were designed and manufactured by LPBF. Tensile tests were carried out at 350 °C, 450 °C and 550 °C. The effects of build direction and temperature on high temperature tensile properties were analyzed and compared. The fatigue tests were carried out at 450 °C, and the strain amplitude was in the range of ±1.5 %. The effects of build direction on the hysteresis loops and the fatigue fracture surfaces of fatigue samples were studied. The results showed that the build direction can affect the kinematic hardening significantly, but it has little effect on isotropic hardening. [ABSTRACT FROM AUTHOR]

• The interface crack between two dissimilar dielectric materials. • The size-effect phenomenon and direct flexoelectricity are considered in constitutive equations. • The mixed FEM formulation with C0 continuous finite elements for independent approximations of displacements and strains. • The influence of the flexoelectricity, micro-stiffness length scale parameter, and material composition in layers is studied. In the present paper, the interface crack between two dissimilar dielectric materials under a mechanical load is investigated with including flexoelectricity effects. Flexoelectricity is a size dependent electro-mechanical coupling phenomenon, where the electric polarization is induced by a strain gradient in dielectrics. The strain gradients may potentially break the inversion symmetry in centrosymmetric crystals and polarization is observed even in all dielectric materials. The polarization is proportional to the strain gradients in the direct flexoelectricity. Layered composite structures are frequently utilized in microelectronics. Due to a poor adhesion of protection layer and basic material, the interface crack can be created there and for the prediction of failure of these structures it becomes essential to investigate distribution of the interfacial stress and strain fields. Governing equations in the gradient theory contain higher-order derivatives than in the standard continuum mechanics. Therefore, a reliable computational tool is required to solve these boundary-value problems. The mixed finite element method (FEM) is developed, where the standard C0 continuous finite elements are utilized for independent approximations of displacements and strains. The constraints between the displacement gradients and strains are satisfied by collocation at Gaussian integration points inside elements. In numerical examples, a parametric study is performed with respect to flexoelectric and elastic coefficients for both material regions. The influence of these parameters on the crack opening displacement is discussed. [ABSTRACT FROM AUTHOR]

In this paper we develop a finite deformation micromechanical framework for modeling rate-dependent failure in unidirectional composites under off-axis loading. The model performance is compared with original experiments on thermoplastic carbon/PEEK composites tested at different strain-rates and off-axis angles. To achieve quantitative agreement with the experiments, a microcrack initiation criterion based on the local stress and the local rate of deformation state in the polymer matrix is proposed. Microcracking is represented by a cohesive zone model, with special attention to the inclusion of geometric nonlinearity in the formulation. In this regard, the cohesive geometric nonlinearity is based on extension of an existing formulation to three-dimensional space. Beside microcracking, the Representative Volume Element (RVE) also accounts for viscoplasticity in the polymer matrix. A recently introduced dedicated arclength control method is utilized to impose a strain-rate on the micromodel. Accordingly, kinematic relations governing the RVE deformation allow for the change in orientation of the micromodel in the loading process. This change in orientation of the microstructure has an important implication on the apparent material strength. [Display omitted] • An RVE model to study failure in UD composites undergoing finite strains is developed. • The model is compared with original experiments on UD carbon/PEEK composite system. • Microcrack initiation based on the polymer deformation rate is proposed. • An arclength model imposes strain-rate on the RVE under an arbitrary off-axis angle. [ABSTRACT FROM AUTHOR]

• The ASME formula used for calculating stress intensity factor for nozzles were verified by linear elastic fracture mechanics finite element analysis. • Five Taiwan domestic RPV nozzles were considered for finite element stress and fracture mechanics analysis. • ASME formula provides conservative results for circular-shape nozzle corner crack but underestimates for elliptical-shaped crack. • The adjusted magnification factors were proposed for the elliptical-shaped nozzle corner crack. Due to the structural discontinuity of geometry having higher stress concentration, the nozzles may dominate the structural integrity of reactor pressure vessel (RPV) system, even the material radiation embrittlement is insignificant. The nonmandatory Appendix G in Section XI of the ASME Boiler and Pressure Vessel code provides a fracture mechanics-based methodology using magnification factors to calculate the stress intensity factor of reference crack tips as long as the stress distribution through the nozzle section is available. This paper establishes various three-dimensional finite element models of Taiwan domestic RPV nozzles to conduct a series of stress and linear elastic fracture mechanics analyses to estimate the stress intensity factors. The circular and elliptical reference corner cracks with depths of one-fourth and one-tenth thickness of the vessel wall along the 45° path are considered. Two evaluation results using the ASME method and the finite element linear elastic fracture mechanics analysis are compared. It is found that the ASME method produces conservative values of stress intensity factor at crack tips of circular corner cracks but underestimates the elliptical corner cracks. Finally, an adjusted magnification factor formula is proposed to obtain more accurate stress intensity factors for elliptical-shaped nozzle corner cracks. [ABSTRACT FROM AUTHOR]

• A thermodynamically consistent PF-CZM with strain gradient elasticity and surface stresses is developed. • The proposed model can characterize the size effect of fracture behavior induced by strain gradient elasticity and surface stresses. • Strain gradient elasticity increases the fracture toughness. • Surface stresses improve the local-fracture strength at the crack tip. • Strain gradient elasticity further enhances the effect of surface stresses by changing the damage distribution at the crack tip. Microstructure and surface stresses play a vital role in the micro- and nano-scale. In this paper, a thermodynamically consistent phase-field regularized cohesive fracture model (PF-CZM) is initially proposed to analyze crack propagation in the micro- and nano-scale, where strain gradient elasticity is introduced by higher-order elastic energy, and surface stresses are obtained using geometrical nonlinearity. After that, the higher-order theory is implemented through a mixed-type formulation finite element method. The specimen size effect of Mode I crack propagation is investigated. It is found that both strain gradient elasticity and surface stresses increase the critical load of crack nucleation, which becomes more pronounced as the size of the specimen decreases. The strain gradient elasticity increases the fracture toughness due to the reduction in stress singularity, while the maximum value of stress is still equal to the fracture strength during crack propagation. The surface stresses improve the local-fracture strength at the crack tip. Finally, the strain gradient elasticity further enhances the effect of surface stresses by changing the damage distribution at the crack tip when surface stresses are taken into account along with strain gradient elasticity. The presented framework has shown great potential for modeling crack propagation in the micro- and nano-scale. [ABSTRACT FROM AUTHOR]

• A multi-layer hydraulic fracture propagation model was established based on hybrid finite-discrete element method. • The main factors which affect the fracture propagation were analysed. • The change of fracture width along fracture height was quantitatively analyzed. During the hydraulic fracturing in shale formation, the mechanical properties and stress field caused by sand and shale interbedding were the major factors affecting the hydraulic fracture propagation. In this paper, a hydraulic fracturing simulation model was proposed based on the hybrid finite-discrete element method, and the factors affecting the fracture propagation were analyzed. The simulation results indicated that the fracture width experienced a sudden decrease when the hydraulic fracture interacted with a bedding plane. The reservoir with high stress difference and Young's modulus was favorable for the opening of bedding plane, and high injection rate was favorable for the longitudinal expansion of hydraulic fracture. This was mainly because the lower stress difference and Young's modulus was, the opening degree of the bedding plane was much smaller, and the less the energy consumption of opening the bedding surface was. [ABSTRACT FROM AUTHOR]

The essential work of fracture methodology (EWF) has been successfully adopted to evaluate the fracture toughness of various metals and polymers. However, some aspects of the methodology are still far less understood, such as the influence of the experimental parameters on EWF measurement in thin metal sheets. In the present paper, the ligament range criterion of the EWF approach was revised for several advanced high-strength steels (AHSS). The validity of the upper and lower ligament length limits given by the ESIS protocol is redefined and rationalized according to the necking capability and the plasticity behaviour of the different AHSS grades. The work provides a new criterion to define the minimum ligament length to be tested, based on the minimum distance required by the crack to fully develop the necking capability of the material. The width constraint is too restrictive and has no effect on the deviation from linearity in the upper range. On the other hand, the maximum ligament length is proven to be controlled by the size of the plastic zone as proposed by the ESIS protocol. • The ligament limits of the essential work of fracture are redefined for high strength sheets. • A new criterion, considering the transition distance, is proposed to define the minimum ligament length. • The mechanical properties and the strain hardening capacity control the failure mechanism in high strength steels. • The fracture mechanism has influence on the lower ligament bound of the essential work of fracture. [ABSTRACT FROM AUTHOR]

• The crack propagation behavior of plane strain micro-plates is presented. • The size-effect in the mode I crack propagation problem is investigated. • The difference in the mechanical properties of the structure during crack propagation is explained. The crack propagation behavior of plane strain micro-plates is studied in this paper using the modified couple stress theory and the phase-field theory. To the best of our knowledge, this is the first time that phase-field formulation for fracture mechanics is established based on the framework of Modified couple stress. Therefore, the goal of the current contribution is twofold: (i) to alternate classical phase-field model (based on Cauchy continua) to include size-effect based on modified couple stress; (ii) to study the size-effect in the mode I crack propagation problem. The results clearly demonstrate the difference in the mechanical properties of the structure during crack propagation when predicted using classical (the size effect is not taken into account) and modified couple stress theories. This distinction is illustrated via specific examples that include clear explanations and a variety of physical implications. This work will be beneficial to scientists doing research on the fracture development process in microstructures. [ABSTRACT FROM AUTHOR]

• New expression of damage evaluation law for both fibres and matrix have been presented. • An expression for the damage parameter function is introduced. • A user-defined subroutine has been adopted to implement a proposed constitutive damage degradation model. • The effectiveness of the proposed method has been examined under low velocity impact. This paper derives a damage evaluation law for fibres and an expression for the damage parameter function. It also proposes an approach to the matrix damage degradation law. A proposed approach to both the constitutive damage degradation model and increment law is developed to predict intralaminar damage evolution in composite laminates. Failure envelopes for different failure criteria are discussed in term of the fracture plane of matrix cracking under compressive load. The damage surface consistency condition is applied to derive a plastic multiplier as a function of the damage plastic flow so that the plastic strain is updated at each time increment and the stress–strain constitutive relationship of the damage model will also be updated. A user-defined subroutine has been adopted to implement a proposed constitutive damage degradation model. The effectiveness of the proposed method has been examined under low velocity impact. The numerical findings confirm that results obtained using the suggested approach are in good agreement with experimental results. [ABSTRACT FROM AUTHOR]

• The effect of build direction on tensile properties of LPBF samples at high temperature. • The variation of microstructure and tensile fracture surfaces of LPBF samples at high temperature. • The build direction has little effect on shape and envelope area of hysteresis loops of LPBF Ti6Al4V samples. • The build direction can affect the kinematic hardening of Ti6Al4V samples significantly, but it has little effect on isotropic hardening. Laser powder bed fusion (LPBF) Ti6Al4V has a great potential to be applied in high temperature vehicle structure. The columnar grains of the LPBF components grow along the build derection. Duo to the specific microstructures, the tensile and fatigue properties of LPBF components are anisotropic. So, the study on high temperature mechanical properties of LPBF Ti6Al4V need to be intestigated further. In this paper, high temperature tensile and fatigue samples were designed and manufactured by LPBF. Tensile tests were carried out at 350 °C, 450 °C and 550 °C. The effects of build direction and temperature on high temperature tensile properties were analyzed and compared. The fatigue tests were carried out at 450 °C, and the strain amplitude was in the range of ±1.5 %. The effects of build direction on the hysteresis loops and the fatigue fracture surfaces of fatigue samples were studied. The results showed that the build direction can affect the kinematic hardening significantly, but it has little effect on isotropic hardening. [ABSTRACT FROM AUTHOR]

• The interface crack between two dissimilar dielectric materials. • The size-effect phenomenon and direct flexoelectricity are considered in constitutive equations. • The mixed FEM formulation with C0 continuous finite elements for independent approximations of displacements and strains. • The influence of the flexoelectricity, micro-stiffness length scale parameter, and material composition in layers is studied. In the present paper, the interface crack between two dissimilar dielectric materials under a mechanical load is investigated with including flexoelectricity effects. Flexoelectricity is a size dependent electro-mechanical coupling phenomenon, where the electric polarization is induced by a strain gradient in dielectrics. The strain gradients may potentially break the inversion symmetry in centrosymmetric crystals and polarization is observed even in all dielectric materials. The polarization is proportional to the strain gradients in the direct flexoelectricity. Layered composite structures are frequently utilized in microelectronics. Due to a poor adhesion of protection layer and basic material, the interface crack can be created there and for the prediction of failure of these structures it becomes essential to investigate distribution of the interfacial stress and strain fields. Governing equations in the gradient theory contain higher-order derivatives than in the standard continuum mechanics. Therefore, a reliable computational tool is required to solve these boundary-value problems. The mixed finite element method (FEM) is developed, where the standard C0 continuous finite elements are utilized for independent approximations of displacements and strains. The constraints between the displacement gradients and strains are satisfied by collocation at Gaussian integration points inside elements. In numerical examples, a parametric study is performed with respect to flexoelectric and elastic coefficients for both material regions. The influence of these parameters on the crack opening displacement is discussed. [ABSTRACT FROM AUTHOR]

In this paper we develop a finite deformation micromechanical framework for modeling rate-dependent failure in unidirectional composites under off-axis loading. The model performance is compared with original experiments on thermoplastic carbon/PEEK composites tested at different strain-rates and off-axis angles. To achieve quantitative agreement with the experiments, a microcrack initiation criterion based on the local stress and the local rate of deformation state in the polymer matrix is proposed. Microcracking is represented by a cohesive zone model, with special attention to the inclusion of geometric nonlinearity in the formulation. In this regard, the cohesive geometric nonlinearity is based on extension of an existing formulation to three-dimensional space. Beside microcracking, the Representative Volume Element (RVE) also accounts for viscoplasticity in the polymer matrix. A recently introduced dedicated arclength control method is utilized to impose a strain-rate on the micromodel. Accordingly, kinematic relations governing the RVE deformation allow for the change in orientation of the micromodel in the loading process. This change in orientation of the microstructure has an important implication on the apparent material strength. [Display omitted] • An RVE model to study failure in UD composites undergoing finite strains is developed. • The model is compared with original experiments on UD carbon/PEEK composite system. • Microcrack initiation based on the polymer deformation rate is proposed. • An arclength model imposes strain-rate on the RVE under an arbitrary off-axis angle. [ABSTRACT FROM AUTHOR]

• Void evolution of AA7075 rolling plate under highly compressive state is studied. • Strain gradient around void varies dramatically and dominates void shape variation. • Void shows expansion and shrinkage on different sections despite highly compression. • Influence of orientations of adjacent grains to the evolution of void is focused. Damage evolution of AA7075-T6 rolling plate with 2 mm thickness under highly compressive stress state, which is generated by spherical indentation, is studied through experiments and simulations. On the cross section of spherical deformation region, micro voids induced by crush of MgZn2 particles are observed by scanning electron microscopy (SEM) and some special characteristics are revealed including ductile tearing of the brittle particle, huddling between neighboring voids and an in-void crack, but no clue of void closure under such heavy compression. Through Electron Back-Scattered Diffraction (EBSD), strain gradient around void was found quite high (70 mm−1) and much higher than the theoretical strain gradient induced by spherical indentation (1.8 mm−1), which will result in a significant hardening effect and preventing the further shrink and closure of micro void. More insights are provided through mechanism-based strain gradient crystal plastic simulations which couples a polycrystalline, full-scale model, and a single crystal submodel. Simulation results verify the elevated strain gradient around microvoid and find strain gradient varies dramatically along the small range of void edge, which is validated by nanoindentation test around the edge of voids. Microvoid evolution controlled by strain gradient shows strong anisotropy on different cross sections. For the void at position D focused in present paper, its area on section perpendicular to Y axis (SecY) increases at the early stage of indentation, despite the compressive stress state. Influence of the orientations of adjacent grains is also studied. Void areas on SecZ and SecY are found more sensitive to the change of orientation of adjacent grain, however, the volume variation show much less sensitivity. [ABSTRACT FROM AUTHOR]

Many components of aerospace and automotive engineering manufactured from forged age-hardening aluminum alloys operate at high temperature in the range 0. 3 T m – 0. 5 T m , where T m is the melting temperature. Experimental data for uni-axial creep on specimens sampled from a forged AA2014 alloy component show that inelastic strain rates depend significantly on the orientation of loading with respect to the material flow direction during the manufacturing stage. Based on the recently developed constitutive model of anisotropic creep, hardening/recovery, softening and overageing processes, this paper addresses experimental analysis and modeling tertiary creep regime up to the final stage of creep rupture. The emphasis is placed on the damage evolution equation in order to account for different damage mechanisms depending on the loading mode and loading direction relative to grain axis: cavitation on elongated grain boundaries as well as decohesions and microcracks around and inside coarse grain particles. Experimental data of creep strain rates for longitudinal and transverse loading directions at 130, 150 and 170 °C have been used to calibrate the model. The validation of the model was carried out by comparing experimental and modeled creep curves in the case of a 30°angle between the loading and the material flow direction during forging. The results show that the assumed damage mechanisms and the developed damage evolution equation are able to reflect both the anisotropic accelerated creep and the time to creep rupture for different stress levels and loading directions. • Principal damage mechanisms for the forged, age hardening AA2014 in the creep regime are identified. • Tertiary creep stage is found to be controlled by overageing of θ ′ phase as well as damage processes including cavities, decohesions and microcracks. • The composite type constitutive model is developed to account for stress redistribution among different microstructural regions. • The model describes creep rates over the entire creep process. • Time to creep fracture for different angles between the loading and the grain axis directions including 0°, 30°, and 90°is predicted with satisfactory accuracy. [ABSTRACT FROM AUTHOR]

• Modified Mazars damage model, for concrete with fracture energy regularization. • Regularization of both tensile and compressive behaviour during the softening branch. • Used classical benchmarks for studying new concrete damage models. • Validation with previous experimental campaigns. • Both constitutive relations for tensile and compressive behaviour, are based on new MC2010 from FIB. This paper presents a modified Mazars damage model, based on a strain formulation, for the physically nonlinear analysis of concrete structures. The main objective is to propose a modified damage model, in which both tension and compression damage evolution laws are regularized using a classical fracture energy methodology. The original loading functions are maintained, including their thermodynamic consistencies. The most relevant modification of the model is introduced in the damage evolutions laws, which are updated in order to produce similar stress–strain relations to those presented in fib Model Code 2010. The softening branch under both compressive and tensile strains is regularized with fracture energy. The damage model is then benchmarked with classical experimental and numerical tests considering monotonic loadings. The new constitutive relation was implemented in the commercial software ABAQUS via user subroutine UMAT. Research needs towards a definition of a generalized damage model with energy regularization are discussed and presented. [ABSTRACT FROM AUTHOR]

• The I-integral is developed for magneto-electro-elastic media with residual strain. • The intensity factors can be solved separately by the I-integral method. • The I-integral is domain-independent for arbitrary material properties. • The interface with jump residual strain affects the I-integral calculations. Magneto-electro-elastic (MEE) materials generally consist of piezoelectric and piezomagnetic constituent phases so that the residual strain often occurs during the manufacturing process. The distributed residual strain and complex interfaces between constituents cause a great challenge to the fracture analysis of MEE materials. Considering the effect of the residual strain, this paper develops an interaction integral (I-integral) method for the extraction of the fracture parameters of an impermeable crack in nonhomogeneous MEE materials. The I-integral method has several merits: 1) it can decouple stress intensity factors (SIFs), electric displacement intensity factor (EDIF) and magnetic induction intensity factor (MIIF); 2) the I-integral is independent of the size of the integration domain, even when the integration domain contains nonhomogeneous and discontinuous material properties. Combined with the extended finite element method (XFEM), the I-integral is adopted to investigate several crack problems subjected to homogeneous, nonhomogeneous and discontinuous residual strains. The I-integral values calculated by different integration domains agree well with each other (relative deviation < 1%) for nonhomogeneous and discontinuous MEE properties. Then, single-crack and multi-crack problems are studied to show the influences of residual strain distributions on the intensity factors. Homogeneous residual strain affects the SIFs dramatically but has a slight influence on the EDIF and MIIF. By comparison, nonhomogeneous residual strains affect the SIFs, EDIF and MIIF significantly. In addition, the residual strain gradients affect the variations of intensity factors with crack location extremely. [ABSTRACT FROM AUTHOR]

In this paper, we use the feature of the strain gradient elasticity theory (SGET) related to the regularization of classical singularity problems. We suggest that the structural analysis of pre-cracked materials can be reduced to failure analysis within SGET by using the appropriate failure criteria formulated in terms of the Cauchy stresses. These stresses are work-conjugated to strains, and they have non-singular values in SGET solutions for the problems with cracks and sharp notches. We confirm our suggestion based on the full-field numerical simulations and provide examples of identification of the length scale parameters of SGET for the known experimental data with pre-cracked brittle and quasi-brittle materials. We show that the identified length scale parameters allow us to predict the failure loads for the experimental samples with different type of cracks by using the maximum principal Cauchy stress criterion. In the experiments with a mixed-mode fracture of the quasi-brittle material (PMMA with inclined cracks), we found that there may arise a transition between the failure determined by the maximum principal stress criterion and the criterion related to the second invariant of the Cauchy stress tensor that can be explained by the change of the stress state triaxiality. • Strain gradient elasticity theory (SGET) is used to predict failure loads for pre-cracked samples. • Failure criteria approach within SGET is proposed. • Failure criteria are formulated in terms of Cauchy stresses, which have finite values in SGET. • Length scale parameters of SGET are identified for different materials. [ABSTRACT FROM AUTHOR]

The phase field model is a very promising method to simulate the damage and fracture behavior of structures and materials. While excellent results are obtained for three-dimensional problems or plane-strain problems, plane-stress problems are usually not handled properly. This paper presents a modification of two existing phase field constitutive models with tension–compression asymmetry, so the plane-stress conditions are satisfied by construction. The modification of the formula is in the expression of the stress–strain relation and the stiffness tensor. The proposed formulation adds nonlinearity in the phase field variable; nevertheless, the staggered iteration for solving the problem is efficiently realized through a quasi-Newton method. Finally, the validity of the proposed modifications is demonstrated through numerical examples. [ABSTRACT FROM AUTHOR]

• An extended Irwin's model is developed with introduction of the Plasticity-affected zone. • The contradiction between classic Irwin's model and the shielding effect of crack-tip plastic zone is resolved in the proposed model. • The effect of crack-tip plastic zone on the crack-tip elastic stress field is quantified. • Crack problems with T-stress can be analyzed by the extended Irwin's model. The effective stress intensity factor derived from Irwin's model is greater than the linear elastic counterpart. This is in contradiction to the shielding effect of crack-tip plastic zone. Besides, the classic Irwin's model underestimates the size of the crack-tip plastic zone compared with Dugdale's model and FE analysis. In this paper, an extended Irwin's model for elastic perfectly-plastic material under small-scale yielding conditions is developed through imposing static equivalence between the plasticity-affected stress field and linear elastic stress field in the plasticity-affected zone. The extended Irwin's model is capable of quantifying the effect of the crack-tip plastic zone on the crack-tip elastic stress field. It reduces to the classic Irwin's model in the limiting case. This new version of Irwin's model provides new insights in elucidating the effect of the crack-tip plastic zone on fracture behavior. [ABSTRACT FROM AUTHOR]

• Dynamic shock and expansion exist in the process of LCO 2 -PB. • Number and direction of cracks increased with the release pressure increasing. • Cracks propagation was affected by confining pressure and LCO 2 volume. • Experimental specimens show two extend models of cracks in coal measures strata. Liquid carbon dioxide phase-transition blasting (LCO 2 -PB) has been applied to improve the permeability coal seam and enhanced coalbed methane recovery (ECBM). However, the mechanical behavior of crack generation and propagation in LCO 2 -PB under true triaxial stresses, has not been studied in detail. In this paper, five small-scale experiments of LCO 2 -PB were carried out with different restraint stresses on concrete blocks (150 × 150 × 150 mm3). Three uniaxial strain-gauges were used to monitor the surface strain of the blocks. The results show that the dynamic shock and expansion exists in the process of LCO 2 -PB. The release pressure markedly affected the relationship between shock and expansion. The expansion of the borehole and the fracture zone decrease with the increase in the confining pressure stress, and it cannot affect the number and direction generated of the blast cracks. The release pressure plays a decisive role in the number of fractures. The propagation process of LCO 2 -PB fracture was affected by the combination of LCO 2 volume and surrounding rock stress field. The increase in the volume of LCO 2 , mainly influenced the length of cracks rather than the number of those. The propagation direction of fractures can be determinate by the effects of confining pressure. The research results will help enhance CBM recovery and reduce the occurrence of the gas disaster. [ABSTRACT FROM AUTHOR]