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Highlights • Strain fields on the surface of a transverse flat specimen are obtained with a DIC system (ARAMIS). • Experimental strain fields obtained from ARAMIS are compared to the Rousselier simulation results. • The Rousselier model is used to predict stress-strain curve and crack propagation of different specimens from welded joints. Abstract In this paper, the fracture behavior of an aluminum laser welded butt joint was studied numerically and experimentally. With the assistance of a digital image correlation (DIC) system, the strain variation of the flat specimen under deformation is obtained. Void sheeting mechanism and shear bands are found on the surface of the specimen to precede rupture. Although initial pores are found in the fusion zone, good predictions are obtained with respect to stress-strain, F-COD as well as fracture resistance J R curves for flat and compact tension (C(T)) specimens, confirming the Rousselier model can predict the fracture behavior of aluminum laser welded joint well, with the Rousselier parameters calibrated from simulation of fracture behavior of notched round specimens. [ABSTRACT FROM AUTHOR]

This paper presents a method for predicting fatigue crack propagation in welded stiffened panels accounting for the effects of residual stresses. Well known power law models were employed to simulate fatigue life for a welded stiffened panel specimen damaged with a central crack. Stress intensity factor values (SIF) were obtained in finite element (FE) analyses by a linear superposition of the SIF values due to the applied load and due to weld residual stresses. The FE models included idealized, rectangular or triangular, residual stress distribution profiles. The effect of welding residual stresses on the crack propagation rate is taken into account by replacing the nominal stress ratio R in the power laws by the effective stress intensity factor ratio R eff . The considered stiffened panel specimen, made of mild steel commonly used in ship structures and manufactured by electric arc welding process, was subjected to the fatigue test with constant amplitude loading until failure occurred. By using the presented method remaining fatigue life of welded stiffened panel specimen was analysed. The simulated crack growth rate was relatively higher in the region of tensile residual stresses and lower between the stiffeners where compressive residual stresses prevail, which is in good agreement with physical principles and experimentally obtained results. [ABSTRACT FROM AUTHOR]

The effect of the microstructure parameters as well as the testing temperature on the impact toughness of 17Mn1Si steel has been studied. The interrelation between the testing temperature during impact bending and deformation and fracture energy consumption has been studied. The relation between fracture energy characteristics at high-rate impact bending and the microstructure of the steel has been established. It is shown that the decrease of the testing temperature leads to almost linear reduction of the impact toughness. [ABSTRACT FROM AUTHOR]

Fracture criteria for prediction of extension of the interface crack and of the crack growth direction in a bimaterial consisting of a homogeneous and a functionally graded material (FGM) with systems of internal defects are studied. The bimaterial is subjected to a heat flux and a tensile load applied at infinity. It is assumed that the thermal properties of the FGM have exponential form. The Young’s modulus and Poisson’s ratio are assumed to be constant. In the previous papers (Petrova and Schmauder, 2011a,b, 2012a,b) asymptotic analytical formulas for the stress intensity factors (SIFs) at the interface crack tips were obtained as a series of a small parameter (the ratio between sizes of the internal and interface cracks). These SIFs are used in fracture criteria to obtain the possible direction of crack propagation and critical loads. The maximum circumferential stress criterion is used and some results for the fracture angles is obtained by the minimum strain energy density in order to compare the predictions for the fracture angles by two fracture criteria. The influence of geometry of the problem (location and orientation of cracks) and the parameters of non-homogeneity of FGMs on the main fracture characteristics is investigated. [ABSTRACT FROM AUTHOR]

• Thermal fracture of functionally graded coatings (FGCs) on a homogeneous substrate is studied. • The effect of residual stresses caused by temperature changes on ΔT (cooling) is investigated. • The mathematical description of the model is based on singular integral equations. • The stress intensity factors and fracture angles were derived. • Combinations of PSZ and mullite as FGCs and Ni superalloy and steel as substrates are used. • Illustrative examples are presented to study the interaction of edge cracks with internal cracks at a weak zone. The problem of fracture of functionally graded coatings (FGCs) on a homogeneous substrate (a semi-infinite medium) is investigated under the influence of thermal and/or mechanical loads (e.g. a heat flux, residual thermal stresses caused by cooling-heating, tension). These loads reflect the most important cases, which arise during the exploitation of FGC structures. The FGC contains pre-existing systems of cracks, such as edge, internal and interface cracks. The mathematical description of the model is based on singular integral equations. The properties of the FGC are continuous functions of the thickness coordinate. Furthermore, the non-homogeneity of the functionally graded material is revealed in the form of corresponding inhomogeneous traction distributions on the surfaces of cracks. This method is approximate and used with the assumption, that the gradation of material properties of the FGC with the depth of the layer is not abrupt. The influence of residual stresses caused by temperature changes on ΔT (e.g. cooling from operating temperatures) is investigated in detail. Different crack patterns (which are reported in experiments and available in the literature) are studied by carrying out numerical experiments with respect to stress intensity factors and fracture angles (a deviation of cracks from the initial direction of propagation). The proposed model in combination with a detailed parametric analysis can help to optimize FGCs in order to improve the fracture resistance of FGC/homogeneous structures. [ABSTRACT FROM AUTHOR]

The microstructure of composite plays a critical role in its mechanical performance. In present work, a series of finite element models are developed to simulate the strength and damage evolution of nanoplatelets reinforced polymer. In order to overcome the mesh issue that occurs in many works due to the extreme high aspect ratios of the nanoplatelets, a novel strategy is proposed to add membrane/shell elements representing nanofillers in a representative volume element. In addition, interfacial debonding can also be simulated within this framework. Furthermore, a modified phase-field method is proposed to model brittle fracture in the polymer matrix. Numerical results show that a quite low volume of nanoplatelets can improve the macroscopic Young's modulus and strength of nanocomposites simultaneously. Interfacial debonding would affect both strength and toughness properties of nanoplatelets reinforced polymer through changing the morphology of cracks. The new modeling strategy in the present work can improve both efficiency and accuracy of finite element modeling nanoplatelets, especially with extremely high aspect ratio reinforced polymers. [ABSTRACT FROM AUTHOR]

• Overview of the available results for Mode III interface crack problems is presented. • Mode III interface crack problem is posed using analytic functions of complex variable. • Closed form analytical solution for interface crack- microcrack interaction is presented. • Solutions for SIFs are discussed with respect to their dependency on bimaterial constants. An overview of the results for Mode III interface crack problems available in the literature, as well as those obtained by the authors, is presented in the paper. The analytical and semi-analytical solutions for the main fracture characteristics (i.e. stress intensity factors and energy release rates) are discussed with respect to their dependency on bimaterial constants. Detailed formulation for the antiplane shear problem for an interface crack interacting with internal cracks is presented using the methods of complex potentials and singular integral equations. Some particular solutions (e.g. for the problem of a singularity interacting with an interface and for the Mode III interface crack) are obtained, and these can serve as benchmark solutions or as parts of other similar problems. The approximate closed-form solution is derived for a special case of the interaction between the interface crack and internal micro-cracks. The resulting form of the solution for the stress intensity factors is rather simple and its structure is easily analyzed. A theoretical analysis of the explicit form of expressions for the stress intensity factors shows the conditions under which the solution for the interface crack depends on the bimaterial mismatch, and those under which it does not depend. This formula also allows to define the condition, when a small internal crack does not influence the stress intensity factor of the interface crack (i.e. invisible for the interface crack). [ABSTRACT FROM AUTHOR]

Interfacial debonding affects the mechanical behaviors of composite structures. In the present work, we developed a new phase-field-based cohesive zone model for modeling debonding at interfaces. The traction-separation law and evolution of phase-field considering the mixed-mode scheme of fracture toughness are given in a variational form. Besides, the present interfacial model can work with the phase-field cohesive zone model for the bulk region, in which a common phase-field value ϕ is shared for both regions. The interaction between the bulk region and interfacial cracking in both displacement, as well as phase-field, are taken into account directly to avoid the over-estimation of the free surface energy. The framework is implemented with the finite element method and validated with several numerical examples. The present work provides a unified approach for modeling quasi-brittle fracture in the bulk region and interfaces and shows its advantage in describing interactions between bulk and interfacial cracking. • A phase-field-based cohesive element is proposed for interfacial failure. • Srength and fracture toughness can be defined independently in different directions. • Closure effect of the interfacial crack can be modeled with given penalty stiffness. • Governing equation is given in a variational form. • Mixed-mode behaviors of interfacial fracture is also considered. • The interaction between interface and matrix is considered by a driving force term. [ABSTRACT FROM AUTHOR]

Interfacial bonding of three different semi-coherent bcc-Fe(110)/graphene interfaces is investigated using the plane-wave pseudopotential method within density functional theory. The analysis of bond lengths, charge densities, charge transfer, magnetic moments and densities of states shows that interfacial adhesion can be understood from the electronic structure. Graphene is considered on Fe(110) surfaces as well as embedded in (110) planes of bulk Fe. Moreover, the influence of single vacancies in graphene is studied in case of graphene on the Fe(110) surfaces. It is found that a single vacancy in graphene leads to a strong increase of interfacial adhesion. The most important contribution to the adhesion is covalent bonding with hybridization of Fe states and C states which is most pronounced for neighboring atoms of the vacancy. [Display omitted] • bcc-Fe(110)/graphene interfaces exhibit strong adhesion due to covalent Fe–C bonds. • Single vacancies in graphene lead to a strong increase of adhesion. • Large magnetic moments are induced at C atoms neighboring a single vacancy. [ABSTRACT FROM AUTHOR]

This paper develops an approach to model the deformation and fracture of heterogeneous materials at different scales (including multiscale modeling) within a discrete representation of the medium. Within this approach, molecular dynamics is used for the atomic-scale simulation. The simply deformable distinct element method is applied for simulating at higher length scales. This approach is proposed to be implemented using a general way to derive relations for interaction forces between distinct elements in a many-body approximation similar to that of the embedded atom method. This makes it possible to overcome limitations of the distinct element method which are related to difficulties in implementing complex rheological and fracture models of solids at different length scales. For an adequate description of the mechanical behavior features of materials at the micro- and mesoscales, two kinds of models that consider grain and phase boundaries within the discrete element framework are proposed. Examples are given to illustrate the application of the developed formalism to the study of the mechanical response (including fracture) of materials with multiscale internal structure. The examples show that the simply deformable distinct element method is a correct and efficient tool for analyzing complex problems in solid mechanics (including mechanics of discontinua) at different scales. [ABSTRACT FROM AUTHOR]

In the present study, Taguchi approach is coupled with fuzzy-multiple attribute decision making methods for achieving better surface quality in constant cutting speed face turning of EN 1.4404 austenitic, EN 1.4462 standard duplex and EN 1.4410 super duplex stainless steels. Two typical multiple attribute decision making techniques were simultaneously adopted to determine multi-surface quality characteristics indices. The differences in rankings among derived indices are solved through converting each crisp values into trapezoidal fuzzy number and unifying them using fuzzy simple additive weight method. The fuzzy numbers are then deffuzified into crisp values employing techniques like; the spread, mode and area between centroid of centroids. Through this procedure, the decision maker is provided with necessary decision tools to optimize the cutting conditions with less sensitivity to the change of weights and no difference in ranking among the deffuzification techniques. Additionally, results of analyses of means and the validation experiments confirm that the optimum cutting conditions derived by this method produce far better surface finish than the best finish obtained during the course of experimentation. Analyses of variance results have shown the predominant effect of feed rate on surface quality. Finally, the collected chip at constant cutting speed and varying feed rates and depth of cuts has shown that friendlier-to-machine chips are obtained when machining austenitic stainless steels than duplex stainless steel grades. [ABSTRACT FROM AUTHOR]

In rock-like materials, mode I and II fracture toughness are distinctive while the compressive strength is much greater than the tensile strength. Besides, mixed-mode fractures instead of pure mode I or II fractures occur under complicated load cases in those materials. Therefore, to capture the mixed-mode cracking process, we developed a mixed-mode phase-field cohesive zone model based on the unified phase-field theory proposed by Wu. The model was built based on a strain energy decomposition scheme and the softening behavior of each mode is controlled by an independent degradation function. Thus, independent values of strength and toughness can be given for different failure modes simultaneously. A simple mixture rule of fracture toughness was introduced to describe the transition between different failure modes. The model can keep variational consistency perfectly and governing equations for displacement- and phase-field, which was never reported in other works. Several numerical examples verified the effectiveness and flexibility of this work. The present work showed a simple but effective way to simulate mixed-mode fracture. • A modified phase-field cohesive zone model is developed for mixed-mode fracture. • A simple mixture rule is utilized to describe the transition between each fracture mode. • The present model can keep the variational consistency perfectly. • Several numerical cases verify the present model. [ABSTRACT FROM AUTHOR]

To gain a deeper insight into the anomalous yield behavior of Ni 3 Al, it is essential to obtain temperature-dependent formation Gibbs energies of the relevant planar defects. Here, the Gibbs energy of the complex stacking fault (CSF) is evaluated using a recently proposed ab initio framework [Acta Materialia, 255 (2023) 118986], accounting for all thermal contributions—including anharmonicity and paramagnetism—up to the melting point. The CSF energy shows a moderate decrease from 300 K to about 1200 K, followed by a stronger drop. We demonstrate the necessity to carefully consider the individual thermal excitations. We also propose a way to analyze the origin of the significant anharmonic contribution to the CSF energy through atomic pair distributions at the CSF plane. With the newly available high-temperature CSF data, an increasing contribution to the energy barrier for the cross-slip process in Ni 3 Al with increasing temperature is unveiled, necessitating the refinement of existing analytical models. [ABSTRACT FROM AUTHOR]

Co(0001)/TaC(01 2 ¯) interfaces with Re impurities are investigated using the plane-wave pseudopotential method within density functional theory. Two interface configurations and several interfacial sites for Re impurities are considered. The calculations reveal that Re doping can lead to more favourable interfaces with lower interface energies. It is shown that the decrease of interface energy can be understood from the electronic structure. Analyses of bond lengths, overlap populations, charge density distributions and densities of state demonstrate the importance of C-Co and C-Re bonds across the interface. Image 1 • Interfacial Re impurities increase interface strength. • Increased interface strength is mainly caused by strong C-Re covalent bonds. • Most favourable configuration of Co/TaC interface is changed by Re doping. [ABSTRACT FROM AUTHOR]

Low cycle fatigue tests for P92 heat-resistant steels (P92 HRS) were conducted at room temperature (RT) and elevated temperature (873 K). The fatigue test results showed that P92 steel showed softening characteristics during fatigue at RT and 873 K, and the increase of temperature and strain amplitude was the main reason for the decrease of uniaxial fatigue life. The specimens before and after fatigue test at two temperatures were observed and analyzed by transmission electron microscope (TEM) coupled with energy-dispersive X-ray spectroscopy (EDS) and selected area electron diffraction (SAED). Microstructure observations revealed that the cyclic softening was caused by the annihilation of dislocations, as well as the fragmentation and polygonization of lath structure. High temperature promoted the formation of subgrains by accelerating the motion of dislocations and migration of low-angle grain boundaries (LABs). With the continuously decreasing of dislocation density, the growth of equiaxed subgrains and the weakening of the precipitation strengthening, the softening rate of the material was further increased until the final fracture occurs. Therefore, the evolution of microstructure of 9Cr martensitic steel during the low cycle fatigue process was deduced and described. • The initial lath structure is changed into equiaxed subgrains with reduced dislocation density. • High temperature promotes the formation and growth of subgrains by accelerating dislocation movement and boundary migration. • The cyclic softening is suppressed by the interactions between dislocations and the precipitates. • At high temperature, this interactions effect is weakened. [ABSTRACT FROM AUTHOR]

Antiphase boundaries (APBs) are crucial to understand the anomalous temperature dependence of the yield stress of Ni 3 Al. However, the required, accurate prediction of temperature-dependent APB energies has been missing. In particular, the impact of magnetism at elevated temperatures has been mostly neglected, based on the argument that Ni 3 Al is a weak ferromagnet. Here, we show that this is an inappropriate assumption and that – in addition to anharmonic and electronic excitations – thermally-induced magnetic spin fluctuations strongly affect the APB energies, especially for the (100)APB with an increase of nearly up to 40% over the nonmagnetic data. We utilize an ab initio framework that incorporates explicit lattice vibrations, electronic excitations, and the impact of magnetic excitations up to the melting temperature. Our results prompt to take full account of thermally-induced spin fluctuations even for weak itinerant ferromagnetic materials. Consequences for large-scale modeling in Ni-based superalloys, e.g., of dislocations or the elastic–plastic behavior, can be expected. [Display omitted] [ABSTRACT FROM AUTHOR]

[Display omitted] • Interfacial debonding of a porous TBC system is studied via SEM image-based FE analysis. • Microstructural pores of SEM image of TBC sample are imported into FE software via CMM. • Pores of TC force the stress to be concentrated adjacent to rough TC/TGO interface and develop TC/TGO interface damage. • Porosity within the BC diminishes stress and damage values along the TGO/BC interface. • Creep leads to stress relaxation of TC up to 24.82 % and lowers the damage level of TGO/BC interface. Numerical analysis of interfacial delamination and the effect of microstructural pores and rough interfaces on the field variables in thermal barrier coatings (TBCs) based on a real scanning electron microscope (SEM) image is performed. The interfacial delamination is modelled by the utilization of cohesive zone method (CZM) in finite element (FE) analysis. The empirical TBC sample considered in this study is constructed via air plasma spray (APS) method and comprises ZrO 2 7 - 8 wt. % Y 2 O 3 ceramic top coat (TC), thermally grown oxide (TGO) made of Al 2 O 3 and NiCrAlY metallic bond coat (BC). A compatible geometry is provided by applying image processing technique to SEM image of the sample's cross-section. SEM image-based geometry imported into FE software to scrutinize the interplay effects of porosity and rough interfaces on temperature fields, thermal stresses and interfacial debonding of TC/TGO and TGO/BC interfaces of the TBC structure. FE analysis reveal that porosity distribution has a prominent role on the stress concentration zones at the sharp corners of pores especially adjacent to undulations of the TC/TGO interface, which is responsible for possible internal cracks and interfacial fracture, respectively. The main findings demonstrate that the porosity near the TC/TGO interface has detrimental effect as leads to aggravation in the TC/TGO interface damage, which causes an increment in TC/TGO interfacial crack length. While, the porosity within the BC has the ability to reduce the stress and damage level along the TGO/BC interface. In addition, considering creep for all layers leads to lower stress levels up to 24.82 % and consequently alleviates the TC/TGO interface damage. [ABSTRACT FROM AUTHOR]

• The physically based TM formulation is a promising numerical method to predict the fatigue short crack initiation, specially for the stent components. • By implementing the current numerical method we can predict the time before the nucleation of the first micro-cracks within the stent components. Most of the micro-components, such as coronary stents, consist of an oligo-crystalline micro-structure. This means that the detection of the few coarse grains which are columnar and parallel to the longitudinal ingot axis is possible. The deformation behavior of such micro-structures is obviously different from polycrystalline materials, since the anisotropic properties of one grain, in relation to its nearest neighbors should be considered. The goal of this study is the simulation of the crack initiation process under a cyclic loading situation in the oligo-crystalline micro-structure of the stent component made of X2CrNiMo-18-15-3. The crack initiation process is simulated employing the physically-based Tanaka-Mura model implemented in Finite Element Method (FEM). The available experimental result data have also been used as the input parameters to the current modelling approach. In this regard the grain size and the grain orientation are changed, and their effect together with the influence of the surface roughness on the fatigue life of the stent components has been studied. [ABSTRACT FROM AUTHOR]

[Display omitted] • Strategy for bridging microscopic and macroscopic crack-growth simulation proposed. • The multiscale model and the concept of the bridging method are integrated. • Reduction of more than 90% in the numerical costs compared to multiscale model. • Accurate and efficient prediction of fatigue life/limit and crack-growth processes. • Can evaluate fatigue failure behaviour of thick components/structures. A strategy for bridging microscopic and macroscopic crack-growth simulations is proposed for efficiently and accurately predicting the fatigue strength of steels by integrating the multiscale model and the concept of the bridging method. Validation by comparing the experimental results of macro-crack specimens and the numerical results of the multiscale model shows a reduction of more than 90% in the numerical costs with the proposed strategy compared to the multiscale model. Only 4.2% and 2.7% errors in fatigue life for the two macro-crack specimens under the maximum loading cases are achieved, whereas no errors in fatigue limits are observed using the proposed strategy, compared to the multiscale model. The accuracy and efficiency of predicted results indicate that the proposed strategy can serve as a robust foundation for evaluating the fatigue failure behaviour of thick components/structures in engineering applications. [ABSTRACT FROM AUTHOR]

• The interface crack between two dissimilar quasicrystal materials. • The gradient theory of thermoelasticity for quasicrystals. • The gradient theory for heat conduction problem. • Decagonal quasicrystal properties. • The mixed FEM formulation with C0 continuous finite elements for independent approximations of displacements and strains. The interface crack problem between two dissimilar materials under a thermal load is analyzed by the gradient elasticity theory since the size effect is expected in the very thin quasicrystal layer. The uncoupled thermoelasticity is considered here, where the thermal fields are independent on mechanical ones. The thermal transport can't be well described by classical Fourier's law in nano-sized structures. Therefore, a novel gradient theory is developed in such structures, where the second derivatives of temperature in the constitutive equation for the high-order heat flux are considered. Moreover, the phonon strain gradients are incorporated into the higher-grade continuum model. Decagonal quasicrystal material properties are considered here. Governing equations and corresponding boundary conditions are derived from the principle of virtual work. The mixed finite element method (MFEM) is developed for a general 2D boundary value problem. Numerical examples are presented to illustrate the phonon, phason and thermal response to external thermal loading within the considered model. [ABSTRACT FROM AUTHOR]

The creep behavior of HR3C austenitic steels was investigated at 650 °C and over the stress range from 150 to 250 MPa for up to 13,730 h. The corresponding microstructure evolution was characterized by optical microscopy (OM), scanning electron microscopy (SEM) and transmission electron microscopy (TEM). In the initial stage of the creep process, the creep-resistance of HR3C steel is enhanced by the precipitation of second-phases particles in the grain and at the grain boundary. Compared with the precipitates inside the grain, the higher nucleation and growth rate of precipitates at the grain boundary is related to the higher interfacial energy and diffusion rate of atoms. The high resolution transmission electron microscopy (HRTEM) and selected area electron diffraction (SAED) results show that the precipitates inside the grain may initially nucleate at dislocation pile-up sites, and the interface coherency between the precipitate and the matrix can be destroyed after a long-term creep process. The TEM morphology indicates that the agglomerated tiny particles interact with the dislocations, contributing mostly to the precipitation strengthening inside the grain during the long-term creep process at 650 °C, while the growth of chain-like M 23 C 6 precipitates at the grain boundary increases the tendency of intergranular cracking as the creep time increased. [ABSTRACT FROM AUTHOR]

Molecular dynamics simulations are used to investigate tensile strengths and failure mechanisms of aluminium nanopolycrystals with an average grain diameter of 8 nm containing dissolved Ni, Cu, Mg or Ti atoms. It is shown that tensile strengths are influenced by several factors such as stacking fault energies as well as types, concentrations and positions of the dissolved atoms. A strong strengthening was found in case of Cu whereas Ni or Ti lead to a moderate increase of strength, while Mg even lowers the tensile strength. It was found that both dislocation processes as well as grain boundary dominated effects contribute to plastic failure mechanisms. Type and concentration of dissolved atoms possess a significant influence on these failure mechanisms. Whereas alloying with Ni, Cu or Mg supports grain boundary dominated failure processes, dissolved Ti atoms lead to a significant increase of stacking faults and dislocations. [ABSTRACT FROM AUTHOR]

• Damage mechanism is investigated using in-situ tensile testing. • 3D Micromechanical FEM is used for modeling DP steels under different stress states. • The MMC damage model was calibrated for the ferrite phase in DP steels using RSM. • The FE model predicted stress–strain curve and fracture strain for different BCs. • The proposed FE model predicted damage mechanisms in the in-situ tensile test. In this paper, the fracture behavior and micro-damage evolution in DP600 and DP980 steels were studied using experimental and numerical methods. First, four specimens with different loading conditions were tested to investigate the influence of the stress state on the fracture behavior and in-situ tensile tests were carried out in order to evaluate damage evolution in the two steels. Afterwards, 3D RVEs based on random martensite phase distribution were generated for both materials and a VUMAT subroutine was utilized to include the Modified Mohr-Coulomb (MMC) damage model in the ferrite phase and predict the macroscopic fracture strain under complex loading conditions. Finally, damage mechanism in the RVE was compared to the in-situ test. It was observed that damage initiation mechanism in DP steels is dependent on the size of ferrite phases. In DP steels with large ferrite phases, strain localization in the middle of the phase caused damage initiation, whereas for steels with smaller ferrite grains, such as DP980, strain localization in the boundary of two phases is the dominant damage initiation mechanism. Furthermore, damage occurred by formation of voids, initiation of micro-cracks near the voids, and propagation and coalescence of these micro-cracks. Also, the response surface methodology can be used to calibrate parameters of the MMC damage model and the resulting FE model can accurately predict the stress–strain curve and fracture strain for all considered loading conditions, except for the shear loading condition. Finally, the proposed micromechanical FE model can be used to predict the same damage mechanisms as the in-situ tensile test. [ABSTRACT FROM AUTHOR]

• MD simulation on crosslinking and deformation of pure and graphene reinforced epoxy. • A new multiscale simulation framework for nanocomposites on the micro- and nanoscale. • Crack simulation in composites by using the phase-field method. A novel multiscale simulation framework was proposed to investigate the mechanical properties of single layer graphene platelets reinforced crosslinked epoxy. Crosslinking reactions in composites were simulated with the molecular dynamics (MD) method in the nanoscale, and the mechanical properties of bulk epoxy and interfaces between unfunctionalized graphene and epoxy were obtained. These mechanical properties from MD method were used in FEM simulation in the microscale. The crack propagation in composites was investigated with the finite element method (FEM) based phase-field method (PFM). The influence of several morphologic factors of graphene platelets on mechanical properties, including volume fractions, distributions of graphene orientations and waviness of graphene, was investigated. Results showed that the increasing graphene volume fraction would lead to the decrease of mechanical properties of composites due to the weak interfacial strength in the present model. Meanwhile, aligned graphene platelets improve all the mechanical properties simultaneously. In addition, the graphene platelets with higher curvatures provide improvement of the overall mechanical properties of the composites because they can block interfacial sliding. The present research suggested that the interfacial strength can be the bottleneck in the graphene reinforced epoxy. [ABSTRACT FROM AUTHOR]

• Analyses of thermoelectric nano-sized structures with cracks. • The size-effect phenomenon is considered by strain-gradients in constitutive equations. • The mixed FEM formulation is applied for numerical implementation. • The influence of the size effect on the crack-opening-displacements is investigated. General 2D boundary value problems with cracks in nano-sized structures of thermoelectric materials are analyzed by the finite element method (FEM). The size-effect phenomenon observed in nano-sized structures is considered by strain-gradients in the constitutive equation for the high-order stress tensor. The variational principle is applied for derivation of coupled thermo-electro-mechanical governing equations. The thermo-electrical fields are fully coupled and the mechanical fields are coupled with temperature only. The mixed FEM with the C0 continuous interpolation for displacements and strains is developed. A collocation approach for kinematic constraints between strains and displacements is applied. The influence of the size effect on variation of crack opening displacements is demonstrated by some numerical examples. [ABSTRACT FROM AUTHOR]

• The influence on the stress state on the mechanical behavior was analyzed by ARAMIS approach which is based on DIC. • The MMC damage model could be used for the prediction of the damage behavior under different stress states for DP steel material. • Three different types of damage initiation mechanisms were observed in DP600 and DP980 steels. • The most important damage initiation mechanisms in DP600 and DP980 were in the middle of large ferrite phase and at the interface of ferrite and martensite phase, respectively. • Two effective micro-crack initiation mechanisms were observed during in-situ test and DP600 and DP980 steels have the same behavior in the micro-crack initiation stage. In this study, the mechanical behavior of two cold rolled commercial dual phase steels (DP) were analyzed on micro and macro scales. First, the anisotropic behavior of these steels were investigated by standard tensile tests in three directions. The results showed that the anisotropy behavior of the fracture strain of DP980 is more pronounced than of DP600. Then, in order to assess the influence on the stress state on the mechanical behavior, four specimens with different stress states were analyzed by ARAMIS approach which is based on digital image correlation (DIC). The ARAMIS results were compared with 3D numerical simulations using the Abaqus/Explicit solver. In this part, the effect of stress state on flow curve and strain distribution in the specimens (i.e. tensile, notched-tensile, shear and bulge specimens) were investigated. To predict the fracture behavior of DP600 and DP980 steels under various loading conditions, the Modified Mohr-Coulomb (MMC) damage model was utilized. A VUMAT subroutine was developed to include a MMC damage model in the 3D models, and good agreement between the numerical and experimental results was observed. Finally, the microstructure failure mechanisms at three different stages (i.e. strain localization, micro-crack initiation and micro-crack coalescence) during uniaxial tensile loading were investigated inside the microstructure of DP600 and DP980 steels using an interrupted in-situ setup. In the results three different damage localizations were observed in both materials, and strain localization in the center of large ferrite phases and at the boundary of ferrite and martensite phases were dominant in DP600 and DP980, respectively. Two different micro-crack initiation mechanisms were observed that were similar in both materials. [ABSTRACT FROM AUTHOR]

The gradient theory of piezoelectricity is developed for 3D analyses of QDs with the functionally graded lattice mismatch between the QD and the matrix. Governing equations in the gradient theory contain higher order derivatives than in conventional approaches. Then, it is needed to apply the C1-elements for approximation of primary fields in the FEM. The mixed FEM with the C0 continuous interpolation and collocation approach for kinematic constraints between strains and displacements is developed. The high-density arrays of quantum dots requires to consider various sizes for the representative volume element of the nanostructured solar cell created by the QD (InAs) and matrix (GaAs). [ABSTRACT FROM AUTHOR]

• Performing fracture tests under different loading, temperature and geometry conditions. • Extracting the corresponding values of crack-tip constraint using FEA. • Extracting J-Q curves under mixed-mode loading conditions. • Modifying J-R curves using crack-tip constraints for mixed-mode loading conditions. • Considering temperature in the modified J-R curve to eliminate the need for experimental testing in future research. The main objective of this study is the precise estimation of the fracture parameters by applying crack-tip constraint under mixed-mode loading conditions. To this aim, an AM60 magnesium alloy with elastic-plastic behavior has been utilized. Fracture tests were conducted using a modified version of Arcan device in mode-I, 45° mixed-mode, and mode-II loading conditions. Different initial crack lengths were used to create a wide range of crack-tip constraints. In addition, experiments have been carried out at different temperatures to enhance the applicability and effectiveness of research in real applications. Using finite element analysis (FEA), the crack-tip constraint, Q , corresponding to the laboratory conditions was extracted. The results show a strong dependency of Q constraint on the loading angle so that by changing the loading angle from mode-I to mode-II, the crack-tip constraint experienced a significant increasing trend, while the dependency on the crack length and temperature is negligible. Finally, the J - Q curves are presented for different temperatures and the corresponding relations are used for predicting the critical values of the J -integral in a specific condition and the obtained results are compared with the experimental results. According to the results, the minimum and maximum differences between the obtained results from the relations and the experimental result are 0.01% and 19.49%, respectively. Moreover, the J-R resistance curve has been modified using the crack-tip constraint. Regarding the obtained results, the minimum and maximum differences between the extracted values and the experimental results were 15.76% and 17.66% respectively. It can be concluded that using the results of this research eliminates the need for conducting the corresponding experimental tests, and the critical values of the J -integral can be obtained with reasonable accuracy by calculating the crack-tip constraint through FEA. [ABSTRACT FROM AUTHOR]

Constitutive equations in gradient theory of quasicrystals are written for phonon and phason stresses, and the higher-order stress tensor. They are expressed by the phonon and phason strains and the gradient of phonon strains. The higher-order elastic parameters are proportional to the conventional elastic stiffness coefficients by the internal length material parameter. Material parameters in constitutive equations correspond to the decagonal quasicrystals. The principle of virtual work is applied to derive governing equations and corresponding boundary conditions. The finite element method (FEM) is developed to solve general 2D boundary value problems in problems described by governing equations for strain-gradient theory of quasicrystals. The path-independent J -integral is also derived for fracture mechanics analysis of such solids. Numerical examples are presented to demonstrate the veracity of the formulations. • Constitutive equations in gradient theory of decagonal quasicrystals. • The mixed FEM with C0 approximation. • The higher-order J -integral formula. [ABSTRACT FROM AUTHOR]