Inclusion-matrix Interface Research Articles

Al2O3-MnS Inclusions and Pitting Corrosion in the Weld Heat-Affected Zone

Manganese sulfide inclusions have been identified as a key factor contributing to the degradation of pitting corrosion resistance in both carbon and stainless steels. However, the precise reasons behind the differential reactivity of various sulfides, with some serving as active sites for pitting while others remain inactive, are not yet fully understood. The effect of debonding occurring at the interface between these inclusions and the steel matrix in relation to pitting corrosion has not been extensively investigated. In this study, an examination of a service-exposed pipeline girth weld was conducted. Immersion testing in blowdown water and multiscale characterization techniques investigated the inclusion-matrix interface debonding within the heat-affected zone. Our findings suggest that interfacial debonding is more likely at the Al2O3- MnS cluster interface. This observation offers a rationale for the selective reactivity of sulfides that form clusters with oxides, highlighting the likelihood that only sulfides clustering with oxides act as active pitting initiation sites.

Voronoi cell finite element method for heat conduction analysis of composite materials.

In this paper, Voronoi cell finite element method (VCFEM) based on assumed flux hybrid formulation has been presented for heat conduction problem of particle reinforced composites material. The heat fluxes satisfying a priori internal thermal balance are directly approximated independently in the matrix and the inclusion respectively. The temperatures on element boundary and matrix-inclusion interface are interpolated by nodal temperature. The thermal balance on the interelement boundary and matrix-inclusion interface is relaxed and introduced into the functional by taking the temperature as Lagrange multiplier. In this way, a functional containing two variables of heat flux and temperature is proposed. Full field heat flux and effective thermal conductivity are obtained. Feasibility and effectiveness of the proposed approach are verified through several numerical examples.

Circular inclusion with a refined linearized version of Steigmann–Ogden model

The plane deformation of an infinite elastic matrix enclosing a single circular inclusion incorporating stretching and bending resistance for the inclusion–matrix interface is revisited using a refined linearized version of the Steigmann–Ogden model. This refined version of the Steigmann–Ogden model differs from other linearized counterparts in the literature mainly in that the tangential force of the interface defined in this version depends not only on the stretch of the interface but also on the bending moment and initial curvature of the interface (the corresponding bending moment relies on the change in the real curvature of the interface during deformation). Closed-form results are derived for the full elastic field in inclusion–matrix structure induced by an arbitrary uniform in-plane far-field loading. It is identified that with this refined version of the Steigmann–Ogden model a uniform stress distribution could be achieved inside the inclusion for any non-hydrostatic far-field loading when R = 3 χ int / λ int (where R is the radius of the inclusion, while λ int and χ int are the stretching and bending stiffness of the interface). Explicit expressions are also obtained for the effective transverse properties of composite materials containing a large number of unidirectional circular cylindrical inclusions using, respectively, the dilute and Mori–Tanaka homogenization methods. Numerical examples are presented to illustrate the differences between the refined version and two typical counterparts of the Steigmann–Ogden model in evaluating the stress field around a circular nanosized inclusion and the effective properties of the corresponding homogenized composites.

Acicular ferrite formation and Mn depletion behavior around the inclusions in Ti-Mg oxide metallurgy steel with different holding times

In this study, the effect of different holding times at 1250 °C on acicular ferrite formation, the inclusion characteristics, and Mn depletion behavior at the inclusion-matrix interface in Ti-Mg oxide metallurgy steel was systematically investigated. The results suggested that the volume fraction of grain boundary products decreased with increased holding time from 60 s to 3600 s, with the volume fraction of acicular ferrite initially increasing and then decreasing. Regarding the inclusion characteristics, different holding times showed no obvious effect on the inclusion type, but they affected the size and area number density of the inclusions. The domain inclusions at different holding times all consisted of MgTi2O4 +MnS, and these inclusions were found to be effective for the nucleation of acicular ferrite. The average diameter of the inclusions increased, and the area number density of the effective inclusions significantly decreased when the holding time was increased from 900 s to 1800 s and 3600 s. Mn-depleted zones (MDZs) with larger widths and higher Mn concentration gradients formed at the inclusion-matrix interfaces at holding times of 60 s and 900 s, and MDZ formation was weakened by the continuous diffusion of Mn when the holding time was increased to 1800 s and 3600 s. At a holding time of 900 s for the Ti-Mg oxide metallurgy steel, the volume fraction and relative nucleation potential of acicular ferrite reached their maximum values, and MDZ formation with the lowest Mn concentration (∼0.8 wt%) was observed around the MgTi2O4 +MnS inclusions. Therefore, 900 s was the optimal holding time for acicular ferrite formation.

Improved micromechanical prediction of short fibre reinforced composites using differential Mori-Tanaka homogenization

Due to the spatial distribution of inclusions in random heterogeneous media, individual inclusions are stressed differently. Mean field homogenization (MFH) methods, a popular homogenization method, cannot account for this variability, instead predicting the same mean value of stress for a particular phase. In this paper, a differential scheme is expanded to calculate the stresses in the individual inclusions, including the scatter and variation of local stresses. The accurate prediction of stress variability of stresses within a particular phase has led to more accurate and realistic modelling of inclusion matrix debonding and inclusion breakage.Extensive benchmarking of the proposed models against finite element (FE) results confirms excellent predictive abilities of scatter at three length scales (effective property, individual inclusions, and matrix-inclusion interface). The potential of modelling stress variability post-onset of damage is also demonstrated.Different realisations of the differential Mori Tanaka (MT) lead to varying predictions of scatter in the individual inclusion stresses. However, the effective properties predictions remain consistent.The prediction of individual inclusion stresses, and their scatter constitutes a significant gap in the literature and has been addressed in this paper. This new scheme could lead to the development of several intricate models of damage in various composites without the need for extensive FE modelling.

Crack initiation mechanism of M50 bearing steel under high cycle fatigue

The fatigue properties of M50 bearing steel under high cycle fatigue were studied by rotating bending fatigue test at room temperature. The fatigue cracks of M50 bearing steel were primarily nucleated at MgO-Al2O3 inclusions and MC/M2C primary carbides. The voids were initiated through inclusion debonding from the matrix and primary carbide cracking under cyclic loading. Small cracks were initiated on the void along the direction perpendicular to the tensile stress. Small cracks propagated at a speed of 8.81 × 10-10 m/cycle with hysteresis in the fine granular area (FGA). When the stress intensity factor range for the subsurface defect was lower than the stress intensity factor range threshold for M50 steel, the initiation stage of fatigue crack was composed of crack nucleation caused by defects and fatigue process in FGA. The fatigue cracks propagated at the fish-eye area (FiE) when the stress intensity factor range at the FGA front exceeded ΔKth. There was a stress concentration at the inclusion-matrix interface or the primary carbide-matrix interface during a long-term cyclic loading which resulted in the nucleation of fatigue cracks. A fatigue crack nucleation model was established based on the true stress at the defect, size of the defect, and number of cycles. A fatigue life model was constructed based on fatigue crack nucleation and fatigue crack propagation processes.

Numerical modelling of rolling contact fatigue damage initiation from non-metallic inclusions in bearing steel

Bearing failure is a cause of concern in a variety of machinery such as turbines, transmissions, drills, engines, etc. It is often associated with rolling contact fatigue (RCF) triggered from damage initiation at non-metallic inclusions (NMI’s). Experimental evidence shows that damage initiation lifetime is highly sensitive to the NMI characteristics and its bonding with the steel matrix. This study numerically investigates the role of NMI features and its bonding with the steel matrix on damage initiation lifetime. NMI characteristics modelled in this study are derived from an experimental investigation of a failed bearing. Simulation results highlight a near to instantaneous debonding at the matrix-inclusion interface followed by accelerated crack initiation. The critical depth for damage initiation shifts towards the surface with the increase in friction coefficient between roller and raceway. The simulations also reveal that larger inclusions show earlier damage initiation, indicating a size effect. The damage hotspots from the simulation results were compared with experimental findings and a hypothesis for crack initiation from a NMI is put forward.

Effect of Frictional Slipping on the Strength of Ribbon-Reinforced Composite.

A numerical–analytical approach to the problem of determining the stress–strain state of bimaterial structures with interphase ribbon-like deformable inhomogeneities under combined force and dislocation loading has been proposed. The possibility of delamination along a part of the interface between the inclusion and the matrix, where sliding with dry friction occurs, is envisaged. A structurally modular method of jump functions is constructed to solve the problems arising when nonlinear geometrical or physical properties of a thin inclusion are taken into account. A complete system of equations is constructed to determine the unknowns of the problem. The condition for the appearance of slip zones at the inclusion–matrix interface is formulated. A convergent iterative algorithm for analytical and numerical determination of the friction-slip zones is developed. The influence of loading parameters and the friction coefficient on the development of these zones is investigated.

The role of inclusion-matrix boundaries in steels fracture processes

The features of the fracture of the interphase inclusion-matrix boundaries under various thermal-deformation and aggressive actions are investigated. The reasons and conditions for the formation of cracks as a result of decohesion of the inclusion-matrix boundaries associated with the concentration of interfacial thermal and deformation stresses are discussed. It was found that the character of decohesion of the inclusion-matrix boundaries (rupture of interatomic bonds of a nonmetallic inclusion and a steel matrix) caused by interphase thermal stresses is due to the conditions of heating and cooling, depending on the type of processing (conventional heating, laser or electromagnetic treatment), which determines the possibility of passing relaxation processes associated with the redistribution of interfacial defects within the specified boundaries. The mechanisms and features of decohesion of the interphase inclusion-matrix boundaries at different methods and temperatures of deformation are discussed. It is shown that the decomposition of the inclusion-matrix boundaries upon deformation occurs in cases of certain types of nonmetallic inclusions (oxides, spinels, some sulfides). For different types of inclusions and steels, parameters have been determined that characterize the cohesive strength of the inclusion-matrix interface depending on the loading conditions. It is shown that decohesion (fracture) of the inclusion-matrix boundary into two free surfaces can be considered as the transformation of interphase misfit dislocations into surface steps as a result of loss of conjugation. The role of inclusion-matrix boundaries in the formation of cracks of fatigue and fatigue-corrosion origin is considered. It is shown that under the influence of aggressive media and cyclic stresses, the structure of the inclusion-matrix interphase boundaries degrades, which is associated not only with the accumulation of interfacial stresses, but also with the facilitation of the penetration of surfactant atoms from the environment along these boundaries. As a result, fatigue-corrosion destruction of the inclusion-matrix boundaries occurs, and the effect of an adsorptive decrease in their strength is manifested.

Negative-stiffness composite systems and their coupled-field properties

Composite materials consisting of negative-stiffness inclusions in positive-stiffness matrix may exhibit anomalous effective coupled-field properties through the interactions of the positive and negative phases, giving rise to extremely large or small effective properties. In this work, effective viscoelastic properties of a continuum composite system under the effects of negative inclusion Young’s modulus ratio $$\lambda _E = E_{\text {inc}}/E_{\text {matrix}}$$ are studied with the finite element method. Furthermore, effective coupled-field properties, such as thermal expansion coefficient, dielectric constants and piezeoelectric constants, are numerically calculated under the effects of negative inclusion bulk modulus ratio $$\lambda _K=K_{\text {inc}}/K_{\text {matrix}}$$ . Stability boundaries are determined by applying small dynamic perturbation to the systems through boundary surfaces, and the system is unstable if its field variables become divergent in time. For viscoelastic composite systems containing small volume fractions, less than $$V_i = 1.5 \%$$ , the systems can be stable up to $$\lambda _E \approx -0.3$$ in 0.3 s under 10 Hz driving frequency. For $$V_i = 5.1 \%$$ case, its stability boundary is around $$\lambda _E \approx 0$$ . Larger inclusion volume fraction reduces allowable negative stiffness in the viscoelastic system. All anomalous peaks found in the coupled-field properties are in the unstable regime, except for the piezoelectric and thermal-expansion anomalies in the composite system with electrically insulated inclusions and large inclusion volume fraction $$V_i = 26.81 \%$$ . Insulated inclusions may cause charge accumulation at the inclusion–matrix interface and boundary surface effects may serve as stabilizing agents to the composite system. Since it is known that negative-stiffness composite is unstable in the purely elastic system in statics, stability enhancement found here in the negative-stiffness systems with viscoelastic and coupled-field effects may be considered as multiphysics-induced stabilization.

Modified closed-form solutions for three-dimensional elastic deformations of a composite structure containing macro-scale spherical gas/liquid inclusions

We re-examine the three-dimensional linearly elastic deformations of a composite structure consisting of an infinite isotropic elastic matrix into which is embedded a macro-sized spherical compressible gas/liquid inclusion. Our main focus lies on the contribution resulting from changes in the initial pressure inside the inclusion during deformation. In this respect, we include not only the effect of the change in pressure induced by the change in volume of the inclusion during deformation but also by the variation of the direction of the pressure with the direction of the normal to the deforming inclusion-matrix interface; this latter contribution has been largely neglected in the majority of studies in this area. In doing so, we incorporate a more complete description of the influence of the initial pressure inside the inclusion on the elastic response of the composite structure when certain external loadings are applied to the matrix. In particular, we obtain an analytical representation for the full displacement field in the matrix in the case of a uniform far-field uniaxial loading and, using effective medium theories, we also derive explicit expressions for the effective properties of the composite structure and illustrate the influence of changes in the initial pressure using numerical examples.

Upper and lower bounds on the creep strain and stress relaxation induced by interface diffusion in metal-matrix particulate composites

In this study, we developed a micromechanics scheme to predict the upper and lower bounds on the creep strain and stress relaxation induced by interface diffusion in metal-matrix particulate composites. The normal stress acting on the matrix-inclusion interface, which is the driving force for interface diffusion, is estimated by using the Hashin-Shtrikman bounds and mean-field micromechanics theory. Analytical solutions of upper and lower bounds on the creep strain under constant stress and the relaxed stress at fixed strain are obtained. Results of this work show that the ultimate creep strain and relaxed stress are only related to the material properties and the percentage of each component, such as volume fraction of inclusion and elastic modulus ratio of inclusion to matrix. The parameters of interface diffusion only influence the rate of creep strain. It is found that the creep deformation and stress relaxation of composites are more sensitive to the volume fraction of inclusion than the elastic modulus ratio. The methodology of this study also applies to analysis of creep deformation of composites where both the matrix creep and interface diffusional creep need to be considered. The present study offers new perspectives for in-depth understanding of creep behavior of composites driven by mass diffusion along inclusion-matrix interface.

New insight into the role of inclusions in hydrogen-induced degradation of fracture toughness: three-dimensional imaging and modeling

ABSTRACT An in-depth understanding of the role of non-metallic inclusions (NMIs) in the hydrogen-induced failure of structural materials is important in the manufacture and application of steels. In this paper we investigated the type, the amount and the distribution of NMIs in pipeline steels and their relation to the susceptibility to hydrogen-induced cracking (HIC). Scanning Electron Microscope (SEM) observation confirmed the interlinking of the microcracks formed at the inclusion-matrix interfaces. By combining with the nondestructive three-dimensional (3D) mapping of crack propagation paths, based on the synchrotron tomography technique, we obtained direct evidence that the cracking initiation at the NMIs and then interlinking on the (nearly) same plane are the main mechanism of HIC failure in X70 steels. We built an elastic-energy-based model, which can be applied to quantitatively predict the HIC-induced dependence of the fracture toughness on NMIs, based on statistical information of the NMIs. The theoretical results show a good agreement with the experimental observation. We proposed a criterion to determine the susceptibility to HIC by the observation of NMIs. We also developed a thermodynamics-based model to analyze the hydrogen trapping at the inclusion-matrix interface and its dependence on the strength of the steel matrix. For the first time, the direct relationship between NMIs and HIC-induced degradation of fracture toughness is obtained.

Modeling of Structural Damage Evolution in Dispersion-Filled Elastomeric Nanocomposites with Regard for Interfacial Interaction

Computer modeling of internal damage evolution in elastomeric nanocomposites with high structural phase inhomogeneity (hard dispersed filler and soft elastomeric matrix) has been carried out. The concentration of filler particles was chosen to be sufficiently high, so that their mutual interaction affected significantly the strength properties of the material. Dispersed inclusions were assumed to be absolutely rigid and durable. Only a finitely deform able incompressible matrix (the mechanical properties of which were set using the neo-Hookean elastic potential) could be damaged. The model takes into account the following specific features of the composite structure: a high stress concentration in the gaps between closely located inclusions, the presence of elastomeric layers with increased stiffness on the surface of filler particles, different interphase contact conditions (full adhesion or slip at the matrix–inclusion interface), and the possibility of anisotropic hardening during uniaxial stretching (due to the reorientation of molecular chains in the elongation direction). The latter factor made it possible to study theoretically the mechanism of formation of high-strength microstrands in the gaps between adjacent particles. The occurrence of such formations in filled elastomers, which was observed in numerous experiments, is a proven fact. A new (anisotropic) fracture criterion has been developed to describe it, because this phenomenon cannot be simulated within the generally accepted strength criteria. The calculations based on this new approach showed that local matrix discontinuities occur not in the gaps between particles (sites of highest stress concentration) but at a certain distance, forming a hollow ring (microstrand) around it. The link between neighboring inclusions is not violated, and the material retains its load-carrying capacity at the macrolevel. Thus, the presence of microstrands is a possible reason for hardening an elastomer when a hard dispersed filler is introduced into it.

Micromechanical Modeling for the Damage Accumulation and Adhesive Wear of Metallic Materials Containing Inclusions

Abstract Metallic materials usually contain some amounts of inclusions which are known to affect their mechanical properties since the bonding strength of the matrix–inclusion interface is relatively low, voids or cracks are thus easily formed under a tensile loading. However, under a contact loading, the effects of subsurface inclusions on the sliding wear of metallic materials are not thoroughly understood. In this work, a micromechanical model is proposed to study the shear fracture and wear of metallic materials containing random inclusions. With the model, crack branching and crack aggregation during contact loading are simulated, and the formation process of sheet-like wear particles is clarified. It is demonstrated that the subsurface micro-cracks, particularly those near inclusions, and their subsequent evolution play a major role in the adhesive wear. This investigation is helpful in understanding the adhesive mechanism of wear, and the proposed model could be a promising approach for the prediction of adhesive wear.

Compressible liquid/gas inclusion with high initial pressure in plane deformation: Modified boundary conditions and related analytical solutions

In the analysis of the elastic behavior of a composite system composed of a solid matrix and a number of compressible liquid/gas inclusions, it is customary to incorporate the change in the magnitude of an inclusion's internal pressure (induced by the change in its volume) during deformation. However, when an inclusion has a relatively high initial pressure, the change in the direction of the pressure during deformation may also be significant, particularly in establishing an accurate boundary condition on the inclusion-matrix interface. This can be attributed to the fact that, during deformation, the change in the direction of the normal to the inclusion's boundary is of the same order as the change in its volume. Accordingly, in this paper, we propose two modified boundary conditions for a general compressible liquid/gas inclusion surrounded by a solid matrix subjected to plane deformation. Specifically, we incorporate changes in both the magnitude and direction of the inclusion's internal pressure during deformation. The corresponding boundary value problems are formulated using complex variable methods with explicit analytical solutions obtained in the particular case when the initial shape of the inclusion is circular and the surrounding matrix is infinite. Concise explicit formulae are also given for evaluating the effective moduli of the corresponding composite system based on the dilute model and the Mori-Tanaka method. Numerical results are presented to illustrate our solutions and to draw comparison with the classical solution in the case of an air bubble inclusion in a soft gel matrix. We find that when the inclusion has a relatively high initial pressure, the classical solution may indeed overestimate the external loading-induced stress concentration around the inclusion and underestimate the effective moduli of the corresponding composite system. In particular, it is shown that a porous material could be significantly strengthened in resisting shear deformation when filled with liquid/gas inclusions of a relatively high pressure even if surface tension effects are neglected: this phenomenon is not captured in classical models.

Raman Scattering in the InSb–MnSb Eutectic Composite

The Raman spectra of bulk samples of the InSb–MnSb eutectic composite and its thin films produced by flash evaporation are studied. In the Raman spectra of the bulk samples, the TO and LO modes of InSb at the frequencies 179.5 and 192.4 cm–1 and a number of peaks at the frequencies 122, 127, 167, 211, and 245.5 cm–1, close to the available theoretical data on the phonon frequencies in MnSb, are observed. In the Raman spectra of the films, the TO mode is shifted to lower energies and corresponds to 178 cm–1, and the LO mode is shifted to higher energies and corresponds to 196 cm–1. The shift of the LO mode to higher frequencies in the composite with respect to the corresponding mode in InSb is apparently caused by strains at the matrix–inclusion interface and by the contribution of scattering at surface phonons to the Raman spectrum.

Комбинационное рассеяние света в эвтектическом композите InSb-MnSb

Raman spectra of bulk samples of the InSb-MnSb eutectic composite and their thin films prepared by the flash evaporation method have been studied. In the Raman spectra observed TO and LO modes at frequencies of 179.5 cm-1 and 192.4 cm-1 correspond to InSb compound and also the peaks at frequencies 122 cm-1, 127 cm-1, 167 cm-1, 211 cm-1, 245.5 cm-1 correspond to theoretical data for MnSb as is well known from literature. The TO mode in the Raman spectra for films is shifted toward lower energies (178 cm-1), but the LO mode is higher (196 cm-1). The high-frequency shift of the LO mode in the composite with compared its value for InSb is probably due to the presence of deformation at the matrix-inclusion interface, as well as the contribution by surface phonons scattering.

Micromechanical Modeling of Fatigue Crack Nucleation around Non-Metallic Inclusions in Martensitic High-Strength Steels

Martensitic high-strength steels are prone to exhibit premature fatigue failure due to fatigue crack nucleation at non-metallic inclusions and other microstructural defects. This study investigates the fatigue crack nucleation behavior of the martensitic steel SAE 4150 at different microstructural defects by means of micromechanical simulations. Inclusion statistics based on experimental data serve as a reference for the identification of failure-relevant inclusions and defects for the material of interest. A comprehensive numerical design of experiment was performed to systematically assess the influencing parameters of the microstructural defects with respect to their fatigue crack nucleation potential. In particular, the effects of defect type, inclusion–matrix interface configuration, defect size, defect shape and defect alignment to loading axis on fatigue damage behavior were studied and discussed in detail. To account for the evolution of residual stresses around inclusions due to previous heat treatments of the material, an elasto-plastic extension of the micromechanical model is proposed. The non-local Fatemi–Socie parameter was used in this study to quantify the fatigue crack nucleation potential. The numerical results of the study exhibit a loading level-dependent damage potential of the different inclusion–matrix configurations and a fundamental influence of the alignment of specific defect types to the loading axis. These results illustrate that the micromechanical model can quantitatively evaluate the different defects, which can make a valuable contribution to the comparison of different material grades in the future.

Influence of Inclusions’ Position on Stress Distribution of Inclusion-matrix Interface

In this paper, the influence of inclusions’ position on stress & strain distribution was researched when inclusions were same size and shape. The finite element method was used to study the position effect of inclusions in the FGH95 P/M superalloys. The shape of inclusions was simplified rotundity in the model. The influence of inclusions which was on the surface, in the sub-surface and in the basic material on stress & strain distribution was studied. There were two cases, the inclusion connected basic material tightly and there was a hole between the inclusion and the basic material. The change rule of interfacial stress & strain distribution caused by the variation of inclusions’ position was given.