Microstructure-based Representative Volume Element Research Articles

Numerical modeling and failure evolution of microstructure-based in-situ TiB2 and TiC+TiB2 reinforced Cu matrix composites

The optimal design of microstructure is the key to further improve the properties of particle reinforced metal matrix composites. In this study, in-situ TiB2 and TiC + TiB2 reinforced Cu matrix composites are used as examples to develop the microstructure-based representative volume element models to describe their damage evolution and strengthening mechanisms. The most critical features including size distribution and morphology of the particles as well as the fracture of metal matrix, brittle damage of ceramic particles and traction-separation debonding of the interface were integrated into the modeling. Simulation results show that the model could well predict the performance of the composite and reveal its damage mechanism. When the particle size is normally distributed, the composite exhibits higher strength due to the size effect of different particles, which is more consistent with the experimental result. Both matrix and ceramic particles in mixed-phase particle reinforced metal matrix composites can be subjected to higher stresses, which results in higher strength of (TiC + TiB2)/Cu composites. Additionally, the spherical TiC particles facilitate the relaxation of stress concentration within the composite, resulting in a synergistic enhancement of strength and ductility. Under compression, localized interface damage first appears around the sharp corners of the hexagonal particles and induces crack initiation toward the matrix. These microcracks are interconnected and propagate along the direction of high stress, eventually leading to the failure of the composite. This work provides the basis and new ideas to reveal the failure mechanism of composites and further optimize their configuration design.

Effect of microstructural constituents and morphological characteristics on low cycle fatigue behaviour of inter-critically annealed 20MnMoNi55 steel

The effect of varying microstructural parameters on the cyclic behaviour of dual-phase steels was studied on the basis of experimental and micromechanical finite-element simulated results. The initial bainitic morphology of as-received 20MnMoNi55 steel was transformed into ferrite and martensite through proper inter-critical heat treatment procedures. Strain-controlled low cycle fatigue tests were conducted at room temperature with different strain amplitudes at a specific strain rate of 10−3/s. The cyclic stress–strain curve, obtained through joining the peak stresses of hysteresis loops corresponding to different strain amplitude, shows an increase in strain hardening with an increase in volume fraction of martensite. Whereas the rate of cyclic softening, considering the decrease in stress amplitude with respect to elapsed cycles, increases with increasing strain amplitude. Inclusive of all affecting microstructural parameters, an original microstructure-based representative volume element associated with a crystal plasticity-based material model was adopted for conducting micromechanical finite-element simulation. In addition to several parameters associated with a crystal plasticity model, consideration of initial geometrically necessary dislocation density in constituent phases resulted in the accurate prediction of a hysteresis loop at low strain amplitude as compared with the experimental results. A variation of stress triaxiality built up in ferrite matrix with martensite fraction along with deformation inhomogeneity between ferrite and martensite was also observed through a strain partitioning phenomenon obtained from finite-element simulated results.

Predictive dual-scale finite element simulation for hole expansion failure of ferrite-bainite steel

A dual-scale finite element model is proposed to investigate the failure of ferrite-bainite (FB) dual-phase steel in the hole expansion test. The first level simulation solves the elastic-plastic deformation behavior with phenomenological isotropic elastic-anisotropic plastic constitutive models, and its resulting local deformation histories are supplied to the second level simulation as boundary conditions. In the second level simulation, the local microstructure evolution is solved and provides the dislocation densities, equivalent plastic strains, and stress triaxiality that measure the local fracture in grain scale. A special formulation for calculating the dislocation density distribution in the form of dislocation pile-up at grain boundary areas is highlighted as the microscale level constitutive law. The microstructural information is provided from image analyses based on grain average image quality (GavgIQ) and grain average misorientation (GAM) values observed using electron backscatter diffraction (EBSD). The data were used to identify the constituent phases of the FB steel as the major input for the microstructure-based representative volume element (RVE). Nanoindentation tests are employed to validate the identified phase and to extract the phase-level mechanical properties. The onset of failure at the hole edge during the hole expansion test is simulated by the proposed dual-scale numerical approach. Thus, both the hole expansion ratio (HER) and the location of failure can be successfully predicted. The example clarifies that the present approach based on local deformation histories and the resultant microstructure evolution with grain-level deformation inhomogeneity can be utilized for understanding the deformation and fracture of multi-phase steels.

3D micromechanical simulation of the mechanical behavior of an in-situ Al3Ti/A356 composite

The mechanical behavior of an in-situ Al3Ti/A356 composite was studied by three-dimensional (3D) micromechanical simulation with microstructure-based Representative Volume Element (RVE) models. A series of 3D RVEs were automatically generated with A356 matrix and icosahedron shaped Al3Ti particles as representative of various microstructures. Ductile damage of matrix and brittle damage of Al3Ti particles were considered, while perfect interfacial bonding between Al3Ti and Al matrix was assumed. Simulation results were validated by experimental stress-strain curves. Furthermore, the effects of the particle size, volume fraction and distribution of Al3Ti on mechanical properties were simulated by controlling the corresponding parameters in RVEs. The simulation results show that the refinement of particles improves the yield strength and elongation. However, the increase of volume fraction or clustering of the particles reduces the elongation evidently. Additionally, the Young's modulus, yield strength and elongation of the Al3Ti/A356 composite were predicted from different RVE models. The prediction shows that the Young's modulus follows the calculation of Tsai-Halpin equation. The yield strengths are close to the micromechanical approach considering both load bearing and coefficient of thermal expansion (CTE) mismatch strengthening contribution. The relationship between elongation and the properties of the Al3Ti particles is set up by a polynomial fitting, which is generally in agreement with reported experimental results.

Practical microstructure-informed dual-scale simulation for predicting hole expansion failure of hyper-burring steel

A practical dual-scale finite element model is developed to enable the formability prediction in the hole expansion of a hyper-burring steel sheet. This numerical approach resorts to the isotropic macroscale hole expansion simulation for calculating the deformation histories near the hole edge, since they are known to be the potential fracture initiation site. The deformation histories are used as boundary conditions in the lower microscale model for calculating the local fracture of the steel sheet. The microscale simulation utilizes the dislocation density based constitutive model and a microstructure-based representative volume element (RVE), with realistic grain morphology taken from experimental microscopy. The fracture initiation at the hole edge region is evaluated from the microscale simulation using four frequently employed uncoupled ductile fracture models, which enable the definition of the critical fracture strain. The proposed dual-scale model can better predict the failure initiation and location near the hole edge when the modeling parameters are calibrated taking into account not only the deformation histories of the hole edge, but also the local stress triaxiality. Moreover, the proposed dual-scale model is applied to analyze the microstructure effect on the hole expansion ratio by providing the insights into the effect of grain size and grain boundary characteristics.

Mechanical properties and fracture of in-situ Al3Ti particulate reinforced A356 composites

The microstructure and mechanical properties of in-situ 5 vol. % Al3Ti/A356 composites were studied either taking account of the effects of T6 heat treatment and strontium (Sr) addition or not. For both as-cast and T6 treated composites, the in-situ Al3Ti particulates are in a blocky morphology with average size of 5–6 μm. Sr modified the Si particulates by reducing their size and aspect ratio, without a noticeable influence on the Al3Ti particulates. Energy dispersive X-Ray spectroscopy (EDS) revealed the existence of Si in the blocky Al3Ti particulates in the as-cast composites likely to form an (Al,Si)3Ti phase. Solutionization at 540 °C for 4 h resulted in the enrichment of Si inside the Al3Ti particulates, raising a question about the stability of (Al,Si)3Ti as reported by others. For both as-cast and T6 treated A356 alloy, the yield strengths were enhanced by in-situ Al3Ti particles, but the elongation was adversely affected. In comparison, the tensile strength and ductility of the Al3Ti/A356 were simultaneous improved with the modification of Sr due mainly to the modification of eutectic Si particles. Microstructure-based representative volume element (RVE) simulations revealed the microscale damage evolution of the studied materials and provided a good prediction of their fracture behavior, substantiated by fractography.

Effect of particle size, fraction and carbide banding on deformation and damage behavior of ferrite–cementite steel under tensile/shear loads

Deformation and damage behavior of ferrite–cementite steel was investigated using microstructure-based representative volume element (RVE) methodology. A series of automatically generated 2D RVEs with ferrite matrix and globular cementite particles were generated as representative of various microstructures. The geometrically necessary dislocation (GND) accumulation at the ferrite–cementite interphase was also studied by introducing an intermediate layer around the cementite particles. Damage mechanisms such as ductile fracture in ferrite matrix, brittle fracture in cementite, and decohesion at ferrite–cementite interphase were considered to study the fracture modes. The relationships between interface strength and particle size were estimated according to the modified Argon criterion and showed satisfactory agreement with related works. The influences of microstructural features, such as particle size, particle fraction and carbide banding, on deformation and damage evolution were investigated under tensile and shear loads. Simulation results indicated that small particle size and particle fraction could postpone the initial decohesion under both tensile and shear loads, while carbide banding can lead to early fracture due to local stress concentration, which has potential to cause the loss of ductility and premature failure. These adverse effects become more severe when more cementite particles remain in the band or the gather density of the cementite particles in the band becomes higher.

Effect of Particle Size and Carbide Band on the Flow Behavior of Ferrite-Cementite Steel

A microstructure-based representative volume element (RVE) method is employed for simulating the mechanical properties of the alloy steel 42CrMo4, a typical ferrite–cementite steel with ferrite (α) and spheroid cementite (θ) phases. A series of 2D RVEs with ferrite matrix and globular cementite particles are generated according to various microstructures, among which the geometrically necessary dislocation (GND) accumulation at the α–θ interphase is introduced as a coating layer around the cementite particles. Satisfactory agreement between the simulation and experimental flow curves can be obtained when the ratio of GND layer thickness to particle diameter is 0.25. On this basis, the influences of some modeling parameters such as element type and boundary conditions, as well as some microstructure features like particle size and carbide band, on the mechanical properties are investigated. The results show that small particle size can increase the strength of the material. Carbide band leads to the microstructure inhomogeneity and early finish of uniform elongation, which is potential to cause the loss of ductility and premature failure. These adverse effects become more severe when more cementite particles remain in band or the cementite particles gather denser in carbide band.

Three-Dimensional Crystal Plasticity Finite Element Simulation of Hot Compressive Deformation Behaviors of 7075 Al Alloy

Three-dimensional crystal plasticity finite element (CPFE) method is used to investigate the hot compressive deformation behaviors of 7075 aluminum alloy. Based on the grain morphology and crystallographic texture of 7075 aluminum alloy, the microstructure-based representative volume element (RVE) model was established by the pole figure inversion approach. In order to study the macroscopic stress-strain response and microstructural evolution, the CPFE simulations are performed on the established microstructure-based RVE model. It is found that the simulated stress-strain curves and deformation texture well agree with the measured results of 7075 aluminum alloy. With the increasing deformation degree, the remained initial weak Goss texture component tends to be strong and stable, which may result in the steady flow stress. The grain orientation and grain misorientation have significant effects on the deformation heterogeneity during hot compressive deformation. In the rolling-normal plane, the continuity of strain and misorientation can maintain across the low-angle grain boundaries, while the discontinuity of strain and misorientation is observed at the high-angle grain boundaries. The simulated results demonstrate that the developed CPFE model can well describe the hot compressive deformation behaviors of 7075 aluminum alloy under elevated temperatures.

Advanced Micromechanical Model for Transformation-Induced Plasticity Steels with Application of In-Situ High-Energy X-Ray Diffraction Method

Compared to other advanced high-strength steels, transformation-induced plasticity (TRIP) steels exhibit better ductility at a given strength level and can be used to produce complicated automotive parts. This enhanced formability comes from the transformation of retained austenite to martensite during plastic deformation. In this study, as a first step in predicting optimum processing parameters in TRIP steel productions, a micromechanical finite element model is developed based on the actual microstructure of a TRIP 800 steel. The method uses a microstructure-based representative volume element (RVE) to capture the complex deformation behavior of TRIP steels. The mechanical properties of the constituent phases of the TRIP 800 steel and the fitting parameters describing the martensite transformation kinetics are determined using the synchrotron-based in-situ high-energy X-ray diffraction (HEXRD) experiments performed under a uniaxial tensile deformation. The experimental results suggest that the HEXRD technique provides a powerful tool for characterizing the phase transformation behavior and the microstress developed due to the phase-to-phase interaction of TRIP steels during deformation. The computational results suggest that the response of the RVE well represents the overall macroscopic behavior of the TRIP 800 steel under deformation. The methodology described in this study may be extended for studying the effects of the various processing parameters on the macroscopic behaviors of TRIP steels.