Micromechanical Simulations Research Articles

Synergistic effects of microstructural inhomogeneity and phase-transformation-induced plasticity for ductility improvements in metallic glass composites

Recent experiments show some successes in ductility improvements in bulk metallic glass (BMG) composite with metastable crystalline second-phase particles that are capable of phase transformation induced plasticity (TRIP), e.g., austenite to martensite upon straining. The underlying mechanisms are yet to be quantified for a few reasons. First, ductility enhanced by TRIP mechanism in crystalline materials is often credited to the delayed necking due to the enhanced work hardening rate, while BMG composites with such metastable second phases never fail by necking. Second, load partitioning amongst austenite and martensite phases and BMG matrix can be probed by in situ diffraction techniques, but its consequence on preventing or delaying the transition from shear bands to failure has not been revealed. In this work, synergistic effects of microstructural inhomogeneity and TRIP mechanism are quantitatively investigated from micromechanical finite element simulations, using the free-volume theory that is capable of explicitly modeling individual shear bands in the BMG matrix and a strain-driven TRIP model that can be calibrated from available neutron diffraction measurements. For metastable second phases to improve the BMG composite ductility, our parametric studies have found that the strength of the BMG matrix has to be in between the strengths of soft austenite and hard martensite phases, thus leading to the effectively confinement of shear bands near the second phase, the reduction of maximum shear band strain, and therefore the improvement of tensile ductility. Our micromechanical simulations also allow us to identify the roles played by geometric factors such percolation and core-shell or inverse core-shell distributions.

An Experimentally Based Micromechanical Framework Exploring Effects of Void Shape on Macromechanical Properties.

A micromechanical simulation approach in a Multi-Scale Modeling (MSM) framework with the ability to consider manufacturing defects is proposed. The study includes a case study where the framework is implemented exploring a cross-ply laminate. The proposed framework highlights the importance of correct input regarding micromechanical geometry and void characteristics. A Representative Volume Element (RVE) model is developed utilizing true micromechanical geometry extracted from micrographs. Voids, based on statistical experimental data, are implemented in the RVE model, and the effects on the fiber distribution and effective macromechanical properties are evaluated. The RVE algorithm is robust and maintains a good surrounding fiber distribution around the implemented void. The local void fraction, void size, and void shape affect the effective micromechanical properties, and it is important to consider the phenomena of the effective mechanical properties with regard to the overall void fraction of an RVE and the actual laminate. The proposed framework has a good prediction of the macromechanical properties and shows great potential to be used in an industrial implementation. For an industrial implementation, weak spots and critical areas for a laminate on a macro-level are found through combining local RVEs.

Tailoring fiber arrangement in subsurface damage layer of unidirectional CFRP composites by reverse multi-pass cutting

While the directionality and integrity of microscopic fiber arrangement play an important role in governing the mechanical properties and deformation behavior of unidirectional carbon fiber reinforced polymer (UD-CFRP) composites, minimizing or eliminating the deformation-induced evolution of fiber arrangement is crucial for maintaining the high performance of the advanced composite materials. In the present work, we elucidate the depth-sensing deformation mechanisms of UD-CFRP under different cutting strategies of conventional single-pass and multi-pass by experiments and corresponding micromechanical finite element simulations. Experimental and simulation results reveal diversiform maps of fiber arrangement evolution in subsurface damage layer under different cutting strategies, as well as their correlations with machined surface quality in terms of surface finish, residual stress and mechanical properties. Subsequently, a novel cutting strategy of reverse multi-pass is proposed to tailor the directionality and integrity of microscopic fiber arrangement in subsurface damage layer, which is accompanied with reduced subsurface damage layer, lowered surface roughness and enhanced hardness and elastic modulus, as compared to the cutting strategy of conventional multi-pass. Current findings provide a theoretical basis for the understanding of formation mechanisms of machined surface of CFRP composites, as well as the rational selection of cutting strategies for improving the machinability of CFRP composites.

Identification of texture characteristics for improved creep behavior of a L-PBF fabricated IN738 alloy through micromechanical simulations

Additive manufacturing (AM) of nickel-based superalloys, due to high temperature gradients during the building process, typically promotes epitaxial growth of columnar grains with strong crystallographic texture in form of a 〈001〉 fibre or a cube texture. Understanding the mutual dependency between AM process parameters, the resulting microstructure and the effective mechanical properties of the material is of great importance to accelerate the development of the manufacturing process. In this work, a multi-scale micromechanical model is employed to gain deeper insight into the influence of various texture characteristics on the creep behavior of an IN738 superalloy. The creep response is characterized using a phenomenological crystal plasticity creep model that considers the characteristic γ–γ′ microstructure and all active deformation mechanisms. The results reveal that the creep strength increases with decreasing texture intensities and reaches its maximum when the 〈001〉 fibre and cube textures are misaligned to the specimen building direction by 45°. The simulations also predict that the uncommon 〈111〉 and 〈110〉 fibres offer significantly higher creep resistance than the typically observed 〈001〉 fibre, which provides a further incentive to investigate AM processing conditions that can produce these unique textures in the material. As the intensities and the alignment of 〈001〉 fibre and cube textures can be attributed to the laser energy density and the scan strategy employed and as the formation of distinct fibre textures depends on the geometry of the resulting melt pool, the laser powder bed fusion process parameters can be optimized to obtain microstructures with features that improve the creep properties.

Mechanical properties of heterogeneous, porous LiFePO4 cathodes obtained using statistical nanoindentation and micromechanical simulations

Among cathode materials for Li-ion batteries, LiFePO4 (LFP) is one of the most relevant for commercial batteries in electric vehicle applications. In this work, the Young’s modulus and the indentation hardness of a commercial composite LiFePO4 cathode are measured using statistical nanoindentation. The influence of the surface roughness, a substrate effect, as well as particle size effect and densification on the measurement are discussed in detail. A focus lies on the analysis of the mechanical properties of the porous secondary LiFePO4 particles and the porosity dependence of the Young’s modulus. The measurements are validated via finite element simulations on reconstructed real microstructures. It was found that the mechanical properties of the secondary LiFePO4 particles are significantly lower than those of bulk LiFePO4 and a porosity dependence of the Young’s modulus was established. The experimental Young’s modulus of the porous LiFePO4 is 47.3GPa and the indentation hardness is 2.5GPa. For porous ceramics such as these, this results in an estimation of the yield strength of 1.5GPa.

Multiscale mechanical consequences of ocean acidification for cold-water corals

Ocean acidification is a threat to deep-sea corals and could lead to dramatic and rapid loss of the reef framework habitat they build. Weakening of structurally critical parts of the coral reef framework can lead to physical habitat collapse on an ecosystem scale, reducing the potential for biodiversity support. The mechanism underpinning crumbling and collapse of corals can be described via a combination of laboratory-scale experiments and mathematical and computational models. We synthesise data from electron back-scatter diffraction, micro-computed tomography, and micromechanical experiments, supplemented by molecular dynamics and continuum micromechanics simulations to predict failure of coral structures under increasing porosity and dissolution. Results reveal remarkable mechanical properties of the building material of cold-water coral skeletons of 462 MPa compressive strength and 45–67 GPa stiffness. This is 10 times stronger than concrete, twice as strong as ultrahigh performance fibre reinforced concrete, or nacre. Contrary to what would be expected, CWCs retain the strength of their skeletal building material despite a loss of its stiffness even when synthesised under future oceanic conditions. As this is on the material length-scale, it is independent of increasing porosity from exposure to corrosive water or bioerosion. Our models then illustrate how small increases in porosity lead to significantly increased risk of crumbling coral habitat. This new understanding, combined with projections of how seawater chemistry will change over the coming decades, will help support future conservation and management efforts of these vulnerable marine ecosystems by identifying which ecosystems are at risk and when they will be at risk, allowing assessment of the impact upon associated biodiversity.

The relationship between mesoscale deformation-induced surface roughness, in-plane plastic strain and texture sharpness in an aluminum alloy

Experimental and numerical studies are performed to reveal an interrelation between mesoscale deformation-induced surface roughening and in-plane plastic strain in an aluminum alloy. Experimentally, roughness evolution in selected subsections of a uniaxially loaded specimen is examined using a stop-and-study technique. The experimental analysis is complemented by the micromechanical simulations for deformation-induced surface roughening in model polycrystals, with special attention being given to the texture effect on roughness characteristics. The experimental and numerical roughness patterns are analyzed in terms of a relative roughness parameter calculated as a ratio of the rough profile length to the profile evaluation length. This parameter is found to correlate exponentially with in-plane plastic strain with the coefficient of determination 0.99, which implies a strong interrelation between the two quantities. The results prove the assumption that in-plane plastic strains accumulated in a loaded material can be evaluated from the estimations of mesoscale surface roughness.

A novel approach to consider triaxial tensile stresses within the framework of a failure criterion

AbstractFor use in micromechanical simulations of continuous fiber reinforced polymers, a more general form of the paraboloid failure criterion by Stassi‐D'Alia for matrix failure was developed with explicit consideration of the hydrostatic tension strength. Regarding polymers, limits for hydrostatic tensile strength based on isotropic linear elasticity could be derived. The comparison of the newly developed extended paraboloid criterion with experimental data for yielding as well as for material separation (fracture) shows good agreement.

An examination of local strain fields evolution in ductile cast iron through micromechanical simulations based on 3D imaging

Microscopic digital volume correlation (DVC) and finite element precoalescence strain evaluations are compared for two nodular cast iron specimens. Displacement fields from \textit{in-situ} 3D synchrotron laminography images are obtained by DVC. Subsequently the microstructure is explicitely meshed from the images considering nodules as voids. Boundary conditions are applied from the DVC measurement. Image segmentation-related uncertainties are taken into account and observed to be negligible with respect to the differences between strain levels. Macroscopic as well as local strain levels in coalescing ligaments between voids nucleated at large graphite nodules are compared. Macroscopic strain levels are consistently predicted. A very good agreement is observed for one of the specimens, while the strain levels for the second specimen presents some discrepancies. Limitations of the modeling and numerical framework are discussed in light of these differences. A discussion of the use of strain as coalescence indicator is initiated.

Many-Scale Investigations of the Deformation Behavior of Polycrystalline Composites: I-Machine Learning Applied for Image Segmentation.

Our work investigates the polycrystalline composite deformation behavior through multiscale simulations with experimental data at hand. Since deformation mechanisms on the micro-level link the ones on the macro-level and the nanoscale, it is preferable to perform micromechanical finite element simulations based on real microstructures. The image segmentation is a necessary step for the meshing. Our 2D EBSD images contain at least a few hundred grains. Machine learning (ML) was adopted to automatically identify subregions, i.e., individual grains, to improve local feature extraction efficiency and accuracy. Denoising in preprocessing and postprocessing before and after ML, respectively, is beneficial in high quality feature identification. The ML algorithms used were self-developed with the usage of inherent code packages (Python). The performances of the three supervised ML models—decision tree, random forest, and support vector machine—are compared herein; the latter two achieved accuracies of up to 99.8%. Calculations took about 0.5 h from the original input dataset (EBSD image) to the final output (segmented image) running on a personal computer (CPU: 3.6 GHz). For a realizable manual pixel sortation, the original image was firstly scaled from the initial resolution 1080 pixels down to 300. After ML, some manual work was necessary due to the remaining noises to achieve the final image status ready for meshing. The ML process, including this manual work time, improved efficiency by a factor of about 24 compared to a purely manual process. Simultaneously, ML minimized the geometrical deviation between the identified and original features, since it used the original resolution. For serial work, the time efficiency would be enhanced multiplicatively.

Optimized Load-Independent Hyperelastic Microcharacterization of Human Brain White Matter

Abstract A micromechanical methodology combined with genetic algorithm (GA) as a global optimization method is used to find the material properties of axons and extracellular matrix (ECM) in corpus callosum which is a part of human brain white matter. Studies have shown that axons are highly oriented in the ECM which enables us to approximate brain white matter as a unidirectional fibrous composite model. Using the one-term Ogden hyperelastic constitutive equations for the constituents and knowing the mechanical response of corpus callosum, GA optimization procedure is used in conjunction with finite element (FE) micromechanical analysis to find optimal material parameters for axon and ECM in three uniaxial loading scenarios of tension, compression, and simple shear. Moreover, by simultaneous fitting to the three loading modes' responses and applying Nelder–Mead simplex optimization method, best-fit parameters are found. The best-fit parameters can be used to approximate the behavior of axons and ECM in different uniaxial loading conditions with the minimum error and hence, can be interpreted as load-independent parameters. Micromechanical simulations by best-fit parameters show maximum stress increase of 2% and 29% for tension and shear and less than 1% reduction for compression mode compared to the case where optimal parameters are used. The findings and the methodology of this study can be employed for constitutive modeling of axonal fibers and its implementation in human head FE model where load-independent parameters are needed for simulating different loading scenarios.

Effect of defects on the constant-amplitude fatigue behavior of as-built Ti-6Al-4V alloy produced by laser powder bed fusion process: Assessing performance with metallographic analysis and micromechanical simulations

The influence of various process parameters on the mechanical behavior (including tensile strength, strain-to-failure and constant-amplitude fatigue performance) of as-built Ti-6Al-4V alloy, produced via laser powder bed fusion (L-PBF) process, is demonstrated using complementary information obtained from mechanical (uniaxial tensile and fatigue) tests, fractography analysis, metallographic analysis and micromechanical simulations. Four different build conditions were considered such that the laser power and velocity were varied for each build while holding the build orientation, hatch spacing, layer thickness, laser spot size and hatch rotation constant. The volumetric energy densities (E) of the four unique builds were: 33 J/mm3, 66 J/mm3, 130 J/mm3 and 180 J/mm3, respectively. Two coupons per build were subjected to constant-amplitude fatigue loading while one coupon per build was subject to uniaxial tensile loading at room temperature. Coupons belonging to Builds 1 and 2 (corresponding to E values of 33 J/mm3 and 66 J/mm3, respectively) had considerably longer fatigue lives compared to coupons from Builds 3 and 4 (corresponding to E values of 130 J/mm3 and 180 J/mm3, respectively).To reconcile the relative lifing capability of the four builds, fractography, two-dimensional (2D) pore analysis, and multiscale finite-element simulation campaigns are detailed. Collectively, these exercises underscore the centrality of pore clustering on the fatigue performance of the builds. Moreover, they highlight the role that microstructural character (viz. grain orientation with respect to loading) plays on the accumulation of plastic strain in the vicinity of pores. Specifically, it is demonstrated that a pore embedded in a grain favorably oriented for slip accumulates a significant amount of plastic strain compared to one embedded in a grain not favorably oriented for slip. Comparing the relative performance and defect character of the four builds, this study suggests that both pore spacing and relative grain hardness act in concert with other fatigue-limiting characteristics including pore size, shape and distance to free surface.

Homogenisation of micromechanical modelling results for the evaluation of macroscopic material properties of brittle ceramics

This paper presents an approach to evaluate the macroscopic properties of ceramic materials based on the homogenisation of the results of micromechanical simulations performed on Representative Volume Elements (RVEs) of polycrystalline microstructures. The RVEs are defined using a bespoke algorithm to generate numerical model geometries statistically representative of the microstructure of polycrystalline ceramics. The material properties of single crystals and grain boundaries, obtained from direct experimental measurements at the relevant scales, are used for the generation of RVEs, which are then subjected to unit load cases. The results of the numerical simulations, performed using the explicit Finite Element Method (FEM), are used to calculate the macroscopic material parameters governing elastic deformation, and brittle failure due to initiation and propagation of cracks at the grain scale. The automated approach adopted to generate and analyse the response of RVEs under a specified set of loading conditions permits a statistically relevant number of simulations to be performed on different combinations of microstructural morphologies, distributions of crystallographic orientations, and defects, thus demonstrating a homogenisation and upscaling methodology that captures several important aspects of the stochastic variability typically exhibited by ceramic materials. The numerical simulations of elastic deformation and brittle failure of polycrystalline alumina (Al2O3) are compared against both experimental measurements and analytical calculations, showing good agreement for both elastic deformation - expressed in terms of homogenised elastic moduli - and failure strength - observed both as changes in the crack pattern at the microscale and when measured as the value of the stress at the onset of failure.

Local Approach of Ductile Rupture Under Cyclic Loading Conditions

Abstract Experiments have shown that ductile failure occurs sooner under cyclic loading conditions than under monotone ones. This reduction of ductility probably arises from an effect called “ratcheting of the porosity” that consists of a continued increase of the mean porosity during each cycle with the number of cycles. Improved micromechanical simulations confirmed this interpretation. The same work also contained a proof that Gurson's classical model for porous ductile materials does not predict any ratcheting of the porosity. In a recent work (Morin et al., 2017, “A Gurson-Type Layer Model for Ductile Porous Solids With Isotropic and Kinematic Hardening,” Int. J. Solids Struct., 118–119, pp. 167–178), the authors proposed a Gurson-type “layer model” better fit than Gurson's original one for the description of the ductile behavior under cyclic loading conditions, using the theory of sequential limit analysis. A very good agreement was obtained between the model predictions and the results of the micromechanical simulations for a rigid-hardenable material. However, the ratcheting of the porosity is a consequence of both hardening and elasticity, and sequential limit analysis (Yang, 1993, “Large Deformation of Structures by Sequential Limit Analysis,” Int. J. Solids Struct., 30(7), pp. 1001–1013; Leu, 2007, “Analytical and Numerical Investigation of Strain-Hardening Viscoplastic Thick-Walled Cylinders Under Internal Pressure by Using Sequential Limit Analysis,” Comput. Methods Appl. Mech. Eng., 196(25–28), pp. 2713–2722; Leblond et al., 2018, “Classical and Sequential Limit Analysis Revisited,” C. R. Méc., 346(4), pp. 336–349.) is strictly applicable in the absence of elasticity. In this work, a proposal is made to take into account elasticity in the layer model through the definition of a new objective stress rate leading to an accurate expression of the porosity rate accounting for both elasticity and plasticity. This proposal is assessed through comparison of its predictions with the results of some new micromechanical simulations performed for matrices exhibiting both elasticity and all types of hardening. Finally, a comparison of the predictions regarding finite element modeling of pipes loaded cyclically is proposed.

Developing parametrically upscaled constitutive and crack nucleation models for the [formula omitted] Ti64 alloy

This paper develops Parametrically Upscaled Constitutive Model (PUCM) and the Parametrically Upscaled Crack Nucleation Model (PUCNM) for a commercially used α/β-phase Ti64 alloy. These thermodynamically consistent macroscopic constitutive models bridge spatial scales through the explicit representation of Representative Aggregated Microstructural Parameters (RAMPs). The PUCNM is an indicator of the probability of crack nucleation in the local underlying microstructure. A symbolic regression-based machine learning method operates on data-sets generated by image-based micromechanical crystal plasticity simulations to derive constitutive coefficients as functions of the RAMPs. The PUCM/PUCNMs development (both calibration and validation) uses data from microstructural characterization as well as mechanical tests, including constant strain-rate, creep, and strain-controlled dwell tests for the Ti64 alloy. Parametric study is conducted with the experimentally-validated PUCM and PUCNM to investigate the effect of RAMPs on dwell fatigue crack nucleation life. Finally, the combined PUCM/PUCNM tool is used for examining the impact of microstructure on fatigue crack nucleation in an engine blade model under simulated operating conditions. The results from these examples clearly exhibit the promise of the PUCM/PUCNM models in predicting fatigue crack nucleation in the microstructure of real structural applications, as well as demonstrating the microstructural influence.

Prediction of Failure Envelope of Calcified Aneurysmatic Tissue

The abdominal aortic aneurysm (AAA) may have a varying degree of calcification where calcium particles are found in different geometrical configurations. The impact of calcification on the failure of aneurysms is not very clear as literature shows contradictory results. This work is dedicated to investigating the impact of calcification on the failure strength of an aneurysmatic wall using micromechanical finite element simulations. A Representative Volume Elements (RVE) consisting of circular and elliptical particles are generated with different volume fractions, which is further extruded in the thickness direction. A two-fibre model is used for modeling anisotropic tissues. Calcium particles are assumed to be elastic. An anisotropic phase-field model is employed to model the failure in the tissue. A unique set of representative material parameters as well as phase-field parameters, like critical fracture energies for isotropic and anisotropic parts, are determined by fitting the model to experimental data, available in the literature. Finite element simulations are being performed on RVEs to generate a failure envelope of the calcified tissues under bi-axial loading conditions. This study will help in better understanding and better prediction of failure in aneurysms.

Micromechanical simulation of silicon rubber reinforced with MMT nanoclay

This work investigates Silicon Rubber (SR) reinforced with Montmorillonite (MMT) nanoclay for its mechanical properties. A micromechanical numerical model, based on a representative volume element (RVE) method for silicon rubber/MMT is developed using a commercial finite element software package. The model uses elastoplastic material model with ductile damage for silicon rubber and a linear elastic model for MMT nano clay. Silicon rubber/MMT nanocomposite is modeled with different weight percentages of MMT varied from 0.2 to 2 %. The nanocomposite show improvement in the properties with an increase in MMT percentage. The RVE model results are compared with the analytical models and are found to be in good agreement.

Efficient non-iterative modelling of pressure-dependent plasticity using paraboloidal yield criterion

A full understanding of the non-linear mechanical response of the polymer is essential for fibre-reinforced polymer composite design because an explicit definition of constitutive material models for the constituents (fibres, matrix, and interface) are prerequisite in micromechanical simulations. Unlike ductile metals, the material behaviour of polymer matrix is characterised by plasticity theories influenced by a combination of distortional and spherical energy dissipation. In this respect, an elastoplastic thermodynamic continuum model derivation is proposed using the paraboloidal yield criterion under isothermal conditions. A non-iterative scheme is developed for the numerical computation of the plastic strain increment multiplier. Both associated and non-associated flow rules are investigated following classical plasticity loading–unloading conditions. It thereby, evades conventional computationally demanding iterative process by replacing it with an exact determination of plastic strain increment. This novel approach highly improves the computational efficiency algorithmically. The real-sized numerical models are investigated and the comparison between simulated and experimental results shows the reliability and unprecedented accuracy of the proposed elastoplastic mathematical model.

Effects of the grain shape and crystallographic texture on the grain-scale mechanical behavior of additively manufactured aluminum alloys

The grain shape and texture effects in aluminum alloys manufactured by selective laser melting are studied numerically in terms of micromechanical simulations. The method of step-by-step packing is adopted to generate the three-dimensional grain morphology typical for these materials. Crystal plasticity finite element simulations of uniaxial tension are performed for two models with random and cube-textured columnar grains inherent in selective laser melting. Comparative analysis of the computational results shows a substantial difference between the microscale stress and strain fields. The presence of cube-textured columnar grains provides more homogeneous stress-strain distributions inside the melt pools and unloads the adjacent regions of fine equiaxed grains, thus reducing high stress concentration in them.

The effects of plasticity mechanisms on micromechanics of composites with fiber waviness defects under compression

Micromechanics simulations of fiber-reinforced polymer-matrix composites with waviness defects are conducted to investigate the effect of constitutive model selection on the nucleation, evolution, and interaction of damage modes under in-plane compression. A 2D finite element model with fibers, matrix and fiber-matrix interfaces is used, considering damage modes at the constituent level (i.e., fiber-matrix interface damage, matrix plasticity, void nucleation and growth). Results show that the pressure-dependency of the polymer matrix is key for accurate predictions of strain localization in the fiber kinking mode and fiber-matrix interface crack behavior and extent at regions of waviness imperfections.