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In this study, the crystal plasticity finite element method was established by coupling the crystal plasticity and finite element method (FEM). The effect of rolling deformation and slip system of polycrystalline Al-Mg-Si aluminum alloy was investigated. The results showed that there was a pronounced heterogeneity in the stress and strain distribution of the material during cold rolling. The maximum strain and shear strain occurred at surface of the material. The smaller the grain size, the lower the strain concentration at the grain boundary. Meanwhile, a smaller strain difference existed between the grain interior and near the boundary. The rotation of grains leads to significant differences in deformation and rotation depending on their initial orientations during the rolling process. The slip system of (11-1)<-110> had a large effect on the plastic deformation, (111)<10-1> is second, and the effect of (1-11)<011> slip system on the plastic deformation is the smallest. After deformation, the grain orientation concentration was increased with deformation. Therefore, both the strength and volume fraction of texture were increased with the increase in rolling deformation. The experimental results of EBSD indicated that the large rolling reduction resulted in severe grain twisting, so the texture strength was increased. The simulation results were in close agreement with the experimental results. This study provides a theoretical basis for the rolling process, microstructure, and performance control of aluminum alloys.
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This research investigates the complex temperature distribution and fatigue behavior of single film-cooling holes manufactured by lasers with different pulse widths in a real flow field. The aerodynamic and heat transfer characteristics of film-cooling holes manufactured using lasers with different pulse widths were analyzed through laser drilling experiments, conjugate heat transfer simulations, and crystal plasticity finite element methods. The study investigated the relationship between changes in the geometric accuracy of the film-cooling holes and the corresponding flow and temperature fields during the film-cooling process. Additionally, the effects of temperature and structural variations on the stress around the holes in a flat plate composed of the second-generation nickel-based single-crystal superalloy DD6 in real flow and temperature fields were studied. The coupling effect of the temperature and stress fields around the holes on the fatigue behavior of the film-cooling holes was examined, and the fatigue damage mechanism of film-cooling holes in complex temperature fields was analyzed. It was found that changes in the blowing ratio do not affect the temperature and stress distributions around the holes but only alter the temperature peak. An increase in the temperature peak results in a decrease in the stress peak. Additionally, the fatigue damage of single film-cooling holes is determined by both the structural defects of the holes and the changes in material behavior due to the temperature around the holes, with the structural influence being more significant.
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The Spherical Tokamak for Energy Production (STEP) environment will include magnetic, thermal, mechanical and environmental loads far greater than those seen in the Joint European Torus campaigns of the past decade or currently contemplated for ITER. Greater still are the neutron peak dose rates of 10-6 displacements per atom, per second, which in-vessel materials in STEP are anticipated to be exposed to. Reduced activation and high-fluence resilience therefore dominate the materials strategy to support the STEP Programme. The latter covers the full life cycle from downselected compositions and new microstructural developments to irradiation-informed modelling and end-of-life strategies. This article discusses how the materials downselection is oriented in plant power trade-off space, outlines the development of an advanced ferritic-martensitic structural steel, describes the 'Design by Fundamentals' mesoscale modelling approach and reports some of the waste mitigation routes intended to make STEP operations as sustainable as possible.This article is part of the theme issue 'Delivering Fusion Energy - The Spherical Tokamak for Energy Production (STEP)'.
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In the serviced components of a 7075 aluminum alloy, the propagation of fatigue crack can be retarded because of the overload effect; however, the corresponding retardation mechanisms are complex. To provide further insights into the retardation mechanisms of 7075 aluminum alloys, this study addresses the crack tip damage response of a cracked 7075 aluminum alloy under an overload effect. Based on the dual-scale modeling approach and the damage-coupled crystal plasticity model, the effect of the microstructure of a 7075 aluminum alloy on the damage behavior ahead of the crack tip under an overload was studied. The factors affecting fatigue damage accumulation ahead of the crack tip, such as dislocation density, the variation in the activities of slip systems, and the orientation effect of the nearest neighbor grains, are described. The results show that for the 7075 aluminum alloy, the compressive residual stress induced by the overload effect not only decreases the number of activated slip systems, but also lowers the rate of increase in dislocation density. This causes a decrease in fatigue damage accumulation during deformation. Moreover, the overload effect decreases the slip system activity as well as the resultant plastic slip; however, the decrease in plastic slip varies with the grain orientation, indicating that the overload effect depends on the grain orientation. It can also be found that both the damage strain energy release rate and lattice strain are influenced by the orientation of the nearest neighbor grains, which can eventually affect the overload effect. These findings contribute to understanding the retardation mechanisms from a microscopic perspective and provide guidance on improving the material design of a 7075 aluminum alloy to some extent.
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This paper describes an application of a machine learning approach for parameter optimization. The method is demonstrated for the elasto-viscoplastic model with both isotropic and kinematic hardening. It is shown that the proposed method based on long short-term memory networks allowed a reasonable agreement of stress-strain curves to be obtained for cyclic deformation in a low-cycle fatigue regime. The main advantage of the proposed approach over traditional optimization schemes lies in the possibility of obtaining parameters for a new material without the necessity of conducting any further optimizations. As the power and robustness of the developed method was demonstrated for very challenging problems (cyclic deformation, crystal plasticity, self-consistent model and isotropic and kinematic hardening), it is directly applicable to other experiments and models.
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Exposure of metals to neutron irradiation results in an increase in the yield strength and a significant loss of ductility. Irradiation hardening is also closely related to the fracture toughness temperature shift or the ductile-to-brittle transition temperature (DBTT) shift in alloys with a body-centered cubic (bcc) crystal structure. Ion irradiation is an indispensable tool in the study of the radiation effects of materials for nuclear energy systems. Due to the shallow damage depth in ion-irradiated materials, the nanoindentation test is the most commonly used method for characterizing the changes in mechanical properties after ion irradiation. Issues that affect the analysis of irradiation hardening may arise due to changes in the surface morphology and mechanical properties, as well as the inherent complexities in nanoscale indentation. These issues, including changes in surface roughness, carbon contamination, the pile-up effect, and the indentation size effect, with corresponding measures, were reviewed. Modeling using the crystal plasticity finite element method of the nanoindentation of ion-irradiated materials was also reviewed. The challenges in extending the nanoindentation test to high temperatures and to multiscale simulation were addressed.
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The fatigue behavior of a high-strength bearing steel tempered under three different temperatures was investigated with ultrasonic frequency and conventional frequency loading. Three kinds of specimens with various yield strengths exhibited obvious higher fatigue strengths under ultrasonic frequency loading. Then, a 2D crystal plasticity finite element method was adopted to simulate the local stress distribution under different applied loads and loading frequencies. Simulations showed that the maximum residual local stress was much smaller under ultrasonic frequency loading in contrast to that under conventional frequency at the same applied load. It was also revealed that the maximum local stress increases with the applied load under both loading frequencies. The accumulated plastic strain was adopted as a fatigue indicator parameter to characterize the frequency effect, which was several orders smaller than that obtained under conventional loading frequencies when the applied load was fixed. The increment of accumulated plastic strain and the load stress amplitude exhibited a linear relationship in the double logarithmic coordinate system, and an improved fatigue life prediction model was established.
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In this study, we investigated the micromechanical deformation and damage behavior of commercially extruded and additively manufactured 316L stainless steels (AMed SS316L) by combining experimental examinations and crystal plasticity modeling. The AMed alloy was fabricated using the laser powder bed fusion (LPBF) technique with an orthogonal scanning strategy to control the directionality of the as-fabricated material. Optical microscopy and electron backscatter diffraction measurements revealed distinct grain morphologies and crystallographic textures in the two alloys. Uniaxial tensile test results suggested that the LPBFed alloy exhibited an increased yield strength, reduced elongation, and comparable ultimate tensile strength in comparison to those of the extruded alloy. A microstructure-based crystal plasticity model was developed to simulate the micromechanical deformation behavior of the alloys using representative volume elements based on realistic microstructures. A ductile fracture criterion based on the microscopically dissipated plastic energy on a slip system was adopted to predict the microscopic damage accumulation of the alloys during plastic deformation. The developed model could accurately predict the stress-strain behavior and evolution of the crystallographic textures in both the alloys. We reveal that the increased yield strength in the LPBFed alloy, compared to that in the extruded alloy, is attributed to the higher as-manufactured dislocation density and the cellular subgrain structure, resulting in a reduced elongation. The presence of annealing twins and favorable texture in the extruded alloy contributed to its excellent elongation, along with a higher hardening rate owing to twin-dislocation interactions during plastic deformation. Moreover, the grain morphology and defect state (e.g., dislocations and twins) in the initial state can significantly affect strain localization and damage accumulation in alloys.
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This study introduces an advanced computational method aimed at accelerating continuum-scale processes using crystal plasticity approaches to predict mechanical responses in cobalt-based superalloys. The framework integrates two levels, namely, sub-grain and homogenized, at the meso-scale through crystal plasticity finite element (CPFE) platforms. The model is applicable across a temperature range from room temperature up to 900 °C, accommodating various dislocation mechanisms in the microstructure. The sub-grain level explicitly incorporates precipitates and employs a dislocation density-based constitutive model that is size-dependent. In contrast, the homogenized level utilizes an activation energy-based constitutive model, implicitly representing the γ' phase for efficiency in computations. This level considers the effects of composition and morphology on mechanical properties, demonstrating the potential for cobalt-based superalloys to rival nickel-based superalloys. The study aims to investigate the impacts of elements including tungsten, tantalum, titanium, and chromium through the homogenized constitutive model. The model accounts for the locking mechanism to address the cross-slip of screw dislocations at lower temperatures as well as the glide and climb mechanism to simulate diffusions at higher temperatures. The model's validity is established across diverse compositions and morphologies, as well as various temperatures, through comparison with experimental data. This advanced computational framework not only enables accurate predictions of mechanical responses in cobalt-based superalloys across a wide temperature range, but also provides valuable insights into the design and optimization of these materials for high-temperature applications.
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Using metal additive manufacturing processes can make up for traditional forging technologies when forming complex-shaped parts. At the same time, metal additive manufacturing has a fast forming speed and excellent manufacturing flexibility, so it is widely used in the aerospace industry and other fields. The fatigue strength of metal additive manufacturing is related to the microstructure of the epitaxially grown columnar grains and crystallographic texture. The crystal plasticity finite element method is widely used in the numerical simulation of the microstructure and macro-mechanical response of materials, which provides a strengthening and toughening treatment and can reveal the inner rules of material deformation. This paper briefly introduces common metal additive manufacturing processes. In terms of additive manufacturing fatigue, crystal plasticity simulations are summarized and discussed with regard to several important influencing factors, such as the microstructure, defects, surface quality, and residual stress.
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The mechanical characteristics of polycrystalline metallic materials are influenced significantly by various microstructural parameters, one of which is the grain size. Specifically, the strength and the toughness of polycrystalline metals exhibit enhancement as the grain size is reduced. Applying severe plastic deformations (SPDs) has a noticeable result in obtaining metallic materials with ultrafine-grained (UFG) microstructure. SPD, executed through conventional shaping methods like extrusion, plays a pivotal role in the evolution of the texture, which is closely related to the plastic behavior and ductility. A number of SPD processes have been developed to generate ultrafine-grained materials, each having a different shear deformation mechanism. Among these methods, linear twist extrusion (LTE) presents a non-uniform and non-monotonic form of severe plastic deformation, leading to significant shifts in the microstructure. Prior research demonstrates the capability of the LTE process to yield consistent, weak textures in pre-textured copper. However, limitations in production efficiency and the uneven distribution of grain refinement have curbed the widespread use of LTE in industrial settings. This has facilitated the development of an improved novel method, that surpasses the traditional approach, known as the nonlinear twist extrusion procedure (NLTE). The NLTE method innovatively adjusts the channel design of the mold within the twist section to mitigate strain reversal and the rotational movement of the workpiece, both of which have been identified as shortcomings of twist extrusion. Accurate anticipation of texture changes in SPD processes is essential for mold design and process parameter optimization. The performance of the proposed extrusion technique should still be studied. In this context, here, a single crystal (SC) of copper in billet form, passing through both LTE and NLTE, is analyzed, employing a rate-dependent crystal plasticity finite element (CPFE) framework. CPFE simulations were performed for both LTE and NLTE of SC copper specimens having <100> or <111> directions parallel to the extrusion direction initially. The texture evolution as well as the cross-sectional distribution of the stress and strain is studied in detail, and the performance of both processes is compared.
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Based on the microscopic polycrystalline fatigue crack propagation (MPFCP) model, the MPFCP behaviours of GH4169 alloy under different micro-notch depths and lengths (constraints) were studied from aspects of MPFCP path, MPFCP rate and stress distribution. The influences of the initial crack angle on MPFCP behaviour were further explored. It was observed that the grain boundary, the grain size and the stress state were different during crack propagation under different constraints, resulting in different MPFCP paths. The MPFCP path was straighter under high constraints, and the MPFCP rate was related to the micro-notch size and the loading direction. The crack tip needed more stress accumulation at low constraints than under high constraints to ensure smooth MPFCP behaviour. The influence of the initial crack angle on the MPFCP path was mainly reflected in the grain interior where the initial crack was located. The initial crack angle had a greater influence on the MPFCP rate than on the MPFCP path.
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High silicon alloyed ductile cast iron (Si-DCI) can show unpredictable brittle fracture which currently prevents a widespread application of this material. The brittleness is associated with local superstructure formation due to silicon segregation which influences the deformation mechanisms of the matrix phase. In order to understand the effect of silicon segregation on the mechanical properties of Si-DCI under monotonous loading, three alloys with different cooling conditions were examined and micromechanical simulations were carried out by using the phenomenological crystal plasticity model. Here, the segregation profiles were determined through multi phase field simulations. The influence of segregation on the mechanical properties was only evident from the model but not from the experimental results. The simulated results show that the toughness of Si-DCI decreases with stronger silicon segregation when ductile damage is considered.
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Laser-powder bed fusion additive manufacturing (LPBF-AM) of metals is rapidly becoming one of the most important materials processing pathways for next-generation metallic parts and components in a number of important applications. However, the large parametric space that characterizes laser-based LPBF-AM makes it challenging to understand what are the variables controlling the microstructural and mechanical property outcomes. Sensitivity studies based on direct LPBF-AM processing are costly and lengthy to conduct, and are subjected to the specifications and variability of each printer. Here we develop a fast-throughput numerical approach that simulates the LPBF-AM process using a cellular automaton model of dynamic solidification and grain growth. This is accompanied by a polycrystal plasticity model that captures grain boundary strengthening due to complex grain geometry and furnishes the stress-strain curves of the resulting microstructures. Our approach connects the processing stage with the mechanical testing stage, thus capturing the effect of processing variables such as the laser power, laser spot size, scan speed, and hatch width on the yield strength and tangent moduli of the processed materials. When applied to pure Cu and stainless 316L steel, we find that laser power and scan speed have the strongest influence on grain size in each material, respectively.
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A thermal elastic viscoplastic self-consistent model is utilized to examine the thermal stress induced by the thermal anisotropy of single crystals during heat treatments. This model considers temperature-dependent elastic constants and critical resolved shear stress associated with thermal dilation. Simulation results demonstrate that under cooling, the elastic lattice strain increases significantly when constrained compared to unconstrained cooling. The deformation mechanism observed under cooling with constraint resembles tension along the constrained direction at room temperature. Polycrystals offer more deformation mechanisms to accommodate thermal anisotropy compared to single crystals, resulting in lower applied stress at the constrained boundary. Among the various observed textures, the maximum amplitude of residual lattice strain follows the following order: rolled > extruded > random. Lower thermal anisotropy in the entire polycrystal structure leads to reduced internal stress. For a single crystal within aggregates, the {00.2} plane experiences tensile lattice strain, while the {10.0} and {11.0} planes undergo compressive lattice strain due to the greater contraction of single crystals along the
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Precipitates are the primary source of strength for the Al-Mg-Si alloy. Aluminum alloy in the peak-aged state mainly contains ß" and ß' precipitates. Most of the literature has only considered the strengthening effect of ß". Here, we develop a single-crystal intensity model including both precipitate enhancement effects for the first time. This model was subsequently implemented into a crystal plastic finite-element method to model the uniaxial tensile process of a polycrystalline aggregate model of Al-Mg-Si alloy. The simulation results for uniaxial stretching are in good agreement with the experimental results, confirming that the constitutive parameters used for the single-crystal strength model with two precipitates are based on realistic physical implications. Furthermore, by comparing the uniaxial tensile simulation results of a peak-aged alloy considering the actual precipitated phase composition of the alloy with those assuming that the precipitated phase is only the ß" phase, the predicted tensile strength of the former is around 5.65% lower than that of the latter, suggesting that the two kinds of precipitation should be separately considered when simulating the mechanical response of Al-Mg-Si alloy. It is highly expected that the present simulation strategy is not limited to Al-Mg-Si alloys, and it can be equally applied to the other age-enhanced alloys.
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In this study, the evolutions of Cube and {115}<161> orientations of a cold-rolled ultra-thin non-oriented silicon steel were investigated using a combination of experimental investigation and the crystal plasticity finite element method (CPFEM). The results show that Cube orientations remain relatively stable when their initial deviation angles from the ideal Cube orientation are less than 12°, even after a 60% cold rolling reduction. However, larger deviations occur due to higher strain near grain boundaries. Furthermore, the {115}<161> orientations, with an initial deviation of ~18° from the ideal Cube orientation, become separated into different orientation regions during cold rolling. Some regions gradually approach the ideal Cube orientation as cold rolling progresses and reach ~12.5° deviation from the ideal Cube at a 40% reduction. This study demonstrates good agreement between simulation and experimental results, highlights the micro-deformation mechanisms during rolling, and offers insights for optimizing the ultra-thin strip rolling process.
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In the rapidly evolving field of additive manufacturing (AM), the predictability of part properties is still challenging due to the inherent multiphysics complexity of the technology. This results in time-consuming and costly experimental guess-and-check approaches for manufacturing each individual design. Through synthesising advancements in the field, this review argues that numerical modelling is instrumental in mitigating these challenges by working in tandem with experimental studies. Unique hierarchical microstructures induced by extreme AM process conditions- including melt pool patterns, grains, cellular-dendritic substructures, and precipitates-affect the final part properties. Therefore, the development of microstructure-informed mechanical models becomes vital. Our review of numerical studies explores various modelling approaches that consider the microstructural features explicitly and offers insights into multiscale stress-strain analysis across diverse materials fabricated by powder bed fusion AM. The literature indicates a growing consensus on the key role of multiscale integrated process-structure-property-performance (PSPP) modelling in capturing the complexity of AM-produced materials. Current models, though increasingly sophisticated, still tend to relate only two elements of the PSPP chain while often focusing on a single scale. This emphasises the need for integrated PSPP approaches validated by a solid experimental base. The PSPP paradigm for AM, while promising as a concept, is still in its infantry, confronting multifaceted challenges that require in-depth, multidisciplinary expertise. These challenges range from accounting for multiphysics phenomena (e.g., advanced laser-material interaction) and their interplay (thermo-mechanical and microstructural evolution for simulating Type II residual stresses), accurately defined assumptions (e.g., flat molten surface during AM or purely epitaxial solidification), and correctly estimated boundary conditions for each element of the PSPP chain up to the need to balance the model's complexity and detalisation in terms of both multiphysics and discretisation with efficient multitrack and multilayer simulations. Efforts in bridging these gaps would not only improve predictability but also expedite the development and certification of new AM materials.
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In this study an improved version of the Discrete RVE Automation and Generation Framework, also called DRAGen, is presented. The Framework incorporates a generator for Representative Volume Elements (RVEs). Several complex microstructure features, extracted from real microstructures, have been added to the generator, to enable it to generate RVEs with realistic microstructures. DRAGen is now capable of reading trained neural networks as well as .csv-files as input data for the microstructure generation. Furthermore, features such as pores and inclusions, martensite bands, hierarchical substructures, and crystallographic textures can be reconstructed in the RVEs. Besides the features, the functionality for different solvers was introduced. Therefore, the code was extended by modules for the generation of Finite Element (FE) and spectral solver input files. DRAGen now has the ability to create models for three powerful multiphysics frameworks used in the community: DAMASK, Abaqus and MOOSE. The evaluation of the features, as well as the simulations performed on sample models, show that the new version of DRAGen is a very powerful tool with flexible applicability for scientists in the ICME community. Also, due to the modular architecture of the project, the code can easily be expanded with features of interest. Therefore, it delivers a variety of functions and possible outputs, which offers researchers a broad spectrum of microstructures that can be used in microstructure studies or microstructure design developments.
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The deformation-induced surface roughening of an Al-Mg alloy is analyzed using a combination of experiments and modeling. A mesoscale oligocrystal of AA5052-O, obtained by recrystallization annealing and subsequent thickness reduction by machining, that contains approx. 40 grains is subjected to uniaxial tension. The specimen contains one layer of grains through the thickness. A laser confocal microscope is used to measure the surface topography of the deformed specimen. A finite element model with realistic (non-columnar) shapes of the grains based on a pair of Electron Back-Scatter Diffraction (EBSD) scans of a given specimen is constructed using a custom-developed shape interpolation procedure. A Crystal Plasticity Finite Element (CPFE) framework is then applied to the voxel model of the tension test of the oligocrystal. The unknown material parameters are determined inversely using an efficient, custom-built optimizer. Predictions of the deformed shape of the specimen, surface topography, evolution of the average roughness with straining and texture evolution are compared to experiments. The model reproduces the averaged features of the problem, while missing some local details. As an additional verification of the CPFE model, the statistics of surface roughening are analyzed by simulating uniaxial tension of an AA5052-O polycrystal and comparing it to experiments. The averaged predictions are found to be in good agreement with the experimentally observed trends. Finally, using the same polycrystalline specimen, texture-morphology relations are discovered, using a symbolic Monte Carlo approach. Simple relations between the Schmid factor and roughness can be inferred purely from the experiments. Novelties of this work include: realistic 3D shapes of the grains; efficient and accurate identification of material parameters instead of manual tuning; a fully analytical Jacobian for the crystal plasticity model with quadratic convergence; novel texture-morphology relations for polycrystal.