Microstructure-sensitive Model Research Articles

Micro-macro modeling of tensile behavior of a friction stir welded hybrid joint of AlSi10Mg parts produced by powder bed fusion and casting

Additive manufacturing (AM) has gained considerable interest due to its ability to produce lightweight parts with hierarchical microstructures. However, the current constraints on the build chamber size in powder-bed fusion type AM processes limit its industrial application. A hybrid welded joint, consisting of an AM-processed and a conventionally manufactured part, can be employed to produce larger components. Due to the varying processing conditions, these hybrid welded joints contain a wide range of microstructural heterogeneities, which influences the mechanical properties of the joint. Using a numerical model to predict the mechanical behavior of welded joints by considering the microstructural variations is essential for the safe and reliable implementation of hybrid welded joints. This study aims to predict the local tensile behavior of each region of a hybrid friction-stir welded joint of AlSi10Mg produced by laser-based powder bed fusion and casting using a microstructure-sensitive model as well as the global tensile behavior by considering the properties of each region using a joint macroscopic model. The results from this modeling approach agree well with the experimental results. Therefore, this method can predict the mechanical behavior of hybrid welded joints and can establish the structure–property relationship in each weld region.

Review on Fatigue of Additive Manufactured Metallic Alloys: Microstructure, Performance, Enhancement, and Assessment Methods.

Additive manufacturing (AM), which is a process of building objects in a layer-upon-layer fashion from designed models, has received unprecedented attention from research and industry because it offers outstanding merits of flexibility, customization, reduced buy-to-fly ratio, and cost-effectiveness. However, the fatigue performance of safety-critical industrial components fabricated by AM is still far below that obtained from conventional methods. This review discusses the microstructural heterogeneities, randomly dispersed defects, poor surface quality, and complex residual stress generated during the AM process that can negatively impact the fatigue performance of as-printed parts. The difference in microstructural origin of fatigue failure between conventionally manufactured and printed metals is reviewed with particular attention to the effects of the trans-scale microstructures on AM fatigue failure mechanisms. Various methods for mitigating the fatigue issue, including pre-process, inter-process, and post-process treatments, are illustrated. Empirical, semi-empirical, and microstructure-sensitive models are presented to predict fatigue strength and lifetime. Summary and outlooks for future development of the fatigue performance of AM materials are provided.

Defect engineering of fatigue-resistant steels by data-driven models

As inclusions are inevitable from the material-producing processes, an engineering concept regarding multiple features of them is needed for material design. In this study, a unique approach integrating physical-meaningful microstructure-sensitive models with the machine-learning-based data-driven model is proposed to reveal the complex relationship between the fatigue life of materials with intrinsic features of inclusions including size, stiffness, thermal properties, and extrinsic stress amplitudes. This high-fidelity presentation of the relation of these variables enables a detailed and systematic analysis of the effects of inclusions on fatigue life. The data-based phase map provides a designing envelope of inclusion features for fatigue-resistant steels.

Micromechanical modeling of the low-cycle fatigue behavior of additively manufactured AlSi10Mg

Factors such as high degrees of design freedom and flexibility in the production process contribute to a continued interest in the additive manufacturing (AM) process in industrial and academic research. The AM-processed components are widely used in industries; however, their use for production of parts under cyclic loading is still limited due to a significant variance in the cyclic behavior and the effect of the AM-associated defects, like porosity or unmelted powder, on the fatigue resistance. Micromechanical modeling approaches can be used to understand the relationship between the microstructure and the cyclic properties of the AM-processed material and thus expedite its employment in safety-critical applications. By using experiments and microstructure-sensitive models, this study aims to examine and to predict the low-cycle fatigue (LCF) behavior of AlSi10Mg parts produced by laser-based powder bed fusion in both the as-built and the direct-aged condition. Fatigue testing reveals higher stress amplitudes and cyclic hardening capabilities for the as-built condition. Direct-aged specimens demonstrate a higher number of cycles to failure at the highest strain amplitude, albeit at lower stress amplitudes when compared to the as-built condition. Both conditions show significant mean stress relaxation during LCF testing at a load ratio of R = 0. The applied modeling framework consists of a J2-plasticity model for the Si-rich phase and a crystal plasticity model for the Al phase. This hybrid model accurately predicts the LCF behavior under various strain amplitudes and ratios for both the as-built and direct-aged conditions of the AlSi10Mg.

Microstructure-sensitive large-deformation model for thermomechanical processing simulations

Current computational mechanics methods lack coupling between remeshing and microstructure-sensitive models. However, this combination is necessary to consider microstructural evolution during large-deformation, thermomechanical forming operations. A model focused on improving microstructure prediction under forming operations through the advancement of remeshing capabilities integrated with crystal plasticity finite element (CPFE) is developed. To enable coupling between remeshing and a large deformation crystal plasticity model, the current 3D adaptivity (i.e., remeshing) capabilities in LS-DYNA were enhanced to be compatible with a CPFE model. These enhancements include developing remapping techniques that properly account for crystallographic texture evolution during deformation. The techniques used for mapping of microstructure-related variables differ from the smooth interpolation schemes typically used for mapping of other field variables such as stress or displacement. It is demonstrated that combining the nonlinear large deformation capabilities of LS-DYNA, microstructure-sensitive remapping, and a CPFE model yields a simulation framework capable of accurately predicting evolution of location-specific forged part microstructures and shear band formation. Greater microstructural accuracy in large-deformation models can lead to improved strength, life, and manufacturing yield of lightweight forged parts.

Statistical aspects of grain-level strain evolution and reorientation during the heating and elastic-plastic loading of a Ni-base superalloy at elevated temperature

The advancement of microstructure-sensitive models for elevated temperature applications requires experimental data at the relevant length scales and usage environments. Towards this goal, we studied the evolution of grain-level strains in a Ni-based superalloy during heating and subsequent loading at elevated temperature. The specimen was heated using two halogen lamps in a furnace designed explicitly for the special load frame used for the synchrotron-based experiment. High energy X-ray diffraction was used to non-destructively characterize the initial 3D microstructure, confirm the temperature of the specimen, and monitor the evolution of grain-level strains, stresses, and orientations through the elastic-plastic transition. The distributions of grain-level normal strains were observed to broaden with elastic loading, whereas elastic-plastic loading led to development of local intergranular “hotspots”, or activation of plastic slip within select grains, that both broaden and skew the grain-level strain distributions. These grain-level strain distributions were fit to a generalized extreme value (GEV) distribution function. The GEV shape parameter is observed to change significantly at the onset of macroscopic plasticity. At the grain scale, more grain reorientation (plasticity) occurred for grains oriented for lower strength-to-stiffness ratios. During the onset of plastic deformation for LSHR at 660∘C load shedding from lower strength-to-stiffness-oriented grains to higher strength-to-stiffness-oriented grains was observed. Additionally, based on the grain-averaged reorientation axis, it was found that LSHR has a preference for activation of multiple slip systems at 660∘C. We conclude with a discussion on the critical need for statistical analysis of such mesoscale data obtained in situ at elevated temperature for the verification/validation of the next generation of microstructure-sensitive models.

A computational and experimental comparison on the nucleation of fatigue cracks in statistical volume elements

The failure of micron-scale metallic components presents significant variability as a result of their size being comparable to microstructural length scales. Indeed, these components do not represent the bulk of the material but correspond to statistical volume elements (SVEs). This work investigates the role of SVEs on fatigue crack nucleation with a novel comparison between microbeam experiments and microstructure-sensitive simulations. We recreate multiple microstructural computational realizations to estimate fatigue crack nucleation lives and orientations by means of physics-based crystal plasticity models. We demonstrate a unique approach to validate microstructure sensitive models and quantify the fatigue crack stochasticity associated with small volumes.

Modeling of the thermo-mechanical response and texture evolution of WE43 Mg alloy in the dynamic recrystallization regime using a viscoplastic self-consistent formulation

This paper presents a microstructure sensitive model for predicting mechanical response and texture evolution of metals in the dynamic recrystallization regime. A recently proposed viscoplastic self-consistent (VPSC) formulation for the prediction of recrystallization driven by strain energy and intragranular misorientation is extended to hexagonal close-packed (hcp) metals. The model is applied to the dynamic recrystallization of magnesium alloy WE43 at different temperatures and strain rates. Model predictions in terms of stress-strain response and texture evolution are compared to the experimental measurements and acceptable agreement is achieved. According to the model predictions, superplastic behavior of nuclei was found to be the dominant softening mechanism at high temperatures and low strain rates. High concentration of precipitates at the grain boundaries and presence of alloying elements are the likely causes of low boundary mobility, resulting in nucleation dominated dynamic recrystallization. Relatively strong basal compression textures indicate dominant activity of basal slip, which can be achieved only through large difference in slip resistance between soft basal and hard prismatic and pyramidal modes.

A non-local damage model for the fatigue behaviour of metallic polycrystals

ABSTRACT The development of fatigue damage in metallic materials is a complex process influenced by both intrinsic (e.g. texture, defects) and extrinsic (e.g. loading mode, frequency) factors. To better understand this process, some efforts have been made to develop microstructure-sensitive models that consider the impact of microstructural heterogeneities on the formation of fatigue cracks. An important limitation of such models is their inability to describe the transition between the nucleation and growth stages in a consistent thermodynamic framework. To circumvent this limitation, a constitutive model, which is appropriate for the description of both nucleation and early growth, is proposed. For this purpose, non-local damage mechanics is used to construct a set of constitutive relations that explicitly considers the progressive stiffness reduction due to the formation of fatigue cracks. Specifically, a damage variable is attached to each slip system, which allows considering both the anisotropic aspect of fatigue damage and closure effects. The spatial gradients of the damage variables are treated as additional state variables to account for the increase of surface energy associated with the formation of fatigue cracks. For the evolution equations to be compatible with the second law of thermodynamics, a modified form of the entropy production inequality is adopted. For illustration purposes, the non-local damage model is implemented in a spectral solver. Some numerical examples are then presented. These examples allow discussing the ability of the proposed model to describe the impact of loading conditions and pre-existing defects on the fatigue behaviour of metallic polycrystals.

Reduced-order microstructure-sensitive protocols to rank-order the transition fatigue resistance of polycrystalline microstructures

The transition fatigue regime between low cycle fatigue (LCF) and high cycle fatigue (HCF) is often addressed in the design and performance evaluation of load-bearing components used in many structural applications. Transition fatigue is characterized by elevated levels of local inelastic deformation in significant regions of the microstructure as compared to HCF. Typically, crystal plasticity finite element method (CPFEM) simulations are performed to model this phenomenon and to rank-order microstructures by their resistance to crack formation and early growth in the regime of transition fatigue. Unfortunately, these approaches require significant computational resources, inhibiting their use to explore novel materials for transition fatigue resistance. Reduced-order, microstructure-sensitive models are needed to accelerate the search for next-generation, fatigue-resistant materials. In a recent study, Paulson et al. (2018) extended the materials knowledge system (MKS) framework for rank-ordering the HCF resistance of polycrystalline microstructures. The efficacy of this approach lies in the reduced-dimensional representation of microstructures through 2-point spatial correlations and principal component analysis (PCA), in addition to the characterization of the HCF response with a small set of performance measures. In this work, these same protocols are critically evaluated for their applicability to rank-order the transition fatigue resistance of the same class of polycrystalline microstructures subjected to increased strain amplitudes. Success in this endeavor requires the formation of homogenization linkages that account for the significantly higher levels of local inelastic deformation and stress redistribution in transition fatigue as compared to HCF. A set of 12 α-titanium microstructures generated using the open access DREAM.3D software (Groeber and Jackson, 2014) are employed for this evaluation.

A microstructure sensitive model for deformation of Ti-6Al-4V describing Cast-and-Wrought and Additive Manufacturing morphologies

Microstructural variations affect deformation response of materials and it is not presented in most of plastic flow prediction models. This work presents a unified description for the deformation response of Ti-6Al-4V (Ti-64) that successfully captures the differences in strength between microstructures produced by conventional cast & wrought routes (C&W) and those obtained by Additive Manufacturing (AM), under various deformation conditions. In the developed model the grain morphology, grain size, phase volume fractions and phase chemical compositions have been linked to the mechanical properties of the studied Ti-64 alloys to predict the effect of processing routes on deformation behaviour of the materials. The model performance has been tested on seven different microstructures from C&W to AM processing routs. It has been found that altering the microstructure greatly affects the yield strength of the tested materials. Additionally, the strength of Ti-64 was found to be mostly affected by the relative volume fraction of α, β and α′, and their respective morphology. The results showed that the model not only successfully predicts the strength of martensitic structures generated through AM but also those obtained by quenching in conventional C&W processing. The findings from this study also suggest that the model could be extended to other titanium alloys within the α + β family.

A microstructure-sensitive location-specific design tool for predicting the yield and creep behavior of LSHR Ni-base superalloy

A microstructure-sensitive model that predicts the strain-rate sensitive flow behavior as well as creep-strain life of a refractory Ni-base superalloy, Low Solvus High Refractory (LSHR), is presented. The model is based on discrete dislocation simulations that are computationally expensive, but the design tool derived from the simulations is fast acting. The model employs experimental data on microstructure and mechanical behavior, as well as the thermodynamic model PANDAT™, to calibrate, validate and verify the use of the model as a design tool. The mechanical properties predicted include flow stress as a function of temperature and strain-rate, as well as time for 0.1-0.2% creep strain as a function of stress and temperature. The model extends prior work of a strain rate sensitive flow stress model developed for IN100 alloy, by calibrating the model to data on LSHR, and by including dislocation creep as well as grain size dependent diffusional creep behavior and predicting time to reach a design creep life in terms of creep strain. The resultant model was found to capture reported data on LSHR, in both subsolvus and supersolvus heat treated conditions. The calibrated model was validated using additional data on yield and creep of LSHR with two other microstructures. The validation makes the model a promising design tool in the engineering of complex heat treat disks, where location-specific properties are desired.

Bayesian uncertainty quantification and propagation for validation of a microstructure sensitive model for prediction of fatigue crack initiation

A microstructure and deformation mechanism based fatigue crack initiation and life prediction model, which links microstructure variability of a polycrystalline material to the scatter in fatigue life, is validated using an uncertainty quantification and propagation framework. First, global sensitivity analysis (GSA) is used to identify the set of most influential parameters in the fatigue life prediction model. Following GSA, the posterior distributions of all influential parameters are calculated using a Bayesian inference framework, which is built based on a Markov chain Monte Carlo (MCMC) algorithm. The quantified uncertainties thus obtained, are propagated through the model using Monte Carlo sampling technique to make robust predictions of fatigue life. The model is validated by comparing the predictions to experimental fatigue life data.

3D Cellular Automata fracture model for porous graphite microstructures

Nuclear graphite has a complex porous microstructure, which depends on raw materials and manufacturing process; porosity can change with radiolytic oxidation and also in the absence of oxidation with very high neutron fluences. Porosity directly affects the fracture process and the graphite tensile strength. To understand the effects of porosity on component strength and its relation to small specimen data, microstructure sensitive models are needed that can simulate the statistics of strength of porous microstructures, also addressing size and strain gradients effects such as notches. This requires multi-scale models that capture the key microstructural features with sufficient fidelity, and also with sufficient computational economy to simulate component behaviour. To achieve this, an innovative technique to calculate the elastic stress distribution in a 3D porous solid under uniaxial or biaxial tension has been developed that uses Cellular Automata. Synthetic microstructures with arbitrary distributions of pore sizes and shapes are created that simulate realistic microstructures; a fracture algorithm simulates failure initiation and crack growth. The model calculates the tensile strength of a microstructure volume for any arbitrary failure criteria; the critical strain energy release rate is used as an example to demonstrate how porosity affects the fracture process. The presented Cellular Automata (CA) model is at least an order of magnitude more efficient than finite element methods of equivalent discretisation; CA are also scale independent and well suited for parallel computing. This would allow large volumes of representative microstructures to be simulated, with a Monte-Carlo based approach to investigate strength variability.

Probabilistic approaches to fatigue with special emphasis on initiation from inclusions

Existing methods for computing the life of critical components in jet engines, such as discs, are based on determining the design allowable forcing function (e.g. stress, strain). This is done by subtracting six standard deviations from the mean of the property in question. For example, if a stress amplitude-based criterion is used, then the design allowable life is given by:Nadesign=Namean-nσastddevwhere:Nadesign=the safe operating design life at a given nominal stress amplitude, σanom.Namean=the mean life at the nominal stress amplitude.σastddev=the experimentally measured standard deviation in life from the mean at the nominal stress amplitude.n=the number of standard deviations or “knock down” from the mean life that will produce an acceptable safe operating life. In the aerospace industry, this value traditionally was 3 but now “6σ” has become common and even the norm.This means that those factors which affect the dispersion of results in the High Cycle Fatigue (HCF) and Very High Cycle Fatigue (VHCF) regimes must be well understood and controlled in order to allow higher operating stresses or, conversely, longer lives at a given operating stress.The fatigue resistance of metallic materials suffers from a number of uncertainties, in particular the dispersion associated with variance in microstructure and a component size effect (i.e. scale effect). At low stresses and longer lives, such dispersions are particularly troublesome since small variations in microstructure, for example, can produce large dispersions or uncertainties in life. An understanding of the life-limiting tail of the defect distribution is crucial for modelling and predicting minimum safe operating fatigue lives.This paper concentrates on the two problems of microstructural variance and on the effect of component or specimen size in introducing uncertainty. In the first part, an attempt is made to summarize the micromechanisms of crack initiation by the formation of intrusions/extrusions along the slip bands in pure metals. This is an attempt to develop microstructural elements which are necessary to model the dispersion in fatigue life. While these features are, for the most part, illustrated by using recent results published on Ni-based and Fe-Ni based superalloys, the procedures are applicable to a wide range of other classes of alloys.In the second part an attempt is made to account for the dispersion associated with specimen or component size in terms of the interaction between the defect distribution and size when fatigue cracks are initiated from inclusions. The case of a Nickel-based alloy, IN 718, in which inclusions are mainly formed by niobium carbides (NbC) is examined in more detail. It is shown how the fatigue resistance of smooth and notched specimens of this material can be simply modelled, knowing the size and the distribution of NbC particles which act as fatigue initiation sites. The approach is further developed to model the fatigue life of notched specimens. The results obtained with this microstructure-sensitive model are compared with those obtained empirically and used in the design of discs in aircraft engines.

A Microstructure-Sensitive Model for Simulating the Impact Response of a High-Manganese Austenitic Steel

Microstructurally informed macroscopic impact response of a high-manganese austenitic steel was modeled through incorporation of the viscoplastic self-consistent (VPSC) crystal plasticity model into the ansys ls-dyna nonlinear explicit finite-element (FE) frame. Voce hardening flow rule, capable of modeling plastic anisotropy in microstructures, was utilized in the VPSC crystal plasticity model to predict the micromechanical response of the material, which was calibrated based on experimentally measured quasi-static uniaxial tensile deformation response and initially measured textures. Specifically, hiring calibrated Voce parameters in VPSC, a modified material response was predicted employing local velocity gradient tensors obtained from the initial FE analyses as a new boundary condition for loading state. The updated micromechanical response of the material was then integrated into the macroscale material model by calibrating the Johnson–Cook (JC) constitutive relationship and the corresponding damage parameters. Consequently, we demonstrate the role of geometrically necessary multi-axial stress state for proper modeling of the impact response of polycrystalline metals and validate the presented approach by experimentally and numerically analyzing the deformation response of the Hadfield steel (HS) under impact loading.

Simulation of the Interaction of Plastic Deformation in Shear Bands with Deformation-Induced Martensitic Phase Transformation in the VHCF Regime

The experimental observation of the microstructural deformation behavior of a metastable austenitic stainless steel tested at the real VHCF limit indicates that plastic deformation is localized and accumulated in shear bands and martensite formation occurs at grain boundaries and intersecting shear bands. Based on these observations a microstructure-sensitive model is proposed that accounts for the accumulation of plastic deformation in shear bands (allowing irreversible plastic sliding deformation) and considers nucleation and growth of deformation-induced martensite at intersecting shear bands. The model is numerically solved using the two-dimensional (2-D) boundary element method. By using this method, real simulated 2-D microstructures can be reproduced and the microstructural deformation behavior can be investigated within the microstructural morphology. Results show that simulation of shear band evolution is in good agreement with experimental observations and that prediction of sites of deformation-induced martensite formation is possible in many cases. The analysis of simulated shear stresses in most critical slip systems under the influence of plastic deformation due to microstructural changes contributes to a better understanding of the interaction of plastic deformation in shear bands with deformation-induced martensitic phase transformation in the VHCF regime.

Viscoplasticity of heterogeneous metallic materials

Viscoplastic behavior of metallic materials is manifested by collective behavior of lattice defects at multiple length scales. The full gamut of length scales, from atomic to macroscopic, is considered in terms of both concurrent and hierarchical multiscale modeling of plasticity of metals. Particular challenges are identified in the realm between atomistic simulations and the scale of dislocation substructure formation in establishing next generation constitutive models. Bottom–up modeling is useful in applications such as fracture or dislocation mediation by interfaces. This is differentiated from top–down modeling that supports design of a material as a hierarchy of sub-systems. Examples of hierarchical microstructure-sensitive models are presented for both Ni-base superalloys and α–β Ti alloys, with emphasis on cyclic deformation behavior. Future directions to advance both discrete dislocation and crystal plasticity theories are discussed, emphasizing the need for additional focus on dislocation sources and dislocation line curvature in modeling scale dependent behavior. Difficulties with low order approximations of the dislocation density distribution, such as second-order gradient theories, are discussed in terms of predictive capability and transferability among geometric configurations. The multiscale nature of the decomposition of the deformation gradient into elastic and plastic parts is discussed in light of sources of incompatibility at each scale considered, with interpretation offered at different scales of Burgers circuits that highlight dislocation substructures and polycrystals, respectively. Recent atomistic studies of dislocation nucleation at grain boundaries are outlined and some thoughts are offered towards potentially fruitful directions to incorporate this understanding into statistical continuum models that account for the role of grain boundary structure as an element of the evolving incompatibility field.

Microstructure-sensitive notch root analysis for dwell fatigue in Ni-base superalloys

Macroscopic viscoplastic constitutive models for γ– γ′ Ni-base superalloys typically do not contain an explicit dependence on the underlying microstructure. Microstructure-sensitive models are of interest in many applications since microstructure can vary in components, whether intentional or not. In such cases, the use of experiments from one microstructure condition to fit macroscopic models may be too limiting. The principal microstructure attributes that can significantly affect the cyclic stress–strain response of γ– γ′ Ni-base superalloys are the grain size and γ′ precipitate volume fraction and size distributions. An artificial neural network (ANN) is used to correlate the material parameters of a macroscale internal state variable cyclic viscoplasticity model with these microstructure attributes using a combination of limited experiments augmented by polycrystal plasticity calculations performed on other (virtual) microstructures within the range characterized experimentally. The trained model is applied to an example of a component fatigue notch root analysis with dwell periods at peak load to demonstrate the methodology and explore the potential impact of microstructure-sensitive constitutive models on life prediction for notched structures subjected to realistic load histories.

Thermally activated fatigue mechanism and life prediction

The elevated temperature, uniaxial fatigue behavior of the precipitation hardened, Ni-based superalloys Waspaloy 1 Waspaloy is a trademark of United Technologies Corporation. 1 and direct age (DA) alloy 718 are examined. The fatigue life is treated as a thermally activated process. An apparent activation energy and apparent activation volume are derived by considering the external work applied and energy stored in the material due to interactions between dislocations and pinning obstacles. A fatigue life relationship is developed and compared to the experimental fatigue behavior. The experimental behavior is adequately explained by the model. The model physical parameters are related to the thermophysical and microstructural properties of each alloy system examined. The variation in fatigue life is also examined based on the microstructure sensitive model parameters. It is proposed that thermal activation enhances fatigue life by reducing stress concentrations responsible for the generation of substructure defects at a critical stress level below where mechanical damage dominates fatigue life.