Internal void closure during the forging of large cast ingots using a simulation approach

Large cast ingots often contain defects or undesirable microstructural features, such as voids and zones related to casting. Some of these features can remain after hot open die forging, which is an important process for converting large cast ingots into wrought components. During the initial cogging and deformation steps prior to the detailed open-die-forging operations, any internal voids should be eliminated. The present work focuses on the closure of internal voids during open die forging so as to produce a sound component. Hot compression tests were conducted to obtain the flow strength of the cast microstructure at different temperatures and strain rates. The measured flow strength data together with other appropriate material properties were used to simulate the forging steps for a large cast ingot. The numerical simulations for the forging deformation and for the internal void behavior were performed using DEFORM-3D™. Actual defects were measured in commercial ingots with an X-ray scanner. The simulation results for the void deformation behavior are compared with voids measured before and after forging. Through the comparison of experimental results and numerical simulation, a criterion for void closure is proposed. The criterion is that a local effective strain value of 0.6 or greater must be achieved for void closure during forging. Such a criterion can be used in conjunction with simulations to insure that a sound component is produced during the hot open die forging of large cast ingots.     

Possibilities and limitations of geometric simplifications for calculations of residual stresses and distortions

The prediction and minimization of welding distortions and the evaluation of the residual stress state after welding using numerical methods are increasingly gaining importance. These numerical models are used to optimize welding processes with respect to distortion. However, the computational time required for a transient 3-D calculation, particularly for large components, often hinders commercial usage of these approaches. Therefore, simulations have to simplify individual aspects. Due to the fact that model verification often failed according to abundant experimental research efforts, it cannot be proven whether the deformations and residual stresses calculated by those simplified models are trustworthy. With the help of the validated simulations of the IIW round robin tests and of variational calculus, this work shows the influences of sheet geometry and model simplifications, e.g. 2-D modelling, on the calculation of distortions and residual stresses. The round robin tests were performed using steel sheets made of an austenitic steel (316 LNSPH) which was bead-on-plate welded by TIG welding. The calculations for a varied sheet geometry show for the investigated process and for large components that a reduction to minimal sheet geometry is necessary and sufficient to determine the longitudinal stresses and the distortions. The transversal stresses are in general extremely sensitive to the sheet geometry.     

Image processing and analysis of 3-D microscopy data

While there are many microstructural parameters that can be measured from a planar two-dimensional (2-D) section through a material, there are many measurements that require knowledge of the full three-dimensional (3-D) microstructure, such as true size and shape of individual objects, connectivity and interfacial curvatures. Serial sectioning and reconstruction can reveal the 3-D microstructure but are often considered to be time consuming and labor intensive. However, what is not often realized is that the majority of the time invested in serial sectioning is spent in the image segmentation, wherein individual objects are digitally identified. This article reviews the current state of image segmentation and novel analysis within 3-D materials science. We will also briefly discuss the future possibilities for more efficient segmentation of digital images for a broader range of materials.     

Progress Toward an Integration of Process–Structure–Property–Performance Models for “Three-Dimensional (3-D) Printing” of Titanium Alloys

Electron beam direct manufacturing, synonymously known as electron beam additive manufacturing, along with other additive “3-D printing” manufacturing processes, are receiving widespread attention as a means of producing net-shape (or near-net-shape) components, owing to potential manufacturing benefits. Yet, materials scientists know that differences in manufacturing processes often significantly influence the microstructure of even widely accepted materials and, thus, impact the properties and performance of a material in service. It is important to accelerate the understanding of the processing–structure–property relationship of materials being produced via these novel approaches in a framework that considers the performance in a statistically rigorous way. This article describes the development of a process model, the assessment of key microstructural features to be incorporated into a microstructure simulation model, a novel approach to extract a constitutive equation to predict tensile properties in Ti-6Al-4V (Ti-64), and a probabilistic approach to measure the fidelity of the property model against real data. This integrated approach will provide designers a tool to vary process parameters and understand the influence on performance, enabling design and optimization for these highly visible manufacturing approaches.     

A Simplified Micromechanical Modeling Approach to Predict the Tensile Flow Curve Behavior of Dual-Phase Steels

Micromechanical modeling is used to predict material’s tensile flow curve behavior based on microstructural characteristics. This research develops a simplified micromechanical modeling approach for predicting flow curve behavior of dual-phase steels. The existing literature reports on two broad approaches for determining tensile flow curve of these steels. The modeling approach developed in this work attempts to overcome specific limitations of the existing two approaches. This approach combines dislocation-based strain-hardening method with rule of mixtures. In the first step of modeling, ‘dislocation-based strain-hardening method’ was employed to predict tensile behavior of individual phases of ferrite and martensite. In the second step, the individual flow curves were combined using ‘rule of mixtures,’ to obtain the composite dual-phase flow behavior. To check accuracy of proposed model, four distinct dual-phase microstructures comprising of different ferrite grain size, martensite fraction, and carbon content in martensite were processed by annealing experiments. The true stress–strain curves for various microstructures were predicted with the newly developed micromechanical model. The results of micromechanical model matched closely with those of actual tensile tests. Thus, this micromechanical modeling approach can be used to predict and optimize the tensile flow behavior of dual-phase steels.     

Computing property variability of polycrystals induced by grain size and orientation uncertainties

Multiscale computational methods that link microscale models to macro-properties have practical significance. It is difficult to obtain probability distribution functions (PDFs) that provide a complete representation of microstructural variability in three-dimensional polycrystalline materials using limited information since this inverse problem is highly ill-posed. We use the maximum entropy (MaxEnt) principle to compute a PDF of microstructures based on given information about a microstructural system. Microstructural features are incorporated into the maximum entropy framework using data obtained from experiments or simulations. Microstructures are sampled from the computed MaxEnt PDF using concepts from computational geometry and Voronoi cell tessellations. These microstructures are then interrogated in virtual deformation tests, and by using homogenization techniques the variability of non-linear macro-properties is computed.     

黏土类陶瓷原型在高温干燥中传质传热的有限元模拟

在某大学开发的直接原型熔射制模技术中,陶瓷材料由于其硬脆特性,加工时容易发生崩裂,因此切削量不能过大,导致加工大型模具时效率较低。研究通过工业机器人直接铣削陶瓷毛坯得到熔射陶瓷原型,但铣削后的黏土类陶瓷生胚原型在高温干燥固结中会发生较大的收缩变形。建立了黏土类原型材料在高温干燥过程中传质传热的数学模型,并在ABAQUS中进行了有限元模拟,得到黏土类原型材料的收缩变形规律,为后续工作打下基础。     

The Interdependence model of grain nucleation: A numerical analysis of the Nucleation-Free Zone

Predictions by a 1-D analytical model and a 3-D numerical model of the formation of the Nucleation-Free Zone (NFZ) surrounding each growing grain during the initial transient of equiaxed solidification are compared. The extent of NFZ formation was studied under different solidification conditions in 1-D, 2-D and 3-D for both single-grain and multiple-grain growth scenarios with different geometric grain arrangements. The previously hypothesised NFZ concept presented by the analytic Interdependence model has been clearly demonstrated to exist for a range of solidification conditions. While there is good agreement between the 1-D numerical and analytic models, the 2-D and 3-D simulations of NFZ formation demonstrate that for some conditions the analytic model should be rederived in spherical coordinates. Further, the strong influence of the overlap of the diffusion fields between neighbouring grains was clearly demonstrated, revealing that the effect of competition between the rate of solute accumulation and cooling rate determines whether or not additional nucleation events are able to occur. It is also shown that a judicious choice of the growth rate term is essential for the analytical model to provide an accurate prediction of NFZ. Application of the computationally intensive 3-D simulations has allowed an improved solution to be derived that can be run at very low computational cost.     

Processing strategies for high-resolution GPR concrete inspections

A high-resolution multi-sensor and multi-polarization Ground Penetrating Radar (GPR) dataset was acquired on a concrete retaining wall. This dataset was characterised as a low pass filter with the help of a moving window spectral analysis. In order to examine the benefits and limits of innovative processing strategies, the dataset was processed with three different methods: classical 2-D processing, full 3-D processing followed by data fusion and inverse scattering followed by data fusion. A comparison of the results for two layers of rebar present in the wall shows that the innovative approaches improve the results for near surface structures when compared to classical 2-D processing. For deeper structures, the benefits of the innovative approaches are limited because of the low pass properties of the concrete.     

Simulation of slip band evolution in duplex Ti–6Al–4V

Formation of slip bands plays an important role in deformation and fatigue processes of duplex Ti–6Al–4V. In this study, shear-enhanced crystal plasticity constitutive relations are proposed to account for the slip softening due to breakdown of the short-range order between titanium and aluminum atoms. A hybrid strategy is developed which allows the softening to occur in slip bands only within the primary α phase, with the degree of localization depending on the specific polycrystalline initial-boundary-value problem and the requirements for compatibility of each grain or phase with its neighbors. The proposed model is calibrated by performing finite-element (FE) simulations on an experimentally studied Ti–6Al–4V alloy. The slip behavior of a Ti–6Al–4V sample subjected to an in situ (scanning electron microscopy (SEM)) tensile test is investigated. A two-dimensional (2-D) FE with 3-D crystal plasticity relations is constructed to represent the microstructure of the Ti–6Al–4V sample. Due to the lack of access to fully 3-D microstructure, a generalized plane-strain condition is used in the FE model which assumes columnar grains that are free of net traction in the direction normal to the surface. The assumption of columnar grains significantly reduces the computational cost. The contours of effective plastic strain are compared with the surface SEM micrographs from experiments at various strain levels. It is shown that the proposed approach for modeling slip bands qualitatively captures experimentally observed slip band behavior.     

Comparing calculated and measured grain boundary energies in nickel

Recent experimental and computational studies have produced two large grain boundary energy data sets for Ni. Using these results, we perform the first large-scale comparison between measured and computed grain boundary energies. While the overall correlation between experimental and computed energies is minimal, there is excellent agreement for the data in which we have the most confidence, particularly the experimentally prevalent Σ3 and Σ9 boundary types. Other CSL boundaries are infrequently observed in the experimental system and show little correlation with computed boundary energies. Because they do not depend on observation frequency, computed grain boundary energies are more reliable than the experimental energies for low population boundary types. Conversely, experiments can characterize high population boundaries that are not included in the computational study. Together the experimental and computational data provide a comprehensive catalog of grain boundary energies in Ni that can be used with confidence by microstructural scientists.     

Estimating the response of polycrystalline materials using sets of weighted statistical volume elements

The traditional representative volume element (RVE) is usually obtained through an iterative procedure based on the convergence of a selected material property. Although RVEs produced in this manner are generally presumed to automatically capture the salient features of the underlying microstructure, they typically do not achieve this requirement. Alternatively, one can identify a weighted set of statistical volume elements (WSVEs) that captures selected dominant components of n-point spatial correlations of the microstructure to prescribed accuracy. The main advantage of using WSVEs is that the key microstructural features are captured within sets of computationally manageable models ensuring reliable calculation of the material behavior and its variance in an efficient manner. In this paper, this concept of WSVEs is applied and validated for a nearly randomly oriented body-centered cubic β-Ti alloy. Specifically, two WSVE sets composed of members with an average of 100 grains and 200 grains, respectively, are derived from a 4300-grain reconstruction of real microstructure based on the dominant two-point spatial correlation statistics identified by principal component analyses. Crystal plasticity formulation is used to model the behavior of the material under selected globally applied loading conditions. The WSVEs obtained in this work were validated by comparing their overall stress–strain responses with those of a traditional 500-grain RVE. Furthermore, the frequency plots of the microscale cumulative shear strains obtained using the WSVEs compared favorably with those obtained using the traditional RVE. It is concluded that WSVE sets based on microstructure provide a viable practical alternative to the traditionally defined RVE in estimating the response of large polycrystalline microstructure datasets, with reasonable accuracy and significantly smaller computational resource needs.     

Multiresolution Modeling of the Dynamic Loading of Metal Matrix Composites

The mechanical behavior of metal matrix composites (MMCs) varies significantly under rapid straining as compared to quasi-static loading and is often dominated by underlying microstructural features (grain structure, porosity, inclusions, and defects). Analysis of the behavior of MMCs under dynamic loading requires theoretical and experimental approaches that integrate the strain rate and microstructural effects. In this article, we introduce a multiresolution modeling capability for studying nonlinear planar wave propagation in heterogeneous materials with an application to MMCs. This framework is based on direct numerical simulation (DNS) and compared to an upscaled microcontinuum model. The DNS explicitly accounts for microstructural features characterizing the materials and is based on a combination of a crystal plasticity formulation for the behavior of the host matrix and the Johnson–Holmquist model for the particulate reinforcements. The nonuniformity of the wave propagating through MMCs is spatially resolved. The results from the mesoscale DNS are used to inform a microcontinuum model that introduces richer kinematics to account for microstructural features without explicitly modeling them and with far fewer total degrees of freedom. A quantitative comparison of the reduced degrees of freedom model against DNS is performed and enables us to draw conclusions on the predictive capability of the microcontinuum model to study the dynamic response of heterogeneous materials.     

A framework for automated analysis and simulation of 3D polycrystalline microstructures. Part 2: Synthetic structure generation

This is the second of a two-part paper intended to develop a framework for collecting data, quantifying characteristics and subsequently representing microstructural information from polycrystalline materials. The framework is motivated by the need for incorporating accurate three-dimensional grain-level morphology and crystallography in computational analysis models that are currently gaining momentum. Following the quantification of microstructural features in the first part, this paper focuses on the development of models and codes for generating statistically equivalent synthetic microstructures. With input in the form of statistical characterization data obtained from serial-sectioning of the microstructures, this module is intended to provide computational modeling efforts with a microstructure representation that is statistically similar to the actual polycrystalline material.     

Non-linear elastic properties of plasma-sprayed zirconia coatings and associated relationships with processing conditions

Low-temperature thermal cycling of plasma-sprayed zirconia coatings via curvature measurements revealed their in-plane non-linear behavior. This feature arises from the unique layered, porous and cracked morphology of thermal-sprayed ceramic materials. The non-linear aspect can be quantified by a novel data interpretation procedure consisting of modified beam bending analysis and inverse analysis. This versatile procedure requires minimum measurement preparation and computational effort, and its non-linear model enables correct data interpretations otherwise not possible with the previous assumption of linear elastic models. Using this procedure, various specimens were tested to investigate the effects of processing conditions. Results are interpreted in the context of microstructural changes in the plasma-sprayed coatings due to differences in particle state upon impact and coating build-up. The implications of this study are significant for the thermo-mechanical design of strain-tolerant ceramic coatings in thermal barrier applications.     

Nondestructive approaches for 3-D materials characterization

Three-dimensional (3-D) microstructural characterization has proven to be indispensable for the thorough understanding of the often highly complex microstructures studied in materials science. However, most 3-D characterization techniques of opaque materials such as metals and ceramics are destructive and therefore prohibit 3-D studies of the dynamic microstructural evolution processes. In this paper we describe two complimentary techniques capable of nondestructive 3-D characterization and provide examples of the application of these techniques to investigate microstructural evolution processes in metallic systems.     

Evaluation of sphericity error from form data using computational geometric techniques

The measurement data for evaluation of sphericity error can be obtained from inspection devices such as form measuring instruments/set-ups. Due to misalignment and size-suppression inherent in these measurements, sphericity data obtained will be distorted. Hence, the sphericity error is evaluated with reference to an assessment feature, referred to as a limacoid. Appropriate methods based on the computational geometry have been developed to establish Minimum Circumscribed, Maximum Inscribed and Minimum Zone Limacoids. The present methods start with the construction of 3-D hulls. A 3-D convex outer hull is established using computational geometric concepts presently available. A heuristic method is followed in this paper to establish a 3-D inner hull. Based on a new concept of 3-D equi-angular line, 3-D farthest or nearest equi-angular diagrams are constructed for establishing the assessment limacoids. Algorithms proposed in the present work are implemented and validated with the simulated data and the data available in the literature.