Computational Materials Engineering

Achieving High Accuracy and Efficiency in Metals Processing Simulations

Maciej Pietrzyk, Lukasz Madej, Lukasz Rauch, Danuta Szeliga

• Publisher: Butterworth-Heinemann
• Year: 2015
• Print ISBN: 9780124167070
• eBook ISBN: 9780124167247
• Topic: Technology & Engineering
• Subtopic: Mathematics General
• Index: Technology & Engineering

Computational Materials Engineering: Achieving High Accuracy and Efficiency in Metals Processing Simulations describes the most common computer modeling and simulation techniques used in metals processing, from so-called "fast" models to more advanced multiscale models, also evaluating possible methods for improving computational accuracy and efficiency.Beginning with a discussion of conventional fast models like internal variable models for flow stress and microstructure evolution, the book moves on to advanced multiscale models, such as the CAFÉ method, which give insights into the phenomena occurring in materials in lower dimensional scales.The book then delves into the various methods that have been developed to deal with problems, including long computing times, lack of proof of the uniqueness of the solution, difficulties with convergence of numerical procedures, local minima in the objective function, and ill-posed problems. It then concludes with suggestions on how to improve accuracy and efficiency in computational materials modeling, and a best practices guide for selecting the best model for a particular application.- Presents the numerical approaches for high-accuracy calculations- Provides researchers with essential information on the methods capable of exact representation of microstructure morphology- Helpful to those working on model classification, computing costs, heterogeneous hardware, modeling efficiency, numerical algorithms, metamodeling, sensitivity analysis, inverse method, clusters, heterogeneous architectures, grid environments, finite element, flow stress, internal variable method, microstructure evolution, and more- Discusses several techniques to overcome modeling and simulation limitations, including distributed computing methods, (hyper) reduced-order-modeling techniques, regularization, statistical representation of material microstructure, and the Gaussian process- Covers both software and hardware capabilities in the area of improved computer efficiency and reduction of computing time

Chapter One

Introduction

There is a wide range of materials, which exhibit unusual in-use properties gained by control of phenomena occurring in meso-, micro-, and nanoscales during manufacturing. Spectacular examples of such materials range from constructional steels (e.g., advanced high strength steels for automotive industry [224]) to a new biocompatible materials for ventricular assist devices [234] or porous materials for orthopedic implants used for replacing diseased joints [337]. The former allows to decrease the transport costs per passenger, based on fuel consumption, and to improve safety of passengers. The latter exhibits excellent fatigue strength and an improved microporosity distribution that facilitates growth of bone tissue and, at the same time, triggers self-healing mechanisms in the event of cracking. Due to potential advances in materials science that could dramatically affect the most innovative technologies, further development in this field is expected. For this to happen, materials science has to be endowed with new tools and methodologies.

Keywords

Computational materials science; digital materials representation; computational multiscale material modeling

There is a wide range of materials, which exhibit unusual in-use properties gained by control of phenomena occurring in meso-, micro-, and nanoscales during manufacturing. Spectacular examples of such materials range from constructional steels (e.g., advanced high strength steels, AHSS, for automotive industry [224]) to a new biocompatible materials for ventricular assist devices [234] or porous materials for orthopedic implants used for replacing diseased joints [337]. The former allows to decrease the transport costs per passenger, based on fuel consumption, and to improve safety of passengers. The latter exhibits excellent fatigue strength and an improved microporosity distribution that facilitates growth of bone tissue and, at the same time, triggers self-healing mechanisms in the event of cracking. Due to potential advances in materials science that could dramatically affect the most innovative technologies, further development in this field is expected. For this to happen, materials science has to be endowed with new tools and methodologies.

On the other hand it is observed that there are several limitations of current procedures for developing material-based innovative technologies in engineering. Mostly, existing data and/or knowledge bases of materials are only available and new technologies have to adapt to them. This constitutes an enormous limitation for the intended goals and scope of development of new quality products. Certainly, availability of materials specifically designed by goal-oriented methods could eliminate that limitation, but this purpose faces the bounds of experimental procedures of material design, commonly based on trial and error procedures. Thus, computational materials science (CMS) with emerging digital materials representation (DMR) concept are research fields, which potentially can offer a support for design of new products with special in-use properties. On the other hand, industry traditionally uses a new computational technology only if it perceives convincing evidence that such technology can substantially reduce the time to bring products to market. Thus, it seems that a natural consequence of dramatic decrease in computational costs associated to simulation and optimization of materials processing would be a factor for acceptance of the CMS and DMR concepts by the industries that routinely deal with engineering materials. Various methods of making computational multiscale material modeling (CMMM) simulations more efficient are presented schematically in Figure 1.1.

Figure 1.1 The idea of making CMMM simulations more efficient.

Development of new materials modeling techniques within the CMS that are tackling various length scales phenomena is enormous. Multiscale analysis in the sense of length and temporal scales has already found a wide range of applications in many areas of science. Advantages have been provided by a combination of a variety of numerical approaches: finite element method (FEM), crystal plasticity finite element method (CPFEM), extended finite element method (XFEM), finite volume method (FVM), boundary element method (BEM), mesh free, multigrid methods, Monte Carlo (MC), Cellular Automata (CA), Molecular Dynamics (MD), Molecular Statics (MS), Level set methods, Fast Fourier Transformation, etc. are being successfully applied in practical applications [215]. These multiscale modeling techniques can be classified into two groups: upscaling and concurrent approaches. In the upscaling class of methods, constitutive models at higher scales are constructed from observations and models at lower, more elementary scales [65]. By a sophisticated interaction between experimental observations at different scales and numerical solutions of constitutive models at increasingly larger scales, physically based models and their parameters can be derived at the macroscale. It is natural that in this approach microscale problem has to be solved at several locations in the macromodel. Thus, classification of the multiscale problems with respect to the upscaling goals and the upscaling costs is needed, which is one of the objectives of this book.

In concurrent multiscale computing, one strives to solve the problem simultaneously at several scales by an a priori decomposition of computational domain. The question, how the fine scale is coupled to the coarse scale, is essential in this approach. Major difficulty in coupling occurs when fine scales and coarse scales are described by different equations, example coupling FE to MD. Various approaches exist to perform decomposition of the problem into fine scales and coarse scales, which essentially differ in how to couple the fine scale to the coarse scale. In other words, the objective is finding a computationally inexpensive, but still accurate, approach to the decomposition problem.

In recent years, a gradual paradigm shift is taking place in the selection of materials to suit particular engineering requirements, especially in high-performance applications. The empirical approach adopted historically by materials scientists and engineers of choosing materials parameters from a database is being replaced by the design based on the DMR concept. Features that span across a large spectrum of length scales are altered and controlled so that the desired properties and performance at the macroscale are achieved. Research efforts, in this aspect, include development of engineering materials by changing the composition, morphology, and topology of their constituents at the microscopic/mesoscopic level. The major barrier that prevents this methodology from being extensively employed in engineering practice is its enormous computational cost. Indeed, the increasing power of new computer processors and, most importantly, development of new methods and strategies of computational simulation opens new ways to face this problem. On the other hand, it seems that increase in computational complexity of material models is even faster and common application of these models in industrial practice is not likely now.

The objective of this book is to show methods of breaking through the barriers that presently hinder development and application of computational materials design. From one side we present CMMM based on the bottom-up, one-way coupled, description of the material structure in different representative scales. On the other side, our intention is to show methods of making CMMM simulations more efficient by means of the synergic exploration and development of two supplementary families of methods:

• Development of reduced-order-modeling (ROM) techniques [285] in order to bring down the associated computational costs to affordable levels (recently high-performance reduced-order-modeling (HP-ROM) was proposed [259]). Model reduction strategies may range from purely physical or analytical approaches to black-box methods (e.g., artificial neural networks). The focus in this book is on model reduction based on sensitivity analysis, practical engineering knowledge, application of metamodeling, and simplification of the computational domain is considered, as well.

• Applications of new heterogeneous computer architectures. These methods of making CMMM simulations less expensive are combined with new methods for the optimal design of the material processing.

The general motivation of the book is to show methods of searching for a balance between CMMM and computational costs, thus resulting in new opportunities for many innovative engineering areas that are currently locked by the complexity and limitations involved in computational materials design. The first part of the book is a review of modeling techniques for processing of materials. Models of various complexity of mathematical formulation and various predictive capabilities are presented and discussed and their accuracy is evaluated. New generation HP-ROM techniques follow. These include development of metamodels and application of statistical representation of the microstructure as a computational domain. Possibilities of high-performance computing (HPC) on the basis of modern computer hardware architectures are also discussed within the scope of the book.

The field of CMMM is extremely wide. Although some of the solutions presented in the book are applicable, in general, to modeling of materials, the main flow of information, and all case studies are connected with macro–micro dimensional scales and with metallic materials.

1.1 Classification of Models

Historically, slab method [41] and upper bound method [12] were commonly used for simulations of metal-forming processes up to late 1960s of the last century. A large number of closed form formulae, which allow calculations of main parameters of the selected processes, have been derived on the basis of these methods (see, e.g., Refs. [300,301]). In the meantime, modeling of phase transformation was based mainly on Johnson, Mehl, Avrami, Kolmogorov (JMAK) equation [13–15,152,166]. This approach was adapted to modeling kinetics of recrystallizations [322] as well as phase transformations [15] and eventually was extensively used to describe microstructure evolution in hot forming.

Problems of materials workability during forming and crack resistance during exploitation were always also very important in modelling materials processing. Therefore, numerous fracture criteria based on the continuum damage mechanics [54] as well as fracture mechanics models [49] were developed and predictive capabilities of numerical models increased further.

Since early 1970s, FEM has become the most popular simulation technique in metal forming. The approach called flow formulation based mainly on works of Kobayashi [163,201] became particularly useful for modeling metal forming. Subsequently, new advanced numerical techniques were used, such as BEM or FVM, but the FEM still remains the most popular method for simulation of metal-forming operations. In 1990s, the FE codes were combined with microstructure evolution models, mentioned above, and fully coupled thermal-mechanical-microstructural simulations became possible [264]. Since then, FE or alternative methods have been used to calculate macroscale parameters such as strains, strain rates, stresses, or temperatures. These methods have been connected with various algebraic or differential equations, which describe phenomena occurring at microscale. Other methods describing microstructure evolution, evolution of dislocations populations, precipitation, phase transformations, or fracture have been solved in each Gauss integration point of the macroscale FE model. In consequence, distribution of the considered microstructural parameters in the volume of the material could also be predicted, which was important from the practical application point of view.

In parallel, more advanced numerical models based on mean field approach such as closed form equations, differential equation (e.g., solution of diffusion equation [261]), or full field approach such as phase field or level set [237] methods were subsequently proposed to deal with material description.

Then new challenges in modeling of metal processing occurred at the beginning of the twenty-first century. Possibility of prediction of microstructural phenomena accounting explicitly for the granular structure of polycrystals was the first challenge, which led to development of sophisticated multiscale models. In these models, usually FE codes are coupled with such discrete methods as CA, MC, or MD. Review of multiscale modeling methods is presented in, for example, Refs. [5,215]. Problem of computing time is the second challenge, which is particularly important when optimization of the metal-forming processes is performed. An optimization problem requires evaluation of the objective function many times before reaching the optimum solution. Analysis of all above-listed models allows proposing the classification shown ...

Table of contents

• Cover image
• Title page
• Table of Contents
• Copyright
• Chapter One. Introduction
• Chapter Two. Toward Increase of the Efficiency of Modeling
• Chapter Three. Conventional Modeling
• Chapter Four. Identification of Material Models and Boundary Conditions
• Chapter Five. Increase Model Predictive Capabilities by Multiscale Modeling
• Chapter Six. Trade off Between Accuracy and Efficiency
• Chapter Seven. Case Studies
• Chapter Eight. Conclusions
• References
• Index