Computational materials engineering : achieving high accuracy and efficiency in metals processing simulations

381 Pages·2015·41.64 MB·English

by  Maciej Pietrzyk Ph.D.

COMPUTATIONAL
MATERIALS
ENGINEERING
COMPUTATIONAL
MATERIALS
ENGINEERING
Achieving high accuracy
and efficiency in metals
processing simulations
MACIEJ PIETRZYK
LUKASZ MADEJ
LUKASZ RAUCH
DANUTA SZELIGA
AGH University of Science and Technology,
Department of Applied Computer Science and Modelling,
al. Mickiewicza 30
30-059 Kraków, Poland
AMSTERDAM(cid:129)BOSTON(cid:129)HEIDELBERG(cid:129)LONDON
NEWYORK(cid:129)OXFORD(cid:129)PARIS(cid:129)SANDIEGO
SANFRANCISCO(cid:129)SINGAPORE(cid:129)SYDNEY(cid:129)TOKYO
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CHAPTERONE
Introduction
There is a wide range of materials, which exhibit unusual in-use properties
gainedby controlofphenomenaoccurring inmeso-,micro-,andnanoscales
during manufacturing. Spectacular examples of such materials range from
constructional steels (e.g., advanced high strength steels, AHSS, for automo-
tive 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, trig-
gers self-healing mechanisms in the event of cracking. Due to potential
advancesinmaterialssciencethatcoulddramaticallyaffectthemostinnovative
technologies,furtherdevelopmentinthisfieldisexpected.Forthistohappen,
materialssciencehastobeendowedwithnewtoolsandmethodologies.
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 con-
stitutes an enormous limitation for the intended goals and scope of devel-
opment of new quality products. Certainly, availability of materials
specifically designed by goal-oriented methods could eliminate that limi-
tation, 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 tech-
nology 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
ComputationalMaterialsEngineering ©2015ElsevierInc.
DOI:http://dx.doi.org/10.1016/B978-0-12-416707-0.00001-6 Allrightsreserved. 1
2 ComputationalMaterialsEngineering
be a factor for acceptance of the CMS and DMR concepts by the indus-
tries that routinely deal with engineering materials. Various methods of
making computational multiscale material modeling (CMMM) simula-
tions more efficient are presented schematically in Figure 1.1.
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),
MolecularStatics(MS),Levelsetmethods,FastFourierTransformation,etc.
arebeingsuccessfullyappliedinpracticalapplications[215].Thesemultiscale
modeling techniques can be classified into two groups: upscaling and con-
currentapproaches.Intheupscalingclassofmethods,constitutivemodelsat
higher scales are constructed from observations and models at lower, more
elementary scales [65]. By a sophisticated interaction between experimental
observationsatdifferentscalesandnumericalsolutionsofconstitutivemodels
atincreasinglylargerscales,physicallybasedmodelsandtheir parameterscan
be derived at the macroscale. It is natural that in this approach microscale
problem hastobesolved atseverallocationsinthemacromodel.Thus,clas-
sification of the multiscale problems with respect to the upscaling goals and
theupscalingcostsisneeded,whichisoneoftheobjectivesofthisbook.
Conventional approach to design of manufacturing cycles
Numerical simulations Join of simulations into
Optimization
of processes manufacturing chain
Optimization-driven approach to design of manufacturing chains
Model reduction:
Practical engineering knowledge
Sensitivity analysis
Reduced-order-modelling
SSRVE
Model selection: Optimization strategy:
Cost
Conventional models reduction Method selection
Multiscale models Hybrid methods
Multiscale approach Model performance: Tuning of parameters
Metamodelling
High performance computing
(Software & Hardware)
Figure1.1 TheideaofmakingCMMMsimulationsmoreefficient.
Introduction 3
In concurrent multiscale computing, one strives to solve the problem
simultaneously at several scales by an a priori decomposition of computa-
tional 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 decom-
position 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,
approachtothedecompositionproblem.
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 histori-
cally by materials scientists and engineers of choosing materials parameters
from a database is being replaced by the design based on the DMR con-
cept. Features that span across a large spectrum of length scales are altered
and controlled so that the desired properties and performance at the mac-
roscale 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 compu-
tational materials design. From one side we present CMMM based on the
bottom-up, one-way coupled, description of the material structure in dif-
ferent 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:
(cid:129) 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)
4 ComputationalMaterialsEngineering
was proposed [259]). Model reduction strategies may range from purely
physical or analytical approaches to black-box methods (e.g., artificial
neuralnetworks).Thefocusinthisbookisonmodelreductionbasedon
sensitivity analysis, practical engineering knowledge, application of
metamodeling,andsimplificationofthecomputationaldomainisconsid-
ered,aswell.
(cid:129) 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 cur-
rently locked by the complexity and limitations involved in computational
materials design. The first part of the book is a review of modeling tech-
niques for processing of materials. Models of various complexity of math-
ematical 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 appli-
cation 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 solu-
tions presented in the book are applicable, in general, to modeling of
materials, the main flowof information, and all case studies are connected
with macro(cid:1)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(cid:1)15,152,166].
This approach was adapted to modeling kinetics of recrystallizations [322]
Introduction 5
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
developedandpredictivecapabilitiesofnumericalmodelsincreasedfurther.
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 techni-
ques 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, precipita-
tion, phase transformations, or fracture have been solved in each Gauss
integration point of the macroscale FE model. In consequence, distribu-
tion 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., solu-
tion of diffusion equation [261]), or full field approach such as phase field
or level set [237] methods were subsequently proposed to deal with mate-
rial description.
Then new challenges in modeling of metal processing occurred at the
beginning of the twenty-first century. Possibility of prediction of micro-
structural phenomena accounting explicitly for the granular structure of
polycrystals was the first challenge, which led to development of sophisti-
cated 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
6 ComputationalMaterialsEngineering
when optimization of the metal-forming processes is performed. An opti-
mization 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 in Figure 1.2.
As seen in Figure 1.2, all above-mentioned various numerical models
are still used depending on required level of complexity and available
computational resources. For simple, fast, and efficient calculations during
optimization of industrial metal-forming processes models based on, for
example, JMAK equations are very common. However, when more
detailed information on material behavior is required more and more
advanced solutions are applied. Unfortunately, higher predictive capabili-
ties are also related with increasing computing time, which is a limiting
factor in wider application of these advanced models.
It can be summarized that, since 1970s FE and alternative methods
have been commonly used for modeling macroscale phenomena and in
this case computing times depend mainly on the complexity and dimen-
sions of the computational domain. Contrary, in recent microscale mod-
els, computing costs are increasing exponentially.
Thus, one of the objectives of this book is presentation of possibility of
improvement of predictive capabilities and computing efficiency of selected
numerical models. If this goal is reached, a noticeable step towards the con-
trol and optimization of metal processing is expected. Application of
Continuum mechanics methods: FEM, FVM, BEM...
Macro
sts FEM
o FEM FEM +
g c FEM + + FEM
putin Closed form C+F μstutrruec- DE (FE2) sMcualltei
m equations (CF):
o slab, upper bound
C
Hall-Petch, JMAK, CA
damage criteria MC
∇D∇c=∂c
Micro Dγ=AεmD0qexp –RQT Phase fie∂ltd Nano MD
Predictive capabilities
On-line Preliminary Process Advanced μstructure
control design design &
optimization
Properties, Fracture
Figure 1.2 Classification of materials processing models with respect to their
predictivecapabilitiesandcomputingcosts.
Introduction 7
multiscale models as tool to increase accuracy of computations will be
discussed. At the same time, solutions based on metamodeling, inverse analy-
sis, sensitivity analysis, or model reduction approaches will be presented
within the book as a tool for increasing the computational efficiency.
1.2 REVIEW OF PROBLEMS CONNECTED WITH
COMPUTING COSTS
Presentation and discussion of problems occurring during numerical
modeling of materials processing is another objective of the book.
Readers interested in solving various numerical problems are directed to
relevant publications, for example, Refs. [69,70,265,383(cid:1)385]. In the
review paper [98], various aspects of evaluation of the efficiency of the
scientific computer simulations were discussed. This evaluation has to be
combined with the role of computer simulations, or even further, with
the expectations of researchers using numerical simulations. A schematic
illustration given in Figure 1.3 shows how numerical models should be
developed and applied. The subsequent steps should be as follows:
(cid:129) Formulation of mathematical models on the basis of knowledge about
the considered process or phenomenon.
(cid:129) Identification of selected parameters in the model, usually using
inverse analysis of results of basic laboratory tests performed in care-
fully controlled conditions.
(cid:129) Validation of the model by evaluation to what extent it is capable to
reproduce characteristic features of the process or phenomenon.
(cid:129) Verification of the model by comparison of the results with available
experimental data.
Physical
reality Prediction
Computer
Observations Theory modelling
Experiment Mathematical Predictive
Logic models
Identification Verification
Validation
Figure 1.3 Schematic illustration of development and application of numerical
models.