Institutional repository of Jönköping University

Institutional repository of Jönköping University
Institutional repository of
Jönköping University
This is an author produced version of a paper published in International Journal of
Cast Metals Research. This paper has been peer-reviewed but does not include the
final publisher proof-corrections or journal pagination.
Citation for the published paper:
Olofsson, J. (2012). Simulation of mechanical behaviour of cast aluminium
components. International Journal of Cast Metals Research, 25(6), 319-327.
Access to the published version may require subscription.
Published with permission from: Maney Publishing
Simulation of Mechanical Behaviour of Cast Aluminium
Components: A Literature Review
Jakob Olofsson
Jönköping University, School of Engineering, Dept. Mechanical Engineering,
Materials and Manufacturing – Casting, P.O. Box 1026, SE-551 11 Jönköping, Sweden
Email: [email protected] Phone: +46 (0)36-10 16 59
A literature review on methods to consider mechanical behaviour of cast aluminium
alloys in finite element method (FEM) simulations of cast aluminium components has
been performed. The mechanical behaviour is related to several microstructural
parameters achieved during the casting process. Three different methods to consider
these microstructural parameters are introduced. One method predicts the mechanical
behaviour of the component using casting process simulation software. The other two
methods implements numerical models for mechanical behaviour of cast aluminium into
the FEM simulation. Applications of the methods are shown, including combinations
with statistical methods and geometry optimisation methods. The methods are
compared, and their different strengths and drawbacks are discussed.
Aluminium, FEM simulation, microstructure, mechanical behaviour
The constantly increasing demands on environmental, safety and economical issues on
vehicles drive the demand for lightweight components with high performance and low
life-cycle cost. By designing lighter components, the weight and the emissions of the
vehicle can be reduced. Simultaneously the mechanical loads, e.g. fatigue load or crash
load, on the component must be considered in order to meet safety and quality
demands. The correct usage of tools such as finite element method (FEM) analyses and
geometry optimisation thus becomes more and more important in order to, in the
design phase, correctly predict the behaviour of the component in service. These tools
are highly dependent on correct input of the mechanical behaviour of the material in the
component in order to accurately and correctly predict the performance of the
Cast aluminium components are manufactured by several different casting processes,
e.g. high/low pressure die casting (HPDC/LPDC), gravity die casting and sand casting.
During the casting process the microstructural characteristics, which determine the
actual performance of the material in the component, are obtained. One important
microstructural characteristic is the secondary dendrite arm spacing, SDAS (λ), which is
as a function of the local solidification time where a short solidification time (i.e. a high
cooling rate) gives a small SDAS.1, 2 SDAS is widely used as a measure of microstructural
refinement,3 but changes in SDAS are also accompanied by several other microstructural
changes.4-7 A decreasing SDAS generally increases the yield strength (YS), 4, 5, 7 the
ultimate tensile strength (UTS)1, 2, 5-9 and the ductility1, 3, 5-7 of the material, but the
trends may have variations due to concurrent changes in size and shape of eutectic Siparticles.9-11 The plastic behaviour and fracture of cast aluminium alloys is furthermore
highly affected by the characteristics12-14 and damage11, 15-18 of the Si-particles, where
especially ductility13 and strain hardening rate is increased with increased aspect ratio
of the Si-particles.15, 16, 19, 20
Damage of the Si-particles consists of three stages: cracking or debonding, microcrack
formation and growth, and local linkage of microcracks,6, 21 and both cracked6, 11, 17, 18 and
debonded18, 22 particles may initiate global fracture. Particle fracture is caused by
incompatibility stresses between particle and matrix,18, 22 and in general larger and
longer particles are more likely to crack.6, 17 The probability of particle-cracking, ppc, can
be described by Weibull statistics as11
  V    m 
p pc  1  exp    p  
  V0   p 0  
where V is the particle volume, V0 is a reference volume, σp is the tensile stress in the
particle, σp0 is a reference stress and m is the Weibull modulus.
The mechanical properties are also reduced by the presence of iron-rich intermetallic
phases, most importantly α-, β- and π-Fe phases,7, 23, 24 and by the structural integrity2532 of the component, i.e. the presence of structural defects such as porosity, oxide films,
macro- and micro-porosity. While yield strength is relatively unaffected by porosity,25-27
both UTS and elongation to fracture decrease with increased amount of porosity.25, 27
Defects generally affect fracture strength, elongation to fracture and fatigue life of cast
aluminium alloys28, 29 and cause variations in properties achieved during the casting
process.30 Elongation to fracture is reported to depend on defects as31, 32
e f  emax 1  f d  G
where fd is the area fraction of defects, emax is the tensile ductility of defect-free material,
i.e. the highest achievable elongation to fracture, and nG is an empirical constant
interpreted as the index of defect susceptibility of the material. A low value of nG implies
that the alloy can tolerate a larger concentration of defects.31
The mechanical behaviour of the material within the component thus originates from
the casting process and will vary throughout the component. Since the local and nonlocal mechanical response of structures are affected by non-uniformity in material
behaviour it is important to consider these local variations of the material behaviour
within the component when analysing the mechanical response of the component.33 In
addition, the manufacturing process leads to variations in material quality, which affects
the performance of the actual component in service. Thus to correctly predict the
behaviour of cast aluminium components, it is important to include the material
behaviour within the specific component in simulations, and to study the variations in
component performance due to the casting process. These parameters vary with the
design of the component, and can to different extents be predicted using casting
simulation software. The current contribution aims to study and discuss different
methods to include material behaviour specific to cast aluminium alloys into finite
element simulations of mechanical behaviour of components. This knowledge is of direct
importance to the process of designing cast components, since it combines knowledge of
design, simulation and casting. All these different aspects need to be considered in order
to be able to design robust and optimised cast aluminium components.
Finite element (FEM) simulations have been extensively used for understanding the
plastic behaviour of cast aluminium alloys on the micro- and meso-scale levels. FEM
based micromechanics approaches have been applied to study the effect of e.g. nonuniformly distributed voids of different shapes and sizes,34, 35 stress distributions
around Si particles,36, 37 the effect of reinforcing particles38 and particle decohesion.39
On the macroscale, i.e. simulations of entire structures, a complete modelling of the
microstructure within the macrostructure is not realistic. Concurrent multi-scale
simulation methods that combine meshes of the entire structure on a macroscopic level
with meshes of a representative volume element describing the micromechanical
behaviour of the material have been presented.40, 41 These methods are highly advanced
and not commonly used in development of industrial components. Instead the
traditional method to use globally constant homogeneous material data acquired from
measured data is still commonly used in the design process of cast aluminium
components. The effects of the casting process on the mechanical behaviour of the
component, such as local variations in SDAS, structural integrity etc., are then not
considered. In the current work three different methods to consider the effect of the
casting process and microstructural parameters on the mechanical behaviour of cast
aluminium in macro-level FEM simulations have been studied. One method predicts the
mechanical behaviour of the component, and two methods include microstructural
behaviour in the FEM simulation based on the internal state variable (ISV) approach.
The ISV approach is reviewed elsewhere,42, 43 but in short aims to capture the effects of a
representative volume element instead of capturing all the complex causes at the
microstructural level. The behaviour of observable state variables (OSVs) e.g.
deformation, are described by a sufficient number of internal state variables (ISVs)
representing the internal structure of the material.43 As long as the macroscale ISV
representation is complete, the complete microstructural arrangement is not
necessary.44 An example of an ISV approach is to describe deformation with formation
and growth of cracks using a constitutive model, i.e. a set of equations describing the
behaviour of an element of the material when subjected to an external influence such as
2.1. The MMP-method
The development of casting simulation software has provided new possibilities to
accurately predict microstructural parameters on a local level throughout a cast
component. The predictions are performed by determining cooling curves and
microstructure evolution during solidification.46, 47 Recent research has been aimed at
relating microstructural parameters that can be locally determined by casting
simulation software to mechanical behaviour,48-51 and to apply these relations to
determine local mechanical behaviour.52 For an A357 alloy with low defect content the
UTS was found to mainly depend on SDAS, grain size, aspect ratio of eutectic Si-particles,
and hardness of the material.48 A microstructural index was defined to combine these
parameters, and by plotting UTS as a function of this index a numerical correlation was
found, able to predict the UTS with an error less than 5%.48 For an A356 alloy no
significant influence of grain size was noted, and UTS respectively YS could be accurately
predicted by combining SDAS, the cross section fraction eutectic Si-particles and the
hardness of the material.49
An add-on module to a commercial casting simulation software has been developed by
Seifeddine et al.50 The module uses the casting simulation software to predict
microstructural parameters and their local variations throughout a cast component
based on solidification models by Wessén et al.47 Chemical compositions of the alloy
within the ranges of (wt-%) Si < 12%, Cu < 4%, Mg < 0.5% and Fe < 0.7%50 may be used.
Based on the predicted microstructural parameters, YS, UTS, elongation to fracture and
their respective local variations throughout the component are determined. The effect of
defects may be accounted for through a user defined dimensionless quality parameter q
which determines the true plastic strain at failure, εpl,f , from a maximum plastic strain,
εpl,f , through the relationship51
 pl, f   pl, max  q
The maximum plastic strain is determined through tensile testing of material re-melted
with a gradient solidification technique that leads to a very low content of defects.52 The
predictions were compared with measured results for an as-cast A354 alloy cylinder
head component, see Fig. 1. A good correlation was obtained for yield strength and
ultimate tensile strength, while the elongation to fracture showed a larger scatter.50
Figure 1: Comparison between yield stregth predicted using the add-on module
developed by Seifeddine et al. and experimentally measured yield strength.50
Figure reprinted with permission from Teksid Aluminum SrL.
The module was recently extended to determine the entire plastic behaviour of the
material. The plastic behaviour is characterised using the Hollomon equation, which
relates true plastic stress, σH, and true plastic strain, εpl, as53
 H  K H   pln
Here the material constants nH and KH are introduced. The strain hardening exponent nH
defines the work hardening capacity of the material, and ranges from zero to unity
where nH=0 corresponds to a perfectly plastic material and nH=1 to a linearly
deformation hardening material. Common values for metallic materials are in the range
0.1-0.5, corresponding to shapes of the plasticity curve as shown in Fig. 2. The constant
KH, commonly known as the strength coefficient, can be expressed as a function of YS and
strain hardening exponent,54 and thus indicates the strength of the material when
evaluated in combination with the strain hardening exponent.
Figure 2: Effect of different values of the strain hardening exponent nH on the shape of
the plastic stress-strain curve predicted by the Hollomon equation.
In the add-on module the parameters in the Hollomon equation have been related to the
local values of Fe-content and SDAS (λ) in the form52
nH  a1  Fe  a2   ln    a3  Fe  a4 
K H  b1  Fe  b2   ln    b3  Fe  b4 
where the constants a1-4 and b1-4 are derived from tensile test data. A strong correlation
between SDAS and both strain hardening exponent and strength coefficient was
reported, and the strain hardening exponent was found to decrease with increasing Fecontent.52
The predicted tensile behaviour of the material can be used as input for subsequent FEM
simulations of a component.55 This method to predict microstructure-based mechanical
properties is further discussed in following sections and will be referred to as the MMP
2.2. The FC-method
A method for FEM simulation of thin-walled cast aluminium components has been
developed by Dørum The plastic material behaviour is described in a parametric
form as
  0 Ai  1  exp  ci   pl,eq 
i 1
where σ is the flow stress, σ0 is the yield stress, and εpl,eq is the equivalent plastic strain.
The hardening parameters Ai and ci are determined for the specific alloy using a leastsquare fitting method to tensile data obtained from uniaxial tensile tests. A material
model implemented in a commercial FEM software in combination with a fracture
criterion is applied to determine when fracture occurs within an element. The fracture
criterion used is the Cockcroft-Latham ductile fracture criterion56
W   max  1 , 0d pl,eq  Wc
in which the value of the Cockcroft-Latham integral W is compared to a critical value at
fracture, Wc, known as the fracture parameter. Fracture is defined to occur when the
value of the Cockcroft-Latham integral reaches the value of the fracture parameter.56
Only tensile stresses are assumed to contribute to damage, thus in the Cockcroft-Latham
integral the maximum principal stress, σ1, is compared to zero. The Cockcroft-Latham
fracture criterion is convenient to use since it is based on only one parameter, Wc, that
can be determined from a single test.57 The fracture criterion is rewritten as an ISV
damage evolution law for the damage variable D according to58
  
D  Wc pl,eq
for  1  0
for  1  0
which has been implemented in an explicit commercial FEM code and calibrated using
simulations and measurements from notched specimen tests and plate bending tests.
Thin-walled components are commonly modelled using shell elements, and in the FC
method layered shell elements with five integration points through the thickness of an
element are used. It is noted by the authors that the stress distribution in the thickness
direction of the shell elements is assumed to be zero, which is not a correct
representation of all stress states.56 HPDC aluminium components experience varying
material properties through their thickness, known as skin effect, where the interior
material generally is less ductile than the surface material. This is accounted for by
assigning different values of the fracture parameter in different layers, thus different
degrees of ductility are allowed before fracture is reached in the specific layer. During
the FEM simulation the layer in which the fracture parameter is reached is inactivated.
When a defined number of layers have been inactivated, the entire element is removed
from the simulation. By studying the removal of elements it is then possible to follow the
evolution of the fracture in the structure.57 Fig. 3 shows the predicted fracture
deformation of a U-profile subjected to a three point bending test, where removed
elements on the front wall indicate fracture. This Fracture Criteria based method will in
the following sections be referred to as the FC method.
Figure 3: Simulated deformation mode for an U-profile (AlSi4Mg alloy) subjected
to three-point bending test using the FC method.56
Figure reprinted with permission from Elsevier.
The FC method has been used to study the effect of statistical variations of mechanical
behaviour in a component.58 The probability of particle fracture, ppf(W), was assumed to
follow a Weibull distribution as58, 59
  V  W m 
 
p pf W   1  exp   
  V0  Wc 0  
where m is the Weibull modulus. Size effects are taken into consideration by using two
scaling ratios, the ratio between the volume of the element (V) and a scaling volume (V0)
respectively the ratio of the Cockcroft-Latham integral W and a scaling fracture
parameter Wc0. FEM simulations of a modified Arcan test with different loading angles
and the fracture parameter as a stochastic variable were performed, together with
actual testing using a high-resolution camera and image analysis software to determine
the effective strain field in the specimen. It was concluded that force-deformation
curves, fracture modes and the effective strain fields were accurately predicted, see Fig.
4. Both simulations and measurements showed differences in crack path between
replicate tests.58
Figure 4: Comparison between (a) measured strain fields and (b) simulated strain fields
using the FC method, of an Arcan test.58
Figure reprinted with permission from Elsevier.
Reduced ductility because of defect formation has been considered using stochastic
fracture parameters on predicted locations in a U-shaped cast component, and the
method was denoted a through-process methodology.59 The HPDC process of the
component profile was simulated in a commercial casting simulation software, using the
simulated average contact time between melt and air as a measure of defect formation.
The upper and lower boundaries of the fracture parameter with varying material quality
were determined by tensile testing. The fracture parameter in the Weibull distribution
in the FEM simulation was for each element assumed to vary linearly with the simulated
average contact time. A number of FEM simulations on three-point bending tests of the
U-shaped profile were performed, with the stochastic fracture parameters resulting in a
scatter in FEM simulation results, see Fig. 5.59
Figure 5: Comparison of predicted behaviour by three stochastic FEM simulations using
the FC-method and three experimental measurements by three point-bending tests.59
Figure reprinted with permission from Elsevier.
2.3. The CTG-method
Damage of Si-particles has previously been discussed as an important contribution to
the plastic behaviour and fracture of cast aluminium alloys. Generally voids or cracks in
metals nucleate on macroscale stress raisers such as inclusions, precipitates, porosities,
oxide films or other secondary phases. Irrespective of nucleation site, damage evolution
is typically divided into three components: void nucleation, void growth and void
coalescence. A damage evolution model has been developed, where void nucleation is
modelled using a time dependent model based on fracture mechanics.60
 t   Ccoeff
  t   d 1 / 2
 exp 
 K IC  f 1 / 3
 4 J 32 
C1    3   C 2  3 / 2  C3 
 27 J 2 
I1 
 
J2 
Here η(t) is the void nucleation density, ε(t) the strain at time t, Ccoeff is a dimensionless
material constant related to initial void nucleation, KIC is fracture toughness and C1, C2
and C3 are alloy specific material parameters determined from mechanical testing with
different stress states. Stress state dependence is included through the stress invariants,
where I1 is the first invariant of stress, and J2 and J3 is the second respectively the third
invariant of deviatoric stress. In the case of Si particles in an Al alloy the length scale d is
the average Si particle size and f the volume fraction of Si particles.
Similarly a void growth model has been developed, formulated as61
2  I1
4 
 V t     R0  exp  t  
 sinh  3  1  n HVG  
3 
2  1  n HVG 
3 J2
 
 
 
where νV(t) is the average void volume at time t, the material constant nHVG is related to
the strain hardening exponent of the Hollomon equation, and R0 is the initial radius of
the voids. The contribution of coalescence is accounted for through a coalescence term.
The models for these three damage components have been implemented in FEM code
using an ISV plasticity approach.61 The material parameters (over 20 alloy specific
material parameters determined through several material tests and regression
analyses) have been determined for a T6 heat-treated A356 alloy. Failure of an element,
modelled as a 50% decrease of the elastic modulus, occurs when the total amount of
damage reaches unity. FEM simulations using the damage evolution model have been
performed on notched tensile test specimens. The results are reported to correspond
well with experimental data, and the stress state dependence of the model is shown to
predict different results for torsion, compression and tension, as shown in Fig. 6.61
Figure 6: Comparison of experimentally measured and numerically predicted behaviour
by the CTG-method for an Al-Si-Mg alloy in torsion, compression and tension.61
Figure reprinted with permission from Elsevier.
The damage evolution model has been used in several studies in combination with
design of experiment (DOE) methodology to investigate the effect and relative
importance of several microstructural parameters on damage evolution.61-67 By using
the method to study the influence of damage on a component subjected to load it was
shown that the weight of the component could be significantly reduced without
increasing the amount of damage obtained in the component. 68 Recent work shows the
process of calibrating the ISV model for a specific alloy,69 and the model is proposed as
the basis for a new design paradigm called "Cradle-to-Grave Simulation-Based Design
with Multiscale Microstructure-Property Modelling",44 able to capture the entire life cycle
of a component from casting through heat-treatment etc. to in-service performance
(load response, fatigue life prediction, crash analyses etc.). This cradle-to-grave method
will in the following sections be referred to as the CTG method.
The CTG method has been applied to account for variations in microstructure,
formulated as an integrated framework for design under uncertainty with multiscale
modelling.70 The CTG method in combination with material uncertainties has also been
used for shape-optimisation of an automotive component.71 The results from
optimisation using the ISV material damage model were compared with the results from
optimisation using the standard plasticity model available in the commercial FEM
software by performing deterministic optimisations for minimum weight. It was shown
that though the two deterministic optimisations resulted in similar weight reductions,
the damage value obtained with the ISV model optimisation was only half the damage
value obtained with the standard plasticity optimisation.71
The three different simulation methods deal with material specific behaviour in
significantly different ways.
• The MMP method predicts component specific mechanical behaviour with local
variations for a wide range of alloys and transfers the information to the FEM simulation
• The FC method uses the functionality of FEM software to include consideration of
alloy specific material behaviour and a fracture parameter, information obtained from
material testing.
• The CTG method extends the functionality of the FEM software by incorporating a
micro-level damage evolution model that uses alloy specific material data obtained from
extensive material testing.
The different methods correspond to different ways of transferring information in the
process of predicting the mechanical behaviour of a cast component. Their application
are thus significantly different, which is schematically illustrated in Fig. 7. This is a result
of the different purposes for which the methods have been developed, and the different
approaches leads to different strengths and drawbacks for the different methods.
The MMP method is a development of the functionalities in casting simulation software
to predict local tensile material behaviour for general components in a wide range of
alloys. The behaviour prediction is based on simulations of the manufacturing process,
and does not need any additional data from material testing. The method has some
limitations, e.g. the effect of structural integrity is limited to the possibility to define a
quality parameter which determines the fracture strain. The approach in equation (3)
can be seen as a simplification of the approach in equation (2), where a susceptibility
index is used to characterise the material’s sensitivity to defects. The predictions of the
plastic behaviour, equations (5) and (6), are based on the Hollomon equation, which is
not able to accurately predict the plastic behaviour of all types of heat treated
aluminium alloys.72 The predictions are based only on Fe-content and SDAS, while other
microstructural parameters such as the characteristics of the Si-particles, are also
known to affect the plastic behaviour, and it is not taken into account that different Ferich phases affect the mechanical behaviour differently. The constants in the
relationships for the parameters of the Hollomon equation have been determined for ascast alloys, and the effect of heat treatment on these parameters have not been
numerically established. Since the method only provides data to the FEM simulation, no
consideration of different stress states is included in the FEM simulation, and no specific
consideration of skin effect has been reported. In general, the MMP method is thus
suitable to predict the mechanical behaviour of the material within as-cast components
of general geometries in a wide range of alloys.
Figure 7: A schematic illustration of the application of the
reviewed simulation methods.
The FC method is aimed at predicting the behaviour of thin-walled components of a
specific alloy subjected to crash-load. The material behaviour is described using alloy
specific hardening parameters, which need to be determined from material testing. No
direct relationship between variations in microstructure and mechanical behaviour is
included, but the fracture parameter may vary through-thickness to consider the skin
effect of die castings, and local variations of the fracture parameter can be used.
Structural integrity may be considered by defining different values of the fracture
parameter, or scaling the fracture parameter with melt-air contact time predicted by
casting simulation software. The melt-air parameter, determined in the pouring stage of
the casting process, is indirectly related to the formation and growth of oxide films. The
parameter is however not a direct measure of the total amount of defects, and its power
to predict the true location of defects is limited. Variations in structural integrity can in
the FC-method be considered through a statistical approach, equation (10), which is
similar to the particle fracture approach shown in equation (1). By using data from
different kinds of tests consideration of stress state dependence may be included in the
FEM simulation. Since the Cockcroft-Latham integral uses the current maximum
principle stress to determine damage evolution it is however not clear how damage
accumulation, e.g. in the case of repeated loading, is treated. The general use of the FC
method is limited by being based on shell elements, which is not appropriate for all
types of load and only suitable for thin-walled components. The FC method is thus
suitable for thin walled components of a specific alloy subjected to crash-loads of
general stress states.
The CTG method is developed for components of general geometry in a specific alloy
subjected to repeated loading. The method is highly involved in the FEM simulation by
determining total microstructural damage evolution as an ISV during the simulation, an
approach that makes the method also useful for cyclic loading. Si particle characteristics
and the size of the Si particles are accounted for in the damage evolution model in the
CTG method. The CTG method uses an initial volume fraction of defects, and may be used
in combination with statistical approaches to study the effect of various initial amounts
of defects. No connection to casting simulation software or specific consideration of skin
effect is however reported in the reviewed literature. Instead, global material
parameters, optionally with statistical variations in areas where experimental
measurements indicate large amount of defects, have been used. The possibilities of
casting simulation software to predict local variations in mechanical behaviour or areas
with a high risk for defects, as in the MMP method respectively the FC method, is thus
not taken into account. This is a drawback since damage evolution should be considered
in the design phase of the product development process, when no actual cast
components are available to enable experimental measurements of the location of
defects. The CTG-method can be used in combination with statistical approaches and
different optimisation approaches. The CTG-method is suitable for components of a
specific alloy of general geometry subjected to general loads.
To select a suitable approach for a specific simulation, the type of simulation to be
performed as well as the purpose of the simulation thus needs to be considered. In order
to perform a FEM simulation using the MMP method, a casting process simulation first
needs to be performed for the specific component. Several casting process related
parameters then need to be known in order to obtain a correct description of the
microstructure within the component, from which the mechanical behaviour is
determined. Both the FC method and the CTG method are highly dependent on
experimentally determined material parameters, but once these parameters have been
obtained the methods can be applied to other components of the same material. The
mechanical behaviour is thus not as component specific as in the MMP method, but is on
the other hand not dependent on a preceding casting process simulation. The FC method
is limited to thin-walled components subjected to crash load, while the CTG method is
applicable to general geometries subjected to a wider range of load types.
In order to perform accurate simulations of the mechanical performance of cast
aluminium components it is important to understand the mechanical behaviour of the
alloy. Three different approaches to consider mechanical behaviour of cast aluminium
alloys in FEM simulations have been studied.
• The MMP method predicts component specific local mechanical behaviour from
microstructural parameters obtained from a casting process simulation.
• The FC method uses layered shell elements and a fracture criterion to simulate
mechanical behaviour of and fracture evolution in thin-walled components.
• The CTG method uses a micro-mechanics based damage evolution model
implemented into the FEM simulation to predict damage and fracture evolution.
The MMP method is able to predict mechanical behaviour for a wide range of as-cast
alloys, while the FC method and the CTG method both require data obtained from
mechanical testing of the specific alloy to be used. Both the FC and the CTG methods
have been used in combination with statistical methods, and the CTG in combination
with optimisation methods. The three methods reviewed have been developed for
different purposes. To determine the appropriate approach and method for a specific
simulation and component the geometry of the component, the type of simulation to be
performed, the objective of the simulation as well as the availability of material data
must be considered.
The School of Engineering at Jönköping University is gratefully acknowledged for
financing the work.
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