Residual stresses in high pressure die castings
Box 2033, 550 02 Jönköping, Sweden
Phone: +46(0)36 - 30 12 00
swecast@swerea.se
http://www.swecast.se
c
2013, Swerea SWECAST AB
Author Report number: Date
Roger Svenningsson and Håkan Svensson 2013-004 2013-05-27
Sammanfattning
I detta arbete har olika metoder för att jämföra mätning av restspänningar genomförts. Både hålborrning och röntgendiffraktion har använts. En spänningsharpa valdes som artificiell komponent för att studera restspänningar i pressgjutna komponenter. Resultaten från mätningarna jämfördes sedan med simulering av restspänningar. En mindre känslighetsanlys genomfördes där olika parameterar varierade som var re-laterade till värmeövergången mellan gjutgods och form. Detta arbete visar tydligt att det går att förvänta sig en förhållandevis stor spridning vid mätningar av restspänningar i pressgjutgods. Detta är särskilt sant för ytspänningar samt områden där det existerar stora spänningsgradienter. Tryckspänningar i ytan var dominerande för alla valda områden. Huvudspänningarna ökade sedan inåt. Simuleringarna utvärderades både i en kvalitativ samt kvantitativ mening. Både relaxation under borrning samt spänningar
utvärder-ades. Det visade sig att det initiala värmeövergångstalet (h0) i kombination med en mycket väl upplöst
modell den första millimetern hade störst inverkan. Ett extremt högt h0gav överlag lägre spänningar i
ytan än vid ett lägre h0. Också spänningsgradienten in från ytan beskrevs också bättre med ett extermet
högt h0. h0hade dock ingen inverkan för spänningarna vid 1 millimeter. Restspänningsmätningar samt
simuleringar genomfördes också på två industriella komponenter, en kokill samt en pressgjuten. Dock var båda dessa efterbehandlade, en blästrad och den andra T6-behandlad, vilket omöjliggjorde jämförelser.
Summary
This study has compared different methods for measuring residual stresses in high pressure aluminium castings. The hole-drilling and X-ray diffraction method were used. A stress lattice were used. The results from the measurements were then compared with simulations of residual stresses. The effect of different heat transfer related parameters were investigated and correlated to measurements. It has in present work been shown that deviations in measured stresses is to be expected, especially at the surface and in positions where large stress gradients are present. Compressive stresses were the dominating stresses at the surface for all measuring points. The principle stresses then increased inwards. The simulations were based on both qualitative and quantitative aspects. Both relaxation of strains during drilling and stresses
were evaluated and compared to measurements. The initial heat transfer coefficient (h0) in combination
with a highly resolved model the first millimeter had the largest impact on the simulation results. The use
of an extremely high h0gave the best results, both from a qualitative and quantitative aspect. A high h0
gave lower stresses at the surface compared with a lower h0. The stress gradient inwards from the surface
were also in better conformity compared to a low h0. The stresses at 1 millimeter were not however
influenced at all from the h0. Simulations were also performed on two industrial components, one die
and one high pressure cast. However, they had been subjected to different post-processing steps after they were cast, one shoot peened and one T6-treated. Therefore no valid comparisons could be performed.
Table of Contens
1 Background 1
2 Introduction 1
3 Objectives and targets 1
4 Literature 2
5 Experiments 3
5.1 Artificial component . . . 3
5.2 Casting sequence . . . 3
5.3 Stress measurements . . . 4
6 Finite Element simulations 4 6.1 Boundary conditions . . . 5
6.2 Material properties . . . 5
6.3 Parametric study . . . 7
7 Results 8 7.1 Stress measurements . . . 8
7.2 Simulation thermal results . . . 8
7.3 Simulation stress results . . . 9
7.3.1 Strain results MP2 . . . 11 7.3.2 Stress results MP2 . . . 11 7.3.3 Stress results MP(1,3) . . . 12 7.3.4 Stress results MP4 . . . 12 8 Industrial application 16 8.1 Stress lattice . . . 16 8.1.1 Procedure . . . 16 8.1.2 Results . . . 16 8.2 Housing . . . 17 8.2.1 Procedure . . . 17 8.2.2 Results . . . 18 8.2.3 Discussion . . . 19 8.3 Cabin bracket . . . 20 8.3.1 Procedure . . . 20 8.3.2 Results . . . 20 9 Discussion 22 10 Conclusions 22 11 Future Work 23 Appendices 25
Appendix A Stress and strain results 25
List of Figures
1 Illustrating stress lattice used in experiment. . . 3
2 Temperature cycling at steady state in the fixed die. . . 4
3 Finite Element Model used for simulations. . . 5
4 Finite Element Model showing boundary conditions applied for the casting. . . 6
5 Heat transfer for quenching . . . 6
6 Illustrating mechanical behaviour of the lattice. . . 7
7 Measured stresses as function of depth at MP13. . . 9
8 Measured stresses as function of depth at MP2. . . 9
9 Measured stresses as function of depth at MP4. . . 10
10 Temperature after time in mould, left low HTC, right right HTC. . . 10
11 Thermal history at surface. . . 11
12 Principle stress at MP2 for RUN 1. . . 12
13 Principle stress at MP2 for RUN 3. . . 13
14 Strain relaxation at MP2 for (a) RUN 1 and (b)RUN 3. . . 14
15 Stresses at MP2 for (a) RUN 1 and (b) RUN 3. . . 15
16 Stress at measuring at, (a) point P2, (b) point P1 and P3 and (c) point P4 . . . 17
17 Illustrating (a) component with measurement equipment and (b) points for stress mea-surements . . . 17
18 Von Mises stress [MPa] . . . 18
19 Stress at measuring point (a) P1, (b) P2 and (c) point P3 . . . 18
20 Measured stresses in all measuring points. . . 19
21 Illustrating (a) component with measurement equipment and (b) points for stress mea-surements . . . 20
22 Von Mises stress [MPa] . . . 21
23 Stress at measuring point (a) P1, (b) P2 and (c) point P3 . . . 21
List of Tables
2 Thermo-physical properties for aluminium alloy used for simulation. . . 63 Mechanical properties for aluminium alloy used for simulation. . . 7
4 Material properties for dies. . . 7
5 Parameters in sensitivity analysis. . . 8
6 Surface stresses measured with X-ray diffraction. . . 8
1
Background
This project focused on residual stresses in high pressure die castings. An artificial component was first studied. Measurements of residual stresses were performed by different methods. Several heat transfer related parameters were studied by means of simulations. Measurements and simulations were also carried out on two industrial components. The project had a budget of 1.9 million SEK and was funded by Vinnova. Following companies were a part of the project.
Company Contact person
Metall Fabriken Ljunghäll AB Mikael Martinsson
Scania CV AB Cecilia Bergquist
Volvo Group Trucks Technology Niklas Köppen
Fundo Components AB Bo Mattsson
Novacast Systems AB Håkan Fransson
Finnveden Gjutal AB Jörgen Henriksson
Table 1: Participating companies in present project.
2
Introduction
Light weight castings can be made even lighter and cost-effective if the internal (residual) stresses created in the production process are considered in the product development phase. Effective simulation of resid-ual stresses and distortion of the castings need to be developed to obtain this. The simulation results also need to be taken into account early in the development process of the component. Reliable predictions of residual stresses in as cast and/or heat treated components are valuable for the industry. If problems due to distortions or detrimental in-service lifetimes of components can be predicted and avoided at an early stage, savings in time and money could be enormous. To be able to predict the development of residual stresses the characteristics of the processes and the materials must be well understood. The industry?s benefits of correct prediction and control of residual stresses are cost reduction due to less straightening of distorted castings, right design faster without costly tool changes late in pre-production and better designs of advanced castings with high technology content.
3
Objectives and targets
Following objectives and targets were defined for present project.
• Increased reliability of residual stress simulation to within 25 % error margin of measured stresses. • Guide-line of residual stress simulation in the product development process in the industry. • Knowledge base which can be used in other areas e.g. other aluminium alloys and heat treated
components.
• Reduces weight of at least 20 % of chosen objects.
4
Literature
High pressure die casting (HPDC) is used to produce high volume, near net shaped aluminium and magne-sium castings. Process simulations are today state of the art in the industry to optimize the HPDC-process, e.g. filling, solidification and cooling, defect predictions and to ensure an overall sound micro-structure of the casting. However, not much attention has been paid on simulation of residual stresses and distor-tions of HPDC-castings. Residual stresses are defined as stresses, which are in self equilibrium, without
any external applied loads. According to [1] residual stresses generally are induced in castings by three
different reasons; (i) hindered contraction because of different cooling rates within the casting (internal boundary conditions applied to the casting), (ii) hindered contraction due to mechanical resistance from the mould (external boundary conditions applied to the casting) and (iii) phase changes during cooling. In order to predict residual stresses and distortions in high pressure die castings accurate modelling of the heat transport between the casting and mould must be accomplished. The transient heat transfer for high pressure die casting is often illustrated by a short high initial heat transfer, which decreases rapidly to a low value in a short period of time. This behaviour can be explained by the following reasons. Heat transfer between the casting and the dies occurs at the contacting top surfaces of the asperities (assum-ing a rough surface on the micro scale) and by conduction through gas in the valleys between asperities. When the metal comes in to contact with the much colder mould the heat transfer between the liquid casting and mould is high due to a good contact situation, and a thin solidified film is formed. The sub-sequent pressurization stage will help to maintain the contact situation and a high heat transfer. Later, as the casting contracts and the pressure drastically decrease, due to gate freezing, this contact situation changes which results in a decrease of heat transfer. Eventually an air gap is formed and the heat transfer drastically decreases because it is only governed by conduction through the gas between the surfaces. Just
recently, the work performed in [2] showed by pressure measurements in the cavity that first decrease in
heat transfer was not related to air gap formation. During the rapid decrease in heat transfer they observed a unchanged pressure in the cavity. They explained that the reason for the drastic decrease was due to a reduced contact quality. At a later stage however, they observed a second reduction of heat transfer which could be attributed to the effect of air gap formation. Heat transfer coefficients for high pressure die cast-ings process have recently been published by [3], [4] and [5]. In the work performed in [3], temperature measurements on an industrial component were carried out. Their results showed a peak value of 42000
W/m2Kabove the liquids temperature. Between liquids and solidus the heat transfer was drastically
re-duced to a constant level of 400 W/m2Kat and below solidus. The results were derived by optimizing the
heat transfer coefficient with simulations performed with the commercial casting code MagmaSOFTTMat
a number of positions of the casting. In [4] measurements was performed on a stair like casting for a
similar aluminium alloy as in [3] and one magnesium alloy. They found that the peak value varied
be-tween 11000-20700 W/m2Kdepending on the thickness of the section. 20700 W/m2Kwas obtained for
a 5 mm thick section. To the author’s knowledge, only a few papers presents results for residual stresses
and distortions for high pressure die castings. In [6] sequential coupled thermo-mechanical simulations
were performed on two different geometries, one stress lattice and one V-shaped geometry, with fairly good results. They used the cutting method to measure the elastic strains. The influence of die
temper-ature, ranging from 140 to 260◦C, and closing time was investigated. No significant difference could
be observed for the stress lattice. Some differences could however be observed for the V-shaped
geom-etry. In [7] distortion (planarity) simulations were performed, on an industrial component. Their results
showed that the most important parameters where the heat transfer coefficient and the initial temperatures. Present study aims to investigate the influence of heat transfer coefficient on the residual stresses for high pressure aluminium die castings. Hole drilling method and X-ray diffractions measurements will be used. Both strain relaxation during drilling and stresses will be evaluated at different locations. A stress lattice was chosen as casting geometry. This type of geometry is well established and has frequently been used for studying residual stresses in castings (e.g. [8] and [9]).
List of symbols
ΓSymx X-symmetry plane
ΓSymz Z-symmetry plane
σ Stress
σy Yield stress
h Heat transfer coefficient
h0 Initial heat transfer coefficient
kgas Conductivity of gas
lgap Gap between casting and mould
surfaces
lmax Maximum limiting gap for heat
transfer
lmin Minimum limiting gap for heat
transfer
ui Translation in i-direction
5
Experiments
5.1
Artificial component
Commonly used high pressure die casting alloy, EN AC-46000,was chosen for the casting trials. The inserts were produced of the hot work tool steel H13 Premium. A stress lattice according to figure 1 (a)
was chosen for the experiments. As stated by [10], stress measurements with the hole drilling method
is only valid for σ < (0.6− 0.7) × σy, where σ denotes stress and σy the yield stress of the material.
This is because stress concentrations at the drilling hole might produce plastic deformation due to stress concentrations. Therefore primarily simulations needed to be performed to ensure that the stress did not exceed the limiting stress. These simulations were performed with the commercial finite element casting
code ProCASTTM. The final dimensions of the stress lattice, which had a constant thickness of 5 mm, are
shown in figure 1 (b).
(a) Stress lattice used in experiment. (b) Overall dimensions of the stress lattice.
Figure 1: Illustrating stress lattice used in experiment.
5.2
Casting sequence
Casting trials were performed the 19th of January 2012 at Ljunhäll AB, Södravi, in Sweden, in an 1350 ton cold chamber machine. To ensure that the castings were casted during a steady state condition, temperature readings were performed. Thermocouples, ungrounded K-element, were placed in the fixed die approximately 5-7 mm from the surface. The temperature readings at steady state is shown in figure
2. Because of no internal cooling of the dies a small continuous increase in temperature (∆T < 5◦C)
during steady state for each cycle were observed. After the castings were removed from the die they were
of cooling had any impact on the formation of residual stresses. A total of 30 casting were produced for stress measurements. 0 20 40 60 80 100 120 140 160 180 200 220 240 260 280 300 110 120 130 140 150 160 170 180 190 200 Time [s] Temper ature [ ◦C] Pos. MP2 Pos. MP1
Figure 2: Temperature cycling at steady state in the fixed die.
5.3
Stress measurements
The hole-drilling method was chosen as the primary method for measurements of residual stresses. The measurements were performed according to ASTM E837-08 standard using strain gauge rosettes. The hole-drilling was performed in intervals of 0.05 mm to a depth of 2 mm. A total of eight stress lattices were evaluated the hole-drilling method. Also X-ray diffraction measurements were performed in order to compare the two measuring methods. Three points (MP1-MP4), illustrated in figure 1 (b), was chosen for evaluation. Stress measurements with the hole-drilling method were performed at Swerea SWECAST and X-ray diffraction measurements were performed at two different companies. All results from the
measurements with the hole-drilling method can be found in [11].
6
Finite Element simulations
Residual stress simulations for castings can be performed in two ways, either sequentially coupled or as fully coupled thermo-mechanical simulations. The uncoupled simulation consists of two linked simula-tions. First the transient thermal simulation is solved. The thermal history each node in the model is then used as thermal load in the subsequent mechanical analysis. In the mechanical simulation considerations of contact between casting and dies needs to be taken into account. In a fully coupled thermal-mechanical simulation both the thermal, mechanical and the contact parts are solved in each increment. All stress simulations in present work were performed as fully coupled simulations with the general Finite Element code Abaqus (version 6.9 and 6.10) and ProCAST (version 2011). The Finite Element Model used for simulations is shown in figure 3 and 4. The model consists of a total of 76 129 coupled first order ele-ments (C3D8T and C3D6T). 18 820 eleele-ments belong to the lattice and 57 309 to the mould. As can be seen very thin elements where used for the first milli-meter on the drilling side. Five elements where used for simulating removal of material during drilling. Several simplifications were made for the simulations. First, symmetry was used and only a quarter of the casting was modelled. Furthermore, no fluid flow sim-ulation was performed before stress simsim-ulation, i.e. constant temperatures were used as initial conditions for both the casting and mould. Pressurizing of the casting and the heat generated from the drilling were left out.
Figure 3: Finite Element Model used for simulations.
6.1
Boundary conditions
Fully thermo-mechanical simulation makes it possible to use a gap dependent heat transfer coefficient. In this work the heat transfer between the casting and the mould was controlled by the step wise function according to equation 6.1, [7]. h0and h was the initial and actual heat transfer coefficient depended on the
gap lgap. lminand lmaxwere limiting gaps controlling the regime of heat transfer. kgaswas the conductivity
of gas in the gap.The use of a limiting gap was needed because of convergence problems.
h= h0 for 0≤ lgap< lmin
h=kgas
lgap for lmin≤ lgap≥ lmax
h= 0 for lgap> lmax
(6.1)
After the casting was removed from the dies (the die opened at 13.5 s) it was either water quenched or left to cool in air down to room temperature. or the water quenching the convective heat transfer according to
figure 5 was used [12], which includes both film and boiling stages. No attempts were made to verify the
thermal history of the quenching. For the air cooled castings a convective boundary conditions was set
to 10 W/m2K. The mechanical boundary conditions are shown in figure 4 and equation 6.2. Symmetry
was used in both x and z directions. During time spent in mould no other constraints were applied to the casting except for contact (PRESSURE OVERCLOSURE=HARD). A frictionless contact was used between the casting and mould and a friction coefficient of 0.1 between the dies. After removal of the casting from the dies a translation constraint was applied in the y-direction at point o to avoid rigid body motion. No clamping forces were applied to the model.
ux= 0 on plane ΓSymx, at all time
uz= 0 on plane ΓSymz, at all time
uy= 0 at point O, after knock out
(6.2)
6.2
Material properties
Lack of available and reliable material data constant properties were used. Data used in present work are presented in tables 2 and 3 for the casting alloy. The thermo-physical properties were taken from
ProCASTTMdata-base where κ is the conductivity, ρ density , CPspecific heat, LH latent heat, Tliqand
Tsol liquids and solidus respectively. For the mechanical properties thermal expansion CT E, Young’s
modulus E and poisson ratio µ were taken from ProCASTTMdata base for a similar alloy due to lack of
approx-ΓSymx
ΓSymz
O
Figure 4: Finite Element Model showing boundary conditions applied for the casting.
0 50 100 150 200 250 300 350 400 450 500 0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000 9,000 10,000 [◦C] [W /m 2× ◦C] Quenching HTC
Figure 5: Heat transfer for quenching
imated at high temperatures according to recommendation from ProCAST user manual. A von Mises strain rate independent material model with multi-linear hardening were used as material model. In fig-ure 6 the stress-strain relation for the lattice is shown.
T (◦C) κ (W/m◦C) ρ (kg/m3) C P (J/kg◦C) LH (J/kg) Tliq (◦C) Tsol (◦C) 50 169 2680 955 367000 588 508 100 169 2680 955 200 169 2680 955 300 169 2680 990 400 169 2680 1035 500 169 2680 3460 508 162 2677 2250 588 78 2500 1303 600 78 2500 1350
T (◦C) CT E (−) E (Pa) µ (−) σyield(Pa)
50 2.19E-05 7.30E+10 0.367 1.50E+08
100 2.19E-05 7.30E+10 0.367 1.47E+08
200 2.19E-05 6.63E+10 0.367 1.18E+08
300 2.19E-05 4.79E+10 0.367 1.00E+08
400 2.52E-05 3.50E+10 0.367 4.50E+07
500 2.64E-05 1.70E+10 0.367 8.00E+06
508 2.60E-05 1.60E+10 0.38 5.00E+06
588 2.31E-05 6.70E+08 0.461 5.00E+06
600 2.31E-05 5.87E+07 0.49 5.00E+06
Table 3: Mechanical properties for aluminium alloy used for simulation.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 0 20 40 60 80 100 120 140 160 180 200 220 240 Strain × 10−2[-] Stress [MP a]
Figure 6: Illustrating mechanical behaviour of the lattice.
T(◦C) κ (W/m◦C) ρ (kg/m3) CP (J/kg◦C) E (Pa) µ (−) CT E (-) 21 42 7740 457 2.3010E+11 0.271 1.57E-05 150 35 7690 529 2.3010E+11 0.271 1.58E-05 371 31 7605 658 2.2400E+11 0.271 1.59E-05 500 30 7558 745 2.0600E+11 0.271 1.61E-05 650 30 7493 897 1.7800E+11 0.271 1.39E-05
Table 4: Material properties for dies.
6.3
Parametric study
A minor sensitivity analysis was performed to evaluate the effect of heat transfer on the residual stresses.
The parameters chosen for evaluation in this work was the initial heat transfer coefficient h0, the
limit-ing distance lminaccording to eq. 6.1 and the initial casting temperature. These parameters were varied
no: h0(W /m×◦C) lmin(µm) Tcast (◦C) Cooling Run 1 7000 20 600 Water Run 2 7000 40 600 Water Run 3 60000 20 600 Water Run 4 60000 40 600 Water Run 5 60000 20 660 Water Run 6 7000 20 660 Water Run 7 7000 20 600 Air Run 8 60000 20 600 Air Run 9 20000 20 600 Water Run 10 20000 5 600 Water
Table 5: Parameters in sensitivity analysis.
7
Results
7.1
Stress measurements
In table 6, surface stress measurements, with the X-ray diffraction method are presented. Measured stresses for company A is in the (x) longitudinal and (y) transverse directions. Company B measured principle stresses. So therefore the stresses can not be compared directly, except at material point MP2 where a biaxial stress state is present with the same directions for both principle and directional stresses. In figure 7 to 9 stresses are shown as a function of depth for each material point. As can be seen, for MP13, there is a large scatter in measured data. Both methods shows compressive stresses at the surface. Stresses from hole drilling shows an increase in stresses inwards, while the X-ray results remain almost constant in depth. For MP2 the near surface stresses are in the same magnitude for both methods. The X-ray measurements performed by company B follows the same trend and magnitude as the hole drilling, i.e. increasing inwards. This is also true for the stress for company A up to 0.2 mm. After that the stresses decreases. For MP4 only hole drilling were performed for in depth stresses. Large deviations can be seen over the entire depth. But the same trend as for previous material point are also valid for MP4, stresses increases as a function of depth.
(MPa) (MPa)
MP2
Company A -27 (longitudinal) -48 (transverse) Company B 3.8 (max. principle) -46 (min. principle) MP1,3
Company A -27 (longitudinal) -48 (transverse) MP4
Company A -36 (longitudinal) -80 (transverse)
Table 6: Surface stresses measured with X-ray diffraction.
7.2
Simulation thermal results
Thermal results are shown in figure 10 for RUN 1 and RUN 3 at the time for casting ejection. As can be seen the temperature is quiet similar. In figure 11 the thermal history for a surface node at MP2 for RUN 1 and RUN 3 is shown. It can be noticed that the temperatures differs to a large extent during the first two seconds. The simulation with the high heat transfer have a drastic drop in temperature at the surface
−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −80 −70 −60 −50 −40 −30 −20 −10 0 10 20 30 40 50 Depth (mm) Stress (MP a) Max princ HD Min princ HD Longit. MP1 C-A Transv. MP1 C-A Longit. MP3 C-A Transv. MP3 C-A
Figure 7: Measured stresses as function of depth at MP13.
−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −80 −60 −40 −20 0 20 40 60 Depth (mm) Stress (MP a) Max princ HD Min princ HD Max princ XRD C-B Min princ XRD C-B Longit. XRD C-A Transv. XRD C-A
Figure 8: Measured stresses as function of depth at MP2.
during the first tens of a second. As time progress for RUN 3 the rate of heat loss decreases. RUN 1 also shows an immediately fast decrease in temperature initially, but not to the extent as RUN 3 for obvious
reasons. At 4 seconds the difference is only about 40◦Cand at 8-10 seconds the temperature is almost
the same.
7.3
Simulation stress results
Principle stress results, at MP2, for RUN 1 and RUN 3 are shown in figure 12 and 13 at the finial time. From these contour plots it can be noticed that the global stress distribution is similar for both RUN 1 and RUN 3 even though RUN 1 generally shows a higher stress level. Considering the minimum principle stress gradient into the casting from the drilling side it can be seen that RUN 3 shows a lower stress level at the surface and a more rapid stress gradient into the casting for the first millimeter compared to RUN 1.
−0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −100 −80 −60 −40 −20 0 20 40 Depth (mm) Stress (MP a) Max princ HD Min princ HD
Figure 9: Measured stresses as function of depth at MP4.
NT11 +1.800e+02 +1.858e+02 +1.917e+02 +1.975e+02 +2.033e+02 +2.092e+02 +2.150e+02 +2.208e+02 +2.267e+02 +2.325e+02 +2.383e+02 +2.442e+02 +2.500e+02 X Y Z NT11 +1.800e+02 +1.858e+02 +1.917e+02 +1.975e+02 +2.033e+02 +2.092e+02 +2.150e+02 +2.208e+02 +2.267e+02 +2.325e+02 +2.383e+02 +2.442e+02 +2.500e+02 X Y Z
Figure 10: Temperature after time in mould, left low HTC, right right HTC.
This holds also for the maximum principle stress. Also worth to notice is that RUN 1 shows more rapid increase in maximum principle stress after the first millimeter seen from the drilling side of the casting. The use of a model with one side with a denser mesh also facilitates evaluation of the mesh dependency. In this model the elements on the drilling side had a thickness of 0.2 mm and the opposite side 1 mm thick elements. From the plots it is clear that the element size has impact on the simulated stresses for both RUN 1 and RUN 3. Generally lower stresses are shown at the drilling side of the lattice. For the analysis performed in NovaStress the reader is reffered to appendix B. No attempts have been made to evaluate these results in depth. However, these results are presented to give the Nova user some indications about the influence of chosen parameters.
0 2 4 6 8 10 12 14 50 100 150 200 250 300 350 400 450 500 550 600 650 Time [s] Temper ature [ ◦C]
Thermal readings at surface
Surface node high HTC Surface node low HTC
Figure 11: Thermal history at surface.
7.3.1
Strain results MP2
The simulation of drilling was performed by simply remove layers of elements in five steps to a depth of 1 millimeter at MP2. The relaxation of strains where then measured in the same direction and at the middle as the gauges for drilling. Strain and stresses were compared in both a qualitative and quantitative manner, i.e. both behaviour and levels were compared. All results are summarized in appendix A. The most important results will be illustrated here. Overall there is a fairly good agreement between measured and simulated strains from a quality point of view, the behaviour of the strain path during relaxation for both e(1,3) and e2 are captured in a reasonable way for all simulations. But from a quantitative point of
view the initial heat transfer coefficient, ho, seems to have the major effect of relaxed strains, see figure
24. For the direction e2 only minor differences between low and high values for hocan be observed. But
for the directions e(1,3) a significant difference can be observed. While the relaxed strains fora high a ho
are within the errors bars at 1 mm, a low horesults in strains outside the error bars at the same distance.
The effect of l0is shown to have only minor influence of strain relaxation, see figure 24 (a-d) in appendix
A. The parameter TCastinghave a considerable influence when hois high but no influence when hois low,
figure 24 (e-f) in appendix A.
7.3.2
Stress results MP2
Measured and simulated stresses are shown at MP2 in figure 15 for RUN 1 and RUN 3. As can be seen both hole drilling and X-ray diffraction measurements shows similar results. It can also be noticed a large
deviation in measured stress, especially up to a distance of 0.5 mm. The results shows that hohas a large
impact of simulated surface stresses. For the low hothe stress at surface is considerable higher than for
the simulations performed with a high ho, figure 15. A low hoseems not capable of capturing the stress
gradient for the principle stresses during the first mm of the lattice in the same way as a high ho(in the
range 20 000 - 60 000 W/m2
×◦C). However, both a low and a high hoare capable of capture the first
principle stress level at a depth of 1 mm. But for the third principle stress non of the simulation are able to
reproduce the stress level at 1 mm. The parameter l0does not have any influence of the simulated stresses.
TCastinghas also no influence of the stresses with a low ho. But for a high ho, TCastinghas influence in terms
of higher stresses at the surface and flatter stress gradients. All stress results for MP2 are presented in figure 25 and 26 in appendix A.
(Avg: 75%) S, Min. Principal −2.000e+07 −1.600e+07 −1.200e+07 −8.000e+06 −4.000e+06 +0.000e+00 +4.000e+06 +8.000e+06 +1.200e+07 +1.600e+07 +2.000e+07 −2.465e+08 X Y Z (a) (Avg: 75%) S, Max. Principal +0.000e+00 +7.000e+06 +1.400e+07 +2.100e+07 +2.800e+07 +3.500e+07 +4.200e+07 +4.900e+07 +5.600e+07 +6.300e+07 +7.000e+07 −1.116e+07 +1.384e+08 X Y Z (b)
Figure 12: Principle stress at MP2 for RUN 1.
7.3.3
Stress results MP(1,3)
For material point MP(1,3), illustrated in 27 and 28 in appendix A, the same influence on the stress
gradient can be observed as the results for MP2. A low h0 are unable to capture the stress gradient
into the material. For the simulations with a low h0a zero or a slightly negative stress gradient can be
observed. But for a high h0a positive stress gradient is observed. Overall a high h0gives more accurate
results compared with a low h0, both in a qualitative and quantitative manner. An inter-medium value
of h0(20 000 W/m2×◦C) gives the same influence of the stresses as for MP2, i.e. gives higher surface
stresses at the same time as the gradient is flatten out to some extent. The parameter l0seems to have no
or only minor influence. However, an increase of TCastingto 660◦Cat the same time as h0is high seems
to flatten the stress gradient into the surface of the lattice.
7.3.4
Stress results MP4
The same trend as for previous material points holds for MP4, see figure 29 in appendix A. A low h0
gives a flatter stress gradient and a high h0a steeper gradient. Non of the simulations, except RUN 5 with
a high h0and TCastingseems to reproduce the minimal stress levels. All other simulations shows lower
stress results compared to measurements. However, the stresses predicted with a high h0 captures the
minimal stress levels in a better way than with a low h0. The final stress at 1 mm for maximum principle
(Avg: 75%) S, Min. Principal −2.000e+07 −1.600e+07 −1.200e+07 −8.000e+06 −4.000e+06 +0.000e+00 +4.000e+06 +8.000e+06 +1.200e+07 +1.600e+07 +2.000e+07 −2.401e+08 X Y Z (a) (Avg: 75%) S, Max. Principal +0.000e+00 +7.000e+06 +1.400e+07 +2.100e+07 +2.800e+07 +3.500e+07 +4.200e+07 +4.900e+07 +5.600e+07 +6.300e+07 +7.000e+07 −1.546e+07 +1.361e+08 X Y Z (b)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 −6 −4 −2 0 2 4 6 h0= 7000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Str ain (-) × 10 − 5 e1 e2 e3 sim e1 sim e2 (a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 −6 −4 −2 0 2 4 6 h0= 60 000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Str ain (-) × 10 − 5 e1 e2 e3 sim e1 sim e2 (b)
0 0.2 0.4 0.6 0.8 1 1.2 1.4 −80 −60 −40 −20 0 20 40 60 h0= 7000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises Max princ XRD Min princ XRD (a) 0 0.2 0.4 0.6 0.8 1 1.2 1.4 −80 −60 −40 −20 0 20 40 60 h0= 60 000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises Max princ XRD Min princ XRD
(b)
8
Industrial application
From an industrial point of view is it not realistic to use huge amount of elements in the thickness of any component due to computational time. Therefore the Finite Element models used here were meshed with fewer elements in the thickness compared to the stress lattice. Also, as normal industrial components usually are of complex nature, the use of brick and wedge elements are not always possible. The use of tetrahedral elements might be necessary. Therefore a combination of tetrahedral and wedge elements was chosen for the industrial components. All stress simulations in this section were performed with the
Finite Element based code ProCASTTM(version 2011) as a fully coupled thermo-mechanical simulations.
The lattice was first analysed. Then followed simulations of two industrial components, one die and one high pressure die cast.
8.1
Stress lattice
The model of the stress lattice contained of a total of 1 600 000 coupled first order tetrahedral elements. 594 000 belonged to the lattice and 1 012 000 to the dies.
8.1.1
Procedure
The analysis procedure was divided into four cases: 1. Thermal cycling
2. Solidification and cooling in mould 3. Casting removal from the tool and cooling 4. Removal of filling system
The thermal cycling was performed with 10 cycles and with the sequence shown in table 7. The tempera-ture of the tool was tuned against measured temperate on the tool shown in figure 7 by adjusting the heat transfer between the tool to the surroundings and spray coefficients. The heat transfer between cast and
tool was defined as 4000 W/m2Kfor liquids and 1000 W/m2Kfor the solidus phase. Casting temperature
has been defined as 588◦C while the casting is small compared to the HPDC machine.
Sequence Time (s)
Start 0
Cooling in die 13.5
Die opening 15.5
Casting removal 21
Spraying fixed die 40
Die close 60
Total cycle time 63.5
Table 7: Approximative casting cycle in experiments.
8.1.2
Results
In figure 16 the results of the residual stress analysis and stress measured at the points shown in figure 1(b).
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −80 −60 −40 −20 0 20 40 60 Depth (mm) Stress (MP a) MP2 Max princ HD Min princ HD von Mises HD Sim von Mises
(a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −80 −60 −40 −20 0 20 40 60 Depth (mm) Stress (MP a) MP1 and MP3 Max princ HD Min princ HD von Mises HD Sim von Mises
(b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −100 −80 −60 −40 −20 0 20 40 60 80 100 Depth (mm) Stress (MP a) MP4 Max princ HD Min princ HD von Mises HD Sim von Mises
(c)
Figure 16: Stress at measuring at, (a) point P2, (b) point P1 and P3 and (c) point P4
8.2
Housing
The model of the housing contained a total of 1 543 000 coupled first order tetrahedral elements, 338 000 wedge elements. 355 000 tetrahedral elements belonged to the casting and 850 000 to the dies.
8.2.1
Procedure
The analysis procedure are divided into three cases: 1. Thermal cycling
2. Solidification and cooling in dies
3. Casting removal from the tool and cooling
Thermal cycling was performed for 10 cycles. The temperature of the tool was tuned get realistic values of the tool by adjusting the heat transfer between the dies to the surroundings and spray coefficients. The
heat transfer between cast and dies was defined as 4000 W/m2Kfor liquids and 1000 W/m2Kfor solidus
phase. Casting temperature has been defined as 588◦C.
(a) (b)
8.2.2
Results
In figure 18 the von Mises stress results shown.
Figure 18: Von Mises stress [MPa]
In figure 19 results of the residual stress analysis are shown at the points shown in figure 17(b). The measured data was based on two measurements in each point. As can be seen there is no large difference of the stress results down to a depth of 0.7 mm. The shot-peening of the surface of the component has caused -100 down to -200 MPa compressive stresses at the depth of 0.1 to 0.3 mm. The shot-peened surface was rather heavily grinded using abrasive paper in order to get good gluing contact of the strain gauges which might affect the stress results close to the surface. Shot-peening of the surface was not included in the simulation. The measured stresses shows tendency to reach the simulated stress at a depth of 0.9-1 mm for measuring point 1 and 2.
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −200 −150 −100 −50 0 50 100 150 200 Depth (mm) Stress (MP a) Max princ HD Min princ HD von Mises HD sim von Mises
(a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −200 −150 −100 −50 0 50 100 150 200 Depth (mm) Stress (MP a) Max princ HD Min princ HD von Mises HD sim von Mises
(b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −200 −150 −100 −50 0 50 100 150 200 Depth (mm) Stress (MP a) Max princ HD Min princ HD von Mises HD sim von Mises
(c)
8.2.3
Discussion
As it can bee seen in figure 20 the shot-peening of the component caused compressive stress at the surface. As previous stated stresses evaluated by the hole-drilling method should not exceed 60 to 70 % of the local
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −200 −150 −100 −50 0 50 100 150 Depth (mm) Stress (MP a) Max princ HD Min princ HD von Mises HD
Figure 20: Measured stresses in all measuring points.
yield stress. This is due to avoid local yielding that is caused by the holes stress raising effect. However, in a radial uniform planar stress field holes does not act as a stress raiser.
8.3
Cabin bracket
The model of the cabin bracket contained of a total of 745 000 coupled first order tetrahedral elements. 141 000 wedge elements and 140 000 tetrahedral elements belonged to the casting and 468 000 tetrahedral elements to the dies.
8.3.1
Procedure
The analysis procedure were divided into four cases. 1. Thermal cycling
2. Tilt, solidification and cooling in dies
3. Casting removal from the tool and further cooling 4. Removal of filling system
The heat transfer between the casting and dies was defined as 2000 W/m2Kfor liquids and 1000 W/m2K
for solidus phase. Casting temperature were set to 720◦C.
(a) (b)
Figure 21: Illustrating (a) component with measurement equipment and (b) points for stress measurements
8.3.2
Results
In figure 22 the von Mises stress results are shown.
In figure 23 the results of the residual stress analysis at the positions shown in figure 21(b). The measured data was based on one measurement at each point. As it can be seen for point 1 and 2 both simulations and measured stresses have the same stress direction but not the same stress levels. For point 3 however, both simulations and measured stresses show the same magnitude but not the same directions.
Figure 22: Von Mises stress [MPa] 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −80 −60 −40 −20 0 20 40 60 80 100 120 140 Depth (mm) Stress (MP a) Max princ HD Min princ HD von Mises HD sim Max princ sim Min princ sim von Mises
(a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −60 −40 −20 0 20 40 60 80 100 120 Depth (mm) Stress (MP a) Max princ HD Min princ HD von Mises HD sim Max princ sim Min princ sim von Mises
(b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 −60 −40 −20 0 20 40 60 80 100 Depth (mm) Stress (MP a) Max princ HD Min princ HD von Mises HD sim Max princ sim Min princ sim von Mises
(c)
9
Discussion
A comparison between measuring methods for residual stresses have been carried out. Both the hole drilling and X-Ray diffraction methods predicts compressive residual stresses at the surface. The stresses then generally increase into the casting. It is obvious from the measurements results that there exists a large scatter in the measured data, both within one method and between methods. This is especially clear when surface stresses are considered. The measured stresses where fairly consistent between the hole drilling and the X-Ray diffraction methods. But it is hard to draw any clear conclusions because of scatter. At position MP2, which has a rather simple stress state without large stress gradients the deviations in the measurements were lower compared to the positions MP1,3 and MP4 where stress gradients and a more complex stress state are present. The larger deviation can probably be attributed to a more complex stress state and lager stress gradients for these positions. Also worth to notice is that no significant differences could be observed between water quenched and air cooled lattices. A probably cause was that a rather uniform temperature due to constant thickness in combination with a low temperature at the start of quenching.
In this work material data, collected from different sources, were held constant due to lack available data or possibilities for testing the material. This needs to be emphasized, because it is the probably the largest source to errors in the simulations. It is well known that the mechanical data effect the residual stresses. However, the simulation shows overall fairly good agreement with the measurements from a quality point of view. The parameters which had the most influence was the heat transfer coefficient, all other parameters had only minor or no influence of simulated stresses. A high initial heat transfer coefficient in combination with thin elements at the surface seems to give more accurate surface stresses than a lower heat transfer coefficient, which is unable to capture the compressive stresses. This may be attributed to that a thin skin solidifies first at the surface, producing initial tensile stresses. Later when the material in the bulk of the lattice solidifies the surface stresses goes to compression while the bulk stresses goes to tensile. At MP2, where a bi-axial stress state is present, the simulations gives the best results. Interesting to notice is however that the simulations captures the stresses at MP13 in a fairly good way even if the conditions for the hole-drilling method not is fulfilled (an infinite long plate). At MP4 the simulations generally shows large deviations between measured and simulated stresses at all depth. As discussed earlier, the large stress gradient is probably the cause of the deviation. For the stresses at 1 millimeter the heat transfer coefficient seems to have only minor relevance. All simulations give approximately the same level of stresses. This is most probably due to that during the cooling of the bulk material the rate of heat transfer is almost the same. From an industrial point of view this is an important finding. Depending on if the surface stresses or bulk stresses are of interest different modelling approached may be necessary. Considering the industrial components larger deviation were observed than for the stress lattice. This may be attributed to different reasons. The main reason is however, for both of the components, probably due to that they exhibited post processing steps after casting. The housing was shoot-peened and the cabin bracket was T-6 treated. This made comparisons impossible. A
10
Conclusions
Present study has shown the importance of modelling of the heat transfer coefficient on formation of residual stresses in high pressure die casting for an artificial component. A minor DOE were performed to investigate the influence of initial heat transfer coefficient, limiting gap, initial temperature of the casting and type of cooling after ejection. Constant material data, gathered from software data-bases and literature were used. The results were evaluated in both a qualitative and quantitative manner with reasonable results depending on the parameter configuration. Simulations of residual stresses of two industrial components were then performed. Following conclusions can be drawn from present work.
• Generally compressive surface residual stresses were present at all points evaluated. A positive stress gradient inwards the material at all points was measured.
• Both X-Ray diffraction and hole drilling measurements gave fairly consistent results for MP2. • Large deviations in stress measurements can be expected if large stress gradients are present,
• No significant difference could be observed in terms of residual stresses for lattices subjected either to water quenching or air cooling after ejection for the stress lattice. The simulated stresses are in fully agreement with this.
• Simulation of strain relaxation during drilling by removal of layers of elements can be considered as satisfactory. Good agreement between measurements and simulations were achieved.
• The initial heat transfer coefficient, h0, has a large impact, both in terms of relaxation of strain
during drilling and on the surface residual stresses. A high initial heat transfer gives a more proper stress gradient into into the casting whereas a low gives a flatter gradient. Using a intermediate
value of 20 000 W/m2×◦Cincrease surface residual stresses and flattens out the stress gradient
compared to a high h0.
• The initial heat transfer coefficient, h0, has only a minor or zero impact on the stress levels 1 mm
into the surface, i.e. it mostly effect the surface stresses.
• The simulated stresses in the industrial components were not possible to compare because of dif-ferent post processing steps after casting.
• Simulations of more complex castings it is recommended to use thermal cycling in order to capture the temperature gradient in the tool.
• The shot-peening of the surface of one component has caused -100 down to -200 MPa stress in the depth of 0.1 to 0.3 mm and a stress below zero until a depth of 0.7 mm.
11
Future Work
Present study has shown the importance of heat transfer modelling. To get more confidence in the simula-tions the need for careful temperature measurements at or near the surface of the casting is essential. The element resolution of the first mm in relation with the initial h0needs also to be studied and verified. Also,
the need of reliable and verified material data is vital, also strain rate dependent, at high temperatures. Therefore it is suggested that a large research program to derive these data for commonly uses aluminium alloys. At last, the effect of shoot peening would be valuable to investigate.
References
[1] T.S.32, Internal stresses in castings, Institute of British Fundrymen 45 (1952) 179–189.
[2] G. Dour, M. Dargusch, C. Davidson, A. Nefd, Development of a non-intrusive heat transfer coeffi-cient gauge and its application to high pressure die casting effect of the process parameters, Journal of Materials Processing Technology 169 (2005) 223–233.
[3] L. Alastair, T. David, A. Cecil, W. David, Determination of the heat transfer coefficient at the met-aledie interface for high pressure die cast alsi9cu3fe, Applied Thermal Engineering 31 (2011) 3996– 4006.
[4] Z. P. Gou, S. M. Xiong, B. C. Liu, M. Li, J. Allison, Effect of process parameters, casting thick-ness, and alloys on the interfacial heat-transfer coefficient in the high-pressure die-casting process, Metallurgical and Materials Transactions A 39A (2008) 2896–2905.
[5] A.Hamasaiid, G. Dour, T. Loulou, M. Dargusch, A predictive model for the evolution of the ther-mal conductance at the casting-die interfaces in high pressure die casting, International Journal of Thermal Sciences 49 (2010) 365–372.
[6] P. Hofer, E. Kaschnitz, P. Schumacher, Simulation of distortion and residual stress in high pressure die casting, modelling and experiments, Materials Science and Engineering 33 (2012) 1–8. [7] G. Campatelli, A. Scippa, A heuristic approach to meet geometric tolerance in high pressure die
casting, Simulation Modelling Practice and Theory 22 (2012) 109–122.
[8] E. Gustafsson, M. Hofwing, N. Strömberg, Simulation and measurement of residual stresses in a stress lattice, in: Proceedings of 2nd International Conference on Simulation and Modelling of Metallurgical Processes in Steelmaking, 2007.
[9] E. Johnson, T. Watkins, J. Schmidlin, S. Dutler, A benchmark study on casting residual stress, Metallurgical and Materials Transactions A 43A (2011) 1487–1496.
[10] N. Rossini, M. Dassisti, K. Benyounis, A. Olabi, Methods of measureing residual stresses in com-ponents, Materials and Design 35 (2012) 572–588.
[11] H. Svensson, Restspänningsmätning aluminium harpor, unpublished work at Swerea SWECAST (2012).
[12] R. Svenningsson, Quenching of an reinforced aluminium disc brake, unpublished work at Swerea SWECAST (2010).
[13] A. Garza-Delgado, A study of casting distortion and residual stresses in die casting, Ph.D. thesis, The Ohio State University (2007).
Appendix A
Stress and strain results
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 −6 −4 −2 0 2 4 6 h0= 7000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Str ain (-) × 10 − 5 MP2 - Run 1 e1 e2 e3 sim e1 sim e2 (a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 −6 −4 −2 0 2 4 6 h0= 7000 W/m2K lmin= 40 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Str ain (-) × 10 − 5 MP2 - Run 2 e1 e2 e3 sim e1 sim e2 (b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 −6 −4 −2 0 2 4 6 h0= 60 000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Str ain (-) × 10 − 5 MP2 - Run 3 e1 e2 e3 sim e1 sim e2 (c) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 −6 −4 −2 0 2 4 6 h0= 60 000 W/m2K lmin= 40 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Str ain (-) × 10 − 5 MP2 - Run 4 e1 e2 e3 sim e1 sim e2 (d) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 −6 −4 −2 0 2 4 6 h0= 60 000 W/m2K lmin= 20 µm Tcasting= 660◦C Ttool= 160◦C Depth (mm) Str ain (-) × 10 − 5 MP2 - Run 5 e1 e2 e3 sim e1 sim e2 (e) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 −6 −4 −2 0 2 4 6 h0= 7000 W/m2K lmin= 20 µm Tcasting= 660◦C Ttool= 160◦C Depth (mm) Str ain (-) × 10 − 5 MP1 and MP3 - Run 6 e1 e2 e3 sim e1 sim e2 (f)0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 7000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP2 - Run 1 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises Max princ XRD Min princ XRD (a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 7000 W/m2K lmin= 40 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP2 - Run 2 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises Max princ XRD Min princ XRD (b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 60 000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP2 - Run 3 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises Max princ XRD Min princ XRD (c) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 60 000 W/m2K lmin= 40 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP2 - Run 4 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises Max princ XRD Min princ XRD (d) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 60 000 W/m2K lmin= 20 µm Tcasting= 660◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP2 - Run 5 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises Max princ XRD Min princ XRD (e) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 7000 W/m2K lmin= 20 µm Tcasting= 660◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP2 - Run 6 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises Max princ XRD Min princ XRD
(f)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 7000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Air cooling Depth (mm) Stress (MP a) MP2 - Run 7 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises Max princ XRD Min princ XRD (a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 60 000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Air cooling Depth (mm) Stress (MP a) MP2 - Run 8 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises Max princ XRD Min princ XRD (b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 20 000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP2 - Run 9 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises Max princ XRD Min princ XRD (c) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 5 000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP2 - Run 10 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises Max princ XRD Min princ XRD
(d)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 7000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP1 and MP3 - Run 1 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 7000 W/m2K lmin= 40 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP1 and MP3 - Run 2 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 60 000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP1 and MP3 - Run 3 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(c) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 60 000 W/m2K lmin= 40 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP1 and MP3 - Run 4 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(d) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 60 000 W/m2K lmin= 20 µm Tcasting= 660◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP1 and MP3 - Run 5 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(e) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 7000 W/m2K lmin= 20 µm Tcasting= 660◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP1 and MP3 - Run 6 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(f)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 7000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Air cooling Depth (mm) Stress (MP a) MP1 and MP3 - Run 7 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 60 000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Air cooling Depth (mm) Stress (MP a) MP1 and MP3 - Run 8 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 20 000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP1 and MP3 - Run 9 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(c) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −80 −60 −40 −20 0 20 40 60 h0= 20 000 W/m2K lmin= 5 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP1 and MP3 - Run 10 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(d)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120 140 h0= 7000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP4 - Run 1 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120 140 h0= 7000 W/m2K lmin= 40 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP4 - Run 2 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120 h0= 60 000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP4 - Run 3 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(c) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120 h0= 60 000 W/m2K lmin= 40 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP4 - Run 4 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(d) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120 h0= 60 000 W/m2K lmin= 20 µm Tcasting= 660◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP4 - Run 5 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(e) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120 h0= 7000 W/m2K lmin= 20 µm Tcasting= 660◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP4 - Run 6 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(f)
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120 h0= 7000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Air cooling Depth (mm) Stress (MP a) MP4 - Run 7 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(a) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120 h0= 60 000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Air cooling Depth (mm) Stress (MP a) MP4 - Run 8 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(b) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120 h0= 20 000 W/m2K lmin= 20 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP4 - Run 9 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(c) 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2 1.3 1.4 −120 −100 −80 −60 −40 −20 0 20 40 60 80 100 120 h0= 20 000 W/m2K lmin= 5 µm Tcasting= 600◦C Ttool= 160◦C Depth (mm) Stress (MP a) MP4 - Run 10 Max princ HD Min princ HD von Mises HD Sim Max princ Sim Min princ Sim von Mises
(d)
Appendix B
Stress results for NovaSTRESS
Table 8 shows the parameters used for stress simulation in NovaSTRESS. The stress results are presented in figure 31 to 35.
Run no: Mould stiffness(−) TCasting(◦C) TMould(◦C)
1 0.2 640 240
1 0.4 640 240
1 0.8 640 240
1 0.4 680 180
1 0.4 640 180
Table 8: Parameters used for stress simulation in NovaSTRESS
Figure 31: Nova stress results for RUN 1, left maximum and right minimum principle stress.
Figure 33: Nova stress results for RUN 3, left maximum and right minimum principle stress.
Figure 34: Nova stress results for RUN 4, left maximum and right minimum principle stress.
