Numerical simulation to predict of the final shape of PM HIP components
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Transcript of Numerical simulation to predict of the final shape of PM HIP components
Numerical simulation to predict the final
shape of PM HIP components
IWM / IAPK Institute, RWTH Aachen University
Augustinerbach 4, 52062 Aachen Germany
Chung Van Nguyen
Email: [email protected]
Phone: +49 241 80 96291
Mobile: +49 176 82106600
2
Content
1 Introduction
2 Densification models
3 Implementation
4 Simulation results
5 Anisotropic shrinkage of PM-HIP components
3
Introduction
The powder HIP production processes
4
Courtesy of KEG GmbH
Anisotropic shrinkage
This problem leads to higher costs for post
processing and longer delivery time.
In order to improve technically and make it
cost efficient, NNS HIP parts must be
produced from the first shot with the
minimal geometrical allowances.
Thus, the main motivation is to create a
HIP simulation tool to replace the “trial and
error” methodology.Courtesy of IWM
5
Content
1 Introduction
2 Densification models
3 Implementation
4 Simulation results
5 Anisotropic shrinkage of PM-HIP components
6
Simulation approach
constitutive equations
휀 = 휀𝑒𝑙 + 휀𝑖𝑛𝑒𝑙 + 휀𝑡ℎ
휀𝑖𝑛𝑒𝑙 = 휀𝑝𝑙
+ 휀𝑐𝑟
Modified from Von Mises yield condition
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d휀𝑖𝑗𝑝
= dλ𝜕f1𝜕σ𝑖𝑗
dλ =
𝜕𝑓1𝜕𝜎𝑖𝑗
∙ 𝑪𝒊𝒋𝒌𝒍𝒆𝒍 d휀𝑖𝑗
𝜕𝑓1𝜕𝜎𝑖𝑗
∙ 𝑪𝒊𝒋𝒌𝒍𝒆𝒍 𝜕𝑓1
𝜕𝜎𝑖𝑗+
𝜕𝑓1𝜕𝜌
∙ 𝜌𝜕𝑓1𝜕𝜎𝑖𝑗
𝛿𝑘𝑘 −𝜕𝑓1𝜕𝑝
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𝜕𝑓1𝜕𝜎𝑖𝑗
∙𝜕𝑓1𝜕𝜎𝑖𝑗
1 2
The plastic deformation calculation bases on the consistency condition, associated flow rule
and the mass conservation principle.
𝑛𝑖𝑗 =𝜕f1𝜕σ𝑖𝑗
𝜕𝑓1
𝜕𝜌=
𝑛∙𝜌𝑛−1 𝐽2−1
3∙𝑛∙𝜌𝑛−1 𝐼1
2
2𝜎𝑒𝑞1 1 2 − ℎ ∙ 𝑚 ∙ 𝜌𝑚−1 − 𝜎0 ∙ 𝑘 ∙ 𝜌𝑘−1)
𝜕𝑓1𝜕𝑝
= − ℎ ∙ 𝜌𝑚 ,= −ℎ1 ∙ 𝜌𝑚
Constitutive equation:
plasticity model
𝑓1 𝜎𝑖𝑗 , 𝜌, 𝑃 = 𝜎𝑒𝑞1 𝜌) − 𝑟1 𝜌, 𝑃 − 𝜎𝑦 𝜌 = 0 1
2
3
4
5
8
휀𝑖𝑛𝑒𝑙 = 휀𝑐𝑟 = 휀𝑐𝑟1 + 휀𝑐𝑟2
휀𝑖𝑗𝑐𝑟 = 휀𝑖𝑗
𝑐𝑟2 = exp −𝑄
𝑅𝑇)𝜎𝑒𝑞2
𝑁𝑛−1 3𝑐 𝜌
2𝑆𝑖𝑗 + 𝑓 𝜌 𝐼1𝛿𝑖𝑗
휀𝑖𝑗𝑐𝑟 = 휀𝑖𝑗
𝑐𝑟2 + 휀𝑖𝑗𝑐𝑟2
= ex p −𝑄
𝑅𝑇)𝜎𝑒𝑞2
𝑁𝑛−11 + 𝑚 −
1
ex p 𝑘휀𝑖𝑗𝑐𝑟
𝑁𝑛−13𝑐 𝜌
2𝑆𝑖𝑗 + 𝑓 𝜌 𝐼1𝛿𝑖𝑗
Constitutive equation:
viscoplasticity model
1
2
3
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Content
1 Introduction
2 Densification models
3 Implementation
4 Simulation results
5 Anisotropic shrinkage of PM-HIP components
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Implementation in UMAT Subroutine
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Different material models
Table 1: Different constitutive equation used for HIP simulation
Model’s name Characteristic
Plastic Elastoplastic 휀𝑖𝑗𝑖𝑛𝑒𝑙 = 휀𝑖𝑗
𝑃𝑙
Viscoplastic Elastoviscoplastic 휀𝑖𝑗𝑖𝑛𝑒𝑙 = 휀𝑖𝑗
𝑐𝑟2
Combined model No.1 Elasto-plasto-viscoplastic 휀𝑖𝑗𝑖𝑛𝑒𝑙 = 휀𝑖𝑗
𝑝𝑙+ 휀𝑖𝑗
𝑐𝑟 = 휀𝑖𝑗𝑝𝑙
+ 휀𝑖𝑗𝑐𝑟2
Combined model No.2 Elasto-plasto-viscoplastic 휀𝑖𝑗𝑖𝑛𝑒𝑙 = 휀𝑖𝑗
𝑝𝑙+ 휀𝑖𝑗
𝑐𝑟 = 휀𝑖𝑗𝑝𝑙
+ 휀𝑖𝑗𝑐𝑟1 + 휀𝑖𝑗
𝑐𝑟2
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Content
1 Introduction
2 Densification models
3 Implementation
4 Simulation results
5 Anisotropic shrinkage of PM-HIP components
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Simulation results of test capsules
Combined models give the best shape prediction with the error below 1,5%
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Content
1 Introduction
2 Densification models
3 Implementation
4 Simulation results
5 Anisotropic shrinkage of PM-HIP components
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Shape and size
Thickness, material properties
Number of weldlines, location
of welded joints
Inhomogeneous powder
distribution
Powder particle size, size
distribution can be different
Temperature, pressure
Temperature gradient
Capsule Powder prior to HIP HIP cycle
PM HIP Production process
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With a homogeneous initial powder distribution with an inhomogeneous initial powder distribution
Influence of capsule thickness
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Influence of initial
powder distribution
Relative density distribution was determined from experiment based on Image Analysis
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Influence of initial powder
distribution
Homogeneous initial powder distribution Powder distribution from experiment
Bending due to the influence of inhomogeneous powder distribution
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Influence of powder particle size
distribution
Table 5-4: Powder particle size fraction of three used powders
Fraction F1 F2 F3 F4 F5 F6
Micron >250 250-212 212-125 125-100 45-100 <45
Powder (P1) 17 16 15 10 28 14
Powder (P2) 17 16 15 10 28 0
Powder (P3) 50 0 20 5 10 15
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Influence of powder particle size
distribution
Influence of different powder distribution distribution
Final shape of capsules which used different powder fractions as shown in the previous slide
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Homogeneous
Powder dis.
Powder dis.
Taken from IA
Capsule No.1 Comparision of
the final shape
Influence of temperature
gradient
Bending due to the influence of temperature gradient
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Optimize capsule’s shape and size
Thank you very much for your attention
Nguyen Van Chung
IAPK – Institut für Anwendungstechnik Pulvermetallurgie und Keramik
an der RWTH Aachen e.V.
Augustinerbach 4
52062 Aachen
www.iapk.rwth-aachen.de