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: c.nguyenvan@iwm.rwth-aachen.de

nvchungdhgt@yahoo.com

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

7

d휀𝑖𝑗𝑝

= dλ𝜕f1𝜕σ𝑖𝑗

dλ =

𝜕𝑓1𝜕𝜎𝑖𝑗

∙ 𝑪𝒊𝒋𝒌𝒍𝒆𝒍 d휀𝑖𝑗

𝜕𝑓1𝜕𝜎𝑖𝑗

∙ 𝑪𝒊𝒋𝒌𝒍𝒆𝒍 𝜕𝑓1

𝜕𝜎𝑖𝑗+

𝜕𝑓1𝜕𝜌

∙ 𝜌𝜕𝑓1𝜕𝜎𝑖𝑗

𝛿𝑘𝑘 −𝜕𝑓1𝜕𝑝

23

𝜕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