Simulation of hot tears in castings

submitted in partial fulfilment of the requirements

for the degree of

Master of Technology (Manufacturing Engineering)

by

B.L.N Lohit Kumar (08310051)

Guide

Dr. B. Ravi

Department of Mechanical Engineering INDIAN INSTITUTE OF TECHNOLOGY BOMBAY

June 2010

i

Declaration of Academic Integrity

“I declare that this written submission represents my ideas in my own words and where

others' ideas or words have been included, I have adequately cited and referenced the original

sources. I also declare that I have adhered to all principles of academic honesty and integrity

and have not misrepresented or fabricated or falsified any idea/data/fact/source in my

submission. I understand that any violation of the above will be cause for disciplinary action

as per the rules of regulations of the Institute”

Date: Signature

Place: Name: B.L.N Lohit

ii

DISSERTATION APPROVAL SHEET

The dissertation entitled Simulation of hot tears in casting by B.L.N Lohit is approved for the degree of Master of Technology in Mechanical Engineering.

Examiners

Supervisors

Chairman

Date: Place:

i

Abstract Hot tearing is one of the most common and serious defects that occurs during the casting of

alloys. It remains a major problem despite decades-long efforts to develop working hot

tearing criteria and to implement those into casting process simulation programs. Hot

tearing is a phenomenon believed to occur during the last stage of solidification. Existing

models allow one to calculate the s t ress -strain and temperature in a casting and to

compare those with the chosen hot tearing criterion. In most successful cases, the

simulation shows the relative probability of hot tearing. None of the existing criteria,

however, can give the answer on whether the hot crack will appear or not and what will be

the extent of hot cracking (position, length, shape). This Project outlines the mechanisms

behind hot tear and tries to correlate the relationship between hot tearing tendency and

geometrical parameters. Initially, the currently available hot tearing criteria are compared.

Crack prone junctions L, T and C are simulated and a relation is correlated between the

tendency of hot tearing and geometrical parameters. The simulations obtained by a

commercial simulation program are compared with available experimental data and the

comparison is found to be good. Hardness of the mold is also one of the important factor, the

effect of which needs to be evaluated, as it results in additional stress in the castings. Gradual

thickness gradients and improved feeding help in decreasing hot tear tendency.

Keywords: Casting, Hot tearing, Simulation, Steel, Strain.

ii

Table of Contents

Abstract I

Table of Contents Ii

List of Figures V

List of Tables Vii

1 Introduction 1-3

2 Literature review 4- 36

3 Problem statement 37-39

1 .1 Hot tears initiation 1

1.2 Theories of hot tearing 3

2 .1 Mechanism of hot tears 4

2.2 Models predicting hot tear 14

2.2.1 Non mechanical criteria 14

2.2.2 Mechanical based criteria 17

2.2.3 Two phase modelling 26

2.3 Summaries of hot tear Mechanisms of hot tear development

30

2.4 Comparison of hot tearing Criteria 34

3.1 Motivation 37

3.2 Goal, Research Objectives, and Scope 38

3.3 Research approach 39

3.4 Organisation of report

39

iii

4 Comparison of hot tearing criteria 40-54

5 Benchmark shape and its analysis 56-66

6 Validation of simulation software 67-71

7 Virtual Experiments and Validation of regression equation 74-92

4.1 Criteria used for prediction 42

4.2 Analysis 1 43

4.3 Analysis 2 49

4.4 Summary 54

5.1 Benchmark shape 56

5.2 Analysis of Benchmark shape 57

5.3 Analysis of variations in Commercial software 61

5.4 Summary 66

6.1 Introduction 67

6.2 Hot Tear model in commercial software 68

6.2 .1 Case 1 68

6.2 .2 Case 2 70

6.2.3 Industrial casting 71

6.3 Summary 73

7.1 Variation of parameters in benchmark shape 75

7.2 Taguchi method for design of experiments 76

iv

8 Conclusions 91-92 8.1 Future scope 92

7.3 Regression analysis on benchmark shapes 80

7.4 Application of the equation on practical castings 86

7.5 Summary 90

Annexure I : Hot tear tendency data for benchmark shapes

93

Annexure II : Properties of steel used in simulation 97

References Acknowledgement

99 102

v

List of Figures

Figure Description Page

1.1 Hot tear in a specimen 2

2 .1 Appearance of Hot tears in Al-cu microstructure specimen 5

2.2 Radiography of Hot spot region showing extent of hot tearing 7

2.3 Mechanisms of film stage tearing 8

2.4 Different length scales of equiaxed dendritic solidification along with suggested hot tearing mechanisms

11

2.5 Summary of hot tearing Mechanisms 13

2.6 Graphical illustration of the method for determining the stress relief period tR and the vulnerable period

16

2.7 Schematic of a columnar grain structure that is used to determine the film thickness

19

2.8 Schematic diagram of the deformation of a semi-solid body due to a constant applied strain rate, for various total strains

20

2.9 Schematic view of the idealized microstructure for a semi – solid constrained liquid film stage in later mushy zone

21

2.10 Two types of temperature dependence of elongation to failure (εp) and linear shrinkage (εsh) in the semi-solid temperature range

22

2.11 Ductility of semi-solid alloys and strain caused by linear shrinkage and configuration of the Semisolid body

24

2.12 Schematics of the formation of a hot tear in between columnar dendrites as a result of a localized strain transmitted by the coherent dendrites below. The pressure in the interdendritic liquid is also indicated

28

2.13 Schematics of the mass balance performed at the scale of a small volume element over which liquid can enter through the vertical faces in order to compensate shrinkage and uniaxial deformation of the solid skeleton along the vertical direction

29

2.14 Schematic illustration of possible hot crack initiators and some crack propagation mechanisms

31

2.15 Fracture surfaces of hot tears in 200-mm round billet produced by DC casting at a casting speed of 200 mm/min (a) Al-1 pct Cu and (b) Al-3 pct Cu ( Eskin and Katergman, 2007).

32

3.1 Research Approach 38

vi

4.1 Approach to predict hot tear 41

4.2 Mg Al Casting geometry 43

4.3 Analysis 1(a) Modeling (b)Meshing (c) Temperature profile 46

4.4 Analysis 1 (a ) Hot tear prediction by RDG (b) Fuerer (c ) actual hot tearing

47

4.6 Stress calculated by LB Criteria 49

4.7 Geometry of steel casting 49

4.8 Analysis 2 (a) Modeling (b)Meshing (c) Temperature profile 52

4.9 Analysis 2 (a) Hot tear prediction by RDG (b) Fuerer (c ) actual hot tearing

53

4.10 Stress calculated by LB Criteria 55

5.1 Parameters of benchmark shapes L and T 56

5.2 Parameters of C shape 57

5.3 Variations in L shape 58

5.4 Variations in C shape 59

5.5 Variations in T shape 60

5.6 Thermal properties of H13 steel 60

5.7 Analysis of L junction in commercial simulation software 62

5.8 Analysis of T junction in commercial simulation software 63

5.9 Analysis of C junction in commercial simulation software 64

5.10 Geometrical shapes showing maximum tendency 65

6.1 (a) Geometry (b) Solid model (c) ProCAST Analysis 69

6.2 Actual hot tear in casting 70

6.3 Hot tear validation with industrial casting 71

6.4 (a) Casting model (b) Casting with feeders 72

vii

6.5 Comparison of actual hot tear location with simulation results

73

7.1 Overall approach 74

7.2 Experimental castings of L shape 87

7.3 Experimental Castings of T shape 88

7.4 Experimental Castings of C shape 89

viii

List of Tables Table Description Page

2.1 Hot tearing Mechanisms 12

2.2 Possible Mechanisms Acting within ‘‘Hot Tearing’ ’ Phenomenon 34

2.3 Summaries of Hot tearing criteria’s 36

4.1 Properties considered in thermo mechanical analysis of casting 44

4.2 Values for mg al alloy for RDG Braccini and LB criteria 45

4.3 Maximum value of pressure difference at nodes susceptible to hot tearing

48

4.4 Properties used for steel in thermo mechanical analysis 50

4.5 Property Values for steel alloy for rdg braccini and lb criteria 51

4.6 Maximum value of pressure difference at nodes susceptible to hot tearing –analysis 2

54

5.1 Variations in Geometry of benchmark L shape 57

5.2 Variations of geometry for T and C benchmark shapes 58

5.3 Input to commercial simulation software 59

5.4 Hot tear tendency values

61

6.1 Modules in simulation software 67

7.1 Variation map for L junction 75

7.2 P values in L shape 76

7.3 Level map for L shape and T shape 77

7.4 Design of Experiments for L and T shape 78

7.5 Design of Experiments for C shape 79

7.6 Values of hot tear tendency for experiments of L shape 80

7.7 Regression Table for L shape 82

7.8 Regression table for T shape 83

ix

7.9 Hot tear value for T shape 84

7.10 Regression values for C shape 85

7.11 Hot tear tendency values for C shape 86

7.12 Geometrical parameters and calculated hot tear values for L junction

87

7.13 Geometrical parameters and calculated hot tear values for T junction

88

7.14 Geometrical parameters and calculated hot tear values for C junction

89

1

Chapter 1

Introduction

Hot tears are identified as cracks, either on the surface or internally in the casting. These

cracks may be large and visible to the naked eye or small and found only by magnetic

particle inspection. They are caused by a combination of thermal effects, such as hot spot

size and casting restraint, such as cores in cylindrical castings. Metal composition can also

affect hot tearing tendency. Hot tearing in any casting is disastrous. Extensive rework is

required with the appearance of any small linear indication on the casting. Either design

or process changes will be proposed to eliminate this defect. However, even the

normal process fluctuations can cause random appearances of this defect during

production. It is possible that previous successful changes do not help eliminate future hot

tear problems. Once hot tears occur in castings, they must be repaired by welding or the

casting must be scrapped. A more fundamental understanding of hot tearing is important

when trying to eliminate this defect from any part or process.

1.1 Hot tear initiation

Solidification of alloys take place in a certain temperature range known as freezing

range, On decreasing temperature, the solid phase nucleates, grows in a form of grains and,

starting from a certain point in the solidification range, grains start to interact with each

other, first by feeling the presence of neighbours, then by contacting and bridging with them,

and finally by forming a continuous skeleton of the solid phase. Prior to configuration of

complete solid phase the acquisition of intrinsic properties such as strength and ductility

takes place.

2

During casting there is a considerable time during which the alloy consists of both solid

and liquid. The material in this semi-solid state is called mushy zone, during this period

the material experiences convection in the liquid region and deformation in the solid region,

convection in liquid region encounters large displacements with low stresses where as the

solid region suffers high stresses with low displacement. This radical different behaviour

accounts to tremendous change in viscosity, both these phenomenon occur in mushy zone

adding to its complexity the behaviour the deformation of the dendritic network depends on

its coherency state and the flow of liquid in now occurs in porous solid phase.

During solidification two major defects related to a lack of feeding can be encountered

in alloys: porosity and hot tears. The first defect is associated with a hydrostatic

depression in the mushy zone combined with segregation of gaseous solute elements

(hydrogen, nitrogen, and carbon monoxide). This depression is associated with the suction

of the liquid in the porous dendritic region due to shrinkage. The models developed for

the prediction of micro porosity formation are, therefore, based on the solution of an

equation coupled with a mass balance and a micro segregation model of gaseous

elements. The formation of hot tears is also linked to a lack of feeding in the mushy zone,

but only for specific regions where the dendritic network is submitted to shear or tensile

stresses. These stresses are induced by differential thermal contraction upon cooling.

Fig. 1.1: Hot tear in a specimen (Par and Weiliwu, 2003)

3

1.1 Theories of hot tearing

Hot tear is believed to be a fracture formed during solidification due to shrinkage and

hindered contraction and lack of feeding, and it initiates in the mushy zone. Hot

cracks or hot tear is one of the major defects in casting industry, because of the complex

mechanisms acting during the solidification of metals, the prediction of the hot

tearing phenomenon is not an easy task. The complex nature of mushy properties adds

additional difficulties when incorporating these in a hot tearing model. However several

attempts have been made to study and predict hot tear that have resulted in development

of several mechanisms predicting hot tear. Earlier criteria were based on stress or feeding

activity (Eskin et al., 2004). Other criteria combining both mechanical and non mechanical

aspects were proposed recently and include several parameters, which are complex in

formulation and implementation in FEM simulations. In spite of so many models being

predicted the accuracy of them is at stake, several researches have compared all the

available criteria and listed the pros and cons in each of them, if the criteria are

used qualitatively, considering that constitutive and fracture data of the mushy zone are

not well known, Only Rappaz-Drezet-Gremaud (RDG)’s criterion might be of value

(Eskin et al., 2004), However Rappaz-Drezet-Gremaud (RDG) c r i t e r ion has many

limitations in its assumptions (Rappaz et al., 1999), and the usage of this criterion for

direct chill casting still remains a question. All these criteria mostly looked upon the

thermo physical properties of the castings and crack initiation and very few theories

concentrated on crack propagation and importance of geometrical parameters.

This project mainly concentrates on correlating the relation between geometric parameters

and hot tearing tendency. For this purpose simpler geometric shapes which are prone to hot

tear are taken and simulated in commercial simulation software. Initially the available hot

tear criteria which predict the occurrence of hot tear were compared on experimental

castings taken from literature.

4

Chapter 2

Literature Review

The transition of liquid to solid is made more complicated for an alloy because the presence

of the mushy zone somehow “mixes” the two behaviours: the deformation of the dendritic

network strongly depends on its coherency state and the flow of liquid now occurs in a porous

solid phase and the physics of hot tear occurrence is also pretty complex.

2.1 Mechanism of hot tear

Hot tearing is recognized as one of the most common and serious defects found in

castings. The typical appearance of hot tearing in the microstructure (Fig.2.1) with a filled

hot tear in an Al-10%Cu alloy (Par and Weiliwu, 2003). The importance of studying and

understanding the occurrence of hot tears in alloys has long been recognized. Various

methods have been used to test and evaluate the severity of hot tears and its related

properties and several theories have attempted to explain their occurrence. From many studies

starting in the 1950s, and reviewed by Novikov and Sigworth (D.G. Eskin et al., 2004), it

appears that hot tears initiate above the solidus temperature and propagate in the

interdendritic liquid film. These results in a bumpy fracture surface covered with a smooth

layer. In DC casting, the name ‘‘mushy zone’’ is misleading, as its top part is actually a

slurry, because the newly formed grains are still suspended in the liquid. Only after the

temperature has dropped below the coherency temperature that is the temperature at which

grain starts interacting, a real mush is formed. The deformation behavior of the mush is very

critical for the formation of pores or hot tears. During solidification, the liquid flow through

the mushy zone decreases until it becomes insufficient to fill initiated cavities so that they

can grow further.

5

Fig. 2.1: Appearance of hot tears in Al-Cu microstructure specimen

(Par and Weiliwu, 2003)

The solidification process can be divided into four stages, based on the permeability of the

solid network.

1. Mass feeding in which both liquids and solids are free to move.

2. Interdendritic feeding, in which the remaining liquid has to flow through the

dendritic network after the dendrites have formed a solid skeleton. A pressure gradient

may develop across the mushy zone by solidification shrinkage occurring deeper in

the mushy zone. However at this stage the permeability of the network is still large

enough to prevent pore formation.

3. Interdendritic separation, in which the liquid network becomes fragmented and

pore formation or hot tearing may occur. With increasing solid fraction, liquid is isolated

in pockets or immobilized by surface tension, also when the permeability of the solid

network becomes too small for the liquid to flow, further thermal contraction of the

solid will cause pore formation or hot tearing.

4. Interdendritic bridging or solid feeding, in which the ingot has developed a

considerable strength and solid-state creep compensates further contraction. At the final

stage of solidification fS (fraction of solid) > 0.9, only isolated liquid pockets remain

and the ingot has a considerable strength. Solid-state creep can now only compensate

solidification shrinkage and thermal stresses.

6

The last two stages are mainly considered (Quack, 1996), since in slurry and during the

interdendritic f eed ing stage in the mush feeding is usually sufficient to avoid any

casting defects. It is mainly the ‘‘interdendritic separation’’ stage in which the ingot is

vulnerable to hot tearing. A large freezing range alloy promotes hot tearing since such an

alloy spends more time in the vulnerable state in which thin liquid films exist between the

dendrites. Apart from these intrinsic factors, the solidification shrinkage and thermal

contraction impose strains and stresses on the solid network, which are required for the

occurrence of hot tearing. It is argued that it is mainly the strain and the strain rate,

which are critical for hot tearing, Stresses do not seem critical as the forces available

during solidification are very high compared to the stresses a semi-solid network can

resist.

A lot of efforts have been devoted to understand the hot tearing phenomenon. The

compilation of research in this field has been done by Novikov and Sigworth, (Zheng et

al., 2001) reviewed the possible causes of hot tearing. (Eskin et al., 2004) have reported

that at low strain rates the grain boundary sliding is the main mechanism of deformation

o f a semi solid body. The load applied to the s e m i -solid body will be accommodated by

a grain boundary displacement that is lubricated by liquid film surrounding the grain.

Prokhorov proposed a model for deformation of the semi-solid body. If two tangential

forces s1 and s2 are applied to the equilibrium semi-solid body, the response of the body

manifests itself as the grain movement and at some point the grains will touch each

other. The liquid covering the grain will circulate to the lowest pressure point.

Further deformation will be possible if the surface tension and resistance to liquid flow

are sufficient to accommodate the stress imposed. If not, a brittle intergranular fracture or

hot tearing will occur. In relation to this theory, Prokhorov postulated that:

1. An increase in film thickness increases the fracture strain

2. A decrease in grain size increases the fracture strain

3. Any non -uniformity of grain size decreases the fracture strain

7

Based on this theory, (Prokhorov, 1962) the main measure for hot tearing is the ductility

of the semi-solid body. A hot tear will occur if the strain of the body exceeds its

ductility. A theory of shrinkage-related brittleness divides the solidification range into

two parts. In the upper part the coherent solid-phase network does not exist. Cracks or

defects occurring in this stage can be healed by liquid flow.

As the solidification progresses and the solid fraction further increases, at a certain stage

or a certain solid fraction a coherent network is formed resulting in fragmentation of the

liquid network and increasing the chances of pore formation. This stage is considered as the

start of linear shrinkage. Since the coherence point, there is a stress called the shrinkage

stress which is imposed onto the semisolid body. The semi-solid body is now under

the influence of these stresses, Fracture or hot tearing occurs if the shrinkage stress

exceeds the rupture stress.

Fig. 2.2: Radiography of Hot tear region showing of hot tearing (Davidson et al., 2003)

8

Pellini suggested a hot tearing theory based on the strain accumulation with the

following main features:

• Cracking occurs in a hot spot region

• Hot tearing is a strain-controlled phenomenon which occurs if the accumulated strain

of the hot spot reaches a certain critical value.

• The strain accumulated at the hot spot depends on the strain rate and time required

for a sample to pass through a film stage (Pellini, 1952).

The most important factor of hot tearing based on this theory is the total strain on the hot

spot region. The total strain is the additive of strain over a period with in which the hot

spot exists. Taking into account that the highest strain accumulates in the liquid film,

Although Pellini mentions a critical value of the accumulated strain, it is not clear whether

it is ductility or another entity. Based on the f i lm-strain theory on hot tearing formation

by Pellini (Pellini, 1952), hot tearing susceptibility generally develops in the mushy zone

at liquid fractions below 10%. It only occurs when stresses exceeding its strength and

ability to deform in the hot tearing temperature range are produced in the metal (in fig.

2.3). While the hot zone is narrow and exists as only a thin film, its strength is inadequate

to withstand the accumulated strain.

(a) (b) (c)

Fig. 2.3: Mechanisms of film stage tearing (Par and weiliwu, 2003)

9

This may be enough to cause hot tearing in the weak liquid film. The three stages are

shown in Fig.2.3.

(a) Solid nuclei together with considerable liquid metal. Hot tearing is not possible at this

stage

(b) Crystals separated by thick liquid film.

(c) Stage just before solidification, thin liquid films separate crystals. The developed strain

concentrations was sufficient to hot tearing

Pellini’s theory is a basis for a hot tearing criterion proposed by (Clyne and Davis, 1979).

Some authors suggest that it is not the strain but the strain rate which is the critical

parameter for hot cracking. More recently, a strain-rate based hot tearing criterion is

proposed by (Rappaz et al., 1999) yet another approach to the hot tearing

phenomenon is the assumption that failure happens at a critical stress. The liquid

surrounding the grain is considered as a stress riser of the semi-solid body (William and

Singer, 1979). In this theory, a liquid-filled crack is considered as a crack initiation. The

propagation of the crack initiator is determined by the critical stress. The critical stress is

mostly determined using the modified Gri f f i th energy balance approach. The

modi f icat ion of the Gri f f i th approach is particularly in accounting for the effect of

plasticity as proposed by (Rowan and Murray, 1950).

Another approach within the fracture mechanics theory is proposed by (Sigworth, 1996)

who considers a possibility of applying a liquid-metal-embrittlement concept to the hot

tearing case. There is also a group of hot tearing theories that consider the hindered feeding

of the solid phase by the liquid as the main cause of hot tearing. Niyama and Feurer use this

approach to derive the hot tearing criterion. Based on this theory, the hot tear will not occur

as long as there is no lack of feeding during solidification. Clyne and Davies give more

attention to the time spent in the mushy state (Eskin et al., 2004). The last stage of

solidification is considered as most susceptible to hot tearing. However, on further

decreasing of the liquid fraction the bridging between adjacent dendrites is established

so that the interdendritic separation is prevented.

10

Several hot tearing criteria have been developed in the past decades. Feurer used the fluid

flow through a porous network to calculate the after feeding by liquid metal. Hot tears

will initiate when this after feeding cannot compensate the solidification shrinkage (Feurer,

1977).

Clyne and Davies defined a cracking susceptibility coefficient (CSC) as the ratio

between the time tV during which the alloy is prone to hot tearing and the time tR during

which stress relaxation and after feeding can take place. These times are defined as the

periods during which the fraction liquid is between 0.1 and 0.01 and between 0.1 and

0.6 respectively. These criteria were combined with a heat flow model describing the

DC casting process by Katgerman. This enabled the determination of the cracking

susceptibility coefficient as a function of the casting parameters. Unfortunately, the above

criteria are restricted in their use because they give only a qualitative indication for the hot

tearing susceptibility (Katergman, 1982).

The first two-phase model, which takes into account both fluid flow and deformation of

the solid network, is the Rappaz–Drezet–Gremaud (RDG) hot tearing criterion (Rappaz et

al., 1999). This criterion is formulated on the basis of after feeding, which is limited by the

permeability of the mushy zone. At the solidification front the permeability is high but

deeper in the mushy zone the permeability is restr icted. A pressure drop along the

mushy zone exists which is a function of this permeability and the strain rate. If the

local pressure becomes lower than a critical pressure, a cavity is initiated. The model is

implemented in a thermo mechanical model for direct chill casting to predict hot tearing

during billet casting. The hot tearing susceptibility is found higher during start-up of the

casting and in the centre of the billet, which agrees with general casting practice. A further

development of this criterion is carried out by (Braccini et al., 2000). They included

plastic deformation of the solid phase and a criterion for the growth of a cavity. They base

their model on two geometric models, one for a columnar dendritic and one for an

equiaxed dendritic structure. Explicit relations are developed for critical strain rates and

they indicate that the critical strain rate decreases with increasing solid fraction.

11

Above the coherency temperature, liquid still present in between the dendrites is

continuous, since the solid dendrite arms have not yet coalesced. Deformation induced by

thermal stresses can, therefore, pull these arms apart quite easily. If the interdendritic liquid

flow can feed such regions, almost nothing is noticed, except may be some local inverse

segregation (‘‘healed’’ hot tears). However, deep in the mushy zone, where the permeability

of the mush is very small, an opening of the non coherent dendritic network by tensile

deformation cannot be compensated for by the liquid and hot tears form (Rappaz et al.,

1999). It is obvious that the actual hot tearing mechanism includes phenomena occurring

on two scales: microscopic (crack nucleation and propagation, stress concentration,

structure coherency, wet grain boundaries) and mesomacroscopic (lack of feeding, stress,

strain, or strain rate imposed on the structure). Fig. 2.4 illustrates these scales during

equiaxed dendritic solidification (Eskin and katergman, 2007). All t he mechanisms

mentioned do no t t ake nucleation completely into account. Table 2.2 summarizes

different approaches of researches across the world.

Fig. 2.4—Different length scales of equiaxed dendritic solidification along with suggested hot tearing mechanisms (Eskin and katergman, 2007)

12

Table 2.1 Hot tear mechanisms

Mechanisms and conditions

Suggested and developed by

Year

Causes of hot tearing Thermal Contraction Hein

Dobatkin Pellini

1935 1948 1952

Nucleation Liquid film or pore as stress Concentrator

Patterson et al. Niyama Rappaz et al. Braccini et al Suyitno et al

1953 1977 1999 2000 2002

Oxide bi-film entrained in the Mush Vacancy clusters at a grain boundary or solid/liquid interface

Campbell Fredriksson et al

1999 2005

Propagations Through liquid film by sliding By liquid film rupture By liquid metal embrittlement

Patterson Williams and Singer Novikov and Novik Pellini Patterson Saveiko Dickhaus Novikov &Sigworth

1953 1960 1963 1952 1953 1961 1994 1966

Conditions Thermal strain cannot be accommodated by liquid flow and mush ductility Pressure drop over the mush reaches a critical value for cavity nucleation Strain rate reaches a critical value that cannot be compensated by liquid feeding and much ductility Stresses and insufficient feeding in the vulnerable temperature range

Pellini Prokhorov Novikov Magnin et al Niyama Guven and Hunt Rappaz et al. Farup and Mo Pellini Prokhorov Rappaz et al. Braccini et al. Bochvar; Lees Clyne and Davies Feurer Kargerman

1952 1962 1966 1996 1977 1988 1999 2000 1952 1962 1999 2000 1942;1946 1975 1977 1982

13

Fig. 2.5: Summary of hot tearing Mechanisms (Eskin and katergman, 2007)

Figure 2.5 also shows that the conditions and causes of hot tearing can be considered on

different length scales, from macroscopic to microscopic. It is worth to note that most of

the existing hot tearing criteria deal with the conditions rather than with the mechanisms

of hot tearing. As suggested by Table 2.1 One can see that, over the years, much more effort

has been put on the conditions required for hot tearing occurrence rather than on the

mechanisms of crack initiation and propagation, different macroscopic and mesoscopic

parameters, such as stress and strain, were considered as critical for the development of hot

tearing. Today, the mesoscopic strain rate is believed to be the most important factor and

some modern models are based on it. The physical explanation of this approach is that

semisolid material during solidification can accommodate the imposed thermal strain by

plastic deformation, diffusion-aided creep, structure rearrangement, and filling of the gaps and

pores with the liquid. All these processes require some time, and the lack of time will result

in fracture. Therefore, there exists a maximum strain rate that the semisolid material can

endure without fracture during solidification (Eskin and katergman, 2007).

14

2.2 Models predicting hot tear

Due to the complexity of the mechanisms involved in hot-tearing formation, the

models developed so far are relatively simple. Most of them are based upon the

consideration of the solidification interval, the existing hot tear ing c r i te r i a , as

reviewed elsewhere, (Hisami et al., 2008) can be conditionally divided into the two

categories: non mechanical and mechanical. The former type of criteria deal with the

vulnerable temperature range, phase diagram, and process parameters, and is represented

by the criteria of Cline and Davies, Feurer and Waterman. The latter type of criteria

involves critical stress critical strain or critical strain rate (Skin and waterman, 2007).

Different casting processes impose specific requirements on the application of hot tearing

criteria. That is why some criteria work better for shape casting, whereas others are more

suitable for direct-chill casting.

2.2.1 Non mechanical criteria

A non mechanical criterion only concentrates on feeding and shrinkage during

solidification. This methodology assumes that hot tearing occurs due to the lack of feeding.

a) Feurer criteria

Feurer’s theory of hot tearing (Feurer, 1977) is a non mechanical criterion that

focuses on feeding and shrinkage during solidification. This approach considers that hot

tearing occurs due to lack of feeding, which is related to the difficulties of the fluid flow

through the mushy zone as a permeable medium competing with solidification

shrinkage (Skin et al., 2004). Feurer considers two terms, SPV and SRG, indicating

maximum volumetric flow rate (feeding term) through a dendrite network and

volumetric solidification shrinkage, respectively. Feurer’s criterion states that hot

tearing is possible if:

SPV < SRG (1)

15

The maximum volumetric flow rate per unit volume through the semisolid dendritic network is formulated as follows,

SPV =����

������ (2)

Ps= Pm +P0=Pc (3) Pm = ρgh (4) ρ = ρSfs+ρlf l (5)

Pc = � ��

�� (6)

where PS, L, c and ( in equation (2) are liquid volume fraction; secondary dendrite arm

spacing; effective feeding pressure; length of porous network that is determined as the

distance between the location at coherency and solidus temperature; the tortuosity

constant of the dendritic network; the viscosity of the liquid phase; respectively. ϒSL is the

solid liquid interface energy; p is the average density of the mush; g is the gravity

constant; h is the distance to the melt surface ρl and ρs are densities of the liquid and solid,

f l and fs are the liquid and the solid volume fractions in the dendrite network, and PO, PM,

and PC are atmospheric, metallostatic, and capillary pressure, respectively. The volumetric

solidification shrinkage is caused by the density difference between solid and liquid phase.

Further the shrinkage velocity is given by

� �� �

�� = = ��

���� (7)

where V is the volume element of the solidifying mush with constant mass and t is time.

The hot cracking susceptibility based on Feurer’s criterion considers SPV is equal to SRV

for the liquid fraction of f:l .

16

b) Clyne and Davis criteria

The hot tearing criterion proposed by Clyne and Davies is based on the theory that in

the last stage of freezing, the liquid is difficult to move freely so that the strain applied

during this stage cannot be accommodated by mass feeding. This last stage of

solidification is considered as the most susceptible to hot tearing (Suyitno et al., 2005).

However on further decreasing of the liquid fraction, bridging between adjacent dendrites

is established so that intedendritic separation is prevented. The cracking susceptibility

coefficient proposed by Clyne and Davies is formulated as the ratio between the vulnerable

time period (hot tearing susceptibility) tr and time available for stress relief process (mass

feeding and liquid feeding) tv:

H.C.S = ����

=����������� ��� (8)

where t0.99 is the time when the volume fraction of solid, fs, is 0.99, t0.9 is the time when fs is

0.9, and t0.4 is the time when fs is 0.4 (Clyne and Davis, 1979).

Fig 2.6 Graphical illustration of the method for determining the stress relief period tR and the vulnerable period (tV) (Skin et al., 2004).

17

c) Katergmans criteria

In Katgerman model, theoretical considerations of (Clyne and Davies, 1979) and (Feurer,

1977) are combined. The model defines the hot tearing index, HCS, as follows:

H.C.S = ���� = ��.����� !

�"���� ! (9)

Where H.C.S is hot criteria susceptibility, tcoh is the time when fs is at the coherency point,

and tcr is the time when feeding becomes inadequate that is determined by using Feurer’s

criterion and is the time for which

SPV = SRG (10)

2.2.2 Mechanical based criteria

A mechanical criteria emphasis only on deformation of the mushy zone rather than on

shrinkage effects of the mushy zone, they are basically stress and strain criteria developed

on the basis of failure of the region where crack induces

a) Stress based criteria

The stress-based criteria of hot tearing are based on the viewpoint that a semisolid body

will fracture if the applied or induced stress exceeds the strength of the body. The first type

of these hot tearing criteria accounts for the fact that a material has a limit stress at which

it fails. This approach can be subdivided into two sets of criteria. The first set is based on

the strength of bulk material and the second set, on the strength of a liquid film trapped

between grain boundaries. Within the second type of stress-based criteria, the hot tearing

susceptibility is derived from an assumption that the material contains defects or the

weakest point, and whether they will be a fracture or not depends on such parameters as:

stress, defects dimensions, configuration etc. Although it is rather difficult to get certain

material property that is comparable to the fracture toughness of solid materials, then idea

18

of applying the fracture mechanics theory would be an interesting topic particularly within

the framework of development of micro-mechanics. A stress-based hot tearing criterion that

uses the strength of liquid trapped between grain boundaries criteria is reported by

Novikov (Dickhaus et a1.,1994).They refer to the stress needed to pull apart two parallel

plates separated by a thin liquid film as to the strength of semi-solid metals. The

assumptions that are applied in this model are the uniform distribution of liquid and no

influence of sliding on the fracture strength. This criterion is expressed as:

#�$ = � % (11)

where # fr i s the fracture stress, ϒ is the surface tension; and b is the film thickness.

The constraints of this model are the negligible viscosity and wetting angle. To overcome

this constraint, (Dickhaus et al., 1994) promote a model proposed by Healy that involves

the viscosity. The separation force of the parallel plates of radius R separated by a liquid

film is given as follows,

Where &' = (�)�*� ( �

%��− �

%�� ) (12)

Where Fz is the force required to increase the film thickness from b1 to b2; i is the

dynamic viscosity; R is the radius of a plate; and t is the time required to increase the film

thickness from b1 to b2. The film thickness is calculated based on Fig. 2.7. Here; the liquid

distribution at grain boundaries is adopted as for columnar crystals. The equation for the

film thickness based on figure can be written as

b = ���-

. (13)

19

Fig .2.7: Schematic of a columnar grain structure that is used to determine the film thickness (Dickhaus et al., 1994)

b) L B criteria D. J. Lahaie and M. Bouchard modified and adapted an existing mechanical criterion for

ho t tearing of the semi-solid body to the deformation mechanisms (Eskin et al., 2004).As

proposed by some researchers (Suhartono at al., 2000), the solid grains of the semi-solid

body in liquid film stage were idealized as an aggregate of regular hexagons for each grain,

as shown in Figure 2.8. Assuming that the liquid and the solid grains in the later stage of

solidification process are incompressible, the body will be thus subjected to a constant

tensile strain rate e, if the feeding is not possible from outside to the liquid channel. Figure

2.8 shows the effect of the imposed deformation. The stress resisting deformation is thus

a function of the total strain ε. Due to thermal concentration, the initiated and

accumulated stress in the semi-solid body can be written as

# = /έ

√( 23!4( [21 − √(

� 23!4 74

�(+ 2 21 + √(

� 23!4 74

�(] (14)

The relationship between h and a can be represented with fraction solid fs as

!3 = √3 <���-=

�-=> (15)

20

Fig. 2.8: Schematic diagram of the deformation of a semi-solid body due to a constant

applied strain rate, for various total strains (Lahaie and Bouchard, 2001).

Therefore the constitutive expression of the internal generated stress in the

body can be calculated as

#? = /έ@ <���-=�-=

>( [<1 − �� <���-=

�-=> 7>�( + 2 <1 + <���-=

�-=> 7>�(] (16)

Where, 7 and A are taken as constants throughout the calculation, m is the parameter of

grain shape, which was 1/2 for columnar and 1/3 for equiaxed respectively (Lahaie and

Bouchard, 2001). Assuming that the semi-solid body of the specimen has a uniform tensile

strain, and the hot tearing fracture surface is intergranular, the tear will initiate at the

solid/liquid interface near the surface. Thus the fracture stress of can be expressed as

#� =� B

C(! ∗ �

�EFG�HI-=I-= JKL

(17)

where, ϒ1/g is the surface energy; f is the total strain on the semi-solid body, and h is the

film thickness. Wherever the internal stress at is greater than the fracture stress �f, hot

tears may occur.

21

Fig. 2.9: Schematic view of the idealized microstructure for a semi – solid

constrained liquid film stage in later mushy zone (Par and Weiliwu, 2003).

c) Willaim and Singer criteria

The stress-based hot tearing criteria that apply fracture mechanics approach is proposed

by Williams and Singer (Eskin et a1., 2004) They modify Griffith cracking criteria for

application as a hot tearing criterion. The original Griffith criterion considers a defect or a

small crack as a stress concen t ra to r and , t here fo re t he initiator of fracture. On

transition t o hot tearing phenomenon, the volume of liquid in the final stage of

solidification substitutes the defect as the crack initiator in the Griffith equation. Williams

and Singer argue that the final liquid is the weakest point and the stress concentrator of

the semi-solid body (Williams and Singer, 1968) . The modified Griffith model is written

as:

#�$ = M *NO�+��PQR�S

�� (18)

Where A is a constant dependent on the grain size and the dihedral angle; fr is the fracture

stress; G is the shear modulus; y is the effective fracture surface energy; VL is the volume of

liquid; and is Poisson’s ratio.

22

d) Strain based criteria

The ductility of semi-solid non-ferrous (including aluminium) alloys was used as a basis for

a hot shortness criterion suggested by Novikov (Eskin et a1., 2004). A characteristic called

a ‘‘reserve of plasticity in the solidification range’’. pr is proposed.

The ‘‘reserve of plasticity’’ pr is actually the difference between the average integrated

value of the elongation to failure εp and the linear shrinkage/contraction εsh i n the brittle (or

effective, or vulnerable) temperature range ∆Tbr (Fig 2.11 a). The hot tearing susceptibility

is then given by

T$ = U∆WX� (19)

Where S is the area between the εp and εsh curves in the brittle temperature range ∆Tbr. If the εsh curve intersects the εp curve (Fig. 2.11 b).

T$ = U��U�

∆WX� (20)

Fig. 2.10 Two types of temperature dependence of elongation to failure (εp) and linear

shrinkage (εsh) i n the semi-solid temperature range (Esksin et a1., 2004).

23

(Magnin et al., 1996) use a similar model for prediction of hot tearing of an Al–4.5% Cu

alloy. They propose that cracking occurs when the maximum principle plastic strain

exceeds the experimentally determined fracture strain in the solidification range. It is

demonstrated that hot cracking is more likely to occur at higher casting speeds, which

is in line with industrial experience. The same approach is also adopted by (Zhao et al.,

2000), for hot tearing prediction in an Al–4.5% Cu alloy. They measure the shrinkage stress

of casting, which is transformed to a critical strain for the formation of a hot tear. The strain

determined from their test is compared with the ductility from the work of (Magnin et al.,

1996). The temperature range where the ductility is lower than the strain induced by

solidification shrinkage is considered as potentially hazardous for hot tearing.

e) Strain rate based criteria

During solidification, alloys are in a two-phase situation: liquid and solid phases are

present though in constantly changing proportion. The liquid–solid phase transformation

leads to the solidification shrinkage and the solid phase then contracts resulting in the

strain development as an effect of geometrical configuration of the solidifying body. The

more complex the shape of the casting, the higher the strain. Based on this fact, hot tearing

criteria that are based merely on the comparison of the ductility of semi-solid alloys and

their solidification shrinkage cannot be used for hot tearing prediction of complex

castings. Prokhorov proposed a hot tearing model which includes the configuration of a

solidifying body (Prokhorov, 1962).

During solidification, solidifying alloys pass through a low-ductility range that is called

the brittle temperature range (BTR). The highest temperature of the brittle temperature

range is known as the upper limit of BTR (Bupper) and the lowest one, as the lower limit of

BTR (Blower). Fig. 2.11 shows a diagram illustrating the BTR; the liquidus temperature

(T1), solidus temperature (Ts), ductility curve (D) and strain curve (e) are also given. The

strength reflecting the appearance of a hot tear is defined as the limitation of strain capacity

in the semi-solid alloy as indicated by the intersection of the strain curve (e) and the

ductility curve (d).

24

Fig. 2.11 Ductility of semi-solid alloys and strain caused by linear shrinkage and configuration of the Semisolid

body (Prokhorov, 1962).

The intersection is determined by the slope of the strain curve (strain rate), the BTR

span and the shape of the D curve within the BTR. As the strain in the solidifying body

is determined by the solidification shrinkage/contraction and the geometrical

configuration, the strain under balance condition can be written as follows

73YY = 7?Z�_7�$\\ (21)

where εapp is the actual strain in the solidifying body; εfree is the free thermal contraction

strain; and εint is the internal strain resulted from the restricted shrinkage/contraction

and thermal stresses as a result of the configuration of the solidifying body.

The reserve of technological strength in the semi-solid state ∆εres) can be approximately

written in the following form:

∆7$\� = ]^?Z − (∆7�$\\ + ∆73YY) (22)

25

The expression is divided by BTR and written as:

∆K�_-`W) = a=bc`W) − ∆KI�__`W) − ∆Kdee`W) (23)

f3YY = f^?Z − f�$\\ (24)

Where α is the strain rate in terms of temperature dependence of the ductility or the

strain. Prokhorov postulated that hot tearing occurs when αres = 0 and, therefore

f3YY = f^?Z − f�$\\ (25)

If Ṫ is the cooling rate during solidification, it can be found that:

έ = fṪ (26)

This is the strain rate in terms of time Substitution of Eq. (16) to Eq. (15) results in

έ$\� = έ^?Z − έ�$\\ – έ3YY (27)

The hot tear will occur in the solidified body if

έ$\� ≪ 0 (28)

And Eq. (27) becomes

26

έ^?Z − έ�$\\ ≪ έ3YY (29)

The strain rate in Eq. (29) varies in different ways with the solidified body configuration or

the design factor. The left-hand side of the equation includes factors that depend on the

alloy composition, and it is the hot tearing criterion. The value of εapp is regarded as a

function of the solidified body configuration. The higher the difference at which the hot

cracking occurs, the worse the solidify body configuration in relation to hot tearing.

Based on the hot tearing criterion described above, the prediction of hot tearing

susceptibility is performed by computing the reserve strain rate εres. Therefore, the hot

tearing can be quantitatively predicted using Eq.27 this criteria is principally similar to the

criterion proposed by Novikov (Eskin et a1., 2004).

The differences are

• Prokhorov’s criterion uses the strain rate as a measure for hot tearing

tendency, while Novikov’s criterion uses the strain

• Prokhorov considers both the configuration of the solidifying body and the

solidification shrinkage/contraction as factors of hot tearing, while the

Strain criterion of Novikov uses only the solidification shrinkage/contraction.

• Prokhorov uses the difference between the lowest ductility of semi-solid body

and the actual strain as the reserve plastic strain, while the Novikov’s criterion

uses the area between the ductility curve and the strain curve in the entire

effective solidification range (Eskin et a1., 2004).

2.2.3. Two phase modelling Two phase modelling essentially takes into account both fluid flow and deformation of

the solid network. Unlike the other mechanical and non mechanical theories, these theories

try to implement both the aspects of feeding and stresses and tend to give better results as

they are much closer to real conditions.

27

a) RDG (Rappaz-Drezzet-Gremaud) criteria

Figure (2.12) is a schematic diagram of the columnar dendritic growth. The dendrites are

assumed to grow in a Bridgman-type configuration, i.e., in a given thermal gradient (G) and

with a velocity (vT) equal to the speed of the liquidus isotherm. This velocity points toward

the right and, therefore, the liquid has to flow from right to left in order to compensate for

shrinkage, the specific mass of the solid being larger than that of the liquid for most

metallic alloys. If the dendritic network is submitted to a tensile deformation rate

perpendicular to the growth direction (εp), the flow should also compensate for that

deformation if no hot tears form. The pressure in the interdendritic liquid is schematically

represented at the bottom of Fig.2.13 it decreases from the metallostatic pressure (pm) near

the dendrite tips. If the pressure falls below a cavitation pressure (pc), a void may form

(black region in Fig. 2.13 and give rise to a crack. Therefore, a hot tear will form at the

critical pressure (Pmin).

Where

T̂ ?Z = T̂ − ∆TK − ∆T�! = T� (30)

The average specific mass (p) = plf l+ psfs , the mean specific mass of the solid and liquid

phases, and (pv) = vlplf l+ vspsfs, is the average mass flow. The volume fraction of liquid (f l)

is equal to (1- fs), and the specific masses of the two phases (ps and p 1) are assumed to be

constant, but not equal.

Considering that the fluid moves along the x-axis only, whereas the solid deforms in the

transverse direction, one has

�k�B�BlB,no�p + �k�-�-l-,qo

�r − sW <�(�-�-) �p + �(�B�B)

�p > = 0 (31)

Fig 2.12 Schematicsresult of a localized st

in the inte

Taking fs as a function of x only

have been introduced together as shown in Eq.

t�u�,p 8 +1 8 vQ w

The entity E(x) is the defo

the distance x of the mushy

be determined from the veloc

zone (Figure 2.13).

Schematics of the formation of a hot tear in between cotrain transmitted by the coherent dendrites beerdendritic liquid is also indicated (Rapaaz et

nction of x only and the deformation rate of the solid along the y

have been introduced together as shown in Eq.32

Q w t�έYxy , u�vt� � t� u�,p 8 +1 8 vQz+yQ , u

formation rate times the volume fraction of

mushy zone. The integration constant C, appearing

velocity of the fluid at x= L, where L is the

28

olumnar dendrites as a elow. The pressure

z et a1., 1999).

and the deformation rate of the solid along the y-direction εp

Q u�vt� , { (32)

solid, cumulated over

appearing in Eq. (32), can

the length of the mushy

Fig 2.13—Schematics element over which liqshrinkage and uniaxial

Indeed, at the tip of the

shrinkage and the cumulated

shrinkage of the whole

identical to that of a plan

mushy zone is equal to - (1

following condition for the consta

T̂ 3p = |� − |

= 180 +�E~Q/���N

Please note that the integrals

thus introducing the tempera

TS are the liquidus temperature

As can be seen, the contr

VT/G, a factor which was

formation (Niyama et al., 1982).

cs of the mass balance performed at the scale oliquid can enter through the vertical faces in or

al deformation of the solid skeleton along the v(Rapaaz et a1 .,1999).

dendrites, the velocity of the fluid must

ulated deformation of the whole mushy zone if

whole mushy zone, given by the mass conserva

nar front and equals -vT. The cumulated de

(1 +1) E (L). Introducing these two expressions

he constant C, (Rapaaz et al., 1999).

Q w �+WQ�-+WQ�+k���-+WQoW�WS x� + 180 ��+~Q/��� N w �-+WQ�

+k���-+WQoW�WS

egrals over x have been replaced by integrals o

perature gradient, G, fs, being two functions of

perature and the temperature at the end of solidif

ribution of shrinkage to the pressure is proportio

already deduced by Niyama for his criterion

1982).

29

of a small volume rder to compensate vertical direction

ust compensate for the

if no void forms. The

conservation equation, is

deformation within the

ons in Eq.32 gives the

Q+ Qo� x� (33)

over the temperature,

of T. The terms TL and

fication, respectively.

oportional to the ratio

erion of microporosity

30

2.3 Summaries of hot tear Mechanisms of hot tear development The challenge nowadays lies not in the adequate description of macroscopic and

microscopic stress-strain situations and their correspondence to the parameters and

properties of the mushy zone, but rather in finding real factors causing the nucleation and

propagation of a hot crack. In fact, some existing theories and models of hot tearing

partially describe these factors with the crack initiator presented as a cavity filled

with liquid or a pore, or an oxide bi film, (Campbell, 1991) and with the crack propagation

path through the liquid film covering grain boundaries. (Eskin and Katergman, 2007). A

comprehensive model and a corresponding hot tearing criterion should include nucleation

and propagation of hot tears and connect these processes to the microstructure evolution

during solidification of the semisolid material; to the macroscopic and microscopic thermo-

mechanical situation in the mushy zone; and to the mechanical (or fracture-mechanical)

properties of the mushy zone. The last two components are well covered by a large body

of publications, though many mechanical properties still need to be determined and the

fracture mechanics potential has not been fully exploited. The correspondence

between the structure evolution during solidification and the crack nucleation and

propagation is studied in much less detail. Let us consider the possible mechanisms of

crack nucleation and propagation.

The nucleation of hot cracks is an almost unexplored phenomenon. Based on these

observations and ‘‘post-mortem’ examination of hot tear surfaces, the following crack

nuclei have been suggested

• Liquid film or liquid pool

• Pore or series of pores

• Grain boundary located in the place of stress concentration

Fig. 2.15 summarizes some of the possible crack initiators. The mechanism of hot tear

formation and propagation can be elucidated from of fractures. Unfortunately, the reports

on hot crack fractures in metallic materials are rare.

Fig. 2.14 —Schematic illustpropagation mec

Most such reports describe the

liquid, when grain boundaries

of crack propagation through

alloys is the classic Al-4 pct

vulnerable solidification range

2006). Much more important is

containing little solute that are

However, the information on

one wanted to summarize the findings a

grain boundaries is an essent

semisolid material gets to the

cracking, i.e., 90 to 95 pct sol

each other, or coalesced this

continuous liquid film as such

2005) show that a hot tear ap

materials and through solid bridges

Although in both cases the fractu

cracking mechanisms are acting

tration of possible hot crack initiators and soechanisms (Eskin and Katergman, 2007).

the cracking of semi solid alloys at relatively

are completely covered with liquid. In this

liquid film by grain separation is obvious. An

Cu alloy. However, alloys with high fractions

range are in practice not susceptible to hot teari

portant is the mechanism of crack formation and propagation

e most susceptible to hot tearing.

semisolid fracture in such alloys is only st

the findings available to date, it would appear

ssential feature of the fracture surface. Moreo

the temperature range of its maximum vul

solid, the greater the fraction of grain boundaries

case, there is no chance for the crack propaga

such a film does not exist. The recent observa

apparently propagates through the liquid film

d bridges in less alloyed materials, as illustrated

racture surface appears to be brittle, one can s

ing.

31

ome crack

ly large fractions of

case, the mechanism

An example of such

ions of liquid in the

ng (Davidson et al.,

propagation in alloys

starting to emerge. If

would appear that bridging of

Moreover, the closer the

vulnerability to hot

boundaries connected to

propagation through a

vations (Eskin et a1.,

ilm in more alloyed

ated in Figure 2.15 .

suggest that different

It is also obvious that the hot

is usually assumed), have sus

adequate feeding of the shrin

tearing but rather ‘‘patches’’ th

One can say that a semisolid all

having a microstructure that

tensile stresses is a self-healing

between grains at high solid

strength and ductility to prevent

enough to supply some liquid to solid

Otherwise, only the mechanis

temperature creep and pore coalescence

Fig. 2.16 Fracture surfaces oa casting speed of 200 mm/mi

crack, like any other crack, can develop cat

sustained growth, or stop. Liquid feeding pla

nking material with liquid does not eliminate

he consequences, which is reflected in the term

alloy containing enough liquid at the last stage

enables adequate permeability of the mush, and

ing material. On the other hand, the developm

fractions in the absence of any liquid would

vent any brittle rupture. Hence, the liquid feedi

e liquid to solid bridges that enables their liquid e

echanisms of ductile fracture (Campbell, 1991)

temperature creep and pore coalescence, will be active.

of hot tears in 200-mm round billet produced min (a) Al-1 pct Cu and (b) Al-3 pct Cu ( Eskin

2007).

32

tastrophically (which

ys a dual role. First,

inate the causes of hot

term ‘‘crack healing.’

ast stage of solidification,

ush, and subjected to

ment of solid bridges

would build up enough

eeding should be just

liquid embrittlement.

(Campbell, 1991), example high

d by DC casting at n and Katergman,

33

The evidence of plastic deformation during hot tearing has been observed in direct

observations and upon examination of fracture surfaces. We can suggest the following

approach to treating the nucleation and propagation of hot cracks. Several distinct

mechanisms are operational in different temperature or compositional ranges or, in other

words, at different fractions of solid. Here, we will consider only the decreasing temperature

as the factor affecting the solid fraction, though the composition is obviously the other factor

that acts in a similar manner .The outline of these mechanisms is given in Table 2.3. Figures

2.14 and 2.15 illustrate the correlation between these mechanisms and the development of the

structure during solidification.

A criterion that can predict not the probability but the actual occurrence and extent of hot

tearing should be based on the application of multiphase mechanics and fracture mechanics to

the failure of semisolid materials, which is today limited by the lack of knowledge about the

actual nucleation and propagation mechanisms. The mechanisms outlined in Table 2.2 are

based on the common sense and interpretation of very few experimental observations.

The best of the available criteria can successfully predict the probability of hot tearing in its

dependence on some casting parameters but fails to forecast the actual occurrence of hot

cracks in ingots and billets. There are two main challenges in this endeavour.

• First, we lack the knowledge of the actual causes of crack nucleation. That is to say,

we do not know exactly what defects or structure defects can act as crack initiators

under particular temperature- stress conditions.

• Second, there is a possibility that different mechanisms of crack propagation and

final failure act in dependence on the fraction of solid at which the fracture occurs

and on the alloy structure. The application of multiphase mechanics and,

eventually, fracture mechanics to the phenomenon of hot cracking looks quite

promising.

The quest for a new hot tearing model and a corresponding hot tearing criterion should focus

on these two research areas.

34

Table 2.2 Possible Mechanisms Acting within ‘‘Hot Tearing’’ Phenomenon

Temperature Range/Fraction of Solid

Nucleation of Crack

Propagation of Crack

Fracture Mode

Between coherency and rigidity temperatures; 50 to 80 pct solid

Below rigidity temperature; 80 to 99 pct solid

Close to the solidus; 98 to 100 pct solid

Grain boundary covered with liquid; shrinkage or gas pore

Pore, surface of particle or inclusion, liquid film or pool, vacancy clusters

Pore, surface of particle or inclusion, segregates at grain boundary, liquid at stress concentration point, vacancy clusters

(a) Liquid film rupture (b) fill ed gap

(a) Liquid film rupture; liquid metal embrittlement of solid bridges

(b) plastic deformation of bridges

a) Liquid metal embrittlement

(b) plastic deformation of bridges, creep

a) Brittle, interganular (b) healed crack

a) Brittle, interganular (b) ductile failure of bridges possible

(a)Brittle,intergranular, transgranular propagation is possible (b) macroscopically brittle or ductile, intergranular; transgranular propagation is possible

2.4 Comparison of hot tearing criteria The basic phenomena that lead to hot cracking are well established and understood, but a

generic criterion that will predict hot cracking under varying process conditions is still not

available. Although the earlier simple criteria based on the thermal history of the casting

have been extended and improved to include shrinkage and deformation, they are still

unable to give reliable predictions under all process conditions. Most of the existing hot

tearing criteria do not incorporate the nucleation and propagation of a hot tear, focusing

more on the macro-, meso-, and microscopic conditions that may result in rupture (Fig

2.5).

The ultimate hot cracking criterion needs to combine aspects of thermal history, shrinkage,

and porosity formation and constitutive behaviour in combination with the evolution of the

semisolid microstructure.

35

Current research efforts are aimed, in particular, at the quantitative description of structure

evolution and its correlation to cracking recently, several mechanical and non mechanical

hot tearing criteria were evaluated by implementing them into a thermo-mechanical model of

DC casting.(Hatami et al., 2008).

The sensitivity of this criterion is, however, a function of correctly chosen values of

properties such as Young’s modulus of the mush, surface tension between liquid

and solid, and permeability of the mush. These parameters are scarcely available and need

to be determined experimentally, while the existing experimental techniques are not reliable.

After comparing the hcs-hot tearing susceptibility obtained from all criteria’s the

following observations have been registered

• Higher cracking sensitivity for higher casting velocity,which is considered in

accordance with casting in practice.

• Further, it shows a higher sensitivity in the billet center, which is in accordance

with casting practice.

• Also it indicates the use of a ramping procedure (lower casting speed during start-

up phase) makes a difference especially in higher casting speed.

• The present approach is not able to correctly predict whether hot tear during DC

casting will occur.Table 2.4 shows summary of the results. This criterion is similar

to RDG (Rappaz Drezzet Gremaud) criterion that is a combined criterion and shows

the greatest potential in reference (Suyitno et al., 2005).

Table 2.3 summarizes the results obtained for the eight criteria. If the criteria are

used quantitatively, it is seen that none of the criteria are able to predict all observations. If

the criteria are used qualitatively, considering that constitutive and fracture data of the

mushy zone are not well known, only RDG (Rappaz Drezzet Gremaud)’s criterion might be

of a good value. But still The RDG (Rappaz Drezzet Gremaud) criterion is based on several

assumptions. During solidification, growth is columnar dendritic and the thermal gradient and

solidification rate are taken as constant. Further, when a cavity is formed, it will lead to a

crack.

Table 2.3 Summaries of Hot tearing criteria’s

36

Observation Fuerer

Clyne &

Davis

Katger-man

Prokhrov Novikov Strain

based

RDG Braccini Present

Increasing

sensitivity for

higher casting

speed

Yes No yes Yes No yes yes yes Yes

Highest sensitivity

in

billet center

Yes No yes Yes No no yes yes Yes

Ramping might

have

positive effect

No No No No No no yes no Yes

Crack NA NA NA Yes NA yes yes NA No

.

The possibility that cavities will lead to porosity and not always to a crack is not included.

(Braccini et al., 2000). Attempted to overcome several of these limitations in their criterion

however, our calculations do not show a significant effect on the predicted hot tearing

tendency.In fact, in the criterion of (Braccini et al., 2000), the metallostatic pressure, which

depends on the depth of sump, is the dominant parameter. Further researches are going on after

(Suyitno et al., 2005) approach predicted hot tears but was very sensitive to the the values

taken.

37

Chapter 3

Problem Definition

The review of literature revealed that the theories of hot tear fail to be accurate in predicting the

hot tears, but some of the theories are close enough in predicting the actual occurrence. As it

was observed in literature review most of the theories failed to give importance to crack

propagation and looked into crack nucleation. This chapter presents the motivation to take up

this research followed by problem definition objectives, scope and approach

3.1 Motivation

Due to the decreasing cost of computers and advances in computing methods from mid 80’s,

computer simulation of foundry process has been developed and improved by both academic

and industry. However prediction of hot tear accurately using simulations is still a challenging

task. Recent theories have shown qualitative results on hot tear occurrence, simulating the hot

tears accurately will help reduce the rejections of castings in industries. Researchers from 1950

have been doing phenomenal work on hot tear prediction, as observed in literature review.

Coupled criteria involving mechanical and non-mechanical aspects of hot tear formation have

been able to predict hot tears more accurately when compared to those criteria which are based

on either mechanical or non-mechanical aspects as shown in literature. Exact prediction of hot

tears in castings is still not accomplished, most of the present theories give importance to crack

nucleation and give less importance to crack propagation. Recently developed coupled Criteria

such as Rappaz-Drezet-Gremaud, Braccini and Suyinto employ shrinkage as well as

deformation aspects which help them to predict hot tears more accurately when compared to the

previous criteria. But to predict hot tear good accuracy further research on crack propagation

need to be done, since at present coupled theories are able to predict crack initiation. These

reasons triggered to compare the existing criteria, optimize them and to investigate the

dependence of geometrical factors in hot tearing initiation.

3.2 Goal, Research Objectives The main goal of this work is

geometrical parameters for junctions such as L, T and C which are prone to hot tearing and

validate their applicability with experimental results,

To achieve the above goal the approach has been defined as follows

Considering the severity of hot tear defects and the possibility of their occurrence, the scope of

the project is limited to hot tear defects in steel sand castings.

Comparision of various hot tearing criteria on castings taken from literature

Design of benchmark shapes which are prone to hot tear

Variation in geomerty of benchmark castings and simulation of the tendency to

tear in these shapes using a commercial software

Regression Analysis to obtain relation between geometrical parameters and hot

tear tendency for the benchmark shapes

Validation of the obtained regression equation with experimental castings

Objectives, and Scope

The main goal of this work is “To correlate the relation between hot tearing

geometrical parameters for junctions such as L, T and C which are prone to hot tearing and

validate their applicability with experimental results,

To achieve the above goal the approach has been defined as follows

Fig 3.1 Research Approach

Considering the severity of hot tear defects and the possibility of their occurrence, the scope of

the project is limited to hot tear defects in steel sand castings.

Comparision of various hot tearing criteria on castings taken from literature

Design of benchmark shapes which are prone to hot tear

Variation in geomerty of benchmark castings and simulation of the tendency to

tear in these shapes using a commercial software

Regression Analysis to obtain relation between geometrical parameters and hot

tear tendency for the benchmark shapes

Validation of the obtained regression equation with experimental castings

38

correlate the relation between hot tearing tendency and

geometrical parameters for junctions such as L, T and C which are prone to hot tearing and

Considering the severity of hot tear defects and the possibility of their occurrence, the scope of

Comparision of various hot tearing criteria on castings taken from literature

Design of benchmark shapes which are prone to hot tear

Variation in geomerty of benchmark castings and simulation of the tendency to

Regression Analysis to obtain relation between geometrical parameters and hot

Validation of the obtained regression equation with experimental castings

39

3.3 Research approach

The solidification and stress simulations were performed using Ansys, ProCAST and

AutoCAST however since the present defect occurs only during the last stages of

solidification the last few time steps are taken into consideration where the solid fraction

is greater than 0.85 ,at this solid fraction values at the corresponding nodes numerical

calculations on the basis of RDG (Rappaz Drezzet Gremaud) approach are carried out to

determine the critical pressure. The theoretical predictions are then compared to the practical

observed tears in the casting.

To correlate the influence of geometrical parameters the following approach was adopted

• Considering simple geometries which are more prone to hot tears

• Simulating the shapes and obtain correlation between geometry and hot tears

• Validating the obtained regression equations with the experimental castings.

3.4 Organisation of report

First chapter of the report contains the introduction. It specifies the problem area through a brief

introduction about hot tearing. The second chapter contains the literature review done. In this

chapter some of the mechanisms and current criteria which are most accurate in predicting hot

tear are listed. The fourth chapter about the different criteria and their ability to predict hot tear.

The fourth chapter highlights the benchmark shape considered for simulations .The next chapter

provides the regression analysis and the influence of geometry on hot tear is tested by applying

the equation to some industrial castings and castings obtained from literature.

40

Chapter 4

Comparison of hot tearing criteria

Castings with known geometry and with practical details of the occurrence of the hot tears

are taken and modelled in ANSYS and after obtaining the pre-requisites of hot tearing

criteria, evaluation of hot tear occurrence is done. The values needed to evaluate are typical

microstructure values such as secondary dendrite arm spacing, surface energy, and

viscosity these values are taken accurate enough for descent predictability. The isothermal

velocity vt is taken as the ratio of cooling rate to thermal gradient as suggested by (Niyama

et al., 1982).

4.1 Criteria Used for Prediction

• Feurer’s criteria is a non mechanical criterion relying entirely on lack of feeding,

the inputs needed to estimate the locations where there is no feeding is obtained and

analyzed on the benchmark castings taken from literature.

• Lahaie and Bouchard criteria is purely a stress based criterion which do not predict

the occurrence, however the values of stresses at the locations susceptible to hot

tear are obtained.

• According to Rappaz-Drezet-Gremaud a coupled criterion, if the critical pressure

drop exceeds 2 kPa then crack occurs.The accuracy of these predictions however

depend on the values taken to predict the criteria’s as these are highly sensitive to the

properties chosen for prediction. Some over predict the occurrence and some

criteria under predict, none of the present criteria’s are accurate as they only

concentrate on nucleation of a crack rather than its propagation

41

a) Approach to predict hot tear

Fig. 4.1: Approach to predict hot tear

b) Thermo-Mechanical Analysis of Castings

Various case studies are taken from industries and research papers and they are analyzed

for possibility of shrinkage porosity in casting using ANSYS. The output of the analysis is

thermal gradient and temperature As well as strain at each node. Various criteria are

calculated with the help of output. The analysis is carried out in three steps as given below

• Pre processing is used to define geometry, material property and element type for the

analysis.

• Processing phase defines analysis type like transient or steady state , apply loads and

solve the problem, it can also be reffered as solution phase.

42

• Post processing is to review the result in the form of graphs or tables. The

general postprocessor is used to review results at one sub step (time step) over the

entire model. The time-history postprocessor is used to review results at specific

points in the model over all time steps.

The following assumptions are made for the analysis:

• In practice the temperature difference between the mould surface and surrounding

air is not substantial hence radiation transfer can be ignored.

• Contact resistance between the mold and cooling material is negligible. Mould cavity

is instantaneously filled with molten metal.

• Outer surface of the mould is initially assumed to be at ambient temperature.

• The bottom surfaces of the casting are always in contact with the mould.

• The vertical surfaces of casting are in contact with the mould i.e. no a i r gap

in between, but the change in heat transfer coefficient for two of the case studies

have been employed and thus virtually creating an air gap.

c) Part Modeling

Modelling consists of defining two parts one is sand mould and other is the castings

with proportional dimensions. Modelling can be done with the help of any available CAD

software and can be inserted in ANSYS using geometry transformation. Model can also be

generated using ANSYS, In ANSYS, and model generation means generation of nodes that

represent the spatial volume.

d) Meshing

The main aim of the analysis is to do a thermo-mechanical analysis with respect to time.

Element, PLANE 13 is chosen in ANSYS® which has capability of coupled analysis

that is structural and thermal analysis. The element has quadratic shape functions.

43

e) Input parameters to ANSYS®

In present work, analysis is carried out for the time from pouring temperature to

solidification temperature. Input parameters required for ANSYS® model are as follows:

• Initial boundary conditions for sand mould, casting and atmosphere air

• Thermal boundary condition is convective heat transfer co efficient.

• Mechanical boundary condition is restricting the degree of freedom at some

sides and of mould.

• Material specifications like density, specific heat and thermal

conductivity, Youngs modulus , thermal expansion coefficient i s required for

sand, cast and atmospheric air.

4.2 Analysis I

The automotive industry is showing greater interest in magnesium alloys as they have a

high strength to weight ratio when compared to steel or aluminum alloys. Because of their

low density, incorporating magnesium alloys into the design of new vehicles decreases

weight and increases fuel efficiency. The figure shows the original geometry features of the

casting on which analysis are done.

Fig. 4.2: Mg-Al casting Geometry (Prokony et al., 2009)

44

This is especially important in helping to reduce carbon emissions that contribute to global

climate change, especially if cast in a permanent mold, the present analysis is to predict hot

tears in AZ91D magnesium alloy in a sand mould. The composition of the AZ91D

magnesium alloy used in the experiments was 8.61% aluminum, 0.6% zinc, 0.23%

manganese, 0.017% silicon, 0.003% copper, 0.0038% iron, 0.0014% nickel, 0.0012%

beryllium, and balance magnesium. Hot t ea r s o f an L -shape Ma g n es i u m ca s t i n g

were determined experimentally by (Bichler et al., 2008).

After obtaining the required temperature profiles, cooling rate and thermal gradient for

the present model, Rappaz-Drezet-Gremaud criteria was obtained at each and every node

when the fraction of solid was in between 0.85-0.98, as the criteria suggest that this is

fraction of solid where hot tear occurs Solid fraction was calculated by lever rule (Gibbs et

al., 2008).

Fs (t) = (TL-t) / (TL-TS) (35)

Here TL,,TS = liqidus,solidus temperature

t = temperature at any instant.

Table 4.1 Properties considered in Thermo-mechanical

analysis of Mg-Al alloy (Prokony et al., 2009)

Properties MG-AL alloy Mould

Density (Kg/m3) 1810 1520

Specific Heat (J/(kg·K) 1050 1000

Heat transfer Coefficient W /m2 6000(600K) 20

Thermal Conductivity W/(m·K) 80 0.8

Solidification Time (s) 350 -

Temperature (K) 993 413

45

Table 4.2 Values for Mg-Al alloy for Rappaz-Drezet-Gremaud, Feurer and Lahaie and Bouchard criteria (Rappaz et al., 1999).

Viscosity mPa.s 1.58

shrinkage β 0.06

strain rate έ 0.0001

Secondary dendrite arm spacing λ µm 76.6

∆T (.K) 125

Surface energy 0.85

Limiting thickness 1 nm

Grain size 30 µm

Parameter (m) ½ ( Columnar)

a (Length of hexagonal side) 19.49 µm

The air gap affects the heat transfer co-efficient this effect was also considered in

present analysis. Due to air-gap formation there is a decrease in heat transfer co-efficient

values, in the present simulation the change in heat transfer co-efficient values were taken

into consideration the graph shows the variation of heat transfer coefficient with temperature.

Transient thermal and structural analysis was carried out for the specific part, the mesh size

was refined for the casting part, the element chosen here was plane 13 ,which is a coupled

element, initially plane 42 was also taken but the results seem to me more better with plane

13 element. The figure shows the modeling meshing and the temperature profile obtained from

ANSYS. Fig 4.3 shows the predictions of the various criteria namely Fuerer, RDG, the actual

location of hot tear is also seen in Fig. 4.3 (c).The location shown by Fuerer and RDG are the

respective critical locations which have exceeded the threshold value limited by these

theories.The effect of air gap was also considered during the solidification process, the value of

heat transfer coefficient was changed to keep track of the increasing air gap.The other theory

was unable to locate the exact location but showed increase in stress values as the solidification

fraction increases as shown in Fig.4.5.

Fig 4.3

(a)

(b)

(c)

Fig 4.3: Analysis 1 (a) Modeling

(b) Meshing

(c) Temperature profile

46

Fig 4.4: Analysis 1

(a)

(b)

(c)

4: Analysis 1 (a) Hot tears Prediction by Feurer,

(b) Hot tears Predicted by Rappaz-Drezet-G

(c) Actual hot tearing

47

Gremaud

48

Table 4.3 Values of maximum pressure difference at nodes susceptible to hot tearing

Node No Temperature Gradient Fraction Of solid

Pressure Difference (Kpa)

32 748.91 3283 0.91272 8.492835

33 748.69 3530 0.91448 7.854095

34 748.4 3676 0.9168 7.925539

35 748.09 4173 0.91928 6.789365

36 747.76 4521 0.92192 6.4464

37 747.33 4403 0.92536 7.867665

38 746.9 4630 0.9288 8.28878

39 746.45 4941 0.9324 8.603259

40 746.04 4989 0.93568 9.900176

41 745.64 5143 0.93888 10.96915

42 745.23 5204 0.94216 12.7744

43 744.79 4993 0.94568 16.94167

44 744.36 5043 0.94912 20.43008

45 743.93 4991 0.95256 26.0132

46 743.47 4626 0.95624 39.02865

1842 756.01 1123 0.85592 13.30623

1843 750.57 1039 0.89944 53.05614

1844 753.25 1081 0.878 25.53164

The last column in table 4.3 shows maximum pressure difference calculated by Rappaz-Drezet-

Gremaud criterion, the critical limit of this pressure difference is 2KPa.

Fig 4.5 Stre

Using Lahaie and Bouchard crite

will occur are calculated, the str

high and they are susceptible to

sensitive values that are used in

the occurrence as shown in the

actual casting produced.

4.3 Analysis II

Fig 4.6 Geometry

ess calculated by Lahaie and Bouchard criter

teria, stresses at the nodes at which the other

resses are calculated at locations whose fracti

o hot tearing, the stress criteria is unable to

order to obtain the stress relation. The other

figure 4.3.It also shows the actual location

ry of steel casting (Monroe and Beckermann,

49

ria

criteria’s say hot tear

tion of solid are very

predict owing to the

er two criteria’s predict

of the hot tear in the

2005)

50

Once hot tears occur in steel castings, they must be repaired by welding or the casting must be

scraped. Considerable effort is spent to eliminate hot tears from castings and many of the

castings are rejected too .In the present case a t shape steel casting is analyzed in this case

As shown in the figure as the ends of the arm are fixed, a coupled analysis that is, a thermo-

mechanical analysis of the present geometry has been done in ANSYS. A plane stress condition

is assumed to do a thermo-mechanical analysis on the casting. The solidification time is

around 150 seconds. Lahaie and Bouchard criteria requires some additional inputs such as grain

size and hexagonal side size which are taken from literature, Transient thermal and structural

analysis was carried out for the specific part, the mesh size was refined for the casting part, the

element chosen here was plane 13 ,which is a coupled element initially plane 42 was also taken

but the results seem to me more better with plane 13 element. After modeling the t-shape the

thermal gradients ,temperature profiles obtained from the thermo mechanical simulation are

given input to the Rappaz-Drezet-Gremaud,Feurer and Lahaie and Bouchard criteria which

calculates the critical value at each and every node and the nodes susceptible to hot tearing

are identified ,it’s known that solid fraction over 0.85-0.95 are prone to hot tearing and hence

calculation of pressure difference is performed at every node where the solid fraction is in

between the required value however the values in the last five sub steps of time are calculated

since at the beginning of solidification of entire casting hot tear cannot form The values taken for

simulation in ANSYS are.

Table 4.4 Properties of steel for thermo-mechanical analysis

Properties Steel Mould(sand)

Density (Kg/m3) 7100 1600

Specific Heat(J/(kg·K) 795 1130

Thermal Conductivity W/(m·K) 37.5 0.856

Heat transfer coefficient W /m2 K 1000 20

Pouring temperature K 1903 -

Thermal expansion /K 1.2E-5 0.9E-5

Poison ratio 0.29 0.2

Young’s modulus Pa 2.1E11 50E6

51

The values required for Feurer criteria are taken from literature and are approximations

to predict hot tear occurrence. Properties taken into consideration by all the three

criteria used to predict the hot tears are listed below. The air gap affects the heat

transfer co-efficient this effect was also considered in present analysis. Due to air-

gap formation there is a decrease in heat transfer co-efficient values, in the present

simulation the change in heat transfer co-efficient values were taken into

consideration the graph shows the variation of heat transfer coefficient with

temperature.

Fig 4.6 shows the predictions of the various criteria namely Fuerer, RDG, the actual

location of hot tear is also seen in Fig. 4.6 (c).The location shown by Fuerer and RDG are

the respective critical locations which have exceeded the threshold value limited by these

theories. The effect of air gap was also considered during the solidification process, the

value of heat transfer coefficient was changed to keep track of the increasing air gap.The

other theory was unable to locate the exact location but showed increase in stress values

as the solidification fraction increases as shown in Fig.4.5

Table 4.5 Properties of steel for Rappaz-Drezet-Gremaud, Feurer and Lahaie and Bouchard criteria (Rappaz et al., 1999)

Properties Value

Viscosity(Pa.s) .0045

Secondary arm spacing(λ)µm 20

Shrinkage factor(β) 0.03

Strain rate(έ) 0.0001

Solidus temperature. K 1777

Liqidus temperature. K 1693

Surface energy 0.05

Limiting thickness 1 nm

Grain size 36 µm

Parameter (m) ½ ( Columnar)

a (Length of hexagonal side) 16.49 µm

52

(a)

(b)

(c)

Fig .4.8: Analysis 2 (a) Modeling

(b) Meshing

(c) Temperature profile

53

(a)

(b)

(c)

Fig 4.9 Analysis 2 (a) Hot tears Prediction by Feurer, (b) Hot tears Predicted by Rappaz-Drezet-Gremaud

(c) Actual hot tearing

54

Table 4.6 Values of maximum pressure difference at nodes susceptible to hot tearing

Node No

Temperature Gradient Fraction Of

Solid

Pressure Difference

(KPa)

1228 1627.1 727.7 0.916 25.17911

1229 1628.2 190.8 0.872 89.30161

1230 1628.6 266 0.856 30.5258

1231 1627.5 761.3 0.9 12.93339

1233 1628.7 761.2 0.852 3.385576

1234 1628.6 716.2 0.856 4.210772

1236 1628.7 263.2 0.852 28.31772

1237 1627.7 702.6 0.892 11.73555

1238 1628.3 211.1 0.868 65.60809

1239 1627.2 681 0.912 24.67964

1248 1627.3 472.6 0.908 44.25916

1249 1626.8 675.6 0.928 48.23515

1251 1628.9 573.1 0.844 4.957802

According to Rappaz-Drezet-Gremaud criterion if the maximum pressure difference

exceeds 2KPa, then hot tear may occur, the last column in Table 4.6 shows the

values of pressure difference at different nodes. The values required to calculate the

maximum pressure difference using this criterion were taken from Table 4.5.

55

Fig 4.10 Stress by Lahie and Bouchard criteria

4.6 Summary

• Feurer over predicts the hot tear in most of the cases-

As seen in simulation results the prediction zone covers the entire zone of

actual hot tear and also some nodes are identified at the boundaries of mould

and cast susceptible to tear ,since this criteria gives only importance to shrinkage

the results are over predicted.

• The actual hot tear is in the zone of Rappaz-Drezet-Gremaud prediction-

The actual hot tear in fact is in the zone of Rappaz-Drezet-Gremaud

prediction, but in addition to it some other nodes are also seen to be susceptible

to hot tear

• Some arbitrary nodes show positive response to tear which may be shrinkage

Porosities- Rappaz-Drezet-Gremaud essentially predicts cavities due to

pressure difference and hence every possibility that the hot tears predicted

from Rappaz-Drezet-Gremaud may be shrinkage porosities cannot be neglected.

• Lahaie and Bouchard criteria-

If the values are accurate then Lahaie and Bouchard criteria may be of good help

as it can be coupled with another criteria, since the values are not accurate

Lahaie and Bouchard fails to identify the real hot tears however very less

number of nodes coincide with actual hot tear.

56

Chapter 5

Benchmark shape and its analysis

As a need of hot tear prediction, a geometry which is more prone to this defect has to be

taken. This chapter highlights the benchmark shape and the proposed variations for further

simulation and experimental work.

5.1 Benchmark shape

Hot tear is a defect that occurs due to hindered contractions near to the hot spot, increased

thermal stresses during the last stages of solidification and many other complex

metallurgical phenomenon during solidification. Junctions are more prone to hot tears,

three different types of junctions were taken initially to correlate the dependence of hot

tear with geometry..

L Junction - Parameters

L1- length of arm L2- length of leg T1- thickness of arm T2- thickness of leg, D- depth

T Junction - Parameters L1- length of arm L2- length of leg

T1- thickness of arm T2- thickness of leg, D- depth

Fig 5.1 Parameters in L and T shape

57

C Junction - Parameters

L1- length of arm, L2- length of leg L1 L3= Length of leg 2 T1- Thickness of arm T2- Thickness of leg 2, Thickness of leg 2 = T3

Fig 5.2 Parameters in C shape

5.2 Analysis of Benchmark shape

The benchmark shapes were initially analyzed in ProCAST and AutoCAST with some

variations in the geometric parameters and their tendency to hot tearing was evaluated, the

variations in L, T and C shape are shown below.

Table 5.1 Variations in Geometry of benchmark L shape

Case Nomenclature L1

Length

of arm

L2

Length

of leg

T1

Thickness

of arm

T2

Thickness

of leg

D

Depth

1 250-100-10-10-50 250 100 10 10 50

2 250-100-50-10-50 250 100 50 10 50

3 250-100-10-50-50 250 100 10 50 50

4 250-100-50-50-50 250 100 50 50 50

58

Case (i) Case (ii) Case (iii) Case (iv)

Fig .5.3 Variations in L shapes

Similarly the T junction as well as the C junctions was simulated with specific variations

to find the possibility of hot tearing. Hot tear is more prone in the junctions having huge

thickness variations, and hence initially thickness parameter was majorly considered. The

C junction has two extra parameters that is lengthand thickness of its second leg. The

table below shows the variations that have been considered,

Table 5.2 Variations of geometry for T and C benchmark shapes

Case Type Nomenclature L1 L2 L3 T1 T2 T3 D

1 T 600-100-12.7-25.4-50 600 100 X 12.7 25.4 X 50

2 T 600-100-12.7-50.8-50 600 100 X 12.7 50.8 X 50

3 T 600-100-25.4-25.4-50 600 100 X 25.4 25.4 X 50

4 T 600-100-50.8-50.8-50 600 100 X 50.8 25.4 X 50

1 C 250-100-150-10-50-100-50 250 100 150 10 50 100 50

2 C 250-100-150-50-10-100-50 250 100 150 50 10 100 50

3 C 250-100-150-10-50-50-50 250 100 150 50 50 50 50

4 C 250-100-150-10-10-10-10 250 100 150 10 10 150 50

59

Case (i) Case (ii) Case (iii) Case (iv)

Fig. 5.4 Variations in C shape

Analysis of these variations of benchmark shape is done using commercial software

program, which directly gives the value of hot tear tendency based on strain rate

calculation, the material properties used for steel. The program uses FDM approach to

evaluate hot tear tendency, the details of the input given to program are listed below.

Table 5.3 Input to simulation software

Analysis Coupled (thermo-mechanical)

Material Steel H13

Stress Module Plastic (steel H13) , Rigid (sand)

Mold Sand

Mesh size 1 mm

Melting temperature 1377

Solidification temperature 1628 K

Liqidus temperature 1746 K

Pouring temperature 1903 K

Initial condition of sand 300 K

60

Case (i) Case (ii) Case (iii) Case (iv)

Fig. 5.5 Variations in T shape.

Fig.5.6 Thermal properties of H13 steel

The Thermal properties are taken from commercial software and the same properties have

been used while using another software program.

0

10

20

30

40

0 500 1000 1500 2000 2500

Temperature (K)

Conductivity (w/mK)

0.00E+00

5.00E-06

1.00E-05

1.50E-05

2.00E-05

0 500 1000 1500 2000

Temperature (k)

Thermal Expansion Coefficient (1/K)

61

Table 5.4 Hot tear tendency values

Junction type Case Hot tear tendency

L 1 .136

2 .22

3 .25

4 .083

T 1 .121

2 .11

3 .114

4 .07

C 1 .71

2 .171

3 .179

4 .308

5.3 Analysis of variations in Commercial simulation software

The properties used to simulate the tendency of hot tearing are taken from Program as

shown in the Fig. 5.6 .The results of the analysis from Fig.5.7 to Fig 5.10 shows the

analsys of all the variations in simulation software .The figures show the tendency to hot

tear, the red region in the figure is the area where there is maximum probablity of a hot

tear occuring, the blue regions are farely safe regions. The software directly gives the

tendency to hot tearing based on stress simulations which could be compared to similar

metals with different geometry.The tendency to hot tearing is mapped by using strain rate.

The geometrical parameters defenitley influenced the tendency to hot tearing. Initially

H13 steel is used for simulation due to better avalibility of properties and since all the

properties are kept constant throughout and its only the geometrical parameters which are

varied, The influence of geometrical parameters on hot tear arae directly reflected.the

following figures shows the analysis of Benchmark shapes in the software , The red area

shows the most susceptable region where tear can occur, in the Fig.5.10 highlights those

geometric variations which have highest possibility of tearing.

62

Case (i)

Case (ii)

Case (iv)

Fig.5.7 Analysis of L junction in commercial simulation software

63

Case (ii)

Case (iii)

Case (iv)

Fig.5.8 T case analysis in commercial simulation software

64

Case (ii)

Case (iii)

Case (iii)

Fig.5.9 Analysis of C junctions in commercial simulation software

65

Case (iii) L shape

Case (i) T Shape

Case (i) C Junction

Fig.5.10 Geometrical shapes showing maximum tendency

66

5.4 Summary

There is a need of better understanding of which geometrical parameters have greater

influence on hot tear tendencies in all of the three beenchmark shapes and also the results

obtained from ProCast which seem to be good, need to be validated so that further virtual

experiments can be carried out by varying all the parameters of the all the three

benchmark shapes and get a commendable relation between the parametres and the hot

tear tendency. Analysis of the initial variations of benchmark shapes were also carrried

out in AutoCAST , as the software gives a better flexibility. But how much change in the

value of hot tear tendency is significant is still unknown .Its also not known whether

ProCAST simulation results can be justified and hence the need for validating Proccast

results with the real industrial cases of hot tear occurs.

67

Chapter 6

Validation of Simulation Software

This chapter focuses on Implementation of commercial software to predict hot tear. Two

different industrial castings were used to validate this commercial finite element code.

6.1 Introduction

ProCAST is a commercial finite element code which can be used to simulate multiple

casting activities such as filling, solidification and defect prediction in continuous as well

as direct chill castings. The software consists of four modules Meshcast, Precast,

ProCAST and Viewcast In addition to hot tears, this program calculates the probable

locations of porosity, principal stresses in the casting, Microstructure properties and many

other results which are important for foundry industries, the following table highlights the

functions of each of the module.

Table 6.1 Modules in Simulation Software

Module Function

Precast - For meshing the geometries

- It identifies and cures flaws in geometries

Precast - For giving boundary conditions

- For initiating the solvers, stress solvers and thermal solvers

ProCAST - Solver which provides the entire results using Datacast which holds

data

Viewcast - It exports the results and it is the module in which we view the obtained

results

- Porosity, Hot tear, Microstructure, Gradients ,temperatures,etc.

68

6 .2 Hot Tear model in Simulation software

During a stress calculation, the simulation software calculates the hot susceptibility to

tearing. The hot tearing indicator allows to model cracks which are forming during the

solidification (i.e. it corresponds to openings in between dendrites which are not yet totally

solidified and which are opening because of a tensile stress). The hot tearing indicator is a

"strain-driven" model based upon the total strain which occurs during the solidification.

The model is computing the elastic and the plastic strain at a given node when the fraction

of solid is between CRITFS (usually 80%) and 99%. There is no parameter for this model

(except CRITFS which is a general stress Run Parameter).

As the amount of plastic strain will strongly depend upon the stress properties in the

mushy zone, the hot tearing indicator should be used to compare different designs with the

same alloy. One should not compare hot tearing indicator levels for different alloys.

6.2 .1 Case 1

Steel castings are prone to hot tear as they are cast in a rather hard mold when compared to

other sand castings owing to tolerances, accuracy and to reduce machining costs. In this

case a steel casting was analyzed using the program which had developed tear at its

junction due to a strong mold which caused a constraint to its free contraction, an elastic-

plastic model of plain carbon steel was taken for stress simulation, which called for both

plastic and elastic modulus and yield strength. The plain carbon steel AISI 1028 properties

were taken from ProCAST (also specified in annexure 2).

The pouring details were taken from literature (Jinwu Kang et al., 1999).The 3d model of

the casting is shown in the Fig.6.1

69

(a)

(b)

(c)

Fig 6.1 (a) Geometry (b) Solid model (c) ProCAST Analysis

70

Fig 6.2 Actual hot tear in casting

The Fig.6.1 shows the area where hot tear can occur as told above the properties and the

other details were taken from literature. The elasto-plastic model was taken as it is nearer

to the practical case. The actual hot tear in the casting is shown in Fig.6.3. As show in the

figure the hot tear occurs at the same place as shown by the program.

6.2.2. Case 2

This case was another case taken from literature. Figure 6.3 show the probable locations of

hot tear predicted by the software and the actual locations (Marco et al., 2004). Hot tearing

occurs when the strains that appear while the metal is still partially solidified cannot be

compensated by liquid feed metal due to the low permeability of the mushy zone. Longer

freezing range alloys, where a liquid film persists between grain boundaries for a greater

time, are more prone to hot tearing. Whether or not it occurs depends on the mechanical

loads that develop due to thermal contraction and the contact constraints of the die wall.

We have found that the total strain, plastic plus elastic, that accumulates between a critical

value of fraction solid such as 0.8 and 1. Is a useful indicator of hot tearing. Relatively

high values of this quantity correlate well with the probability of hot tearing.

71

Fig.6.3 Hot tear validation with industrial casting (Marco et al., 2004)

It corresponds to a plastic strain driven model where accumulated plastic strains allow

cracks to nucleate and grow. All the plastic strain is considered, including plastic strains

formed in the mushy zone. The model couples the stress calculation with the porosity

calculation. The presence of porosity, corresponding to a void fraction indicator, will

increase the risk of cracking. The location of actual hot tear and the one predicted by the

program are almost similar, this shows the predicting ability of software, subject to

boundary conditions and material properties. The present case is taken from literature

(Marco et al., 2004).However it helps in justifying the ability of this commercial software

to predict hot tear.

6.2.3 Industrial casting

An industrial casting of steel was taken from Vulkan technologies, Pune. The casting had

hot tear as shown in fig. 6.5 .The part model of the casting was modeled as per the number

of feeders provided during actual casting practice. The part model of the casting is shown

in fig 6.4. The casting had large thickness gradients which could have been one of the

possibilities of the tear formation. The feeders provided were also very large thus

increasing the area of hot spot. These could have been the reasons of tear formation. The

huge thickness gradient can be reduced to decrease the chances of hot tear formation.

72

(a)

(b)

Fig.6.4 (a) Casting model

(b) Casting with feeders

The model with feeders was simulated in commercial simulation software. The properties

were modified as per the grade of steel. The simulation results were than compared to the

actual hot tear location in the castings. The tear locations in simulations were in good

accordance with the actual location.

Fig.6.5 Comparison of actual

6.3 Summary

The ability of this commercial software was validated using two castings taken from

literature, this enables us to go further and simulate the virtual experiments by varying

geometrical parameters so that correlation of the equation is possible. Since fewer accurate

properties of metals are present, sometimes there may be errors due to ap

the property values. However in this case the accurate values are taken and since

validation has been done the next chapter highlights the design of experiments which

include good combinations of all variations to get a good equation.

Fig.6.5 Comparison of actual hot tear location with simulation results

The ability of this commercial software was validated using two castings taken from

literature, this enables us to go further and simulate the virtual experiments by varying

geometrical parameters so that correlation of the equation is possible. Since fewer accurate

properties of metals are present, sometimes there may be errors due to ap

the property values. However in this case the accurate values are taken and since

validation has been done the next chapter highlights the design of experiments which

include good combinations of all variations to get a good equation.

73

hot tear location with simulation results

The ability of this commercial software was validated using two castings taken from

literature, this enables us to go further and simulate the virtual experiments by varying

geometrical parameters so that correlation of the equation is possible. Since fewer accurate

properties of metals are present, sometimes there may be errors due to approximation of

the property values. However in this case the accurate values are taken and since

validation has been done the next chapter highlights the design of experiments which

Chapter 7

Virtual Experiments and Validation

To correlate the relation between hot tear susceptibility and the junction’s geometric

parameters, simulation results of number of variations of ea

This chapter highlights the nu

taguchi technique. In the present chapter the following approach has been followed.

Variation of geometric parameters of benchmark shape and simulation of all the

Optimising the number of simulation trials by using Taguchi technique

Simulations of the reduced trials in commercial simulation software to predict hot tear

Regression analysis to obtain relation between the hot tear tendency and the geometrical parameters which were varied

Validation on experimental castings and castings taken from literature

Virtual Experiments and Validation

To correlate the relation between hot tear susceptibility and the junction’s geometric

parameters, simulation results of number of variations of each of the parameters is needed.

his chapter highlights the number of virtual experiments and their optimization using

In the present chapter the following approach has been followed.

Fig. 7.1: Overall approach

Variation of geometric parameters of benchmark shape and simulation of all the shapes in a commercial software

Optimising the number of simulation trials by using Taguchi technique

Simulations of the reduced trials in commercial simulation software to predict hot tear tendency

Regression analysis to obtain relation between the hot tear tendency and the geometrical parameters which were varied.

Validation on experimental castings and castings taken from literature

74

Virtual Experiments and Validation

To correlate the relation between hot tear susceptibility and the junction’s geometric

ch of the parameters is needed.

mber of virtual experiments and their optimization using

In the present chapter the following approach has been followed.

Variation of geometric parameters of benchmark shape and simulation of all the

Optimising the number of simulation trials by using Taguchi technique

Simulations of the reduced trials in commercial simulation software to predict hot tear

Regression analysis to obtain relation between the hot tear tendency and the

Validation on experimental castings and castings taken from literature

75

Both AutoCAST and ProCAST are used to simulate the variations in benchmark

shapes.the reason for using both the softwares for simulations are

• To cross check the results and reduce the error.

• AutoCAST is more flexible which readily gives the time at required fractions .

• ProCAST uses a FEM based method which deals with nodes , and AutoCAST

gives more flexibility as it is based on geometry.

7.1 Variation of parameters in benchmark shape

Geometrical parameters of each of the three junctions are varied which directly

corresponds to change in hot tear tendency values. In addition to that the susceptibility

may also depend on other thermal properties like gradient, cooling rate, however since

level cannot be fixed to solidification time and gradient, Initially taguchi method was not

used and the simulation was carried out with around 76 variations to see the influence of

the variables . Insignificant parameters can be then removed and then Taguchi technique

could be used to increase the significance of each of the parameters as well as reduce the

errors and improve the accuracy. Variation of L junction is shown in the given table. All

the simulations of these variations were also performed on AutoCAST other than a

commercial software to have a better accuracy of thermal data such as gradient and

solidification time. Thermal gradient value was taken from AutoCAST and a new time

parameter was introduced.

Table 7.1 Variation map for L junction

Variation in

parameter

L1 L2 T1 T2 D Number of

experiments

D 250 100 10 50 20- 100 6

L1 and L2 100-1500 100-2000 10 50 50 30

T1 and T2 250 100 10-100 10-300 50 20

Random 100-400 70-500 10-200 10-300 20-100 20

76

Table 7.2 P values in L shape

L1 L2 T1 T2 TG

P Value 0.304 0.0137 5.49E-10 0.001 0.87

Here in Table 7.2 TG is thermal gradient, the rest are geometrical parameters for L shape.

A similar variation map as in Table 7.1 was prepared for C and T shape and all the

simulations were carried out in two commercial software’s (Appendix 1). It was seen that

there was not much significance of thermal gradient values and the regression analysis

showed a lesser value of P. P value shows how significantly the relation is established.

Higher P values suggest that the relations are arbitrary. Ideally it should be nearer to zero.

As shown the P value of thermal gradient is very high, the thermal gradient (TG) values

are taken from AutoCAST .Thermal gradient is highly correlated to other geometric

factors and hence the effect of it is reduced. Since the geometrical factors are varied more

and hence the influence of this on thermal gradient is high this is possibly one of the

reasons for this outcome.

7.2 Taguchi method for design of experiments

The significance map for the experiments performed for the variations as shown in Table

7.1 is shown in Table 7.2. The results show poor significance values when regression was

performed and also since the thermal gradient and other factors had less influence, the

parameters could now be varied in levels as per Taguchi’s requirement which helped in

reducing each of experiments from over 1000 to as less as 16. However the significance

value (R2) depends on the number of experiments and hence all those experiments that

were done before was merged with these sixteen results to obtain better results and

significance. Minitab software was used to design experiments as per Taguchi method,

then number of levels considered for each of the geometrical parameter was four and the

numbers of geometrical parameters were 5 and hence the matrix obtained was a 4 level

and five factors as shown in Table 7.3. The number of factors and the levels are same for

both T as well as L junctions. The levels map that is the variation used in L and T

junctions are shown below.

77

Table 7.3 Level map for L shape and T shape

L shape

Level 1 Level 2 Level 3 Level 4

L1 50 150 250 350

L2 50 150 250 350

T1 10 40 70 100

T2 10 40 70 100

D 10 40 70 100

T Shape

L1 150 250 350 450

L2 50 150 250 350

T1 10 40 70 100

T2 10 40 70 100

D 30 50 70 90

Here the values represents the levels , that is L1 – 1 is the first level of the variable L1 that

is 50 , similarly the value D - 4 means the fourth level of the variable D, which

corresponds to 90 in the case of L junction. These sixteen simulations were performed and

analyzed in both the software programs mentioned above to get a regression equation

based on geometrical parameters which correspond to hot tear susceptibility, a new

parameter Time that is solidification time during 80% to 100 % where there are maximum

chances of hot tear occurrence is also introduced, this value is taken from AutoCAST

owing to its flexibility. Thermal gradient and critical time was taken from AutoCAST.

Critical time = t1.00 –t0.80 ( 35)

t1.00 – Time taken for solidi fraction is 1.00

t0.80 – Time when the fraction of solid is 0.8

78

Table 7.4 Design of Experiments for L and T shape

L1 L2 T1 T2 D

1 1 1 1 1

1 2 2 2 2

1 3 3 3 3

1 4 4 4 4

2 1 2 3 4

2 2 1 4 3

2 3 4 1 2

2 4 3 2 1

3 1 3 4 2

3 2 4 3 1

3 3 1 2 4

3 4 2 1 3

4 1 4 2 3

4 2 3 1 4

4 3 2 4 1

4 4 1 3 2

Similarly in C shape the geometrical parameters were fixed, In C shape the number of

factors were seven, and hence the suitable level –factor system obtained from Minitab

software. One parameter was varied for six levels and the remaining six factors were

varied to three levels each, to finally obtain an 18 row matrix for C shape. The matrix

designed for C shape is shown in Table 7.5. All the experiments design given by

minitab were modeled and analyzed by two commercial softwares. The results are than

analysed and a regression model in between the geometrical parameters and the hot

tear was correlated.

79

Table 7.5 Design of experiments for C shape

L1 L2

L3 T1 T2 T3 D

1 (50) 1 (50) 1 (50) 1 (10) 1 (10) 1 (10) 1 (10)

1 (50) 2 (150) 2 (150) 2 (50) 2 (50) 2 (50) 2 (50)

1 (50) 3 (250) 3 (250) 3 (90) 3 (90) 3 (90) 3 (90)

2 (150) 1 (50) 1 (50) 2 (50) 2 (50) 3 (90) 3 (90)

2 (150) 2 (150) 2 (150) 3 (90) 3 (90) 1 (10) 1 (10)

2 (150) 3 (250) 3 (250) 1 (10) 1 (10) 2 (50) 2 (50)

3 (250) 1 (50) 2 (150) 1 (10) 3 (90) 2 (50) 3 (90)

3 (250) 2 (150) 3 (250) 2 (50) 1 (10) 3 (90) 1 (10)

3 (250) 3 (250) 1 (50) 3 (90) 2 (50) 1 (10) 2 (50)

4 (350) 1 (50) 3 (250) 3 (90) 2 (50) 2 (50) 1 (10)

4 (350) 2 (150) 1 (50) 1 (10) 3 (90) 3 (90) 2 (50)

4 (350) 3 (250) 2 (150) 2 (50) 1 (10) 1 (10) 3 (90)

5 (450) 2 (150) 3 (250) 1 (10) 2 (50) 1 (10) 3 (90)

5 (450) 1 (50) 2 (150) 3 (90) 1 (10) 3 (90) 2 (50)

5 (450) 3 (250) 1 (50) 2 (50) 3 (90) 2 (50) 1 (10)

6 (550) 1 (50) 3 (250) 2 (50) 3 (90) 1 (10) 2 (50)

6 (550) 2 (150) 1 (50) 3 (90) 1 (10) 2 (50) 3 (90)

6 (550) 3 (250) 2 (150) 1 (10) 2 (50) 3 (90) 1 (10)

The table shows the variations of each of the parameters for example 6(550) in column L1

means it’s the sixth level and the value of the level is 550, Here all dimensions are in mm .

All these eighteen simulations and the other performed before taguchi method were

considered and used to obtain a regression equation to map hot tear with geometrical

parameters.

80

The simulations of the experiments that were designed using Taguchi method were carried

out in two commercial softwares, furher a regression equation is obtained for hot tear

tendency for each of the benchmark shapes and their validity with practical cases and

some other cases obtained from literature is tested.

7.3 Regression analysis of Benchmark shapes

(a) L shape

The sixteen simulations as suggested by Minitab software were simulated to obtain the

tendency to hot tearing by using a commercial simulation software and AutoCAST. The

latter was used to obtain the critical time factor which is difference of solidification time

when the fraction of solid was 0.8 and 1.

The material used was cast steel AISI 1040, the values used in both the softwares were

same and can be referred at annexure 2. The material model for stress was elasto-plastic

and the mold was considered to be rigid. Throughout these sixteen experiments except for

the geometric parameters, no other property was changed, so that the best possible

correlation of variation of hot tear susceptibility with geometrical parameters could be

obtained. Table 7.6 shows the hot tear tendency values for each of the sixteen virtual

experiments carried out.

T critical = T1.0- T0.8 (36)

Where,

Tcritical = a time based factor influencing hot tear tendency

T1.0 = total solidification time

T0.8 = time when the fraction of solid is around 80 %.

The value was taken in min.

81

Table 7.6 Values of hot tear tendency for experiments of L shape

Case L1 L2 T1 T2 Depth Critical

Time

(AutoCAST)

Hot tear

Tendency

1 50 50 10 10 10 0.058 0.06

2 50 150 40 40 40 1.14 0.07

3 50 250 70 70 70 3.03 0.144

4 50 350 100 100 100 5.77 0.147

5 150 50 40 70 100 3.52 0.075

6 150 150 10 100 70 3.74 0.14

7 150 250 100 10 40 1.59 0.178

8 150 350 70 40 10 0.13 0.06

9 250 50 70 100 40 1.51 0.079

10 250 150 100 70 10 0.12 0.109

11 250 250 10 40 100 1.48 0.183

12 250 350 40 10 70 1.52 0.133

13 350 50 100 40 70 3.72 0.09

14 350 150 70 10 100 4.04 0.217

315 350 250 40 100 10 0.14 0.07

16 350 350 10 70 40 1.39 0.147

These are the results obtained for L shape from both the commercial software, thermal

gradient was also taken into consideration and it was found that it had less significance,

However since each of the parameters have significant influence on hot tear values, thus

it’s very difficult to accurately interpret the physical significance, for example depth and

critical time each have significant influence on hot tear but the effect of only one is seen

because time and depth are again correlated to each other, same is the case with thermal

gradient also. Different combinations of the geometrical parameters were taken and the

regression line with the best possible R2 value was taken into consideration.

82

Since the regression equation with high R2 value, less p value and more t value shows that

the regression equation is not random. In short these parameters that are R2, T and P can

significantly tell about the feasibility of the regression line.

The regression equation obtained by regression analysis of the experiments done on L

junction and including the previous simulations done as Equation is of the form

�. �. � = ��3 ∗ ��% ∗ ��� ∗ ��. ∗ ]\ ∗ �� (37)

Where,

H.T.S = hot tearing susceptibility

L1 = length of the arm,

T1= Thickness of arm,

L2 = length of leg,

T2 = Thickness of leg,

T = Critical time,

D- Depth.

And a, b, c, d, e, f– Exponential coefficients.

The R2 value is 98.5 which shows the accuracy to which it will predict, the p value of each

of the variables shows the significance, lesser the p value more the significance, and

similarly more the t value significance is better. The following table highlights the

coefficients obtained by regression analysis.

Table 7.7 Regression Table for L shape

a b c D e f

Coefficient 0.17687 0.12518 -0.516

-0.26047 -0.285 0.2604

P value 0.016488 0.04 0.19 4.9E-12 0.9E-5 0.18E-4

T Value 2.75404 4.53931 -7.84791 -5.10977 -8.18 2.90489

83

The values corresponding to coefficients are the absolute values to which the parameters

would be raised as suggested by Eq (41).the critical time is measured form simulation of

the experiments using AutoCAST.

(b) Regression analysis of T junction

T junction had five variable parameters with the total number of experiments turning out

to be sixteen as the case was same as L junction, Hot tearing tendencies of the these

castings were simulated .The material properties were of plain carbon steel, same as that

of the L shape . Refer annexure 1.Table 7.8 highlights the coefficients of T shape obtained

after the regression analysis of the simulation experiments (Table 7.9). The equation is of

the form,

�. �. � = ��3 ∗ ��% ∗ ��� ∗ ��. ∗ ]\ ∗ �� (38)

Where,

H.T.S = hot tearing susceptibility

L1 = length of the arm,

T1= Thickness of arm,

L2 = length of leg,

T2 = Thickness of leg,

T = Critical time,

D- Depth.

And a, b, c, d, e, f– Exponential coefficients.

Table 7.8 Regression table for T shape

L1 L2 T1 T2 D T

-0.19106 0.29757 -0.29406 -.45854 -0.00783 0.549816 Coefficient

0.006 0.000638 0.000527 7.37E-06 0.95 7.69E-06 P value

-3.03157 4.080263 -4.163 -6.09322 -0.0583 6.073297 T Value

84

Table 7.9 Hot tear tendency values for T shape

S.No L1 L2 T1 T2 D

Critical

Time Hot Tear

1 150 50 10 10 30 0.2 0.076

2 150 150 40 40 50 1.48 0.096

3 150 250 70 70 70 3.23 0.127

4 150 350 100 100 90 5.59 0.147

5 250 50 40 70 90 4.2 0.11

6 250 150 10 100 70 3.77 0.22

7 250 250 100 10 50 2.3 0.294

8 250 350 70 40 30 0.85 0.064

9 350 50 70 100 50 2.25 0.085

10 350 150 100 70 30 0.77 0.07

11 350 250 10 40 90 1.58 0.18

12 350 350 40 10 70 1.46 0.42

13 450 50 100 40 70 3.94 0.08

14 450 150 70 10 90 3.65 0.258

15 450 250 40 100 30 0.98 0.08

16 450 350 10 70 50 1.97 0.187

The p values show the significance of the relation whether the relation is arbitrary or

discrete. The value of 0.95 shows that the parameter D is less significant as again the

critical Time and depth are correlated. Table 8.4 shows the values of the hot tear tendency.

c) Regression analysis of C junction

C junction has seven variable parameters with the total number of experiments turning out

to be eighteen; hot tearing tendencies of these castings were simulated. The material

properties were of plain carbon steel, same as that of the L shape (Appendix 2).

85

The equation is of the form

�. �. � = ��3 ∗ ��% ∗ �(� ∗ ��� ∗ ��. ∗ �(! ∗ ]\ ∗ �� (39)

Where,

H.T.S = hot tearing susceptibility

L1 = length of the arm,

T1= Thickness of arm,

L2 = length of leg 1,

L3 = Length of leg 2

T2 = Thickness of leg 1,

T3 = thickness of leg 3,

T = Critical time,

D- Depth.

And a, b, c, e, d, e, f, g, h – Exponential coefficients.

The coefficient values corresponds to the values given by the Annova regression

analysis(Table 7.10) , the p values correspond to the significance of the given coefficients.

Table 7.11 highlights the hot tear values at both the right and the left junctions in the c

shape.

Table 7.10 Regression Values for C shape

Larm L1 L2 Tarm T1 T2 Time

Coefficient 0.48 -0.28 X -0.922 .1037 -0.03 .168 Right

P Value 4.4E-0.5 0.01 X 3.89E-14 0.01 0.64 0.01 Right

Larm L1 L2 Tarm T1 T2 D

Coefficient 0.305 - 0.11 0.10 -0.92 0.24 -0.24 0.18 Left

P value 0.04 0.4 0.5 7.35E-11 0.04971 0.04557 0.04 Left

86

Table 7.11 Hot tear tendency values for C shape

L1 L2 L3 T1 T2 T3 D Time

Hot tear

(left )

Hot tear

(right)

50 50 50 10 10 10 10 0.06 0.055 0.07

50 150 150 50 50 50 50 1.69 0.045 0.045

50 250 250 90 90 90 90 5.93 0.05 0.05

150 50 50 50 50 90 90 3.94 0.07 0.069

150 150 150 90 90 10 10 0.11 0.075 0.85

150 250 250 10 10 50 50 1.39 0.162 0.28

250 50 150 10 90 50 90 2.77 0.97 1.06

250 150 250 50 10 90 10 0.17 0.1 0.07

250 250 50 90 50 10 50 2.29 0.063 0.188

350 50 250 90 50 50 10 0.14 0.127 0.106

350 150 50 10 90 90 50 2.46 1.03 1.1

350 250 150 50 10 10 90 2.29 0.142 0.19

450 150 250 10 50 10 90 2.83 1.4 0.51

450 50 150 90 10 90 50 2.59 0.19 0.11

450 250 50 50 90 50 10 0.26 0.101 0.12

550 50 250 50 90 10 50 2.41 0.1 0.185

550 150 50 90 10 50 90 4.81 0.17 0.13

550 250 150 10 50 90 10 0.38 0.7 0.25

7.4 Application of the equation on practical castings

a) Validation of L Junction

Experimental castings of L junctions were made with 0.2 carbon steel, the castings

radiography image shows a hot tear at the junction. Also few other castings were made of

L shapes but with different geometric parameters which did not have any type of tears.

87

Case 1 Case 2

Fig. 7.2 Experimental castings of L shape

Case 1 (fig.7.2) shows a case where a hot tear appears, case 2 had no hot tears even after

ultrasonic testing and radiography inspection. The geometrical parameters of both the

cases are different even though the both are L shaped junctions. These cases are simulated

in commercial software to obtain critical time that is the time taken to cool from 0.8 solid

fraction to 1.The feasibility of the equation is now checked by substituting the required

geometric parameters.

As shown the hot tear equation shows less hot tear susceptibility value for the sound

casting, these values may not give the critical casting for a visible hot tear, but given two

geometries of L junction it shows which is more susceptible to hot tearing.

Table 7.12 Geometrical parameters and calculated hot tear values for L Junction

Case L1 L2 T1 T2 D Time Hot tear

1 240 240 30 30 30 3.6 .21

2 50 50 50 10 30 1.8 0.106

88

Table 7.13 Geometrical parameters and calculated hot tear values for T junctions

L1 L2 T1 T2 depth Time Hot tear

tendency

Visible

hot tear

Case 1 660 101 12.7 25.4 25.4 0.85 .11 Tear

Case 2 660 101 25.4 50.8 25.4 1.11 .07 No tear

Case 3 914 101 50.8 50.8 25.4 .97 .05 No tear

b) Validation of T Junction

T shaped castings of steel with carbon 0.23 % was taken from literature (Monreo and

Beckerman, 2005). Several castings were casted with changes in geometrical parameters

some of the castings were found to have hot tear defect and some of them were sound. The

different geometrical parameters are taken from (Monoe and Beckermmann, 2005) and are

analyzed by using the equation obtained from the regression analysis as shown in Table

7.13, the values however couldn’t justify a critical value above or below which tear would

occur, but the equation could justify that there is decrease in the value of hot tearing

susceptibility for the shapes which doesn’t tear as shown in Table 7.13, Hence the

equation could be used to compare to same type of castings with different geometrical

parameters.As shown in fig.7.3 case 1 shows a tear and hence comes up with a greater hot

tear susceptibility value than case 2 which doesn’t tear.

Fig.7.3: Experimental Castings of T shape (Monroe and beckermann, 1999)

89

Table 7.14 Geometrical parameters and calculated hot tear values for C junction

Larm L1 L2 Tarm T1 T2 Critical

Time

Right Left

400 105 105 20 150 25 11.96 .69 .98

100 60 60 10 50 20 1.85 .50 0.64

c) Validation of C junction

Experimental castings of C shape were casted in sand mold and it was observed that there

was no hot tear formed, steel with C wih 0.3 % of carbon was taken for the experimental

purpose .This casting was compared with another casting with the cross section of C taken

from literature (Kang et al., 1999). The geometrical parameters for the two castings to be

used in the regression equation are shown in Table 7.15 .The One with more tearing has

shown more tendency value, however the cross section of casting which tore is imagined

as C. The actual geometry of casting which tore is same as shown in Fig. 6.1 .The cross

section is imagined to be in C shape to apply this equation. As shown in Table 7.14 the

values of the tendencies at the right and the left end show that the one which has earlier

developed a hot tear is more prone, that is the value of hot tearing tendency is higher.

Fig. 7.4: Experimental castings of C shape

90

7.5 Summary

The three regression equations were obtained and were applied on different castings.

• All the three regression equations obtained by the experiments help to predict

which geometry has greater tendency to tear when casted.

• However the critical value of hot tearing tendency after which tear can occur could

not be determined, since the hot tearing tendency values should be compared to

same material

• Also the number of practical experiments with hot tears should be high to justify

the Occurrence of hot tear at a threshold value.

• The parameters in equation are itself correlated and hence it is difficult to justify

the influence of some of the parameters.

• Mold was assumed rigid throughout the simulation, but practically mold is not 100

percent rigid, and hence a rigidity factor should be introduced.

• As far as comparison of two geometries is considered, the equation can give fairly

good result.

91

Chapter 8

Conclusions

An attempt to come up with a criterion to predict hot tear tendency based on geometrical

parameters for junctions prone to hot tear was accomplished, the following conclusions

are drawn from the work.

• Analysis of hot tear in the early stages of designing is a difficult task for a design

engineer, by predicting the tendency of hot tear before hand, scrap can be avoided.

• To sustain the competition and to improve the product quality and reduce lead

time, foundries need to reduce the defects. Defect analysis at earlier stages will

enable the casting engineer to avoid wastage of time and material during actual

trails.

• Junctions being the critical areas in casting, L, C, T were analyzed and a regression

fit between the geometric parameters of these shapes and hot tearing tendency was

correlated.

• The regression fit was validated with experimental castings and the results were

found in accordance with the practical case, the casting which developed a hot tear

showed a higher value of tendency.

• The need for developing regression equations of hot tears for some other junctions,

is identified.

• The present equation is only for steel sand combination, a need to develop a new

equation for other alloys and other types of moulds could help further to generalize

the equation.

• The best of the available criteria for predicting hot tear in continuous castings was

used to predict the hot tear in simple shapes. However the property values required

for prediction were sparsely available.

92

• The present equation is a simple and convenient equation based on geometrical

parameters which could be used readily at design stage.

• Almost all the complex castings are the complex combinations of junctions, hot

tear tendency can be evaluated by cutting them down into simple cross sections.

• The ability of ProCAST to predict the hot tear was validated with castings already

having tears.

8.1 Scope of Future Work

The future work which can be carried out in this project is as follows

• It is useful to extend the scope of the project to all the casting processes and all

materials. Currently it is limited to steel sand castings.

• In the current work the assumption made during simulation was that the mold is

always rigid, an experiment varying the mould hardness would further help in

giving accurate values of hot tearing tendency.

• The equations for predicting the hot tear in more complex junctions can be

developed and few more parameters can be included in future.

• The dependence of pouring temperature on hot tearing tendency can also be

correlated to increase the accuracy of the equation.

93

Annexure

Annexure 1: Hot tear tendency data for benchmark shapes

a) L shape - experiments results

Depth L1 L2 T1 T2 Time Gradient

Hot tear

tendency

20 250 100 10 50 0.429043 6.62 0.148

30 250 100 10 50 1.083333 7.91 0.174

50 250 100 10 50 1.402373 8.41 0.24

80 250 100 10 50 1.836158 9.6 0.33

100 250 100 10 50 2.063492 9.8 0.376

50 250 100 10 10 0.190678 4.72 0.136

50 250 100 10 30 0.821168 6.6 0.188

50 250 100 50 10 1.300578 5.82 0.22

50 250 100 20 10 0.4 5.8 0.168

50 250 100 20 20 0.642857 7.63 0.07

50 250 100 20 50 1.5 8.81 0.12

50 250 100 30 10 0.737705 6.42 0.16

50 250 100 30 30 0.882353 7 0.07

50 250 100 50 50 1.607143 11 0.083

50 250 125 10 50 1.5 8.34 0.243

50 250 250 10 50 1.363636 7.01 0.183

50 250 500 10 50 0.155172 7.13 0.192

50 250 1000 10 50 0.75 6.5 0.17

50 500 125 10 50 1.875 8.3 0.35

50 500 250 10 50 1.666667 7 0.333

50 500 500 10 50 1.5 6.8 0.24

50 500 1000 10 50 1.451613 6.5 0.17

50 1000 250 10 50 1.875 6.5 0.2

50 1000 500 10 50 1.730769 6.5 0.2

50 1000 1000 10 50 1.607143 6.8 0.342

50 1500 200 10 50 3 7.33 0.3

50 1500 250 10 50 2.866242 6 0.53

50 1500 500 10 50 2.5 5.8 0.596

50 1500 800 10 50 2.368421 6.77 0.43

50 1500 750 10 50 2.319588 5.36 0.41

50 1500 1000 10 50 2.25 6.36 0.515

50 1500 1500 10 50 1.184211 6.35 0.5

50 1500 2000 10 50 1.216216 6.53 0.43

50 200 250 10 50 1.451613 7 0.209

50 250 200 10 50 1.451613 7.5 0.168

20 100 200 10 70 0.371901 4.64 0.144

20 200 100 70 10 0.321429 5.32 0.123

20 500 250 100 50 0.432692 5 0.101

30 250 500 50 100 0.9 7 0.07

30 300 100 50 10 1.607143 6.58 0.16

94

40 500 100 100 20 1.607143 6.52 0.092

50 500 200 100 300 2.8125 12.2 0.07

60 100 300 50 80 2.727273 12.02 0.013

70 400 400 30 10 0.9 6.07 0.211

80 400 300 200 100 4.5 15.3 0.15

100 300 300 10 30 0.821168 7.71 0.143

100 400 100 10 10 0.190678 514 0.32

30 200 100 20 100 0.882353 7.13 0.1

40 300 150 16 80 1.5 7.1 0.112

50 400 200 24 120 2.8125 9.39 0.106

60 200 300 30 150 3 10.1 0.07

30 100 200 40 200 0.661765 8.45 0.07

30 200 100 30 90 0.849057 8.1 0.06

40 300 150 16 48 1.323529 8.19 0.09

50 400 200 70 210 2.142857 11.26 0.1

60 200 300 50 150 3 10.8 0.083

20 100 200 40 120 0.36 6.81 0.05

20 100 70 50 10 0.32 6.36 0.07

40 200 100 80 20 1.31 6.35 0.012

50 300 150 100 20 2.08 6.53 0.01

40 250 200 80 15 1.42 7 0.12

60 300 100 20 20 0.75 7.5 0.06

80 350 100 30 10 0.81 4.64 0.146

100 350 100 80 10 4.48 5.32 0.114

100 350 100 80 50 4.44 6.36 0.065

100 350 100 80 80 4.59 6.35 0.05

b) T shape experiments results

L1 L2 T1 T2 D time Hot tearTendency

150 50 10 10 30 0.2 0.076

150 150 40 40 50 1.48 0.096

150 250 70 70 70 3.23 0.127

150 350 100 100 90 5.59 0.147

250 50 40 70 90 4.2 0.11

250 150 10 100 70 3.77 0.22

250 250 100 10 50 2.3 0.294

250 350 70 40 30 0.85 0.064

350 50 70 100 50 2.25 0.085

350 150 100 70 30 0.77 0.07

350 250 10 40 90 1.58 0.18

350 350 40 10 70 1.46 0.42

450 50 100 40 70 3.94 0.08

450 150 70 10 90 3.65 0.258

450 250 40 100 30 0.98 0.08

450 350 10 70 50 1.97 0.187

95

660 101 12.7 25.4 25.4 0.85 0.121

660 101 12.7 50.8 25.4 1.12 0.11

660 101 25.4 25.4 25.4 0.85 0.114

660 101 25.4 50.8 25.4 1.11 0.05

660 101 50.8 25.4 25.4 0.97 0.07

914 101 50.8 50.8 25.4 0.97 0.05

914 101 25.4 25.4 25.4 0.81 0.07

914 101 25.4 25.4 25.4 1.09 0.075

c) C shape experiment results

L1 L2 L3 T1 T2 T3 Hot tear(L) Hot tear(R)

250 100 150 10 50 100 0.57 0.25

250 100 150 10 50 100 0.7 0.54

250 100 150 10 50 100 0.72 0.75

250 100 150 10 50 100 1.04 1.04

350 100 150 10 50 100 1.06 1.27

150 100 150 10 50 100 0.638 0.589

150 50 100 10 50 100 0.357 0.6

150 100 200 10 50 100 0.613 0.634

150 150 300 10 50 100 0.632 0.7

250 50 150 10 50 100 0.76 1.2

250 100 200 10 50 100 0.91 1.07

250 150 300 10 50 100 0.94 1.25

350 150 400 10 50 100 1.09 1.29

500 50 150 10 50 100 0.94 1.15

500 150 300 10 50 100 1.48 1.45

500 100 400 10 50 100 1.2 1.53

250 100 150 20 50 100 0.436 0.374

250 100 150 30 60 120 0.215 0.143

250 100 150 40 20 80 0.144 0.114

250 100 150 50 10 100 0.273 0.109

250 100 150 50 50 50 0.179 0.07

250 100 150 70 20 100 0.15 0.084

350 150 300 50 10 150 0.171 0.125

350 150 300 10 10 150 0.35 0.62

150 100 150 10 10 150 0.164 0.308

150 100 150 50 10 150 0.172 0.112

100 50 100 20 30 50 0.21 0.07

300 200 400 30 10 80 0.133 0.156

150 70 140 50 30 100 0.129 0.107

350 150 250 100 10 100 0.138 0.08

250 100 150 10 50 16 0.509 0.324

250 100 150 10 50 25 0.74 0.58

250 100 150 10 50 40 0.77 0.92

250 100 150 10 50 70 0.63 0.86

250 100 150 10 50 130 1.1 0.91

250 100 150 10 50 170 0.71 1.35

250 100 150 10 30 100 0.691 0.634

96

250 100 150 10 80 100 1.04 0.95

250 100 150 10 100 100 1.01 1.01

250 100 150 10 150 100 0.92 0.92

250 150 100 10 50 10 0.313 0.139

250 250 50 10 100 50 0.75 0.6

300 200 100 10 70 20 0.56 0.44

300 200 50 20 20 20 0.08 0.114

350 300 150 20 70 20 0.23 0.112

97

Annexure 2: Properties of steel used in simulation

Temperature

conductivity Thermal conductivity

2.30E+01 2.50E+01

2.00E+02 2.63E+01

5.00E+02 2.73E+01

6.00E+02 2.78E+01

8.00E+02 2.81E+01

8.50E+02 2.84E+01

9.00E+02 3.04E+01

1.00E+03 3.12E+01

1.10E+03 3.42E+01

2.00E+03 3.42E+01

Temperature Density

2.45E+02 7.63E+03

2.65E+02 7.62E+03

2.85E+02 7.61E+03

3.05E+02 7.61E+03

3.25E+02 7.60E+03

3.45E+02 7.60E+03

3.65E+02 7.59E+03

3.85E+02 7.58E+03

4.05E+02 7.58E+03

4.25E+02 7.57E+03

4.45E+02 7.56E+03

4.65E+02 7.56E+03

4.85E+02 7.55E+03

5.05E+02 7.55E+03

5.25E+02 7.54E+03

5.45E+02 7.53E+03

5.65E+02 7.53E+03

5.85E+02 7.52E+03

6.05E+02 7.51E+03

Temerature Youngs modulus

2.48E+02 2.10E+05

3.38E+02 2.07E+05

4.28E+02 2.00E+05

5.18E+02 1.89E+05

6.08E+02 1.75E+05

6.98E+02 1.58E+05

7.88E+02 1.41E+05

8.78E+02 1.25E+05

9.68E+02 1.05E+05

1.06E+03 8.60E+04

1.15E+03 6.62E+04

98

1.24E+03 4.67E+04

1.33E+03 2.80E+04

1.37E+03 1.80E+04

1.38E+03 1.52E+04

1.39E+03 1.25E+04

1.40E+03 9.92E+03

1.41E+03 7.38E+03

1.42E+03 5.00E+03

1.43E+03 2.94E+03

1.44E+03 1.67E+03

Temperature Poison ratio

2.48E+02 3.63E-01

3.68E+02 3.63E-01

4.88E+02 3.63E-01

6.08E+02 3.63E-01

7.28E+02 3.63E-01

8.48E+02 3.63E-01

9.68E+02 3.63E-01

1.09E+03 3.63E-01

1.21E+03 3.63E-01

1.33E+03 3.63E-01

1.38E+03 3.67E-01

1.39E+03 3.72E-01

1.40E+03 3.79E-01

Temperature

Thermal expansion

coefficient

3.58E+02 1.43E-05

5.98E+02 1.52E-05

7.78E+02 1.51E-05

8.38E+02 1.52E-05

8.98E+02 1.26E-05

1.02E+03 1.42E-05

1.14E+03 1.53E-05

1.26E+03 1.61E-05

1.37E+03 1.66E-05

1.38E+03 1.65E-05

1.40E+03 1.64E-05

1.41E+03 1.63E-05

1.42E+03 1.60E-05

1.43E+03 1.55E-05

1.47E+03 1.47E-05

99

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