〉〉 Fusion of Core Technologies

Analysis of Deformation Twin and Mechanical Strength
Using Simulation Model in the Deformation Microstructureof Copper Alloy
Hidemichi Fujiwara*, Hiroshi Kaneko*

Recently, the compatibility of the strength, the workability, and the high conductivity are needed in copper alloy materials which are produced by controlling the
combined process of the cold working and the aging treatment, in response to size reduction ofelectronic connectors and increase of the assembly density, and in improving the performance ofelectronic devices. Especially, in the solution hardening alloys, the microstructure change in cold
working process becomes a very important factor, although the microstructure change behavior
is extremely complex. In this report, the calculation model to evaluate the microstructure changes resulting from the introduction of dislocation, the creation of dislocation cell/substructure andthe deformation twin, and the effect of the dynamic recovery in deformation processing, was proposed. And the microstructure change due to cold working processing was analyzed with thismodel regarding a relationship between a processing condition, the microstructure, and the flow
stress. By applying evaluations to various Cu-Zn-Si system alloys which have different stacking
fault energy, the validity of the calculation model was confirmed by comparing the experimental
and the calculated results. And the concept of the microstructure control in the deformation twin
creation based on results of this model calculation was summarized.

ABSTRACTINTRODUCTION
1.1.INTRODUCTION
Recently, along with the higher performance of electronics devices, size reduction of connectors and increase of
the assembly density are in progress. Based on the structure controlling of the Copper alloy through a sophisticated combination of the cold working and the aging treatment, a high conductive material, which has both astrength and a workability required as a practical material,
have been manufactured. Especially, in the solution hardening alloys, the structure change in the cold working
processing becomes a very important factor in controllingits property. Since the phenomenon is very complex, amodeling of the phenomenon and a calculation model
based on it are required to control the alloy structure.
Therefore, for the purpose of this report, we constructeda model taking into account the dislocation introduction
on the structure change due to the processing distortion
introduction, the creation of the dislocation cell/subgrain
structure, the effect of the deformation twin creation andthe dynamic recovery effect. In addition to analyzing a
relationship between the processing condition, the strucReprinted translation from Copper and Copper Alloy, Journal ofJapan Institute of Copper, 58, vol.1 (2019)*

ture state and the flow stress, we compared and verified
the experimental results and the calculation results for
Cu-Zn-Si system alloys whose stacking fault energy,
which greatly affects the deformation twin creation, canbe controlled by the alloy composition. And, based on the
results, in addition to examining the validity of the model,
based on the results obtained from the model calculation,
the concept of the structure control on the work hardening alloy was summarized.

ANALYSIS
METHODAND
PROCEDURE
2.2.ANALYSISMETHODAND
PROCEDURE
2.1 Analysis Model for Working Structure Simulation
Figure 1 shows a typical manufacturing process of the
Copper alloy and it schematically illustrates the microstructure change during the cold rolling of the Copper
alloy. According to the report by Paul et al.1), a large difference in the microstructure creation state is caused
between the case where the refinement of the dislocation
cell progresses in the crystal grains and the case where
the deformation twin is preferentially formed.
Based on this microstructural change, the structure
simulation model in the working process of the Copper
alloy was studied.

Laboratories for Fusion of Core Technologies, R&D Division

Furukawa Electric Review, No. 51 202024

Analysis of the Deformation Twin and the Mechanical Strength Using a Simulation Model in the Deformation Microstructure of Copper Alloy

Low reduction

High reduction

G
（110）
[001]

Slip/Deformation of
dislocation creation

Non deformation twin
（Cell stracture）

Y
（111）
[112]

Micro shear band

Brass
（110）
<112>

Rotation caused bymultiple deformation
twin and micro
shear band

Y
（111）
[112]

Deformation twin

Multiple Micro shear band

Figure 1 Schematic illustration of microstructure change
during cold rolling in copper alloy.

2.1.1 Definitions of the conditions to form the deformation twin during working treatment
Based on the deformation twin creation, the structurechange in the working process is considered to occur as
follows. As shown in Figure 2, a flow stress competition
occurs between the stress τcell for creating the substructure such as the dislocation cells and a creation stressτtwin of the deformation twin, and a deformation occurs
in a mode that results in a lower flow stress. It means
that, the deformation twin is formed when τcell>τtwin.
Therefore, It is considered that only when the condition ofτcell>τtwin is satisfied in the deformation process, thedeformation twin is generated, and the conditions for a
pre-creation stage of a multi-micro shear band structure
is completed.

Flow stressτ

Increase of dislocation densityτcell
Stacking fault energy
High

Low

Increase of deformation twinτtwin
Deformation strain εFigure 2 Schematic illustration about the effect of stacking
fault energy on flow stress in Copper alloy during cold
deformation.

2.1.2 Relation equation between the strain mode andthe shear deformation amount
Equation (1) is obtained by defining the slip deformation
due to the dislocation cell creation and the deformation
due to the deformation twin with the shear deformation
amount dγ.
dγ=(1- F )dγg +γt dF(1)Here, F is the deformation twin fraction, γg is the shear
strain due to the slip, γ t is the twin shear strain. 2) In
Equation (1), the important thing is the criteria for thegeneration and growth of the deformation twin caused by〉〉 Fusion of Core Technologies

the shear deformation. As previously defined, the condition of τcell>τtwin, that is, the magnitude of τcell /τtwin
directly affects the change for the strain ε of the deformation twin fraction, then it can be shown in Equation (2).
dF=(1- F)m·dε(2)Here, m is defined as, m=nk1log (τcell /τtwin).
nk1 is a variable related to a nucleation frequency of thedeformation twin, and since a grain boundary density isequivalent to a nucleation site density per unit area, there
is an effect of proportionality to 1/D, also there is aneffect that the larger the restrained shear force δτr
between the crystal grains the more suppressed thedeformation twin creation 3). And there is a relationshipproportional to the 1/2 power of the crystal grain size D
as the reciprocal (1/δτr). Based on these nk1 can be considered to be a coefficient proportional to D -1/2 dependingon the product. Therefore, the creation of the deformation
twin is a model depending on the crystal grain size before
the working treatment.
Also, a creation stress of the dislocation cell depends
on the initial gran size and the dislocation density, and thecreation stress of the deformation twin is the sum of thecreation stress of the extended dislocation and the creation stress of the stacking fault, then these stresses aredefined by Equation (3) and Equation (4) 4).
τ cell=2Aμb/δ+αμbρ 1/2(3)τtwin=2Aμb1 /δ+Esf /b1 /n(4)Here, Esf is the stacking fault energy, A and α are constants both 1.0. μ is the shear elastic modulus, ρ is thedislocation density, b is Vurgers vector, b1 is the partial
dislocation Vurgers vector, n is the stacking fault stressconcentration factor (n=0.2), and δ is the cell size in theregion where twins are not formed.
2.1.3 Relationship between the shear strain amountand the change in the dislocation structure
The dislocation density change in the deformation twin isdefined by Equation (5) 2).
dρ/dγ=1/(b· Λ1)- f·ρ(5)Λ1 is 1/D+1/t+k√ρ, D is the crystal grain size, t is thedeformation twin distance and k is a constant (=0.1).
On the other hand, the dislocation density change inthe matrix is defined by Equation (6).
dρ/dγ=1/(b·Λ)- f·ρ(6)Here, Λ is 1/D+k√ρ, f is a fitting term (dynamic recovery
parameter) taking into account an effect that shows
decrease in the dislocation density due to the dynamic
recovery effect, and is greatly affected by the working
condition. The following definition was made in consideration of Zener-Hollmon factor based on the effect of theworking strain rate and the working temperature.
f=Pfr /log(ED ·Rsf · exp(E/R · (1/Tw ))(7)Here, Pfr, Rsf are fitting constants, ED is the strain rate, E
Furukawa Electric Review, No. 51 2020

25

Analysis of the Deformation Twin and the Mechanical Strength Using a Simulation Model in the Deformation Microstructure of Copper Alloyis the diffusion activation energy of the copper, R is thegas constant and Tw is the working temperature.
2.1.4 Relationship between the shear strain amount γ
and the structure change in the cell structure
Since the dislocation cell creation rate also changes
depending on the dislocation density, these considerations are defined as in Equation (8), using the model proposed by Nes et al.5).
The change in the cell size per the shear strain is determined by the balance between the size change dδ-/dγ
due to the strain and the coarsening of the cell dδ+/dγ
due to the dynamic recovery.
dδ /dγ=dδ +/dγ+dδ -/dγ(8)Applying the relationship of Equation (8) to the change
in the cell size within the deformation twin,dδ /dγ=Vd· b · Bg√ρ· {exp(-(Usd -PVa)/(kTw))}(9a)dδ -/dγ=-√3b1/2 · δ 5/2 /(φ3/2· δini · Kiv )(9b)+2δ ini is the initial dislocation cell size, Tw is the working
temperature, Usd, P, Va are values related to the dynamic
recovery activation energy of the dislocation.
On the other hand, applying the relationship ofEquation (8) to the change in the dislocation cell size
within the matrix,dδ +/dγ=Vd · b 2· Bg√ρ · {exp (-(U sd -PVa ) / (kT ) ) }(10a)dδ -/dγ =-√3b1/2 · δ 5/2 /(φ 3/2 · δ ini · K iv )(10b)This δ ini is limited to the deformation twin distance, thenthe cell refinement is easy to be caused by the initialstage of the deformation. Here, the values used by Nes
et al.5) were used to the model calculation from Equation(9a) to Equation (10b).
2.1.5 Relationship between the creation limit of thedeformation twin and the micro shear band
As shown in Figure 1, as the working treatment proceeds,
as the refinement proceeds in the dislocation cell within
the deformation twin, and the micro shear band crossing
the deformation twin is formed. This phenomenon is considered to be caused by the change of the deformationmode, since the dislocation cell within the deformation
twin is getting closer to the refinement limit.
Though, there is no clear report about the critical valueof the dislocation cell size within the deformation twin, it
is considered that the value is close to 10 nm which isequivalent to the crystal grain refinement limit δ crit .
Therefore, considering that due to the strain ε sb , whichis generated by the creation of the micro shear band, thedeformation strain by the deformation twin creation is
reduced by ε sb , the equation of the generation and thegrowth shown in Equation (2) can be rewritten as follow.
dF=(1-F)m · d(ε - εsb )(2b)By expressing the ratio Rsb (=εsb /ε) which is the ration
between the deformation twin creation related strain εand the micro shear band creation related strain ε sb, it canbe explained as in Equation (11) in the three dimensional〉〉 Fusion of Core Technologies

structure model of the expand volume theory, by using
the dislocation cell sizeδtwin within the deformation twin
and the critical value δ crit (=10 nm).
Rsb =1- exp{k twin · (δ crit /δ twin ) 3 }(11)Here, k twin is the fitting parameter and by using theabove Equation, it is available to calculate and evaluate
the creation progress state of the deformation twin inconsideration of the micro shear band creation.
2.1.6 Relationship between the structure parameterand the flow stress/proof stress
From the above shown relationship, the flow stress in thedislocation cell structure region and the flow stress in the
deformation twin creation region can be obtained fromthe Equation (12) 6).
σw =σ0 + K1 ρ1/2 +K 2 δ -1+K 3d twin-1/2(12)Here, σ0 is the yield stress of the single crystal, ρ is thedislocation density, δ is the dislocation cell size, d twin is
the deformation twin distance, Kn (n=1~3) is a parameter
depending on the Taylor factor. When the share of stressin the non-deformation twin region is σ w (M), and the shareof stress in the deformation twin region is σ w (T), the flow
stress σ w f in the working process of the entire structure isshown in Equation (13).
σwf =(1-F ) · σw (M)+F · σw (T)(13)2.1.7 Calculation procedure using the working structure simulation model
The calculation procedure in this simulation model is asfollow.
At first, obtain each flow stress of the matrix and of thedeformation twin region in the case of the unit shear
strain is applied, from the calculation results of the dislocation density and the cell size taking into account the
dynamic recovery effect. And based on this, the deformation twin creation state corresponding to the working
strain is calculated.
The next procedure is to calculate the strength property(the flow stress) from the obtained structure parametervalue.
On proceeding with the calculation, in order to determine the deformation twin creation stress, the stacking
fault energy, the working condition and the initial structure
are very important influencing factors.
Then, the values were verified using literature values
from Ab-initio calculation 7), and the correspondence
between the calculation results and the alloy compositions were examined.
In addition, regarding the effect of the working condition and the initial structure, the evaluation was proceeding under the calculation condition that enables the comparison with the prototype evaluation results on Cu-Zn-Si
system alloys.
2.1.8 Experimental structural property evaluation with
the Copper alloy
The Copper alloy, with 5 to 30 mass% of Zn and 0.03 to
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Analysis of the Deformation Twin and the Mechanical Strength Using a Simulation Model in the Deformation Microstructure of Copper Alloy

3.2 Numerical Study on the Simulation Parameters
The stacking fault energy was reported to be 0.055 J/m2
for 5%Zn alloy and 0.014 J/m 2 for 30%Zn alloy, andaccording to the evaluation by Ab-initio cluster variational
calculation 7) , 0.03 J/m 2 for 5%Zn-0.5%Si alloy and
0.010-0.014 J/m2 for 30%Zn-0.5%Si alloy. In this calculation, the values shown in Table 1 were used. As shown in
Figure 3, regarding the effect of the initial crystal grain
size D on the deformation twin distance t, specimenmaterials were processed in different sizes for
Cu30%Zn0.03%Si alloy, and the lamella distance of twin
was measured using the transmission electron microscope. Then, the relationship of Equation (14) was
obtained. And this relation was used for the calculation.
T=0.0025D+23.0[nm](14)Lamellar distance of deformation twin（T/nm）

0.5 mass% of Si, was melted, casted and hot-rolled andthe thickness was adjusted to 2.5 mm by cold- rolling.
Then it was heated for 2 hours and air cooled at 380°C
and the roll-working treatment was applied within therange of 1.6 to 2.5 of strain. After these treatment, theCopper alloy was evaluated on 0.2% proof stress by thetensile test, on the structure analysis by X-ray diffraction(XRD) with a {111} diffraction intensity/total peak intensity,and on the lamella distance of the deformation twin by atransmission electron microscope.
In addition, the deformation twin fraction was calculated by normalization of the {111} diffraction intensity ratio/
total peak ratio through the powder method. Further, inorder to investigate the influence of the working temperature, the materials were kept at room temperature and at
liquid nitrogen temperature were rolled, and the similarevaluations were performed.

120

RESULTS
3.3.RESULTS
3.1 Calculated Alloy Composition
As the alloy evaluation data, used to examine the correspondence with the simulation calculation values, a comparison was made with the alloys having compositions
shown in Table 1.
Table 1

Alloy compositions used for experimental evaluation,model calculation and stacking fault energy evaluated7)
from Ab-initio calculation based on alloy compositions.
Zn(mass%)

Si(mass%)

30Zn0.03Si

30.2

0.031

0.015

30Zn0.5Si

32.5

0.45

0.013

5Zn0.03Si

5.1

0.021

0.034

5Zn0.5Si

5.0

0.39

0.030

Alloy symbol

T [nm]=0.0025 D+23

100

Table 2

Stacking fault energy(J/m2)

80
60
40
20
0

0

5000

10000

15000

20000

25000 30000 35000

Initial grain size（D/nm）

Figure 3 Relationship between the initial grain size and thelamellar distance of deformation twin in Copper-Zincalloys.

Other simulation parameter values used in this model
calculation are shown in Table 2.

The values of parameter and constant used in the simulation model.

(1) Calculation of the deformation twin creation
M0

Taylor factor

0.3µ

Shear modulus

48.3 × 109 N/m2bVurgers vector of the full dislocation

0.3615/ √2 nm

b1

Vurgers vector of the partial dislocation

0.3615/ √6 nm

n k1

Parameter of dependency in grain size

5.6 × 10 −4・D −1/2

Pfr

Fitting parameter of the dynamic recovery

70

Rsf

Fitting parameter of the dynamic recovery

1 × 10 5

E

Activation energy of the Copper diffusion

70 kJ/mol(2) Criteria of the Micro shear band creation
ktwin

Fitting parameter in formation of the micro shear band

5(3) Calculation of the strength property
K1

Fitting parameter in the effect of the dislocation

AµbM0（A=1.0）

K2

Fitting parameter in the effect of the deformation twin

A1 µbM0（A1 =1.0）

K3

Fitting parameter in the effect of the grain size

A2 µb1/2 M0（A2 =0.5）

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27

3.3

Comparison Between the Model Calculation andthe Experimental Results
3.3.1 Calculation results
The calculation results of the work hardening property,
the deformation twin fraction and the dislocation cell size
within the deformation twin, based on the simulations
performed under the condition of room temperature(297 K) and the low strain rate 1/s, are shown in Figure 4,
Figure 5 and Figure 6.
As the stacking fault energy decreases, the deformation
twin creation starts from the low strain amount region,and the tendency of the work hardening is to occur moreeasily due to the effect of the accumulation of the dislocation caused within the deformation twin and the cellrefinement.
In this model calculation, the increase of the flow stressfrom the strain was more remarkable as the reduction of
stacking fault energy.

Flow stress（σ/Pa）

1.6E+09
1.4E+09
1.2E+09
1E+09
8E+08

SFE 0.010 J/m2
SFE 0.012 J/m2
SFE 0.015 J/m2
SFE 0.020 J/m2
SFE 0.025 J/m2
SFE 0.030 J/m2
SFE 0.034 J/m2

6E+08
4E+08
2E+08
0
0.0

1.0

2.0
Strain（ε）

3.0

Fraction of deformation twin（F）

Figure 4 Calculation results of the flow stress-strain curve invarious stacking fault energy alloys.
2(SFE: 0.01~0.034 J/m , D=10 μm)
1.0

SFE 0.010 J/m2
SFE 0.012 J/m2
SFE 0.015 J/m2
SFE 0.020 J/m2
SFE 0.025 J/m2
SFE 0.030 J/m2
SFE 0.034 J/m2

0.9
0.8
0.7
0.6
0.5
0.4
0.3
0.2
0.1
0.0

0.0

0.5

1.0

1.5
2.0
Strain（ε）

2.5

3.0

Figure 5 Calculation results of the deformation twin
fractionstrain curve in various stacking fault energy
alloys.
2(SFE: 0.01~0.034 J/m , D=10 μm)

Dislocation cell size in twin（δ/m）

Analysis of the Deformation Twin and the Mechanical Strength Using a Simulation Model in the Deformation Microstructure of Copper Alloy〉〉 Fusion of Core Technologies

8E-08
7E-08
6E-08
5E-08
4E-08
3E-08
2E-08
1E-08
0
0.0

SFE 0.010 J/m2
SFE 0.012 J/m2
SFE 0.015 J/m2
SFE 0.020 J/m2
SFE 0.025 J/m2
SFE 0.030 J/m2
SFE 0.034 J/m2

1.0

2.0
Strain（ε）

3.0

Figure 6 Calculation results in the change of dislocation cellsize in various stacking fault energy alloys.
2(SFE: 0.01~0.034 J/m , D=10 μm)

3.3.2 Effects of the Alloy Composition (Stacking Fault
Energy) and the Initial Structure
Figure 7 shows the relation between the flow stress at theplastic strain ε=1.6 obtained from the calculation and the
0.2% proof stress of the specimen experimentally processed at the plastic strain ε=1.6, also shows the correspondence between the calculated and the experimental
values of the deformation twin fraction. Here, those having the multiple data in the same alloy system, including
the data at different initial grain sizes and working temperatures. It can be seen that the experimental proof
stress corresponds well to the calculated value. And, thevalue on the deformation twin fraction obtained by the
structure analysis on the processed sample has relatively
good correspondence with the calculated value. At astrain amount of 1.6, due to the difference in the stacking
fault energy, 400 MPa or more of strength difference wascaused, this is considered to be extreme.
For a Cu30%Zn0.05%Si alloy with a composition
equivalent to 0.015 J/m 2 of the stacking fault energy,
under the condition of different initial crystal grain sizes,
the strain amount dependence of the deformation twin in
the creation state was compared between the experimental values and the calculated values as shown in Figure 8.
And it was confirmed that as the grain size increases
the amount of strain, which accelerate the deformation
twin, increases. With this model, it is considered that theevaluation of the contribution to the creation process andthe strength of the deformation twin are possible. Figure 9shows the relationship between the calculated flow stressand the one experimentally obtained 0.2% proof stress. It
can be seen that even with the working strain amount of
1.6, a strength difference of approximately 100 MPa
occurs due to the difference in the initial crystal grain
size.

Furukawa Electric Review, No. 51 202028〉〉 Fusion of Core Technologies

Analysis of the Deformation Twin and the Mechanical Strength Using a Simulation Model in the Deformation Microstructure of Copper Alloy

30Zn0.5Si(0.013 J/m2)

(a)

800

Experimental deformation twin（F）

0.2% Proof stress（MPa）

1000

30Zn0.03Si(0.015 J/m2)

600

400

5Zn0.5Si(0.030 J/m2)

200

05Zn0.03Si(0.034 J/m2)
0

200

400

600

800

1

(b)

0.8

30Zn0.5Si(0.013 J/m2)

30Zn0.03Si(0.015 J/m2)

0.6

0.4
5Zn0.5Si(0.030 J/m2)

0.2

0

1000

5Zn0.03Si(0.034 J/m2)
0

0.2

0.4

0.6

0.8

1

Calculated deformation twin（F）

Calculated ﬂow stress（MPa）

0.6

grain size 5 µm

0.5Volume fraction of deformation twin（F）

Volume fraction of deformation twin（F）

Figure 7 Relationship between calculated and experimental results in (a) the strength property and (b) the fraction of deformation
twin at the condition of strain ε=1.6 .

(a)grain size 30 µm

0.4
0.3
0.2
0.1
0

0

0.5

1

1.5

2

0.6

(b)

calculated :grain size 5 µm

0.5calcurated:grain size 30 µm

0.4
0.3
0.2
0.1
0

0

0.5

1

1.5

2

Strain（ε）

Strain（ε）

9.0E+088.0E+08
7.0E+08
6.0E+08
5.0E+08
4.0E+08
3.0E+082.0E+08
1.0E+08
0.0E+00

the deformation twin creation process on the initial crystal
grain size, since there are some difference in correspondence relation between the experimental values and thecalculated values, for more detailed analysis , it is necessary to consider not only the initial crystal grain size but
also the influence of the initial texture.

calculated ﬂow stress: grain size 5 µm
calcurated ﬂow stress: grain size 30 µm
0.2% Proof stress: grain size 5 µm
0.2% proof stress: grain size 30 µm

0

0.5

1
Strain（ε）

1.5

2Figure 9 Calculated Stress-strain curve and 0.2% proof stressevaluated experimentally at deformation strain ε=1.6 in
2
Cu30%Zn0.03%Si alloy. (SFE: 0.013 J/m )Figure 10 shows the evaluation result of the effect on
the creation process of the deformation twin when the initial crystal grain size of Cu30%Zn0.5%Si alloy ischanged more. It can be confirmed both from the experimental results and the calculation results, that the effectof the suppression on the creation of the deformation
twin is expressed. However, regarding the dependence ofVolume fraction of defomation twin（F）

Flow stress and proof stress（σ/Pa）

Figure 8 Fraction of deformation twin-strain curve in (a) the experimental evaluation and (b) the model calculation at2
the condition of stacking fault energy: 0.015 J/m in Cu30%Zn0.03%Si alloy.

0.6
0.5

Cu30Zn0.5Si
SFE: 0.013 J/m2

0.4
0.3

ε=1.6

0.2

Experimental
Calculated

0.10＠Strain rate: 10 sec -1

0

50

100

150

200

250

300

Grain size before deformation（D/µm）

Figure 10 The effect of the grain size before deformation to
the volume fraction of deformation twin shown withcalculated and experimentally evaluated results at thecondition of deformation strain in Cu30%Zn0.5%Si
2alloy. (SFE: 0.013 J/m )Furukawa Electric Review, No. 51 202029

Analysis of the Deformation Twin and the Mechanical Strength Using a Simulation Model in the Deformation Microstructure of Copper Alloy

600.0

（a）

180 K
（LN2）
280 K
（RT)

500.0
400.0
300.0
200.0
100.0
0.0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

Strain（ε）

700.0
Calcurated ﬂow stress（σ/MPa）

0.2% Proof stress（σ/MPa）

700.0〉〉 Fusion of Core Technologies（b）

180 K, 10 sec -1

600.0

280 K, 10 sec -1

500.0

380 K, 10 sec -1

400.0
300.0
200.0
100.0
0.0
0.0

0.5

1.0

1.5

2.0

2.5

3.0

Strain（ε）

Figure 11 Stress-strain curve in (a) the experimental evaluation and (b) the model calculation at the condition of stacking fault energy
20.034 J/m in various deformation temperature in Cu5%Zn0.03%Si alloy.

3.3.3 Effects of the working condition
Figure 11 shows the correspondence between the experimental values and the calculation values of the work
hardening property of the Cu5%Zn0.03%Si alloy with thestacking fault energy of 0.030 J/m2, one was kept in room
temperature another was cooled by the liquid nitrogen(equivalent to 180 K) and were rolled out.
It was experimentally confirmed that the liquid nitrogencooling rolling has a better work hardening property thanthe one of the room temperature rolling, and this is corresponding to the calculation values. It is necessary to take
into account the effect of the working heat generation on
the correspondence between the experimental working
temperature and the working temperature of the model
calculation, and the verification with higher accuracy will
be a future issue. Based on the results obtained for thistime, the effect of the working temperature appears as astrength difference of about 60 - 80 MPa at 1.6 strain
amount, based on the experimental values and the calculation values.

CONSIDERATION
4.4.CONSIDERATION
4.1

About the Structure Control Using theDeformation Twin Creation and the Work
Hardening Property
Comparing Figure 4, Figure 9 and Figure 11 which show
the flow stress change behavior obtained by the calculation, it can clearly be considered that the stacking fault
energy, that is, the alloy composition gives the largest
influence to the strength change caused by the working
treatment. However, on the other hand, the alloy with low
stacking fault energy of 0.010 J/m 2 tends to be suppressed by the creation of the deformation twin as shownin Figure 5. Because, when strain amount exceeds 2.0,
the dislocation cell size comes closer to the refinement
critical value of 10 nm as shown in Figure 6, and the contribution of the strain increases due to the creation of the
micro shear band. This indicates that, materials withsmall stacking fault energy are structurally restricted in alarge working strain region of over 2.0 strain amount, andhave the possibility to lower the work hardening property.
Also, considering by taking the effect of the initial crystal
size as an example, the grain size gives large effect on
the lamella distance of the deformation twin, and by
reducing the initial crystal grain size, the refinement of thedislocation cell size within the deformation twin becomeseasier. So, it can be considered that this similarly affects
the deformation twin and the creation of the micro shear
band.
This fact indicates that the factors of the alloy composition and the initial crystal grain size do not simply affect ina synergistic manner on the strength properties. Then,based on these effects, when the alloy composition andthe working initial structure state were used as parameters, we examined how the working structure creationand the changes in the strength properties were affected.
4.2 About the Concept of the Structure Control of
the Deformation Twin Forming Alloy
Figure 12 shows the results of the modeling calculation
for the consideration of the effects of the stacking fault
energy and the initial crystal grain size in the working process on the deformation twin creation also the refinement
and the change in the strength of the dislocation cellstructure. When the strain is applied to the material with
1 μm and 30 μm of the initial grain size, which has a highstacking fault energy of 0.03 J/m2, at the strain amountε of 2.5, the creation of the deformation twin proceeds toabout 52% under the condition of the small initial grain
size (1 μm). But, under the condition of the large grainsize, the creation of the deformation twin proceeds only
to about 16%, and it is resulting in that smaller the initial
grain size is the higher strength is obtained by the work
hardening. On the other hand, when the stacking fault
energy is as low as 0.01 J/m2, by using the material withthe small initial crystal grain size of 1 μm in diameter, due
to the working strain, the deformation twin creation proceeds from the low strain amount state and the refinement of the dislocation cell proceeds from the low strain
working condition, and it is considered that the high
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Analysis of the Deformation Twin and the Mechanical Strength Using a Simulation Model in the Deformation Microstructure of Copper Alloy

Flow stress（σ/Pa）

1.4E+09
1.2E+09
1E+09

ε=1.0
ε=1.6
ε=2.5

8E+08
6E+08
SFE: 0.01 J/m D: 30 µm
2

4E+08
2E+08
0
0.00

SFE: 0.03 J/m2 D: 30 µm

0.20

0.40

1.6E+09（a）

SFE: 0.01 J/m2 D: 1 µm
SFE: 0.03 J/m2 D: 1 µm
SFE: 0.01 J/m2 D: 30 µm
SFE: 0.03 J/m2 D: 30 µm

0.60

1.4E+09
Flow stress（σ/Pa）

1.6E+09

1.2E+09
1E+09〉〉 Fusion of Core Technologies

SFE: 0.01 J/m2 D: 1 µm
SFE: 0.03 J/m2 D: 1 µm
SFE: 0.01 J/m2 D: 30 µm
SFE: 0.03 J/m2 D: 30 µm

（b）

ε=1.0
ε=1.6
ε=2.5

8E+08
6E+08
4E+08
2E+08

0.80

1.00

Fraction of deformation twin（F）

0
1.00E-09

1.00E-08

1.00E-07

Dislocation cell size（δ/m）

Figure 12 Calculated results of (a) the stress-deformation twin fraction curve and (b) the stress-dislocation cell size at the condition2
2of stacking fault energy: 0.01 J/m and 0.03 J/m .

strength properties can be expected in the low strain
working state (ε=1.6). Further , on the other hand, in theworking treatment of the high strain amount region(ε=2.5), the creation of the micro shear band and its multiplexing occur preferentially, so the change in thestrength properties on the strain amount is smaller.
Against these trends, it is considered that, in the material
with the same stacking fault energy and the large initial
crystal grain size (30 μm), even the strain amount, atwhich the creation of the deformation twin is activated,
shifts to a slightly higher side, but due to the effect ofwidening the lamellar distance of the deformation twin
formed by the coarsening of crystal grain, the refinementof the dislocation cell is greatly eased and the creation of
the micro shear band also shifts to the high strain amountregion. As a result, under the high strain working condition of ε=2.5, since the effect of the initial crystal grain
reverses against the deformation twin fraction and thestrength, compared with the stage of the strain amountε=1.6, then the larger initial crystal grain possible lead tothe higher work hardening property. As described above,
considering the structure change and the strengthchange due to the working condition, in case of the material with the low sacking fault energy, in the high working
stress region, the competition is caused between the creation of the multi-micro shear band and the refinement of
the dislocation cell, the occurrence of a specific behavior
is suggested and it is considered to be an important factor in the material property designed under the high working strain state. In the future, by applying this model calculation, it is necessary to search for the optimum structure design condition of the work hardening series alloys
in consideration of the alloy compositions, the various
structure parameters and the working conditions.

CONCLUSION
5.5.CONCLUSION
1. The working structure calculation model was developed taking into account the structure state which isdetermined based on the balance of the flow stressnecessary for the refinement of the dislocation celland the introduction of the deformation twin, also
taking into account the strain model in which theworking deformation limit, which is created by thedislocation cell refinement limit, is relaxed due to theintroduction of the micro shear band.
2. In this calculation model, calculation was performedin consideration of CuSiZn alloy composition, the initial crystal structure and the working condition, andgood correlation was obtained as a results of examining the correspondence with the experimental
results.
3. By using this calculation model, the influence of various parameters on the working structure creation
can be understood, and it was found that important
knowledge can be obtained in proceeding the work
hardening system alloy composition designing andthe process designing.
ACKNOWLEDGEMENT
We would like to thank and to express our sincere gratitude on proceeding with this study with the theme “R&D
for the designing technology and the manufacturing technology on the innovative super high strength copper alloy
utilizing the Energy and Environmental new technology
leading program/ Hetero-nano structure.” by New Energy
and Industrial Technology Development Organization(NEDO) in 2018. In addition, We would like to thank Prof.
Hiroshi Otani and Asistant Prof. Katsunori Enoki ofTohoku University's Institute of Multidisciplinary Materials
Science, and Prof. Hiroshi Utsnomiya of Osaka
University’s Graduate School of Engineering, for theircooperation in promoting this research.
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Analysis of the Deformation Twin and the Mechanical Strength Using a Simulation Model in the Deformation Microstructure of Copper Alloy〉〉 Fusion of Core Technologies

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