Author's Accepted Manuscript

Characterization of microstructural damageevolution during tensile deformation of anear-α titanium alloy: Effect of microtexture

Sony Punnose, Amretendu Mukhopadhyay,Rajdeep Sarkar, Vikas Kumar

PII: S0921-5093(14)00281-0DOI: http://dx.doi.org/10.1016/j.msea.2014.03.022Reference: MSA30870

To appear in: Materials Science & Engineering A

Received date: 12 February 2013Revised date: 4 March 2014Accepted date: 6 March 2014

Cite this article as: Sony Punnose, Amretendu Mukhopadhyay, Rajdeep Sarkar,Vikas Kumar, Characterization of microstructural damage evolution duringtensile deformation of a near-α titanium alloy: Effect of microtexture, MaterialsScience & Engineering A, http://dx.doi.org/10.1016/j.msea.2014.03.022

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Characterization of microstructural damage evolution during tensile deformation of a near-� titanium alloy: Effect of microtexture

Sony Punnose, Amretendu Mukhopadhyay, Rajdeep Sarkar and Vikas Kumar

Defence Metallurgical Research Laboratory, Hyderabad – 500 058, India

Abstract

The microstructural damage evolution during tensile deformation of a near-� titanium alloy has been characterized using ultrasonic nonlinear parameter. Evolution of damage state in the interrupted tensile specimens at different strain levels has been correlated with the second order nonlinear ultrasonic parameter. It is shown that the second order ultrasonic parameter do not change monotonically with increasing strain. The variation in nonlinear ultrasonic parameter is shown to be function of both the density of dislocation substructure and preferred crystallographic orientations that evolve during tensile deformation. The presence of microtexture predominantly affects the harmonics generation from the dislocation substructure. Physical basis for the above observation has been established using a dislocation string vibration model. Infrared thermal imaging has been used to map the evolution of damage along the gauge length of the specimens in order to take into account the in-homogeneities of deformation.

Key words: Nonlinear ultrasonic, tensile deformation, micro texture, microstructural damage, titanium alloy.

Corresponding author

Sony Punnose

Scientist

Defence Metallurgical Research Laboratory

PO-Kanchanbagh

Hyderabad-500058, INDIA

Ph: +91 40 24586786

Fax: +91 40 24340683

Email: sony@dmrl.drdo.in

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1. Introduction

Nonlinear ultrasonic technique has been widely used for detection of early stages of damage

or defects in various components. The technique makes use of nonlinear response of

materials and related frequency changes of the input signal. The nonlinearity in materials

arises either due to diffuse lattice defects or isolated defects such as cracks, delaminations etc.

There are various experimental ways to measure the frequency change that arises due to these

nonlinearities. Meo et al. [1] have used nonlinear elastic wave spectroscopy method such as

nonlinear resonance ultrasound and nonlinear wave modulation technique to detect damage in

composite material. Goursolle et al. [2] have combined nonlinear elastic wave spectroscopy

and time reversal techniques to precisely detect microinhomogeneities like cracks. Hirsekorn

et al. [3] have used the method to study the interface damages in composite laminates. Van

Den Abeele et al. have successfully used nonlinear resonant ultrasound spectroscopy [4] and

nonlinear wave modulation spectroscopy [5] to determine damage in engine components and

shown that these techniques are far more sensitive than linear acoustic methods. Solodov [6,

7] has used very high amplitude excitation to study contact acoustic nonlinearity, instability

and chaos. Apart from the characterization of macro defects nonlinear ultrasonic technique

has widely been used for characterization of early stages of microstructural degradation due

to in-service damages viz., the fatigue damage studies in structural materials [8-10], and

creep damage studies [11-12]. The technique has been employed to study the precipitation

hardening kinetics in aluminum alloy [13-14], ageing behaviour in maraging steel [15], to

characterize changes in carbon content in martensitic steel [16], volume fraction of second

phase precipitates [17], thermal degradation in ferritic steel [18], and in-situ fatigue damage

assessment [19-20]. Thus, the technique is proven to be very useful to characterize the finer

microstructural changes associated with early stages of damage in materials. However, the

major concerns towards the technological viability of the technique are the need for access to

both sides of a component and the issue of repeatability and interpretation of results in

complex microstructures. Researchers have used surface wave such as Lamb wave [21-22],

Rayleigh wave [23-24] to overcome the difficulty in having access to both sides of a

component. The repeatability of measurements and the associated scatter is believed to

originate from the nonlinearity in electronic circuits, uncertainties due to variations in

couplant thickness, the coupling coefficient between the transducers and sample. Efforts have

been made to address these issues. Use of non-collinear mixing technique [25-26] has shown

to largely eliminate the system nonlinearities. Li Sun et al. [27] have reported a method to

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minimize the effect of coupling for better repeatability of the measurements. Although these

techniques have addressed the issue to a large extent but harmonic generation in a complex

microstructure and the uncertainty associated with it is still not resolved properly. In a recent

study, Mukhopadhyay et al. [28] have shown that the scatter in non linear ultrasonic (NLU)

measurement can originate from the variation in crystallographic anisotropy apart from the

other sources of nonlinearity. In the present study, implications of such findings on the

characterization of evolution of microstructural damage during tensile deformation of a near-

� Timetal@ 834 titanium alloy have been studied. It has been established that harmonics

generation depends largely on the state of crystallographic anisotropy of the alloy. The

presence of microtexture in the material controls the harmonics generation from the

dislocation substructure that evolves during deformation. The resultant anisotropy in

harmonics generation manifests as a significant scatter in the measured data.

2. Experimental study

The Titanium alloy of nominal composition (wt. %) (Ti-5.5Al-4Sn-4Zr-0.3Mo-1Nb-0.5Si-

0.06C) was solution annealed at 1025° C for 2 hrs followed by oil quenching. The solution

annealed alloy was subsequently aged at 700° C for 2 hrs followed by air cooling. Tensile

specimens having 18 mm gauge length were prepared from heat treated rod of 20 mm

diameter. Figure 1 shows the schematic diagram of the specimen used for testing. Tensile

tests were carried out at room temperature using a computer controlled INSTRON 5500R

testing machine at a crosshead speed of 1.0 mm/min. Interrupted tensile tests were carried out

at five strain (total) levels at (a) 0.8 % (b) 1.5 % (c) 4.0 % (d) 5.6 % (e) 7.2 % and one

specimen was tested up to fracture. NLU measurements were carried out on all the

interrupted specimens and on the fractured and virgin specimens. An infrared camera with

focal panel array detector made of InSb was used to map temporal and spatial temperature

evolution along the specimen gauge length of the specimen during tensile deformation. The

resolution of the camera was 20 mK at 25° C. From the thermal evolution pattern, the area of

highest thermal activity along the gauge length has been marked in all the five interrupted

specimens. NLU measurements have been carried out on those locations.

A high power ultrasonic system (RITEC SNAP RAM-5000) was used for ultrasonic

measurements. The experimental setup is shown in Figure 2. An RF tone burst of a certain

frequency and pulse width was transmitted into the material under study, and the “distorted”

signal was recorded in through transmission mode. Specimens were insonified at a

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fundamental frequency of 10 MHz and second harmonics along with the fundamental signal

was received by a high power 20 MHz Lithium Niobate transducer. By varying the input

excitation voltage, a series of fundamental (A1) amplitudes were generated and the

corresponding second harmonics (A2) amplitudes were recorded. Slopes of A2 vs. A12 plot

were measured for series of A1 values. Second harmonics based nonlinear parameter which is

a material dependent property was measured using the following relationship [29-30]

22

2 21

8' Az A��

��

where �’ is the second harmonics based nonlinear parameter, � is the longitudinal velocity

and z is the thickness of specimen. Since the measurements of fundamental and second

harmonics are not in terms of displacement, the nonlinear response is expressed in terms of

A2/A12 measured in 1/mV. Hence, the ‘relative’ term is used to describe nonlinear parameter.

For each specimen, the measurements were carried out at two perpendicular faces with

respect to the tensile axis of the specimen. To ensure the reproducibility of the experimental

data, measurements were repeated more than ten times for each face and �’ values reported is

the average of these measurements. Values thus obtained are normalised with respect to the

minimum �’ value obtained on each face. Normalised �’ values for the two faces are denoted

as �’xx and �’yy. Ultrasonic longitudinal velocity was also measured on these two faces at the

same locations keeping the orientation fixed. Ultrasonic velocity was measured using 10

MHz transducer in the pulse echo mode using the NLU system. Transit time across the

specimens was measured through a frequency scan (10 MHz) for two consecutive echoes.

Time of flight was calculated from the slope of the phase versus frequency curve. By

measuring the difference in the slope of phase frequency curve, the transit time is calculated

as

2 1

2 14 ( )

r r

FTransit timeN N

� �

�

� ���

(2)

where N2 and N1 are the echo numbers. The numerator term of RHS of equation (2)

represents the difference in the slope of phase frequency curve, where (�r1 / �F) and (�r2 /

�F) represent slopes of the phase frequency curve for first and second echoes, respectively.

The slopes have been calculated based on the linear least square analysis of the phase-versus-

(1)

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frequency data for the two echoes. Ultrasonic velocity was calculated from the transmit time

using the following relationship

���������� ���������

����������� (3)

Ultrasonic velocities obtained along the two perpendicular directions are denoted as Vxx and

Vyy and corresponds to �’xx and �’yy respectively.

Specimen for optical microscopy has been prepared by conventional methods and Kroll’s

reagent has been used as etchant. Orientation imaging microscopy has been carried out on the

specimen to determine the variation in the crystallographic orientation change along the wave

propagation path. A Field Emission Gun Scanning Electron Microscope (FEG-SEM) with

Electron Back Scattered Diffraction (EBSD) facility has been used. The EBSD scans have

been done with 0.25 �m step size. Transmission Electron Microscopy (TEM) analysis has

been carried out on the specimens to determine the evolution of dislocation substructures

during tensile deformation. Specimens for TEM were prepared by cutting the slice from the

location where the highest thermal activity has been recorded. Specimens were electro-

polished by twin jet electro-polishing in a 30% nitric acid + 70% methanol solution (by

volume) at –35oC.

3. Results

The variations in normalised relative �’xx and �’yy as a function of percentage strain are shown

in Figure 3. The plot reveals that �’xx and �’yy values are different at different strain levels and

shows different trend as a function of strain. Further, it can be seen that the difference

between the values of �’xx and �’yy is maximum at 5.6 % strain. The total change in �’ value

(noted for �’xx) is ~ 34 %, while the difference in the values between �’xx and �’yy at 5.6 %

strain is ~ 27 %. �’xx and �’yy values were measured at different strain levels using different

specimens. As plastic deformation is inherently in-homogeneous in nature the choice of

measurement locations for specimens is also vital as the measurements were made on

different specimens interrupted up to different strains. Infrared thermal imaging has been

carried out to identify the location of maximum deformation along the gauge length of

specimens. This ensures that �’xx and �’yy values are measured from the location of increasing

deformation in terms of evolution of dislocation substructure as the measurements have been

carried out at the place of highest thermal activity (Figure 3) for different specimens.

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Thermal evolution pattern along the gauge length (Figure 3) for specimens interrupted at a)

1.5 % b) 4.0 % c) 7.2% strain levels reveal such in-homogeneities in the evolution of

deformation microstructure. The variations in ultrasonic longitudinal velocity in the two

perpendicular directions have been shown in Figure 4. It is observed that there is considerable

anisotropy in the values of Vxx and Vyy also. Further, it can be noticed that the difference in

Vxx and Vyy is maximum at the strain level (5.6 %), where the difference between �’xx and

�’yy is the highest. Detailed microstructural characterization has been carried out to

understand the typical trend and the anisotropy in values of �’s. Figure 5 shows the optical

micrograph of the un-deformed specimen. The microstructure consists of primary �p (~ 15 %

by volume) in the transformed � matrix. The matrix of transformed � consists of � laths that

form in the prior � grain upon cooling from solution treatment temperature. Figure 6(a-d)

shows the EBSD map with the misorientation profiles along the three directions.

Misorientation profiles clearly show that there is considerable anisotropy in the orientation

distribution of grains in the specimens. Figure 7(a-d) shows bright field TEM images (near

� � �������orientation) for specimen interrupted at a) 0.8 % strain, b) 1.5 % strain, c) 4.0 %

strain and d) 7.2 % strain levels. TEM reveals that with increase in strain, the dislocation

density increases.

4. Discussion

From the results presented in Figure 3 it can be seen that nonlinear ultrasonic parameters do

not vary monotonically with deformation. Both �’xx and �’yy decrease initially then show an

overall increase but the two �’ values show a different trend. It is interesting to note that the

total change in �’xx value is ~ 34 %, at the same time the difference between �’xx and �’yy is

also very large (Figure 3). For a given specimen, �’xx and �’yy values were measured in the

same location but the orientation of the specimen with respect to tensile axis was changed by

90°. Hence, the difference between the measured values of �’xx and �’yy could have originated

either due to the presence of preferred grain orientations in the specimen or because of

measurement errors. It is evident from Figure 3 that errors due to experimental uncertainty

(reflected as error bars) are significantly less than the difference in the values between �’xx

and �’yy at 5.6 % strain. This is further substantiated by measurements done on specimens

interrupted at other strain levels. For a particular strain level, the extent of damage in terms of

defect substructure remains unchanged with change in orientation since the measurement

location has been fixed. This implies that the difference between �’xx and �’yy possibly

originate from the variation in the orientation distributions of grains with respect to wave

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propagation direction. In order to fully understand the reason behind the anisotropy in �’

values, phenomenon of harmonics generation has been studied in the present alloy.

Considering the higher order terms in the dislocation string vibration model [31], Hikata et al.

[32] have shown that in a single crystal the harmonics generation due to nonlinear dislocation

vibration is a function of dislocation density, dislocation loop length, and bias stress as

3 4 211 1

3 2

24'

5R L C

G b�

�� �

� � � � � � � � � (4)

where � is conversion factor from shear strain to longitudinal strain, R is the Schmid factor,

� is dislocation density, L is pinned dislocation segment length, C11 is the second order

Huang elastic coefficient, �1 is applied stress, G is the shear modulus of the material, b is

Burgers vector. The above equation holds for the value of �’ in single crystals and it can also

be extended for �’ in polycrystalline materials. In polycrystalline solids cumulative

harmonics generation process and the corresponding value of �’ will depend on the

orientation distribution of grains as a whole in addition to the contribution of each grain

(crystallites). The overall harmonics generation will vary as function of R integrated over all

the grains along the wave propagation direction. In this regard Mukhopadhyay et al. [28]

have shown that presence of preferred grain orientation in polycrystalline materials leads to

anisotropy in harmonics generation. Thus, depending upon the measurement direction the

value of �’ will change even for a specimen deformed up to certain level of strain.

In the present alloy, the matrix of transformed � consists of � laths (Figure 5) that form in the

prior � grain upon cooling from solution treatment temperature. Formation of ��lath from the

parent � matrix is associated with Burger orientation relationship (OR) [33- 34] as:

[{0001}�// {110} � and <1 1�2 0>��// <1�1 1>�]

For a given {011} plane, only two <111> directions are possible, and the growth direction of

any lath in one {011} plane must corresponds to the two variants of Burger OR. This leads to

12 variants of � lath. Thus, orientations of � laths vary depending upon the variant it selects

during formation from the � phase. From Figure 6 it can be clearly seen that the orientation

distribution of the grains varies widely along different directions. Thus, depending upon the

wave propagation direction laths orientation distribution varies (Figure 6) that results in

significant variation in the interaction of ultrasonic wave with the insonified volume. As the

degree of randomness in orientation varies with respect to the wave propagation direction, the

randomness in the orientation of slip systems in the aggregate changes concomitantly. The

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parameter R (integrated over all the grains) will have different values for different

propagation directions. Consequently, nonlinear ultrasonic parameter measured along

different directions will have different values according to Eq. (4). Hence, with the change in

specimen orientation during measurement, �’ values ( �’xx and �’yy ) are different. With this

understanding we now probe into the implications of the presence of microtexture on the

NLU characterization of the microstructural damage evolution.

With the increase in deformation orientation distribution of laths changes further. This gives

rise to macroscopic anisotropy. From the anisotropy in the ultrasonic velocity measurement

(Figure 4) it can be concluded that in the present case crystallographic orientation distribution

of laths changes with deformation. From Figure 7 it is also seen that with the increase in

deformation dislocation density inside laths increases. Thus, both dislocation substructure and

texture changes with increasing deformation. According to Eq. (4) and from the above

discussion it can be concluded that both these factors i.e. dislocation density change and

evolution of texture will affect the NLU parameter. The variation in NLU parameter should

be function of both the evolution of dislocation substructure and crystallographic orientation

of � laths. Contribution of each lath towards harmonics generation will depend upon the

evolution of dislocation substructure and the aggregate contribution of all the laths will

depend upon the evolution of orientation distribution of laths.

Initially when the effect of microtexture was not dominant, (as evident from the negligible

difference between �’xx and �’yy) both the �’ values decrease. The initial decrease in the �’

values can be attributed to the change in dislocation substructure inside individual laths. From

Figure 7(a) & 7(b) it can be seen that initially dislocation density increases and evolution of

dislocation substructure is uniform. The evolution of uniformly distributed dislocation

substructure leads to faster rate of decrease in L (pinned dislocation segment length) as

compared to increase in dislocation density (�) and according to Eq. (4) this reduces �’

values when the dislocation density is low. In the latter stage of deformation thick

dislocation network forms as is evident from Figure 7(c) & &7(d). In this stage increase in

the dislocation density dominates over the decrease in the L value. This leads to higher

contribution of individual laths towards harmonics generation process and correspondingly �’

values increase at large strain levels. In the latter stage the effect of evolution of texture is

also prominent and this is evident from the anisotropy in the ultrasonic velocity measurement

(Figure 4). The difference between Vxx and Vyy increases and is highest at 5.6% strain

wherein �’xx and �’yy values also show highest anisotropy. Thus, in the latter stage of

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deformation though NLU parameter increases but the effect of texture gives rise to the

anisotropy in measurements. The anisotropy in the measurement of NLU parameter thus, can

lead to misinterpretation of results and improper characterization of the evolution of damage

microstructure. Implication of this finding is serious as the choice of measurement direction

plays a vital role in the interpretation of results. This can be understood in the following

discussion with respect to the present study.

Changes in �’xx and �’yy values as a function of percentage strain have been obtained from

interrupted specimens. NLU parameters thus, obtained from one of the two faces

perpendicular to the tensile axis was arbitrarily marked as �’xx and other as �’yy.

Consequently, random NLU measurement can give any value of �’ within the band marked in

Figure 3. This in turn can mask the overall change in �’. Hence, a proper interpretation of

NLU results in a complex microstructure requires careful consideration of all the aspects

discussed. For proper characterization of microstructural damage the measurements cannot

be random. In the absence of a firsthand knowledge of microtexture/texture, both ultrasonic

velocity measurements and NLU measurements at two perpendicular directions are required

for qualitative evaluation of microstructural damage. Further study to quantify the relative

contribution of dislocation substructure and texture on the NLU parameter is required and is

currently underway. This will be useful for proper characterization of evolution of

microstructural damage vis-à-vis texture.

Nevertheless, the present study shows that NLU measurement can be a very sensitive

technique for characterization of evolution of damage microstructure but care must be

ensured during the measurement as well as in the interpretation of results. The sensitivity of

NLU technique over conventional ultrasonic technique in detection of finer microstructural

changes is evident from the much higher change in �’ values as compared to the change

ultrasonic longitudinal velocity. It is evident from the present study that both crystallographic

orientation change and dislocation density change during deformation contributes towards the

change in NLU parameter. Formation of dense dislocation networks leads to increase in the

harmonics generation but the evolution of preferred crystallographic orientation leads to a

significant anisotropy. Both these factors have to be considered while characterizing

evolution of damage microstructure using NLU technique.

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5. Conclusion

(i) The present study establishes that both the evolution dislocation substructure and the

presence of microtexture play a significant role in ultrasonic harmonics generation. It has

further been shown that such an understanding (i.e. the role of microtexture) is essential for

proper interpretation of damage microstructure using NLU parameter.

(ii) During tensile deformation of near-� titanium alloy the NLU parameter has been shown

to vary as a function of both the evolution of dislocation substructure and crystallographic

orientation of the individual � laths.

(iii) The study highlights that presence of microtexture can give rise to substantial scatter if

the measurements are done at random and can even lead to misinterpretation of the NLU

results. Thus, the revelation evokes significant implications in interpretation of damage state

of polycrystalline materials using nonlinear ultrasonic (NLU) technique.

(iv) Characterization of damage microstructure with concomitant evolution of

texture/microtexture in material requires both ultrasonic velocity and NLU measurements at

two perpendicular directions.

Acknowledgements

The authors wish to acknowledge the financial support from DRDO. The support rendered by

the members of EMG, MBG, TAG, and NDTG of DMRL are gratefully acknowledged.

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List of figures

Figure 1. Schematic of the specimen used for testing.

Figure 2. Block diagram of the experimental set up for measuring nonlinear ultrasonic parameters.

Figure 3. Variation in normalised relative �’ as a function of % Strain and the corresponding

thermal evolution pattern along the gauge length for specimens interrupted at a)1.54 %

strain, b) 4.1 % strain, and c) 7.2 % strain.

Figure 4. Variation in longitudinal phase velocity as a function of % strain.

Figure 5. Optical micrograph of heat treated undeformed specimen.

Figure 6. EBSD map of transformed � matrix of an interrupted specimen along with

misorientation profiles along three directions indicated in the map.

Figure 7. Transmission electron micrographs showing dislocation substructure in the internal

region of � laths in specimens interrupted at (a) 0.8 % strain, (b) 1.5 % strain, (c) 4.0 %

strain, and (d) 7.2 % strain.

Figu

re 1

. Sch

emat

ic o

f the

spec

imen

use

d fo

r tes

ting.

Figu

re(s

)

Figure 2. Block diagram of the experimental set up for measuring nonlinear ultrasonic parameters.

50 Ω Load

Filter/Diplexer Stage 1

Filter/Diplexer Stage 2

1 2

Sample RHS signal

Splitter

High Pass Filter Stage 1 of 2

High Pass Filter Stage 2 of 2

Low Pass Filter Stage 2 of 2

Low Pass Filter Stage 1 of 2

Recvr. Input High Power RF Out RITEC

RAM-5000

Figure 2

Figure 3. Variation in normalised relative β’ as a function of % Strain and the corresponding thermal evolution pattern along the gauge length for specimens interrupted at a)1.5 % strain, b) 4.0 % strain, and c) 7.2 % strain.

Figure 3

Figure 4. Variation in longitudinal phase velocity as a function of % strain.

Figure 4

Prim

ary α p

α la

ths

Figu

re 5

. Opt

ical

mic

rogr

aph

of th

e he

at tr

eate

d un

defo

rmed

spec

imen

Figu

re 5

Dis

tanc

e (μ

m)

110

0 30

60

90

30

60

90

Misorientation (°)

80

0 20

40

60

30

60

90

Misorientation (°)

Dis

tanc

e (μ

m)

0 20

40

60

30

60

90

Misorientation (°)

Dis

tanc

e (μ

m)

(a)

(d)

(c)

(b)

Figu

re 6

. EB

SD m

ap o

f tra

nsfo

rmed

β m

atrix

of

an i

nter

rupt

ed s

peci

men

alo

ng w

ith m

isor

ient

atio

n pr

ofile

s al

ong

thre

e di

rect

ions

indi

cate

d in

the

map

.

Figu

re 6

Figure 7. Transmission electron micrographs showing dislocation substructure in the internal region of α laths in specimens interrupted at (a) 0.8 % strain, (b) 1.5 % strain, (c) 4.0 % strain, and (d) 7.2 % strain.

(a) (b)

200 nm 200 nm

(c)

200 nm

(d)

200 nm

Figure 7