Crack Initiation and Growth in a Notched NiTi Shape Memory Alloy Sheet Wei Tong, Hong Tao, and Nian Zhang Department of Mechanical Engineering, Yale University, New Haven, CT ABSTRACT

An experimental investigation was carried out to study the crack initiation and growth in a single-edge notched NiTi shape memory alloy sheet under tension. It is observed that a crack initiated at the tip of a V-shape notch before the peak axial load was reached and it grew steadily across the width of the NiTi sheet until final fracture. In-plane crack-tip deformation fields at various stages of the crack growth were measured based on an image correlation technique and the crack-tip opening displacement (CTOD) and crack-tip opening angle (CTOA) were subsequently determined. The fracture surface of the NiTi sheet was dimpled based on scanning electron microscopy examinations.

INTRODUCTION

Shape memory materials such as NiTi alloys have found increasing applications in medical devices and MEMS components [1]. Most experimental and modeling efforts on the NiTi shape memory alloys have focused primarily on the thermal-mechanical deformation characteristics and their micromechanisms [2-9]. Fatigue and fracture failure is one of important design considerations in many NiTi shape memory alloy products [1,10,11] but extensive experimental investigations are lacking [11]. As NiTi shape memory alloys used in MEMS and other applications often in the form of wires, thin strips and films, the traditional fracture and fatigue testing methodologies developed for bulk specimens to obtain plane-strain fracture toughness data in conventional structural design analyses may not be feasible. Direct experimental characterization of the fracture and fatigue properties of NiTi shape memory alloy strips and films is thus desirable. We reported in this paper a research effort on measuring the crack-tip plastic deformation field of a single-edge notched NiTi shape memory alloy sheet by in-situ monitoring the crack initiation and growth at the notch. MATERIAL AND EXPERIMENTAL PROCEDURE

The material studied in this investigation is a NiTi shape memory alloy (Nitinol SM495) obtained from Nitinol Devices and Components (Fremont, CA). The nominal composition of the NiTi sheet is 54.8wt% Ni and 45.2wt% Ti with only a trace amount of O, H, and C. The transformation temperature (Af) is 60°C and typical mechanical properties of Nitinol SM495 wires at ambient conditions are listed in Table 1. The thin strip form (with a dimension of 50mm long, 7mm wide, and 0.25mm thick) of the Nitinol SM495 in the as-received condition was tested. A rectangular strip of the Nitinol SM495 sheet was clamped down at both ends and stretched quasi-statically under displacement control by a compact desktop tensile tester (100mm-by-125mm-by-50mm in total dimensions, a total crosshead travel of 50mm, and a load cell of 4,400N maximum capacity). A total of four cycles of combined mechanical loading (at a strain rate of 5x10-5 1/s for a total strain of 4-4.5%) and thermal annealing (at the temperature of 120°C for 5 minutes in a resistance heating furnace in air) were first used to train the NiTi shape memory alloy sheet under uniaxial tension. Once the steady-state stress-strain behavior was achieved, a 90° V-notch with a depth of 2mm was made at one of the edges of the deformed rectangular NiTi strip (i.e., before thermal annealing to recover its original shape). A total of three cycles of the same combined mechanical loading and thermal annealing were then used to

Mat. Res. Soc. Symp. Proc. Vol. 785 © 2004 Materials Research Society D7.7.1

deform the single-edge notched NiTi sheet. In the third cycle of the mechanical loading, the notched NiTi sheet was stretched to final fracture.

One of the flat surfaces of the NiTi sheet was sprayed with fine white paint speckles to aid the crack-tip deformation field measurements by an image correlation analysis [12,13]. Mechanical tests were paused frequently so digital images (640-by-480 pixels, 8-bit grayscale) of the NiTi strip were acquired during the entire course of each test. Digital images of the NiTi sheet were also taken before and after each thermal annealing treatment so the residual strains if any can be determined for each loading cycle. The imaging system used in this study includes a Computar 55mm telecentric lens (Edmund Scientific Inc.), a monochromic CCD video camera, and a frame grabber board. Each digital image was acquired by averaging a total of 60 video frames to minimize noises [14] and digital images up to 200 were recorded for each test. The recorded digital images were analyzed by an image correlation based surface deformation mapping software developed in our lab to obtain both the average strains in the center section of the un-notched NiTi sheet and the whole-field strain distributions around the notch and the growing crack-tip of the notched NiTi sheet. Details on the strain mapping via the image correlation analysis have been given elsewhere [15,16]. The errors in local in-plane displacements, rigid body rotation, and strain measurements were estimated to be about 0.02 pixels, 0.02° and 400x10-6 respectively for a macroscopically homogenous field [14].

Table.1 Typical Mechanical Properties of Nitinol SM495 Wires*

Loading plateau stress @ 3% strain 100 MPa Ultimate tensile strength 1100 MPa Shape memory strain (maximum) 8% Total elongation (minimum) 10% Coefficient of Thermal Expansion 6.6x10-6/°C Modulus of elasticity 28-41 GPa

* Nitinol Devices and Components (Fremont, CA).

0 0.01 0.02 0.03 0.04 0.05

True Strain

0

20

40

60

80

100

120

140

160

Tru

eF

low

Str

ess

(MP

a)

SM2 (Test A,B,C, and D)

A

B

C

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NiTi SM-495

0 1 2 3 4

Axial Displacement (mm)

0

100

200

300

400

500

Axi

alLo

ad(N

)

NiTi SM-495

SM2 (Test E, F, and G)

EF

G

Fig.1 Tensile stress-strain curves of the un-notched NiTi sheet.

Fig.2 Force-displacement curves of the V-notched NiTi sheet.

D7.7.2

EXPERIMENTAL RESULTS The uniaxial tensile stress-strain curves of the NiTi sheet obtained from the first four cycles of mechanical loading and thermal annealing are shown in Fig.1. Only the mechanical loading part (i.e., tensile tests #A-#D) is shown here. The thermal annealing results are given in Table 2. Except the first tensile stress-strain curve (#A), the subsequent three tensile tests #C, #B and #D gave similar (though somewhat softened) stress-strain response. The loading plateau stress at 1.5% is reduced from 98 MPa to about 50-58 MPa after the first mechanical stretching and thermal annealing. The residual axial strains before and after tensile loading are slightly over 4% for test #A and 3.6-3.7% for the other three tests #B-#D. The residual axial strains before mechanical loading and after thermal annealing in each test cycle show about ten folds of reduction from 0.18% to 0.015-0.026%. A steady-state uniaxial tensile stress-strain response was clearly reached in the NiTi sheet by the end of test #D.

Table.2 Residual Axial Strains in the NiTi Sheet

Test No. A B C D Tensile (unloaded) 4.08% 3.72% 3.73% 3.63%

Annealed 0.180% 0.063% 0.015% 0.026%

1

5

57 7

7

7

9

9

9

9

911

Level Er115 0.05013 0.04511 0.0399 0.0347 0.0295 0.0233 0.0181 0.013

SDMAP-3D

3 3

55

5

7

7

7

7

7

7

7 7

9

11

Level Er115 0.05113 0.04511 0.0399 0.0347 0.0285 0.0223 0.0161 0.010

SDMAP-3D

Fig.3 Notch-tip deformation field at the end of test #E. Fig.4 Notch-tip deformation field at the end of test #F.

1

3

5

5

5

7 9

13

Level Er115 0.10713 0.09611 0.0859 0.0747 0.0645 0.0533 0.0421 0.031

SDMAP-3D

Fig. 5 Notch-tip deformation field just prior to the crack initiation (Test #G). The axial load is 458.5 N.

1 3 5

7

7

9

9

1 1

1 1

1 3 1 5

L e v e l R o t 1 5 2 . 2 1 7 1 3 1 . 5 3 7 1 1 0 . 8 5 6 9 0 . 1 7 5 7 - 0 . 5 0 6 5 - 1 . 1 8 7 3 - 1 . 8 6 7 1 - 2 . 5 4 8

S D M A P - 3 D

Fig.6 In-plane rigid body rotation field just prior to the

crack initiation (Test #G).

The load-displacement data for the three mechanical tests #E, #F, and #G of the V-

notched NiTi sheet are given in Fig.2. The results from tests #E and #F overlap with the early part of the results of test #G, indicating again the steady-state response of the NiTi sheet. The small load drops shown on the curves in Fig.2 correspond to the times when the test was paused and digital images of the notched NiTi sheet were acquired. No cracking was visibly detected under optical microscopy at the ends of both tests #E and #F. The axial strain distribution

D7.7.3

around the notch at the peak load level in each test shown in Fig.3 and Fig.4 respectively is found to be very similar and the maximum strain at the notch tip is about 5% or slightly higher. The tensile axis is horizontal and both strain contour maps cover the entire width of the NiTi sheet around the notch region. The axial strain distribution in test #G at the load level of 458.5 N (just prior to the crack initiation at the notch) is shown in Fig.5. A maximum strain level of 10% and higher exists at the notch tip. Fig.6 shows the in-plane rigid body rotation field of the notched NiTi sheet just prior to the crack initiation and the free boundary regions along each side of the notch edge have a rotation of 2.2° to 2.5°.

Fig. 7. Cumulative (on the left) and incremental (on the right) axial strain contour maps of the cracked

NiTi sheet at selected loading steps. The numbers on the incremental strain contour maps are the axial load level (unit: N).

1

1

1

3

3

5 5

7

9

11

Level Er115 0.12113 0.10511 0.0889 0.0727 0.0555 0.0383 0.0221 0.005

SDMAP-3D

1

33 35

5

77

99

1 1

1315

Level Er115 0.25813 0.22711 0.1979 0.1667 0.1355 0.1053 0.0741 0.043

SDMAP-3D36

1

1

1

3 3

5

5

7

7

911

13

Level Er115 0.07413 0.06411 0.0539 0.0437 0.0335 0.0233 0.0121 0.002

SDMAP-3D

1

3

3

3

3

5

5

7

7

91113

Level Er115 0.21113 0.18611 0.1629 0.1387 0.1145 0.0903 0.0661 0.042

SDMAP-3D

42

1

1

1

3

3

5

79

12

13Level Er115 0.04813 0.04211 0.0359 0.0287 0.0215 0.0143 0.0071 0.000

SDMAP-3D

1

1

3

3 3

3

5

5

7

7

9

9

11

13

15

Level Er115 0.18513 0.16511 0.1449 0.1247 0.1035 0.0833 0.0631 0.042

SDMAP-3D46

1

1

1

3

35

713

Level Er115 0.04213 0.03611 0.0309 0.0247 0.0185 0.0123 0.0061 -0.000

SDMAP-3D

1 1

3 3

3

3

3

5

57

11

Level Er115 0.16013 0.14311 0.1269 0.1097 0.0925 0.0743 0.0571 0.040

SDMAP-3D48

3 3

3

5

5

5

791

113

Level Er115 0.13913 0.12511 0.1109 0.0967 0.0825 0.0683 0.0531 0.039

SDMAP-3D

1

1

3

35

79

13

Level Er115 0.03313 0.02811 0.0239 0.0187 0.0145 0.0093 0.0041 -0.001

SDMAP-3D48

D7.7.4

A small crack initiated at the tip of the notch around a load level of 469 N and grew longer and longer along the width direction of the NiTi sheet upon further stretching. A collection of the crack-tip deformation fields of the growing crack is shown in Fig.7 after the peak load level of 486 N was reached. The strain contour maps on the left are cumulative strains (i.e., the total deformation from the initial unloaded state) and the strain contour maps on the right are incremental strains (i.e., the current increment in strain from the previous load step). Although the entire ligament of the NiTi sheet along the width direction was fully plastically deformed (the minimum axial strain is 3.9% to 4.3% near the lower edge way below the crack), most of the plastic deformation occurred around the crack tip region. Axial strains more than 20% were measured around the crack-tip region. Using the two sides of the growing crack near the region of the initial notch tip, both the crack-tip opening displacement (CTOD) and crack-tip opening angle (CTOA) were measured using the crack-tip deformation field data and some of the results are summarized in Fig.8. At the normalized crack length (i.e., the current crack length a is divided by the initial width of the NiTi sheet W=7mm) of 0.14, the crack-tip opening angle begins to reach a constant level of 7-7.5°.

0 0.1 0.2 0.3 0.4

Normalized Crack Length (a/W)

2

3

4

5

6

7

8

Cra

ck-T

ipO

peni

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ngle

(deg

.)

0

0.2

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0.6

0.8

Cra

ck-T

ipO

pen

ing

Dis

pla

cem

ent(

mm

)CTOANiTi SM495

CTOD

Fig.8 The measured CTOD and CTOA of the growing crack in the NiTi sheet.

Fig.9. Fracture surface of the ruptured NiTi sheet.

DISCUSSIONS AND CONCLUSIONS The NiTi SM495 sheet investigated here shows the typical shape memory effects upon

mechanical stretching up to 4% and subsequent thermal annealing at 120°C. The steady-state stress-strain response was reached rather quickly (only one training cycle was needed!). Even with a V-shaped notch, the NiTi sheet exhibits repeatable thermal-mechanical responses when the maximum axial strain is about 5% and the maximum axial load is about 110-120 N during each loading cycle. Only when the NiTi sheet was subjected to a four-times overload of 469 N, a crack began to nucleate at the notch tip region. Significant crack growth occurred after the axial load reached its peak value of 486 N and appeared to reach a steady-state growth stage soon after. Experimental measurements on the crack-tip deformation field show a significant level of plastic deformation (as high as 20%) over a relatively large region ahead of the crack-tip. Large scale yielding is attributed to the predominantly plane stress state in thin ductile sheets. The surface of the ruptured NiTi sheet was examined by a scanning electron microscope (Phillips

D7.7.5

XL-30) and it shows the classical cuplike depressions of dimple rupture (see Fig.9). Nucleation, growth, and coalescence of voids from the Ti3Ni4 precipitates are responsible for the crack initiation and growth observed in the NiTi sheet [11]

In conclusions, the image correlation based deformation mapping technique has been successfully applied to study the crack initiation and growth in a single-edge notched NiTi thin sheet. The experimental data obtained here can be used to assess detailed fracture toughness and micromechanics of damage analysis of the shape memory alloy by finite element models.

ACKNOWLEDGMENTS

The authors would like to acknowledge the assistance of Dr. J. Chappron and Dr. X. Gong of Nitinol Devices and Components, Inc. (Fremont, CA) for providing the special processed NiTi SM495 sheet samples used in this investigation. REFERENCES

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