Experimental and Computational Evaluation of Crack-tip Displacement Field and Transformation Zone in NiTi Academic research paper on "Materials engineering"

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Materials Today: Proceedings 2S (2015) S763 - S766

International Conference on Martensitic Transformations, ICOMAT-2014

Experimental and computational evaluation of crack-tip displacement field and transformation zone in NiTi

N. Shafaghi, B. Haghgouyan, C.Can Aydiner, G. Anlas*

Department of Mechanical Engineering, Bogazici University, 34342 Bebek, Istanbul, Turkey

Abstract

Mechanical properties of NiTi shape memory alloy (SMA) were obtained using uniaxial tensile testing and dog-bone specimens. Critical crack tip opening displacement (CTOD) was measured at room temperature on compact tension (CT) specimens using experimental methods of elastic-plastic fracture mechanics (EPFM). To observe the effect of martensitic phase transformation on CTOD, tests were also carried out above martensite deformation temperature (Md). To obtain the displacement and strain fields around the crack tip, under Mode-I loading, digital image correlation (DIC) was used. The extent of transformation zone was calculated using the measured strain field. Finite element analyses were carried out to solve the 2D CT specimen problem under Mode-I loading. Critical CTOD values were calculated for both superelastic and austenitic NiTi for comparison purposes. Size of the transformation zone at the crack tip was also calculated together with crack face opening displacement. The computational and experimental results were compared and discussed. CTOD measurements showed that the phase transformation ahead of the crack tip, improves the fracture behavior of NiTi.

©2015TheAuthors.Publishedby ElsevierLtd.This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Selectionand Peer-reviewunderresponsibility of thechairsof thelnternational Conference onMartensiticTransformations2014. Keywords: Nitinol shape memory alloy; fracture mechanics; crack opening displacement; phase transformation

1. Introduction

Shape memory alloys (SMAs) are capable of recovering large strains upon heating (shape memory effect) or through removal of load (superelasticity) because of undergoing martensitic phase transformation. The

* Corresponding author. Tel.: +90-212-359-6402. E-mail address: anlas@boun.edu.tr

2214-7853 © 2015 The Authors. Published by Elsevier Ltd. This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).

Selection and Peer-review under responsibility of the chairs of the International Conference on Martensitic Transformations 2014. doi:10.1016/j.matpr.2015.07.394

transformation occurs between a parent phase (austenite) and a product phase (martensite) which can be induced either by a change in temperature or stress. Nitinol (NiTi), a nearly equiatomic mixture of nickel and titanium is the most known and widely used SMA. Increasing NiTi applications especially in medical and aerospace industries drew researchers' attention to fracture of this alloy and many studies have been carried out to understand its fracture mechanism. Among these studies, relatively few works were done to understand the effect of martensitic phase transformation on fracture parameters of NiTi. Gollerthan et al. [1,2], investigated fracture behavior of martensitic, superelastic and austenitic (with no transformation) NiTi and calculated fracture toughness (KIC) values. They calculated the size of the transformation zone using linear elastic fracture mechanics (LEFM) and assuming its similarity to plastic zone in common material. Tong et al. [3], used digital image correlation (DIC) to obtain displacement field at the crack tip and measure crack tip opening displacement (CTOD) and crack tip opening angle (CTOA) in thin rectangular strip with V-notch. Daly et al. [4] obtained strain field at the crack tip of edge-cracked NiTi strips using DIC and evaluated the shape and size of the transformation zone. Maletta et al. [5] studied the effects of temperature in stress intensity factor of single edge crack NiTi specimens using linear elastic fracture mechanics. They reported a small increase of the critical stress intensity factor with increasing the temperature.

2. Experimental

Uniaxial tensile tests were carried out to observe the stress-strain behavior of superelastic NiTi with austenite finish temperature (Af) of 16 °C and composition of 55.99 % (wt.%) nickel. Dog-bone specimens were cut from 1mm thick NiTi sheets by electro discharge machining (EDM) as shown in Fig.la. ASTM F2516 was used for specimen geometry and test procedure. Tests were performed in displacement control mode using an INSTRON-8801 test machine. Effect of martensitic transformation on stress-strain behavior was explored by loading and unloading NiTi specimens at both room temperature and above martensite deformation temperature Md (100 °C).

Pre-cracked compact tension (CT) specimens (Fig.1b) were used for CTOD tests at room temperature and 100 °C according to ASTM E1290. Tests were carried out using INSTRON-5848 test machine and load line displacement (LLD) was measured by a crack opening displacement (COD) gauge. An increasing displacement was applied to specimens until fracture. Load versus LLD was recorded and critical CTOD values were calculated using following relation:

where aY = (ays + oUTS)/2, aYS is yield or 0.2% offset yield strength, oUTS is tensile strength, K is the Mode-I stress intensity factor and E' is the effective Young's modulus. Ap is the area under the plot of load versus plastic component of clip gauge opening displacement that corresponds to the onset of unstable brittle crack extension. B, a and W are specimen thickness, crack size and width respectively. m and ^ are constants that depend on material and specimen geometry.

DIC [6] was used to obtain displacement and strain fields near the crack tip of precracked NiTi CT specimens (Fig. 1c) at room temperature. To measure the displacements the specimen was painted in white and then a random pattern with enough number of discrete and well-sized speckles (3 to 5 pixels) was created on its surface by spraying black paint as shown in Fig.1d. Images were taken using a CCD camera (Pike Allied Vision Technologies) with a 50mm lens (Edmund Optics-Double Gauss 54690) and the field of view was 13.87x13.09 mmxmm (916x864 pixelsxpixels). Specimen was loaded in displacement control under Mode-I until fracture. Images which were taken at stress free condition (undeformed) and at very last step right before failure (deformed) are compared to obtain the in-plane displacement field in y direction (uy) near the crack tip using an in-house software. Using the displacement data, strain along the direction normal to the crack tip (eyy) was calculated by numerical differentiation. Using the obtained strain field and considering the strain values at which phase transformation starts and ends in stress-strain curve, transformation boundaries near the crack tip of NiTi CT specimen were estimated.

K,2 yAp

— +-—-

E' B(W - a)

Fig. 1. Test specimens (a) dog-bone; (b) CT for CTOD tests; (c) CT for DIC tests; (d) speckle pattern.

3. Results and Discussion

Stress-strain curves obtained from uniaxial tensile tests at both temperatures are illustrated in Fig. 2a. It can be seen that at 100 °C, the reversibility due to phase transformation is not observed anymore and residual strain is achieved at the end of unloading. Elastic modulus is measured to be approximately 43 GPa and 70 GPa at room temperature and at 100 °C, respectively.

Fig. 2b shows the Load versus LLD obtained from CTOD tests. According to the results, for each load value, the corresponding LLD are smaller in the test at 100 °C compared to the test at room temperature. Using this, one can predict that the CTOD value would also be smaller at 100 °C. To show this, critical CTOD values corresponding to the onset of unstable crack extension were obtained using the load-LLD curves and Equation (1) to be 0.009 mm at room temperature and 0.006 mm at 100 °C. This indicates that phase transformation occurring at the crack tip of NiTi, increases the material resistance to crack extension.

Displacement (uy) and strain (eyy) fields obtained using DIC is shown in Fig. 3a and Fig. 3b, respectively. From Fig. 3b it can be seen that martensitic phase transformation is initiated in the plane of the crack and is extended along two lobs above and below the crack plane. Given that martensitic transformation starts at 1% strain and ends at 5.8%, the boundaries of transformation zone can be estimated using the strain field. Fully transformed region extends from crack tip to approximately 0.25 mm on the crack plane (9=0).

-Room temperature

---High temperature

3 4 Strain (%)

-Room temperature

---High temperature

0.20 0.30 LLD (mm)

Fig. 2. Test results at room temperature and 100 °C (a) stress-strain curves; (b) load-LLD curves.

Fig. 3. DIC results (a) displacement field; (b) strain field.

4. Finite Element Analysis

2D superelastic and austenitic NiTi CT specimens were studied numerically. The ABAQUS UMAT subroutine for superelastic SMAs [7] was used to model superelastic NiTi. An eight node biquadratic plane stress quadrilateral element with reduced integration (CPS8R) was used. Fig. 4a presents the mesh geometry. The displacement (uy) along the crack surfaces for superelastic and austenitic (no phase transformation) models was obtained and plotted in Fig. 4c. The displacement was measured under the applied load at which unstable crack growth occurred during CTOD experiments. J-integral values were calculated and critical CTOD values were obtained using the relation S=J/moy to be ¿=0.007 mm for superelastic and ¿=0.005 mm for austenitic NiTi. Like the experimental results, CTOD value decreased when martensitic phase transformation was suppressed. Phase transformation regions were also obtained for same load magnitude as shown in Fig.4b. SDV21 represent the martensitic volume fraction (£). The size of fully transformed zone was calculated to be approximately 0.17 mm which is close to the result obtained from strain field measured by DIC.

Fig. 4. (a) Mesh geometry of CT specimen (b) transformation zone at crack tip (c) displacement of crack faces.

4. Summary and Conclusion

This paper summarizes the experimental and computational investigation of displacement field and transformation zone near the crack tip of NiTi CT specimen. Stress-strain curves showed that increasing the temperature above 100 °C prevents the stress induced phase transformation. Measured LLD values were smaller when the transformation was prevented at crack tip. A similar trend was observed in critical CTOD values. The displacement and strain distribution near the crack tip were obtained using DIC at room temperature and fully transformed zone was estimated just prior to unstable crack extension. Critical CTOD calculations using finite elements agreed well with experimental results i.e. CTOD decreases when martensitic transformation is prevented. Transformation near the crack tip was also studied using volume fraction of martensite and fully transformed region was obtained and compared to results measured by DIC and a reasonable agreement between the two was observed.

References

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[2] S. Gollerthan, M. Young, A. Baruj, J. Frenzel, W. Schmahl, G. Eggeler, Acta Mater. 57 (2009) 1015-1025.

[3] W. Tong, H. Tao, N. Zhang, Mat. Res. Soc. Symp. Proc. 785 (2004).

[4] S. Daly, A. Miller, G. Ravichandran, K. Bhattacharya, Acta Mater. 55 (2007) 6322-6330.

[5] C. Maletta, E. Sgambitterra, F. Furgiuele, Fatigue Fract. Eng. M. (2013) 1-10.

[6] T.C. Chu, W.F. Ranson, M. A. Sutton, Exp. Mech. 25 (1985) 232-244.

[7] F. Auricchio, R.L. Taylor, J. Lubliner, Comput. Method. Appl. M. 146 (1997) 281-312.