Effect of contact conditions during thermo-mechanical contact between ...
Tribology International 55 (2012) 100–107
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Effect of contact conditions during thermo-mechanical contact between a thermal flying height control slider and a disk asperity Wenping Song a,c,n, Andrey Ovcharenko b, Bernhard Knigge b, Min Yang b, Frank E. Talke c a
School of Mechatronics Engineering, Harbin Institute of Technology, China Western Digital Corporation, San Jose, USA c Center for Magnetic Recording Research, University of California, San Diego, CA, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 January 2012 Received in revised form 10 May 2012 Accepted 22 May 2012 Available online 7 June 2012
A three-dimensional thermo-mechanical model is developed for the transient contact between a thermal flying height control (TFC) slider and a disk asperity. The effect of contact conditions is investigated, including the friction coefficient and the circumferential disk velocity. The damage of the read–write shields due to contacts with disk asperities is studied along with the maximum temperature at the location of the read element. The effect of diameter and material properties of the asperity is also investigated. Strong dependence of deformation and maximum temperature is observed as a function of the diameter and material properties of the asperity. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Thermo-mechanical contact Asperity Media defect TFC slider
1. Introduction To increase recording density in hard disk drives, thermal flying-height control (TFC) sliders have recently been implemented [1–3]. Thermal flying height control sliders are designed to reduce the flying height of the read/write element by locally heating the area near the read/write element, thereby causing a thermal protrusion that reduces the head–disk spacing in the area of the read/write element. In the last few years, the physical spacing between the read/write element and the disk has decreased to the order of a few nanometers [2]. At such small spacing, the occurrence of slider disk contacts becomes increasingly more likely. Contacts occur predominantly in areas of the disk where inclusions or so-called ‘‘media defects’’ are present. Media defects have their origin in the sputtering process, i.e., any foreign particles present during sputtering can cause the formation of defects on the surface of the disk. In Fig. 1(a), a scanning electron microscope image of a typical disk defect, generally described as disk ‘‘asperity’’, is shown. A cross section of the same asperity can be seen in Fig. 1(b) [4]. Contacts between asperities on the disk surface and the slider can cause abrasive and adhesive wear, as well as high interfacial temperatures at the read/write element. Both effects are highly undesirable for the
n Corresponding author at: School of Mechatronics Engineering, Harbin Institute of Technology, China. E-mail address: [email protected] (W. Song).
0301-679X/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.triboint.2012.05.016
durability of a disk drive. Fig. 2 shows typical scratch marks in the area of the read/write element of a TFC slider, caused by contacts between disk asperities and the slider [4]. Damage of the read/ write element can cause loss of the read signal, and even failure of a head. Contacts between disk asperities and the slider are generally referred to as ‘‘thermal asperity’’ events [5–12]. Many studies had been undertaken in the past to reduce the damaging effect of disk asperities, including modifications of the air bearing surface (ABS) [7–9] and implementation of algorithms to improve signal processing [10–12]. Yuan and Liu [7] proposed a novel read/write head, in which the read-back sensor was located far away from the contact area of the head–disk interface. Sharma et al. [8,9] found that the damage due to ‘‘thermal asperity’’ events is reduced by using an air bearing surface with a U-shaped slider rail and a central airflow channel. Advanced algorithms for improved signal processing were proposed in Refs. [10–12]. Local temperature rise in the read element due to media defects can cause magnetic degradation of the read element. Magnetic degradation is associated with the change of the exchange anisotropy at the interface between ferromagnetic and anti-ferromagnetic materials in the read head structure [13]. Degradation occurs if the read head temperature exceeds a critical temperature, the so-called ‘‘blocking temperature’’ [13–15]. Hence, whenever the blocking temperature is exceeded, the head performance degrades, leading to failure of a hard disk drive. Recently, Lee and Yeo [16] developed a thermo-mechanical model to simulate the contact between a disk asperity and a slider.
W. Song et al. / Tribology International 55 (2012) 100–107
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inclusion 100 nm Fig. 1. Typical asperity in magnetic media: (a) SEM top view and (b) focused ion beam cross section. The dashed line in (a) shows the position at which the focused ion beam image shown in (b) was obtained [4].
the disk asperity and the TFC slider. The effect of material properties and the diameter of asperities is also studied and discussed.
2. Modeling
Fig. 2. Atomic force microscope image of typical scratches in a slider due to contact with an asperity on the disk surface [4].
They modeled the slider as diamond-like carbon (DLC) material and the disk asperity as a spherical cap with disk substrate material properties. A maximum flash temperature of 390 1C was reported and failure of the protective DLC coating on the slider was attributed to graphitization of DLC material. Song et al. [4] developed a time-dependent thermo-elastic–plastic contact model to investigate the mechanical and thermal response of the read/write sensor area of a TFC slider during contacts with alumina and nickel–phosphorus asperities. They observed a large temperature rise in the read/write shields as well as scratching and wear due to plastic deformation. The goal of the current study is to extend the work of Song et al. [4], who developed a model for contact between a thermal flying height control slider and a disk asperity, to a wider range of contact conditions than was done in the original paper. In particular, the formation of scratches in the read–write shields is investigated. The maximum temperature at the read element location is obtained as a function of the friction coefficient, the circumferential disk velocity, as well as the interference between
Fig. 3 shows a schematic of the model used in this paper for contact between a thermal protrusion on a TFC slider and an asperity on the disk. As can be seen from Fig. 3, the asperity on the disk surface is modeled as a cylinder with diameter d and a spherical cap on the top with total height h. The asperity moves with the disk at the circumferential velocity Vx. In this study, the height h was chosen to be 15 nm. The thermal protrusion on the slider is modeled as a sphere with radius RTP. The location of the heater, the read/write element, and the read and write shields is also shown in the figure. As indicated in Fig. 3, the interference d between the disk asperity and the TFC slider is defined as the distance between the top of the disk asperity and the bottom of the thermal protrusion on the TFC slider. A thermo-elastic–plastic material model as described by Hallquist [17] was used (see Appendix A.1). In the numerical model, we assume that the material properties of the disk, the slider, and the read–write shields correspond to material properties of NiP, alumina (Al2O3) and NiFe, respectively. NiP and Al2O3 asperities are studied. A summary of the material properties is given in Table 1. The constitutive material model used in this study accounts for elastic–plastic deformation with isotropic strain hardening of 2%. Fig. 4 shows the finite element model of contact between the thermal protrusion on the TFC slider and the asperity on the disk, which was previously reported in Ref. [4]. Since the width of the read and write elements is much smaller than the width of the shields, we neglected the width of the read and write elements compared to the width of the shields. In Fig. 4, the location of the read and write element is denoted by two dashed lines. The mass of the slider was assumed to be 0.5 mg. An initial temperature of 300 K was assumed for both the disk and the disk asperity. Due to the temperature increase generated by the heater in the slider as described by Li et al. [3], an initial temperature of 315 K was taken for the slider (Al2O3 #1), and an initial temperature of 335 K was taken for the read shields, the write shields, and the alumina area of the slider (Al2O3 #2). The details and validation of the finite element model can be found in Ref. [4]. Similar to Ref. [4], the thermo-mechanical contact problem between disk asperity and thermal protrusion of the TFC slider
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TFC slider d h
Asperity
Heater Read shields
R TP = 5 mm Write shields
Read element Asperity
Disk
Thermal protrusion Write element
Vx
Fig. 3. Schematic of contact between asperity on disk and thermal protrusion on TFC slider.
1.0
Table 1 Material properties.
b
Al2O3a
NiFeb
114 3.0 8000 0.31 13.3 440 4.4
400 6.4 3890 0.23 5.5 780 1.3
205 1.7 8440 0.22 12 440 35
[21]. [23].
Al2O 3 #1 (I)
Read shields (II)
Al2O 3 #2 (III)
Write shields (IV)
0.0 -0.5 Scratch depth, D
NiPa
Scratch Depth of Write Shields (nm)
Young’s modulus, E (GPa) Yield strength, Y (GPa) Density, r (kg/m3) Poisson ratio, n Thermal expansion coefficient (10 6 K 1) Heat capacity, H (J kg 1 K 1) Thermal conductivity, k (W m 1K 1) a
Scratch width, W
0.5
-1.0 -1.5 -2.0 -2.5 -3.0 -3.5 -4.0 -300
-200
-100 0 100 Width of Write Shields, z (nm)
200
300
Fig. 5. Typical scratches in the write shields as a function of interference [4] (m ¼0.2, Vx ¼20 m/s and Al2O3 asperity). Scratch depth and scratch width correspond to maximum plastic deformation during a single contact.
z y
x
Read element
Write element
Disk Asperity
Fig. 4. Finite element model of contact between asperity on disk and thermal protrusion on TFC slider.
was solved using the commercially available finite element package LS-DYNA [17]. The momentum equation was solved by explicit time integration. A backward integration scheme was used to solve the thermal equilibrium. The thermal energy dissipated during a contact was assumed to be equal to the frictional energy generated. The thermal energy generated by plastic deformation was not considered in this study. Thermal convection and radiation are not considered in our study. To fulfill the Block postulate [18], the temperature between the asperity on the disk surface and the thermal protrusion of the slider is assumed to be the same at opposing contacting nodes.
3. Results and discussion In this study, we assume that the write element is closest to the disk surface [4]. Fig. 5 shows numerical results for the profile of a typical scratch in the write shields for interference d of 5 nm,
10 nm and 13 nm, respectively. Here, the scratch depth D and the scratch width W were taken to be equal to the maximum values of the plastic deformation during a single transient contact. Because of symmetry, only one half of the scratch profiles was calculated. The scratch profiles shown in Fig. 5 were plotted by reflecting the calculated scratch profile with respect to the xy plane (see Fig. 4). We observe that the scratch width and scratch depth decrease with increasing interference d. A pile up of material is also noticeable on both sides of the scratch. Fig. 6 shows the scratch depth and scratch width in the read and write shields as a function of interference for an asperity diameter of 300 nm and 1000 nm, respectively. A friction coefficient of m ¼0.2 and a circumferential disk velocity of Vx ¼20 m/s were assumed [19]. We observe from Figs. 6(a) and (c) that the scratch depth in the read and write shields increases nearly linearly with interference d. On the other hand, the scratch width in the read and write shields increases less than linear with an increase in the interference d (Figs. 6(b) and (d)). It is apparent that the increase in the scratch depth and scratch width is related to the increase in contact pressure and stresses with increasing interference. As shown in Figs. 6(a) and (c), the scratch depth in the read shields approaches zero if d r3 nm. In addition, the scratch depth in the write shields approaches zero if d r1 nm. This result indicates that in the limit of very small interference, mainly elastic deformation is present. Comparing the scratch depth and scratch width for the asperities with diameter of 300 nm and 1000 nm, respectively,
W. Song et al. / Tribology International 55 (2012) 100–107
1200 Read shields
Read shields Scratch Width, W (nm)
Scratch Depth, D (nm)
4
Write shields
3
d = 300 nm 2
1
1000
Write shields
800
d = 300 nm
600 400 200 0
0 0
3
6
9
15
12
0
1200
4 Scratch Width, W (nm)
Write shields
3
d = 1000 nm 2
1
3
6
9
12
15
9
12
15
Read shields
Read shields Scratch Depth, D (nm)
103
1000
Write shields d = 1000 nm
800 600 400 200 0
0 0
3
6
9
12
15
0
3
6
Fig. 6. Scratch dimensions versus interference d in read and write shields: (a) scratch depth for d ¼ 300 nm, (b) scratch width for d ¼300 nm, (c) scratch depth for d ¼1000 nm, and (d) scratch width for d ¼1000 nm (m ¼ 0.2, Vx ¼20 m/s and an Al2O3 asperity).
I
III
II
IV
0.20
Read shields
0.10
0.05
Al2O3 #2
0.15
Write shields
d = 300 nm d = 1000 nm
Al2O3 #1
Maximum Plastic Strain
0.25
0.00 0
3
6
9
12
15
Coordinate, X (µm) Fig. 7. Maximum plastic strain in slider for an Al2O3 asperity with a diameter of 300 nm and 1000 nm, assuming Vx ¼20 m/s, d ¼ 13 nm and m ¼0.2.
we observe that the asperity with larger diameter gives smaller values of scratch depth in both the read and the write shields. It is apparent that this is related to the reduction in contact pressure with increasing diameter of disk asperities. On the other hand, as the diameter of disk asperities increases, the scratch width in both the read and the write shields increases due to the larger contact area. Thus, a larger asperity causes a shallower and wider scratch compared to a smaller asperity assuming the same height for both asperities.
Fig. 7 shows the maximum plastic strain in the slider for an Al2O3 asperity with a diameter of 300 nm and 1000 nm, respectively, assuming Vx ¼20 m/s, d ¼13 nm and m ¼0.2. The regions I–IV correspond to the same regions shown in Fig. 4. As can be seen in Fig. 7, negligible plastic deformation is observed in the Al2O3 regions due to the high yield strength of Al2O3 (see Table 1). On the other hand, severe plastic deformation occurs in the soft read and write shields. We also observe that the maximum plastic strain in the ead shields increases with an increase in the X coordinate due to the increasing interference with the disk asperity. In the write shields, the plastic strain increases initially reaching a maximum value at X¼12 mm, corresponding to the location of the write element. This is because the write element on the thermal protrusion is assumed to be closest to the disk surface in this study. Additionally, the plastic strain in the read and write shields is found to be larger for a small asperity of d¼300 nm than for a larger asperity of d¼ 1000 nm. This is consistent with the scratch depth shown in Fig. 6. In Fig. 8, the maximum temperature at the location of the read element is plotted as a function of interference d. We observe from Fig. 8 that the maximum temperature at the location of the read element increases with increasing interference due to the increasing contact pressure, and therefore heat generation. In addition, we observe from Fig. 8 that the maximum temperature at the location of the read element increases with increasing the asperity diameter. This finding is further explained in Figs. 9 and 10. Fig. 9 shows the temperature on the top surface of an alumina (Al2O3) asperity with a diameter of 300 nm and 1000 nm, respectively, as a function of the contact time assuming Vx ¼20 m/s,
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d ¼13 nm and m ¼0.2. The simulation of a typical contact can be divided into four regions denoted by I–IV. In region I, contact occurs between the asperity and the alumina region; in region II, contact occurs between the asperity and the read shields; in region III, contact occurs with the second alumina region, and, finally, in region IV, contact occurs with the write shields. We 400 Maximum Temperature at Reader Location, Tmax (K)
dd=300 = 300nm nm 380
dd=1000 = 1000nm nm
360 340 320 300 3
0
6
9
12
15
IV
Write shields
500
III
nm nm dd=300 = 300 nm nm dd=1000 = 1000
700 600
II
Al2O3 #2
I 800
Read shields
900
Al2O3 #1
Temperature on the top of TA, T (K)
Fig. 8. Maximum temperature at the location of the read element as a function of interference d (m ¼ 0.2, Vx ¼20 m/s and an Al2O3 asperity).
400 300 0.0
0.2
0.4 0.6 Contact Time, t (µs)
0.8
Fig. 9. Temperature on the top of an Al2O3 asperity with a diameter of 300 nm and 1000 nm, respectively, as a function of contact time, assuming Vx ¼ 20 m/s, d ¼ 13 nm and m ¼0.2.
observe from Fig. 9 that in the alumina regions I and III the temperature is lower for the asperity with d ¼1000 nm than the asperity with d ¼300 nm. This is due to the fact that the asperity with larger diameter has a smaller contact pressure and, consequently, lower frictional heating. However, in regions II and IV, corresponding to the read and the write shields, the temperature for the asperity with d¼1000 nm is slightly larger than for the asperity with d¼ 300 nm. This is in agreement with results in Fig. 8. In addition, we observe that the temperature in the regions of the read and write shields decreases slower for an asperity with d¼1000 nm than for an asperity with d ¼300 nm. To better understand the results in Fig. 9, we have plotted in Fig. 10 the temperature distributions just before and after the transition from region I to region II, corresponding to contact times t ¼0.3 ms and 0.34 ms, respectively. The solid horizontal lines below the temperature distributions in Fig. 10 indicate the size and location of the contact zone. We note, that the regions I and II shown in Fig. 10 correspond to the time periods in which the asperity makes contacts with the alumina region I and the read shields of region II, respectively. The maximum temperatures in the alumina region I, TAl2O3 and the maximum temperature in the read shields region II, Tr are inserted in Fig. 10. Comparing Figs. 10(a) and (c), we observe that at t ¼0.3 ms, the maximum temperature in region I is higher for the asperity with d¼300 nm than for the asperity with d¼1000 nm. This is in agreement with the results in Fig. 9. However, we observe from Figs. 10(b) and (d) that the maximum temperature in the read shield is larger for the case of d ¼1000 nm than for d¼300 nm. This is because that the larger asperity is still in partial contact with the alumina region I when contact starts with the read shields in region II (Fig. 10(d)). This partial contact with the alumina region for the larger asperity leads to larger heat generation compared to the smaller asperity which is entirely in contact with the conductive shields (Fig. 10(b)), and, therefore, results in much smaller frictional heating. Fig. 11 shows the scratch depth and scratch width in the write and read shields for a 300 nm and 1000 nm asperity, respectively, as a function of the friction coefficient. For this calculation, we have assumed that the circumferential disk velocity is Vx ¼20 m/s and that the interference is d ¼13 nm. We observe from Figs. 11(a) and 10(c), that the scratch depth in the read and write shields increases slightly with an increase in the friction coefficient. This suggests that the scratch depth of the read/write element could be reduced if the friction coefficient is reduced. From Figs. 11(b) and (d), we observe that the effect of the friction
Fig. 10. Temperature distributions for an Al2O3 asperities with diameter of d ¼300 nm and d ¼ 1000 nm, respectively, assuming Vx ¼ 20 m/s, d ¼13 nm and m ¼0.2. The results are shown just before and during the transition from region I to region II (see Fig. 9), corresponding to contact time t ¼0.3 ms and 0.34 ms, respectively. Solid lines below each figure indicate the contact zone.
W. Song et al. / Tribology International 55 (2012) 100–107
1200
3 2 Read shields 1
Write shields d = 300 nm
Scratch Width, W (nm)
Scratch Depth, D (nm)
4
Read shields
1000
Write shields
800
d = 300 nm 600 400 200 0
0 0
0.1
0.2
4
0.3
0.4
0.5
0
Write shields
3
0.1
0.2
0.3
0.4
0.5
1200
Read shields Scratch Width, W (nm)
Scratch Depth, D (nm)
105
d = 1000 nm 2 1 0
1000 800 600
Read shields
400
Write shields d = 1000 nm
200 0
0
0.1
0.2
0.3
0.4
0.5
0
0.1
0.2
0.3
0.4
0.5
Fig. 11. Scratch dimensions versus coefficient of friction in read and write shields: (a) scratch depth for d ¼ 300 nm, (b) scratch width for d ¼300 nm, (c) scratch depth for d ¼1000 nm and (d) scratch width for d ¼1000 nm (d ¼ 13 nm, Vx ¼20 m/s and an Al2O3 asperity).
450 Maximum Temperature at Reader Loation, Tmax (K)
450
Maximum Temperature at Reader Location, Tmax (K)
d = 300 nm d = 1000 nm
420 390 360 330
d = 300 nm d = 1000 nm
420 390 360 330 300 0
300 0
0.1
0.2
0.3
0.4
0.5
Fig. 12. Maximum temperature at the location of the read element as a function of the coefficient of friction (d ¼13 nm, Vx ¼20 m/s and an Al2O3 asperity).
coefficient on the scratch width in the read and write shields is small. The maximum temperature at the location of the read element (Fig. 12) increases linearly with an increase in the friction coefficient. The maximum temperature at the location of the read element for the case of m ¼0.5 is about 440 K, approaching the blocking temperature of the read element, which is around 470 K [13–15]. This indicates that the flash temperature during contact between a disk asperity and the read element of a slider can reach the blocking temperature. It also suggests that disk lubricants should be chosen to exhibit a low coefficient of friction and low interface temperature. Fig. 13 shows the maximum temperature at the location of the read element for asperities with a diameter of 300 nm and 1000 nm, respectively. We observe that the maximum tem-
10 20 30 40 50 Circumferential Velocity, Vx ( m/s)
Fig. 13. Maximum temperature at the location of the read element as a function of circumferential disk velocity (d ¼13 nm, m ¼ 0.2 and an Al2O3 asperity).
perature at the location of the read element increases linearly with increasing circumferential disk velocity. This suggests that asperities located at the outer diameter on the disk are likely to cause larger thermal damage compared to those located at the internal diameter. The above statement applies also to disk drives with higher rotational spindle compared to drives with lower rotational speed, assuming the asperity is located at the same diameter. The scratch depth and scratch width in the read–write shields for NiP asperity are shown in Fig. 14(a) and (b), respectively. Fig. 14(c) shows a comparison of the volume of the plastic zone for NiP and Al2O3 asperities. A friction coefficient of m ¼0.2, a circumferential disk velocity of Vx ¼20 m/s and a diameter of d¼300 nm were assumed for this case. Comparing Figs. 14(a) and (b) with Figs. 6(a) and (b), respectively, we observe that the values of the scratch depth and the scratch width are larger for the Al2O3 asperity than for the NiP asperity. This indicates that Al2O3
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W. Song et al. / Tribology International 55 (2012) 100–107
350
Read shields
Scratch Width, W (nm)
Scratch Depth, D (nm)
4
Write shields
3
Asperity: NiP 2 1
Read shields
300 Write shields Asperity: NiP
250 200 150 100 50 0
0 0
3
6
9
12
15
0
3
6
9
12
15
9
12
15
Plastic Zone Volume in Read Shields, Vp (10-3·µm3)
120 Al2O3 Al2O3
100
NiP
80 60 40 20 0 0
3
6
Fig. 14. Scratch dimensions in read and write shields versus interference: (a) scratch depth for NiP asperity, (b) scratch width for NiP asperity and (c) volume of plastic zone in the read shields for NiP and Al2O3 asperities (Vx ¼ 20 m/s, m ¼0.2 and d ¼300 nm).
Maximum Temperature at Reader Location, Tmax (K)
400 Al Al2O3 2O3 380 NiP 360 340 320 300 0
3
6
9
12
15
Fig. 15. Maximum temperature at the location of the read element as a function of interference (Vx ¼20 m/s, m ¼ 0.2 and d ¼300 nm).
asperities can cause deeper and wider scratches in the read and write shields than NiP asperities keeping other conditions the same. From Fig. 14(c), we can observe that the volume of the plastic zone is larger for the case of an Al2O3 asperity than for the case of a NiP asperity. This is because higher contact pressure, and, therefore, larger residual plastic deformation occurs in the case of the harder and stiffer Al2O3 asperity. In addition, it is important to note that plastic deformation may still occur inside the read and the write shields even though the residual deformation at the surface is close to zero. This is consistent with numerical results showing that the location where the first plastic deformation occurs is in the interior of the body, i.e., below the contact surface [20]. As shown in Fig. 15, the maximum temperature at the location of the read element is higher for the case of an Al2O3 asperity,
than for the case of a NiP asperity. This is due to the fact that the larger contact pressure induced by the harder Al2O3 asperity causes an increase in frictional heating. In addition, the Al2O3 asperities do not conduct thermal flux as efficiently as NiP asperities, mainly due to difference in their thermal conductivities (see Table 1). From Fig. 15, we can also observe that the maximum temperature at the location of the read element for NiP and alumina asperities becomes similar for d r5 nm and approaches 335 K for d ¼3 nm which equals to the originally assumed value of the temperature. Finally, we investigated the effect of disk velocity on scratch depth and width. Varying the disk velocity in the range of 10 m/ srVx r50 m/s, assuming an Al2O3 asperity with m ¼0.2 and d ¼13 nm, we found that the scratch depth and width in the read and write shields are independent of the disk velocity. This is due to the assumption that the material model used in this study does not consider strain rate effects.
4. Conclusions The effect of contact conditions on scratch dimensions in the read–write shields and the maximum temperature at the location of the read element during contact between a thermal protrusion on a TFC slider and an asperity on a disk were investigated. The effect of diameter and material properties of the asperity was also investigated. The following conclusions can be drawn: (1) The scratch depth and scratch width in the read and write shields is a strong function of the interference between the asperity and the thermal protrusion on the slider. An increase in the interference leads to deeper and wider scratches. However, the effect of the friction coefficient and the circumferential disk velocity on the scratch dimensions is small.
W. Song et al. / Tribology International 55 (2012) 100–107
(2) An increase in the diameter of an asperity leads to shallower and wider scratches in the read and write shields. In addition, hard and stiff asperities cause deeper and wider scratches compared with soft and compliant ones. (3) Large values of interference, large friction coefficients, and high circumferential disk velocities can cause a high temperature at the location of the read element. (4) For large values of interference, high values of the friction coefficient and large circumferential disk velocity used in this study, the temperature at the location of the read element approach the blocking temperature of the read element. For most practical situations, the blocking temperature does not seem to be exceeded, and it is likely that plastic deformation is the dominant failure mechanism causing degradation of the read element.
Acknowledgments We would like to thank Dr. Raj Thangaraj, Dr. John Ji and Dr. Leo Volpe from Western Digital Corporation for helpful discussions with this paper. Wenping Song would like to thank the China Scholarship Council (CSC) and Prof. Guangyu Zhang from Harbin Institute of Technology, for supporting his Ph.D. studies at UCSD.
Appendix A A.1. Thermo-elastic–plastic material model A thermo-elastic–plastic material model was used as described by Hallquist [17] and implemented in previous studies by Song et al. [4] and Ovcharenko et al. [21,22]. Stress is calculated based on both elastic strain and thermal strain. The thermal strain rate is determined by the coefficient of thermal expansion a and temperature T as
e_ Tij ¼ aT_ dij
ð1Þ
At each step in the calculation, the stress is updated elastically and checked whether it exceeds the isotropic yield function
f¼
1 sY ðTÞ2 Sij Sij 2 3
ð2Þ
where Sij is the deviatoric stress tensor. In this study, the yield strength in uniaxial tension sY is assumed to be temperature independent (Table 1). If the stress is less than the elastic limit, no change is made; if the stress exceeds the elastic limit, the stress deviator is scaled back by a factor fs, i.e., Snij þ 1 ¼ f s Snij , where the factor fs is defined as
s
Y f s ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3=2ÞSnij Snij
ð3Þ
In this case, the effective plastic strain is updated by the increment qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1f s Þ ð3=2ÞSnij Snij p Deef f ¼ ð4Þ G þ 3Ep
107
where G is the shear modulus and Ep is the plastic hardening modulus, the latter assumed to be equal to 2% of Young’s modulus. In our study, the material properties were assumed to be independent of temperature (Table 1).
References [1] Kurita M, Xu J, Tokuyama M, Nakamoto K, Saegusa S, Maruyama Y. Flyingheight reduction of magnetic-head slider due to thermal protrusion. IEEE Transactions on Magnetics 2005;41(10):3007–9. [2] Zheng H, Li H, Talke FE. Numerical simulation of a thermal flying height control slider with dual heater and insulator elements. IEEE Transactions on Magnetics 2009;45(10):3628–31. [3] Li H, Zheng H, Fritzsche J, Amemoya K, Talke FE. Simulation of flying height and response time of thermal flying height control sliders with thermal insulators. IEEE Transactions on Magnetics 2010;46(6):1292–4. [4] Song W, Ovcharenko A, Yang M, Zheng H, Talke FE. Contact between a thermal flying height control slider and a thermal asperity. Microsystem Technology, 2012, 2012, http://dx.doi.org/10.1007/s00542-012-1591-0. [5] Choa S-H, Sharma V. Sensitivity and rejection of thermal asperities in a hard disk drive. Journal of Magnetism and Magnetic Materials 2002;241(2–3): 466–74. [6] Stupp SE, Baldwinson MA, Mcewen P, Crawford TM, Rogers CT. Thermal asperity trends. IEEE Transactions on Magnetics 1999;35(2):752–7. [7] Yuan Z, Liu B. Anti-thermal asperity head: design and performance analysis. Journal of Magnetism and Magnetic Materials 2000;209(1–3):166–8. [8] Sharma V, Kim S-H, Choa S-H. Head and media design considerations for reducing thermal asperity. Tribology International 2001;34(5):307–14. [9] Sharma V, Kim S-H, Choa S-H. The effects of slider design on thermal asperity rejection capability. Journal of Mechanical Science and Technology 2001;15(3):281–90. [10] Dorfman V, Wolf JK. A method for reducing the effects of thermal asperities. IEEE Transactions on Magnetics 2001;19(4):662–7. [11] Mathew G, Tjhia I. Thermal asperity suppression in perpendicular recording channels. IEEE Transactions on Magnetics 2005;41(10):2878–80. [12] Erden MF, Kurtas EM. Thermal asperity detection and cancellation in perpendicular magnetic recording systems. IEEE Transactions on Magnetics 2004;40(3):1732–7. [13] Nogues J, Schuller IK. Exchange bias. Journal of Magnetism and Magnetic Materials 1999;192:203–32. [14] Kools JCS. Exchange-biased spin-valves for magnetic storage. IEEE Transactions on Magnetics 1996;32(4):3165–84. [15] Pinarbasi M, Metin S, Gill H, Parker M, Gurney B, Carey M, et al. Antiparallel pinned NiO spin valve sensor for GMR head application. Journal of Applied Physics 2000;87(9):5714–9. [16] Lee S, Yeo C-D. Thermal–mechanical contact and micro-wear in head disk interface. In: ASME/STLE international joint tribology conference, 2011. [17] Hallquist JO. LS-DYNA theoretical manual. Livermore, CA: Livermore Software Technology Corporation; 2006. [18] Block H. Theoretical study of temperature rise at surfaces of actual contact under oiliness lubricating conditions. Proceedings of the Institute of Mechanical Engineers General Discussion of Lubrication 1937;2:222–35. [19] Ovcharenko A, Yang M, Chun K, Talke FE. IEEE Transactions on Magnetics 2010;46(3):770–7; Ovcharenko A, Yang M, Chun K, Talke FE. Effect of impact conditions and slider corner radius on the thermal–mechanical response during slider–disk contacts. IEEE Transactions on Magnetics 2010;46(10):3760–6. [20] Brizmer V, Kligerman Y, Etsion I. The effect of contact conditions and material properties on the elasticity terminus of a spherical contact. International Journal of Solids and Structures 2006;43:5736–49. [21] Ovcharenko A, Yang M, Chun K, Talke FE. Simulation of magnetic erasure due to transient slider–disk contacts. IEEE Transactions on Magnetics 2010; 46(3):770–7. [22] Ovcharenko A, Yang M, Chun K, Talke FE. Transient thermomechanical contact of an impacting sphere on a moving flat. ASME Journal of Tribology 2011;133(3):031404. [23] Material properties provided by Western Digital Corporation.
Contents lists available at SciVerse ScienceDirect
Tribology International journal homepage: www.elsevier.com/locate/triboint
Effect of contact conditions during thermo-mechanical contact between a thermal flying height control slider and a disk asperity Wenping Song a,c,n, Andrey Ovcharenko b, Bernhard Knigge b, Min Yang b, Frank E. Talke c a
School of Mechatronics Engineering, Harbin Institute of Technology, China Western Digital Corporation, San Jose, USA c Center for Magnetic Recording Research, University of California, San Diego, CA, USA b
a r t i c l e i n f o
a b s t r a c t
Article history: Received 30 January 2012 Received in revised form 10 May 2012 Accepted 22 May 2012 Available online 7 June 2012
A three-dimensional thermo-mechanical model is developed for the transient contact between a thermal flying height control (TFC) slider and a disk asperity. The effect of contact conditions is investigated, including the friction coefficient and the circumferential disk velocity. The damage of the read–write shields due to contacts with disk asperities is studied along with the maximum temperature at the location of the read element. The effect of diameter and material properties of the asperity is also investigated. Strong dependence of deformation and maximum temperature is observed as a function of the diameter and material properties of the asperity. & 2012 Elsevier Ltd. All rights reserved.
Keywords: Thermo-mechanical contact Asperity Media defect TFC slider
1. Introduction To increase recording density in hard disk drives, thermal flying-height control (TFC) sliders have recently been implemented [1–3]. Thermal flying height control sliders are designed to reduce the flying height of the read/write element by locally heating the area near the read/write element, thereby causing a thermal protrusion that reduces the head–disk spacing in the area of the read/write element. In the last few years, the physical spacing between the read/write element and the disk has decreased to the order of a few nanometers [2]. At such small spacing, the occurrence of slider disk contacts becomes increasingly more likely. Contacts occur predominantly in areas of the disk where inclusions or so-called ‘‘media defects’’ are present. Media defects have their origin in the sputtering process, i.e., any foreign particles present during sputtering can cause the formation of defects on the surface of the disk. In Fig. 1(a), a scanning electron microscope image of a typical disk defect, generally described as disk ‘‘asperity’’, is shown. A cross section of the same asperity can be seen in Fig. 1(b) [4]. Contacts between asperities on the disk surface and the slider can cause abrasive and adhesive wear, as well as high interfacial temperatures at the read/write element. Both effects are highly undesirable for the
n Corresponding author at: School of Mechatronics Engineering, Harbin Institute of Technology, China. E-mail address: [email protected] (W. Song).
0301-679X/$ - see front matter & 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.triboint.2012.05.016
durability of a disk drive. Fig. 2 shows typical scratch marks in the area of the read/write element of a TFC slider, caused by contacts between disk asperities and the slider [4]. Damage of the read/ write element can cause loss of the read signal, and even failure of a head. Contacts between disk asperities and the slider are generally referred to as ‘‘thermal asperity’’ events [5–12]. Many studies had been undertaken in the past to reduce the damaging effect of disk asperities, including modifications of the air bearing surface (ABS) [7–9] and implementation of algorithms to improve signal processing [10–12]. Yuan and Liu [7] proposed a novel read/write head, in which the read-back sensor was located far away from the contact area of the head–disk interface. Sharma et al. [8,9] found that the damage due to ‘‘thermal asperity’’ events is reduced by using an air bearing surface with a U-shaped slider rail and a central airflow channel. Advanced algorithms for improved signal processing were proposed in Refs. [10–12]. Local temperature rise in the read element due to media defects can cause magnetic degradation of the read element. Magnetic degradation is associated with the change of the exchange anisotropy at the interface between ferromagnetic and anti-ferromagnetic materials in the read head structure [13]. Degradation occurs if the read head temperature exceeds a critical temperature, the so-called ‘‘blocking temperature’’ [13–15]. Hence, whenever the blocking temperature is exceeded, the head performance degrades, leading to failure of a hard disk drive. Recently, Lee and Yeo [16] developed a thermo-mechanical model to simulate the contact between a disk asperity and a slider.
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inclusion 100 nm Fig. 1. Typical asperity in magnetic media: (a) SEM top view and (b) focused ion beam cross section. The dashed line in (a) shows the position at which the focused ion beam image shown in (b) was obtained [4].
the disk asperity and the TFC slider. The effect of material properties and the diameter of asperities is also studied and discussed.
2. Modeling
Fig. 2. Atomic force microscope image of typical scratches in a slider due to contact with an asperity on the disk surface [4].
They modeled the slider as diamond-like carbon (DLC) material and the disk asperity as a spherical cap with disk substrate material properties. A maximum flash temperature of 390 1C was reported and failure of the protective DLC coating on the slider was attributed to graphitization of DLC material. Song et al. [4] developed a time-dependent thermo-elastic–plastic contact model to investigate the mechanical and thermal response of the read/write sensor area of a TFC slider during contacts with alumina and nickel–phosphorus asperities. They observed a large temperature rise in the read/write shields as well as scratching and wear due to plastic deformation. The goal of the current study is to extend the work of Song et al. [4], who developed a model for contact between a thermal flying height control slider and a disk asperity, to a wider range of contact conditions than was done in the original paper. In particular, the formation of scratches in the read–write shields is investigated. The maximum temperature at the read element location is obtained as a function of the friction coefficient, the circumferential disk velocity, as well as the interference between
Fig. 3 shows a schematic of the model used in this paper for contact between a thermal protrusion on a TFC slider and an asperity on the disk. As can be seen from Fig. 3, the asperity on the disk surface is modeled as a cylinder with diameter d and a spherical cap on the top with total height h. The asperity moves with the disk at the circumferential velocity Vx. In this study, the height h was chosen to be 15 nm. The thermal protrusion on the slider is modeled as a sphere with radius RTP. The location of the heater, the read/write element, and the read and write shields is also shown in the figure. As indicated in Fig. 3, the interference d between the disk asperity and the TFC slider is defined as the distance between the top of the disk asperity and the bottom of the thermal protrusion on the TFC slider. A thermo-elastic–plastic material model as described by Hallquist [17] was used (see Appendix A.1). In the numerical model, we assume that the material properties of the disk, the slider, and the read–write shields correspond to material properties of NiP, alumina (Al2O3) and NiFe, respectively. NiP and Al2O3 asperities are studied. A summary of the material properties is given in Table 1. The constitutive material model used in this study accounts for elastic–plastic deformation with isotropic strain hardening of 2%. Fig. 4 shows the finite element model of contact between the thermal protrusion on the TFC slider and the asperity on the disk, which was previously reported in Ref. [4]. Since the width of the read and write elements is much smaller than the width of the shields, we neglected the width of the read and write elements compared to the width of the shields. In Fig. 4, the location of the read and write element is denoted by two dashed lines. The mass of the slider was assumed to be 0.5 mg. An initial temperature of 300 K was assumed for both the disk and the disk asperity. Due to the temperature increase generated by the heater in the slider as described by Li et al. [3], an initial temperature of 315 K was taken for the slider (Al2O3 #1), and an initial temperature of 335 K was taken for the read shields, the write shields, and the alumina area of the slider (Al2O3 #2). The details and validation of the finite element model can be found in Ref. [4]. Similar to Ref. [4], the thermo-mechanical contact problem between disk asperity and thermal protrusion of the TFC slider
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TFC slider d h
Asperity
Heater Read shields
R TP = 5 mm Write shields
Read element Asperity
Disk
Thermal protrusion Write element
Vx
Fig. 3. Schematic of contact between asperity on disk and thermal protrusion on TFC slider.
1.0
Table 1 Material properties.
b
Al2O3a
NiFeb
114 3.0 8000 0.31 13.3 440 4.4
400 6.4 3890 0.23 5.5 780 1.3
205 1.7 8440 0.22 12 440 35
[21]. [23].
Al2O 3 #1 (I)
Read shields (II)
Al2O 3 #2 (III)
Write shields (IV)
0.0 -0.5 Scratch depth, D
NiPa
Scratch Depth of Write Shields (nm)
Young’s modulus, E (GPa) Yield strength, Y (GPa) Density, r (kg/m3) Poisson ratio, n Thermal expansion coefficient (10 6 K 1) Heat capacity, H (J kg 1 K 1) Thermal conductivity, k (W m 1K 1) a
Scratch width, W
0.5
-1.0 -1.5 -2.0 -2.5 -3.0 -3.5 -4.0 -300
-200
-100 0 100 Width of Write Shields, z (nm)
200
300
Fig. 5. Typical scratches in the write shields as a function of interference [4] (m ¼0.2, Vx ¼20 m/s and Al2O3 asperity). Scratch depth and scratch width correspond to maximum plastic deformation during a single contact.
z y
x
Read element
Write element
Disk Asperity
Fig. 4. Finite element model of contact between asperity on disk and thermal protrusion on TFC slider.
was solved using the commercially available finite element package LS-DYNA [17]. The momentum equation was solved by explicit time integration. A backward integration scheme was used to solve the thermal equilibrium. The thermal energy dissipated during a contact was assumed to be equal to the frictional energy generated. The thermal energy generated by plastic deformation was not considered in this study. Thermal convection and radiation are not considered in our study. To fulfill the Block postulate [18], the temperature between the asperity on the disk surface and the thermal protrusion of the slider is assumed to be the same at opposing contacting nodes.
3. Results and discussion In this study, we assume that the write element is closest to the disk surface [4]. Fig. 5 shows numerical results for the profile of a typical scratch in the write shields for interference d of 5 nm,
10 nm and 13 nm, respectively. Here, the scratch depth D and the scratch width W were taken to be equal to the maximum values of the plastic deformation during a single transient contact. Because of symmetry, only one half of the scratch profiles was calculated. The scratch profiles shown in Fig. 5 were plotted by reflecting the calculated scratch profile with respect to the xy plane (see Fig. 4). We observe that the scratch width and scratch depth decrease with increasing interference d. A pile up of material is also noticeable on both sides of the scratch. Fig. 6 shows the scratch depth and scratch width in the read and write shields as a function of interference for an asperity diameter of 300 nm and 1000 nm, respectively. A friction coefficient of m ¼0.2 and a circumferential disk velocity of Vx ¼20 m/s were assumed [19]. We observe from Figs. 6(a) and (c) that the scratch depth in the read and write shields increases nearly linearly with interference d. On the other hand, the scratch width in the read and write shields increases less than linear with an increase in the interference d (Figs. 6(b) and (d)). It is apparent that the increase in the scratch depth and scratch width is related to the increase in contact pressure and stresses with increasing interference. As shown in Figs. 6(a) and (c), the scratch depth in the read shields approaches zero if d r3 nm. In addition, the scratch depth in the write shields approaches zero if d r1 nm. This result indicates that in the limit of very small interference, mainly elastic deformation is present. Comparing the scratch depth and scratch width for the asperities with diameter of 300 nm and 1000 nm, respectively,
W. Song et al. / Tribology International 55 (2012) 100–107
1200 Read shields
Read shields Scratch Width, W (nm)
Scratch Depth, D (nm)
4
Write shields
3
d = 300 nm 2
1
1000
Write shields
800
d = 300 nm
600 400 200 0
0 0
3
6
9
15
12
0
1200
4 Scratch Width, W (nm)
Write shields
3
d = 1000 nm 2
1
3
6
9
12
15
9
12
15
Read shields
Read shields Scratch Depth, D (nm)
103
1000
Write shields d = 1000 nm
800 600 400 200 0
0 0
3
6
9
12
15
0
3
6
Fig. 6. Scratch dimensions versus interference d in read and write shields: (a) scratch depth for d ¼ 300 nm, (b) scratch width for d ¼300 nm, (c) scratch depth for d ¼1000 nm, and (d) scratch width for d ¼1000 nm (m ¼ 0.2, Vx ¼20 m/s and an Al2O3 asperity).
I
III
II
IV
0.20
Read shields
0.10
0.05
Al2O3 #2
0.15
Write shields
d = 300 nm d = 1000 nm
Al2O3 #1
Maximum Plastic Strain
0.25
0.00 0
3
6
9
12
15
Coordinate, X (µm) Fig. 7. Maximum plastic strain in slider for an Al2O3 asperity with a diameter of 300 nm and 1000 nm, assuming Vx ¼20 m/s, d ¼ 13 nm and m ¼0.2.
we observe that the asperity with larger diameter gives smaller values of scratch depth in both the read and the write shields. It is apparent that this is related to the reduction in contact pressure with increasing diameter of disk asperities. On the other hand, as the diameter of disk asperities increases, the scratch width in both the read and the write shields increases due to the larger contact area. Thus, a larger asperity causes a shallower and wider scratch compared to a smaller asperity assuming the same height for both asperities.
Fig. 7 shows the maximum plastic strain in the slider for an Al2O3 asperity with a diameter of 300 nm and 1000 nm, respectively, assuming Vx ¼20 m/s, d ¼13 nm and m ¼0.2. The regions I–IV correspond to the same regions shown in Fig. 4. As can be seen in Fig. 7, negligible plastic deformation is observed in the Al2O3 regions due to the high yield strength of Al2O3 (see Table 1). On the other hand, severe plastic deformation occurs in the soft read and write shields. We also observe that the maximum plastic strain in the ead shields increases with an increase in the X coordinate due to the increasing interference with the disk asperity. In the write shields, the plastic strain increases initially reaching a maximum value at X¼12 mm, corresponding to the location of the write element. This is because the write element on the thermal protrusion is assumed to be closest to the disk surface in this study. Additionally, the plastic strain in the read and write shields is found to be larger for a small asperity of d¼300 nm than for a larger asperity of d¼ 1000 nm. This is consistent with the scratch depth shown in Fig. 6. In Fig. 8, the maximum temperature at the location of the read element is plotted as a function of interference d. We observe from Fig. 8 that the maximum temperature at the location of the read element increases with increasing interference due to the increasing contact pressure, and therefore heat generation. In addition, we observe from Fig. 8 that the maximum temperature at the location of the read element increases with increasing the asperity diameter. This finding is further explained in Figs. 9 and 10. Fig. 9 shows the temperature on the top surface of an alumina (Al2O3) asperity with a diameter of 300 nm and 1000 nm, respectively, as a function of the contact time assuming Vx ¼20 m/s,
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d ¼13 nm and m ¼0.2. The simulation of a typical contact can be divided into four regions denoted by I–IV. In region I, contact occurs between the asperity and the alumina region; in region II, contact occurs between the asperity and the read shields; in region III, contact occurs with the second alumina region, and, finally, in region IV, contact occurs with the write shields. We 400 Maximum Temperature at Reader Location, Tmax (K)
dd=300 = 300nm nm 380
dd=1000 = 1000nm nm
360 340 320 300 3
0
6
9
12
15
IV
Write shields
500
III
nm nm dd=300 = 300 nm nm dd=1000 = 1000
700 600
II
Al2O3 #2
I 800
Read shields
900
Al2O3 #1
Temperature on the top of TA, T (K)
Fig. 8. Maximum temperature at the location of the read element as a function of interference d (m ¼ 0.2, Vx ¼20 m/s and an Al2O3 asperity).
400 300 0.0
0.2
0.4 0.6 Contact Time, t (µs)
0.8
Fig. 9. Temperature on the top of an Al2O3 asperity with a diameter of 300 nm and 1000 nm, respectively, as a function of contact time, assuming Vx ¼ 20 m/s, d ¼ 13 nm and m ¼0.2.
observe from Fig. 9 that in the alumina regions I and III the temperature is lower for the asperity with d ¼1000 nm than the asperity with d ¼300 nm. This is due to the fact that the asperity with larger diameter has a smaller contact pressure and, consequently, lower frictional heating. However, in regions II and IV, corresponding to the read and the write shields, the temperature for the asperity with d¼1000 nm is slightly larger than for the asperity with d¼ 300 nm. This is in agreement with results in Fig. 8. In addition, we observe that the temperature in the regions of the read and write shields decreases slower for an asperity with d¼1000 nm than for an asperity with d ¼300 nm. To better understand the results in Fig. 9, we have plotted in Fig. 10 the temperature distributions just before and after the transition from region I to region II, corresponding to contact times t ¼0.3 ms and 0.34 ms, respectively. The solid horizontal lines below the temperature distributions in Fig. 10 indicate the size and location of the contact zone. We note, that the regions I and II shown in Fig. 10 correspond to the time periods in which the asperity makes contacts with the alumina region I and the read shields of region II, respectively. The maximum temperatures in the alumina region I, TAl2O3 and the maximum temperature in the read shields region II, Tr are inserted in Fig. 10. Comparing Figs. 10(a) and (c), we observe that at t ¼0.3 ms, the maximum temperature in region I is higher for the asperity with d¼300 nm than for the asperity with d¼1000 nm. This is in agreement with the results in Fig. 9. However, we observe from Figs. 10(b) and (d) that the maximum temperature in the read shield is larger for the case of d ¼1000 nm than for d¼300 nm. This is because that the larger asperity is still in partial contact with the alumina region I when contact starts with the read shields in region II (Fig. 10(d)). This partial contact with the alumina region for the larger asperity leads to larger heat generation compared to the smaller asperity which is entirely in contact with the conductive shields (Fig. 10(b)), and, therefore, results in much smaller frictional heating. Fig. 11 shows the scratch depth and scratch width in the write and read shields for a 300 nm and 1000 nm asperity, respectively, as a function of the friction coefficient. For this calculation, we have assumed that the circumferential disk velocity is Vx ¼20 m/s and that the interference is d ¼13 nm. We observe from Figs. 11(a) and 10(c), that the scratch depth in the read and write shields increases slightly with an increase in the friction coefficient. This suggests that the scratch depth of the read/write element could be reduced if the friction coefficient is reduced. From Figs. 11(b) and (d), we observe that the effect of the friction
Fig. 10. Temperature distributions for an Al2O3 asperities with diameter of d ¼300 nm and d ¼ 1000 nm, respectively, assuming Vx ¼ 20 m/s, d ¼13 nm and m ¼0.2. The results are shown just before and during the transition from region I to region II (see Fig. 9), corresponding to contact time t ¼0.3 ms and 0.34 ms, respectively. Solid lines below each figure indicate the contact zone.
W. Song et al. / Tribology International 55 (2012) 100–107
1200
3 2 Read shields 1
Write shields d = 300 nm
Scratch Width, W (nm)
Scratch Depth, D (nm)
4
Read shields
1000
Write shields
800
d = 300 nm 600 400 200 0
0 0
0.1
0.2
4
0.3
0.4
0.5
0
Write shields
3
0.1
0.2
0.3
0.4
0.5
1200
Read shields Scratch Width, W (nm)
Scratch Depth, D (nm)
105
d = 1000 nm 2 1 0
1000 800 600
Read shields
400
Write shields d = 1000 nm
200 0
0
0.1
0.2
0.3
0.4
0.5
0
0.1
0.2
0.3
0.4
0.5
Fig. 11. Scratch dimensions versus coefficient of friction in read and write shields: (a) scratch depth for d ¼ 300 nm, (b) scratch width for d ¼300 nm, (c) scratch depth for d ¼1000 nm and (d) scratch width for d ¼1000 nm (d ¼ 13 nm, Vx ¼20 m/s and an Al2O3 asperity).
450 Maximum Temperature at Reader Loation, Tmax (K)
450
Maximum Temperature at Reader Location, Tmax (K)
d = 300 nm d = 1000 nm
420 390 360 330
d = 300 nm d = 1000 nm
420 390 360 330 300 0
300 0
0.1
0.2
0.3
0.4
0.5
Fig. 12. Maximum temperature at the location of the read element as a function of the coefficient of friction (d ¼13 nm, Vx ¼20 m/s and an Al2O3 asperity).
coefficient on the scratch width in the read and write shields is small. The maximum temperature at the location of the read element (Fig. 12) increases linearly with an increase in the friction coefficient. The maximum temperature at the location of the read element for the case of m ¼0.5 is about 440 K, approaching the blocking temperature of the read element, which is around 470 K [13–15]. This indicates that the flash temperature during contact between a disk asperity and the read element of a slider can reach the blocking temperature. It also suggests that disk lubricants should be chosen to exhibit a low coefficient of friction and low interface temperature. Fig. 13 shows the maximum temperature at the location of the read element for asperities with a diameter of 300 nm and 1000 nm, respectively. We observe that the maximum tem-
10 20 30 40 50 Circumferential Velocity, Vx ( m/s)
Fig. 13. Maximum temperature at the location of the read element as a function of circumferential disk velocity (d ¼13 nm, m ¼ 0.2 and an Al2O3 asperity).
perature at the location of the read element increases linearly with increasing circumferential disk velocity. This suggests that asperities located at the outer diameter on the disk are likely to cause larger thermal damage compared to those located at the internal diameter. The above statement applies also to disk drives with higher rotational spindle compared to drives with lower rotational speed, assuming the asperity is located at the same diameter. The scratch depth and scratch width in the read–write shields for NiP asperity are shown in Fig. 14(a) and (b), respectively. Fig. 14(c) shows a comparison of the volume of the plastic zone for NiP and Al2O3 asperities. A friction coefficient of m ¼0.2, a circumferential disk velocity of Vx ¼20 m/s and a diameter of d¼300 nm were assumed for this case. Comparing Figs. 14(a) and (b) with Figs. 6(a) and (b), respectively, we observe that the values of the scratch depth and the scratch width are larger for the Al2O3 asperity than for the NiP asperity. This indicates that Al2O3
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W. Song et al. / Tribology International 55 (2012) 100–107
350
Read shields
Scratch Width, W (nm)
Scratch Depth, D (nm)
4
Write shields
3
Asperity: NiP 2 1
Read shields
300 Write shields Asperity: NiP
250 200 150 100 50 0
0 0
3
6
9
12
15
0
3
6
9
12
15
9
12
15
Plastic Zone Volume in Read Shields, Vp (10-3·µm3)
120 Al2O3 Al2O3
100
NiP
80 60 40 20 0 0
3
6
Fig. 14. Scratch dimensions in read and write shields versus interference: (a) scratch depth for NiP asperity, (b) scratch width for NiP asperity and (c) volume of plastic zone in the read shields for NiP and Al2O3 asperities (Vx ¼ 20 m/s, m ¼0.2 and d ¼300 nm).
Maximum Temperature at Reader Location, Tmax (K)
400 Al Al2O3 2O3 380 NiP 360 340 320 300 0
3
6
9
12
15
Fig. 15. Maximum temperature at the location of the read element as a function of interference (Vx ¼20 m/s, m ¼ 0.2 and d ¼300 nm).
asperities can cause deeper and wider scratches in the read and write shields than NiP asperities keeping other conditions the same. From Fig. 14(c), we can observe that the volume of the plastic zone is larger for the case of an Al2O3 asperity than for the case of a NiP asperity. This is because higher contact pressure, and, therefore, larger residual plastic deformation occurs in the case of the harder and stiffer Al2O3 asperity. In addition, it is important to note that plastic deformation may still occur inside the read and the write shields even though the residual deformation at the surface is close to zero. This is consistent with numerical results showing that the location where the first plastic deformation occurs is in the interior of the body, i.e., below the contact surface [20]. As shown in Fig. 15, the maximum temperature at the location of the read element is higher for the case of an Al2O3 asperity,
than for the case of a NiP asperity. This is due to the fact that the larger contact pressure induced by the harder Al2O3 asperity causes an increase in frictional heating. In addition, the Al2O3 asperities do not conduct thermal flux as efficiently as NiP asperities, mainly due to difference in their thermal conductivities (see Table 1). From Fig. 15, we can also observe that the maximum temperature at the location of the read element for NiP and alumina asperities becomes similar for d r5 nm and approaches 335 K for d ¼3 nm which equals to the originally assumed value of the temperature. Finally, we investigated the effect of disk velocity on scratch depth and width. Varying the disk velocity in the range of 10 m/ srVx r50 m/s, assuming an Al2O3 asperity with m ¼0.2 and d ¼13 nm, we found that the scratch depth and width in the read and write shields are independent of the disk velocity. This is due to the assumption that the material model used in this study does not consider strain rate effects.
4. Conclusions The effect of contact conditions on scratch dimensions in the read–write shields and the maximum temperature at the location of the read element during contact between a thermal protrusion on a TFC slider and an asperity on a disk were investigated. The effect of diameter and material properties of the asperity was also investigated. The following conclusions can be drawn: (1) The scratch depth and scratch width in the read and write shields is a strong function of the interference between the asperity and the thermal protrusion on the slider. An increase in the interference leads to deeper and wider scratches. However, the effect of the friction coefficient and the circumferential disk velocity on the scratch dimensions is small.
W. Song et al. / Tribology International 55 (2012) 100–107
(2) An increase in the diameter of an asperity leads to shallower and wider scratches in the read and write shields. In addition, hard and stiff asperities cause deeper and wider scratches compared with soft and compliant ones. (3) Large values of interference, large friction coefficients, and high circumferential disk velocities can cause a high temperature at the location of the read element. (4) For large values of interference, high values of the friction coefficient and large circumferential disk velocity used in this study, the temperature at the location of the read element approach the blocking temperature of the read element. For most practical situations, the blocking temperature does not seem to be exceeded, and it is likely that plastic deformation is the dominant failure mechanism causing degradation of the read element.
Acknowledgments We would like to thank Dr. Raj Thangaraj, Dr. John Ji and Dr. Leo Volpe from Western Digital Corporation for helpful discussions with this paper. Wenping Song would like to thank the China Scholarship Council (CSC) and Prof. Guangyu Zhang from Harbin Institute of Technology, for supporting his Ph.D. studies at UCSD.
Appendix A A.1. Thermo-elastic–plastic material model A thermo-elastic–plastic material model was used as described by Hallquist [17] and implemented in previous studies by Song et al. [4] and Ovcharenko et al. [21,22]. Stress is calculated based on both elastic strain and thermal strain. The thermal strain rate is determined by the coefficient of thermal expansion a and temperature T as
e_ Tij ¼ aT_ dij
ð1Þ
At each step in the calculation, the stress is updated elastically and checked whether it exceeds the isotropic yield function
f¼
1 sY ðTÞ2 Sij Sij 2 3
ð2Þ
where Sij is the deviatoric stress tensor. In this study, the yield strength in uniaxial tension sY is assumed to be temperature independent (Table 1). If the stress is less than the elastic limit, no change is made; if the stress exceeds the elastic limit, the stress deviator is scaled back by a factor fs, i.e., Snij þ 1 ¼ f s Snij , where the factor fs is defined as
s
Y f s ¼ qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð3=2ÞSnij Snij
ð3Þ
In this case, the effective plastic strain is updated by the increment qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ð1f s Þ ð3=2ÞSnij Snij p Deef f ¼ ð4Þ G þ 3Ep
107
where G is the shear modulus and Ep is the plastic hardening modulus, the latter assumed to be equal to 2% of Young’s modulus. In our study, the material properties were assumed to be independent of temperature (Table 1).
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