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Deposition of plating metals to improve crack growth life
International Journal of Fatigue 23 (2001) 259–270 www.elsevier.com/locate/ijfatigue
Deposition of plating metals to improve crack growth life P.S. Song b
a,*
, B.C. Sheu b, H.H. Chou
b
a Department of Civil Engineering, Dahan Institute of Technology, Sincheng, Hualien, 971 Taiwan, ROC Department of System Engineering, Chung Cheng Institute of Technology, Dashi, Taoyuan, 335 Taiwan, ROC
Received 8 December 1999; received in revised form 13 July 2000; accepted 31 July 2000
Abstract In this work, cracks in AISI 4130 low-alloy steel specimens were artificially filled with closure materials through plating on the crack faces. Premature crack closure occurred and in doing so, retarded the subsequent crack extension. The closure materials included plating metals such as electroless and electroplated nickel, and electroless copper. This work investigated how the mechanical properties and in-crack distribution of these plating metals affect crack retardation. The extent to which specimen thickness, crack prop-opening load and sucker site affect crack retardation was also studied. Experimental results indicate that the strength of the plating metal and the deposit thickness T2 affect the post-plate crack propagation the most, while deposit volume is the next most influential factor. In the case of satisfactory crack face plating, crack growth rate decreased substantially and even caused crack arrest. Finally, the elastic-wedge model can accurately predict crack development after the infiltration of electroless nickel plating. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Crack retardation; Artificial closure; Electroless nickel; Elastic-wedge model
1. Introduction Elber’s discovery of plasticity-induced crack closure ushered in numerous closure studies [1]. These studies have established various closure mechanisms, including (i) oxide debris or other corrosion products wedged between crack surfaces [2], (ii) microscopic roughness of the fatigue fracture surfaces [3], (iii) viscous fluids penetrated inside the crack [4], and (iv) stress or straininduced phase transformations [5]. These mechanisms indicated that crack closure is mostly due to blockage caused by ingress of foreign objects into a crack. This finding raised the possibility that artificially introducing foreign objects into a crack might induce premature crack closure for crack growth retardation, and that this technique could be used to develop crack-arresting methods [6–12]. Kitagawa et al. [6] injected strain-gage adhesive into cracks in aluminum alloy specimens and increased closure levels and reduced crack propagation rate. Meanwhile, related investigations have demon* Corresponding author. Tel.: +886-3-826-3936; fax: +886-3-8263936. E-mail addresses: [email protected] (P.S. Song), [email protected] (H.H. Chou).
strated that, although a needle tip [7] and a shin stock [8] significantly increase the closure level, they only slightly decrease crack growth rate. Recently, aqueous aluminum suspension [9], epoxy resin with various reinforcing powders [10], low-viscosity epoxies [11], electrodeposited nickel, solder and adhesive [12] have been used as artificial closure materials. These closure materials generally extended the crack growth life to various extents. In this work, electroless nickel (EN), electroless copper (EC), and electroplated nickel (EPN) were used as a closure wedge. According to our results, these materials perform better than the conventional epoxy-based infiltrants [9–11] in terms of adhesion and thermal resistance, and in surviving the alternating action of fatigue loads. Additionally, an efficient solution sucking method is used to infiltrate more electrolytes into the narrow crack openings for a thicker and more widespread deposit, favoring crack closure development and retarding the accompanying crack propagation. Furthermore, the relationship between the plating-induced retardation and the strength and topography of the closure wedge is characterized by using optical microscopy (OM), scanning electronic microscopy (SEM) and an Xray fluorescence thickness tester to microscopically
0142-1123/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 1 1 2 3 ( 0 0 ) 0 0 0 8 4 - 0
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identify the topography of deposits. Finally, the rigidwedge model and the elastic-wedge model are adopted to accurately predict the infiltrant-induced crack retardation. A comparison of the predictions with the experimental results is also made.
2. Materials and experimental procedures Compact tension specimens of thickness 3.5 or 8 mm and width 50.8 mm were machined from a round bar of commercial AISI 4130 low-alloy steel. Table 1 lists the mechanical properties of the steel. A 10-ton-capacity servo-hydraulic testing system (MTS 810) was used for fatigue testing with a stress intensity range of ⌬K=26 MPa √m. This range was kept constant through manual load shedding. A load ratio of R=0.1 and a triangular waveform at 20 Hz were employed during the test. Crack length was measured to a resolution of 0.01 mm with a traveling microscope. The fatigue loading was interrupted after a 7-mm pre-crack was grown from the starter notch. A static load was then applied to 0.95 or 1.5 times the maximum stress intensity, Kmax, to open the crack in order to insert a hardened-steel wedge into its mouth. The back-face strain was monitored so as not to overload the specimen beyond the indicated loading level during the insertion. The higher crack prop-opening load of 1.5 Kmax was employed for a wider crack opening. The wider opening promoted more electrolytes into the crack and improved the thickness and distribution of the deposit on the crack surface. The wedged-open specimens were immersed in an electroplating tank to deposit the EN, EC and EPN on the crack surfaces. Fig. 1 schematically depicts the plating system used in this study. Table 2 lists the operating conditions and bath compositions for the above materials. Prior to plating, a sucker was applied to mask the region surrounding the pre-crack on one of the side surfaces of the test specimens. During the masking process, the center of the sucker was pointed towards the midpoint of the pre-crack. The sucker was connected to a vacuum pump that had a base pressure of 10⫺5 torr. The plating operation was stopped when the flow of electrolytes in the recycling cell was almost undetect-
Fig. 1. Schematic illustration of the infiltration of the artificial-wedge by the electroless plating and electroplating methods.
able. After plating, the specimen was dried to prevent oxide closure [15]. The specimen was then refatigued to the previous ⌬K level of the baseline growth rate (苲7.4×10⫺5 mm/cycle). As a control, an overload test was carried out on the infiltrant-free specimen (OL1) which opened at 1.5 Kmax. Closure development was measured with a back-face strain gage. The offset procedure, similar to that employed by Kikukawa et al. [16], was employed to identify the crack opening stress intensity. A higher ratio of signal to noise was achieved by using a low-pass filter when the loading frequency was reduced to 0.05 Hz during the closure measurement. The closure level was quantified in terms of the fraction U. U⫽
Kmax−Kop ⌬Keff ⫽ , Kmax−Kmin ⌬K
(1)
in which Kmax, Kop, and Kmin denote the maximum, opening and minimum stress intensities of the load cycle, respectively. In addition, ⌬Keff and ⌬K are the effective and the nominal stress intensity factor ranges, respectively. 3. Results and discussion 3.1. The baseline fatigue crack growth data The constant-loading amplitude test indicated that the crack growth rate (mm/cycle) and ⌬K (MPa √m) could be related through Paris’ law as follows:
Table 1 Mechanical properties of AISI 4130 low-alloy steel and the electroless plating materials
Tensile strength (MPa) Yield strength (MPa) Elongation (%, in 5 cm) Young’s modulus (GPa) Hardness (Vickers, 25 g) a b
4130 alloy steel
Electroless nickel
Electroless copper
559 415 32 210 262
800–1100a -1a 60a 476
350–370b 205–235b 5b -120
The data referred to the similar plating solution reported by Weil et al. [13]. The data referred to the similar plating solution reported by Vatakhov and Weil [14].
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Table 2 Bath compositions and operating conditions for plating materials Electroless nickel 쐌 nickel from NIKLAD 796 electroless nickel solutiona 쐌 pH=4.8–5 쐌 agitation=air pump
쐌 temperature=(90–95)±2°C
Electroless copper 쐌 OPC-750 electroless copper solutionb 쐌 pH=12.7–13.1
쐌 agitation=air pump
쐌 temperature=50±2°C
쐌 temperature=50±2°C 쐌 anode=S-NICKELd
쐌 boric acid=40 g/l 쐌 wetting agent=0.7 g/l 쐌 current density=1 A/dm2
Electroplating nickel 쐌 nickel from nickel sulfamatec=81 g/l 쐌 pH=3.8–4.2 쐌 agitation=air pump a b c d
Witco Chemical Co. Ltd., USA. Okuno Chemical Industries Co. Ltd. Japan. ATO Chemical Inc., USA. Inco Ltd. NY, USA.
da ⫽5.43⫻10−9(⌬K)2.89. dN
(2)
In view of the closure effect, Eq. (2) was modified according to Elber’s modification to the Paris relation, and the resulting equation is given as: da ⫽3.85⫻10−8(⌬Keff)2.36. dN
(3)
With the available information on the applied ⌬K and Kop, the crack growth rate can be predicted using Eq. (3). Different closure materials may vary the magnitude of crack growth retardation, and the magnitudes can be represented through the parameter of life extension. This parameter is the difference between the number of cycles that a crack takes to reach the 85% level of the pre-plate growth rate over the retardation prevailed distance, and the number of cycles for the normal growth through the preceding distance. 3.2. Retardation after the plating operation at the crack prop-opening load of 0.95 Kmax Fig. 2 illustrates the typical crack length–number of cycles curve for specimens EN5 and EC3 with a thickness of 3.5 mm. In EN5, the life extension reached 438,000 cycles, almost two times that for EC3. The retardation development can be seen in Fig. 3. Before the plating operation, the fatigue crack propagated at a rate of 苲7.4×10⫺5 mm/cycle. However, after the plating the propagation rate fell to 7.1×10⫺6 in EN5 and to 1.9×10⫺5 mm/cycle in EC3. The minimized growth rate then recovered to the baseline level over a crack growth increment of more than 10 mm. Fig. 4 shows the development of crack closure for the two specimens. The
value of U dropped to its minimum immediately after the plating process, and this behavior matched the growth trends as shown in Fig. 3. The minimum U values were 0.16 and 0.48 for EN5 and EC3, respectively. Similar tests were repeated on specimens EN6 and EC4. These specimens followed the retarding behavior trends of EN5 and EC3. Table 3 lists the respective minimum U values and the degrees of life extension. It shows that EN performed better than EC in retarding crack growth. This phenomenon may result from the strength of the infiltrant, as discussed in the next section. Experimental results provide further insight into the effect of plating metals on retarding crack growth in specimens of various thicknesses. The current experiments were also carried out on some 8-mm-thick specimens. Table 3 reveals that life extension was approximately 175,000 cycles for EN10 and 258,000 cycles for EN11. These extension values were lower by a factor of 2 than those for the 3.5-mm-thick specimens. When EC was the plating metal it produced the same result. Thus, a greater specimen thickness implies a weaker retardation effect, with all plating processes being equal. This is probably because crack closure degree was insignificant under conditions of plane-strain [17,18], and the deposits covered the crack faces to a lesser extent. Fig. 5 presents the retardation effect of EPN on crack growth. According to this figure, the resulting retardation trends were qualitatively close to those described above. The minimum fatigue crack growth rate reached 3.3×10⫺5 mm/cycle for specimen EPN2. The minimum U value was 0.59 and the accompanying life extension was 21,000 cycles. Thus in life extension EPN was obviously inferior to EN and even to EC. The inferiority of EPN can be explained by two factors. First, the electroplating process created excessive buildup around the
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Fig. 2. Crack length versus cycle behavior of the specimens filled with electroless nickel (EN5) and electroless copper (EC3) at 0.95 Kmax crack prop-opening load. The arrow shows the position of the crack tip during the plating operation.
Fig. 3. Crack growth rate versus crack length behavior of the specimens filled with electroless nickel (EN5) and electroless copper (EC3) at 0.95 Kmax crack prop-opening load. The arrow shows the position of the crack tip.
edges, thus impeding the flow of electrolytes into the crack [19]. Second, the anode nickel continuously dissolved impurities into the bath and created a barrier inside the crack. The metal deposits on the crack surfaces were therefore imperfect. The closure effect and the retardation magnitude were thus reduced. According to the preceding argument, electroless plating was superior to electroplating in its potential as an appropri-
Fig. 4. Crack closure versus crack length behavior of the specimens filled with electroless nickel (EN5) and electroless copper (EC3) at 0.95 Kmax crack prop-opening load. The arrow shows the position of the crack tip during the plating operation.
ate technique in creating artificial crack closure. The observation of crack closure and the resulting retardation in the current research did not corresponded to the observations of ur-Rehman and Thomanson [12]. In their work, electroplating nickel produced a stronger closure effect than that of electroless nickel. This inconsistency is probably due to the unsatisfactory performance of their infiltration method.
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Table 3 Retardation behavior at 0.95 Kmax crack prop-opening load Infiltration material (specimen thickness)
Specimen no.
Umin
Life extension (cycles)
Electroless nickel (3.5 mm)
EN5 EN6 EN10 EN11 EC3 EC4 EC5 EC6 EPN2 EN3* EN4*
0.16 0.12 0.24 0.25 0.48 0.42 0.51 0.44 0.59 0.14 0.18
438,000 557,000 175,000 258,000 211,000 286,000 106,000 142,000 21,000 1,006,000 819,000
Electroless nickel (8 mm) Electroless copper (3.5 mm) Electroless copper (8 mm) Electroplated nickel (3.5 mm) Electroless nickel (3.5 mm)
*The marked specimens were plated with a sucker positioned at crack tip. The other specimens were plated with a sucker positioned at midpoint of the pre-crack.
Fig. 5. Crack growth rate versus crack length behavior of the specimens filled with electroplating nickel at 1.5 Kmax (EPN1) and 0.95 Kmax (EPN2) crack prop-opening load, and overloaded at 1.5 Kmax (OL1). The arrow shows the position of the crack tip during the plating operation, and overloading application.
3.3. Retardation after the plating operation at the crack prop-opening load of 1.5 Kmax Fig. 6 illustrates the growth trends in the 3.5-mm-thick specimen at the crack prop-opening load of 1.5 Kmax for the cases with and without metal deposits. The life extension was 32,000 cycles without deposits, and increased by factors of 25.7 and 13.9 for specimens EN2 and EC2, respectively. These increases were mainly due to the effects of crack prop-opening load and metaldeposit induced closure. Fig. 7 shows the cracking rate with or without the metal deposits at the crack prop-
Fig. 6. Crack length versus number of cycle behavior of the specimens filled with electroless nickel (EN2), electroless copper (EC2) at 1.5 Kmax crack prop-opening load, and overloaded at 1.5 Kmax (OL1). The arrow shows the position of the crack tip during the plating operation, and overloading application.
opening load of 1.5 Kmax. This figure reveals that the crack subjected to the crack prop-opening load only (specimen OL1) gradually decreased, and the accompanying retardation climaxed at some distance behind the position of the opening load. This phenomenon did not occur with the plated crack. In the plated specimens, metal deposits maximized retardation immediately after the plating operation. Fig. 8 shows the closure developments in specimens EN2, EC2, and OL1. The closure value decreased steeply to 0.13 immediately after plating for EN2, suggesting that EN performed better than EC in crack closure based on the wedge-opening load of 1.5 Kmax. Table 4 details the retardation results
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provides a higher likelihood of metal depositing inside the crack faces. 3.4. Effect of sucker sites on crack growth retardation Varying the sucker sites along the cracked ligament during the plating process influenced the deposit distribution. This work also considered the pre-crack tip to be a sucker site. Thus, the metal deposits approached the pre-crack front to increase the crack closure effect. Table 3 indicates that at the crack prop-opening load of 0.95 Kmax, the relevant life extension was up to 819,000 cycles in specimen EN4* and was greater in specimen EN3*. These magnitudes of life extension are twice those of EN5 and EN6 with the midpoint of the precrack as a sucker site. Table 4 shows that at the crack prop-opening load of 1.5 Kmax, specimen EN1* extended its life for crack arrest which lasted over 3,000,000 cycles; furthermore, the associated value of Umin was as low as 0.08 and stayed unchanged through the period. Fig. 7. Crack growth rate versus crack length behavior of the specimens filled with electroless nickel (EN2), electroless copper (EC2) at 1.5 Kmax crack prop-opening load, and overloaded at 1.5 Kmax (OL1). The arrow shows the position of the crack tip during the plating operation, and overloading application.
Fig. 8. Crack closure versus crack length behavior of the specimens filled with electroless nickel (EN2), electroless copper (EC2) at 1.5 Kmax crack prop-opening load, and overloaded at 1.5 Kmax (OL1). The arrow shows the position of the crack tip during the plating operation, and overloading application.
for all specimens at the crack prop-opening load of 1.5 Kmax. Comparison of Tables 3 and 4 reveals that a wider crack opening could extend the fatigue life with the same plating materials, mainly because a wider crack space
3.5. Effect of the deposit topography on crack growth retardation X-ray fluorescence was used to measure the thickness of the deposits on crack surfaces. The scanning area covered the surface of the pre-crack. Within the scanning area, 150 locations were specified for measuring the thickness of deposits. Fig. 9 presents a schematic representation of the X-ray scanning area. The topography according to X-ray scanning data of deposits for specimens EN2 and EN5 is illustrated in Figs. 10 and 11, respectively. According to these figures, the thickness of the nickel deposits gradually increased with crack length behind the pre-crack tip, and reached a maximum at the starter notch. The deposit thickness was greater along the sucker-free side than along the suck-masked side. The difference in thickness arose from the concentration gradient of nickel ion during deposition. This uneven distribution of nickel deposit inhibited the transmission of stresses between crack surfaces and closure wedge during unloading, and therefore the closure effect decreased slightly. Fig. 12 illustrates the 3-D topography of the deposit in specimen EN1* with the pre-crack tip as a sucker site. The deposit thickness was uniform over the crack face, except for one region in the vicinity of the crack front. In this region, the deposited metal had a thickness of up to 18 µm. Fig. 13 displays the profile of EN deposits within about 0.1 mm of the crack tip on the sucker-free side surface of specimen EN1*. The gap between the crack front and the nickel deposit tip was as narrow as 5 µm, thus indicating that the nickel deposits came very close to the crack tip. The approaching-crack-tip deposits indicated the satisfactory result of the plating operation, and further development of the crack was halted.
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Table 4 Retardation behavior in 3.5-mm-thick specimens at 1.5 Kmax crack prop-opening load Infiltration material
Specimen no.
Umin
Life extension (cycles)
Electroless nickel
EN2 EN1* EC1 EC2 EPN1 OL1
0.13 0.08 0.39 0.45 0.52 0.76
82,300 arrest 640,000 445,000 99,000 32,000
Electroless copper Electroplated nickel Pure 1.5 Kmax overload
*The marked specimen was plated with a sucker positioned at the crack tip. The other specimens were plated with a sucker positioned at the midpoint of the pre-crack.
Fig. 9. Schematic representation of the X-ray scanning area on the deposits inside a crack.
Fig. 10. Topography of electroless nickel deposits on the crack surface in the specimen EN2 after the plating operation at 1.5 Kmax crack prop-opening load.
The topography of the deposited metals provides further understanding of the crack growth retardation. Five parameters describe the deposit topography, as defined in the following: 앫 Maximum thickness of the deposits on the entire precrack face, T1
Fig. 11. Topography of electroless nickel deposit on the crack surface in the specimen EN5 after the plating operation at 0.95 Kmax crack prop-opening load.
Fig. 12. Topography of electroless nickel deposit on the crack surface in the specimen EN1* after the plating operation at 1.5 Kmax crack prop-opening load.
앫 Average thickness of the deposits between the midpoint and the tip of the pre-crack, T2 앫 Average thickness of the deposits from the mid-point of the pre-crack to the starter notch of the test specimen, T3 앫 Average of T2 and T3, namely T4 앫 Volume of the deposits on the whole face of the precrack, V
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Fig. 13. Deposit profile of electroless nickel in the specimen EN1* after the plating operation at 1.5 Kmax crack prop-opening load.
Table 5 displays the data on the five parameters and the life extension for all specimens in the presence of EN and EC. Of the five parameters, V and T2 were most significant in retarding crack growth. Generally, the greater the volume of metal deposited, the greater the life extension. This relationship was reflected between specimens EN3* and EN4*, and between specimens EN5 and EN6, etc. The average thickness, T2, also influenced growth retardation, and had more influence than parameter V in life extension. For example, although specimen EN2 had a V value about 1.5 times that of specimen EN1*, EN1* was superior to EN2 in life extension. The superiority was mainly due to the greater deposit thickness, T2, in EN1*. The thicker neartip deposit further promoted crack closure, which increased the fatigue life of a specimen. This finding correlated with the theoretical inference in [15,20,21]. 3.6. Effect of the mechanical properties of plating metals on crack growth retardation Table 1 lists the mechanical properties of the EN and EC deposits. These properties play a prominent role in
retarding crack growth. For instance, specimens EC were generally twice as high as specimen EN in their values of T2–T4, and V; conversely, specimens EN were two times greater than specimens EC in life extension. This was due to the higher strength of the EN deposit. A stronger deposit has a higher likelihood of surviving the alternation of fatigue loading, thus facilitating a longer specimen life. The strength-related deformation, which occurred in the EN and EC deposits during the fatigue process, is detailed as follows. Fig. 14(a) presents a profile of the copper deposits filling a crack in specimen EC2 at the crack prop-opening load of 1.5 Kmax. The profile suggests that the plating metal was deposited over almost the entire crack faces. Fig. 14(b) illustrates the deformation copper deposit squeezed between the crack faces after the removal of the crack-opening load. The deformation was measured at 10 locations, equally spaced along the cracked ligament between the starter notch and the pre-crack tip. The measurements revealed that removing the crack prop-opening load of 1.5 Kmax could reduce deposit thickness by 8.7–46.7%. As the specimen cycling extended to 430,000 cycles, the deposit thickness reduced by 0–10.6%, mostly by 5% upward [14]. This indicates the dominance of plastic deformation in the closure wedge through the fatigue loading. Consequently, the growth transients following electroless copper plating were not predicted using the rigid- and elastic-wedge models. During the fatigue test for a typical EN specimen, the removal of 1.5 Kmax crack prop-opening load subsequently reduced the deposit thickness by around 5–25%. As the specimen was tested to be 430,000 cycles, the deposit thickness reduced by 0–2%, mostly by less than 1% [13], indicating the dominance of elastic deformation in the electroless nickel wedge through the fatigue loading. These reductions showed that the EN deposit was stronger than the EC.
Table 5 The relationship between the plating conditions, deposit topography characteristics and life extension Infiltration material (specimen thickness)
Specimen no.
Crack prop- T1 (µm) opening load
T2 (µm)
T3 (µm)
T4 (µm)
V (10⫺3 mm3)
Life extension (cycles)
Electroless nickel (3.5 mm)
EN2 EN5 EN6 EN1* EN3* EN4* EN10 EN11 EC1 EC2 EC3 EC4 EC5 EC6
1.5 Kmax 0.95 Kmax 0.95 Kmax 1.5 Kmax 0.95 Kmax 0.95 Kmax 0.95 Kmax 0.95 Kmax 1.5 Kmax 1.5 Kmax 0.95 Kmax 0.95 Kmax 0.95 Kmax 0.95 Kmax
4.2 3.4 3.6 6.9 5.0 4.8 2.4 2.6 9.1 7.6 7.0 6.5 5.8 6.4
8.1 4.1 5.1 3.4 1.2 1.0 3.2 4.2 13.4 12.1 8.3 10.6 9.4 10.8
6.1 3.8 4.4 5.2 3.1 2.9 2.8 3.4 11.3 9.9 7.7 8.6 7.6 8.6
123 69 78 83 45 41 143 166 232 220 170 193 397 468
832,000 438,000 557,000 arrest 1,005,000 819,000 175,000 258,000 640,000 445,000 211,000 286,000 106,000 142,000
Electroless nickel (8 mm) Electroless copper (3.5 mm)
Electroless copper (8 mm)
11.9 10.8 11.0 18.0 10.1 8.9 6.3 7.2 16.2 14.0 10.7 12.0 11.5 12.5
P.S. Song et al. / International Journal of Fatigue 23 (2001) 259–270
Fig. 15.
267
Schematic representation of a rigid-wedge model [15].
Fig. 16. Schematic representation of an elastic-wedge model [21].
Fig. 14. (a) Deposit profile in the specimen EC2 after electroless copper plating at 1.5 Kmax crack prop-opening load. (b) Deformation of the electroless copper deposits after removing the prop-opening load corresponding to (a).
Additionally, the EN has a micro-hardness of 476 HV, or about four times that for the EC. A harder plating metal implies a higher likelihood that the resulting deposit can carry the loads being transmitted across the fracture surfaces. Thus, specimens of EN displayed a greater reduction in ⌬Keff and a stronger retardation effect. 3.7. Predictions of the post-plate growth rate using the wedge models Several researchers have attempted to model crack closure behavior. Suresh and Ritchie [15] proposed a rigid-wedge model using a concept known as oxide debris-induced crack closure, thus quantifying the levels of crack closure. Fig. 15 schematically depicts the rigidwedge model with a semi-infinite rigid wedge formed inside a linear elastic crack. The wedge has a thickness of h1, and the tip of the wedge is located at a distance a1 from the crack tip. The closure stress intensity at the crack tip due to the wedge is given as follows:
Fig. 17. a crack.
Kop⫽
Schematic representation of the real deposits profile inside
冪a
h1E⬘ 4p
2p
(4)
1
where E⬘=E, Young’s modulus of specimen material for plane stress, E⬘=E/(1⫺n2) for plane strain (n=Poisson’s ratio). Additionally, Chen et al. [21] proposed the elasticwedge model, as illustrated in Fig. 16. This model was developed with an elastic wedge inside a finite-width elastic crack. The wedge has width w=w1 and thickness h=h1, and the centerline of the wedge is situated at a distance a1 behind the crack tip. The closure stress intensity transmitted through the crack tip is
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Fig. 18. Comparison of measured and predicted crack growth rates in specimens (a) EN2, (b) EN3*, (c) EN5, and (d) EN10 after electroless nickel plating.
Kop⫽
冢
冪 a ⫹K
1 lh1E⬘ 1+l 8
2p 1
min
冣
(5)
8E1w1 l= where E1 is Young’s modulus of the wedge. ph1E⬘ The E⬘ is the same as that in Eq. (4). Each of the two preceding wedge models was used in conjunction with Eq. (3) to predict the post-plate crack growth. This work used electroless nickel as a model closure material for crack growth predictions. For the
parameters in Eqs. (4) and (5), the EN-related values are determined as follows. First, E was taken at 210 GPa, and n was taken as 0.3. Parameter h1 had a value twice as great as for the observed thickness in the on-precrack-face deposits, because of the similarity in deposit thickness between the upper and lower faces of the precrack. Fig. 17 schematically represents the real deposit profile. The initial value of a1, defined in the rigid-wedge model, was found to be 10 µm according to the observations made using OM and SEM, and this value gradually increased with increasing post-plate crack length. Parameter E1 was taken as 60 GPa in reference to the study of Weil et al. [13], in which the tension specimen was 25-µm thick, similar to that of the thin deposit wedge in this work.
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For a crack containing multiple wedges, the wedge immediately next to the crack tip affects the closure stress intensity the greatest, as indicated in [22,23]. The present work supported this finding. The deposit thickness T2 between the midpoint and the tip of the pre-crack influenced life extension the most. Therefore, the values of such parameters as a1, h1, and w1 in Eqs. (4) and (5) were established in relation to the dimensions of the deposit between the midpoint and tip of the pre-crack. An attempt was made to more accurately reflect the morphology of the deposits on crack closure by dividing the near-crack-tip EN deposits into two parts, with widths of w1 and w1* (Fig. 17). For the elastic-wedge model, w1 and w1* were taken to be 1.74 mm (1.75 mm⫺10 µm) and 1.75 mm, respectively. The length, a1, was the distance from the crack tip to the central line of each part. For the w1 part, a1 carried an initial value of 0.88 mm (0.87 mm+10 µm). Meanwhile, for the w1* part, it carried an initial value of 2.625 mm (0.875 mm+1.75 mm). With respect to the rigid-wedge model, w1 and w1* were taken as having the same values as the elasticwedge model, where the length a1 denoted the distance from the crack tip to the tip of each part. For the w1 part, a1 was initially taken as 10 µm. Meanwhile, for the w1* part, it was initially taken as 1.75 mm. The superposition principle was employed to estimate the contribution of the two deposits to crack closure [22,24]. Fig. 18 compares the predicted and measured crack growth rates in specimens EN2, EN3*, EN5, and EN10. For specimen EN3*, the measured growth rate fell between the predictions of the rigid- and elastic-wedge models. In the other specimens, the rigid-wedge model predicted a higher growth rate than the elastic-wedge model did, indicating that the elastic-wedge model can more accurately predict the post-plate crack growth phenomena.
4. Conclusions 1. The current plating metals differed in terms of their levels of closure performance and magnitude of growth retardation. At the crack prop-opening load of 0.95 Kmax, life extension ranged between 438 and 557 kilocycles in the presence of EN, which was roughly twice as long as that for EC. This difference is because EN is stronger than EC. Meanwhile, EPN has negative properties of edge buildup and an impurityblocking effect. These properties limited the usefulness of EPN as a crack-growth life extender. Accordingly, although using this plating metal also resulted in life extension, the degree of extension was less than for other electroless plating metals. 2. The magnitude of crack prop-opening load and the site of the sucker are essential in the post-plate growth retardation. The higher crack prop-opening load of 1.5
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Kmax made a wider crack opening possible and this allowed more metal to be deposited over the pre-crack faces. The pre-crack tip, as a sucker site, minimized the gap between the deposited metals and the precrack front. The greater amount of deposited metal together with the smaller gap maximized the resulting crack closure, and the subsequent crack growth was retarded or even halted. 3. The effect of metal plating on crack growth can be understood through the deposit topography. Of the five topography parameters, deposit thickness (T2) dominated the post-plate crack retardation, whereas deposit volume (V) exerted comparatively less effect on growth retardation. 4. In the case of EC, elastic- and rigid-wedge models were not employed because the fatigue loading caused plastic deformation in most of the deposits. In the case of EN, the deposit largely performed as an elastic wedge between the surfaces of the fatigue crack. Moreover, the elastic-wedge model predicted the post-plate crack growth rate more accurately than the rigid-wedge model did.
Acknowledgements The authors thank the National Science Council of the Republic of China for financially supporting this research under Contract No. NSC-86-2212-E-014-003.
References [1] Elber W. The significance of fatigue crack closure. Damage tolerance in aircraft structures, ASTM STP 486. Philadelphia: American Society for Testing and Materials, 1971:230–42. [2] Suresh S, Zamiski GF, Ritchie RO. Oxide-induced crack closure: an explanation for near threshold corrosion fatigue crack growth behavior. Metall Trans 1981;12A:1435–43. [3] Haliday MD, Beevers CJ. Non-closure of crack and fatigue crack growth in β-heat treated Ti-6Al-4V. Int J Fract 1979;15(1):R27–30. [4] Endo K, Okada T, Komai K, Kiyota M. Fatigue crack propagation of steel in oil. Bull JSME 1972;15:1316–23. [5] Hornbogen E. Martensitic transformation at a propagating crack. Acta Metall 1978;26:147–52. [6] Kitagawa H, Toyohira S, Ikeda K. A new method of arresting fatigue crack growth by artificial wedge. In: Proc. Int. Conf. on Fract. Mech. in Eng. Applns, National Aeronautical Laboratory (Bangalore, India): Sijthoff and Noordhoff, 1979:281–92. [7] Vecchio RS, Crompton JS, Hertzberg RW. Anomalous aspects of crack closure. Int J Fract 1986;31:R29–33. [8] Hertzberg RW, Newton CH, Jaccard R. Crack closure: correlation and confusion. Mechanics of Fatigue Crack Closure, ASTM STP 982. Philadelphia: American Society for Testing and Materials, 1988:139–48. [9] Shin CS, Hsu SH. Fatigue life extension by an artificially induced retardation mechanism. Eng Fract Mech 1992;43(4):677–84. [10] Sheu BC, Song PS, Shin CS. The effect of infiltration induced
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crack closure on crack growth retardation. Scripta Metall 1994;31(10):1301–6. Sharp PK, Clayton JQ, Clark G. Retardation and repair of fatigue cracks by adhesive infiltration. Fatigue Fract Eng Mater Struct 1997;20(4):605–14. UR-Rehman A, Thomason PF. The effect of artificial fatiguecrack closure on fatigue-crack growth. Fatigue Fract Eng Mater Struct 1993;16(10):1081–90. Weil R, Lee JH, Kim I, Parker K. Comparison of some mechanical and corrosion properties of electroless and electroplated nickel–phosphorus alloys. Plating Surface Finishing 1989;February:62–6. Vatakhov P, Weil R. The effects of substrate attachment on the mechanical properties of electrodeposits. Plating Surface Finishing 1990;March:58–61. Suresh S, Ritchie RO. Some considerations on the modeling of oxide-induced fatigue crack closure using solutions for a rigid wedge inside a linear elastic crack. Scripta Metall 1983;17:575–80. Kitukawa M, Jono M, Tanaka K. Fatigue crack closure behaviour at low stress intensity level. In: Proc. Second Int. Conf. on Mech-
anical Behavior of Materials, Boston, 1976:254–77. [17] Shuter DM, Geary W. The influence of specimen thickness on fatigue growth retardation following an overload. Int J Fatigue 1995;17(2):111–9. [18] Flect NA, Smith RA. Crack closure—is it just a surface phenomenon? Int J Fatigue 1982;4:157–60. [19] Lowenheim FA. Electroplating. McGraw-Hill, 1978, pp. 147– 155. [20] Beevers CJ, Bell K, Carlson RL, Starke EA. A model for fatigue crack closure. Eng Fract Mech 1984;19(1):93–100. [21] Chen DL, Weiss B, Stickler R. A model for crack closure. Eng Fract Mech 1996;53(4):493–509. [22] Riemelmoser FO, Pippan R. Crack closure: a concept of fatigue crack growth under examination. Fatigue Fract Eng Mater Struct 1997;20(11):1529–40. [23] Nakamura H, Kobayashi H. Analysis of fatigue crack closure caused by asperities using the modified Dugdale model, ASTM STP 982. Philadelphia: American Society for Testing and Materials, 1988:459–74. [24] Carlson RL, Beevers CJ. A multiple asperity fatigue crack closure model. Eng Fract Mech 1984;20(4):687–90.
Deposition of plating metals to improve crack growth life P.S. Song b
a,*
, B.C. Sheu b, H.H. Chou
b
a Department of Civil Engineering, Dahan Institute of Technology, Sincheng, Hualien, 971 Taiwan, ROC Department of System Engineering, Chung Cheng Institute of Technology, Dashi, Taoyuan, 335 Taiwan, ROC
Received 8 December 1999; received in revised form 13 July 2000; accepted 31 July 2000
Abstract In this work, cracks in AISI 4130 low-alloy steel specimens were artificially filled with closure materials through plating on the crack faces. Premature crack closure occurred and in doing so, retarded the subsequent crack extension. The closure materials included plating metals such as electroless and electroplated nickel, and electroless copper. This work investigated how the mechanical properties and in-crack distribution of these plating metals affect crack retardation. The extent to which specimen thickness, crack prop-opening load and sucker site affect crack retardation was also studied. Experimental results indicate that the strength of the plating metal and the deposit thickness T2 affect the post-plate crack propagation the most, while deposit volume is the next most influential factor. In the case of satisfactory crack face plating, crack growth rate decreased substantially and even caused crack arrest. Finally, the elastic-wedge model can accurately predict crack development after the infiltration of electroless nickel plating. 2001 Elsevier Science Ltd. All rights reserved. Keywords: Crack retardation; Artificial closure; Electroless nickel; Elastic-wedge model
1. Introduction Elber’s discovery of plasticity-induced crack closure ushered in numerous closure studies [1]. These studies have established various closure mechanisms, including (i) oxide debris or other corrosion products wedged between crack surfaces [2], (ii) microscopic roughness of the fatigue fracture surfaces [3], (iii) viscous fluids penetrated inside the crack [4], and (iv) stress or straininduced phase transformations [5]. These mechanisms indicated that crack closure is mostly due to blockage caused by ingress of foreign objects into a crack. This finding raised the possibility that artificially introducing foreign objects into a crack might induce premature crack closure for crack growth retardation, and that this technique could be used to develop crack-arresting methods [6–12]. Kitagawa et al. [6] injected strain-gage adhesive into cracks in aluminum alloy specimens and increased closure levels and reduced crack propagation rate. Meanwhile, related investigations have demon* Corresponding author. Tel.: +886-3-826-3936; fax: +886-3-8263936. E-mail addresses: [email protected] (P.S. Song), [email protected] (H.H. Chou).
strated that, although a needle tip [7] and a shin stock [8] significantly increase the closure level, they only slightly decrease crack growth rate. Recently, aqueous aluminum suspension [9], epoxy resin with various reinforcing powders [10], low-viscosity epoxies [11], electrodeposited nickel, solder and adhesive [12] have been used as artificial closure materials. These closure materials generally extended the crack growth life to various extents. In this work, electroless nickel (EN), electroless copper (EC), and electroplated nickel (EPN) were used as a closure wedge. According to our results, these materials perform better than the conventional epoxy-based infiltrants [9–11] in terms of adhesion and thermal resistance, and in surviving the alternating action of fatigue loads. Additionally, an efficient solution sucking method is used to infiltrate more electrolytes into the narrow crack openings for a thicker and more widespread deposit, favoring crack closure development and retarding the accompanying crack propagation. Furthermore, the relationship between the plating-induced retardation and the strength and topography of the closure wedge is characterized by using optical microscopy (OM), scanning electronic microscopy (SEM) and an Xray fluorescence thickness tester to microscopically
0142-1123/01/$ - see front matter 2001 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 2 - 1 1 2 3 ( 0 0 ) 0 0 0 8 4 - 0
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identify the topography of deposits. Finally, the rigidwedge model and the elastic-wedge model are adopted to accurately predict the infiltrant-induced crack retardation. A comparison of the predictions with the experimental results is also made.
2. Materials and experimental procedures Compact tension specimens of thickness 3.5 or 8 mm and width 50.8 mm were machined from a round bar of commercial AISI 4130 low-alloy steel. Table 1 lists the mechanical properties of the steel. A 10-ton-capacity servo-hydraulic testing system (MTS 810) was used for fatigue testing with a stress intensity range of ⌬K=26 MPa √m. This range was kept constant through manual load shedding. A load ratio of R=0.1 and a triangular waveform at 20 Hz were employed during the test. Crack length was measured to a resolution of 0.01 mm with a traveling microscope. The fatigue loading was interrupted after a 7-mm pre-crack was grown from the starter notch. A static load was then applied to 0.95 or 1.5 times the maximum stress intensity, Kmax, to open the crack in order to insert a hardened-steel wedge into its mouth. The back-face strain was monitored so as not to overload the specimen beyond the indicated loading level during the insertion. The higher crack prop-opening load of 1.5 Kmax was employed for a wider crack opening. The wider opening promoted more electrolytes into the crack and improved the thickness and distribution of the deposit on the crack surface. The wedged-open specimens were immersed in an electroplating tank to deposit the EN, EC and EPN on the crack surfaces. Fig. 1 schematically depicts the plating system used in this study. Table 2 lists the operating conditions and bath compositions for the above materials. Prior to plating, a sucker was applied to mask the region surrounding the pre-crack on one of the side surfaces of the test specimens. During the masking process, the center of the sucker was pointed towards the midpoint of the pre-crack. The sucker was connected to a vacuum pump that had a base pressure of 10⫺5 torr. The plating operation was stopped when the flow of electrolytes in the recycling cell was almost undetect-
Fig. 1. Schematic illustration of the infiltration of the artificial-wedge by the electroless plating and electroplating methods.
able. After plating, the specimen was dried to prevent oxide closure [15]. The specimen was then refatigued to the previous ⌬K level of the baseline growth rate (苲7.4×10⫺5 mm/cycle). As a control, an overload test was carried out on the infiltrant-free specimen (OL1) which opened at 1.5 Kmax. Closure development was measured with a back-face strain gage. The offset procedure, similar to that employed by Kikukawa et al. [16], was employed to identify the crack opening stress intensity. A higher ratio of signal to noise was achieved by using a low-pass filter when the loading frequency was reduced to 0.05 Hz during the closure measurement. The closure level was quantified in terms of the fraction U. U⫽
Kmax−Kop ⌬Keff ⫽ , Kmax−Kmin ⌬K
(1)
in which Kmax, Kop, and Kmin denote the maximum, opening and minimum stress intensities of the load cycle, respectively. In addition, ⌬Keff and ⌬K are the effective and the nominal stress intensity factor ranges, respectively. 3. Results and discussion 3.1. The baseline fatigue crack growth data The constant-loading amplitude test indicated that the crack growth rate (mm/cycle) and ⌬K (MPa √m) could be related through Paris’ law as follows:
Table 1 Mechanical properties of AISI 4130 low-alloy steel and the electroless plating materials
Tensile strength (MPa) Yield strength (MPa) Elongation (%, in 5 cm) Young’s modulus (GPa) Hardness (Vickers, 25 g) a b
4130 alloy steel
Electroless nickel
Electroless copper
559 415 32 210 262
800–1100a -1a 60a 476
350–370b 205–235b 5b -120
The data referred to the similar plating solution reported by Weil et al. [13]. The data referred to the similar plating solution reported by Vatakhov and Weil [14].
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261
Table 2 Bath compositions and operating conditions for plating materials Electroless nickel 쐌 nickel from NIKLAD 796 electroless nickel solutiona 쐌 pH=4.8–5 쐌 agitation=air pump
쐌 temperature=(90–95)±2°C
Electroless copper 쐌 OPC-750 electroless copper solutionb 쐌 pH=12.7–13.1
쐌 agitation=air pump
쐌 temperature=50±2°C
쐌 temperature=50±2°C 쐌 anode=S-NICKELd
쐌 boric acid=40 g/l 쐌 wetting agent=0.7 g/l 쐌 current density=1 A/dm2
Electroplating nickel 쐌 nickel from nickel sulfamatec=81 g/l 쐌 pH=3.8–4.2 쐌 agitation=air pump a b c d
Witco Chemical Co. Ltd., USA. Okuno Chemical Industries Co. Ltd. Japan. ATO Chemical Inc., USA. Inco Ltd. NY, USA.
da ⫽5.43⫻10−9(⌬K)2.89. dN
(2)
In view of the closure effect, Eq. (2) was modified according to Elber’s modification to the Paris relation, and the resulting equation is given as: da ⫽3.85⫻10−8(⌬Keff)2.36. dN
(3)
With the available information on the applied ⌬K and Kop, the crack growth rate can be predicted using Eq. (3). Different closure materials may vary the magnitude of crack growth retardation, and the magnitudes can be represented through the parameter of life extension. This parameter is the difference between the number of cycles that a crack takes to reach the 85% level of the pre-plate growth rate over the retardation prevailed distance, and the number of cycles for the normal growth through the preceding distance. 3.2. Retardation after the plating operation at the crack prop-opening load of 0.95 Kmax Fig. 2 illustrates the typical crack length–number of cycles curve for specimens EN5 and EC3 with a thickness of 3.5 mm. In EN5, the life extension reached 438,000 cycles, almost two times that for EC3. The retardation development can be seen in Fig. 3. Before the plating operation, the fatigue crack propagated at a rate of 苲7.4×10⫺5 mm/cycle. However, after the plating the propagation rate fell to 7.1×10⫺6 in EN5 and to 1.9×10⫺5 mm/cycle in EC3. The minimized growth rate then recovered to the baseline level over a crack growth increment of more than 10 mm. Fig. 4 shows the development of crack closure for the two specimens. The
value of U dropped to its minimum immediately after the plating process, and this behavior matched the growth trends as shown in Fig. 3. The minimum U values were 0.16 and 0.48 for EN5 and EC3, respectively. Similar tests were repeated on specimens EN6 and EC4. These specimens followed the retarding behavior trends of EN5 and EC3. Table 3 lists the respective minimum U values and the degrees of life extension. It shows that EN performed better than EC in retarding crack growth. This phenomenon may result from the strength of the infiltrant, as discussed in the next section. Experimental results provide further insight into the effect of plating metals on retarding crack growth in specimens of various thicknesses. The current experiments were also carried out on some 8-mm-thick specimens. Table 3 reveals that life extension was approximately 175,000 cycles for EN10 and 258,000 cycles for EN11. These extension values were lower by a factor of 2 than those for the 3.5-mm-thick specimens. When EC was the plating metal it produced the same result. Thus, a greater specimen thickness implies a weaker retardation effect, with all plating processes being equal. This is probably because crack closure degree was insignificant under conditions of plane-strain [17,18], and the deposits covered the crack faces to a lesser extent. Fig. 5 presents the retardation effect of EPN on crack growth. According to this figure, the resulting retardation trends were qualitatively close to those described above. The minimum fatigue crack growth rate reached 3.3×10⫺5 mm/cycle for specimen EPN2. The minimum U value was 0.59 and the accompanying life extension was 21,000 cycles. Thus in life extension EPN was obviously inferior to EN and even to EC. The inferiority of EPN can be explained by two factors. First, the electroplating process created excessive buildup around the
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Fig. 2. Crack length versus cycle behavior of the specimens filled with electroless nickel (EN5) and electroless copper (EC3) at 0.95 Kmax crack prop-opening load. The arrow shows the position of the crack tip during the plating operation.
Fig. 3. Crack growth rate versus crack length behavior of the specimens filled with electroless nickel (EN5) and electroless copper (EC3) at 0.95 Kmax crack prop-opening load. The arrow shows the position of the crack tip.
edges, thus impeding the flow of electrolytes into the crack [19]. Second, the anode nickel continuously dissolved impurities into the bath and created a barrier inside the crack. The metal deposits on the crack surfaces were therefore imperfect. The closure effect and the retardation magnitude were thus reduced. According to the preceding argument, electroless plating was superior to electroplating in its potential as an appropri-
Fig. 4. Crack closure versus crack length behavior of the specimens filled with electroless nickel (EN5) and electroless copper (EC3) at 0.95 Kmax crack prop-opening load. The arrow shows the position of the crack tip during the plating operation.
ate technique in creating artificial crack closure. The observation of crack closure and the resulting retardation in the current research did not corresponded to the observations of ur-Rehman and Thomanson [12]. In their work, electroplating nickel produced a stronger closure effect than that of electroless nickel. This inconsistency is probably due to the unsatisfactory performance of their infiltration method.
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263
Table 3 Retardation behavior at 0.95 Kmax crack prop-opening load Infiltration material (specimen thickness)
Specimen no.
Umin
Life extension (cycles)
Electroless nickel (3.5 mm)
EN5 EN6 EN10 EN11 EC3 EC4 EC5 EC6 EPN2 EN3* EN4*
0.16 0.12 0.24 0.25 0.48 0.42 0.51 0.44 0.59 0.14 0.18
438,000 557,000 175,000 258,000 211,000 286,000 106,000 142,000 21,000 1,006,000 819,000
Electroless nickel (8 mm) Electroless copper (3.5 mm) Electroless copper (8 mm) Electroplated nickel (3.5 mm) Electroless nickel (3.5 mm)
*The marked specimens were plated with a sucker positioned at crack tip. The other specimens were plated with a sucker positioned at midpoint of the pre-crack.
Fig. 5. Crack growth rate versus crack length behavior of the specimens filled with electroplating nickel at 1.5 Kmax (EPN1) and 0.95 Kmax (EPN2) crack prop-opening load, and overloaded at 1.5 Kmax (OL1). The arrow shows the position of the crack tip during the plating operation, and overloading application.
3.3. Retardation after the plating operation at the crack prop-opening load of 1.5 Kmax Fig. 6 illustrates the growth trends in the 3.5-mm-thick specimen at the crack prop-opening load of 1.5 Kmax for the cases with and without metal deposits. The life extension was 32,000 cycles without deposits, and increased by factors of 25.7 and 13.9 for specimens EN2 and EC2, respectively. These increases were mainly due to the effects of crack prop-opening load and metaldeposit induced closure. Fig. 7 shows the cracking rate with or without the metal deposits at the crack prop-
Fig. 6. Crack length versus number of cycle behavior of the specimens filled with electroless nickel (EN2), electroless copper (EC2) at 1.5 Kmax crack prop-opening load, and overloaded at 1.5 Kmax (OL1). The arrow shows the position of the crack tip during the plating operation, and overloading application.
opening load of 1.5 Kmax. This figure reveals that the crack subjected to the crack prop-opening load only (specimen OL1) gradually decreased, and the accompanying retardation climaxed at some distance behind the position of the opening load. This phenomenon did not occur with the plated crack. In the plated specimens, metal deposits maximized retardation immediately after the plating operation. Fig. 8 shows the closure developments in specimens EN2, EC2, and OL1. The closure value decreased steeply to 0.13 immediately after plating for EN2, suggesting that EN performed better than EC in crack closure based on the wedge-opening load of 1.5 Kmax. Table 4 details the retardation results
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provides a higher likelihood of metal depositing inside the crack faces. 3.4. Effect of sucker sites on crack growth retardation Varying the sucker sites along the cracked ligament during the plating process influenced the deposit distribution. This work also considered the pre-crack tip to be a sucker site. Thus, the metal deposits approached the pre-crack front to increase the crack closure effect. Table 3 indicates that at the crack prop-opening load of 0.95 Kmax, the relevant life extension was up to 819,000 cycles in specimen EN4* and was greater in specimen EN3*. These magnitudes of life extension are twice those of EN5 and EN6 with the midpoint of the precrack as a sucker site. Table 4 shows that at the crack prop-opening load of 1.5 Kmax, specimen EN1* extended its life for crack arrest which lasted over 3,000,000 cycles; furthermore, the associated value of Umin was as low as 0.08 and stayed unchanged through the period. Fig. 7. Crack growth rate versus crack length behavior of the specimens filled with electroless nickel (EN2), electroless copper (EC2) at 1.5 Kmax crack prop-opening load, and overloaded at 1.5 Kmax (OL1). The arrow shows the position of the crack tip during the plating operation, and overloading application.
Fig. 8. Crack closure versus crack length behavior of the specimens filled with electroless nickel (EN2), electroless copper (EC2) at 1.5 Kmax crack prop-opening load, and overloaded at 1.5 Kmax (OL1). The arrow shows the position of the crack tip during the plating operation, and overloading application.
for all specimens at the crack prop-opening load of 1.5 Kmax. Comparison of Tables 3 and 4 reveals that a wider crack opening could extend the fatigue life with the same plating materials, mainly because a wider crack space
3.5. Effect of the deposit topography on crack growth retardation X-ray fluorescence was used to measure the thickness of the deposits on crack surfaces. The scanning area covered the surface of the pre-crack. Within the scanning area, 150 locations were specified for measuring the thickness of deposits. Fig. 9 presents a schematic representation of the X-ray scanning area. The topography according to X-ray scanning data of deposits for specimens EN2 and EN5 is illustrated in Figs. 10 and 11, respectively. According to these figures, the thickness of the nickel deposits gradually increased with crack length behind the pre-crack tip, and reached a maximum at the starter notch. The deposit thickness was greater along the sucker-free side than along the suck-masked side. The difference in thickness arose from the concentration gradient of nickel ion during deposition. This uneven distribution of nickel deposit inhibited the transmission of stresses between crack surfaces and closure wedge during unloading, and therefore the closure effect decreased slightly. Fig. 12 illustrates the 3-D topography of the deposit in specimen EN1* with the pre-crack tip as a sucker site. The deposit thickness was uniform over the crack face, except for one region in the vicinity of the crack front. In this region, the deposited metal had a thickness of up to 18 µm. Fig. 13 displays the profile of EN deposits within about 0.1 mm of the crack tip on the sucker-free side surface of specimen EN1*. The gap between the crack front and the nickel deposit tip was as narrow as 5 µm, thus indicating that the nickel deposits came very close to the crack tip. The approaching-crack-tip deposits indicated the satisfactory result of the plating operation, and further development of the crack was halted.
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265
Table 4 Retardation behavior in 3.5-mm-thick specimens at 1.5 Kmax crack prop-opening load Infiltration material
Specimen no.
Umin
Life extension (cycles)
Electroless nickel
EN2 EN1* EC1 EC2 EPN1 OL1
0.13 0.08 0.39 0.45 0.52 0.76
82,300 arrest 640,000 445,000 99,000 32,000
Electroless copper Electroplated nickel Pure 1.5 Kmax overload
*The marked specimen was plated with a sucker positioned at the crack tip. The other specimens were plated with a sucker positioned at the midpoint of the pre-crack.
Fig. 9. Schematic representation of the X-ray scanning area on the deposits inside a crack.
Fig. 10. Topography of electroless nickel deposits on the crack surface in the specimen EN2 after the plating operation at 1.5 Kmax crack prop-opening load.
The topography of the deposited metals provides further understanding of the crack growth retardation. Five parameters describe the deposit topography, as defined in the following: 앫 Maximum thickness of the deposits on the entire precrack face, T1
Fig. 11. Topography of electroless nickel deposit on the crack surface in the specimen EN5 after the plating operation at 0.95 Kmax crack prop-opening load.
Fig. 12. Topography of electroless nickel deposit on the crack surface in the specimen EN1* after the plating operation at 1.5 Kmax crack prop-opening load.
앫 Average thickness of the deposits between the midpoint and the tip of the pre-crack, T2 앫 Average thickness of the deposits from the mid-point of the pre-crack to the starter notch of the test specimen, T3 앫 Average of T2 and T3, namely T4 앫 Volume of the deposits on the whole face of the precrack, V
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Fig. 13. Deposit profile of electroless nickel in the specimen EN1* after the plating operation at 1.5 Kmax crack prop-opening load.
Table 5 displays the data on the five parameters and the life extension for all specimens in the presence of EN and EC. Of the five parameters, V and T2 were most significant in retarding crack growth. Generally, the greater the volume of metal deposited, the greater the life extension. This relationship was reflected between specimens EN3* and EN4*, and between specimens EN5 and EN6, etc. The average thickness, T2, also influenced growth retardation, and had more influence than parameter V in life extension. For example, although specimen EN2 had a V value about 1.5 times that of specimen EN1*, EN1* was superior to EN2 in life extension. The superiority was mainly due to the greater deposit thickness, T2, in EN1*. The thicker neartip deposit further promoted crack closure, which increased the fatigue life of a specimen. This finding correlated with the theoretical inference in [15,20,21]. 3.6. Effect of the mechanical properties of plating metals on crack growth retardation Table 1 lists the mechanical properties of the EN and EC deposits. These properties play a prominent role in
retarding crack growth. For instance, specimens EC were generally twice as high as specimen EN in their values of T2–T4, and V; conversely, specimens EN were two times greater than specimens EC in life extension. This was due to the higher strength of the EN deposit. A stronger deposit has a higher likelihood of surviving the alternation of fatigue loading, thus facilitating a longer specimen life. The strength-related deformation, which occurred in the EN and EC deposits during the fatigue process, is detailed as follows. Fig. 14(a) presents a profile of the copper deposits filling a crack in specimen EC2 at the crack prop-opening load of 1.5 Kmax. The profile suggests that the plating metal was deposited over almost the entire crack faces. Fig. 14(b) illustrates the deformation copper deposit squeezed between the crack faces after the removal of the crack-opening load. The deformation was measured at 10 locations, equally spaced along the cracked ligament between the starter notch and the pre-crack tip. The measurements revealed that removing the crack prop-opening load of 1.5 Kmax could reduce deposit thickness by 8.7–46.7%. As the specimen cycling extended to 430,000 cycles, the deposit thickness reduced by 0–10.6%, mostly by 5% upward [14]. This indicates the dominance of plastic deformation in the closure wedge through the fatigue loading. Consequently, the growth transients following electroless copper plating were not predicted using the rigid- and elastic-wedge models. During the fatigue test for a typical EN specimen, the removal of 1.5 Kmax crack prop-opening load subsequently reduced the deposit thickness by around 5–25%. As the specimen was tested to be 430,000 cycles, the deposit thickness reduced by 0–2%, mostly by less than 1% [13], indicating the dominance of elastic deformation in the electroless nickel wedge through the fatigue loading. These reductions showed that the EN deposit was stronger than the EC.
Table 5 The relationship between the plating conditions, deposit topography characteristics and life extension Infiltration material (specimen thickness)
Specimen no.
Crack prop- T1 (µm) opening load
T2 (µm)
T3 (µm)
T4 (µm)
V (10⫺3 mm3)
Life extension (cycles)
Electroless nickel (3.5 mm)
EN2 EN5 EN6 EN1* EN3* EN4* EN10 EN11 EC1 EC2 EC3 EC4 EC5 EC6
1.5 Kmax 0.95 Kmax 0.95 Kmax 1.5 Kmax 0.95 Kmax 0.95 Kmax 0.95 Kmax 0.95 Kmax 1.5 Kmax 1.5 Kmax 0.95 Kmax 0.95 Kmax 0.95 Kmax 0.95 Kmax
4.2 3.4 3.6 6.9 5.0 4.8 2.4 2.6 9.1 7.6 7.0 6.5 5.8 6.4
8.1 4.1 5.1 3.4 1.2 1.0 3.2 4.2 13.4 12.1 8.3 10.6 9.4 10.8
6.1 3.8 4.4 5.2 3.1 2.9 2.8 3.4 11.3 9.9 7.7 8.6 7.6 8.6
123 69 78 83 45 41 143 166 232 220 170 193 397 468
832,000 438,000 557,000 arrest 1,005,000 819,000 175,000 258,000 640,000 445,000 211,000 286,000 106,000 142,000
Electroless nickel (8 mm) Electroless copper (3.5 mm)
Electroless copper (8 mm)
11.9 10.8 11.0 18.0 10.1 8.9 6.3 7.2 16.2 14.0 10.7 12.0 11.5 12.5
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Fig. 15.
267
Schematic representation of a rigid-wedge model [15].
Fig. 16. Schematic representation of an elastic-wedge model [21].
Fig. 14. (a) Deposit profile in the specimen EC2 after electroless copper plating at 1.5 Kmax crack prop-opening load. (b) Deformation of the electroless copper deposits after removing the prop-opening load corresponding to (a).
Additionally, the EN has a micro-hardness of 476 HV, or about four times that for the EC. A harder plating metal implies a higher likelihood that the resulting deposit can carry the loads being transmitted across the fracture surfaces. Thus, specimens of EN displayed a greater reduction in ⌬Keff and a stronger retardation effect. 3.7. Predictions of the post-plate growth rate using the wedge models Several researchers have attempted to model crack closure behavior. Suresh and Ritchie [15] proposed a rigid-wedge model using a concept known as oxide debris-induced crack closure, thus quantifying the levels of crack closure. Fig. 15 schematically depicts the rigidwedge model with a semi-infinite rigid wedge formed inside a linear elastic crack. The wedge has a thickness of h1, and the tip of the wedge is located at a distance a1 from the crack tip. The closure stress intensity at the crack tip due to the wedge is given as follows:
Fig. 17. a crack.
Kop⫽
Schematic representation of the real deposits profile inside
冪a
h1E⬘ 4p
2p
(4)
1
where E⬘=E, Young’s modulus of specimen material for plane stress, E⬘=E/(1⫺n2) for plane strain (n=Poisson’s ratio). Additionally, Chen et al. [21] proposed the elasticwedge model, as illustrated in Fig. 16. This model was developed with an elastic wedge inside a finite-width elastic crack. The wedge has width w=w1 and thickness h=h1, and the centerline of the wedge is situated at a distance a1 behind the crack tip. The closure stress intensity transmitted through the crack tip is
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Fig. 18. Comparison of measured and predicted crack growth rates in specimens (a) EN2, (b) EN3*, (c) EN5, and (d) EN10 after electroless nickel plating.
Kop⫽
冢
冪 a ⫹K
1 lh1E⬘ 1+l 8
2p 1
min
冣
(5)
8E1w1 l= where E1 is Young’s modulus of the wedge. ph1E⬘ The E⬘ is the same as that in Eq. (4). Each of the two preceding wedge models was used in conjunction with Eq. (3) to predict the post-plate crack growth. This work used electroless nickel as a model closure material for crack growth predictions. For the
parameters in Eqs. (4) and (5), the EN-related values are determined as follows. First, E was taken at 210 GPa, and n was taken as 0.3. Parameter h1 had a value twice as great as for the observed thickness in the on-precrack-face deposits, because of the similarity in deposit thickness between the upper and lower faces of the precrack. Fig. 17 schematically represents the real deposit profile. The initial value of a1, defined in the rigid-wedge model, was found to be 10 µm according to the observations made using OM and SEM, and this value gradually increased with increasing post-plate crack length. Parameter E1 was taken as 60 GPa in reference to the study of Weil et al. [13], in which the tension specimen was 25-µm thick, similar to that of the thin deposit wedge in this work.
P.S. Song et al. / International Journal of Fatigue 23 (2001) 259–270
For a crack containing multiple wedges, the wedge immediately next to the crack tip affects the closure stress intensity the greatest, as indicated in [22,23]. The present work supported this finding. The deposit thickness T2 between the midpoint and the tip of the pre-crack influenced life extension the most. Therefore, the values of such parameters as a1, h1, and w1 in Eqs. (4) and (5) were established in relation to the dimensions of the deposit between the midpoint and tip of the pre-crack. An attempt was made to more accurately reflect the morphology of the deposits on crack closure by dividing the near-crack-tip EN deposits into two parts, with widths of w1 and w1* (Fig. 17). For the elastic-wedge model, w1 and w1* were taken to be 1.74 mm (1.75 mm⫺10 µm) and 1.75 mm, respectively. The length, a1, was the distance from the crack tip to the central line of each part. For the w1 part, a1 carried an initial value of 0.88 mm (0.87 mm+10 µm). Meanwhile, for the w1* part, it carried an initial value of 2.625 mm (0.875 mm+1.75 mm). With respect to the rigid-wedge model, w1 and w1* were taken as having the same values as the elasticwedge model, where the length a1 denoted the distance from the crack tip to the tip of each part. For the w1 part, a1 was initially taken as 10 µm. Meanwhile, for the w1* part, it was initially taken as 1.75 mm. The superposition principle was employed to estimate the contribution of the two deposits to crack closure [22,24]. Fig. 18 compares the predicted and measured crack growth rates in specimens EN2, EN3*, EN5, and EN10. For specimen EN3*, the measured growth rate fell between the predictions of the rigid- and elastic-wedge models. In the other specimens, the rigid-wedge model predicted a higher growth rate than the elastic-wedge model did, indicating that the elastic-wedge model can more accurately predict the post-plate crack growth phenomena.
4. Conclusions 1. The current plating metals differed in terms of their levels of closure performance and magnitude of growth retardation. At the crack prop-opening load of 0.95 Kmax, life extension ranged between 438 and 557 kilocycles in the presence of EN, which was roughly twice as long as that for EC. This difference is because EN is stronger than EC. Meanwhile, EPN has negative properties of edge buildup and an impurityblocking effect. These properties limited the usefulness of EPN as a crack-growth life extender. Accordingly, although using this plating metal also resulted in life extension, the degree of extension was less than for other electroless plating metals. 2. The magnitude of crack prop-opening load and the site of the sucker are essential in the post-plate growth retardation. The higher crack prop-opening load of 1.5
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Kmax made a wider crack opening possible and this allowed more metal to be deposited over the pre-crack faces. The pre-crack tip, as a sucker site, minimized the gap between the deposited metals and the precrack front. The greater amount of deposited metal together with the smaller gap maximized the resulting crack closure, and the subsequent crack growth was retarded or even halted. 3. The effect of metal plating on crack growth can be understood through the deposit topography. Of the five topography parameters, deposit thickness (T2) dominated the post-plate crack retardation, whereas deposit volume (V) exerted comparatively less effect on growth retardation. 4. In the case of EC, elastic- and rigid-wedge models were not employed because the fatigue loading caused plastic deformation in most of the deposits. In the case of EN, the deposit largely performed as an elastic wedge between the surfaces of the fatigue crack. Moreover, the elastic-wedge model predicted the post-plate crack growth rate more accurately than the rigid-wedge model did.
Acknowledgements The authors thank the National Science Council of the Republic of China for financially supporting this research under Contract No. NSC-86-2212-E-014-003.
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