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ELSEVIER Journal of Materials Processing Technology 53 (1995) 211-218
Materials Processing Technology
The frequency role on cyclic damage: Reflection on electronic materials/devices Y. Katz, M. Kupiec and A. Bussiba
NRCN - P.O.Box 9001, Beer-Sheva 84190, ISRAEL
Frequency effects in fatigue as related to structural reliability of electronic materials/devices still remain a long term goal. Here, complexities arise by realizing that more than a single time dependent micromechanism might dominate. To achieve some progress, intensive experimental activities were conducted in different crystal - structures and in non-metallic systems. The study found that at least in metals, under isothermal conditions, the fatigue crack propagation rate (FCPR) actually increased as the frequency decreased even without environmental interactions. These effects become substantial in materials in which the activation enthalpy for deformation exceeded values of about 0.5e.v, which accentuated at low temperatures. In metals, these issues are analyzed in the light of crack-tip dislocation-interaction model with emphasis to some proposed constitutive equations. Attempts for more realistic simulation techniques in metals, ceramics and polymers might give insights into the generic frequency effects in cyclic damage.
1. INTRODUCTION
Structural reliability in semiconductors, integrated circuits or micro-structural devices provide enough incentives for comprehensive studies. As such, further activities here, might lead to adequate requirements match, or assessment refinements. The current investigation is centered on the frequency, affecting cyclic damage, activated by mechanical or thermal fatigue. This is an unsettled problem on several levels. Generally, cyclic deformation produces the typical features of dislocation structures manifested by cyclic hardening, softening or the generation of microdefects. Consequently, temperature or crack-tip deformation rate (frequency) effects can be paramount, frequently associated only to environmental interactions. In the case of creep or environmental effects, the role of the frequency on damage is naturally accepted, while it is far less recognized or hardly identified (experimentally) in the so called "pure" fatigue damage. Elsevier Science S.A. 0924-0136(95)01978-N
SSD1
212
Y. Katz et aL / Journal of Materials Processing Technology 53 (1995) 2 1 1 2 1 8
The current study is centered on twofold objectives; (i) To initiate more of a synthesized research by enabling some physical insights into frequency effects on cyclic damage in different crystal structures and in non metallic systems. (ii) To elaborate on dislocation dynamics versus quasi-static models starting from "pure" fatigue damage toward deformation/environment interactions. It is the current understanding that such basic elements in fatigue resistance are essential in order to develop methologies for structural assessments under quite complicates circumstances. These refer also to refined life predictions by recognizing the frequency (to be at least potentially) a strong influencing variable. Within a fracture mechanics framework, the frequency effects during fatigue were observed and analyzed, including the role of transients due to crack tip deformation-rate transitions.
2. E X P E R I M E N T A L P R O C E D U R E
Mainly, in metallic solids the material approach was guided by crystal symmetry argumentations, influencing as such the deformation behavior. Aluminum alloy (Al-Li 8090), steel (AISI 4340) and uranium alloys (U-0.75Ti) served only as screening materials representing the FCC, BCC and Orthorhombic systems respectively. Thus, dislocation mobility aspects were introduced in a wide range of deformation behavior with remarkable anisotropic effects. This was really desired allowing to gather some volume of experimental findings, before dealing with the modeling approach section. Basically, this parametric study emphasized the fatigue crack propagation regime by establishing possible effects on the FCPR curves. For the metallic systems, prefatigued three-point-bending specimens, 10x10x55 (in mm) were used, for tension-tension fatigue crack propagation tests. Temperature range consisted of 153 to 296K with frequency range of 10-1 to 102 Hz under two load ratios. The low-frequency tests were performed on a computerized servo-hydraulic machine, For the high frequency tests, a computerized electro-resonance bending machine was utilized. Crack length was measured and tracked by using both; an electrical crack gage beside crack opening displacement gage (COD). Closure load values were determined from a load-COD curve which was continuously recorded by a digital scope with memory capability. Fine scale microstructural features were examined by TEM and SEM. In addition, fracture mode classification along the three stages of the FCPR curve were established, while the role of frequency, temperature and the load ratio effects were particularly emphasized. Fracture surface observations of fatigue striations and crystallographic habits were included also in cases where FCPR transients were activated by sudden frequency changes. Finally, some activities in amorphous polymers such as polymethyl-metacrylate (PMMA) was included. Here, precracked single edge notch specimens (SEN) were utilized. The fatigue crack extension was optically tracked in order to establish da/dN vs. AK curves. Generally, a frequency range between 1 to 80 Hz was applied at room temperature with load ratio of R,~0. Striations, discontinuous growth bands and mode transitions were supplemented by SEM observations.
213
Y. Katz et al. / Journal of Materials Processing Technology 53 (1995) 211-218
3. E X P E R I M E N T A L R E S U L T S AND DISCUSSION
For the currently tested metals a consistent trend prevailed. This differed in polymeric systems as will be addresses and analyzed briefly. Even so it became evident that in metals the frequency rate is highly dependent on the deformation mechanisms. The current materials selection from AL-Li alloy to the low symmetry U-0.75Ti alloy represented activation enthalpy values for deformation of about 0.2-0.8e.v, alluding at possible origins in dislocations dynamics. For the AI-Li case with typical planar slip, frequency effects were established at 153K as shown in Fig. 1. However more has to be done in order to substantiate the role of activation processes as related to other extrinsic parameters. For example, closure, static modes isothermal conditions become significant whenever a local approach is attempted. This point is illustrated in Fig. 2 indicating the load ratio effect on FCPR for the Al-Li 8090 alloy. Crack tip extrinsic effects were observed also from FCPR transients activated by sudden frequency variations. Beside crack rate transients, fracture mode transitions occurred as illustrated for AI-Li alloy in Fig. 3. Substantial frequency effects were observed in the AISI 4340 and the U-0.75Ti alloys. Crack extension rates and fracture surface features for the AISI 4340 are illustrated in Figs. 4 and 5 respectively. Along this, experimental findings for the U-0.75Ti alloy are given in Figs. 6 and 7. In contrast the strong thermal effects in the U-0.75Ti alloy are given in Fig. 8. Just for completeness some results for the PMMA polymer are shown in Figs. 9 and 10 with emphasis to variations in the fatigue discontinuous bands due to the frequency.
AK= 12 MPa.m 1/2
10-2~ -~, 1 0 - 3 ~
~ 1 o -4 z
• 296K [] 153K []
~
--•
z
~>" 10 -4 ~
-
10_5 ~
10_6
10 -5 : I IIIlllll I I[llllll I IIIIllll I IIit[111 10 -2 10 "1 100 101 102
10 .7
.=0.1 9R=0.3 I I III 101
I
T
Frequency(Hz)
AK (MPa.m 1/2)
Figure 1. Frequency effect on FCPR in Al-Li 8090 at two temperatures for a constant AK.
Figure 2. Load ratio effect on FCPR in ALLi 8090 at 150K and 10Hz.
214
Y, Katz et al. /Journal o f Materials Processing Technology 53 (1995) 211-218
Figure 3. Fracture mode transitions in Al-Li 8090 at 296K, activated by high (20Hz) to low (0.1Hz) and high (20Hz) frequency jumps.
10 -3 /
~ 10"4z -
,,....¢
Z
o 0 . 1 Hz O 1.0 H z ± 1 0 Hz • 1 7 0 Hz
-~ 10-5~
10 AK (MPa.m 1/2) Figure 4. Frequency effect on FCPR in AISI Figure 5. SEM fractograph for AISI 4340 at 4340 at 296K. 296K. f=0.1Hz, AK=14MPa.m 1/2. (crack front direction is pointed).
Y. Katz et al. / Journal of Materials Processing Technology 53 (1995) 211-218
,-, 10-3-
215
0
z
10"4_ 10"5-
lO-610"7
// ~ ~/ i o/ /"
• 0.01 Hz ¢0.1 Hz (31 Hz • 10 Hz
~,
O 150 Hz
IIII I I I I I 101 zXK (MPa.m 1/2)
Figure 6. Frequency effect on FCPR in U0.75Ti alloy at 296K
Figure 7. SEM fractograph in U-0.75Ti alloy at 296K. &K= 15 MPa.m 1/2, f=0.1Hz
Concerning only the dislocation dynamic aspects for the metals, the rationale sequence followed the dislocation group dynamic models, in the spirit of Yokobori et al. [1] which has been modified by Gerberich et al. [2]. Assuming that a fatigue microcrack had already been introduced, dislocations exist as a plastic wake behind the crack tip [3]. The application of fatigue cycles activate the dislocations, emitted and moved towards a microstructural barrier. Thus, pile-up instability might result in a new quasi-equilibrium crack tip position. The main point here is that the local - crack tip field and dislocation mobility with a given microstructure, become essential in the model. ~, 10-3~
10-4
z
•
_
•~ l O ' S z ~ 10 -6
III
I
• 296K o 173K I
I
I
I L
101 AK (MPa.m u2) Figure 8. Temperature effect on FCPR in U0.75Ti alloy at 10Hz.
216
Y. Katz et aL / Journal of Materials Processing Technology 53 (1995) 211~18
10 ° ~_
103
10-1
102 ~ o o
10_2
101 2:
10 -3
100 10° AK (MPa.m 1/2)
Figure 9. Discontinuous band size in PMMA and the corresponding number of cycles N* per band. T=296K.
Figure 10. Fatigue discontinuous bands in PMMA at 296K. AK=1.2MPa.m 1/2, f=80Hz.
Further, assuming that only stresses beyond some threshold count, or that only the positive part of cyclic stresses contribute to crack extension, thus; da - -
V -~
dN
(1)
2f
where: f is the frequency and V is the average dislocation group velocity. For V;
f'c~ -~m -U* V= mv01/×~-01~ + exp kT
(2)
V0 = velocity at o0; m = strain rate sensitivity; crxi = local crack - tip stress at xi; U* = activation energy controlling the dislocation velocity. For a given temperature, the local stress is estimated by: f R )n/(l+n) = ~.rncr / ' ' P / Oxi ys[ Xi )
(3)
~Lm - a factor introducing the dynamics rate response. Rp - Reversed plastic zone. n = cyclic strain hardening. Equations 1-3 enabled within a fracture mechanics framework to express the crack extension rate in terms of the remote stress intensity factor. Moreover, this formulation include the frequency role in a partial form given by; where;
Y. Katz et aL / Journal of Materials Processing Technology 53 (1995) 211-218
da (1 /
dN
(4)
~--
where; ct indicates the frequency sensitivity, while the values of
217
13ys,
Rp, n and x i are
determined or supported experimentally. The striking result was that even x i can be evaluated reasonably well from fractographic fine-scale features. (For example, in the U-Ti case x i was between 0.2 -1.21am along the frequency range). Thus, based solely on a dislocation dynamic model in metals the FCPR values are expected to decrease as the applied frequency increases. This trend beside the significant role of the temperature was actually confirmed experimentally. Notice that some deviations occurred for frequencies of 150 or 170 Hz. The origin for this behavior is due to the non-isothermal condition (in terms of quasi-adiabatic heat) as illustrated in Figs. 4 and 5. Additionally, it is interesting to evaluate the frequency sensitivity in the tested polymer. As illustrated in Figs. 9 and 10 the trend of the inverse dependency of the FCPR with the frequency prevailed also in the PMMA. These findings support the study by Skibo et al. [4] associated with other mechanisms. As explained by the mentioned study hysteretic heating at the crack tip might cause crack blunting which reduces the FCPR in numerous polymeric solids. This phenomena if global or local might influence strongly the material sensitivity to the frequency. Nevertheless, in polymers too, the frequency variable requires assessment and might be excluded only by cause. As addressed by Burkhard et al. [5] electronic assemblies and components experience high mechanical loading from both; vibrations and thermally induced stresses. Clearly operational reliability modeling and failure analysis developments are important. This by considering some major components as wire bonds, plated-through holes, seals and solder points. In this context the dominant variables need to be established for further progress. Recognizing the complex hybrid structures formed out by dissimilar materials the current study emphasizes only partial aspects in metals and polymers. Nevertheless, as concluded by Yao and Shang [6] cyclic damage is frequency dependent in ceramics at an elevated temperatures. The frequency response of materials are complicated but excluding this parameter from constitutive properties demands careful assessments. Basically it seems that at least several origins for time dependent effects exist and related to; (i) Dislocation dynamic aspects. (ii) Visco elastic/plastic response due to elevated temperatures. (iii) Intrinsic properties for local heat sources. (iv) Environmental and combined effects. Although the present study is centered mainly on the aforementioned origin (i), dimensional aspects, distinction between initiation and propagation require further elaboration. However, it is the authors opinion that the role of frequency in crack initiation is hardly explored realizing also some advanced models based on extremely fine scale observations [7]. Cumulative damage for fatigue crack initiation in terms of surface displacement upset and slip spacing still depends on dislocation dynamics, friction stress beside the time dependent mechanisms associated with creep or environment. Accordingly, it becomes apparent that life simulation techniques, should include beside the singularity strength (for the crack tip field) the frequency and temperature as affecting variables [8]. The advantage here is that in terms of interactive effects the constitutive formulation of the frequency allows calculation procedures. Following this, more options are
218
Y. Katz et al. / Journal of Materials Processing Technology 53 (1995) 211-218
enable to develop a partition based view by realizing that the overall damage prediction is mechanistically controlled. These avenues appear promising not only for single materials but also to modify models for integrated circuits packages.
4. CONCLUSIONS
(1) Frequency effects as related to cyclic damage might be substantial even without environmental interactions. These are even accentuated at low temperatures. (2) A dislocation dynamic approach might assist in establishing sound constitutive equations for cyclic damage assessments. Experimental findings revealed consistent trends with physical insights. (3) Such views incorporated in structural reliability analysis of electronic materials/devices seems to be beneficial. (4) Although aimed for application requirements, the fundamental views on fatigue resistance are important. In this context, crack-tip dislocation model might shed light on the dynamic aspects of cyclic damage.
ACKNOWLEDGMENT
The authors gratefully acknowledge Mr. E. Woodbeker from the NRCN for his experimental assistance.
REFERENCES
1. T. Yokobori, M. Kawasaki and T. Yoshimura; in ICF2, P.U Pratt (ed.), p. 803, Chapman and Hall, 1969. 2. W.W. Gerberich, D.L. Davidson, X.F. Chen and C.S. Lee, Engng. Fract. Mech., 28 (1987) 505. 3. HF. Kanninen and C. Atkinson, Int. J. Fracture, 16 (1979) 271 4. M.D. Skibo, R.W. Hertzberg and J.A. Manson; in Fracture 71, 3 ICF4, University of Waterloo Press, Ontario, Canada, 1127 (1971). 5. A.H. Burkhard, J.M. Kallis, L.B. Duncan, M. F. Kanninen and D.O. Harris, in ICF7, K. Salama et al. (eds.), Pergamon Press, 977 (1989). 6. D. Yao and J.K. Shang, Acta Metall, ~ 5890 (1994). 7. S.E Harvey, P.G Marsh and W.W. Gerberich, Acta Metall, 44~23493 (1994). 8. T. Shimizu, A. Nishimura and S. Kawai, in Fatigue 90, H.Kitagawa and T. Tanaka (eds.), 2~ MCEP Ltd., Birmingham UK. 993, (1990).
ELSEVIER Journal of Materials Processing Technology 53 (1995) 211-218
Materials Processing Technology
The frequency role on cyclic damage: Reflection on electronic materials/devices Y. Katz, M. Kupiec and A. Bussiba
NRCN - P.O.Box 9001, Beer-Sheva 84190, ISRAEL
Frequency effects in fatigue as related to structural reliability of electronic materials/devices still remain a long term goal. Here, complexities arise by realizing that more than a single time dependent micromechanism might dominate. To achieve some progress, intensive experimental activities were conducted in different crystal - structures and in non-metallic systems. The study found that at least in metals, under isothermal conditions, the fatigue crack propagation rate (FCPR) actually increased as the frequency decreased even without environmental interactions. These effects become substantial in materials in which the activation enthalpy for deformation exceeded values of about 0.5e.v, which accentuated at low temperatures. In metals, these issues are analyzed in the light of crack-tip dislocation-interaction model with emphasis to some proposed constitutive equations. Attempts for more realistic simulation techniques in metals, ceramics and polymers might give insights into the generic frequency effects in cyclic damage.
1. INTRODUCTION
Structural reliability in semiconductors, integrated circuits or micro-structural devices provide enough incentives for comprehensive studies. As such, further activities here, might lead to adequate requirements match, or assessment refinements. The current investigation is centered on the frequency, affecting cyclic damage, activated by mechanical or thermal fatigue. This is an unsettled problem on several levels. Generally, cyclic deformation produces the typical features of dislocation structures manifested by cyclic hardening, softening or the generation of microdefects. Consequently, temperature or crack-tip deformation rate (frequency) effects can be paramount, frequently associated only to environmental interactions. In the case of creep or environmental effects, the role of the frequency on damage is naturally accepted, while it is far less recognized or hardly identified (experimentally) in the so called "pure" fatigue damage. Elsevier Science S.A. 0924-0136(95)01978-N
SSD1
212
Y. Katz et aL / Journal of Materials Processing Technology 53 (1995) 2 1 1 2 1 8
The current study is centered on twofold objectives; (i) To initiate more of a synthesized research by enabling some physical insights into frequency effects on cyclic damage in different crystal structures and in non metallic systems. (ii) To elaborate on dislocation dynamics versus quasi-static models starting from "pure" fatigue damage toward deformation/environment interactions. It is the current understanding that such basic elements in fatigue resistance are essential in order to develop methologies for structural assessments under quite complicates circumstances. These refer also to refined life predictions by recognizing the frequency (to be at least potentially) a strong influencing variable. Within a fracture mechanics framework, the frequency effects during fatigue were observed and analyzed, including the role of transients due to crack tip deformation-rate transitions.
2. E X P E R I M E N T A L P R O C E D U R E
Mainly, in metallic solids the material approach was guided by crystal symmetry argumentations, influencing as such the deformation behavior. Aluminum alloy (Al-Li 8090), steel (AISI 4340) and uranium alloys (U-0.75Ti) served only as screening materials representing the FCC, BCC and Orthorhombic systems respectively. Thus, dislocation mobility aspects were introduced in a wide range of deformation behavior with remarkable anisotropic effects. This was really desired allowing to gather some volume of experimental findings, before dealing with the modeling approach section. Basically, this parametric study emphasized the fatigue crack propagation regime by establishing possible effects on the FCPR curves. For the metallic systems, prefatigued three-point-bending specimens, 10x10x55 (in mm) were used, for tension-tension fatigue crack propagation tests. Temperature range consisted of 153 to 296K with frequency range of 10-1 to 102 Hz under two load ratios. The low-frequency tests were performed on a computerized servo-hydraulic machine, For the high frequency tests, a computerized electro-resonance bending machine was utilized. Crack length was measured and tracked by using both; an electrical crack gage beside crack opening displacement gage (COD). Closure load values were determined from a load-COD curve which was continuously recorded by a digital scope with memory capability. Fine scale microstructural features were examined by TEM and SEM. In addition, fracture mode classification along the three stages of the FCPR curve were established, while the role of frequency, temperature and the load ratio effects were particularly emphasized. Fracture surface observations of fatigue striations and crystallographic habits were included also in cases where FCPR transients were activated by sudden frequency changes. Finally, some activities in amorphous polymers such as polymethyl-metacrylate (PMMA) was included. Here, precracked single edge notch specimens (SEN) were utilized. The fatigue crack extension was optically tracked in order to establish da/dN vs. AK curves. Generally, a frequency range between 1 to 80 Hz was applied at room temperature with load ratio of R,~0. Striations, discontinuous growth bands and mode transitions were supplemented by SEM observations.
213
Y. Katz et al. / Journal of Materials Processing Technology 53 (1995) 211-218
3. E X P E R I M E N T A L R E S U L T S AND DISCUSSION
For the currently tested metals a consistent trend prevailed. This differed in polymeric systems as will be addresses and analyzed briefly. Even so it became evident that in metals the frequency rate is highly dependent on the deformation mechanisms. The current materials selection from AL-Li alloy to the low symmetry U-0.75Ti alloy represented activation enthalpy values for deformation of about 0.2-0.8e.v, alluding at possible origins in dislocations dynamics. For the AI-Li case with typical planar slip, frequency effects were established at 153K as shown in Fig. 1. However more has to be done in order to substantiate the role of activation processes as related to other extrinsic parameters. For example, closure, static modes isothermal conditions become significant whenever a local approach is attempted. This point is illustrated in Fig. 2 indicating the load ratio effect on FCPR for the Al-Li 8090 alloy. Crack tip extrinsic effects were observed also from FCPR transients activated by sudden frequency variations. Beside crack rate transients, fracture mode transitions occurred as illustrated for AI-Li alloy in Fig. 3. Substantial frequency effects were observed in the AISI 4340 and the U-0.75Ti alloys. Crack extension rates and fracture surface features for the AISI 4340 are illustrated in Figs. 4 and 5 respectively. Along this, experimental findings for the U-0.75Ti alloy are given in Figs. 6 and 7. In contrast the strong thermal effects in the U-0.75Ti alloy are given in Fig. 8. Just for completeness some results for the PMMA polymer are shown in Figs. 9 and 10 with emphasis to variations in the fatigue discontinuous bands due to the frequency.
AK= 12 MPa.m 1/2
10-2~ -~, 1 0 - 3 ~
~ 1 o -4 z
• 296K [] 153K []
~
--•
z
~>" 10 -4 ~
-
10_5 ~
10_6
10 -5 : I IIIlllll I I[llllll I IIIIllll I IIit[111 10 -2 10 "1 100 101 102
10 .7
.=0.1 9R=0.3 I I III 101
I
T
Frequency(Hz)
AK (MPa.m 1/2)
Figure 1. Frequency effect on FCPR in Al-Li 8090 at two temperatures for a constant AK.
Figure 2. Load ratio effect on FCPR in ALLi 8090 at 150K and 10Hz.
214
Y, Katz et al. /Journal o f Materials Processing Technology 53 (1995) 211-218
Figure 3. Fracture mode transitions in Al-Li 8090 at 296K, activated by high (20Hz) to low (0.1Hz) and high (20Hz) frequency jumps.
10 -3 /
~ 10"4z -
,,....¢
Z
o 0 . 1 Hz O 1.0 H z ± 1 0 Hz • 1 7 0 Hz
-~ 10-5~
10 AK (MPa.m 1/2) Figure 4. Frequency effect on FCPR in AISI Figure 5. SEM fractograph for AISI 4340 at 4340 at 296K. 296K. f=0.1Hz, AK=14MPa.m 1/2. (crack front direction is pointed).
Y. Katz et al. / Journal of Materials Processing Technology 53 (1995) 211-218
,-, 10-3-
215
0
z
10"4_ 10"5-
lO-610"7
// ~ ~/ i o/ /"
• 0.01 Hz ¢0.1 Hz (31 Hz • 10 Hz
~,
O 150 Hz
IIII I I I I I 101 zXK (MPa.m 1/2)
Figure 6. Frequency effect on FCPR in U0.75Ti alloy at 296K
Figure 7. SEM fractograph in U-0.75Ti alloy at 296K. &K= 15 MPa.m 1/2, f=0.1Hz
Concerning only the dislocation dynamic aspects for the metals, the rationale sequence followed the dislocation group dynamic models, in the spirit of Yokobori et al. [1] which has been modified by Gerberich et al. [2]. Assuming that a fatigue microcrack had already been introduced, dislocations exist as a plastic wake behind the crack tip [3]. The application of fatigue cycles activate the dislocations, emitted and moved towards a microstructural barrier. Thus, pile-up instability might result in a new quasi-equilibrium crack tip position. The main point here is that the local - crack tip field and dislocation mobility with a given microstructure, become essential in the model. ~, 10-3~
10-4
z
•
_
•~ l O ' S z ~ 10 -6
III
I
• 296K o 173K I
I
I
I L
101 AK (MPa.m u2) Figure 8. Temperature effect on FCPR in U0.75Ti alloy at 10Hz.
216
Y. Katz et aL / Journal of Materials Processing Technology 53 (1995) 211~18
10 ° ~_
103
10-1
102 ~ o o
10_2
101 2:
10 -3
100 10° AK (MPa.m 1/2)
Figure 9. Discontinuous band size in PMMA and the corresponding number of cycles N* per band. T=296K.
Figure 10. Fatigue discontinuous bands in PMMA at 296K. AK=1.2MPa.m 1/2, f=80Hz.
Further, assuming that only stresses beyond some threshold count, or that only the positive part of cyclic stresses contribute to crack extension, thus; da - -
V -~
dN
(1)
2f
where: f is the frequency and V is the average dislocation group velocity. For V;
f'c~ -~m -U* V= mv01/×~-01~ + exp kT
(2)
V0 = velocity at o0; m = strain rate sensitivity; crxi = local crack - tip stress at xi; U* = activation energy controlling the dislocation velocity. For a given temperature, the local stress is estimated by: f R )n/(l+n) = ~.rncr / ' ' P / Oxi ys[ Xi )
(3)
~Lm - a factor introducing the dynamics rate response. Rp - Reversed plastic zone. n = cyclic strain hardening. Equations 1-3 enabled within a fracture mechanics framework to express the crack extension rate in terms of the remote stress intensity factor. Moreover, this formulation include the frequency role in a partial form given by; where;
Y. Katz et aL / Journal of Materials Processing Technology 53 (1995) 211-218
da (1 /
dN
(4)
~--
where; ct indicates the frequency sensitivity, while the values of
217
13ys,
Rp, n and x i are
determined or supported experimentally. The striking result was that even x i can be evaluated reasonably well from fractographic fine-scale features. (For example, in the U-Ti case x i was between 0.2 -1.21am along the frequency range). Thus, based solely on a dislocation dynamic model in metals the FCPR values are expected to decrease as the applied frequency increases. This trend beside the significant role of the temperature was actually confirmed experimentally. Notice that some deviations occurred for frequencies of 150 or 170 Hz. The origin for this behavior is due to the non-isothermal condition (in terms of quasi-adiabatic heat) as illustrated in Figs. 4 and 5. Additionally, it is interesting to evaluate the frequency sensitivity in the tested polymer. As illustrated in Figs. 9 and 10 the trend of the inverse dependency of the FCPR with the frequency prevailed also in the PMMA. These findings support the study by Skibo et al. [4] associated with other mechanisms. As explained by the mentioned study hysteretic heating at the crack tip might cause crack blunting which reduces the FCPR in numerous polymeric solids. This phenomena if global or local might influence strongly the material sensitivity to the frequency. Nevertheless, in polymers too, the frequency variable requires assessment and might be excluded only by cause. As addressed by Burkhard et al. [5] electronic assemblies and components experience high mechanical loading from both; vibrations and thermally induced stresses. Clearly operational reliability modeling and failure analysis developments are important. This by considering some major components as wire bonds, plated-through holes, seals and solder points. In this context the dominant variables need to be established for further progress. Recognizing the complex hybrid structures formed out by dissimilar materials the current study emphasizes only partial aspects in metals and polymers. Nevertheless, as concluded by Yao and Shang [6] cyclic damage is frequency dependent in ceramics at an elevated temperatures. The frequency response of materials are complicated but excluding this parameter from constitutive properties demands careful assessments. Basically it seems that at least several origins for time dependent effects exist and related to; (i) Dislocation dynamic aspects. (ii) Visco elastic/plastic response due to elevated temperatures. (iii) Intrinsic properties for local heat sources. (iv) Environmental and combined effects. Although the present study is centered mainly on the aforementioned origin (i), dimensional aspects, distinction between initiation and propagation require further elaboration. However, it is the authors opinion that the role of frequency in crack initiation is hardly explored realizing also some advanced models based on extremely fine scale observations [7]. Cumulative damage for fatigue crack initiation in terms of surface displacement upset and slip spacing still depends on dislocation dynamics, friction stress beside the time dependent mechanisms associated with creep or environment. Accordingly, it becomes apparent that life simulation techniques, should include beside the singularity strength (for the crack tip field) the frequency and temperature as affecting variables [8]. The advantage here is that in terms of interactive effects the constitutive formulation of the frequency allows calculation procedures. Following this, more options are
218
Y. Katz et al. / Journal of Materials Processing Technology 53 (1995) 211-218
enable to develop a partition based view by realizing that the overall damage prediction is mechanistically controlled. These avenues appear promising not only for single materials but also to modify models for integrated circuits packages.
4. CONCLUSIONS
(1) Frequency effects as related to cyclic damage might be substantial even without environmental interactions. These are even accentuated at low temperatures. (2) A dislocation dynamic approach might assist in establishing sound constitutive equations for cyclic damage assessments. Experimental findings revealed consistent trends with physical insights. (3) Such views incorporated in structural reliability analysis of electronic materials/devices seems to be beneficial. (4) Although aimed for application requirements, the fundamental views on fatigue resistance are important. In this context, crack-tip dislocation model might shed light on the dynamic aspects of cyclic damage.
ACKNOWLEDGMENT
The authors gratefully acknowledge Mr. E. Woodbeker from the NRCN for his experimental assistance.
REFERENCES
1. T. Yokobori, M. Kawasaki and T. Yoshimura; in ICF2, P.U Pratt (ed.), p. 803, Chapman and Hall, 1969. 2. W.W. Gerberich, D.L. Davidson, X.F. Chen and C.S. Lee, Engng. Fract. Mech., 28 (1987) 505. 3. HF. Kanninen and C. Atkinson, Int. J. Fracture, 16 (1979) 271 4. M.D. Skibo, R.W. Hertzberg and J.A. Manson; in Fracture 71, 3 ICF4, University of Waterloo Press, Ontario, Canada, 1127 (1971). 5. A.H. Burkhard, J.M. Kallis, L.B. Duncan, M. F. Kanninen and D.O. Harris, in ICF7, K. Salama et al. (eds.), Pergamon Press, 977 (1989). 6. D. Yao and J.K. Shang, Acta Metall, ~ 5890 (1994). 7. S.E Harvey, P.G Marsh and W.W. Gerberich, Acta Metall, 44~23493 (1994). 8. T. Shimizu, A. Nishimura and S. Kawai, in Fatigue 90, H.Kitagawa and T. Tanaka (eds.), 2~ MCEP Ltd., Birmingham UK. 993, (1990).