Creep J-integral Range Research Articles

Effect of Hold Time on Crack Growth Behavior of Pb-Containing and Pb-Free Solders

Four types of loading waveforms were adopted to investigate the effect of hold time on crack growth behavior of Sn-37Pb and Sn-3.0Ag-0.5Cu solders: a sinusoidal waveform, triangular waveform, and trapezoidal waveform with hold times of 1 s, 5 s, and 10 s, and a triangular waveform with hold time of 10 s at maximum tensile load. The experimental results showed that the crack growth behavior of both solders tested under sinusoidal and triangular waveforms without any hold time was predominantly cycle dependent. On the other hand, the crack growth behavior of both solders tested under trapezoidal waveforms with hold times of 1 s, 5 s, and 10 s and triangular waveforms with hold time of 10 s was predominantly time dependent. Under cycle-dependent conditions the crack growth data were a function of J-integral range, while under time-dependent conditions the crack growth data were not a function of the creep J-integral range but rather of the C* parameter.

Creep-Fatigue Crack Growth in Sn-3.0Ag-0.5Cu Solder

This paper studies the creep-fatigue crack growth in Sn-3.0Ag-0.5Cu lead-free solder. Strain controlled push-pull low cycle crack growth tests were performed using fast-fast (pp), fast-slow (pc), slow-fast (cp), and slow-slow (cc) strain waveforms at 313K. The fastest crack growth rate was found in the pc waveform, followed by the cp, cc and pp waveforms. Crack growth rates in the pp waveform were well correlated with the cyclic J-integral range and fatigue J-integral range and those in the pc, cp and cc waveforms with the creep J-integral range. No creep-fatigue interaction was found in the correlation of the crack growth rate with the J-integral ranges. The crack grew perpendicular to the specimen axis in the pp waveform. In the cases of the pc, cp and cc waveforms, the crack grew in the perpendicular direction to the specimen axis initially and branched in the direction about 45 degrees to the specimen axis.

Recent Progress of Experimental and Measuring Technology. Evaluation of Crack Propagation for Sn63-Pb37 Solder Bumps.

Fatigue life estimation of solder bumps is one of the most critical technologies for the development of ball grid array packages. Since the recent trend in the package development is toward smaller solder bumps, the estimation of the crack initiation and initial crack propagation rate is essential in the reliability design. In this study, mechanical fatigue tests were carried out using Sn63-Pb37 solder bump specimens. The initial crack propagation rate of the solder bumps was estimated based on the load drop, because the crack observation with destructive test is not suitable for the uniform evaluation of many results. A simple estimation of the crack propagation based on the linear damage law was applied. The trend of the simple estimation results corresponded well with the experimental results of crack propagation. The estimation method of crack propagation based on the fracture mechanics was also examined so as to reduce error in reliability design. Creep J-integral range was calculated using the elastic-creep FEM analysis. The relationship between the crack propagation rate and creep J-integral range was obtained. It was confirmed that the initial crack propagation of micro solder joints could be accurately evaluated using the creep J-integral range.

Effect of the Intermediate Hold on the Creep-Fatigue Crack Propagation. Intermediate Tensile Hold during Unloading.

Creep-fatigue crack propagation tests using type 304 stainless steel have been carried out under intermediate tensile load hold during an unload process in order to study the effect of the load hold position. A finite element analysis was carried out to investigate the fracture mechanics parameter. The results obtained were as follows. (1) As for the finite element analysis, the application of the fracture mechanics parameter, creep J-integral J′, was found to be effective under the intermediate tensile load hold condition as well as under the maximum load hold condition. (2) The crack propagation rate was correlated well with the fracture mechanics parameter, creep J-integral range (ΔJc), under the intermediate tensile load hold condition as well as under the maximum load hold condition.

Evaluation of Creep-Fatigue Crack Propagation of Sn-37 Pb Solder.

The fatigue life estimation of micro solder joints is one of the most critical technologies for the reliable IC packages. In recent years, it is considered that the development of estimation methods for the crack propagation based on the fracture mechanics approach is important to the life prediction. In this study, the crack propagation behavior of Sn-37 Pb solder was investigated. Fatigue tests using CT specimens were carried out under 0.1 Hz, 0.01 Hz and 0.001 Hz. As a result, the crack propagation rate was correlated well with the fatigue J-integral range independently of the frequency. On the other hand, the fracture surfaces for all conditions were intergranular creep types. The creep-fatigue tests under stress waveforms with tensile hold (cp-type) and with tensile and compressive hold (cc-type) were carried out at room temperature using CCT specimens. The relationship between the crack propagation rate and the creep J-integral range was obtained. The crack propagation rate under the cc-type condition was lower than the one under the cp-type condition for the same value of creep J-integral range.

Evaluation of Creep-Fatigue Crack Propagation in Surface Cracked Pipe.

A study was conducted to evaluate the crack propagation behavior in a surface cracked pipe at elevated temperatures. The fatigue and creep-fatigue crack propagation tests were carried out for 316FR steel pipe (base metal pipe and weldment pipe) under four point bending at 650°C. Fracture mechanics parameters. fatigue J-integral range (ΔJj) and creep J-integral range (ΔJc), were estimated by the simplified analysis method based on the reference stress approach. The estimated crack propagation behavior was compared with the experimental results. It was confirmed that the proposed method in this paper gave a good estimate.

Initiation and Growth of Cavities and Cracks along Grain Boundaries in Type 304 Stainless Steel under Creep-Fatigue Condition

Creep-fatigue tests of Type 304 stainless steel were carriedout using smooth round bar specimens. Cavities and small cracksinitiated inside the specimen were observed on the cross-section bymeans of a scanning laser microscope. The results obtained aresummarized as follows. (1) From the beginning of the creep-fatigue test,spherical cavities appear at random locations on grain boundaries, oneafter another. (2) The cavities on the grain boundaries perpendicular tothe stress axis preferentially grow, and change shape from spherical toflat oblate (or crack-like). (3) When the ligament area on a grainboundary plane reduces to a half, the cavities coalesce and bring abouta complete break of the grain boundary, which is defined as theinitiation of a small crack. (4) Mean growth rate of cavities and crackslocates in the vicinity of the crack propagation law which can bederived from the relationship between the propagation rate of largecrack and creep J-integral range fortime-dependent fatigue of Type 304 stainless steel.

ＳＵ３０４の高温疲労き裂伝ぱに及ぼす予クリープ疲労損傷の影響

Creep fatigue tests were conducted on smooth specimens of a Type 304 stainless steel under a tensile stress hold (cp-type) condition at 1073K, and pre-creep damage was introduced in the form of small intergranular cracks distributed uniformly through the thickness. Macrocrack propagation tests in the high temperature fatigue were then carried out with the pre-damaged specimens. The results obtained are summarized as follows:(1) The pre-damage accelerated the successive macrocrack propagation in cp-type fatigue at 923K for an equal value of creep J-integral range, ΔJc, which governs the crack propagation rate of virgin material in time dependent fatigue.(2) Although the crack propagation rate of pre-damaged material in cp-type fatigue at 1073K was faster than that at 923K for ah equal ΔJc, it coincided with that of virgin one. The multiple small cracks were found on the specimens of virgin material as well as pre-damaged one near the macrocrack, which implied that the small cracks were generated not only in prior creep fatigue but also during the propagation test. Thus, the acceleration in cp-type is caused by the small cracks.(3) The crack propagation rate of pre-damaged material in cycle dependent (pp-type) fatigue was nearly 10 times faster than that of virgin one. The observation of crack morphology revealed that the accelerated fatigue crack propagation was caused by the coalescence with intergranular small cracks.

酸化物分散強化型超合金Ｉｎｃｏｎｅｌ ＭＡ７５４のクリープ疲労き裂伝ぱ

Crack propagation behavior was examined in creep-fatigue at high temperatures using center cracked plate (CCP) specimens of an oxide (Y2O3) dispersion strengthened (ODS) superalloy, Inconel MA754, manufactured by mechanical alloying and a Ni-base superalloy without oxide dispersion, Nimonic 75. The Inconel MA754 has coarse elongated grains whereas the Nimonic 75 has fine homogeneous ones. The results obtained are summarized as follows.(1) The transverse crack propagation of the Inconel MA754 at 1273K and 1173K was strongly affected by the microstructure. The crack arrested temporarily at the grain-boundaries perpendicular to the propagation direction while it propagated fast at the midway.(2) The average crack length through the thickness of specimen, which included about 15 grains, was measured by means of the DC potential drop technique during the test of Inconel MA754. The length increased smoothly without the crack arrest and the propagation rate was correlated well with the creep J-integral range.(3) Little difference was observed in the dl/dN-ΔJc relations between the Inconel MA754 and the Nimonic 75 (at 1173K and 1073K).(4) The crack propagation of the Inconel MA754 was much slower than that of the Nimonic 75. This high resistance of ODS superalloy against creep-fatigue crack propagation was caused by the excellent creep deformation property due to the oxide dispersion.

Surface crack propagation in plate specimens of 1Cr-1Mo-1/4V turbine rotor steel under creep-fatigue condition.

It is important to know the crack propagation behavior under creep-fatigue condition in order to insure the security of high temperature components. In this study, crack propagation tests were conducted using two sizes of plate specimens of a 1Cr-1Mo-1/4V forged steel with a through or surface crack at 550°C. Regardless of the specimen size and crack shape, the crack propagation rate was correlated well with creep J-integral range, whereas it was not with elastic stress intensity factor nor net section stress. A numerical simulation method was successfully developed for the surface crack propagation on the basis of the relationship between crack propagation rate and creep J-integral range.

交流電位差法を用いたＳＵＳ３０４とＴｉ‐１７の荷重制御下およびき裂中央開口変位制御下のクリープ疲労き裂伝ぱ試験

The a.c. electric potential method was adopted for the crack length measurement in high temperature fatigue tests. The method was found easy to get the same relationship between the electric potential and the crack length as that in the d.c. potential method, when a constant a.c. of the relatively low frequency of 93Hz was supplied to the plate specimens of SUS304 stainless steel and titanium alloy, Ti-17, with a center crack or double edge cracks. Fatigue crack propagation tests were conducted on SUS304 at 600°C and on Ti-17 at 482°C under the trapezoidal waveforms with tension hold time in the crack center opening displacement (CCOD) control as well as the load control conditions. A creep-dominated, time-dependent relationship between the crack propagation rate, dl/dN, and the creep J-integral range, ΔJc, in the CCOD control condition was in good agreement with that in the load control condition, although the CCOD control test was a kind of ΔJc-decreasing tests. The titanium alloy, Ti-17, showed a lower bound of the available dl/dN-ΔJc data band of some heat resisting steels.

Ｃｒ‐Ｍｏ‐Ｖ鋼およびＳＵＳ３０４鋼の熱疲労き裂伝ぱと破損寿命評価

In order to investigate the fracture mechanics law of macroscopic crack propagation in thermal fatigue, strain-controlled thermal fatigue tests on Cr-Mo-V rotor steel and SUS304 stainless steel were carried out by using a notched specimen. A smooth specimen was also employed for thermal fatigue tests under the same conditions as the crack propagation tests to discuss the applicability of the fatigue life law (i.e., the strain-energy-parameter approach) derived from the macroscopic crack propagation law to thermal fatigue life evaluation.The results obtained were summarized as follows:(1) The characteristics of thermal fatigue crack propagation could be classified into two types (i.e., cycle-dependent and time-dependent) by applying the transition criterion between the types.(2) The fracture modes in the cycle-and time-dependent thermal fatigue were of transgranular and intergranular types, respectively.(3) The fatigue J-integral range, ΔJf, was a fracture mechanics parameter controlling the crack propagation rate, dl/dN, in the cycle-dependent thermal fatigue, while the creep J-integral range, ΔJc, in the time-dependent thermal fatigue. In this case, rapid straining could be successfully applied to the partition of the inelastic strain into plastic and creep components for evaluating the ΔJc-value. The crack propagation law (i.e., the dl/dN-ΔJf and dl/dN-ΔJc relations) in thermal fatigue was identical with that obtained in isothermal fatigue.(4) The thermal fatigue failure life of the smooth specimen was correlated with the strain-energy parameter, and the correlation agreed with that in isothermal fatigue. Also, it could be predicted from the crack propagation characteristics obtained by using the notched specimen.

Evaluation of the creep-fatigue crack propagation rate of 2 1/4Cr-1Mo steel.

A series of experiments were performed in order to clarify creep-fatigue crack propagation behavior and also to identify the parameter that characterizes the crack growth rate of 2 1/4 Cr-1 Mo steel at 500°C. The following results were obtained (1) Under cyclic loading with tensile load hold, the creep crack propagation during the tensile load hole was dominant. (2) While the crack growth rate was steady during the tensile load hold, the crack opening displacement increased radically right after the load hold started and afterwards increased steadily to the end of the tensile load hold. The radical increase of the crack opening displacement right after the tensile load hold was found not to be due to the crack growth. (3) The creep-fatigue crack propagation rate was characterized by the creep J-integral range calculated from the steady increase of the crack opening displacement during the tensile load hold, as is shown by Eq. (1) in the text.

High-temperature fatigue crack propagation under cyclic temperature.

In order to investigate crack propagation behavior of thermal fatigue on the basis of non-linear fracture mechanics, crack propagation tests were conducted for isothermal fatigue at several temperatures and for cyclic temperature fatigue. The results obtained were summarized as follows. (1) The fracture mechanics laws in isothermal fatigue dl/dN-ΔJf and dl/dN-ΔJc relations where dl/dN was crack propagation rate, ΔJf was fatigue J-integral range and was ΔJc was creep J-integral range) showed little dependence on temperature. (2) A simple evaluation method of the values of ΔJf and ΔJc in thermal fatigue was proposed. (3) Crack propagation under cyclic temperature could be divided into two types which were cycle-dependent and time-dependent. dl/dN had good correlations with ΔJf and ΔJc for each type, respectively. (4) The transient condition between two types was given by a function of ΔJf and ΔJc. (5) The same fracture mechanics laws were obtained in isothermal and cyclic temperature fatigue.

クリープき裂伝ぱに及ぼす繰返し応力変動の影響

In order to investigate the effect of cyclic stress change on creep crack propagation, deformation tests on smooth specimens and crack propagation tests on notched specimens of 0.16% carbon steel were carried out at 673K (400°C) under a time-dependent fatigue condition.The crack propagation rate in time-dependent fatigue was much faster than that in static creep. It was owing to the acceleration of creep strain rate in the vicinity of crack tip because the dynamic recovery took place in the compression period. In these tests, the effect of the transition from small scale creep to large scale creep was small. The crack propagation rate had fairly good correlation with the experimentally evaluated creep J-integral range, Delta;Jc, which was equivalent to the analytically evaluated creep J-integral range based on the deformation property in time-dependent fatigue.In detail, however, the crack propagation rate in time-dependent fatigue was rather slower than that in static creep for an equal Delta;Jc value. It was concluded to be attributable to the existence of the incubation time of crack propagation during the tensile stress hold time in time-dependent fatigue. The equivalent creep J-integral range, (Delta;Jc)eq, which was the effective component of Delta;Jc for the creep crack propagation rate under a fatigue condition could be evaluated by the following equation;(Delta;Jc)eq=Delta;Jc/γ, γ=1+C11-R/C2+τH, where C1 and C2 are constants, R is the stress ratio, τH is the nondimensional tensile stress hold time.

The effect of one slow-fast strain cycle on the fatigue crack growth behavior of SUS 304 stainless steel at elevated temperature

Fatigue crack growth behavior of SUS 304 stainless steel when one slow-fast strain cycle was introduced to the fast-fast strain cycles was investigated at 600 °C. It was found that the fatigue crack growth rate in the fast-fast strain cycles was accelerated by the introduction of one slow-fast strain cycle. It was also found that there was a linear relationship between the size of the region where the acceleration occurred and the value of creepJ-integral range, ΔJC, which was produced just when one slow-fast strain cycle was introduced. To investigate the above acceleration, the longitudinal section through the specimen was observed. It was shown that the wedge-type cracks were produced at the grain boundaries and that they contributed to the above acceleration. Based on the results thus obtained, the predicting procedure of crack growth curve when one slow-fast strain cycle was introduced to the fast-fast strain cycles was proposed. As the result, it was shown that the predicted crack growth curve was in good agreement with the experimental one.

ＳＵＳ３０４鋼およびＮｉ‐Ｍｏ‐Ｖ鋼の高温低サイクル疲労き裂伝ぱ特性と破壊形態

In order to investigate the behavior of elevated temperature low cycle fatigue crack propagation in Type 304 stainless and 2.5Ni-0.5Mo-0.1V ferritic steels, load-controlled low-cycle fatigue tests were carried out on notched specimens under four kinds of loading waveform (i, e., PP-, PC-, CP- and CC-types).The results obtained were summarized as follows:(1) Type 304 stainless steelThe crack propagation rate, dl/dN, was correlated well with the fatigue J-integral range, ΔJf, in P-type (i, e., PP- and PC- types) fatigue tested at 973K and 823K. The striations, of which width was found to be nearly equal to dl/dN, were observed on their fracture surfaces.On the other hand, dl/dN in C-type (i. e., CC- and CP-types) fatigue tested at 973K was correlated well with the creep J-integral range, ΔJc. The fracture mode in this case was of intergranular type. However, good correlation of dl/dN with ΔJc as well as ΔJf wasn't obtained in C-type fatigue at 823K, where the fracture mode was of mixed (i, e., intergranular and transgranular) type. This appeared to be caused by creep-fatigue interaction.(2) Ni-Mo-V steelIn the same way of the above stainless steel, dl/dN in P- and C-type fatigue at 823K were correlated well with ΔJf and ΔJc, respectively. However, there was no difference in fracture mode between these two types, both of which exhibited the transgranular fracture mode.

高温におけるＳＵＳ３０４ステンレス鋼のＦａｓｔ‐Ｆａｓｔ型疲労き裂の進展挙動に及ぼす１サイクルのＳｌｏｗ‐Ｆａｓｔひずみの導入の影響

The fatigue crack growth behavior of SUS 304 stainless steel when one slow-fast strain cycle was introduced to the fast-fast strain cycles was investigated at the temperature of 873K. It was found that the fatigue crack growth rate in the fast-fast strain cycles was accelerated by the introduction of one slow-fast strain cycle. It was also found that there was a linear relationship between the size of the region where the above acceleration occurred and the value of creep J-integral range which was produced just when one slow-fast strain cycle was introduced. The distribution of hardness just below the fracture surface, where the above acceleration occurred, was similar to the one in the pure slow-fast strain cycle fatigue. From the results thus obtained, it was thought that the one slow-fast strain cycle affected the stress-strain field at the crack tip and contributed to the acceleration of crack growth rate.