RPG Load Research Articles

G0301101 き裂進展を考慮したスポット溶接部の疲労寿命解析(第1報,スポット溶接部の疲労き裂アスペクト比の計測)

Although resistance spot welded joints are widely applied for fabrication of the monocoque body of cars, fatigue strength of the joints are less than the base materials in general. It is very important for satisfying the structural integrities of car bodies to evaluate the fatigue performance of spot welded joints. On the other hand, the S-N curves approach for the fatigue life prediction, which is commonly applied in the structural design stages, cannot give the fatigue crack growth history. Therefore, the fracture mechanics approach for estimating the fatigue crack growth history is expected. Improved effective stress intensity factor range based on the RPG load criterion and the numerical simulation method of fatigue crack growth which consider the fatigue crack opening and closing behaviour of the crack proposed by authors' group can be powerful method to estimate fatigue crack growth history under arbitrary loading sequences. This procedure could be applied not only a through thickness crack but also surface cracks from a sound stress concentration part. However, the changing manner of aspect ratio of a surface crack, which corresponds to the relationship between the aspect ratio and the dimensionless crack depth, must be given in advance. The aspect ratios of a fatigue surface crack occurred at the spot welded toe in SPCC270, SPCD270 and SPC440 steels, which are commonly applied for car bodies, during the growth were measured and confirmed the characteristics of behaviour of the aspect ratio for spot welded joints.

Experiment and Analysis of Influence of Ultrasonic Peening on Fatigue Life in Pad Welded Joint

Effects of ultrasonic peening on fatigue life of pad welded joint were analyzed by fatigue life analysis method by RPG load. It's noted that the ultrasonic peening is one of the most effective method for improving fatigue life of welded joint. Ultrasonic Impact Treatment, UIT, was adopted in this study as the ultrasonic peening method. A significant increase in fatigue life was observed on the pad welded joint with UIT treated weld toe. The improvement was estimated mainly due to compressive residual stress introducing, stress concentration reducing and grain refining in weld toe area. Estimated fatigue life by FLARP was consistent with experimental result.

3529 応力比が疲労き裂進展特性に及ぼす影響のRPG荷重による解析(S14-2 FLARPによる疲労き裂発生伝播シミュレーション(2),S14 FLARPによる疲労き裂発生伝播シミュレーション)

3529 応力比が疲労き裂進展特性に及ぼす影響のRPG荷重による解析(S14-2 FLARPによる疲労き裂発生伝播シミュレーション(2),S14 FLARPによる疲労き裂発生伝播シミュレーション)

3538 重ね継手の疲労寿命に及ぼす超音波ピーニングの影響のFLARPによる解析(S14-4 FLARPによる疲労き裂発生伝播シミュレーション(4),S14 FLARPによる疲労き裂発生伝播シミュレーション)

Effects of ultrasonic peening on fatigue life of pad welded joint were analyzed by fatigue life analysis method by RPG load. It's noted that the ultrasonic peening is one of the most effective method for improving fatigue life of welded joint. Ultrasonic Impact Treatment, UIT was adopted in this study as the ultrasonic peening method. A significant increase in fatigue life was observed on the pad welded joint with UIT treated weld toe. The improvement was estimated mainly due to compressive residual stress introducing, stress concentration reducing and grain refining in weld toe area. Estimated fatigue life by FLARP was consistent with experimental result.

3530 RPG荷重決定のためのヒステリシスループ測定条件の考察(S14-2 FLARPによる疲労き裂発生伝播シミュレーション(2),S14 FLARPによる疲労き裂発生伝播シミュレーション)

3530 RPG荷重決定のためのヒステリシスループ測定条件の考察(S14-2 FLARPによる疲労き裂発生伝播シミュレーション(2),S14 FLARPによる疲労き裂発生伝播シミュレーション)

A Study on Plastic Shrinkage Coefficient of Crack Opening/Closing Model at a Crack Extension

In the previous paper, we developed a simulation model of fatigue crack opening and closing phenomena for predicting RPG load under an arbitrary stress distribution field. By using the simulation model, effects of stress ratio and residual stress distribution on fatigue crack propagation rate are quantitatively assessed. However, it became clear that the estimated fatigue life is longer than experimental one under decreased maximum load while keeping minimum load and a overload condition.In this paper, we considered the plastic shrinkage at an immediate generation of new crack surface for the purpose of solving the above problem and modified the above simulation model. And then, we carried out fatigue crack propagation analyses under various conditions and compared the estimated RPG loads and crack growth curves with the experimantal ones. As a result, it is confirmed that modified simulation model is appreciable to various amplitude fatigue loading tests.

Physical meaning of ΔKRP and fatigue crack propagation in the residual stress distribution field

Previous papers have shown ΔKRP to be a useful parameter describing fatigue crack propagation behavior, where ΔKRP is an effective stress intensity factor range corresponding to the excess RPG load (re-tensile plastic zone's generated load) in which the retensile plastic zone appears under the loading process. In this paper, the relationship between ΔKRP and the zone size (ω̃) (which is smaller between the tensile plastic zone at maximum load and the compressive plastic zone at minimum load) was investigated using a crack opening/closing simulation model so as to consider a physical meaning of ΔKRP. As a result, it becomes clear that ΔKRP dominates the zone size ω̃ where fatigue damage mostly occurs. This result supports the following crack propagation equationdadN=C(ω̃)mwhere C and m are material constants.Simulation and fatigue crack propagation tests were then carried out for compact tension (CT), center cracked tension (CCT) and four points bend (4PB) specimens under constant amplitude loading to obtain C and m values for HT-50 steel. Fatigue crack propagation tests were also carried out under constant amplitude loading using CCT specimens with residual stress distribution due to flame gas heating at the center line or edge lines. The T specimen introduced tensile residual stress at the tip of a notch, and the C specimen introduced compressive residual stress. It therefore becomes clear that tensile residual stress leads to a decrease in RPG load, while compressive residual stress leads to increase in RPG load, and that the simulation results are in good agreement with the experimental RPG load. It also becomes clear that simulated crack growth curve using the simulated ω̃ and the above equation is in good agreement with the experimental curve. It is understood that tensile residual stress creates only a slight increase in crack propagation rate and compressive residual stress create a big decrease a crack propagation rate.

疲労き裂先端ひずみ変化の詳細観察

It is well known that the crack opening/closure phenomenon found by Elber plays an important role in the fatigue crack propagation behavior under any kind of loading condition. On the other hand, the retensile plastic zone's generated load (RPG Load) was newly proposed by Toyosada as for a fatigue crack propagation parameter in place of the crack opening/closure load. However, the accuracy of usual measurements seems to be not sufficient to discuss the fatigue crack opening/closure phenomenon quantitatively.In this paper, for the purpose of proper understanding of the fatigue crack opening/closure phenomenon, a detailed observation of change in strain near the fatigue crack tip was carried out. And successful measurement of the hysteresis curve of load vs. strain (ε') with high accuracy was made. By introducing the curve of compliance (dε'/dp) and the change rate of compliance (d2ε'/dp2) during one cycle, the following conclusions have been obtained.1) The unloading part of the hysteresis curve is found to be “S” shape, and the point of inflection of the unloading part is considered to be the crack closure point as Nisitani pointed out. So if the accuracy of measurement is high enough to be able to obtain a smooth curve of compliance, the crack closure point can be measured automatically as the maximum point of the unloading part of this curve.2) The loading part of the curve of compliance is found to be “S” shape, and the point of inflection of the loading part is considered to be the RPG point. So if the accuracy of measurement is high enough to be able to obtain a smooth curve of the change rate of compliance, the RPG point can be measured automatically as the minimum point of the loading part of this curve.3) Even though the accuracy of measurement is high, it seems to be difficult to measure automatically the crack opening point, because it shows no distinguished feature.

疲労き裂伝ぱを律するパラメータに関する考察

It is generally believed that ΔKeff is the most appropriate parameter which controls the fatigue crack propagation rate. On the other hand, the difference of the crack closing load from the crack opening load or the difference of the re-tensile plastic zone's generated load (RPG Load) from the crack opening load was also pointed out. However, the accuracy of usual measurements seems to be not sufficient to discuss quantitatively the above mentioned difference, in other words, the superiority of one of the fatigue crack propagation parameters ΔKop, ΔKcl, and ΔKRP.Under this background, successful measurement of the change in strain near fatigue crack tip with high accuracy was made in our previous report, and in this paper, matured consideration on the fatigue crack propagation parameter on the basis of the experimental results was carried out. From dividing the loading and unloading processes into several characteristic areas on the basis of the tendency which the compliance and the change rate of compliance show, the following observations have been obtained as conclusions.(1) In the unloading process, it seems to be impossible to isolate the area corresponding to the creation of the re-compressive plastic zone and there is also doubt about using the stress intensity factor because of the influence of crack closing. So it seems to be rational to adopt the area in the loading process, corresponding to the creation of the re-tensile plastic zone, for the fatigue crack propagation parameter.(2) According to the experimental results, it is clear that the re-tensile plastic zone's generated point disagrees with the crack opening point.(3) From the facts described above (1) & (2), it may be concluded that ΔKRP, not ΔKop nor ΔKcl, is considered the most suitable parameter which controls the fatigue crack propagation.

Physical meaning of ΔKRP and assessment of fatigue crack propagation life for structures

In the previous paper, we showed that logarithmic curve of da/dNΔKRP was linear even in the range of stage I as well as stage II of a long crack. Moreover we developed the simulation model of fatigue crack opening and closing phenomena in an arbitrary stress distribution field for the purpose of obtaining RPG load. By using the simulation model, effects of stress ratio and delayed retardation on fatige crack propagation are quantitatively assessed.In this paper, for the purpose of understanding the physical meaning of ΔKRP, the relation between ΔKRP and the zone size (ω) which is smaller size between tensile plastic zone at maximum load and compressive plastic zone at minimum load in one loading cycle is investigated by using the simulation model. As a result, it becomes clear that ΔKRP represents indirectory the zone size 63 recieving fatigue damage ahead of a crack.On the other hand, the equivalent distribution stress is introduced for the estimation of fatigue crack propagation life in complex elements, which is difined as stress distribution in an infinitely wide plate giving the same K value in the elements. Then fatigue life is assessed by using the simulation program inputting the equivalent distribution stress. Estimated fatigue life is good agreement with experimental one under constant amplitude loadings and storm model loadings. However estimated fatigue life is longer than experimental one under overload condition.

The significance of RPG load for fatigue crack propagation and the development of a compliance measuring system : M. Toyosada & T. Niwa, International Journal of Fracture, 67(3), 1994, pp 217–230

In can be postulated that fatigue crack does not grow if no damage occurs in the vicinity of the crack tip. Damage may occur beyond the Re-tensile Plastic zone's Generated load (RPG load) in the vicinity of a crack tip under loading process. We propose an effective stress intensity factor range (Δ K RP) corresponding to the period in which the re-tensile plastic zone appears, in place of ΔK eff proposed by Elber [1], for a fatigue crack propagation parameter. We then consider the small change of compliance for a cracked body under cyclic loading, for the purpose of measuring RPG load as well as crack opening load and crack closing load. Moreover a subtraction circuit which can measure the small change of compliance during fatigue test is developed and an automatic controlled system which can control the adequate values of resistance in the circuit and the output voltage range from strain amplifiers for minimizing relative noise level is also developed. Then fatigue crack propagation tests of CT specimens were carried out with various stress ratios of constant amplitude loadings. Moreover ΔK th tests with the conditions of constant stress ratio and constant maximum load with increasing stepwise minimum load were also carried out. It becomes clear that the logarithmic curve of ΔK RP—crack propagation rate appears to be linear in a wide range from the region of very slow growth rate to the region of stable growth rate. On the other hand, threshold phenomenon appears only circumstantially due to the particular loading pattern on ΔK eff based on the crack opening load and ΔK eff cl based on the crack closing load. Moreover ΔK RP gives the quantitative effect of stress ratio on fatigue crack propagation rate.

Fatigue Crack Propagation Behavior in the Field of Residual Stress Distribution

In the previous paper, a simulation model of fatigue crack opening and closing phenomena in an arbitrary stress distribution field for the purpose of obtaining RPG load is shown.From the calculation and experimental results of RPG load, the effects of stress ratio and delayed retardation on fatigue crack propagation are quantitatively assessed. Moreover it becomes clear that the stopping condition of fatigue crack propagation is ΔKRP≤0.In this paper, fatigue crack propagation tests in residual stress distribution field are carried out. Two types of center notched specimens are prepared : one is that gas heating is made at the center line of the specimen which leads to tensile residual stress field in the middle part of the specimen, the other at near the edges of the specimen which leads to compressive residual stress field in the middle part of the specimen. It becomes clear that tensile residual stress descends RPG load and compressive residual stress raises RPG load. Moreover if the large compressive residual stress exists, crack closes even when tensile yield zone generates at the crack tip under loading process. In this case, plastic zone could not grow until crack becomes fully open.Simulated RPG load is in good agreement with experimental one even in the field of residual stress distribution. And compressive residual stress has a large effect of decreasing the fatigue crack propagation rate. These effects can be successfully estimated by the simulation model.

The significance of RPG load for fatigue crack propagation and the development of a compliance measuring system

In can be postulated that fatigue crack does not grow if no damage occurs in the vicinity of the crack tip. Damage may occur beyond the Re-tensile Plastic zone's Generated load (RPG load) in the vicinity of a crack tip under loading process. We propose an effective stress intensity factor range (Δ K RP) corresponding to the period in which the re-tensile plastic zone appears, in place of ΔK eff proposed by Elber [1], for a fatigue crack propagation parameter. We then consider the small change of compliance for a cracked body under cyclic loading, for the purpose of measuring RPG load as well as crack opening load and crack closing load. Moreover a subtraction circuit which can measure the small change of compliance during fatigue test is developed and an automatic controlled system which can control the adequate values of resistance in the circuit and the output voltage range from strain amplifiers for minimizing relative noise level is also developed. Then fatigue crack propagation tests of CT specimens were carried out with various stress ratios of constant amplitude loadings. Moreover ΔK th tests with the conditions of constant stress ratio and constant maximum load with increasing stepwise minimum load were also carried out. It becomes clear that the logarithmic curve of ΔK RP—crack propagation rate appears to be linear in a wide range from the region of very slow growth rate to the region of stable growth rate. On the other hand, threshold phenomenon appears only circumstantially due to the particular loading pattern on ΔK eff based on the crack opening load and ΔK eff cl based on the crack closing load. Moreover ΔK RP gives the quantitative effect of stress ratio on fatigue crack propagation rate.

Phenomena of Delayed Reterdation and Crack Stopping Condition for a Long Fatigue Crack

Fatigue crack propagation tests with various stress ratios and stepwise decreasing maximum load while keeping minimum load are carried out for center notched tension specimens. In these tests, RPG load (Re-tensile Plastic zone's Generated load), crack length and number of cycles are measured by using our newly developed measuring system in the 1st report.We also calculate RPG load by using our developed simulation model of crack opening/closing phenomena based upon Dugdale model in the 5th report with various shrinkage coefficients α of plastic deformation due to emancipate internal force in newly generated crack surface at an immediate crack growth. Then we obtain α value for the steel used with comparing between simulated RPG load and measured one for the testing condition of R=0.05. By using the obtained α value, RPG loads for other stress ratios (R=0.3 and 0.5) are calculated by using the simulation model. As a result, simulated RPG loads are in very good agreement with measured RPG loads for R=0.3 and R=0.5.Then a crack growth curve for each testing condition is calculated by using ΔKRP from simulated RPG load and also shows in very good agreement with measured crack growth curve for each stress ratio.RPG load increases just after decreasing maximum load and reaches maximum and then decreases gradually as a crack advances in the cases of decreasing load with small magnification. Then delayed deterdation effects appear and delayed life increases with larger decrement of maximum load. It is also comfirmed that simulated RPG load using above α value is in good agreement with measured RPG load for these cases. It becomes also clear that crack growth curve in case of decreasing maximum load can be assessed quantitatively by using ΔKRP based upon the simulated RPG load.Moreover it is confirmed that larger decrement of maximum load in stepwise loading leads to stopping a crack even when final maximum load with large decrement of maximum load is larger than RPG load. This is because RPG load increases rapidly just after decreasing maximum load and approaches to final maximum load in case of large decrement of maximum load both in experiments and simulations. Simulated crack growth curve by ΔKRP using calculated RPG load in this case is also in good agreement with experimental one.Therefore it can be expressed that the condition of stopping a crack is ΔKRP_??_0 for a long crack. In other word, it becomes clear that ΔKth or (ΔKeff)th is not a material constant.

Simulation of RPG load

Newman showed crack opening/closing model during fatigue crack propagation under uniform stress field which was based on the Dugdale model, but modified to leave plastically deformed materials along the crack surface as the crack advances. In his model, however, he neglected the change of stress distribution ahead of a crack during loading process in the calculation of crack opening load. Moreover he also neglected the elastic deformation for a materials along the crack surface. Therefore he introduced plastic constrainted factor of 3.5 which was larger than the appropriate value of 1.21 obtained from comparison between COD's by elasto plastic FEM and those by Dugdale model for center notched specimens for the purpose of fitting experimental crack opening load.In this paper, Newman's model is modified to solve his neglected problems mentioned above and is expanded to arbitrary stress distribution field for the purpose of obtaining re-tensile plastic zone's generated load (RPG load). Moreover we consider plastic shrinkage at newly generated fracture surface during unloading process which corresponds to a part of deformation due to emancipation of acting force with a magnification of yield stress at an immediate growth of a crack in the region of fictitious crack in Dugdale model.Some calculation results are shown for understanding the effect of the plastic shrinkage at newly generated surfaces and the change of loading. Simulated results suggest that the effect of stress ratio and the effect of delayed reterdation due to decreasing maximum load become small as the plastic shrinkage becomes large.

Assessment of Fatigue Life for a Crack Emanated from a Notch -Algorithm of Fatigue Life Assessment by ΔKRP Approach without Distinguishing between the Crack Initiation and the Propagation-

In the previous paper, we showed that logarithmic curve of ΔKRPda/dN was linear even in the ranges of stages I and II of a long crack. In other words, threshold phenomenon appears only circumstantially due to applying ΔK or ΔKeff which involve the term not related to the crack extension force such as elastic deformation in addition to the term related to the crack driving force.In this paper, we carried out fatigue crack initiation/propagation test for CT specimens with a notch of root radius 1 mm. Fatigue cracks initiated in the mid-thickness at a notch root as surface cracks. Having considered the change of an aspect ratio of surface cracks before and after coalescence from previous studies for a surface crack propagation and a change of measured RPG load (Re-tensile Plastic zone's Generated load), it was confirmed that the logarithmic curve of ΔKRPda/dN for a physically small crack of which the length was greater than one microstructural grain size and smaller than a uniform through-thickness crack was in good agreement with that for a long crack.Moreover, for a microstructural short crack which is less than one grain size, it is postulated that dislocations do not exceed beyond barriers such as a grain boundary and a pearlite zone in a ferritepearlite microstructure when loading range appearing tensile plastic zone keeps constant. Then, the equivalent ΔK value is obtained from a plastic zone size. Therefore, from the measured RPG load, equivalent ΔKRP is defined for a microstructural short crack, relating that ΔKRP represents compressive plastic zone at minimum load for a long crack. By using equivalent ΔKRP for a microstructural short crack and ΔKRP for a physically small crack and a long crack, crack propagation curves are calculated for a crack emanated from a notch root without distinguishing between crack initiation and propagation. The calculated crack propagation curves are in very good agreement with experimental ones.These results indicate that the fatigue life can be prolonged if the grain size is made small. However, we might not be able to expect any drastic improvement if the maximum grain size is greater than about 10 μm. Moreover qualitative studies were also made for the phenomenon about stopping crack and coaxing effect by using the algorithm.

Fatigue crack propagation law for wide range from very slow crack growth rate region to stable crack propagation rate region

In the first report, we proposed a fatigue crack propagation parameter ΔKRP from the view point of the appearance of cyclic tensile plastic zone at a crack tip in replace of ΔKeff based upon the crack opening load. Moreover the automatic measuring system was developed for the purpose of obtaining the re-tensile plastic zone's generated load (RPG load) as well as crack opening load and crack closing load during fatigue crack propagation.In this report, fatigue crack propagation tests of CT specimens were carried out with various stress ratios of constant amplitude loadings. Moreover ΔKth tests with the conditions of constant stress ratio and constant maximum load with increasing stepwise minimum load were also carried out. These tests were conducted by using above developed system. It becomes clear that ΔKRP gives the quantitative effect of stress ratio on fatigue crack growth rate and the relation of logarismic ΔKRP and logarismic crack propagation rate appears to be linear in the wide range from very slow crack growth rate region to stable crack growth region.On the other hand, threshold phenomenon appears only circumstantially due to the paticular loading pattern on ΔKeff based on the crack opening load and ΔKeffcl based on the crack closing load.