Surface Small Cracks Research Articles

An evolutionary analysis method for small cracks in drive shafts based on cross-scale modeling

Due to the significant scale and complex operating conditions of drive shafts, experimental analysis of small crack evolution becomes challenging. This study presents a cross-scale modeling approach to analyze the evolution of small cracks in drive shafts. Firstly, by employing the sub-model method and the variable-node finite element method, two mesoscale models based on crystal plasticity theory are integrated into a macroscale model, constructing a cross-scale analysis model for small crack evolution. Then, by measuring the heterogeneous deformation degree in the mesoscale models, models for surface small crack initiation and propagation, accounting for heterogeneous deformation, are developed. Besides, energy-based models for internal small crack nucleation and propagation are established. To simulate the initiation and propagation of surface small cracks, the study utilizes a mesoscale variable-node shell model incorporating the Crystal Plasticity Finite Element Method (CPFEM), coupled with the Crystal Plastic Coupling Extended Finite Element Method (CP-XFEM). From the simulation results, a cross-section of the mesoscale solid model is extracted to establish a polycrystalline plasticity mesoscale cross-section model. Then, utilizing the element deletion method in ABAQUS, simulations for internal small crack nucleation and propagation are performed. The findings demonstrate that the cross-scale model effectively reflects the irregular propagation rate of microscopic small cracks. The propagation patterns of surface small cracks are generally consistent, with more significant path deviations observed in models exhibiting significant grain orientation differences. In the latter stages of internal small crack propagation, as the number of failed grains rises, stress concentration in the microstructure intensifies, resulting in a significant acceleration phase in crack propagation and a significant decrease in propagation life.

Estimating the fatigue behaviour of welded joints

The present work is concerned with an attempt to predict the fatigue strength of welded joints by means of a fracture mechanics approach that takes into account the fatigue behaviour of short cracks. The methodology estimates the fatigue crack propagation rate as a function of the difference between the applied driving force and the material threshold for crack propagation, a function of crack length. The fatigue strength of butt-welded specimens stressed transversely was analyzed. Experimental results from the literature were used for comparisons. Good estimations are obtained by using only the fatigue limit and the fatigue propagation threshold for long cracks corresponding to the base metal, and the applied stress distribution along the crack path obtained from simple FE models. The influence of parameters like plate thickness, initial crack length and reinforcement angle on fatigue strength of butt-welded joints can be analyzed and results have shown good agreement with experimental results and trends. In order to verify the ability of the methodology to estimate the fatigue behaviour of welded joints, a dedicated experimental methodology had to be implemented for the detection and monitoring of the development of surface small cracks initiated at weld toes. Some results of a multi-strain gauges technique implemented for those purposes are also shown.

ＳＵＳ３０４の内部き裂型クリープ疲労粒界破壊 表面き裂型との相違

Creep-fatigue tests of a Type 304 stainless steel are conducted and cracking behavior is observed. The results obtained are summarized as follows; Intergranular fracture under creep-fatigue conditions at high temperatures is classified into inner cracking type and surface cracking one. The crack initiation inside of a specimen in the former type is caused by the growth and coalescence of grain boundary diffusive cavities and the fracture is brougth about by the coalescence of distributed small cracks at the final stage of life. On the other hand, the cracks at the surface in the latter type is attributed to the grain boundary sliding and the fracture is caused by the growth of surface small cracks. The inner cracks tend to appear at lower tensile strain rate, at higher compressive strain rate, and at higher temperature. A fracture mechanism map is proposed on the basis of the experimental observation.

Surface small crack growth behaviour in low-cycle fatigue at elevated temperature and application limit of macroscopic crack growth law: Okazaki, M., Yada, T. and Endoh, T. Nucl. Eng. Des. Jan. (II) 1989 111, (1), 123–134

This is the third of three papers generated from a recent study on crack-opening-area analysis of circumferentially cracked pipes for leak-before-break applications. The first two papers1, 2[Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part I—Analytical models. International Journal of Pressure Vessels and Piping, (this issue). Rahman, S., Brust, F. W., Ghadiali, N. and Wilkowski, G., Crack-opening-area analyses for circumferential through-wall cracks in pipes. Part II—Model validations. International Journal of Pressure Vessels and Piping, (this issue).] dealt with crack-opening-area analysis of pipes assuming simple loading, pipe and crack geometries, and boundary conditions. This paper (Part III—Off-center cracks, restraint of bending, thickness transition, and weld residual stresses) examines several practical aspects of crack-opening-area analysis involving off-center cracks, restraint of pressure-induced bending, girth-weld nozzle cracks at thickness transition, and weld-induced residual stresses. Currently, there are no engineering methods or guidelines available to analyze pipes under these conditions. Both linear-elastic and elastic–plastic finite element analyses were conducted to determine quantitatively their effects on various crack-opening characteristics. From the results of these analyses, recommendations are made on how an off-center crack can be analyzed based on fracture-mechanics equations for a centered crack. It was found when the restraint of bending effects become important and how they should be taken into account. Cracks located in the thickness transition with thickness gradients on both sides of a nozzle girth weld were analyzed. Finally, simplified finite element simulations were performed to determine if the residual stresses should be considered and when they become important for crack-opening evaluations.

Surface small crack growth behavior in low-cycle fatigue at elevated temperature and application limit of macroscopic crack growth law

Surface small crack growth behavior of Type 304 stainless steel in low cycle fatigue under fast-fast and slow-fast cyclings was investigated at a temperature of 873 K, by means of the smooth specimens with various grain sizes. It was shown that once the small cracks had grown up to a few grains size, they predominantly propagated with strain cycling, while most of small cracks stopped propagating when they grew up to one grain size. It was also shown that the small crack growth rate significantly slowed down where the crack length was integral multiple of the grain size. Above behavior resulted from the grain boundaries temporarily impeding the small crack growth. The crack length below which the grain boundaries affected the small crack growth rate was also given as function of the relative length to the grain size. Furthermore, the small crack growth rate was compared with the macroscopic crack growth one. In fast-fast cycling, the small crack growth rate was about ten times as large as as the macroscopic crack growth one where its length was comparable to the grain size. Based on the results thus obtained, the application limit of macroscopic crack growth law to the surface small crack growth was discussed. The macroscopic crack growth law was not applicable to the small crack growth, until the crack length was about ten times average grain size in fast-fast and slow-fast cyclings.

Surface Small Crack Growth Behavior of Type 304 Stainless Steel in Low-Cycle Fatigue at Elevated Temperature

Surface small crack growth behavior of Type 304 stainless steel during low cycle fatigue under fast-fast and slow-fast cyclings was investigated at a temperature of 873 K by using the smooth specimens which had the different grain sizes. It was shown that the crack, which had already grown up to a few grain size, predominantly propagated with strain cycling, and that it was very important for the safety assessment of the components in service to detect the crack of a few grain sizes. It was also shown that small crack growth rate showed the minimum when they arrived at the grain boundaries. Above behavior resulted from that the grain boundaries temporarily impeded the small crack growth. The crack length below which the grain boundaries notably affected the small crack growth rate was also given as the function of relative length to the average grain size. Furthermore, the small crack growth rate was compared with the macroscopic crack growth one. In fast-fast cycling, the small crack growth rate was about ten times as large as the macroscopic crack growth one, where its length was comparable to the grain size. Based on the results thus obtained, the application limit of macroscopic crack growth law to the surface small crack growth was discussed. The application limit proportionally increased with the grain size, and it was about ten times average grain size in both fast-fast and slow-fast cyclings.

ＳＵＳ３０４鋼のクリープ・疲労条件下の高温低サイクル疲労における微小表面き裂の進展挙動

The surface small crack growth behavior of SUS304 stainless steel under fast-fast and slow-fast strain controlled low-cycle fatigue conditions was investigated at 873K with the specimens having different grain sizes. It was shown that the cumulative probability of crack length distribution in both fast-fast and slow-fast cyclings could be represented by a Weibull distribution as a function of crack length in the early stage of fatigue life. In the stage after the half fatigue life, the cumulative probability of crack length distribution showed a knee, and a small number of main cracks grew predominantly. The knee occurred when the crack length was comparable to one grain size. It was also shown that the surface small crack growth rate showed the minimum value when the cracks arrived at the grain boudaries. The above behavior resulted from that the grain boundaries temporarily impeded the small crack growth. Furthermore, the small crack growth rate was compared with the macroscopic crack growth rate. The law for the macroscopic crack growth was applicable to the small crack growth in slow-fast cycling, up to the crack length being one grain size. On the other hand, the small crack growth rate in fast-fast cycling was about ten times as large as the macroscopic crack growth rate in the region where the crack length was smaller than or comparable to the grain size.

ＳＵＳ３０４鋼の高温低サイクル疲労における微小き裂の発生と初期成長の観察

An accurate prediction of fatigue fracture at elevated temperatures depends on the elucidation of the small crack initiation and propagation behavior. Experimental studies on the small cracks, however, have been quite limited. In this study, two types of high-temperature low-cycle fatigue tests, C-P type of a trapezoidal stress waveform with tension hold and P-P type of a high-frequency triangular stress waveform, were conducted by using smooth specimens of 304 stainless steel, and the behavior of initiation and early growth of surface small cracks was observed continuously during the tests with a high-temperature microscope. Furthermore, a detailed study was made by the interrupted tests with the replicas or scanning electron microscopy. The results obtained are summerized as follows. (1) The crack of C-P type fatigue initiates at a grain boundary between two triple points as it opens uniformly and gradually. (2) The crack growth to the adjacent grain boundary in the early stage of C-P type fatigue is caused through the same process as the crack initiation, showing a stepwise and discontinuous manner. (3) The process mentioned at (1) is the process of growth and coalescence of voids on the grain boundary owing to the grain boundary sliding. (4) The crack initiation of P-P type fatigue takes place at the intersection of slip bands and a grain boundary, and most of the cracks propagate along the grain boundaries in the early stage of fatigue. (5) The crack growth rate of P-P type fatigue decreases suddenly when the crack tip comes near to the triple point. (6) The fracture mechanisms of C-P type fatigue and P-P type fatigue are quite alike to that of creep and that of low cycle fatigue at room temperature, respectively.

Growth of small crack and an evaluation of life based on its property in low cycle fatigue.

The smooth specimen of JIS S35C and SNCM 439 steels, which were heat-treated in several conditions, were low-cycle fatigued. Then, the growth rate of surface small crack, da/dN, was analyzed in terms of the cyclic J-integral range, ΔJ, and the strain intensity factor range, ΔKe. The crack growth rates plotted against ΔJ and ΔKe are approximately expressed by linear lines on a log-log diagram. The considerable scatter inherent in problems of a small crack, however, almost cover the small difference in the crack growth property among materials. As a result, the universal equations can be established for da/dN vs. ΔJ and da/dN vs. ΔKe relations, independently of kinds of materials used. The equations derived from combining the above two relations with the cyclic stress-strain curve describe well the fatigue life curve which bends downwards in the regime of the lower plastic strain range in materials of a high strength and low ductility as well as usual Coffin-Manson plots.