Creep behavior and life assessment of anisotropic bicrystals with a void and without void in different kinds of grain boundaries

Based on crystallographic theory, a creep constitutive relationship and a life predictive model have been presented. The crystallographic creep constitutive relationship has been implemented as a user subroutine ’CRPLAW' to MACR. Bicrystal models containing a void in the grain boundary and bicrystal model without void have been studied by the finite element method. Different loading direction has been studied in order to show the influence of relative direction of loading to grain boundary on the creep behavior of the bicrystals. The numerical results of bicrystal models show that there are a high stress gradient and stress concentration near the void and grain boundary. The existing of the void has strong influence on creep durability life of the crystal. The stress distribution and creep strain characterization are dependent on the crystallographic orientations of the two crystals and the grain boundary direction as well as the existing of the void and loading directions. It is shown that the bicrystal model of the loading direction perpendicular to the grain boundary has the highest creep strain and creep damage, while that model of the of the loading direction parallel to the grain boundary has the minimum. This above conclusion is also same to the growth of void.     

Self-consistent Constitutive Modeling of the Creep Damage Behaviour of Nickel-base Directionally Solidified Superalloys with Different Grain Orientations

A self consistent creep damage constitutive model is developed for nickel-base directionally solidified superalloys. Grain degradation and grain boundary voiding are considered. The model parameters are determined from the creep test data of single crystal and directionally solidified superalloy with a special grain orientation. The numerical analysis shows that the model creep damage behaviours of nickel-base directionally solidified superalloys with difFerent grain orientations are in good agreement with the experimental data.     

CREEP LIFE OF AISI 316 STAINLESS STEEL SUBJECTED AT 550°C TO STEP CHANGES IN TENSILE LOAD

Abstract— A phenomenological model of cumulative creep damage combining simulated grain boundary cavitation with internal redistribution of stress is developed and matched to constant load tensile creep data for an AISI 316 stainless steel tested at 550°C. The model is shown to predict the creep life of the material when it is subjected to single step changes in load provided the strain rates subsequent to the change are imposed in the model. It is inferred that this supports current suggestions that cavitation failure may be strain controlled.     

The effect of the diffusion creep behavior on the TSV-Cu protrusion morphology during annealing

As through-silicon vias (TSVs) are key structural elements of 3D integration and packaging, creep deformation, which causes TSV-Cu protrusion, is critical for TSV reliability. Here, the effect of the diffusion creep behavior on the TSV-Cu protrusion morphology is analyzed using experiment and simulation. The protrusion morphology of TSV-Cu after annealing treatment is examined using a white light interferometer. The diffusion creep mechanism of TSV-Cu is determined by observation of the TSV-Cu microstructure using a scanning electron microscopy and a focused ion beams. The TSV-Cu grain size is measured using an electron backscatter diffraction system. The diffusion creep rate model of TSV-Cu is deduced based on the energy balance theory and is introduced into the finite element model to clarify the influence of diffusion creep on TSV-Cu protrusion. It is determined that the diffusion creep of TSV-Cu is mainly caused by grain boundary diffusion and grain boundary sliding. The diffusion creep strain rate is positively correlated with the ambient temperature and the external load but negatively correlated with the grain size. The amount of TSV-Cu protrusion increases with decreasing grain size. The simulation results show that the “donut”-shaped protrusion morphology is more likely to occur in TSV-Cu with smaller grain sizes near the sidewall region of the via.     

A steady-state model for diffusion-controlled fracture

Elevated temperature cracking associated with embrittlement from intergranular diffusion of impurities is studied using cohesive zone model for small-scale creep, diffusion and damage. The constitutive equation for the cohesive zone is coupled with stress-assisted diffusion of impurities into the grain boundary. A Kachanov-type damage model is used to describe the effect of impurity concentration on grain boundary strength. Numerical studies reveal the influence of various material parameters and loading conditions on the cracking process.     

Creep–fatigue life of Sn–8Zn–3Bi solder under multiaxial loading

This paper describes a creep–fatigue life of Sn–8Zn–3Bi solder under multiaxial loading. A push–pull and a reversed torsion tests were carried out using seven types of strain waveforms, which are a fast–fast, a fast–slow, a slow–fast and a slow–slow waveforms and three types trapezoidal strain waveforms with different strain holding times. The strain waveforms had a significant effect on creep–fatigue life and the shortest creep–fatigue life was found in the slow–fast strain waveform while the longest life in the slow–slow waveform in the push–pull and the reversed torsion tests. Creep–fatigue life in the reversed torsion test was approximately twice longer than that in the push–pull test at each strain waveform. Applicability of common used creep–fatigue damage models for life evaluation was discussed based on the obtained experimental results and only a grain boundary sliding model could evaluate the lives within a small scatter.     

Microstructural modelling of creep crack growth from a blunted crack

The effect of crack tip blunting on the initial stages of creep crack growth is investigated by means of a planar microstructural model in which grains are represented discretely. The actual linking-up process of discrete microcracks with the macroscopic crack is simulated, with full account of the underlying physical mechanisms such as the nucleation, growth and coalescence of grain boundary cavities accompanied by grain boundary sliding. Results are presented for -controlled mode I crack growth under small-scale damage conditions. Particular attention is focused on creep constrained vs. unconstrained growth. Also the effect of grain boundary shear stresses on linking-up is investigated through shear-modified nucleation and growth models. The computations show a general trend that while an initially sharp crack tends to propagate away from the original crack plane, crack tip blunting reduces the crack growth direction. Under unconstrained conditions this can be partly rationalized by the strain rate and facet stress distribution corresponding to steady-state creep. This revised version was published online in August 2006 with corrections to the Cover Date.     

Creep damage and grain boundary precipitation in power plant metals

Abstract

There is clear evidence that creep damage in power plant steels is associated with grain boundary precipitates. These particles provide favourable nucleation sites for creep damage such as grain boundary cavities and microcracks. Monte Carlo based grain boundary precipitation kinetics is combined with continuum creep damage mechanics (CDM) to model both the microstructural evolution and creep behaviour in power plant metals. It is found that grain boundary precipitates, such as M₂₃C₆ in most Cr containing ferritic steels, are harmful to the creep properties of the material, in line with experimental observations. It is also found that to improve the creep behaviour of the material, means should be found either to increase the proportion of MX type particles, such as VN, or to decrease or remove the larger grain boundary precipitates, such as M₂₃C₆. Hafnium has been ion implanted into thin foils of a 9 wt-%Cr ferritic steel to study the effect of hafnium on the grain boundary precipitation kinetics. It is found that the implantation of hafnium to the steel completely prohibits the formation of the common grain boundary M₂₃C₆ particles. Instead, two new types of precipitates are formed. One is hafnium carbide, which is an MX type precipitate, and is very small in size and has a much higher volume fraction as compared with the volume fraction of VN in conventional power plant ferritic steels. The other is Cr- and V-rich nitride of formula M₂N. CDM modelling shows that implantation of hafnium can markedly improve the creep property of the material. In addition, the replacement of M₂₃C₆ with hafnium carbide increases the concentration of Cr in the matrix and is expected to improve the intergranular corrosion resistance of the material.     

On the initiation of wedge-type cracks at grain-boundary triple junctions during high-temperature creep

The typical grain boundary cracks are often formed at the grain-boundary triple junction as a result of blocking of grain-boundary sliding. However, a theoretical discussion has not fully been made on the nucleation of grain corner cracks at high temperatures where diffusional recovery occurs. In this study, a continuum mechanics model which incorporated the recovery effect by diffusion of atoms has been developed to explain the initiation of wedge-type cracking during high-temperature creep. A good agreement was found between the result of calculation based on this model and experimental results in austenite steels. It was considered that there is a critical creep rate for wedge-type cracking. The model was also applied to the prediction of the rupture life in creep.     

Local approach applied to creep-fatigue crack initiation and crack growth in circumferentially notched 316L tubes under combined tension and cyclic thermal shocks

This study concerns the application of the local approach to creep-fatigue crack initiation and creep crack growth in components submitted to combined mechanical and thermal loadings leading to intergranular damage. The purpose is to assess the remaining life of a structure with a crack detected during in service inspection or with a geometrical singularity. A new numerical method based on finite element computations and on a damage model relying on quantitative observations of grain boundary damage is proposed. The numerical results obtained are in good agreement with experimental data. They also fit them better than the classical global approach predictions.     

Effects of creep ductility and notch constraint on creep fracture behavior in notched bar specimens

The creep rupture life of U-type notched specimens and smooth specimens has been calculated based on the ductility exhaustion damage model using stress-dependent creep ductility. Effects of creep ductility and notch constraint on creep fracture behaviour in notched bar specimens have been investigated. The results show that the U-type notch exhibits notch strengthening effect under a wide range of stress level and notch constraint condition (notch acuity) for creep ductile materials. The lower equivalent stress in notched specimens plays main role for reducing creep damage and increasing rupture life. The rupture life of notched specimens of creep brittle materials (with lower creep ductility) decreases with the increase in stress level and notch constraint. With increasing creep ductility and decreasing notch constraint, the degree of the notch strengthening effect increases. In creep life designs and assessments of high-temperature components containing notches, the material creep ductility, notch constraint and stress levels need to be fully considered.     

Damage and Residual Life Assessment of Bends for X20CrMoV12.1 Main Steam Pipe after Long-Term Service

The bent sections from a main steam pipe in a thermal power plant in Shanghai were examined after 165,000 h service at 550 °C under 13.73 MPa pressure. The residual life of the bend sections is determined by evaluation of the service stresses and testing to obtain creep rupture data. Metallographic analysis and tensile, impact, and hardness tests are also conducted. These combined tests show that the properties of the steel deteriorated during service, displaying embrittlement tendencies; the corresponding microstructures exhibit grain boundary weakening and creep damage characteristics. However, considering no evidence of localized damage in the form of creep cavitation or surface cracks was observed in the examined parts, considering the residual life of the bends at service condition, they are adequate for an additional 44,000 h of operation. It is recommended that a health assessment should be taken after 25,000 h service exposure for safety reasons.     

On Grain Size Dependence of Minimum Creep Rate

The available experimental results have beensummarized concerning the effect of grain size onminimum creep rate.There are two types of creeprate-grain size relations.One is that there is a criti-cal grain size above which creep rate is independentof grain size,below which creep rate increases withthe decrease of grain size.The other is that there isan intermediate grain size at which creep resistanceis optimum.The first relation usually occurs athigher temperatures(>0.5 T_m),and intermediatestress ranges,while the second relation at interme-diate temperature ranges(0.4-0.5 T_m)and higherstresses.For the two types of creep rate-grain sizerelations,the increase of the creep rates with the de-crease of grain size for small grain sizes is all due tograin boundary sliding.For large grain sizes,a dis-location climb mechanism is dominant in creepdeformation for the first relation,while aHall-Perch grain boundary strengthening effect isbelieved to play an important role by dislocationglide mechanism for the second relation.     

Creep behaviour leading to Type IV cracking for service-exposed 1.25Cr-0.5Mo steel welds

To ensure reliability of elevated temperature components, the creep behaviour of weldment must be predicted since the ultimate failures mostly take place at this tiny region. In the case of low alloy ferritic steels, the most likely failure mode of equipment operated for long hours should be Type IV cracking, which is defined as preferential damage evolution at the Intercritical HAZ (ICZ). Despite the importance of this phenomenon, there have been some uncertainties remained unsolved. In order to elucidate the cause and accelerating factors of Type IV cracking, creep behaviours of cross-weld and the ICZ microstructure have been examined in the present work using service-exposed 1.25Cr-0.5Mo steel.Onset time to Type IV failure significantly reduced when tested by spirally notched cross-weld specimens as a result of concentrated damage accumulation at the root of a vee notch, revealing that multiaxaial stress state could play a key role in Type IV failure.The feature of creep damage suggests that grain boundary damage leading to Type IV cracking is caused by the sliding of grain boundaries around fine grains which are considered to be the products of partial transformation during welding. Heterogeneous damage evolution to the level of facet cracking surrounded by damage free grains raises the fundamental question on the validity of a generally accepted assumption, namely, that stress of grains associated with a grain boundary cavity will be off-loaded. As a matter of fact, a clear evidence that grain boundary cavitation accelerates the strain rate at the tertiary regime has not been observed in creep curves of simulated ICZ specimens, owning a bimodal microstructure expected at the ICZ in whole gauge length.Difference in the susceptibility to Type IV cracking has been found in materials with the same alloying elements and the vulnerability of the ICZ microstructure is not necessarily dependent upon creep strength of parent material.Considerable metallurgical factors to shorten the onset time to Type IV damage and the effectiveness of strain rate measurement as a potential technique for the life assessment shall be discussed.     

Notch effect on creep damage for Hastelloy C276-BNi2 brazing joint

The brazed structures have geometrical discontinuities like fillets working as notches. These notches have great effect on creep crack initiation and propagation. This paper studies the notch effect on creep damage for Hastelloy C276-BNi2 brazed joint, and the effects of notch type, notch radius and notch angle on creep damage have been investigated. The results show that the creep damage initiates in the filler metal. Different notch types bring different stress states, and generate different stress triaxialities and equivalent creep strains (CEEQs), leading to different creep damages. The maximum creep damage is generated in the notch tip for V-type notch, while the maximum creep damage is located at 0.4 mm away from the notch tip for C-type notch. For U-type notch, the location of the maximum creep damage moves from the notch tip to the inside gradually as the notch radius increases. With the increase of notch radius and notch angle, the failure time of creep damage increases for U-type and V-type notches, while it decreases for C-type notch. The creep failure is prone to happen to V-type notch because it belongs to sharp notch.     

A new empirical life prediction method for stress controlled fatigue-creep interaction

Based on the Hull-Rimmer creep cavity growth theory, a new life prediction method is developed taking the equivalent grain boundary cavity radius as a damage parameter. This method is applicable for stress controlled mode. It involves the effects of fatigue, static creep and cyclic creep during the fatigue-creep interaction. By employing this method, the fatigue-creep life is assessed for 1.25Cr0.5Mo steel at 520 °C and 540 °C. The predicted lives are compared with the tested ones and a good agreement is found between them.     

Analysis of the coupled effect of plastic damage and creep damage in nimonic 80A at finite deformation

The coupled effect and the anisotropic feature of plastic damage and creep damage in Nimonic 80A are analysed with special emphasis on the finite deformation and the material spin of the damaged material. In view of that both the plastic and the creep damage are governed by the formation of grain boundary cavities, it is first assumed that the states of plastic damage and creep damage are represented in terms of symmetric second-rank damage tensors Ω^P and Ω^C, the sum of these tensors Ω = Ω^P + Ω^C represents the damage state of the material. The evolution equations of these variables are established on the basis of the experimental observations on the nucleation and growth of microscopic cavities. The creep constitutive equation of the material, on the other hand, is formulated by taking account of the acceleration due to material damage as well as the material softening caused by the formation of the dislocation network at particle interfaces. Finally, creep damage process at finite deformation of Nimonic 80A at 750°C subjected to prior plastic damage brought about by the plastic prestrain at room temperature is analysed. The numerical results are compared with the corresponding experimental results to discuss the validity of the proposed theory. Though considerable rotation of principal damage direction was observed in the process of torsional creep, its effect on the creep damage process was found to be rather small.     

Application of a model for grain boundary sliding to high temperature flow of carrara marble

It has been demonstrated that grain boundary sliding may contribute up to 50 percent of the total strain during experimental, high temperature deformation of Carrara Marble (Schmid, Paterson and Boland, 1980), yet the creep behavior was characterized by a high stress exponent and an apparent thermal dependence related to volume diffusion of carbon in calcite. By adopting the model of Gifkins (1976, 1977) for dislocation accommodated grain boundary sliding, incorporating Nabarro's model of creep by climbing edge dislocations (Weertman, 1975) and using the experimentally determined relationship between stress and subgrain (recrystallized grain) size, a model is developed which fits the high temperature creep data very well. In effect, the model assumes that deformation occurs by a combination of climb of edge dislocations and dislocation accommodated grain boundary sliding. It is shown that the model can be easily and reasonably extended to include creep by climb-controlled dislocation glide.     

Comparative creep damage assessments using the various models

The creep fracture characteristics of a conventionally cast (CC) MARM-002 superalloy were studied for creep conditions of 1173 K/200–400 MPa using different approaches including the Kachanov-Rabotnov type continuum damage mechanics, grain boundary damage accumulation, and Chen-Argon diffusional cavity growth. A rapid improvement in creep rupture life can be achieved by reducing the Kachanov-Rabotnov damage rate () below a critical value of this rate. It is possible that a large improvement in creep resistance would be made by decreasing grain boundary damage rate rather than continuum damage rate since the minimum creep rate (_m) accelerates rapidly without changing the parameter .     

Application of a mechanism-based creep damage model to creep crack growth in a 12% chromium steel

In creep resistant steels, several mechanisms contribute to the degradation of creep properties under long-time service conditions. Most important are the coarsening of the carbide and subgrain structure and grain boundary cavitation. A mechanism-based creep damage model is developed, including a Chaboche type viscoplastic model¹ for transient creep, the Rodin and Parks model² for cavitation damage and a microstructurally motivated softening equation. The model parameters are adjusted to a set of creep curves for a 12% chromium steel (X20 CrMoV12 1) and to quantitative microstructural measurements. The combined model is implemented in the finite element code ABAQUS. Tests on compact specimens are successfully modeled.