Cavity Growth Model Research Articles

Creep damage evolution by cavity nucleation and growth considering the cavity closure under cyclic loading conditions

AbstractCreep damage assessment is crucial for ensuring the long‐term reliability of key components operating at high temperatures. However, the existing studies on creep damage are mainly focused on constant loading conditions, while the effect of cyclic loading, which is a common loading mode in practice, remains unclear. In this paper, a series of stress‐controlled cyclic creep tests on the Inconel 718 superalloy were performed to investigate the influence of cyclic loading on creep damage evolution. The ex‐situ microstructural analyses, including fracture surface observations and EBSD measurements, were conducted to reveal the damage mechanisms under cyclic creep conditions. Furthermore, a cavity nucleation and growth model that accounts for the additional cavity closure was developed for the healing effect of cyclic creep damage evolution. The prediction results were consistent with the experimental data of cavity nucleation life and experimental life within a factor of 2.

Recent progress on the modelling of the minimum creep strain rate and the creep cavitation damage and fracture

ABSTRACT Modelling of the long-term creep damage and lifetime is very challenging due to their strong stress level dependence. Aiming at developing a set of creep damage constitutive equations suitable for long-term service, research was carried out in modelling of the minimum creep strain rate, creep cavitation damage and rupture, and the coupling between creep cavitation damage and creep deformation. Firstly, based on the stress driven concept, the cavity nucleation model and cavity growth model were calibrated together using cavity histogram. Then, a simple analytical equation was derived to model creep cavitation damage. Furthermore, the creep cavitation damage model offered the theoretical background and supports for the stress-based extrapolation method and time-based extrapolation method. Two case studies were carried to explore the opportunities. This paper summarizes some of the progresses. This paper contributes to the generic methodology as well as the specific knowledge to the topic area.

Modelling of cavity growth during the superplastic flow of a fine-grained Ti–6Al–4V titanium alloy processed by direct rolling

ABSTRACT Ti–6Al–4V fine-grained plates were manufactured using a rolling method and then subjected to superplastic tensile tests at varying temperatures and strain rates on an AG 250KNE electronic tensile testing machine. The superplastic behaviours of the plates were also tested. A cavity-growth model was established and the changing laws of energy during cavity growth and microstructure evolution of superplastic deformation were predicted. The Ti–6Al–4V alloy possessed the maximum elongation rate of 886% at 840°C and a strain rate of 5 × 10−4 s−1. The strain-rate sensitivity index m for this alloy was 0.54. The mechanism of superplastic deformation was established to be strain-induced grain-boundary slip, and the mechanism of cavity growth to be plasticity-controlled cavity coalescence and growth.

High-temperature creep life prediction of 9%Cr steel based on creep cavitation modelling

ABSTRACT In present work, the creep rupture life of 9% Cr heat-resistant steel (P91) was evaluated based on the creep cavitation modelling. At 873 K, a series of creep rupture tests were carried out under the stresses of 140–190 MPa to achieve several sets of ruptured specimens . The constrained and unconstrained models of cavity growth were introduced to investigate the creep behaviour of P91 steel. The obtained results showed that the rupture mechanism of these specimens was mainly attributed to the ductile rupture under the present creep conditions. Besides, reasonable extrapolations were calculated to predict the creep rupture life of P91 steel by combining different constitutive equations with the cavity growth model. It suggested that the model predictions with constraints were better than those with unconstrained conditions. In particular, the Sinh equation based constrained cavity model shows greater potential in predicting the long-term creep life of P91 steel.

Basic Creep-Fatigue Models Considering Cavitation

Cavitation plays a central role during creep-fatigue. During recent years, fundamental models for initiation and growth of creep cavities that do not involve any adjustable parameters have been developed. These models have successfully been used to predict creep rupture data for austenitic stainless steels again without using adjustable parameters. However, it appears that basic models have not yet been applied to creep-fatigue assessments. A summary of the fundamental cavitation models is given. A model for monotonous deformation is transferred to cyclic loading. The parameter values are kept except that the dynamic recovery constant is raised due to increased interactions between dislocations during cycling. This model is successfully compared with observed LCF and TMF hysteresis loops. A new model for cavity growth due to plastic deformation is presented. The model is formulated in such a way that the condition for constrained growth is automatically satisfied. In this way, it is avoided to overestimate the growth rate.

Correlation of creep fracture lifetime with microstructure evolution and cavity behaviors in G115 martensitic heat-resistant steel

In order to deepen the understanding towards the creep rupture lifetime of G115 martensitic heat-resistant steel, a series of creep tests using 130–200MPa loading stresses at 923K were carried out to investigate the as-crept microstructural characteristics and cavity behaviors. The significant microstructure deformation and a dramatic increase in the areal density of high-angle grain boundaries occur when the stress loading is over 160MPa. Apart from the strain concentration at elongated grain boundaries and refined grains, the elevated stress also leads to the appearance of a strong α-fiber texture with {001}<110>//RD. The nucleation and growth of cavities can be effectively accelerated by the stress elevation, and ductile fracture is determined as the dominate mechanism within the test stresses. However, a transition towards brittle intergranular fracture is observed due to the rapid coarsening of Laves phase. Furthermore, a good prediction for creep lifetimes of G115 steel has been obtained based on the constrained diffusional cavity growth model.

The development of creep damage constitutive equations for high Cr steel

ABSTRACTThis paper reports (1) an application of the modified hyperbolic sine law to P92 for the minimum creep strain rate over a wider range of stress level, and 2) the calibration of the creep cavity fracture model and its applications to such as P92, E911 and MARBN alloys. It was motivated by the original development of creep cavitation based creep rupture model and application to other alloys, and the need of creep strain and stress relation over a wider range of stress. The results include: (1) the calibration of creep cavity fracture model for E911, and the pre-required cavity nucleation and growth models, for E911, (2) the creep lifetime and stress relation coefficient U’ for P92, and (3) the relationship of the cavity nucleation rate coefficient A2 and stress level for MARBN cross-welds. This paper contributes to the specific knowledge and the methodology. It anticipates that this methodology will find its value and application in modelling other fractures such as ductile and fatigue.

In situ nanotomography study of creep cavities in Al-3.6-Cu alloy

Cavity growth during high temperature deformation has been extensively studied theoretically, but experimental investigation of nucleation and early stages of growth has been limited. In this work, in situ nanotomography investigation of cavity nucleation and growth during high temperature deformation (7.9 MPa, 698 K), has been carried out in Al −3.6 wt% Cu alloy. This model alloy allows controlled generation of second phase particles to promote cavity nucleation and has hence been chosen for the study. Fast 3D imaging using synchrotron X-Rays with 100 nm pixel size and scan time of 7 s has been done to track nucleation and volumetric growth of individual cavities during deformation. Using this, change in shape of cavities with straining has been studied. Also, the change of volumetric cavity growth rate vs equivalent radius of individual cavities has been compared to existing models of cavity growth by diffusion and plasticity. It was seen that several pre-existing porosities were present in the alloy, while very few cavity nucleations were observed. The experimental data of growth rate matched well with the studied models and it was concluded that cavities initially grew by diffusion, while the growth mechanism changed to plasticity near failure.

Basic modelling of creep rupture in austenitic stainless steels

Creep rupture can happen in two ways, brittle and ductile creep rupture. Brittle creep rupture of austenitic stainless steels proceeds with the nucleation, growth and coalescence of grain boundary cavities. A creep cavity nucleation model has been developed previously, which considers cavity nucleation at particles and sub-boundary corners due to grain boundary sliding. A modified constrained cavity growth model has been used to describe the cavity growth behavior with combination of the cavity nucleation models. In this paper, the brittle creep rupture has been analyzed by combining the cavity nucleation and growth models. The physically based models where no adjustable parameters were involved were used to predict the brittle creep rupture strength. On the other hand, previously developed basic models for ductile creep rupture based on exhaustion of the creep ductility have been used. The creep rupture strength of common austenitic stainless steels has been predicted quantitatively by taking both ductile and brittle rupture into account. The predicted rupture times for ductile rupture are longer than those for brittle rupture at high stresses and low temperatures with a reversed situation at low stresses and high temperatures. This reproduces the characteristic change in slope in the creep rupture curves.

Creep cavity growth models for austenitic stainless steels

Diffusion controlled cavity growth models tend to exaggerate the growth rate. For this reason it is essential to take into account the restrictions caused by creep rate of the surrounding material, so called constrained growth. This has the consequence that the stress that the cavities are exposed to is reduced in comparison to the applied creep stress. Previous constrained growth models have been based on linear viscoplasticity. To avoid this limitation a new model for constrained growth has been formulated. Part of the work is based on a FEM study of expanding cavities in a creeping material. Compared with the previous constrained cavity growth models, the modified one gives lower reduced stresses and thereby lower cavity growth rates. By using recently developed cavity nucleation models, the modified creep cavity growth model can predict the cavity growth behaviour quantitatively for different types of austenitic stainless steels, such as 18Cr10Ni, 17Cr12NiNb and 17Cr12NiTi.

Brittle rupture of austenitic stainless steels due to creep cavitation

Basic creep cavitation models have been used to predict brittle rupture of austenitic stainless steels. It involves the grain boundary sliding models, which is the basis of the creep cavitation models, the recently developed cavity formation models and the constrained cavity growth models. The individual creep cavitation models are verified with experimental observations. Brittle rupture due to creep cavitation that appears as intergranular failure is found to be dominant at high temperatures and long creep exposure times.

Experimental and simulated displacement in cracked specimen of P91 steel under creep conditions

The assessment of crack initiation and propagation under creep conditions is important in the remaining life prediction of pipe components for power generation industry. One of the most successful analytical parameters for describing crack propagation under steady-state creep conditions is the C*-Integral that depends strongly on the material’s creep behavior and the resulting load-line displacement. This study deals with the determination and optimization of a creep model for a P91 grade steel operating at 600 °C. After a good fit provided by the model with uniaxial creep tests was found, the creep behavior of compact type C(T) specimens was modeled to predict creep crack growth (CCG) rates. A modified Cocks and Ashby power law creep controlled cavity growth model was used to compute the creep crack propagation rates. Load-line deflection was found to be strongly dependent on the primary creep strain rate. Lastly, good correlation between the experimental CCG results and the predicted CCG rates from the simulations were found.

Autonomous Repair Mechanism of Creep Damage in Fe-Au and Fe-Au-B-N Alloys

Abstract The autonomous repair mechanism of creep cavitation during high-temperature deformation has been investigated in Fe-Au and Fe-Au-B-N alloys. Combined electron-microscopy techniques and atom probe tomography reveal how the improved creep properties result from Au precipitation within the creep cavities, preferentially formed on grain boundaries oriented perpendicular to the applied stress. The selective precipitation of Au atoms at the free creep cavity surface results in pore filling, and thereby, autonomous repair of the creep damage. The large difference in atomic size between the Au and Fe strongly hampers the nucleation of precipitates in the matrix. As a result, the matrix acts as a reservoir for the supersaturated solute until damage occurs. Grain boundaries and dislocations are found to act as fast transport routes for solute gold from the matrix to the creep cavities. The mechanism responsible for the self-healing can be characterized by a simple model for cavity growth and cavity filling.

Superplastic Instability and Damage Evolution of AZ31B Magnesium Alloy Shee

Superplastic instability and damage evolution of AZ31B magnesium alloy sheet were investigated in this paper. Maximum elongation of 216% and strain rate sensitivity of 0.36 were obtained at 723k and a strain rate of 1×10-3s-1, whose fracture was due to the growth and interlinkage of cavities that nucleated at grain boundary. After superplastic tensile tests and quantitative analysis of cavity volume fraction, A cavity growth model were established, and the damage evolution equation based on the law of the micro-damage evolution and statistical mechanics was derived out, and damage characteristic parameters as well as the critical value of damage variable were identified so as to provide a theoretical ground on which the plastic forming technology of magnesium alloy sheet can be optimized.

A Gurson-type model accounting for void size effects

In this paper we present an extension of the Gurson model of cavity growth which includes the void size effect. To this end, we perform the limit analysis of a hollow sphere made up of a Fleck and Hutchinson’s strain gradient plasticity material. Based on the trial velocity field of Gurson, we derive an approximate closed form expression of the macroscopic criterion. The latter incorporates the void size dependency through a non dimensional parameter defined as the ratio of the cavity radius and the intrinsic length of the plastic solid. The accuracy of this approximate criterion is demonstrated by its comparison with numerical data. In the last part of the paper we present a complete plasticity model involving the damage rate and a power-law strain hardening of the matrix. It is shown that the cavity size effect has a strong dependency on damage growth as well as on the stress strain response.

Osmotic cavitation of elastomeric intraocular lenses

In recent years, traditional rigid materials have been replaced with softer elastomers in intraocular lenses to minimize the size of the required surgical incision, thereby reducing patient recuperation time. However, water-filled cavities that may impact visual acuity are found in many of these new implants. We demonstrate that the cavitation observed in vivo can occur due to an osmotic pressure difference between the aqueous solution within the cavity and the external media in which the lens is immersed. By reducing the osmolarity of the external solution from 300 to 0mM, we observe an increase in cavity volume of almost a factor of 30. Further, we have developed a model for cavity growth assuming the controlling factor is diffusion of hydrophilic molecules from the polymer matrix into the cavity. We find that the experimental observations are consistent with the model and suggest that oligomeric species generated during polymerization are responsible for the observed cavitation.

Steady-State Model for Estimating Gas Production from Underground Coal Gasification

A pseudo-one-dimensional channel model has been developed to estimate gas production from underground coal gasification. The model incorporates a zero-dimensional steady-state cavity growth submodel and models mass transfer from the bulk gas to the coal wall using a correlation for natural convection. Simulations with the model reveal that the gas calorific value is sensitive to coal reactivity and the exposed reactive surface area per unit volume in the channel. A comparison of model results with several small-scale field trials conducted at Centralia in the U.S.A. show that the model can make good predictions of the gas production and composition under a range of different operating conditions, including operation with air and steam/oxygen mixtures. Further work is required to determine whether the model formulation is also suitable for simulating large-scale underground coal gasification field trials.

Cavity Growth Simulation in 2.25Cr–1Mo Steel Under Creep-Fatigue Loading

High temperature components in thermal power plants are subjected to creep-fatigue loading where creep cavities initiate and grow on grain boundaries. Development of a quantitative evaluation method of cavity growth is important for reliable maintenance of these components. In this study, a creep-fatigue test was carried out at 600°C on 2.25Cr–1Mo steel in a scanning electron microscope, and continuous observation of cavity growth behavior during the test was made. Based on the cavity growth observation, existing cavity growth models were modified and the simulated results using the modified model were compared to the observed cavity growth behavior. From the observation, spherical shape cavities initiate and grow up to their length of 2μm on the grain boundaries at the initial stage of damage, and then these cavities change their shape to cracklike and grow until their length reaches around 10μm. Finally, cracklike cavities coalesce with each other to form one microcrack along a grain boundary. It can be concluded that cavity growth rates are controlled by diffusion and power law creep under constrained conditions, based on the theoretical consideration of cavity growth mechanism. Through these discussions, a new cavity growth model was proposed by modifying conventional models. Both spherical and cracklike cavity growth rate equations were derived from the modified cavity growth model. It was indicated that the measured cavity growth rate was well predicted by the growth rate equations, derived from the modified model, and a cavity growth simulation result corresponds to the change in the maximum cavity size with number of cycles under the creep-fatigue loading.

Study on Cavity Growth in Uniaxial Tension of ZK60 Magnesium Alloy

Cavity growth is a typical microstructure feature in superplastic forming (SPF) of materials. Substantial growth and interlink of cavities in superplastic deformation usually lead to reduction in elongation, even to failure. Consequently, it is necessary to investigate the mechanism and model of cavity growth. In this paper, experimental studies on cavity growth were carried out by means of superplastic tension of ZK60 magnesium alloys. Scanning electronic microscope (SEM) was employed for observation of fractography. Experimental cavity radius and volume fraction were determined by optical microscopy and corresponding picture-based analysis software. It is found that, the fractured surfaces after a superplastic elongation have a mixed characteristic of intergranular cavities and dimples. Further, the cavity growth is identified to follow a exponentially increasing mode.

A constitutive model for cavitation and cavity growth in rubber-like materials under arbitrary tri-axial loading

In this paper, we attempted to construct a constitutive model to deal with the phenomenon of cavitation and cavity growth in a rubber-like material subjected to an arbitrary tri-axial loading. To this end, we considered a spherical elementary representative volume in a general Rivlin’s incompressible material containing a central spherical cavity. The kinematics proposed by [Hou, H.S., Abeyaratne, R., 1992. Cavitation in elastic and elastic-plastic solids. J. Mech. Phys. Solids 40, 571–722] was adopted in order to construct an approximate but optimal field. In order to establish a suitable constitutive law for this class of materials, we utilized the homogenisation technique that permits us to calculate the average strain energy density of the volume. The cavity growth was considered through a physically realistic failure criterion. Combination of the constitutive law and the failure criterion enables us to describe correctly the global behaviour and the damage evolution of the material under tri-axial loading. It was shown that the present models can efficiently reproduce different stress states, varying from uniaxial to tri-axial tensions, observed in experimentations. Comparison between predicted results and experimental data proves that the proposed model is accurate and physically reasonable. Another advantage is that the proposed model does not need special identification work, the initial Rivlin’s law for the corresponding incompressible material is sufficient to form the new law for the compressible material resulted from cavitation procedure.