Void Growth Simulation Research Articles

Numerical simulation of void growth in front of a blunting crack-tip in plastically compressible solids

Effect of plastic compressibility on void growth ahead of a moving crack-tip is investigated numerically for a mode I crack subjected to plane strain deformation with small-scale yielding. Exploration is made for quasi-static finite deformations of isotropic hardening elastic–viscoplastic solids. For comparison purpose, both plastically incompressible and plastically compressible solids are considered to study the crack-tip deformation, void growth and interaction between the crack-tip and a nearby void by examining the near tip distributions of plastic strain, hydrostatic stress, effective stress and stress triaxiality. The plastic compressibility is found to have strong effect on the crack-tip deformation and stress–strain fields in the ligament and void region. The shape of void growth in front of the crack-tip is significantly influenced by the plastic compressibility. The present results show that in the case of plastically compressible solids, the rate of void growth in the direction perpendicular to the crack plane is more than the corresponding in the direction parallel to the crack and this observation is in sharp contrast to the void growth behavior observed in plastically incompressible solids. The predictions of the crack-tip and void interaction in the presence of plastic compressibility may be very helpful in understanding the crack growth and void coalescence in some relatively newer materials having very high energy absorption capacity, highly desired electrical and thermal as well as radiation-resistant properties, properties of bioimplants, etc.

A phase field computational procedure for electromigration with specified contact angle and diffusional anisotropy

Electromigration in electrical interconnects with high current density causes voids to form and grow near the cathode. These voids can possibly grow large enough to cause open circuit failure. The simulation of electromigration void nucleation and growth is challenging because of the complex interaction of electrical, thermal and mechanical fields that lead to the observed voids. In this paper, a phase-field approach is developed to study void growth due to electromigration taking into account diffusional anisotropy and specified contact angle. Consideration of anisotropy and contact angle is critical in applications including electronic assemblies that most commonly use Sn-based solder interconnects. In such systems, Sn exhibits significant anisotropy in its self-diffusivity, which assumes importance in small solder joints that are known to contain only a few grains. Furthermore, the contact angle at the void-bonding pad-solder triple junction is known to influence the void size and shape. To the best of the authors’ knowledge, only anisotropy in surface diffusivity has been considered in phase-field electromigration literature, whereas the contact angle at a triple junction has not been considered. The developed phase-field model incorporates effects of both contact angle and anisotropy in self-diffusivity. The model is used to simulate systems with different contact angles and dominant directions of diffusion. It is observed that diffusional anisotropy plays a more dominant role in failure, while the contact angle dictates evolution of the shape of voids.

Atomistic simulation of void growth by emitting dislocation pair during deformation

The growth of voids has an important influence on the crack and fracture of metal materials. A new atomistic method, i.e., the phase field crystal, is used to simulate the void evolution and dislocation emission of the lattice deformation process. During the deformation process, the void changes its shape as the applied strain increases. Influenced by the direction of the strain application and the orientation of the lattice atoms, the void is transformed from the original circular shape to a square shape. As the strain increases, a pair of dislocation is generated on left and right sides of the void, and pushes out on the two sides. Then, the dislocation pair is emitted from the void, and departs from it, and does the climbing movement. Finally, the dislocation pair is broken down into two independent dislocations. Using the model of the void launching dislocation, the interaction among dislocations and void in the deformation process is analyzed, and the influence of the void emitting dislocation in the void growth in the deformation process is revealed.

Molecular dynamics simulation of void nucleation, growth and closure of nano-Cu/Al films under cyclic loading

In this paper, molecular dynamics method is used to simulate the evolution mechanism of void nucleation, growth and closure of diffusion-welded copper/aluminum bilayer film under cyclic loading condition with a strain-to-width ratio of <i>R</i> = –1. It is found that under cyclic loading condition, the voids mainly nucleate inside the aluminum side of the copper/aluminum bilayer film, and two kinds of evolution modes of voids I and II are found. The void I nucleates at the position of the gap defect produced by the Kirkendall effect when the copper-aluminum diffuses to form the bilayer film. Under this nucleation mode, after the gap defects have become void, the void moves into the area where copper atoms are relatively dense inside the OTHER structure on the aluminum side. When gaps accumulate to form voids, the voids grow at a fixed position. The void II on the aluminum side nucleates at the position of the gap defect formed by overcoming the stair-rod dislocation and then remains motionless in the process of nucleation, growth and closure. Comparing with the void I, the stress corresponding to the nucleation of void II is large, the growth speed of the void II is fast and the size of the void II is slightly large in the process of strain loading. The void II closure speed is also faster in the strain unloading stage. The two kinds of voids have two common characteristics in the process of nucleation, growth and closure. 1) Both kinds of voids nucleate at the position of the gap defect inside OTHER structure on the aluminum side. 2) In the process of voids growth and closure, both kinds of voids have the same shape changes. In the void growth stage, both kinds of voids first grow along the strain loading direction, then expand in the direction perpendicular to the strain loading direction, and finally, the shapes of two kinds of voids tend to become spherical. In the stage of void closure, the two kinds of voids are first compressed into ellipsoidal shape along the strain loading direction, and then disappear from both ends of the void to the center of the void in the direction perpendicular to the strain loading direction. In the subsequent cyclic loading process, none of new voids appears again at the position where the voids disappearred, but the nucleation of voids at other position of gap defect forms inside the other structure located on the aluminum side.

Evaluation of Gurson yield function dependencies through large-scale void growth simulations

Numerical simulation of void growth from thousands of randomly distributed particles is used to assess the functional dependence of the Gurson model. Shock loading of the model region followed by a ramped pressure release creates a smoothly varying velocity field in which the void growth is inertially stabilized. The pressure, effective stress, and void fraction are obtained from the simulation for comparison with the Gurson model. The results show that the pressure-void fraction relation from the model reasonably follows the simulation data, but the numerical data exhibit significantly greater void fraction dependence on the effective stress than the Gurson model.

CrMoV鍛鋼のクリープボイド成長に及ぼす繰返し負荷の影響

Thick high temperature components in thermal power plants such as turbine rotors are subjected to creep-fatigue loading under cycles of start - steady state - stop operation. The creep-fatigue damage gradually proceeds in these components. Therefore it is important to clarify damage extension mechanism under the creep-fatigue loading to develop accurate life assessment methods for reliable operation. In this study, a stress control creep-fatigue test with 10 minutes stress hold time at the maximum stress was conducted in a scanning electron microscope to clarify void growth behavior during the test. A strain control creep-fatigue test with 5 hours strain hold was also performed to observe void initiation and growth condition by interrupting the tests. From the observation, round shape voids initiated around 15% of the life and grew by changing the shape to a crack-like, and rate of void growth is considered to be accelerated by cyclic loading based on the fact that size of the maximum void under the creep-fatigue loading is larger than that under the static creep loading. According to the observation results, the previous proposed void growth rate equation was multiplied by acceleration factor. The acceleration factor is assumed to be dependent on applied strain range. The maximum void growth behaviors under both the stress and strain creep-fatigue loadings were accurately predicted by the extended void growth simulation procedure to the creep-fatigue loading considering influence of hold time on the acceleration factor.

CrMoV鍛鋼環状切欠き試験片のボイド成長シミュレーションに基づくクリープ損傷評価

Creep damage preferentially extends at a stress concentration portion in high temperature components such as steam turbine rotors. Therefore development of an accurate damage assessment method for creep damage process at the stress concentration portion under multiaxial stress states is necessary to maintain reliable operation. In this study, creep tests using a plain specimen and two kinds of round bar notch specimens with different notch radius on a CrMoV forging steel have been conducted to clarify effect of stress conditions on creep damage extension process. Three dimensional finite element creep analyses have been performed to discuss relation between the creep damage and stress conditions. Creep rupture time of the plain specimen is shorter than those of the notch specimens. Creep rupture time of the notch specimen with lower stress concentrate factor is longer than that with higher stress concentration factor. In the notch specimens, the maximum stresses occur at notch root at initial loading and portions of the maximum stresses gradually change to inside of the specimens with time due to stress redistribution. Triaxial tensile stress yields at the notch root sections with different distributions of the triaxiality factor depending on the notch radius. Void number densities at the maximum stress portion in the notch specimens are ten times larger than that in the plain specimen. The void growth simulation method developed previously was applied to predict the void number density under multiaxial stress states in the notch specimens. Distributions of the void number density from notch root to center of the specimen both in the notch specimens were quantitatively predicted by the void growth simulation method. An equation, which predicts change of void number density with time under a certain maximum stress and a triaxiality factor, was derived based on the void growth simulation under different multiaxial stress states.

The Simulation of Void Growth along Curvilinear Crack Front

In this study, simulations of the voids in the crack plane along the curvilinear crack front were analyzed. The analyses were conducted for different load stages. The results of numerical analysis were compared with fractographic pictures of the specimen in question.

Unsteady Numerical and Experimental Study of Cavitation in Axial Pump

This paper presents an experimental and three-dimensional numerical study of unsteady, turbulent, void growth and cavitation simulation inside the passage of the axial flow pump. In this study a 3D Navier-Stokes code was used (CFDRC, 2008) to model the two-phase flow field around a four blades axial pump. The governing equations are discretized on a structured grid using an upwind difference scheme. The numerical simulation used the standard K-e turbulence model to account for the turbulence effect. The numerical simulation of void growth and cavitation in an axial pump was studied under unsteady calculating. Pressure distribution and vapor volume fraction were completed versus time at different condition. The computational code has been validated by comparing the predicated numerical results with the experiment. The predicted of cavitation growth and distribution on the impeller blade also agreed with that visualized of high speed camera.

Molecular dynamics modeling and simulation of void growth in two dimensions

The mechanisms of growth of a circular void by plastic deformation were studied by means of molecular dynamics in two dimensions (2D). While previous molecular dynamics (MD) simulations in three dimensions (3D) have been limited to small voids (up to ≈10 nm in radius), this strategy allows us to study the behavior of voids of up to 100 nm in radius. MD simulations showed that plastic deformation was triggered by the nucleation of dislocations at the atomic steps of the void surface in the whole range of void sizes studied. The yield stress, defined as stress necessary to nucleate stable dislocations, decreased with temperature, but the void growth rate was not very sensitive to this parameter. Simulations under uniaxial tension, uniaxial deformation and biaxial deformation showed that the void growth rate increased very rapidly with multiaxiality but it did not depend on the initial void radius. These results were compared with previous 3D MD and 2D dislocation dynamics simulations to establish a map of mechanisms and size effects for plastic void growth in crystalline solids.

An object-oriented finite element framework for multiphysics phase field simulations

The phase field approach is a powerful and popular method for modeling microstructure evolution. In this work, advanced numerical tools are used to create a framework that facilitates rapid model development. This framework, called MARMOT, is based on Idaho National Laboratory’s finite element Multiphysics Object-Oriented Simulation Environment. In MARMOT, the system of phase field partial differential equations (PDEs) are solved simultaneously together with PDEs describing additional physics, such as solid mechanics and heat conduction, using the Jacobian-Free Newton Krylov Method. An object-oriented architecture is created by taking advantage of commonalities in the phase field PDEs to facilitate development of new models with very little effort. In addition, MARMOT provides access to mesh and time step adaptivity, reducing the cost for performing simulations with large disparities in both spatial and temporal scales. In this work, phase separation simulations are used to show the numerical performance of MARMOT. Deformation-induced grain growth and void growth simulations are also included to demonstrate the muliphysics capability.

Damage Evolution and Life Prediction of a P91 Longitudinal Welded Tube Under Internal Pressure Creep

The clarification of creep damage mechanism and the establishment of remaining life prediction methods of longitudinal welded piping of P91 steel are important subjects to maintain a reliable operation of boilers in thermal power plants. Internal pressure creep tests were conducted on P91 steel longitudinal welded tubes to characterize the evolution of creep damage with time and to evaluate a life prediction method. Interrupted creep tests were performed for damage observation in addition to rupture tests. Three dimensional finite element creep analyses of the longitudinal welded tube specimens were conducted to identify the stress and creep strain distributions within the specimen during creep. Failure occurred at a heat affected zone (HAZ) without a significant macroscopic deformation. It was found that the initiation of creep voids had concentrated at the midthickness region in the HAZ rather than in the surface. The creep analysis results indicated that the triaxial tensile stress yielded at the midthickness region in the HAZ due to difference of creep deformation property among the base metal, the HAZ, and the weld metal. It was suggested that the triaxial stress state caused acceleration of the creep damage evolution in the HAZ, resulting in internal failure of the tube specimens. A rupture time prediction method of the welded tube is proposed based on the maximum principal stress and the triaxial stress factor in the HAZ. The void growth behavior in the HAZ was well predicted by the previously proposed void growth simulation method by introducing a void initiation function to the method.

Electromigration performance of Through Silicon Via (TSV) – A modeling approach

The electromigration (EM) performance of Through Silicon Via (TSV) in silicon interposer application are studied using Finite Element (FE) modeling. It is found that thermo-mechanical stress is the dominant contribution factor to EM performance in TSV instead of the current density. The predicted failure site is dependent on the process technology, and exhibits asymmetric behavior if different process is used between the top and bottom metallization of a TSV. Modeling is also done for two different coverage patterns of top metallization, namely (i) the metal line covers the via completely, and (ii) the metal line only extends to the centre of the via, covering half of the via. The simulation results of the latter model show the existence of a second EM failure site and worse EM performance is expected. This additional possible EM failure site is further confirmed through dynamic simulation of void growth.

Damage assessment method of P91 steel welded tube under internal pressure creep based on void growth simulation

Development of creep damage assessment methods for longitudinal welded piping of P91 steel is important and an urgent subject to maintain reliable operation of boilers in ultra super critical thermal power plants. Internal pressure creep tests were conducted on P91 steel longitudinal welded tubes to characterize the evolution of creep damage in a heat-affected zone (HAZ) of the longitudinal welded pipe. Failure occurred at a heat-affected zone without significant macroscopic deformation. It was found that initiation of creep voids had concentrated at mid-thickness region rather than surface. Three-dimensional finite element (FE) creep analysis of the creep tested specimens was conducted to identify stress and creep strain distribution within the specimen during creep. Finite element creep analysis results indicated that triaxial tensile stress yielded at the mid-thickness region of the HAZ. It was suggested that the triaxial stress state caused acceleration of the creep damage evolution in the heat-affected zone resulting in internal failure of the tube specimens. Void growth behavior in the heat-affected zone was well predicted with the previously proposed void growth simulation method by introducing void initiation function to the method. A “limited strain” was defined as rupture criterion and dependency of the maximum stress and multiaxiality on the “limited strain” was derived by the void growth simulation. Creep damage distribution in the HAZ under the internal creep test was calculated by proposed damage assessment method.

Uniaxial Creep Rupture Property of Mod.9Cr-1Mo Steel Weld Joint and Proposal of Creep Damage Evaluation Method

Modified 9Cr-1Mo steels (P91) have been used for high temperature steam pipes in ultra super critical power plants not only in Japan but also in other countries. Since weld joints of P91 indicate lower creep damage resistance than base metal, it is necessary to establish damage assessment method for weld joints of P91 to maintain reliable operation. In this study, creep tests have been conducted on a P91 to identify creep rupture life property of weld joints, and creep damage process in heat affect zone (HAZ) has been clarified by interrupting the creep tests. As a result, it was found that creep rupture time of the weld joints reduced to about 1/5 of the base metal and creep voids have already initiated at 20% of creep life in the HAZ. Size and number of voids in the HAZ increased with increasing creep damage. Stress distribution within the weld joint specimen was calculated by a finite element analysis of a weld joint model consisting of base metal, weld metal and HAZ. It was indicated that creep strain accumulated in the HAZ preferentially resulting in Type IV failure of the weld joint specimen. Creep rupture time of the weld joint can be predicted by creep strain rate in the HAZ and “limited creep strain” defined in this study. Authors proposed the creep void growth simulation method in the previous study based on void kinetics. This method applied to creep void growth simulation in the HAZ of the P91 weld joint. It was confirmed that quantitative void growth behavior could be predicted by the void growth simulation method.

Numerical Simulation of Void Growth Induced Creep Rupture in HAZ at Elevated Temperature

In structural welded joints after long-term service under elevated temperature, fracture occurred mainly in the heat affected zone (HAZ). Recently, the nucleation and growth of creep voids in the fine-grained HAZ of weldments, recognized as Type IV fracture, has become an important problem for ferritic heat resisting steel. In this paper, a new computational model was presented to analyse the void growth induced creep damage development in HAZ. The new constitutive model based on continuum damage mechanics (CDM) equations is combined with a micromechanism-based model in order to account for the void growth process, which is different from the previous studies of creep damage. Material properties used for the creep damage computations are fitted from actual creep test data. Basic benchmark tests were performed to verify the new computational model. Then the model was used to study the creep damage development in the welded joints where four different material properties, base material, coarse-grained HAZ, fine-grained HAZ, and weld material, are taken into account. The numerical simulation results for creep lifetimes agreed well with the experimental results.

A201 改良9Cr-1Mo鋼溶接継手のクリープ損傷予測法の開発(材料強度評価-1,OS-6 保全・設備診断技術(3),一般講演,地球温暖化防止と動力エネルギー技術)

In this study, creep tests have been conducted on a P91 to identify creep rupture life property of the weld joints, and creep damage process in heat affect zone (HAZ) has been clarified by producing creep damaged materials. As results, it was found that creep rupture time of the weld joints reduced to about 1/5 of the base metal and creep voids have already initiated at 20% of the creep life in the HAZ. Size and number of voids in the HAZ increased with increasing creep damage. Creep rupture time of the weld joint can be predicted by creep strain rate in the HAZ and limited creep strain defined in this study. It was confirmed that quantitative void growth behavior could be predicted by the void growth simulation method.

Simulation of void growth and coalescence behavior with 3D crystal plasticity theory

The influence of crystallographic orientation on the void growth and coalescence in FCC single crystal is numerically simulated with the three dimensional crystal plasticity finite element method, which is implemented with the rate dependent crystal plasticity theory as user material subroutine. A 3D unit cell including one sphere void or two sphere voids is employed with three-dimensional 12 slip systems. The computed results of four single crystals with different crystallographic orientations are compared. The results of the simulations have shown that the crystallographic orientation has significant influences on the growth behavior of void, which includes the growth direction and shape of voids. Crystallographic orientation also plays a role in void coalescence, and the width of inter-void ligament is dependent on the position of voids and crystallographic orientation. If the link line of the centers of voids is parallel to the maximal void growth direction, crystal tends to show coalescence effect more easily.

Creep Void Growth Simulation of Local Area in a Steam Turbine Rotor

In order to reduce maintenance cost of high temperature components in aged thermal power plants, it is necessary to improve accuracy of remaining life assessment methods. High temperature components such as steam turbine rotors are operated under creep loading condition where creep voids initiate and grow on grain boundaries. Development of a void growth prediction method is important for reliable maintenance of these components. Purposes of this study are to clarify void growth behavior of a turbine rotor material under creep loading condition, and to develop void growth simulation program that can predict damage extension process in the components under actual operating condition quantitatively. Creep tests have been conducted on a 1Cr-Mo-V forging material and creep damaged specimens were produced by interrupting the tests. From observation of the creep damaged specimen, spherical shape voids initiate and grow up to their length of 2μm on the grain boundary at initial stage of damage, and then these voids change their shape to crack-like to grow until their length reaches around 10μm. Finally, crack-like voids coalesce each other to form one micro crack along grain boundary. It can be concluded that void growth rate is controlled by diffusion and power law creep under constrained condition based on theoretical consideration of void growth mechanism. Through these discussions, a new void growth model was proposed by modifying conventional models. A void growth simulation program was developed by incorporating the void growth model into a personal computer. It was confirmed that void growth process under the creep condition in the experiment was well predicted by the simulation program. The simulation program was also applied to predict creep void growth behavior in an actual steam turbine rotor during operation.

The Void Growth Simulations in the Hyper-Elastic Material with Multiple Seeds

The behaviors of a material are nonlinear in the large deformed region. The hyper elastic models can describe such non linear materials. If the hyper elastic material is applied to the hydrostatic tensile load, the void begins to grow when the load exceed the critical value. It is important to study the coalescence of the void growth in order to consider the destruction of the material. In this paper, the void growth simulations in the hyper-elastic material with multiple seeds are studied. The unit rectangular cell with small voids is subjected to the hydrostatic tensile load. This problem can be analyzed by FEM. However, the simulation with the larger number of the voids is not possible. Thus, the CA (Cellular Automaton) is used to describe the behaviors of the void coalescence and the possibility of CA is discussed.