Journal articles: 'Void nucleation and growth'

1

Lee, J. H., and Y. Zhang. "A Finite-Element Work-Hardening Plasticity Model of the Uniaxial Compression and Subsequent Failure of Porous Cylinders Including Effects of Void Nucleation and Growth—Part I: Plastic Flow and Damage." Journal of Engineering Materials and Technology 116, no. 1 (January 1, 1994): 69–79. http://dx.doi.org/10.1115/1.2904257.

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Gurson’s mixed hardening plasticity model (which takes into account the progressive damage due to void nucleation and growth of an initially dense material), with strain and stress-controlled nucleations, was used in a large deformation finite element program to study the plastic flow and damage in the uniaxial compression of cylinders under sticking friction. Effects of strain hardening, nucleation models, yield surface curvature, and geometry on the distributions and evolutions of stresses, strains, mean stress, void fractions, and coalescence are studied in detail. Using Gurson’s isotropic hardening model, positive mean and axial stresses developed at the bulge of the cylinder with growth of voids at latter stages of deformation. Due low stress triaxiality (Σm/σe<0.6) at the bulge, the process is nucleation rather than growth dominated for the majority of the cases studied. At failure, the maximum void fraction at the bulge among all cases studied is 0.085 and is far less than the critical void fraction (≈0.15) for coalescence.

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Chen, Bin, X. Peng, Xiang Guo Zeng, X. Wu, and S. Chen. "A Constitutive Model for Casting Magnesium Alloy Based on the Analysis of a Spherical Void Model." Materials Science Forum 546-549 (May 2007): 221–24. http://dx.doi.org/10.4028/www.scientific.net/msf.546-549.221.

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Casting magnesium alloys are heterogeneous materials containing numerous voids. Assuming the voids are spherical, in the present investigation, the evolution equations of the growth and nucleation of the voids have been presented. Combining the evolution equation of the void growth with that of the void nucleation, the evolution rule of the voids was obtained. Based on the void evolution rule a nonclassical elastoplastic constitutive model involving void evolution was developed. The corresponding numerical algorithm and finite element procedure were developed and applied to the analyses of the elastoplastic response and the porosity of casting magnesium alloy. The calculated results show the satisfactory agreement with experiments.

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Williams, Cyril Labode. "Void Mediated Failure at the Extremes: Spallation in Magnesium and Aluminum." Metals 12, no. 10 (October 5, 2022): 1667. http://dx.doi.org/10.3390/met12101667.

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This paper reviews the role of void nucleation, growth, and coalescence on the spall failure process in light metals. Based on the review of the open literature, the preponderance of evidence show that void nucleation, growth, and coalescence are prevalent in light metals such as HCP magnesium and FCC aluminum alloys. The as-received microstructure and its evolution play a crucial role on how voids nucleate, grow, and coalesce. Nucleation of voids in these light metals and metallic alloys can be either homogeneous and heterogeneous but at high enough stresses, both homogeneous and heterogeneous nucleation can be activated simultaneously. Secondary phase particles and intermetallics can strongly influence spall failure, through matrix-precipitate/intermetallic debonding or precipitate/intermetallic cracking during shock compression. Studying spall failure through modeling has proven to be an invaluable tool in developing a fundamental understanding of void nucleation, growth, coalescence, and consequent spall failure. However, since new alloys are currently been developed, more experimental and modeling research are needed to further understand how spall failure initiate and grow in these new alloys.

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Chen, Jie, Darby J. Luscher, and Saryu J. Fensin. "The Modified Void Nucleation and Growth Model (MNAG) for Damage Evolution in BCC Ta." Applied Sciences 11, no. 8 (April 9, 2021): 3378. http://dx.doi.org/10.3390/app11083378.

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A void coalescence term was proposed as an addition to the original void nucleation and growth (NAG) model to accurately describe void evolution under dynamic loading. The new model, termed as modified void nucleation and growth model (MNAG model), incorporated analytic equations to explicitly account for the evolution of the void number density and the void volume fraction (damage) during void nucleation, growth, as well as the coalescence stage. The parameters in the MNAG model were fitted to molecular dynamics (MD) shock data for single-crystal and nanocrystalline Ta, and the corresponding nucleation, growth, and coalescence rates were extracted. The results suggested that void nucleation, growth, and coalescence rates were dependent on the orientation as well as grain size. Compared to other models, such as NAG, Cocks–Ashby, Tepla, and Tonks, which were only able to reproduce early or later stage damage evolution, the MNAG model was able to reproduce all stages associated with nucleation, growth, and coalescence. The MNAG model could provide the basis for hydrodynamic simulations to improve the fidelity of the damage nucleation and evolution in 3-D microstructures.

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Wciślik, Wiktor, and Sebastian Lipiec. "Voids Development in Metals: Numerical Modelling." Materials 16, no. 14 (July 14, 2023): 4998. http://dx.doi.org/10.3390/ma16144998.

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The article is a continuation of two previous review papers on the fracture mechanism of structural metals through the nucleation, growth and coalescence of voids. In the present paper, the literature on the numerical modelling of void nucleation and development has been reviewed. The scope of the work does not include porous material models and their numerical implementation. As part of the discussion on void initiation, nucleation around second phase particles and nucleation as an effect of the discontinuity of the crystal structure were discussed separately. The basic void cell models, finite element method (FEM) models of periodically distributed particles/voids and models based on the results of the observations of the actual microstructure of materials have been characterised. Basic issues related to the application of the cohesive approach in void nucleation modelling have been considered. A separate issue is the characteristics of atomistic simulations and peridynamic modelling, which have been developed in recent years. Numerical approaches to modelling the growth and coalescence of voids are described, with particular emphasis on the influence of the stress state and strain localisation. Basic conclusions from the simulation are presented, pointing to the contribution of FEM modelling to the understanding of microstructural phenomena leading to ductile fracture.

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Lim, L. G., and F. P. E. Dunne. "Modelling void nucleation and growth in axisymmetric extrusion." Proceedings of the Institution of Mechanical Engineers, Part B: Journal of Engineering Manufacture 211, no. 4 (April 1, 1997): 285–97. http://dx.doi.org/10.1243/0954405971516266.

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Elastic-viscoplastic constitutive equations, with kinematic and isotropic hardening, are employed to model the deformation behaviour of an aluminium alloy in extrusion. Constitutive equations are also employed for void nucleation and growth, which are fully coupled with the deformation behaviour. The material model is employed to investigate the roles of void nucleation and growth in extrusion defect formation. It has been shown that central bursting is a void growth controlled process. The existence of nucleated voids only leads to central burst formation with the existence of appropriate stress states which lead to void growth. The results obtained show excellent agreement with well-established limit diagrams, obtained analytically and experimentally. The results also show that for a given combination of area reduction and semi-cone die angle, the introduction of friction tends to inhibit the formation of central bursting, but increases the likelihood of surface tearing/cracking. The tendency to inhibit central burst formation with increasing friction results from the reduction in the levels of tensile hydrostatic stress, which therefore reduce the rate of void growth. A comparison of the results obtained using kinematic and isotropic hardening in the extrusion process showed that significantly different residual stress fields are obtained for the two cases. This is of importance, for example, in the case of multipass extrusion or where the residual stress field is to be used subsequently in design analysis.

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Wan, Ya-Ting, Jian-Li Shao, Guang-Ze Yu, Er-Fu Guo, Hua Shu, and Xiu-Guang Huang. "Evolution of Preset Void and Damage Characteristics in Aluminum during Shock Compression and Release." Nanomaterials 12, no. 11 (May 28, 2022): 1853. http://dx.doi.org/10.3390/nano12111853.

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It is well known that initial defects play an essential role in the dynamic failure of materials. In practice, dynamic tension is often realized by release of compression waves. In this work, we consider void-included single-crystal aluminum and investigate the damage characteristics under different shock compression and release based on direct atomistic simulations. Elastic deformation, limited growth and closure of voids, and the typical spall and new nucleation of voids were all observed. In the case of elastic deformation, we observed the oscillatory change of void volume under multiple compression and tension. With the increase of impact velocity, the void volume reduced oscillations to the point of disappearance with apparent strain localization and local plastic deformation. The incomplete or complete collapsed void became the priority of damage growth under tension. An increase in sample length promoted the continuous growth of preset void and the occurrence of fracture. Of course, on the release of strong shock, homogeneous nucleation of voids covered the initial void, leading to a wider range of damaged zones. Finally, the effect of the preset void on the spall strength was presented for different shock pressures and strain rates.

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Maire, Eric, Stanislas Grabon, Jérôme Adrien, Pablo Lorenzino, Yuki Asanuma, Osamu Takakuwa, and Hisao Matsunaga. "Role of Hydrogen-Charging on Nucleation and Growth of Ductile Damage in Austenitic Stainless Steels." Materials 12, no. 9 (May 1, 2019): 1426. http://dx.doi.org/10.3390/ma12091426.

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Hydrogen energy is a possible solution for storage in the future. The resistance of packaging materials such as stainless steels has to be guaranteed for a possible use of these materials as containers for highly pressurized hydrogen. The effect of hydrogen charging on the nucleation and growth of microdamage in two different austenitic stainless steels AISI316 and AISI316L was studied using in situ tensile tests in synchrotron X-ray tomography. Information about damage nucleation, void growth and void shape were obtained. AISI316 was found to be more sensitive to hydrogen compared to AISI316L in terms of ductility loss. It was measured that void nucleation and growth are not affected by hydrogen charging. The effect of hydrogen was however found to change the morphology of nucleated voids from spherical cavities to micro-cracks being oriented perpendicular to the tensile axis.

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Steglich, Dirk, Husam Wafai, and Jacques Besson. "Anisotropic Plastic Deformation and Damage in Commercial Al 2198 T8 Sheet Metal." Key Engineering Materials 452-453 (November 2010): 97–100. http://dx.doi.org/10.4028/www.scientific.net/kem.452-453.97.

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Deformation anisotropy of sheet aluminium alloy 2198 (Al-Cu-Li) has been investigated by means of mechanical testing of notched specimens and Kahn-type fracture specimens, loaded in the rolling direction (L) or in the transverse direction (T). Contributions to failure are identified as growth of initial voids accompanied by a significant nucleation of a second population of cavities and transgranular failure. A model based on the Gurson-Tvergaard-Needleman (GTN) approach of porous metal plasticity incorporating isotropic voids, direction-dependent void growth, void nucleation at a second population of inclusions and triaxiality-dependent void coalescence has been used to predict the mechanical response of test samples. The model has been successfully used to describe and predict the direction-dependent deformation behaviour, crack propagation and, in particular, toughness anisotropy.

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10

Basaran, C., H. Ye, D. C. Hopkins, D. Frear, and J. K. Lin. "Failure Modes of Flip Chip Solder Joints Under High Electric Current Density." Journal of Electronic Packaging 127, no. 2 (September 15, 2004): 157–63. http://dx.doi.org/10.1115/1.1898338.

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The failure modes of flip chip solder joints under high electrical current density are studied experimentally. Three different failure modes are reported. Only one of the failure modes is caused by the combined effect of electromigration and thermomigration, where void nucleation and growth contribute to the ultimate failure of the module. The Ni under bump metallization–solder joint interface is found to be the favorite site for void nucleation and growth. The effect of pre-existing voids on the failure mechanism of a solder joint is also investigated

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11

Yang, Xin, Han Zhao, Xuejun Gao, Zhenlin Chen, Xiangguo Zeng, and Fang Wang. "Molecular dynamics study on spallation fracture in single crystal and nanocrystalline tin." Journal of Applied Physics 132, no. 7 (August 21, 2022): 075903. http://dx.doi.org/10.1063/5.0099331.

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Spallation fracture in ductile metals with low melting points is an important scientific concern of dynamic fracture. Classical spallation and micro-spallation simulations of single crystal (SC) and nanocrystalline (NC) tin were carried out using non-equilibrium molecular dynamics at shock pressures of 13.5–61.0 GPa. The shock wave velocity had no effect on the waveform evolution in the SC Sn but not in the NC Sn. The front width of the stress wave in the classical spallation of the NC Sn was predominantly affected by grain boundary sliding. The atomic trajectory technique was first introduced to reproduce the evolutionary processes of void growth and coalescence quite effectively. In the classical spallation, the differences in void evolution behavior of SC and NC Sn were mainly reflected in nucleation position, spatial distribution, and growth zone, while their evolutionary behaviors were shared in the micro-spallation. In the NC model, for the classic spallation, voids mostly nucleated at grain boundaries and grew along grain boundaries, resulting in intergranular fractures; for the micro-spallation, voids nucleated at the grain boundary and inside the grain, resulting in intergranular, intragranular, and transgranular fractures. Furthermore, the void volume fraction followed the bilinear rise at the early nucleation and growth stages, and the critical transition point fundamentally signified the initiation of void nucleation to growth.

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12

Rao, U. S., and R. C. Chaturvedi. "Sheet Metal Forming Limits Under Complex Strain Paths Using Void Growth and Coalescence Model." Journal of Engineering Materials and Technology 108, no. 3 (July 1, 1986): 240–44. http://dx.doi.org/10.1115/1.3225875.

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It is well established that ductile fracture occurs by nucleation, growth and coalescence of voids. Several models have been developed to predict limits under constant strain ratio paths considering void inhomogeneity and void growth. In this paper the void growth and coalescence model developed by Rao and Chaturvedi for predicting forming limits under constant strain ratio paths, has been extended for predicting forming limits under two stage strain paths. The predicted results have been compared with experimental results of Ishigaki and analyzed.

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13

Guo, Yi, Chaitanya Paramatmuni, and Egemen Avcu. "Void Nucleation and Growth from Heterophases and the Exploitation of New Toughening Mechanisms in Metals." Crystals 13, no. 6 (May 24, 2023): 860. http://dx.doi.org/10.3390/cryst13060860.

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Heterophases, such as precipitates, inclusions, second phases, or reinforcement particles, often drive void nucleation due to local incompatibilities in stresses/strains. This results in a significant life-limiting condition, as voids or their coalescence can lead to microcracks that reduce the ductility and fatigue life of engineering components. Continuum-mechanics-based analytical models have historically gained momentum due to their relative ease in predicting failure strain. The momentum of such treatment has far outpaced the development of theories at the atomic and micron scales, resulting in an insufficient understanding of the physical processes of void nucleation and growth. Evidence from the recent developments in void growth theories indicates that the evolution of voids is intrinsically linked to dislocation activity at the void–matrix interface. This physical growth mechanism opens up a new methodology for improving mechanical properties using hydrostatic pressurization. According to the limited literature, with a hydrostatic pressure close to 1 GPa, aluminium matrix composites can be made 70 times more ductile. This significant ductility enhancement arises from the formation of dislocation shells that encapsulate the heterophases and inhibit the void growth and coalescence. With further investigations into the underlying theories and developments of methods for industrial implementations, hydrostatic pressurization has the potential to evolve into an effective new method for improving the ductility and fatigue life of engineering components with further development.

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14

Worswick, M. J., H. Nahme, and J. Fowler. "Spall through void nucleation, growth and coalescence." Le Journal de Physique IV 04, no. C8 (September 1994): C8–623—C8–628. http://dx.doi.org/10.1051/jp4:1994894.

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15

Leon, R., J. A. Colon, K. C. Evans, D. T. Vu, V. Blaschke, B. Bavarian, E. T. Ogawa, and P. S. Ho. "Void evolution and its dependence on segment length in Cu interconnects." Journal of Materials Research 19, no. 11 (November 1, 2004): 3135–38. http://dx.doi.org/10.1557/jmr.2004.0408.

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Void evolution during electromigration was studied by recording void nucleation, growth, and displacements at various intervals during thermal (240 °C) and electrical stress tests (2 × 106 amps/cm2) of Cu interconnects. Structural data was collected for various serially arranged line segment lengths and correlated with resistance and increases in resistance due to electromigration-induced thinning and voiding. These results allowed determination of void growth rates in Cu interconnects. Void nucleation and growth show a clear dependence on segment length. Void formation did not occur at the via/interconnect interface, which improved interconnect reliability by allowing extensive voiding before catastrophic failure.

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Guo, Xiang Hui, and Hai Yun Hu. "Non-Equilibrium Statistical Theory of Void Microstructure Evolution in Irradiated Metals." Applied Mechanics and Materials 364 (August 2013): 568–72. http://dx.doi.org/10.4028/www.scientific.net/amm.364.568.

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The non-equilibrium statistical theory was used as a theoretical approach to modeling and predicting void evolution in metal materials. Fokker-Plank equation was introduced as the kinetic equation for the void evolution, from which the probability density distribution function of voids could be obtained. From the micro-mechanism of metal's irradiation damage, void growth rate equation was obtained using spherical Weilv model and control diffusion theory, and then was simplified based on appropriate assumptions. According to the probability density distribution function of void, a series of macro-mechanical characteristics caused by void growth can be calculated, such as: the critical radius of the void nucleation, the average radius of void. Thus the correlation between the void microstructure evolution and the macroscopic properties of metals can be achieved.

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Tekoğlu, C., J. W. Hutchinson, and T. Pardoen. "On localization and void coalescence as a precursor to ductile fracture." Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences 373, no. 2038 (March 28, 2015): 20140121. http://dx.doi.org/10.1098/rsta.2014.0121.

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Two modes of plastic flow localization commonly occur in the ductile fracture of structural metals undergoing damage and failure by the mechanism involving void nucleation, growth and coalescence. The first mode consists of a macroscopic localization, usually linked to the softening effect of void nucleation and growth, in either a normal band or a shear band where the thickness of the band is comparable to void spacing. The second mode is coalescence with plastic strain localizing to the ligaments between voids by an internal necking process. The ductility of a material is tied to the strain at macroscopic localization, as this marks the limit of uniform straining at the macroscopic scale. The question addressed is whether macroscopic localization occurs prior to void coalescence or whether the two occur simultaneously. The relation between these two modes of localization is studied quantitatively in this paper using a three-dimensional elastic–plastic computational model representing a doubly periodic array of voids within a band confined between two semi-infinite outer blocks of the same material but without voids. At sufficiently high stress triaxiality, a clear separation exists between the two modes of localization. At lower stress triaxialities, the model predicts that the onset of macroscopic localization and coalescence occur simultaneously.

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Liu, W., H. Zhou, Z. Meng, J. Li, and S. Huang. "Less damage accumulation of aluminum alloy sheet during electromagnetic forming based on Gurson-Tvergaard-Needleman model." IOP Conference Series: Materials Science and Engineering 1238, no. 1 (May 1, 2022): 012019. http://dx.doi.org/10.1088/1757-899x/1238/1/012019.

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Abstract The formability of aluminum alloy sheet is usually improved during electromagnetic forming (EMF). Here, the ductility enhancement mechanism was investigated on the basis of Gurson-Tvergaard-Needleman (GTN) model. The parameters of GTN models under quasi-static tension and EMF conditions were respectively determined by inverse identification. For AA2024-O aluminum alloy sheet under quasi-static tension, the initial void volume fraction is identified as 0.006, the critical void volume fraction where voids begin to aggregate is 0.075, the void volume fraction of nucleating particles is 0.131 and the mean nucleation strain is 0.44. With the similar initial void volume fraction, the other parameters under EMF condition are determined as 0.045, 0.055 and 0.58. The evolution curve of void volume fraction with strain were compared under EMF condition and quasi-static tension. The results show that the total growth of void volume fraction is less under EMF condition than that under quasi-static tension. A box part with inclined flange was preliminary achieved by electromagnetic forming process. The GTN model was finally verified by comparing the numerical and experimental results.

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Tang, Yan, Chao Xie, Jianbin Chen, and Xiaofeng Wang. "Atomistic Insights into the Competition between Damage and Dynamic Recrystallization Stimulated by the Precipitate Mg17Al12 in Magnesium Alloys." Metals 12, no. 4 (April 7, 2022): 633. http://dx.doi.org/10.3390/met12040633.

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Precipitates are closely related to ductile damage and dynamic recrystallization (DRX) in magnesium alloys. Using molecular dynamics simulation and the embedded atomic method, the competition between damage and DRX stimulated by the precipitate of magnesium alloys is investigated. The effects of precipitate distribution and dimensions on the void nucleation, dislocation emission, void growth, and DRX of magnesium alloys are quantitatively discussed. It is found that compared to the system with a pre-existing void, the system with a single precipitate has two extra stages during damage evolution, namely atomic disorder and void nucleation, and its strength is clearly better. Void growth is attributed to the dislocation emission from void tips. Keeping the same volume fraction and varying the dimensions and spacings of the precipitates, the results show that the refinement and densification can increase the deformation compatibility of the system, hindering void nucleation and elevating the toughness. This can be attributed to the reduction in stress concentration and the prevalence of the particle-stimulated DRX.

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Huynh, Nam N., Cheng Lu, Guillaume Michal, and A. Kiet Tieu. "A Misorientation Dependent Criterion of Crack Opening in FCC Single Crystal." Materials Science Forum 773-774 (November 2013): 293–311. http://dx.doi.org/10.4028/www.scientific.net/msf.773-774.293.

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This paper proposes a criterion for crack opening in FCC single crystals based on analyses of lattice orientation and interface energy of two adjacent crystals in a crystal plasticity finite element model (CPFEM). It also demonstrates the implementation of the criterion in Abaqus/Standard to simulate crack initiation and propagation in single-edged notch single crystal aluminium samples. Elements in the FEM mesh that have crystalline structures satisfying the crack opening criterion are removed from the mesh at the end of every loading step and FEM analyses are restarted on the new mesh in the next loading step. Removed elements effectively act as voids in the material due to crack nucleation. Similarly, the coalescence of newly removed elements at the end of a loading step with the existent ones simulates crack growth in the material. Two advantages of this approach are noted. Firstly, crack nucleation and its subsequent growth in the material is simulated solely based on lattice evolution history in the material without any presumptions of crack paths or regions where cracks are likely to occur. Secondly, as the criterion for crack nucleation is evaluated based on, and thus changes with, the lattice evolution during loading, a predefined energy criterion for crack opening, which could be erroneous, is avoided. Preliminary results of void nucleation and void growth around the notch tip in Cube and Brass oriented samples using CPFEM modelling appear to agree with molecular dynamics simulations of void growth in FCC single crystals.

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Chandra, Abhijit, and Viggo Tvergaard. "Void Nucleation and Growth during Plane Strain Extrusion." International Journal of Damage Mechanics 2, no. 4 (October 1993): 330–48. http://dx.doi.org/10.1177/105678959300200402.

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Surh, Michael P., Jess B. Sturgeon, and Wilhelm G. Wolfer. "Void nucleation, growth, and coalescence in irradiated metals." Journal of Nuclear Materials 378, no. 1 (August 2008): 86–97. http://dx.doi.org/10.1016/j.jnucmat.2008.05.009.

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Jeong, C. S., Bum Joon Kim, and Byeong Soo Lim. "Creep Characteristics and Micro-Defects of Main Steam Pipe Steel at High Temperature." Key Engineering Materials 326-328 (December 2006): 1129–32. http://dx.doi.org/10.4028/www.scientific.net/kem.326-328.1129.

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The initiation and growth of micro-defects such as micro cracks and voids usually causes the failure of long term operated structural components at high temperature. In this study, the creep characteristics and void nucleation and growth characteristics of P92 steel which is used as main steam pipe material in power plant were investigated at several temperatures and loading conditions. The area fraction of void increased with increase of test temperature, stress, and load holding time. In case of internal defect presence, micro-voids initiated in the early stage of loading period and resulted in the increased load line displacement and crack growth rate. The microvoids were found to form along the prior austenite grain boundaries and at the martensite packet boundaries.

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GROH, SEBASTIEN, ESTEBAN B. MARIN, and M. F. HORSTEMEYER. "NANOSCALE VOID GROWTH IN MAGNESIUM: A MOLECULAR DYNAMICS STUDY." International Journal of Applied Mechanics 02, no. 01 (March 2010): 191–205. http://dx.doi.org/10.1142/s1758825110000421.

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Molecular dynamics calculations were carried out in single crystal magnesium specimens to reveal the dependence of strain rate, temperature, and orientation of the crystal on damage evolution as defined by pore growth. Two specific crystallographic orientations [0001] and [Formula: see text] were examined. During a [0001] tensile test, twin boundaries developed at the void surface leading to a constraint on the [Formula: see text] crystallographic orientation. On the other hand, during the [Formula: see text] tensile deformation, emission of shear loops in the prismatic slip planes arose when void growth initiated. Furthermore, analysis of the damage components (nucleation, growth and coalescence) revealed that a large number of small voids nucleated that rapidly grew and fractured the specimens independent of the temperature and the strain rate.

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Rajput, Ashutosh, and Surajit Kumar Paul. "Effect of void in deformation and damage mechanism of single crystal copper: a molecular dynamics study." Modelling and Simulation in Materials Science and Engineering 29, no. 8 (November 9, 2021): 085013. http://dx.doi.org/10.1088/1361-651x/ac3051.

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Abstract The current study investigates the deformation and damage mechanism of single crystal copper in the presence of a void located at the copper cell center. Tensile and compressive deformations are conducted in two loading modes, uniaxial and triaxial. Alteration in mechanical properties is observed due to the presence of void in different deformation modes. In uniaxial deformation, a smooth gradient in stress and strain distribution are evident before dislocation nucleation, i.e. in the elastic domain. However, inhomogeneity in stress and strain distribution are noted during the plastic deformation, i.e. after dislocations emission. Stress concentration remains high near the void surface ahead of the dislocation emission. Stress and strain concentration play a substantials role in nucleating defects (i.e. dislocation and stacking fault) from the void surface. Moreover, the void growth in tension and void shrinking in compression are found due to the emission/shrink of dislocations from the void surface. Consequently, an effective rate of dislocation emission enhances the growth rate of the void, as it happens in triaxial tensile deformation.

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Siroky, Georg, Elke Kraker, Dietmar Kieslinger, Ernst Kozeschnik, and Werner Ecker. "Micromechanics-based damage model for liquid-assisted healing." International Journal of Damage Mechanics 30, no. 1 (August 25, 2020): 123–44. http://dx.doi.org/10.1177/1056789520948561.

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This work presents a damage evolution framework including liquid-assisted healing. The model incorporates contributions from void size, void pressure, surface tension and liquid pressure. Experimental motivation for the damage-healing model is provided with in-situ melting experiments, where the evolution of the void distribution under monotonic tension is illustrated. The damage evolution is based on nucleation and growth of voids, which are modeled in a unified creep and plasticity framework. The proposed damage formulation introduces a void collective, which computes the void distribution in the material and allows to describe void collapse using the Rayleigh-Plesset equation. The necessary conditions for healing are discussed with use of model results. Particularly, the role of external load during healing, the dependence on liquid viscosity and surface tension are investigated.

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Zapara, Maksim, Nikolai Tutyshkin, and Wolfgang H. Müller. "Growth and Closure of Voids in Metals at Negative Stress Triaxialities." Key Engineering Materials 554-557 (June 2013): 1125–32. http://dx.doi.org/10.4028/www.scientific.net/kem.554-557.1125.

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Damage of metals subjected to large plastic deformations typical for forming processes is mainly governed by void nucleation, growth and coalescence. An opposite process may occur in deformation processes with negative stress triaxialities: the closure of strain-induced defects under large hydrostatic pressure. Understanding the mechanisms of damage growth and healing under plastic deformation of metals is still an urgent problem. In order to solve it a theoretical framework for anisotropic ductile damage based on a physically motivated concept for changes in the void volume and shape was recently developed [6]. Strain-induced damage was experimentally determined during uniaxial compression of cylindrical metallic specimens with artificial voids represented by fully-trough drilled holes. It was revealed that the governing physical mechanism of failure is a change in void shapes due to compressive stresses at low negative stress triaxialities in contrast to the growth of voids volume due to high positive stress triaxialities in the processes with dominating tensile stresses. The tensorial model presented in [6] proved to be able to describe kinetics of ductile damage, failure as the ultimate damage, and the closure of voids at negative stress triaxialities.

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Vu, Cong Hoa, Do Won Seo, and Jae Kyoo Lim. "Analysis of Spherical Void Growth and Coalescence in Metal Plastic Straining Process." Key Engineering Materials 297-300 (November 2005): 2837–42. http://dx.doi.org/10.4028/www.scientific.net/kem.297-300.2837.

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Ductile fracture occurs due to micro-void nucleation, growth and finally coalescence into micro-crack. In this study a new ductile fracture condition that based on the microscopic phenomena of void nucleation, growth and coalescence was proposed. Using this condition and combining with finite element model to predict the fracture locations in bulk metal forming. The macroscopic behavior of the material is described according to the flow rules of Levy-Mises. An idealized spherical void within an finite matrix is assumed. The void volume is calculated by taking the increasing volume of the continuum, caused by plastic straining, incorporated in the yield functions. In the model there includes the strain-hardening coefficient of the Ludwik-Holomom stress-strain relationship and concentration of stress. The accumulated damage value is a phenomenon in this model. The results show that it is in close accordance with observations of some experimental specimens. However, in order to obtaining the high trustiness many experiments have to be carried out.

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29

Šidjanin, L., and S. Miyasato. "Void nucleation and growth in dual phase steel wires." Materials Science and Technology 5, no. 12 (December 1989): 1200–1206. http://dx.doi.org/10.1179/mst.1989.5.12.1200.

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Thomson, C. "Modeling void nucleation and growth within periodic clusters of particles." Journal of the Mechanics and Physics of Solids 47, no. 1 (December 4, 1998): 1–26. http://dx.doi.org/10.1016/s0022-5096(98)00088-x.

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31

Fleck, N. A., J. W. Hutchinson, and V. Tvergaard. "Softening by void nucleation and growth in tension and shear." Journal of the Mechanics and Physics of Solids 37, no. 4 (January 1989): 515–40. http://dx.doi.org/10.1016/0022-5096(89)90027-6.

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32

Zhang, Hao, Guoqiang Liu, Ning Guo, Xiangbin Meng, Yanbin Shi, Hangqi Su, Zhe Liu, and Bingtao Tang. "Damage Evolution of Hot Stamped Boron Steels Subjected to Various Stress States: Macro/Micro-Scale Experiments and Simulations." Materials 15, no. 5 (February 25, 2022): 1751. http://dx.doi.org/10.3390/ma15051751.

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Hot stamping components with tailored mechanical properties have excellent safety-related performance in the field of lightweight manufacturing. In this paper, the constitutive relation and damage evolution of bainite, martensite, and mixed bainite/martensite (B/M) phase were studied. Two-dimensional representative volume element (RVE) models were constructed according to microstructure characteristics. The constitutive relations of individual phases were defined based on the dislocation strengthening theory. Results showed that the damage initiation and evolution of martensite and bainite phases can well described by the Lou-Huh damage criterion (DF2015) determined by the hybrid experimental–numerical method. The calibrated damage parameters of each phase were applied to the numerical simulation, followed by the 2D RVE simulations of B/M phase under different stress states. To study the influence of martensite volume fraction (Vm) and distribution of damage evolution, the void nucleation and growth were evaluated by RVEs and verified by scanning electron microscope (SEM). Three types of void nucleation modes under different stress states were experimentally and numerically studied. The results showed that with the increase of Vm and varying martensite distribution, the nucleation location of voids move from bainite to martensite.

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33

Huang, Y., A. Chandra, and N. Y. Li. "Void-nucleation vs void-growth controlled plastic flow localization in materials with nonuniform particle distributions." International Journal of Solids and Structures 35, no. 19 (July 1998): 2475–86. http://dx.doi.org/10.1016/s0020-7683(97)00145-5.

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Wciślik, Wiktor, and Sebastian Lipiec. "Void-Induced Ductile Fracture of Metals: Experimental Observations." Materials 15, no. 18 (September 18, 2022): 6473. http://dx.doi.org/10.3390/ma15186473.

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The paper presents a literature review on the development of microvoids in metals, leading to ductile fracture associated with plastic deformation, without taking into account the cleavage mechanism. Particular emphasis was placed on the results of observations and experimental studies of the characteristics of the phenomenon itself, without in-depth analysis in the field of widely used FEM modelling. The mechanism of void development as a fracture mechanism is presented. Observations of the nucleation of voids in metals from the turn of the 1950s and 1960s to the present day were described. The nucleation mechanisms related to the defects of the crystal lattice as well as those resulting from the presence of second-phase particles were characterised. Observations of the growth and coalescence of voids were presented, along with the basic models of both phenomena. The modern research methods used to analyse changes in the microstructure of the material during plastic deformation are discussed. In summary, it was indicated that understanding the microstructural phenomena occurring in deformed material enables the engineering of the modelling of plastic fracture in metals.

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35

Noolu, Naren J., Nikhil M. Murdeshwar, Kevin J. Ely, John C. Lippold, and William A. Baeslack. "Degradation and failure mechanisms in thermally exposed Au–Al ball bonds." Journal of Materials Research 19, no. 5 (May 2004): 1374–86. http://dx.doi.org/10.1557/jmr.2004.0184.

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During the manufacturing and the service life of Au–Al wire bonded electronic packages, the ball bonds experience elevated temperatures and hence accelerated interdiffusion reactions that promote the transformation of the Au–Al phases and the growth of creep cavities. In the current study, these service conditions were simulated by thermally exposing Au–Al ball bonds at 175 and 250 °C for up to 1000 h. The Au–Al phase transformations and the growth of cavities were characterized by scanning electron microscopy. The volume changes associated with the transformation of the intermetallic phases were theoretically calculated, and the effect of the phase transformations on the growth of cavities was studied. The as-bonded microstructure of a Au–Al ball bond typically consisted of an alloyed zone and a line of discontinuous voids (void line) between the Au bump and the bonded Al metallization. Thermal exposure resulted in the nucleation, growth, and the transformation of the Au–Al phases and the growth of cavities along the void line. Theoretical analysis showed that the phase transformations across and lateral to the ball bond result in significant volumetric shrinkage. The volumetric shrinkage results in tensile stresses and promotes the growth of creep cavities at the void line. Cavity growth is higher at the crack front due to stress concentration, which was initially at the edge of the void line. The crack propagation occurs laterally by the coalescence of sufficiently grown cavities at the void line resulting in the failure of the Au–Al ball bonds.

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Međo, Bojan, Marko Rakin, Nenad Gubeljak, and Aleksandar Sedmak. "Application of Complete Gurson Model for Prediction of Ductile Fracture in Welded Steel Joints." Key Engineering Materials 399 (October 2008): 13–20. http://dx.doi.org/10.4028/www.scientific.net/kem.399.13.

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Ductile fracture process includes three stages: void nucleation, their growth and coalescence. The voids nucleate due to the fracture or separation of non-metallic inclusions and secondary-phase particles from the material matrix. Micromechanical models based on the Gurson plastic flow criterion are often used for analysis of ductile fracture. They consider the material as a porous medium in which the effect of voids on the stress-strain state and plastic flow cannot be neglected. Another important property of the Gurson criterion is that the hydrostatic stress component influences the plastic flow of the material.

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Miloud, M. Hadj, A. Imad, N. Benseddiq, B. Bachir Bouiadjra, A. Bounif, and B. Serier. "A numerical analysis of relationship between ductility and nucleation and critical void volume fraction parameters of Gurson–Tvergaard–Needleman model." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 11 (February 15, 2013): 2634–46. http://dx.doi.org/10.1177/0954406213476232.

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Gurson–Tvergaard–Needleman model is widely used to describe the three stages of ductile tearing: nucleation, growth and the coalescence of micro-voids. The aim of this article is to study the relationship between volume fraction of voids and the fracture strain ɛf. The effects of the volume fraction of nucleation, fN, and the critical volume fraction, fc, were analysed. These parameters play crucial roles in the process of ductile damage. A phenomenological analysis is carried out to study the relationship between the different void volume parameters and the fracture strain ɛf. A method is proposed for the determination of fN and fc, knowing the experimental fracture strain ɛf. The experimental parameters are extracted from the load–diametric contraction curve of an axisymmetric notched tensile bar test AN2.

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Shao, Jie, He Ping Guo, Zhi Qiang Li, and X. Q. Han. "Cavitation Behavior of Fine-Grained 1420 Al-Li Alloy during Superplastic Deformation." Materials Science Forum 551-552 (July 2007): 633–38. http://dx.doi.org/10.4028/www.scientific.net/msf.551-552.633.

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This paper deals with the cavity formation and growth behavior of fine-grained 1420 Al-Li alloy during superplastic forming. The results indicated that there were many sub-micron cavities pre-existing at the particle-matrix interface and these sub-micron cavities grew initially under deformation. Different from uniaxial tension, the cavities nucleation under biaxial tension was combinable effect of stress concentration and matrix/particle de-cohesion. With the strain and temperature increasing, the total number and the average size of cavities increased. By the calculations, it was seen that diffusional growth process dominates the initial stage of void growth, and for void radii>~1.7μm, void growth was mainly controlled by plasticity.

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Fukahori, Tomoaki, Shinichi Suzuki, Naoya Yamada, Masatoshi Aramaki, and Osamu Furukimi. "Effect of Microstructure on Formation of Ductile Fracture Surface in Steel Plate." Advanced Materials Research 409 (November 2011): 678–83. http://dx.doi.org/10.4028/www.scientific.net/amr.409.678.

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In recent years, high strength steel plates for building and pipelines have been required to improve ductile fracture properties, assuming ground deformation in earthquake-prone region. The ductile fracture is performed by the result from coalescence of micro-voids followed by the nucleation and growth [1]. Fractured surface morphology reflects the void coalescence process, so it is important to consider the relationship between the fracture surface morphology and the micro-voids formation beneath the fractured surface to consider the ductile fracture properties. The voids nucleate sites are mainly particles such as inclusions or precipitates, and grain boundries. These voids grow and coalesce according to three modes. The first mode is directly coalescence of voids followed by growth [2]. The second one is the coalescence of voids caused by shear deformation followed by internal necking between voids [3]. The third one is the coalescence of voids caused by micro-voids nucleation in shear band between two larger voids [4]. It is expected that these modes influence local elongation property which is one of the indices for ductile fracture property through the formation of fractured surface. In this study, local deformation energy which is measured by load-displacement curve in tensile test is examined by focusing the voids nucleation, growth and coalescence, for high tensile strength plates of TS480-830MPa which is controlled by the microstructure through the cooling rate of heat treatment. The deformation energy is useful to consider the ductile fracture property of steel plates which have a different tensile strength.

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Kim, Jong Bong, and Jeong Whan Yoon. "Analysis of the Necking Behaviors with the Crystal Plasticity Model Using 3-Dimensional Shaped Grains." Advanced Materials Research 684 (April 2013): 357–61. http://dx.doi.org/10.4028/www.scientific.net/amr.684.357.

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Without initial imperfection and damage evolution model, it is difficult to analyze the necking behavior by finite element analysis with continuum theory. Moreover, the results are greatly dependent on the size of the initial imperfection. In order to predict necking phenomenon without geometric imperfection, in this study, a crystal plasticity model was introduced in the 3-dimensional finite element analysis of tensile test. Grains were modeled by an octahedron and different orientations were allocated to each grain. Damage model was also used to predict the sudden drop of load carrying capacity after necking and to reflect the void nucleation and growth on the severely deformed region. Well-known Cockcroft-Latham damage model was used. Void nucleation, growth and coalescence behavior during necking were predicted reasonably.

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41

Chen, Liang, Lihui Wu, Yu Liu, and Wei Chen. "In situ observation of void evolution in 1,3,5-triamino-2,4,6-trinitrobenzene under compression by synchrotron radiation X-ray nano-computed tomography." Journal of Synchrotron Radiation 27, no. 1 (January 1, 2020): 127–33. http://dx.doi.org/10.1107/s1600577519014309.

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The formation and development of voids in 1,3,5-triamino-2,4,6-trinitrobenzene crystals under compression were characterized in situ by X-ray nano-computed tomography. Benefiting from high spatial resolution (30 nm) and excellent imaging contrast, the X-ray nano-computed tomography images revealed the presence of a small fraction of inhomogeneous structures in the original crystal (volume ratio ∼1.2%). Such an inhomogeneity acts as a nucleation of voids and produces stress concentration during compression, which leads to continuous growth of the voids under loading. Meanwhile, the results further reveal that the developing voids are not isotropic: voids with higher surface roughness and irregular structures are easier to break and form new micro-voids. These new voids with higher irregular structures are weaker and easier to break into smaller ones compared with the originals, leading to the development of voids along these weak zones. Finally large voids form. The experiments allow direct investigation of void formation and development, which helps in studying the mechanisms of void development and energetic materials deterioration during manufacturing and transporting.

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42

Goodhew, P. J. "The nucleation of cavities at grain boundaries." Proceedings, annual meeting, Electron Microscopy Society of America 45 (August 1987): 288–91. http://dx.doi.org/10.1017/s0424820100126299.

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Cavity nucleation and growth at grain and phase boundaries is of concern because it can lead to failure during creep and can lead to embrittlement as a result of radiation damage. Two major types of cavity are usually distinguished: The term bubble is applied to a cavity which contains gas at a pressure which is at least sufficient to support the surface tension (2g/r for a spherical bubble of radius r and surface energy g). The term void is generally applied to any cavity which contains less gas than this, but is not necessarily empty of gas. A void would therefore tend to shrink in the absence of any imposed driving force for growth, whereas a bubble would be stable or would tend to grow. It is widely considered that cavity nucleation always requires the presence of one or more gas atoms. However since it is extremely difficult to prepare experimental materials with a gas impurity concentration lower than their eventual cavity concentration there is little to be gained by debating this point.

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43

Huber, G., Y. Brechet, and T. Pardoen. "Predictive model for void nucleation and void growth controlled ductility in quasi-eutectic cast aluminium alloys." Acta Materialia 53, no. 9 (May 2005): 2739–49. http://dx.doi.org/10.1016/j.actamat.2005.02.037.

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44

Semenov, A. A., and C. H. Woo. "Interfacial energy in phase-field emulation of void nucleation and growth." Journal of Nuclear Materials 411, no. 1-3 (April 2011): 144–49. http://dx.doi.org/10.1016/j.jnucmat.2011.01.100.

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45

Rokkam, Srujan, Anter El-Azab, Paul Millett, and Dieter Wolf. "Phase field modeling of void nucleation and growth in irradiated metals." Modelling and Simulation in Materials Science and Engineering 17, no. 6 (August 24, 2009): 064002. http://dx.doi.org/10.1088/0965-0393/17/6/064002.

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46

Margolin, BZ, GP Karzov, VA Shvetsova, and VI Kostylev. "MODELLING FOR TRANSCRYSTALLINE AND INTERCRYSTALLINE FRACTURE BY VOID NUCLEATION AND GROWTH." Fatigue & Fracture of Engineering Materials & Structures 21, no. 2 (February 1998): 123–37. http://dx.doi.org/10.1046/j.1460-2695.1998.00474.x.

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47

Jiang, Zhaoxiu, Zheng Zhong, Puchu Xie, Yonggang Wang, and Hongliang He. "Characteristics of the damage evolution and the free surface velocity profile with dynamic tensile spallation." Journal of Applied Physics 131, no. 12 (March 28, 2022): 125104. http://dx.doi.org/10.1063/5.0082361.

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The spalling behavior of ductile metals is a process involving void nucleation, growth, and coalescence. Limited by diagnostic techniques, spallation experiments only provide the free surface velocity profiles and the information about recovered targets, but some quantitative damage evolution information about the spalling target is lacking. In this research, the damage nucleation seeds are randomly arranged on the grain boundary in the central region of a target with grain geometry, and a two-dimensional mesoscale numerical model of a plate impact spall experiment is established. By analyzing the free surface velocity profile and the stress history, it is demonstrated that the spall strength obtained with the pull-back velocity essentially corresponds to the maximum tensile stress at the target center. The effects of the impact stress and the stress pulse duration on the dynamic characteristics of the void growth and coalescence are analyzed in-depth by using the damage evolution dissipation energy and the plastic strain contours at different times. The dynamic process of the damage evolution determines the characteristics of the oscillation after the pull-back signal. The stress history controls the damage degree and the kinetic process of the target in the spallation damage process. The impact stress has the most important effect in determining the damage evolution rate, while the stress pulse duration only affects the void coalescence process and irrelevant to the void growth. The damage degree of the void growth and the coalescence process are the result of the joint action of the impact stress and the pulse duration.

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48

Liu, B. X., S. L. Lai, and J. G. Sun. "Effects of alloying and treatment on void swelling of 316 stainless steels." Journal of Materials Research 6, no. 8 (August 1991): 1650–54. http://dx.doi.org/10.1557/jmr.1991.1650.

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Several samples of type 316 stainless steels, which were treated differently and modified with minor elements (such as Ti, Nb, etc.), were irradiated by 1 MeV electrons in HVEM at temperatures ranging from 823 K to 883 K. Void swelling behavior of the steels was investigated, and three parameters, i.e., swelling, void density, and void size, were measured. The results show that prior cold work improves the swelling resistance of type 316 stainless steels more effectively than solid-solution treatment. It is also shown that Ti is the best alloying element studied that can suppress void nucleation and its growth drastically by acting as sinks and impeding dislocation climb, resulting in the reduction of void swelling.

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Yu, Tao, Masataka Yatomi, and Hui Ji Shi. "Numerical Simulation of Void Growth Induced Creep Rupture in HAZ at Elevated Temperature." Advanced Materials Research 33-37 (March 2008): 441–48. http://dx.doi.org/10.4028/www.scientific.net/amr.33-37.441.

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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.

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Sharma, Pradeep, and Abhijit Dasgupta. "Micro-Mechanics of Creep-Fatigue Damage in PB-SN Solder Due to Thermal Cycling—Part I: Formulation." Journal of Electronic Packaging 124, no. 3 (July 26, 2002): 292–97. http://dx.doi.org/10.1115/1.1493202.

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This paper presents a micro-mechanistic approach for modeling fatigue damage initiation due to cyclic creep in eutectic Pb-Sn solder. Damage mechanics due to cyclic creep is modeled with void nucleation, void growth, and void coalescence model based on micro-structural stress fields. Micro-structural stress states are estimated under viscoplastic phenomena like grain boundary sliding, its blocking at second-phase particles, and diffusional creep relaxation. In Part II of this paper, the developed creep-fatigue damage model is quantified and parametric studies are provided to better illustrate the utility of the developed model.

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Journal articles on the topic 'Void nucleation and growth'

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