Stochastic modelling in design of mechanical properties of nanometals

Phys. Status Solidi (c)

Iwankiewicz

2010

Self Cite

The driving force for limited thermal stability of Nano‐Poly‐Crystals is high concentration of internal energy. This makes them to undergo significant changes when exposed to temperatures exceeding one‐third their melting points. Two processes are expected to take place under such temperatures which reduce the internal energy: (a) grain growth i.e. reduction in total grain boundary (GB) surface area or GB volume fraction and (b) reduction of GB energy per surface area. This paper proposes a theoretical approach that couples knowledge from energy method with that from stochastic differential equations to study the energy released from nanometals during grain growth. The basic Physics of the mechanisms leading to grain growth in nanomaterials is applied. The proposed model is tested on polycrystalline nano‐aluminium samples. The impacts of annealing time, mean grain size, grain size dispersion and annealing temperatures are tested. It is anomalously revealed that on comparing the various mechanisms of grain growth, the greatest amount of energy is released from nanomaterial if grain growth is due to Grain Rotation‐Coalescence (GRC) mechanism only, followed by that due to simultaneous GRC and Grain Boundary Migration (GBM) processes and least by that due to GBM only. The energies involved in T1 events, T2 events and in rotating the grains before coalescence during GRC have also been dealt with. On comparing the different physical activities taking place during growth, it is revealed that the largest amount of energy is released from materials in which grains rotate, translate and grow at constant force. This is followed by the amount of energy involved with rotating or translating the grains at constant size and least by the energy released due to changing grain size at constant force. It is also found that the rate of release of energy initially decreases rapidly, and then very slowly approaching zero during grain growth. Thus, one may conclude from the principle of stationary potential energy that the nanomaterial attains energy equilibrium in the long run. Thus, the driving force for grain growth at larger grain sizes is not more the grains' internal energy concentration. (© 2010 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

Section: Resultssupporting

confidence: 86%

“…The yield stress of a grain in a nanomaterials undergoing a plastic deformation is given as [8][9][10] …”

Section: Methodsmentioning

confidence: 99%

The evolution of internal energy released from nanomaterials during grain growth

Phys. Status Solidi (c)

Iwankiewicz

2010

Self Cite

“…where 1 is local critical grain size, and are constants, ( ) is change of the Wiener process, 1 = 1 2 1 defines rate of grain breakage, = (1 + / 1 ), = 4( )(ℎ )/(( )( )), = {ln( 1 / )}, and = 1 exp{(inf)/ } as given by [6,10]. Since 3 evolves (i.e., decreases) as a fraction or proportion (Ratio 1 ) of 1 during grain refinement, 3 can be represented by…”

Section: Models Derivationmentioning

confidence: 99%

“…This relationship has its shortcoming since infinite refinement does not lead to infinite yield stress. The HPR model was modified by Zhao and Jiang [9] to reveal the Reverse Hall-Petch Relationship (RHPR), which was later modified by Tengen et al [10] to consider the stochastic nature of grain size.…”

Section: Introductionmentioning

confidence: 99%

Stochastic Effect of Grain Elongation on Nanocrystalline Materials Strain and Strain Rate Produced by Accumulative Roll-Bonding and Equal Channel Angular Pressing

Sob

Alugongo

Advances in Materials Science and Engineering

2017

Severe plastic deformation techniques are acknowledged to produce elongated grains during fabrication of nanostructured materials. Previous models relating grain size to mechanical properties considered only equivalent radius, thus ignoring other approaches of measuring grain sizes such as semiminor axis, semimajor axis, and major axis radii that determine true grain shape. In this paper, stochastic models of nanomaterials mechanical properties that include the ignored parameters have been proposed. The proposed models are tested with data from nanocrystalline aluminum samples. The following facts were experimentally observed and also revealed by the models. Grain elongates to a maximum value and then decreases with further grain refinement due to grain breakages. Materials yield stress increases with elongation to a maximum and then decreases continuously. The varying approaches of measuring grain radius reveal a common trend of Hall-Petch and Reverse Hall-Petch Relationship but with different critical grain sizes. Materials with high curvature grains have more enhanced yield stress. Reducing strain rates leads to materials with more enhanced yield stress, with critical strain rates values beyond which further reductions do not lead to yield stress enhancement. It can be concluded that, by considering different approaches of measuring grain sizes, reasons for different yield stress for nanomaterials that were observed but could not be explained have been dealt with.

“…first and second) observations is that both mean grain size and grain size dispersion should simultaneously be used when designing and modelling nanomaterials' mechanical properties (i.e. grain size distribution is important) [9,10,13]. While remarkable success has been achieved on the concurrent employment of mean grain size and grain size dispersion in modelling and designing of nanomaterials' mechanical properties, it has also been, thirdly, acknowledged that nanomaterials from similar samples produced to the same mean grain size and the same dispersion may have different mechanical properties [9-11,13].…”

Section: Introductionmentioning

confidence: 99%

Designing nanomaterials with desired mechanical properties by constraining the evolution of their grain shapes

2011

Nanoscale Res Lett

Grain shapes are acknowledged to impact nanomaterials' overall properties. Research works on this issue include grain-elongation and grain-strain measurements and their impacts on nanomaterials' mechanical properties. This paper proposes a stochastic model for grain strain undergoing severe plastic deformation. Most models deal with equivalent radii assuming that nanomaterials' grains are spherical. These models neglect true grain shapes. This paper also proposes a theoretical approach of extending existing models by considering grain shape distribution during stochastic design and modelling of nanomaterials' constituent structures and mechanical properties. This is achieved by introducing grain 'form'. Example 'forms' for 2-D and 3-D grains are proposed. From the definitions of form, strain and Hall-Petch-Relationship to Reversed-Hall-Petch-Relationship, data obtained for nanomaterials' grain size and conventional materials' properties are sufficient for analysis. Proposed extended models are solved simultaneously and tested with grain growth data. It is shown that the nature of form evolution depends on form choice and dimensional space. Long-run results reveal that grain boundary migration process causes grains to become spherical, grain rotation coalescence makes them deviate away from becoming spherical and they initially deviate away from becoming spherical before converging into spherical ones due to the TOTAL process. Percentage deviations from spherical grains depend on dimensional space and form: 0% minimum and 100% maximum deviations were observed. It is shown that the plots for grain shape functions lie above the spherical (control) value of 1 in 2-D grains for all considered grain growth mechanisms. Some plots lie above the spherical value, and others approach the spherical value before deviating below it when dealing with 3-D grains. The physical interpretations of these variations are explained from elementary principles about the different grain growth mechanisms. It is observed that materials whose grains deviate further away from the spherical ones have more enhanced properties, while materials with spherical grains have lesser properties. It is observed that there exist critical states beyond which Hall-Petch Relationship changes to Reversed Hall-Petch Relationship. It can be concluded that if grain shapes in nanomaterials are constrained in the way they evolve, then nanomaterials with desired properties can be designed.