Thermal induced nanovoid evolution in the vicinity of an immobile austenite-martensite interface

Ghaedi

Barchiesi

et al. 2020

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In the present work, the effect of a pre-existing nanovoid on martensitic phase transformation (PT) is investigated using the phase field approach. The nanovoid is created as a solution of the coupled Cahn–Hilliard and elasticity equations. The coupled Ginzburg–Landau and elasticity equations are solved to capture the martensitic nanostructure. The above systems of equations are solved using the finite element method and COMSOL code. The austenite ( A)–martensite ( M) interface propagation is investigated without the nanovoid and with it for different nanovoid misfit strains and different temperatures. With the nanovoid, the evolution of the moving interface is changed even before it reaches the nanovoid surface due to the nanovoid stress concentration. It is also found that for small misfit strains, pre-transformation occurs near the nanovoid. For larger misfit strains, martensite nucleates and grows near the nanovoid surface and coalesces with the moving interface. The nanovoid shows a promotive effect on the PT with an increase in the rate of transformation, which is discussed based on the transformation work distribution. The effect of the nanovoid is more pronounced on a curved interface. The nanovoid-induced martensitic growth is mainly dependent on the transformation strain tensor. Examples for different transformation strains are presented where a stable non-complete transformed sample with no void becomes unstable in the presence of the nanovoid. The presented model and results will help to develop an interaction model between nanovoids and multiphase structures at the nanoscale.

Section: Phase Field Modelmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

The effect of a pre-existing nanovoid on martensite formation and interface propagation: a phase field study

Ghaedi

Barchiesi

et al. 2020

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“…Examples are the higher-order strain gradient theories [1–7], the rotation gradient or couple-stress theories [8–12] and the nonlocal elasticity theory [13–16]. It is worthy of note that there exists also the phase field theory as a continuum approach, which includes strain nonlocality and has been broadly used for the micro/nanoscale simulation of dislocations [17,18], various types of phase transformations (PTs) [19–21], cracks [22,23] and nanovoids [24–28]. Among the mentioned theories, the nonlocal elasticity theory, which is a prevalent approach to study the static and dynamic behavior of nanostructures, is the focus of this paper.…”

Section: Introductionmentioning

confidence: 99%

Free vibration analysis of nonlocal nanobeams: a comparison of the one-dimensional nonlocal integral Timoshenko beam theory with the two-dimensional nonlocal integral elasticity theory

Danesh

2021

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Beam theories such as the Timoshenko beam theory are in agreement with the elasticity theory. However, due to the different nonlocal averaging processes, they are expected to yield different results in their nonlocal forms. In the present work, the free vibration behavior of nonlocal nanobeams is studied using the nonlocal integral Timoshenko beam theory (NITBT) and two-dimensional nonlocal integral elasticity theory (2D-NIET) with different kernels and their results are compared. A new kernel, termed the compensated two-phase (CTP) kernel, is introduced, which entirely compensates for the boundary effects and does not suffer from the ill-posedness of previous kernels. Using the finite element method, the free vibration analysis is performed for different boundary conditions based on the first three natural frequencies. For both the NITBT and 2D-NIET with both the two-phase (TP) and CTP kernels, the nonlocal parameter has a softening effect on the natural frequencies for all the boundary conditions, without observing the paradoxical behaviors of the nonlocal differential theory. For both theories, the softening effect of the nonlocal parameter is more pronounced for the TP kernel compared to the CTP kernel. The sensitivity of the 2D-NIET to the nonlocal parameter is found to be higher than that of the NITBT. Also, the softening effects for different vibration modes are compared to each other for both theories and both kernels. The obtained results can be extended for various important beam problems with nonlocal effects and help obtain a better understanding of applicable nonlocal theories.

“…A PFA was proposed in Vance and Millett [48] in which energy potential consists of chemical, gradient and elastic energies and revealed the effect of elastic anisotropy on diffusion of voids. The combined 1D-RWM and CH model was proposed in Javanbakht and Sadegh Ghaedi [49] to capture the nanovoid evolution under irradiation. Despite the lack of mechanics term, various interactions of structural defects were considered in their model [40].…”

Section: Introductionmentioning

confidence: 99%

“…The nanovoid migration was studied with the help of a velocity term accounting for the vapour transport in Vance and Millett [48]. A PFA was recently presented to study the nanovacancy evolution in the vicinity of an austenite–martensite interface [49]. The significant effects of nanovoids on phase transformations were studied by Javanbakht and colleagues [50-52].…”

Section: Introductionmentioning

confidence: 99%

Effect of a thermodynamically consistent interface stress on thermal-induced nanovoid evolution in NiAl

Ghaedi

2021

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In the present work, the effect of a thermodynamically consistent inelastic interface stress on nanovoid evolution in NiAl is studied. Such interface stress is introduced for the solid–gas interface of nanovoids within the concept of the phase field approach. The Cahn–Hilliard (CH) equation using the Helmholtz free energy describes the evolution of nanovoid concentration. The interface stress changes the total stress distribution and affects the elastic stress field. Thus, due to the significant effect of the elastic energy on nanovoid dynamics, it can indirectly affect nanovoid nucleation and growth. The highly nonlinear coupled CH and elasticity equations are solved using the finite element method and the COMSOL code. The coupling appears due to the presence of the nonlinear nanovoid inelastic strain in the total strain, the presence of the nonlinear inelastic interface stress in the stress tensor and the presence of elastic energy in the Helmholtz free energy. Several examples of thermal-induced nanovoid evolutions are presented to investigate the effect of the solid–gas interface stress. The obtained results show the significant effect of the interface stress on the total stress distribution, and consequently a different distribution of thermodynamic driving force which can affect the nanostructure evolution and the deformation. Mainly, the interface stress represents a promotive effect on nanovoid growth which results in a faster nanovoid growth and a larger nanovoid concentration and region.