Distribution Of Deformation Energy Research Articles

Effects of TiB2 particles on deformation behavior, softening mechanisms and recrystallization texture of hot-compressed Fe-TiB2 composites

Fe-TiB2 composites, also termed as high modulus steel, offer a promising solution to the challenge of achieving both lightweight and high stiffness materials. However, the presence of TiB2 particles in Fe-TiB2 composites results in poor hot-workability. Therefore, understanding the effects of TiB2 particles on the hot deformation behavior, dynamic recrystallization (DRX), and microstructural evolution of Fe-TiB2 composites is crucial for optimizing their hot-working process. In this study, we elucidated the effects of TiB2 particles on deformation behavior and dynamic softening behavior by conducting a series of isothermal compression tests on as-cast Fe-TiB2 composites and as-cast base alloys (control group) at temperatures of 800–1200 °C, strains of 0.36–1.2, and strain rates of 0.01–1 s⁻1. Using electron backscatter diffraction, we characterized the microstructures of composites and base alloys, showing that TiB2 particles induce a DRX process through particle stimulated nucleation (PSN) at low temperatures and promote continuous dynamic recrystallization (CDRX) at high temperatures. The presence of TiB2 particles have significantly affected the dislocation movement and distribution, which changes the deformation energy distribution and thus facilitates different DRX behaviors under various thermal deformation conditions. Additionally, the microstructure resulting from DRX through PSN exhibits significant texture weakening and grain refinement, presenting a promising method for fabricating ultrafine-grained Fe-TiB2 composites.

Damage evolution of coal with a strong bursting liability and 3D measurement method for elastic deformation energy distribution

When coal with a strong bursting liability is disturbed by a load, catastrophic instability disasters and rockbursts can easily occur. Loaded coal with a strong bursting liability undergoes complex damage evolution and failure behavior due to the intricate interplay among loads, gangue, fractures, and the coal matrix. Intuitively quantifying and characterizing the complex discontinuous structural features, deformation fields, and energy fields within coal is the foundation for the scientific analysis and prevention of disaster mechanisms caused by rockbursts. Therefore, studying the distribution and evolutionary processes of deformation fields and energy fields caused by the evolution of discontinuous structures within coal is highly important for the prevention and control of coal mine rockburst disasters and the protection of coal mine safety during mining operations. In this study, a series of X-ray computed tomography (X-CT) tests were conducted on coal specimens with varying gangue contents under uniaxial compressive loading. The X-CT images clearly illustrated the internal damage evolution of coal with a strong bursting liability, revealing fracture propagation, shear bands, and localized failure under varying loading conditions. Image segmentation was employed to quantitatively analyze the development of damage in coal with a strong bursting liability, revealing the influence patterns of gangue content on the prepeak deformation localization and strength of coal. Additionally, using digital volume correlation, the 3D volumetric displacement and strain of loaded impact-prone coal were determined based on the changes in natural speckle images. The nonuniform distribution of strain was mainly caused by the nonuniform distribution of gangue and pore fractures at the microscopic scale, which explains the localized deformation in coal materials. Importantly, this study provides new full-field strain tensor data and a novel method for measuring the elastic deformation energy of the 3D deformation and cracking processes of loaded coal.

Analysis of the influence of a pseudo-random number generator type on the kinetics of the cellular automata recrystallization model

Models based on discrete simulation methods, i.e., cellular automata (CA) or Monte Carlo (MC), often contain probabilistic elements in the code to capture the stochastic character of material behaviour. They can be related to various physical aspects reflected in the model, e.g., heterogeneous energy distribution or random crystallographic orientation assignment to subsequent grains. Therefore, the paper's main aim is to analyze the influence of such random elements in the CA recrystallization model used to predict the material microstructure morphology after thermo-mechanical treatment. The first part of the work presents the available tools for pseudo-random number generation and the main elements of the investigated CA recrystallization model. Different variants of input data preparation prior to the simulation, including deformation energy distribution, are shown. The role of the investigated pseudo-random number generators (rand, lcg, mt, ranlux) and their distribution (uniform, normal, lognormal) is highlighted in this part. Finally, the input data are used to perform simulations of recrystallization progress, and the effect of pseudo-random number generation parameters on transformation kinetics and growth of recrystallized grains is evaluated. With this work, we have demonstrated that the choice of the generator type, particularly the method of its distribution, influences the simulation results in the form of final material morphology.

Damage distribution mechanism of common low-rise steel frame structures

In order to research the damage distribution mechanism of common low-rise steel frame structures under dynamic action, this paper took the column-to-beam strength ratio αi and column base form as the main parameters to research the seismic performance of common low-rise steel frames. To achieve this goal, 24 models of common low-rise steel frame structures were designed and analyzed by elasto-plastic time history analysis method; and the predominant periods of seismic waves are similar to the fundamental periods of these models. This paper focuses on the demand performance of each model such as the distribution of maximum inter-story drift ratio (MIDR), the deformation concentration rate of the first floor dR1, the ductility ratio μ and cumulative plastic ductility ratio η of the beams and columns; and clarifies the relationship between the damage mechanism of common low-rise steel frame structures and column-beam strength ratio αi and column base form in the first place. After that, to investigate the effect of each parameter on the structural energy dissipation, the plastic deformation energy distribution of each model was also studied in this paper. Finally, the mathematical equations of the seismic input energy and plastic deformation energy were studied, which can apply to common low-rise steel frame structures in the resonant state. It can provide a reference for engineers to choose the column-to-beam strength ratio αi and the column base form in the design of low-rise steel frame structures.

Simulation of strain induced abnormal grain growth in aluminum alloy by coupling crystal plasticity and phase field methods

A mesoscale modeling methodology is proposed to predict the strain induced abnormal grain growth in the annealing process of deformed aluminum alloys. Firstly, crystal plasticity finite element (CPFE) analysis is performed to calculate dislocation density and stored deformation energy distribution during the plastic deformation. A modified phase field (PF) model is then established by extending the continuum field method to consider both stored energy and local interface curvature as driving forces of grain boundary migration. An interpolation mapping approach is adopted to transfer the stored energy distribution from CPFE to PF efficiently. This modified PF model is implemented to a hypothetical bicrystal firstly for verification and then the coupled CPFE-PF framework is further applied to simulating the 2D synthetic polycrystalline microstructure evolution in annealing process of deformed AA3102 aluminum alloy. Results show that the nuclei with low stored energy embedded within deformed matrix tend to grow up, and abnormal large grains occur when the deformation is close to the critical plastic strain, attributing to the limited number of recrystallized nuclei and inhomogeneity of the stored energy.

A spatial upscaling method for describing the three-body potential of a diamond lattice structure

A spatial upscaling method that efficiently describes the three-body potential of diamond lattice structures is proposed in this paper. The spatial scale of the bulk single-crystal diamond can be increased without increasing the computational complexity by balancing the weighting factor with the atomic-scale Tersoff potential and the mass of its constituents. The statistical averages and fluctuations in the thermodynamic equilibrium were reproduced within acceptable error limits. The model used to represent the mechanical behavior of diamond-structured materials was further expanded to simulate polycrystalline diamond structures under mechanical deformation. An empirical scaling formula was applied to attenuate localized stresses generated at the surfaces and grain boundaries. The upscaled model successfully reproduced the deformation energy distribution under spherical indentation observed from the all-atom-based simulation model.

Mechanical evaluation of bidirectional surface deformation in contact between nanometer-sized carbon particle and copper substrate: A molecular dynamics approach

In this work, we investigate the subsurface mechanical behavior of a diamond-structured nanocarbon particle (dNP) and a copper substrate (CS) at nanocontact using molecular dynamic (MD) simulations of indentation and scratching processes. An individual interatomic force field is assigned for each atomic pair for the precise evaluation of the subsurface of both the dNP and the CS. In addition, the bidirectional distribution of deformation energy is examined with the surface deformation of both the dNP and the CS is allowed. The bidirectional distribution of deformation energy is presented as an increment of the potential energy of the CS and the periodic motion of carbon atoms. Furthermore, considering a continuum volume element within the subsurface of the CS with a comprehensive representation of the mechanical deformation distribution by the MD simulations, we propose a methodology for dealing with nanoscale contacts in the classical mechanics of materials considering the discrete deformation gradient in all-atom detail. A preference of the translational direction of the dNP suggests an underlying analysis technique in evaluation of nanocontact-induced subsurface deformation for a precise mechanical design of the nanoscale contact problems.

How global DNA unwinding causes non-uniform stress distribution and melting of DNA.

DNA unwinding is an important process that controls binding of proteins, gene expression and melting of double-stranded DNA. In a series of all-atom MD simulations on two DNA molecules containing a transcription start TATA-box sequence we demonstrate that application of a global restraint on the DNA twisting dramatically changes the coupling between helical parameters and the distribution of deformation energy along the sequence. Whereas only short range nearest-neighbor coupling is observed in the relaxed case, long-range coupling is induced in the globally restrained case. With increased overall unwinding the elastic deformation energy is strongly non-uniformly distributed resulting ultimately in a local melting transition of only the TATA box segment during the simulations. The deformation energy tends to be stored more in cytidine/guanine rich regions associated with a change in conformational substate distribution. Upon TATA box melting the deformation energy is largely absorbed by the melting bubble with the rest of the sequences relaxing back to near B-form. The simulations allow us to characterize the structural changes and the propagation of the elastic energy but also to calculate the associated free energy change upon DNA unwinding up to DNA melting. Finally, we design an Ising model for predicting the local melting transition based on empirical parameters. The direct comparison with the atomistic MD simulations indicates a remarkably good agreement for the predicted necessary torsional stress to induce a melting transition, for the position and length of the melted region and for the calculated associated free energy change between both approaches.

Coupled mechanism of compression and prying-induced rock burst in steeply inclined coal seams and principles for its prevention

Rock bursts frequently occur in steeply inclined and extremely thick coal seams (SIETCS), posing severe challenges to safe mining. To reduce the risk of rock burst in SIETCS, this study investigated the mechanisms of the rock bursts occurrence in SIETCS and formulated the principles for its prevention. To this end, field investigation, geophysical monitoring, theoretical analyses, and numerical simulation were employed. Mechanical models have been developed for a “steeply inclined suspended roof structure” and a “steeply inclined suspended rock pillar structure”, which are relevant to the rock burst mechanisms. The elastic deformation energy distribution functions for both models have been obtained, and the factors influencing the elastic deformation energy have been analyzed. The sources of microseismic (MS) events associated with rock bursts monitored in the typical SIETCS (with a dip angle of 87°) are mainly concentrated in the roof and interlayer rock pillar, making up 17.0% and 60% of the events recorded, respectively. The elastic deformation energy of the roof and rock pillar is mainly influenced by the dip angle of the coal seam, the lateral pressure coefficient, and the supporting force coefficient. The peak stress of the coal body at the compressive and prying area is 1.7 times of the horizontal tectonic stress. The minimum normal and tangential dynamic load stresses generated by the recorded rock bursts are 84.5 MPa and 48.6 MPa, respectively; such stress levels exert strong destructive forces when superimposed with static stress. The analytical results of the failure law of rock burst, MS monitoring, mechanical model, numerical simulation, and elastic deformation energy function of the typical SIETCS identify the main causes of rock burst as the high static stress of a coal body under the coupled action of compressive and prying effects of roof and rock pillar and the dynamic stress caused by breakage of the roof and rock pillar. The damage models and the damage process by which a rock burst is induced have been constructed. Three mechanisms by which a rock burst can occur in SIETCS are proposed. Finally, prevention principles of load-reduction and prying-reduction for rock burst in SIETCS have been developed.

Investigating the Stored Deformation Energy Distribution in a Polycrystalline Metal using a Dislocation Density-based Crystal Viscoplasticity Theory

Investigating the Stored Deformation Energy Distribution in a Polycrystalline Metal using a Dislocation Density-based Crystal Viscoplasticity Theory

Modeling of load transmission and distribution of deformation energy before and after healing of basal dental implants in the human mandible

The purpose of this study was to present the amount and distribution of pressure, stress, and deformation energy when basal implants in the mandible are restored with a bridge which is loaded at two different stages of bone healing. The model geometry and material properties of the mandible were gained from CT scans of a human mandible. The material model used in this study defined bone as an inhomogeneous, linear elastic isotropic material. The masseter and temporal muscles were considered as rigid connections between the bones in typical positions and directions. The rotation axis was simulated in the temporomandibular joint. The loading force of 450 N was assumed to be in the middle between the left molar and left canine implant. In freshly operated bone, the total deformation energy is 30% higher than in healed bone, due to the defined energy absorbing soft bone areas. Approximately 90% of the deformation energy is absorbed by the bone, regardless of the healing state of the bone. The immediate rigid implant splinting distributes peak forces. To cope with these energies, the necessity of a reduction of total masticatory forces or the use of additional implants for force distribution should be considered individually.

Adaptive mesh refinement and automatic remeshing in crystal plasticity finite element simulations

In finite element simulations dedicated to the modelling of microstructure evolution, the mesh has to be fine enough to: (i) accurately describe the geometry of the constituents; (ii) capture local strain gradients stemming from the heterogeneity in material properties. In this paper, 3D polycrystalline aggregates are discretized into unstructured meshes and a level set framework is used to represent the grain boundaries. The crystal plasticity finite element method is used to simulate the plastic deformation of these aggregates. A mesh sensitivity analysis based on the deformation energy distribution shows that the predictions are, on average, more sensitive near grain boundaries. An anisotropic mesh refinement strategy based on the level set description is introduced and it is shown that it offers a good compromise between accuracy requirements on the one hand and computation time on the other hand. As the aggregates deform, mesh distortion inevitably occurs and ultimately causes the breakdown of the simulations. An automatic remeshing tool is used to periodically reconstruct the mesh and appropriate transfer of state variables is performed. It is shown that the diffusion related to data transfer is not significant. Finally, remeshing is performed repeatedly in a highly resolved 500 grains polycrystal subjected to about 90% thickness reduction in rolling. The predicted texture is compared with the experimental data and with the predictions of a standard Taylor model.

An inverse method applied to the determination of deformation energy distributions in the presence of pre-hardening stresses

This paper presents an experimental procedure to estimate the deformation energy distribution within plane samples submitted to mechanical loading. This procedure combined a digital image correlation (DIC) technique giving in-plane displacement fields with an identification method that separately provided fields of material properties and stress distributions developed during the loading. The method was first applied to simulated data to characterize the capabilities of the image processing. Finite element computations were first performed on a complex structure using a standard linear kinematical hardening model to generate multistage loadings leading to heterogeneous displacements and distributions of deformation energy. Loads and displacements were then used as inputs to check the robustness of the image processing by comparing the identified deformation energy fields with the computed ones. The procedure was then applied to experimental data. Tests were conducted under conditions similar to the numerical tests. The identification of a linear kinematical hardening model gave deformation energy patterns showing a good agreement with the simulated results, even in the presence of residual stresses induced by a pre-hardening.

Geometrical imperfection and adiabatic shear banding

This work addresses the effect of small geometrical imperfections on adiabatic shear band (ASB) formation. The separate effect of the length and radius of short notches is systematically investigated in AM50 and Ti6Al4V alloys, using shear compression specimens. It is observed that the length of the imperfection does not influence ASB formation in these experiments. By contrast, the notch-root radius appears to be the dominant parameter for the two materials, in perfect agreement with the analytical predictions of Dinzart et al. [The catastrophic development of shear localization in thermoviscoplastic materials. J Phys 1994; IV(C8): 435–40]. The distribution of deformation energy over the gauge length is modeled numerically. The calculated average dynamic deformation energy levels are quite similar to those that are measured for the two investigated alloys. It is concluded that the global measure of the dynamic deformation energy provides valuable information about ASB failure from geometrical imperfections.

Surface flattening based on energy model

This paper presents a method for three-dimensional surface flattening, which can be efficiently used in three-dimensional computer aided garment design. First, a facet model is used to present a complex surface. Then, a spring–mass model based on energy function is used to flatten the 3D mesh surfaces into 2D patterns. The surface elastic deformation energy distribution is depicted by a color graph, which determines a surface cutting line. The method presented here can efficiently solve flattening problems for complex surfaces. The accuracy of a developed surface can easily be controlled locally. Thus, compared to earlier methods, this method provides more flexibility for solving CAD and CAM problems.

Topological solitons and dislocations in two- and three-dimensional anisotropic crystals

The well-known one-dimensional Frenkel-Kontorova model is modified and generalized to describe topological point defects and dislocations in anisotropic crystals of higher dimensions. The main point of our modification is that a substrate periodic potential in the Frenkel-Kontorova model is not considered as a given external spatially periodic force, but it is constructed in a self-consistent manner, such that any disturbance in one of the chains causes a violation of spatial periodicity in the adjacent chains of the crystal. Static and moving soliton (kink and antikink) solutions are found numerically in two- and three-dimensional anisotropic crystals. Bound states of kink-antikink and kink-kink (antikink-antikink) pairs and their dynamical properties are studied. Arrays of soliton states are shown to form dislocations of the edge type and their deformation energy distribution on the crystal lattice is calculated. In finding the soliton profiles and energy distributions on the lattice, we apply the minimization scheme that has proven to be an effective numerical method for seeking solitary wave solutions in complex systems. The collision dynamics of the point defects are also investigated.

Deformation energetics of chain defects of polyethylene

The deformation energetics of static polyethylene chain defects were determined by means of molecular mechanics and energy minimization. The eight defects considered in our study were dispira- tion and dislocation (both interstitial- and vacancy-like), disclination, chain twist boundary (90' and MOO), and partial dislocation boundary. For these defects, energy minimized structures were calculated under action of tensile forces. It was found that one group of defects had moduli and deformation energetics identical with those of an all-trans chain, whereas the other group of defects had substantially lower mod- uli and a different deformation behavior. From the analysis of the distribution of deformation energy over the several degrees of freedom and by comparison to an all-trans chain, it could be concluded that defects inside a crystalline matrix are not weak links in polyethylene fibers. Weak links were concluded to be chains having higher moduli than the surrounding matrix (for example, taut tie molecules and especially entanglements in amorphous domains).