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Initial dislocation structure for cases of high (a: 1.75 × 10¹³ m⁻²) and low (b: 0.35 × 10¹³ m⁻²) initial dislocation densities. The crystallographic orientations are given in the figure. The dislocation walls are represented using blue shades. The dashed lines with green arrows denote the direction on which the shear strain is applied. The dash-dot lines show the directions on which the dislocations propagate.
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High-frequency testing (HFT) is useful for accelerated fatigue testing of conventional materials that typically serve under low-frequency loading conditions, as well as for the assessment of the robustness of microelectromechanical systems which typically experience high-frequency service conditions. Using discrete dislocation dynamics, we attempt...
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It is often assumed that the Peierls stress of single dislocations can reflect accurately the macroscopic yield stress. Here, dislocation dynamics simulations show that the yield stress‐to‐Peierls stress (Y/P) ratio remains within a small range of ≈0.3 ± 0.1, over a wide range of initial dislocation density, mobile dislocation fraction, and tempera...
Citations
... [55,56] When the dislocation density within the veins reaches a critical value, the veins then collapse into dislocation walls that are separated by larger distances. The gradual generation of more dislocation walls in linear arrays constitutes the formation of persistent slip bands (PSBs), whose formation and operation typically causes cyclic softening [54][55][56][57][58]. ...
... The dislocations moved reciprocally in the form of extended dislocations during the saturation stage. This phenomenon has also been found in some research, and they pointed out that cyclic plastic deformations are typically achieved by the simple to-and fromotion of dislocations, resulting in little dislocation multiplication [58][59][60]. However, the extended dislocations only crossed the Ni/Ni 3 Al interface and sheared the Ni 3 Al phase at 300 K, while the extended dislocations were limited in the narrow Ni channels at other temperatures. ...
Cyclic loading is the main contributor to fatigue failures in mechanical components. In this paper, the fatigue deformation behavior of nickel-based single crystal superalloys was investigated through molecular dynamics methods. It was found that the fatigue process can be divided into the hardening stage and the saturation stage. The stress amplitude, dislocation density and number of planar faults fluctuated before the saturation stage, but they were relatively stable in the saturation stage. The Perfect dislocations at the interface decomposed into Shockley dislocations with temperature increase before fatigue. The decomposition process became more dramatic as fatigue began. As the fatigue continued, the extended dislocations in the Ni phase gradually got rid of the Ni/Ni3Al interface and sheared the Ni3Al phase, leading to the generation of antiphase boundaries. The extended dislocation moved reciprocally when the fatigue reached the saturation stage. The difference was that the extended dislocations crossed the interface at 300 K but not at other temperatures.
... The deformation displayed anelastic or microplastic, which deviates from linear elasticity [6,7], especially for multiple alloys [8][9][10]. This anelastic or microplastic behaviour made drastic effect on the life time assessment, as well as fatigue strength [11][12][13] and dimensional stability [14]. The elastic modulus reduced with strain increasing due to nonlinear elasticity [6,15], which further influenced the prediction accuracy of springback [16][17][18]. ...
Tensile and compressive pre-yield mechanical behavior of a rolled AZ31 Mg alloy sheet was studied by cyclic loading–unloading tests along rolling direction (RD) and transverse direction (TD). The results show that the mechanical response of pre-yielding is not linear elasticity. Microplasticity with irreversible strain and energetic dissipation is observed during tension. While anelasticity with reversible strain and dissipative energy is detected during compression. A stress dependent varied elastic modulus model was built by introducing a stress factor to capture the asymmetric behavior. Three model parameters are tensile yield strength, initial elastic modulus and critical modulus at tensile yield point. Consequently, this model is verified by comparison with the experimental observations. The anelastic and micro-plastic deformation are ascribed to the glide of mobile dislocations. The asymmetric behavior of tension and compression is clarified by the nucleation mechanism of {10–12} twinning.
... First Eshelby [11] and later Koehler and DeWit [6] connected the apparent elastic constants, which are lower than the theoretical constants, to the bowing out of pinned dislocation segments. Knowledge of pre-yield mechanical behaviour has already proven important in the design of forming methods [12] , micro-mechanical systems [13] and ultrasonic measurement techniques [14] . An outstanding example is the physical-phenomenological full-field numerical crystal plasticity model of single crystallites, which is often interpreted as describing the critical shear stress needed to free (or activate) dislocations with the average segment length [21] . ...
... In this work, the fundamental understanding on the effects of dislocation network geometry on the pre-and at-yield constitutive behaviour is expanded. The obtained knowledge will aid in the future design of forming methods [12] and micro-mechanical systems [13] . The main contribution is incorporating dislocation densities with varying character in predicting the pre-yield mechanical behaviour of materials with a generic Poisson's ratio. ...
Intricate knowledge of dislocation networks in metals has proven paramount in understanding the constitutive behaviour of these materials but current experimental methods yield limited information on the characteristics of these networks. Recently, the isotropic anelastic response of metals has been used to investigate complex dislocation networks through the well-known phenomenon that the observed elastic constants are influenced by dislocations. Considering the dependence of the behaviour of a Frank-Read (FR) source on its initial dislocation character and using discerning characteristics of dislocations, i.e. Burgers vector, line sense and slip system, the present paper takes dislocation character, crystal structure and dislocation network geometry into account and obtains the anisotropic mechanical response for a generic Poisson’s ratio. In this work, the tensile test tangent moduli and yield points are presented for spatially uniform and nonuniform dislocation distributions across slip systems. First, the reversible shear strain of the FR source is derived as a function of initial dislocation character. The area swept by a mobile and initially straight dislocation segment pinned at both ends is given as an explicit function of the line stress. Secondly, the anisotropic anelastic strain ontribution of FR sources to the total pre- and at-yield strain in single crystallites is alculated. For a given normal stress and superposition of the principal infinitesimal linear elastic lattice strain and anelastic dislocation strain, the tangent moduli are presented.
The moduli and the inception of plastic flow have a notable dependence on initial dislocation character, spatial dislocation distribution and loading direction.
... For instance, in the high-cycle regime, it explains the increase of the fatigue life with the increase of the frequency by the reduction of time for the strain-rate sensitive dissipative process in the material. The effect of increase of the fatigue life with the increase of frequency of loading in the high-cycle regime has been confirmed experimentally in iron-nickel-based alloys [77,78] and polycrystalline copper [79] and in large-scale numerical simulations of the dislocation dynamics [80]. Very often high-frequency fatigue testing is used as a replacement of the low-frequency testing just to save on time and energy [81]. ...
I developed a comprehensive theory of plasticity, damage and failure, which is independent of the micromechanical mechanism of plasticity. It includes all major components of the mechanical behavior of ductile materials, e.g. strain/work-hardening and Bauschinger effect, and covers all regimes of viscoplastic tensile/compressive loading/unloading. The theory is based on the concepts of free energy and damage parameter and has the attributes of both rate-dependent and rate-independent plasticity, kinematic and isotropic hardening. The ultimate failure of a specimen is defined as a point of critical value of the damage parameter. The theory provides justification for Drucker’s ad hoc condition of instability, elucidates the strength-ductility/toughness conflicts and hints at the means of resolving them. The theory describes diverse phenomena of Lüders stress, creep, internal friction, and fatigue on the same self-consistent basis. In quasi-static low-cycle fatigue, I derive a Paris-type equation between the rate of degradation and cyclic plastic work and reveal a Coffin-Manson power-law relationship between the number of cycles to failure and plastic-strain amplitude. In dynamic fatigue, I find two regimes—low-cycle and high-cycle—whose loading amplitudes are separated by the yield point. The two regimes have significantly different dependencies on the frequency and viscosity. In this publication, I present the theory and computer simulations of a homogeneous viscoplastic body subjected to various conditions of isothermal strain-controlled uniaxial loading. In the follow-up publications, I will expand the theory on the cases of inhomogeneous three-dimensional bodies subjected to multiaxial loading at variable temperatures and compare the results to the experiments. Complete version of the theory can be used for the full-cycle cradle-to-grave design of new materials in service.
... Since the microscopic material behavior is captured naturally within the dynamics of the microstructural evolutions [47], DDD directly accounts for the effect of the material intrinsic length scale on the plastic responses. As a result, DDD simulations have emerged as a powerful computational tool in investigating microscale plasticity phenomena, including lattice and grain boundary effects [38,155], dislocation network [112], the behavior of thin films [15,113,119,142], and dislocation boundaries [68]. Despite these advances, the high computational costs of discrete dislocation simulations have limited the applicability of these models to simple geometries and length scales of 10µm and time scales of 1ms [117]. ...
Multiscale models of materials, consisting of upscaling discrete simulations to continuum models, are unique in their capability to simulate complex materials behavior. The fundamental limitation in multiscale models is the presence of uncertainty in the computational predictions delivered by them. In this work, a sequential multiscale model has been developed, incorporating discrete dislocation dynamics (DDD) simulations and a strain gradient plasticity (SGP) model to predict the size effect in plastic deformations of metallic micro-pillars. The DDD simulations include uniaxial compression of micro-pillars with different sizes and over a wide range of initial dislocation densities and spatial distributions of dislocations. An SGP model is employed at the continuum level that accounts for the size-dependency of flow stress and hardening rate. Sequences of uncertainty analyses have been performed to assess the predictive capability of the multiscale model. The variance-based global sensitivity analysis determines the effect of parameter uncertainty on the SGP model prediction. The multiscale model is then constructed by calibrating the continuum model using the data furnished by the DDD simulations. A Bayesian calibration method is implemented to quantify the uncertainty due to microstructural randomness in discrete dislocation simulations (density and spatial distributions of dislocations) on the macroscopic continuum model prediction (size effect in plastic deformation). The outcomes of this study indicate that the discrete-continuum multiscale model can accurately simulate the plastic deformation of micro-pillars, despite the significant uncertainty in the DDD results. Additionally, depending on the macroscopic features represented by the DDD simulations, the SGP model can reliably predict the size effect in plasticity responses of the micropillars with below 10% of error.
... Since the microscopic material behavior is captured naturally within the dynamics of the microstructural evolutions [47], DDD directly accounts for the effect of the material intrinsic length scale on the plastic responses. As a result, DDD simulations have emerged as a powerful computational tool in investigating microscale plasticity phenomena, including lattice and grain boundary effects [155,38], dislocation network [112], the behavior of thin films [119,15,142,113], and dislocation boundaries [68]. Despite these advances, the high computational costs of discrete dislocation simulations have limited the applicability of these models to simple geometries and length scales of 10µm and time scales of 1ms [117]. ...
Multiscale models of materials, consisting of upscaling discrete simulations to continuum models, are unique in their capability to simulate complex materials behavior. The fundamental limitation in multiscale models is the presence of uncertainty in the computational predictions delivered by them. In this work, a sequential multiscale model has been developed, incorporating discrete dislocation dynamics (DDD) simulations and a strain gradient plasticity (SGP) model to predict the size effect in plastic deformations of metallic micro-pillars. The DDD simulations include uniaxial compression of micro-pillars with different sizes and over a wide range of initial dislocation densities and spatial distributions of dislocations. An SGP model is employed at the continuum level that accounts for the size-dependency of flow stress and hardening rate. Sequences of uncertainty analyses have been performed to assess the predictive capability of the multiscale model. The variance-based global sensitivity analysis determines the effect of parameter uncertainty on the SGP model prediction. The multiscale model is then constructed by calibrating the continuum model using the data furnished by the DDD simulations. A Bayesian calibration method is implemented to quantify the uncertainty due to microstructural randomness in discrete dislocation simulations (density and spatial distributions of dislocations) on the macroscopic continuum model prediction (size effect in plastic deformation). The outcomes of this study indicate that the discrete-continuum multiscale model can accurately simulate the plastic deformation of micro-pillars, despite the significant uncertainty in the DDD results. Additionally, depending on the macroscopic features represented by the DDD simulations, the SGP model can reliably predict the size effect in plasticity responses of the micropillars with below 10% of error
... While models of anelastic effects are typically motivated by the concept of pinned dislocations bowing under the action of shear stress, prior work [17] using discrete dislocation dynamics (DDD) has suggested that anelasticity may involve more complex processes of disentanglement (or depinning) of the dislocation network. Other DDD work has highlighted similar complexities -for example with [18] focusing on cyclic loading and the influence of dislocation mobility. In this contribution, we formulate a model that is meant to capture the additional anelastic strain associated with disentanglement and that is coupled to an evolving dislocation density. ...
Many experiments of interest, particularly those meant to probe flow strength response under dynamic conditions, involve reversals in the loading condition. Transients in the material response during these reversals can significantly influence experimental observables. In materials for which deformation is mediated by the motion of dislocations, aspects of the transients are thought to be associated with motion of dislocations during the transient; and the strains so produced are sometimes described as being anelastic. Appropriate formulations for anelastic response can be distinct from standard models used to capture plasticity response over larger monotonic strains. We present results from a new anelasticity formulation and its numerical implementation. In this formulation, the anelastic strain production is influenced by the characteristics of the dislocation network, with these characteristics evolving over the course of material deformation.
... The distributions of von Mises stresses in the two structures at the moment when the average equivalent plastic strain in the PSB is 0.01 are shown in Fig. 16. A typical plastic strain amplitude experienced by PSBs is 0.01, regardless of the cyclic strain amplitude [43][44][45][46]. Under this condition, the remotely applied deformation for the single PSB and triple PSB structure is automatically consistent with a lower and a higher stress amplitude, which is in qualitative correspondence with the instances provided in Fig. 15(b) and (d). ...
Fully-reversed cyclic bending tests were conducted on uncoated and Cr-coated 316 stainless steel specimens. At high stresses, the uncoated specimens outperformed the Cr-coated ones, while the trend reversed at low stresses. For Cr-coated specimens subjected to high stress amplitude loading, experimental observations showed crack initiation at the Cr/substrate interface due to shear steps formed from dislocation activities in the substrate—a conclusion supported by accompanying finite element analysis. Interfacial crack initiation was not observed under low stress amplitudes. This difference in fatigue crack initiation mechanisms induced an opposite trend in fatigue life between high and low stress amplitudes.
... Instead, localized plastic deformation occurs due to elastic incompatibilities among grains and local stress risers [9,10]. The cyclic plastic deformations are typically achieved by the simple to-and fro-motion of dislocations, resulting in little dislocation multiplication and cyclic hardening/softening [11][12][13]. The accumulation of fatigue damage is largely associated with the screw dislocations, whose motion is likely to generate irreversible cyclic deformation, due to interruptive events such as cross-slip [10,11]. ...
Keywords: Ni-base superalloys Alloy design Antiphase boundary energy L1 2 structure Cluster expansion Density functional theory A B S T R A C T Mechanical and fatigue performance of γ-γ 0 Ni-base superalloys are strongly affected by the antiphase boundary energy (APBE) of the γ 0 precipitates which, in turn, is dictated by the alloy's composition. Due to the multi-component character of these alloys, establishing composition-APBE relationships are challenging, even though the qualitative effect of individual solutes on the APBE may be known. This work attempts to utilize density functional theory-based cluster expansion calculations to systematically assess the effect of composition on the APBE of the γ 0 phases in Ni-base superalloys. We aim to elucidate the influence of not only one single element but also multiple coexisting alloying elements on the γ 0 APBE. By explicit consideration of configurational disorder via Monte Carlo sampling, the effect of temperature on the APBE has also been analyzed. This work reveals that (1) effects of individual solute element M on the APBE energy obtained in an isolated, ternary condition (i.e. in Ni 3-x Al 1-y M xþy) does not directly translate to a multi-solute case and that (2) the mutual synergistic interactions among different solute elements are not negligible. Based on the present results, an empirical master equation that predicts the APBE based on the composition of the γ 0 phases has been obtained.
