Nucleation Stress Research Articles

Energy Budget and Fast Rupture on a Near‐Excavation Fault: Implications for Mitigating Induced Seismicity

AbstractReducing seismicity during excavation is a challenge faced by mining and the associated slip development on a near‐excavation fault under deep‐mining stress conditions is considered as an analog for understanding earthquake initiation mechanisms. In this paper, the quasi‐static slipping on a dipping fault near a horizontal tunnel was numerically studied by incrementally increasing horizontal stress. The equilibrium of the fault, which obeys a slip‐weakening friction law, is formulated by a boundary integral approach. The calculated rupture size is a function of the dimensionless factors derived by scaling from geometrical, loading, and friction conditions. The results show that the rupture becomes runaway at a critical stress level and prior to this, the slip zone either extends continuously and aseismically or experiences finite rapid extensions. Energy dissipated in friction in the presence of tunnel‐induced stress heterogeneity can arrest fast rupture events resulting in regained equilibrium. The energy radiated from arrested events, using an energy budget analysis, depends on the resulting fault strength change, the rupture arrest length, and the strain energy change during the event. These preceding energy radiations can mitigate the magnitude of runaway events. As the critical slip‐weakening distance decreases, the critical stresses for nucleation of both runaway and arrested events are reduced, but the energy radiated by arrested events does not always decrease because the rupture arrest length varies. The results of this study may help identify the initiation mechanisms for runaway ruptures and assess the seismic potential of a rock mass during excavation.

Scale genesis by dark matter and its gravitational wave signal

Classical scale invariance (CSI) may shed light on the weak scale origin, but the realistic CSI extension to the standard model requires a bosonic trigger. We propose a scalar dark matter (DM) field $X$ as the trigger, establishing a strong connection between the successful radiative breaking of CSI and DM phenomenologies. The latter forces the breaking scale to approximately $\mathcal{O}(\mathrm{TeV})$. It brightens the test prospect of this scenario via a gravitational wave, a sharp prediction of CSI phase transition (CSIPT), which is first order and has strong supercooling. Moreover, we carefully deal with some techniques which are commonly used to analyze CSIPT but may be missed. In particular, we clarify the imprecision of Witten's formula used in the single field case to calculate the bubble nucleation rate and stress that the essence of Witten's approximation is the validity of high-temperature expansion.

On the grain size dependence of shock responses in nanocrystalline sic ceramics at high strain rates

Shock induced plasticity, structural phase transitions, as well as dynamic failure in nanocrystalline SiC ceramics, with grain sizes varying from ~2 to ~32 nm, are investigated systematically using large scale molecular dynamics simulations. Shock particle velocities are varied from 1 to 5 km/s in order to study elastic and plastic behavior. Multiple non-monotonic grain-size dependent mechanical properties of nanocrystalline SiC are elucidated. Deformation twinning identified at Up = 2 km/s is reduced with decreasing grain size with a breakdown between dG = 6 to 10 nm. Statistics from grain size effects on the phase transformation from Zinc-Blend to Rock-Salt structure at different particle velocities are obtained. The characteristics of failure shift from classical spall to micro-spall as Up is increased from 1 to 5 km/s. Spall strengths are evaluated by an indirect free-surface method, akin to experimental measurements, and a direct method evaluating the atomic stress tensor at the point of spallation. Differences between the two methods at high strain rates are discussed in detail. The direct method provides a measure of ultimate spall strength, while the indirect method shows pronounced agreement with the nucleation stress. An unexpected grain size dependence of the tensile strengths is also identified, which is similar to a theoretically predicted trend in nanoscale systems. Our results provide new support to the grain size dependence of mechanical properties of nanocrystalline system at high strain rates, which could benefit the design of nanocrystalline ceramics.

Nucleation properties of isolated shear bands.

Shear banding, or localization of intense strains along narrow bands, is a plastic instability in solids with important implications for material failure in a wide range of materials and across length scales. In this article, we report on a series of experiments on the nucleation of single isolated shear bands in three model alloys. Nucleation kinetics of isolated bands and characteristic stresses are studied using high-speed in situ imaging and parallel force measurements. The results demonstrate the existence of a critical shear stress required for band nucleation. The nucleation stress bears little dependence on the normal stress and is proportional to the shear modulus. These properties are quite akin to those governing the onset of dislocation slip in crystalline solids. A change in the flow mode from shear banding to homogeneous plastic flow occurs at stress levels below the nucleation stress. Phase diagrams delineating the strain, strain rate and temperature domains where these two contrasting flow modes occur are presented. Our work enables interpretation of shear band nucleation as a crystal lattice instability due to (stress-assisted) breakdown of dislocation barriers, with quantitative experimental support in terms of stresses and the activation energy.

Damage evolution and spall failure in copper under complex shockwave loading conditions

The damage evolution and spall behavior of copper under complex shockwave loading conditions were investigated using plate impact experiments with conical targets. Sweeping tensile waves were generated by the interaction of the released waves that were reflected from the free surfaces of the impactor and the cone surface. From the free-surface velocity profiles measured by multi-channel velocimetry, the classic pull-back spall signals were observed in incipient and complete spallation experiments. The spall strength estimated from the pull-back velocity strongly depended on the loading path and the loading wave profile. Post-experiment analysis based on the soft-recovery technique revealed that the damage distributions were very different from the bottom to the top of the conical target, but the corresponding free-surface velocity data measured at different locations suggested that similar responses occurred, which indicated that the spall strength was the critical threshold stress of micro-void nucleation or early growth. The fractography analysis of the fracture surfaces showed that metal micro-spheres were scattered in deep dimples, which indicated that the increase in temperature due to local severe plastic deformation around the voids was important. With the same set of model parameters, the plate impact spallation experiments with plane and conical targets were simulated using a critical damage evolution model. A good agreement was obtained between the simulations and experiments, which demonstrated the model capabilities for predicting the spall responses of metals under complex shockwave loading.

On the theoretical and phase field modeling of the stress state associated with ferroelastic twin nucleation and propagation near crack tip

Ferroelastic domain switching is considered as that a twin undergoes a lattice orientation described by a deviatoric eigenstrain in this work. A continuum analysis, based on Eshelby equivalent inclusion theory, is derived to study the nucleation and evolution of twin near a pre-existing crack tip (Mode-I) in a mono-phase tetragonal crystal, in an attempt to achieve a better understanding of the contribution that twinning makes to the toughening effect. The analysis develops progressively from the homogenous isotropic, inhomogeneous isotropic to the general anisotropic conditions; and several analytical solutions are evidenced through phase field simulations. Two important critical stresses, defined as the nucleation stress and the fracture-induced twinning (FIT) stress, are found to determine the twin evolution; specifically, the nucleation stress is related to the twinning in a defect-free solid, and the FIT stress is related to the twinning in the vicinity of crack tip. Moreover, considering the inhomogeneity effect, the change of the stress intensity factor (SIF) due to a ferroelastic twin is derived, which provides evidence that the modulus toughening effect originating from the elastic misfit between the parent and twin can be ignored at a relative low applied SIF. Theoretical analysis and phase field simulations both clarify that the shielding/anti-shielding effect to the crack tip is dependent on the nucleation location and the twin size during evolution. The best toughening formula of a ferroelastic ceramic can be obtained by decreasing the FIT stress and increasing the change of SIF simultaneously through adjusting certain material parameters.

Associating damage nucleation and distribution with grain boundary characteristics in Ta

The effect of grain boundary (GB) characteristics (as represented by misorientation angle) on its dynamic response is investigated by sampling a large set of 185 GBs in Ta bi-crystals. These GBs encompass both ordered and disordered structures – typically referred to as metastable structures, in order to reflect the diversity in the local atomic structure observed in realistic GBs. The results reveal four distinct regimes in damage distribution and failure modes as a function of misorientation angle. The above trends also correlate with the variation in the corresponding void nucleation stress.

Dislocation nucleation in CoNiCrFeMn high entropy alloy

In this work, the homogeneous and heterogeneous nucleation of dislocations in a representative face-centered-cubic high entropy alloy (HEA) CoNiCrFeMn is studied by combining molecular dynamics simulations and continuum mechanics modeling. It is found that as compared to conventional metals such as Cu, HEAs have relatively low activation energy but require high athermal stress for dislocation nucleation. This seemingly odd behavior originates from the uniquely low (even negative) stacking fault energy in HEAs that leads to low critical nucleation radius and low activation volume for dislocation nucleation.

Simulating hydrogen in fcc materials with discrete dislocation plasticity

We have performed discrete dislocation plasticity simulations of hydrogen charged microcantilever bend tests on an fcc material at realistic hydrogen concentrations. This was achieved by accounting for the near-core solute-solute interactions which was found to reduce the dislocation nucleation time and stress. Dislocation pile-ups were observed at the neutral mid plane of the cantilever, and hydrogen was found to increase the number of dislocations in the pile-ups. Meanwhile, hydrogen was observed to decrease the flow stress due to the reduced dislocation core force. This was in contrast to the first-order hydrogen elastic shielding mechanism which was found to be negligible at realistic concentrations. Local stress elevation was observed in the presence of hydrogen in simulations which included an obstacle close to the free surface of the microcantilever, indicating how hydrogen might induce premature stress controlled failure.

In situ measurement and modelling of the growth and length scale of twins in α -uranium

Twinning is an important deformation mechanism in crystalline materials. Twins nucleate, then grow, forming a discrete pattern of deformation bands with a certain thickness. The mechanism for twin growth is not completely understood. We present a simple phase field model which captures the physics of twin growth and reproduces the details observed during in situ electron backscatter diffraction experiments on $\ensuremath{\alpha}$-uranium. The interaction between residual dislocations at twin interfaces and mobile dislocations in untwinned regions increases the stress needed for twin growth. This is described by a nonlocal term in the proposed constitutive equations: the nucleation stress of a twin increases proportionally to the twin phase field in a neighborhood. Competition between slip and twinning favors the nucleation of a new twin rather than the growth of a preexisting twin. The phase field model is coupled with a crystal plasticity finite element solver that includes the plastic deformation due to twinning. Simulations are able to reproduce the number of twins and their thicknesses as a function of the strain observed during in situ electron backscatter diffraction experiments. The stress-strain curve is also reproduced. This comparison allows the values of the nucleation stress and the interaction strength between residual and mobile dislocations to be found. It also gives an estimation of the density of residual dislocations that is consistent with the observed twin thickness. This model can be applied to understand microstructural effects in materials using twinning as a strengthening mechanism.

Experimental stress state-dependent void nucleation behavior for advanced high strength steels

The influence of microstructure and stress state, as defined by the stress triaxiality and Lode parameter, on micro-void nucleation was evaluated experimentally for two 800 MPa Advanced High Strength Steels (AHSS), one a Complex-Phase CP800 alloy, with a ferritic-bainitic microstructure, and the other a Dual-Phase DP780 ferritic-martensitic steel. Four plane stress specimen geometries (simple shear, hole tension, v-bend and biaxial Nakazima) were adopted, providing stress triaxiality and Lode parameter values ranging from in-plane shear to biaxial tension under approximately constant stress states until failure. This approach facilitated determination of the relationship between void nucleation and macroscopic stress state. Damage histories were developed from interrupted samples using 3D micro-tomography and quantitative stereology measurement of void nucleation paired with in situ digital image correlation (DIC) strain measurements during the mechanical testing. The trends in damage evolution are strongly linked to the stress state, with very little void nucleation under shear deformation but extensive void damage under biaxial tension for both materials. A dependency of the nucleation rate on Lode parameter was also demonstrated. A higher rate of damage accumulation was observed for the DP780 steel compared to damage in the CP800 steel for all loading conditions highlighting the strong influence of initial microstructure. An analytical framework is proposed to obtain the local stress-state and equivalent plastic strain history from direction integration of the measured DIC strain histories, using a measured hardening law and assumed anisotropic yield function (Yld91) to develop the link between nucleation and the macroscopic stress state. A stress-state dependent nucleation model is proposed by introducing a nucleation strain surface as a function of stress-triaxiality and Lode parameter using a modified form of the strain-based Chu and Needleman nucleation criterion.

Atomic-scale investigation on the structural evolution and deformation behaviors of Cu–Cr nanocrystalline alloys processed by high-pressure torsion

Abstract A systematic investigation based on high-resolution transmission electron microscopy (HRTEM) and quantitative analysis was carried out to gain insights into the structural evolution and deformation behaviors of 57 wt%Cu - 43 wt%Cr dual-phase alloys deformed by high pressure torsion (HPT). Nanometer-sized grains were obtained, with Cu and Cr grain size being reduced from 33.7 nm to 17.4 nm and 35.6 nm to 18.6 nm respectively after deformation with 5 rotations and 25 rotations. During the early deformation stage, in a way, grain refinement in Cu was controlled by the interaction between Cr solutes (or clusters) that was forced to dissolve into Cu matrix and extended dislocations motion. At the higher strain condition, the deformation mode became more complicated and the grain refinement of Cu and Cr can be affected by solute effects and constraint effect during severe plastic deformation in this dual-phase system. In addition, inverse grain-size effect on stacking fault (SF) and twinning tendencies was observed in Cu under different deformation conditions. A critical grain size was calculated to describe the required shear stress for partial dislocation nucleation. HRTEM investigations and statistical analysis on twins observed in 25 rotations-strained sample reveal that the twins are associated with the grain boundary activities and the recovery procedure in the extremely fine grain size region. These atomic-scale observations provide new views in understanding the deformation mode, especially twinning behavior in the extremely fine grain size range below the critical grain size that are hardly obtained in experiments.

Robust and reproducible fabrication of large area aluminum (Al) micro/nanorods arrays by superplastic nanomolding at room temperature

Large-scale preparation of aluminum (Al) micro/nanorods is reported by directly nanomolding of pure Al with bulk metallic glass (BMG) molds at room temperature. Combined with experiments and theoretical modeling, the critical dislocation nucleation stress in Al is determined, which is generally challenge to decouple from the propagation of dislocations. Benefited from the excellent mechanical properties of BMGs, the BMG molds are found to be used repeatedly. Therefore, the proposed method is intrinsically a low-cost process and could guide the high-throughput fabrication of metal nanostructures, as well as facilitate their applications such as in plasmons and wear-resisting superhydrophobic surfaces.

Effect of Al content on the critical resolved shear stress for twin nucleation and growth in Mg alloys

The effect of Al atoms in solid solution on the critical resolved shear stress for twin nucleation and growth was analyzed by means of the combination of diffusion couples with compression tests in micropillars oriented for twinning. The critical resolved shear stress for twin nucleation was higher than that for twin growth and both increased by the same amount with the Al content. Nevertheless, the increase was small (≈ 10 MPa) for 4 at%Al but large (up to 60–70 MPa) for 9 at%Al. These results were in agreement with Labusch-models based on first principles calculations in the dilute regime (< 5 at%Al). Comparison with recent data in the literature showed that Al atoms are more effective in increasing the critical resolved shear stresses for twin nucleation and growth than for basal slip. Finally, compression tests in micropillars oriented along [0001] showed the critical shear stress for pyramidal slip increased rapidly with the Al content from 98 MPa in pure Mg to 250 MPa in Mg-9 at%Al. Overall, the presence of Al atoms decreased slightly the plastic anisotropy of Mg (understood as the critical resolved shear stress ratios between non-basal and basal plastic deformation mechanisms).

The development of creep damage constitutive equations for high Cr steel

ABSTRACTThis paper reports (1) an application of the modified hyperbolic sine law to P92 for the minimum creep strain rate over a wider range of stress level, and 2) the calibration of the creep cavity fracture model and its applications to such as P92, E911 and MARBN alloys. It was motivated by the original development of creep cavitation based creep rupture model and application to other alloys, and the need of creep strain and stress relation over a wider range of stress. The results include: (1) the calibration of creep cavity fracture model for E911, and the pre-required cavity nucleation and growth models, for E911, (2) the creep lifetime and stress relation coefficient U’ for P92, and (3) the relationship of the cavity nucleation rate coefficient A2 and stress level for MARBN cross-welds. This paper contributes to the specific knowledge and the methodology. It anticipates that this methodology will find its value and application in modelling other fractures such as ductile and fatigue.

Does the stacking fault energy affect dislocation multiplication?

This paper investigates the interdependence of the stacking fault energy (SFE) and the stress required for dislocation multiplication. For this purpose copper-aluminum (Cu-Al) alloys with varying Al content are investigated by spherical nanoindentation. The load-displacement curve shows a characteristic pop-in, which is interpreted as elastic-plastic transition and correlated to the dislocation source nucleation and/or activation stress. The statistical analysis of the pop-in behaviour documents a strong dependence of the maximum shear stress beneath the indenter on the Al content, which cannot be explained by a variation in shear modulus. Instead, the pop-in stress clearly increases with increasing stacking fault energy.

Incipient spallation of high purity copper under non-one-dimensional strain shock waves

A new spallation experimental method by using conical target is proposed. Based on the analysis of wave propagation, the basic principle of spallation experiment of conical target is discussed. Then incipient spallation of high purity (HP) copper under non-one-dimensional strain shock wave is studied experimentally by using a gas gun setup. The damage distribution characteristics and micro-mechanism of conical HP copper target are analyzed. The intrinsic relationship between the characteristics of free surface velocity profiles and damage evolution is explored. The results indicate that 1) continuous damage zones including different damage states appear in the conical HP copper target with initial spallation from the bottom of cone to the top of cone along the direction parallel to the cone surface, which is attributed to the spatial evolution of the amplitude and duration time of tensile stress in the conical target; 2) quantitative statistical analysis of damage inside conical HP copper target reveals that the nucleation and early growth of micro-voids are random, while the coalescence of micro-voids has significant localization characteristics; 3) the normal free surface particle velocity profiles with typical pull-back spallation signals at different locations of conical HP copper target are measured by multi-channel photon Doppler velocimetry. Comparing with the damage distribution characteristics, it is revealed that the spallation strength based on pull-back velocity is independent of damage, and is the critical nucleation stress of micro-voids. But the slope and amplitude of pull-back rebound velocity depend on damage evolution process, which relates to the change of damage evolution rate and stress relaxation caused by damage degree respectively.

The key role played by dislocation core radius and energy in hydrogen interaction with dislocations

It is generally believed that the H-induced reduction in dislocation energy plays a key role in modifying dislocation behaviors in the process of hydrogen embrittlement. Here, we examine the factors that lead to H reducing the line energies of the edge and screw dislocations in bcc Fe by atomistic simulations. Grand canonical Monte Carlo simulations are conducted to obtain the distribution of H around the dislocations. We find that H mainly aggregates at the dislocation cores and the H concentration in the elastic field of dislocations is extremely low. The direct consequences of such a distribution pattern of H are as follows. (i) In contrast with previous studies, H induces no change in the shear modulus of the systems containing dislocations. (ii) H increases the core radii and decreases the core energies of the dislocations, which are the only factors leading to the reduction of dislocation line energy by H. (iii) H brings little effect on the stress field of either the edge or screw dislocation, implying that H induces almost no stress-shielding effect on dislocations. A linear relation between the critical shear stress for homogeneous dislocation nucleation and logarithmic bulk H concentration is thus revealed, based on the atomistic result of the H-induced increase in the core radius and decrease in the core energy of the dislocations. The present results indicate that the dislocation-dislocation interaction in the presence of H, which is the key ingredient for the H-enhanced localized plasticity mechanism for hydrogen embrittlement, can be easily evaluated by the linear elastic theory of dislocations if the core radius and energy of dislocations are properly described.

Macroscopic modeling of strain-rate dependent energy dissipation of superelastic SMA dampers considering destabilization of martensitic lattice

Superelastic shape-memory alloys (SMAs) are unique smart materials with a considerable energy dissipation potential for dynamic loadings with varying strain-rates. The energy dissipation arises from a hysteretic phase transformation of the polycrystalline atomic grid structure. In fact, the nucleation from austenite to martensite phase and vice versa exhibits a strong thermomechanical coupling. The hysteresis depends on the latent heat generated by the austenitic-martensitic transformation and the convection of that heat. Due to the thermomechanical coupling, the martensitic nucleation stress level and thus the propagation of martensitic phase fronts strongly depends on the material temperature. High strain-rate interferes with the release of the latent heat to the environment and determines quantity, position and propagation of martensitic transformation bands. Lastly, high strain-rate reduces the hysteresis surface. The propagation velocity and quantity of martensitic bands have an impact on martensitic phase stability. The degree of atomic disorder and accordingly the change in entropy influences the reverse phase transformation from martensite to austenite. In other words, the stability of the martensitic state affects the stress level of the reverse transformation. However, in phenomenological superelastic SMA models, which are used to simulate energy dissipation behavior, the effects of the rate-dependent entropy change are not considered in particular. To incorporate the rate-dependent entropy change, we improved a one-dimensional numerical model by introducing an additional control variable in the free energy formulation for solid-solid phase transformation of superelastic SMAs. In this model, the observed effects of the strain-rate on the reverse transformation are taken into account by calculating the rate-dependent entropy change. A comparison of the numerical results with the experimental data shows that the model calculates the dynamic superelastic hysteresis of SMAs more accurately.

Crystal structure and composition dependence of mechanical properties of single-crystalline NbCo2 Laves phase

Extended diffusion layers of the cubic C15 and hexagonal C14 and C36 NbCo2 Laves phases with concentration gradients covering their entire homogeneity ranges were produced by the diffusion couple technique. Single-phase and single-crystalline micropillars of the cubic and hexagonal NbCo2 Laves phases were prepared in the diffusion layers by focused ion beam (FIB) milling. The influence of chemical composition, structure type, orientation and pillar size on the deformation behavior and the critical resolved shear stress (CRSS) was studied by micropillar compression tests. The pillar orientation influences the activated slip systems, but the deformation behavior and the CRSS are independent of orientation. The deformation of the smallest NbCo2 micropillars (0.8 µm in top diameter) appears to be dislocation nucleation controlled and the CRSS approaches the theoretical shear stress for dislocation nucleation. The CRSS of the 0.8 µm-sized NbCo2 micropillars is nearly constant from 26 to 34 at.% Nb where the C15 structure is stable. It decreases as the composition approaches the Co-rich and Nb-rich boundaries of the homogeneity range where the C15 structure transforms to the C36 and the C14 structure, respectively. The decrease in the CRSS at these compositions is related to the reduction of shear modulus and stacking fault energy. As the pillar size increases, stochastic deformation behavior and large scatter in the CRSS values occur and obscure the composition effect on the CRSS.