Dynamic Strain Research Articles

Experimental study on plastic deformation of alluvial silty sand under traffic cyclic loading

With the development of highway construction, alluvial silt is gradually used as roadbed filler, but its dynamic characteristics are less studied. Based on the highway section from Luanzhou to Qingtuoying of G508, the plastic strain and dynamic stress-dynamic strain development law of alluvial silty sand under cyclic loading are analyzed by GDS dynamic triaxial test. The results show that under the action of a small range of dynamic stress amplitude, the soil sample is not destroyed, and the number of cycles is 1000 times, which is the critical point at which the axial total strain gradually tends to be stable. When the dynamic stress amplitude is 300 kPa, the total axial strain increases linearly, and the soil sample is destroyed. The cumulative plastic strain of the alluvial silt is the smallest when the optimum water content is 8.0 %, the confining pressure is 80 kPa, and the frequency is 1Hz.At this time, the cyclic load has a dense effect on the soil, and the soil structure does not fail. The dynamic stress-strain relationship of alluvial silty sand conforms to the R. L. Kondner hyperbolic model. The greater the confining pressure and the closer the moisture content to the optimal moisture content, the greater the dynamic strength. The research results are helpful to provide reference for other similar projects.

Dynamic response and blast resistance mechanism of polyurea coating on RC slab during contact explosions

Polyurea (PU) coated reinforced concrete (RC) has been widely studied in structural strengthening under contact explosion, however, experimental investigations on dynamic response and failure mechanism of the coating during explosion remain scarce. In this paper, four contact explosion experiments are conducted on uncoated and rear side coated RC slabs. Dynamic strains and dynamic deformation of the coating are obtained by large-range strain gauges and a proposed measurement method based on a high-speed camera. Dynamic response characteristics of the coating are discussed and the blast resistance mechanism is further analyzed. Additionally, the effect of coating rebounding on the RC substrate and the effect of explosive placement on the coating are discussed. The results show that PU coating dissipates the blast energy through elastic deformation, plastic deformation, rupture and debonding. Glass transition at high strain rate may cause the rupture of the coating, and coating thickening significantly reduces the tensile strain rate under the same contact explosion conditions. With the development of breach and spalling of the RC substrate, PU coating on the rear side can be divided into four zones, and the blast resistance mechanism of the coating varies in different zones. Additionally, the elastic potential energy release of the coating may produce a secondary impact on the RC substrate. Coatings are more severely damaged when contact explosives are placed in locations that avoid rebars and should be considered as the most unfavorable load for the retrofitting of RC structures.

The effect of Mn content on a novel Al–Mg–Si-Sc-Zr alloy produced by laser powder bed fusion: The microstructure and mechanical behavior

Scandium is very expensive and limits the application potential of Sc containing alloys. A novel high-strength Al–Mg–Mn-Sc-Zr alloy was designed for reducing Sc. Multiple strengthening mechanisms were utilized for designing this alloy, especially for the solid solution strengthening which benefits from ultrahigh cooling. With the addition of Mn and Si, the strength of our alloy reaches comparable level of similar alloys while the Sc content is 40–60 % less than them. The effect of Mn addition on microstructure and mechanical properties were carefully studied. Near full-dense samples with relative density >99.88 % were obtained with the help of overlapping prediction model. The continuous Mg2Si network was observed with Si introduction and broken up with increasing Mn content. According to the tensile experiment results and corresponding calculations, it was considered that the thermal stability and the effect of precipitate strengthening was slightly deteriorated. However, obvious improvement of the tensile strength was observed with increasing Mn addition, and the ductility maintains in a certain range. After aging at 280 °C for 4 h, the sample of 1.4 wt% Mn exhibits the highest ultimate strength of 497.08 ± 7.22 MPa, and possesses a considerable ductility of 8.01 ± 0.34 %. The Portevin-Le Chatelier (PLC) effect was observed in stress-strain curves, which reflects a dynamic strain aging of mobile dislocations and solute atoms. After aging, the stress amplitude and waiting time of serration flow decrease obviously, because of the introduction of bypassing precipitates and reduction of diffusion time. Compared with other similar alloys, our alloy exhibited comparable yield strength and elongation, but considerable advantages in material costs resulting from lower Sc content. It will offer not only an idea for alloy design utilizing the ultra-high solid solubility of elements, but also a feasible way to further expand application field of high-strength Al-based alloys through reducing the material costs.

Dynamic relative regional lung strain estimated by computed tomography and electrical impedance tomography in ARDS patients

BackgroundIn the acute distress respiratory syndrome (ARDS), specific lung regions can be exposed to excessive strain due to heterogeneous disease, gravity-dependent lung collapse and injurious mechanical ventilation. Computed tomography (CT) is the gold standard for regional strain assessment. An alternative tool could be the electrical impedance tomography (EIT). We aimed to determine whether EIT-based methods can predict the dynamic relative regional strain (DRRS) between two levels of end-expiratory pressure (PEEP) in gravity-non-dependent and dependent lung regions.MethodsFourteen ARDS patients underwent CT and EIT acquisitions (at end-inspiratory and end-expiratory) at two levels of PEEP: a low-PEEP based on ARDS-net strategy and a high-PEEP titrated according to EIT. Three EIT-based methods for DRRS were compared to relative CT-based strain: (1) the change of the ratio between EIT ventilation and end-expiratory lung impedance in arbitrary units ([ΔZAU low-PEEP/EELIAU low-PEEP]/[ΔZAU high-PEEP/EELIAU high-PEEP]), (2) the change of ΔZ/EELI ratio calibrated to mL ([ΔZml low-PEEP/EELIml low-PEEP]/[ΔZml high-PEEP/EELIml high-PEEP]) using CT data, and (3) the relative change of ∆ZAU (∆ZAU low-PEEP/∆ZAU high-PEEP). We performed linear regressions analysis and calculated bias and limits of agreement to assess the performance of DRRS by EIT in comparison with CT.ResultsThe DRRS assessed by (ΔZml low-PEEP/EELIml low-PEEP)/(ΔZml high-PEEP/EELIml high-PEEP) and ∆ZAU low-PEEP/∆ZAU high-PEEP showed good relationship and agreement with the CT method (R2 of 0.9050 and 0.8679, respectively, in non-dependent region; R2 of 0.8373 and 0.6588, respectively, in dependent region; biases ranging from − 0.11 to 0.51 and limits of agreement ranging from − 0.73 to 1.16 for both methods and lung regions). Conversely, DRRS based on EELIAU ([ΔZAU low-PEEP/EELIAU low-PEEP]/[ΔZAU high-PEEP/EELIAU high-PEEP]) exhibited a weak negative relationship and poor agreement with the CT method for both non-dependent and dependent regions (R2 ~ 0.3; bias of 3.11 and 2.08, and limits of agreement of − 2.13 to 8.34 and from − 1.49 to 5.64, respectively).ConclusionChanges in DRRS during a PEEP trial in ARDS patients could be monitored using EIT, based on changes in ΔZmL/EELIml and ∆ZAU. The relative change ∆ZAU offers the advantage of not requiring CT data for calibration.

Speckle-Tracking Analysis of the Right and Left Heart after Peak Exercise in Healthy Subjects with Type 1 Diabetes: An Explorative Analysis of the AppEx Trial.

In eight healthy participants with Type 1 diabetes (T1D) exercise-related dynamic cardiac remodeling was analyzed by performing two-dimensional echocardiography, including deformation analysis of the left-ventricular (LV) global longitudinal strain (LV-GLS), and the deformation pattern of the left atrium (LA) and right ventricle (RV) at rest and post-peak performance on a bicycle. The feasibility echocardiographic speckle-tracking analysis was performed on eight asymptomatic participants with T1D (n = 8, male n = 5, age: 23-65 years). The obtained echocardiographic data were compared for various echocardiographic parameters at rest and post exercise. Across our participating T1D individuals no structural echocardiographic abnormalities of concern could be revealed. All participating T1D subjects showed preserved contractile reserve of the LV and no significant diastolic dysfunction. Significant differences were found for the phasic LA contractile strain pattern at rest and post exercise (p < 0.001), whereby the dynamic RV (p = 0.5839 and p = 0.7419) and LV strain pattern (p = 0.5952) did not reveal significant differences in comparison to resting conditions. This descriptive secondary outcome analysis describes preserved contractile reserve of the LV and elucidates dynamic modification of the phasic LA contractile deformation pattern in asymptomatic T1D individuals after exhaustive exercise on a bicycle.

Experimental study on dynamic properties of flax fiber reinforced recycled aggregate concrete

Recycling waste concrete is critical to land use and reduction of landfills. It is a good option to recycle the waste coarse aggregates from it and add them to the concrete matrix. Due to the existence of new and old interface transition zones (ITZs), the quasi-static compressive strength of recycled aggregate concrete is lower than that of natural aggregate concrete, which limits the widespread application of recycled aggregate concrete. In order to improve its engineering application of recycled aggregate concrete, the dynamic compressive properties were studied. Thus, based on a Split Hopkinson Pressure Bar (SHPB) device, the effects of strain rate and recycled coarse aggregate (RCA) replacement ratio on the failure mode, dynamic compressive strength, critical strain and toughness were investigated. It was found that increasing the strain rate led to the aggravation of the specimen damage and growth of the dynamic compressive strength, toughness and critical strain. At a high strain rate, the strain rate effect changed the failure mode of recycled aggregate concrete. This reduced the performance difference between recycled and natural aggregate concrete, in terms of the dynamic compressive strength. The recycled aggregate concrete had a similar toughness to the natural aggregate concrete. Although the growth of the RCA replacement ratio decreased the dynamic compressive strength and increased the critical strain, it had a little effect on the toughness. In order to reduce the brittleness of the recycled aggregate concrete and improve its deformability, non-synthetic, green and low-consumption flax fibers were incorporated into the concrete matrix, and its dynamic compressive behaviors were studied experimentally accordingly. Tests verified that the addition of flax fibers significantly reduced the damage and increased the critical strain. Especially when the strain rate was greater than 200 s-1, flax fiber reinforced recycled aggregate concrete exhibited a superior energy consumption ability. Based on the experimental data, empirical equations were proposed to describe the dynamic compressive strength, critical strain and toughness at different strain rates.

High-Spatial-Resolution Dynamic Strain Measurement Based on Brillouin Optical Correlation-Domain Sensors

Brillouin-scattering-based sensors have been widely applied in distributed temperature or strain measurement in recent 20 years. Brillouin optical correlation-domain technology has extensive development and application prospects because of its millimeter-level spatial resolution, distribution measurement, and high accuracy. Traditional Brillouin-scattering-based sensors, requiring a time-consuming frequency-sweep process, struggle to achieve dynamic strain measurement. In this article, Brillouin optical correlation-domain analysis and reflectometry based on fast-sweep frequency and slope-assisted methods will be reviewed. The main merits, drawbacks, and performances of these schemes are compared, and the avenues for future research and development of these two technologies are also explored.

Strengthening mechanisms and microstructural evolution of medium manganese steel under dynamic and static loading

The study analyzes the deformation strengthening mechanisms of medium manganese steel under dynamic and static loading conditions. Different austenite volume fractions (7.4 %, 19.1 %, 30.9 %, 37.7 %) were obtained by varying the heat treatment temperatures (640 °C, 660°C, 680 °C, 700 °C). Results show a linear increase in austenite volume fraction with higher annealing temperature, while carbon content in austenite decreases. Yield strength initially decreases and then increases with annealing temperature. The mechanical properties of all four temperature-tested steels show a clear strain rate dependence in the high strain rate range, with strength increasing with strain rate. Quasi-static conditions no significant strain rate sensitivity. 680 °C test steel's quasi-static deformation is mainly governed by the transformation-induced plasticity (TRIP) effect and dislocation slip in body-centered cubic (bcc) crystals. Dynamic deformation after a strain of 0.14 shows a weakened TRIP effect, and dislocation strengthening in bcc crystals becomes dominant despite a large amount of untransformed austenite. During quasi-static deformation, 700 ℃ test steel exhibits strain hardening due to the TRIP effect at low strains and significant dislocation strengthening in bcc crystals at high strains. Although the TIRP effect is initially suppressed during dynamic deformation, it lasts for a long time. The combined effects of the TRIP effect and martensite dislocation strengthening determine the deformation strengthening mechanisms. Additionally, an optimized Voce model with strain rate strengthening term is proposed. It can well describe the mechanical behavior under dynamic strain rate.

Effect of Cr content in temperature-dependent mechanical properties and strain hardening of a twinning-induced plasticity steel

This study aims at assessing and analyzing the effect on the mechanical behavior at temperatures between 25 °C and 350 °C of the Cr additions (5 % and 10 %) to a TWIP steel (Fe–22Mn-0.6C). We conducted tensile tests and characterized the microstructure after deformation by light microscopy, X-ray diffraction (XRD) and FEG-SEM-EBSD. Different temperature-dependent strengthening mechanisms were determined. Mechanical twinning, Dynamic Strain Aging (DSA), and slip bands were the predominant mechanisms, with a combination of them depending on the stacking fault energy (SFE). The SFE decreases with the chromium content and increases with temperature, influencing the percentage of mechanical twinning generated during plastic deformation and consequently, affecting the strain hardening rate (SHR). There exists a direct relationship between strain hardening rate with temperature of deformation and mechanical twinning. DSA was observed and its effect on strain hardening was analyzed in detail.

Emergence and growth of faults during earthquakes: Insights from a dynamic elasto-plastic continuum model

I use a dynamic two-dimensional plane strain model of an elasto-plastic (Mohr-Coulomb) material with velocity-weakening friction to numerically simulate the emergence and propagation of shear fractures that accumulate slip intermittently during earthquakes. The model considers a 10 × 10 km block of homogeneous crust with a small weak inclusion, subjected to slow simple shear. Results show that deformation is distinctly bimodal, consisting of long periods (lasting ca. 50–200 years) where deformation is dominantly elastic separated by rapid sliding events lasting a few seconds during which time deformation is strongly localised on narrow plastic shear bands (faults). In terms of energy expenditure, the interseismic period is overwhelming dominated by accumulation of elastic strain energy whereas during earthquakes, most of the drop in elastic strain energy is consumed (dissipated) by plastic work. Model earthquakes have maximum slip rates of a few meters per second, involve a few meters of slip and result in drop of mean differential stress of several megapascals. Most earthquakes are complex events involving near-simultaneous rupture of multiple fault segments that propagate at supershear velocities (close to the P-wave speed) while they also induce a significant amount of more diffuse off-fault inelastic deformation. Earthquakes may involve formation of new faults and/or reshear on previously formed faults, which are favourably reactivated owing to their low pressure. Most individual faults establish much of their length early, whereas during subsequent events they continue to accumulate displacement at virtually constant length. As the confining pressure is increased, ruptures are more dynamic, which leads to increasingly widespread inelastic deformation. Overall, the models highlight the complex temporal and spatial interactions that exist between different faults within an array that communicate especially during earthquakes through static and dynamic changes in the stress field.

Pursuing ultrastrong and ductile medium entropy alloys via architecting nanoprecipitates-enhanced hierarchical heterostructure

Nanoprecipitate-strengthened medium/high entropy alloys (M/HEAs) with ultrahigh strengths and unusual physical properties represent promising candidates for structural applications. However, further strengthening these materials usually relies on increasing the volume fraction of nanoprecipitates and/or introducing harder intermetallics that inevitably sacrifice the ductility. Here, we report a strategy to break this trade-off in a Co-Cr-Ni-based MEA by architecting a hierarchical heterostructure that integrates high-volume fraction (up to ∼30%) D022-γ’’ nanoprecipitates, shearable and non-shearable intermetallic particles, with a low stacking fault energy (SFE) matrix with heterogeneous grain structure. This hierarchical heterostructure can arouse hybrid strengthening mechanisms and lead to cross-scale and dynamic strain partitioning during plastic deformation, contributing to a superior strain-hardening capability and an excellent combination of the yield / ultimate tensile strength of 1323 MPa / 1690 MPa and 29% tensile elongation. This study provides a promising paradigm to design ultrastrong and ductile metallic materials via controlling multiscale microstructural heterogeneities.

Deformation and damage mechanisms during clockwise diamond and counter clockwise diamond thermomechanical fatigue in Timetal 834 alloy

In the present investigation, the thermomechanical fatigue (TMF) behavior of Timetal 834 alloy was studied under clockwise diamond (CWD) and counter clockwise diamond (CCD) loading conditions. These tests were conducted within 723 K ↔ 873 K temperature range at the strain amplitudes of Δεm/2 = ±0.6% and ±1.0%. The cyclic softening behavior observed under CWD-TMF condition at both strain amplitudes, is attributed to shearing of coherent Ti3Al precipitates. Contrarily, the alloy exhibits both cyclic hardening and softening responses under the CCD-TMF conditions. This additional hardening response is attributed to the occurrence of dislocation–dislocation interactions coupled with dynamic strain aging. The present study reveals that both phase angle and strain amplitude affect the TMF life. The alloy exhibited relatively lower fatigue life under CCD-TMF condition than under CWD-TMF condition, at both strain amplitudes. Transmission electron microscopy analyses of the post-deformed specimens reveal that the dislocation arrangements are similar in both loading conditions at Δεm/2 = ±0.6%, while being distinctively different at Δεm/2 = ±1.0%. At higher strain amplitude, the fatigue life is significantly reduced under CCD-TMF condition. Fractographic analyses indicate the involvement of oxidation damage during both the TMF loading conditions. However, its effect is more pronounced under CCD-TMF than under CWD-TMF condition.

A quantitative insight into strain hardening behavior of typical Hadfield steel under dynamic load

In this paper, the critical threshold associated to the activating of strain hardening capacity with respect to typical Hadfield steel Mn13Cr2 was explored quantitatively utilizing a Separated Hopkinson Press Bar (SHPB). The strain hardening behavior of the Mn13Cr2 under dynamic load was investigated, systematically, and the strain hardening mechanisms involved in different plastic deformation conditions were illuminated. Results indicated the overall plastic deformation process under different dynamic loads could be divided into three stages, including the (LHS), the (HHS) as well as the parabolic hardening stage (PHS). The critical transformation strength (CTS) from LHS to the HHS showed a trend of increasing first and then decreasing with the shock pressure increasing from 0.1 MPa to 0.8 MPa, and the maximum hardening effect with respect to the studied Mn13Cr2 steel could be activated at dynamic load threshold of 0.6 MPa with max CTS of ∼493.6 MPa. Dislocation-dominated strengthening mechanism and C–Mn atomic dipoles strengthening mechanism induced by dynamic strain aging were responsible for the excellent strain hardening capability when the impact load was increased above 0.6 MPa.

Dynamic properties of EPS beads lightweight soil mixed with polypropylene fiber

EPS beads lightweight soil composite is a new type of artificial geotechnical material, with low density and high strength characteristics, which can be widely used and plays an important role in engineering projects. To study the dynamic properties of EPS beads lightweight soil mixed with polypropylene fiber (FELS) under cyclic loading, dynamic triaxial test was conducted on EPS beads lightweight soil mixed with polypropylene fiber (FELS) with different EPS contents, cement contents, and confining pressures. The results showed that under the same dynamic stress, the dynamic strain increased with the increase of EPS content and decreased with the increase of cement content and confining pressure. The dynamic shear modulus decreased with the increase of EPS content and increased with the increase of cement content and confining pressure. The inverse of the dynamic shear modulus showed an excellent linear relationship with the dynamic strain. The attenuation model of the dynamic shear modulus ratio of FELS was established. The more the EPS content was, the greater the damping ratio was. The damping ratios of the samples with different EPS contents increased slowly and close to one another in the early stage of dynamic stress loading. However, they rapidly increased in the late stage, and the gaps among them were noticeable. The damping ratio was negatively correlated with the cement content and the confining pressure. Combined with the macroscopic mechanical properties, the microscopic SEM observation was carried out to analyze the microscopic mechanism of FELS.

Excellent dynamic properties and corresponding deformation mechanisms in a microband-induced plasticity steel with dual-heterogeneous structure

A dual-heterogeneous structure with dual phases and heterogeneous grains was designed in a high Mn microband-induced-plasticity (MBIP) steel. The heterogeneous structured sample exhibits similar dynamic shear yield strength, while exhibiting enhanced dynamic uniform shear strain and dynamic shear toughness by 36 % and 47 %, respectively, as compared to the homogeneous structured sample. The strain hardening mechanisms contributing to the excellent dynamic shear properties in the heterogeneous structured sample have been revealed. Firstly, the superior hetero-deformation-induced hardening capability of the heterogeneous structured sample arises from a higher density of geometrically necessary dislocations induced in each phase. Secondly, a pronounced strain rate effect is observed in body-centered cubic (BCC) grains and face-centered cubic (FCC) ultra-fine grains, leading to an elevated level of strain rate sensitivity. Finally, the MBIP effect is also observed in FCC coarse grains under dynamic loading. Moreover, the MBIP effect in FCC ultra-fine grains is more likely to occur at high strain rates due to the emergence of single-wall domain boundaries, which is not observed during quasi-static tensile testing. The present results provide new routes for designing impact-tolerant structures in advanced metals and alloys.

Study on dynamic recrystallization of ultra-high strength 22MnB5 steel during hot rolling

The effect of deformation temperature and strain rate on the recrystallization behavior of ultra-high strength hot formed 22MnB5 steel was systematically studied by isothermal compression experiments, and the microstructure was characterized and analyzed. The results show that the peak stress and peak strain of 22MnB5 steel decrease with increasing deformation temperature and increase with increasing strain rate. The dynamic recrystallization of 22MnB5 steel is more sensitive to temperature and less affected by strain rate. The recrystallization behavior is significant during isothermal deformation above 1323 K. Based on the hyperbolic sinusoidal constitutive equation, the accurate prediction model of dynamic recrystallization grain size and a dynamic recrystallization critical strain model for 22MnB5 steel were established. The relationship between recrystallization austenite grain size and deformation temperature and deformation amount was obtained as follows: d=4.1×103[ε·exp(350.38/RT)]. The critical strains of complete recrystallization and complete non-crystallization at each deformation temperatures were determined by the critical strain model, which can provide a basis for the optimization design of rolling process parameters.

Experiment on the impact response of aluminum alloy wood core sandwich composites

In this work, a protective structure with 2A12T4 aluminum alloy as the panel material and plywood as the core layer was designed. Penetration experiments were performed by firing multiple projectiles from a light gas gun. The impact behavior, damage mode, absorbed energy, and residual strength of the interlayer after impact were studied. The dynamic response and the failure of the interlayer were analyzed. Disbonding, fiber fracture, buckling, shear, and core fracture between the metal layer and the composite layer of the front panel were observed. The impact resistance of the sandwich plate was also studied. Based on the results of the experiments and numerical simulations, failure determination of the plywood core layer was achieved using the Hashin criterion, and a finite element model was established using ABAQUS software. High-speed impact testing was performed with a Hopkinson pressure bar. The stress–strain relationship under a high dynamic strain rate is given here, and the energy absorption efficiency under loading in different directions was analyzed. Finite element analysis of the representative volume elements in the wood microstructure was also carried out. The results reported here can be used to guide optimal design of sandwich structures suitable for use under high-speed impact conditions.

Characterizing stable nanocrystalline Cu-Ta behavior and failure dynamics under extremes of strain rate, strain, temperature and pressure by modified dynamic tensile extrusion

This work presents characterization of thermo-mechanically stable, bulk nanocrystalline (NC) Cu-Ta alloys under a combination of extreme states using high-temperature, dynamic tensile extrusion experiments. The NC Cu-Ta was subjected to high dynamic strain rates up to 105/s, large plastic strains of 100–500 %, and high homologous temperatures greater than 50 %TM. This combination of thermo-mechanical conditions provides a unique look at how these extremely stable microstructures can accommodate and reconfigure under situations where dislocation activity is the most extreme, given constitutive relationships between strain rate, dislocation nucleation, and plastic work. Elevated temperature tests results reveal NC Cu-1Ta alloys are capable of forming a coherent jet, (25 mm in length by 1.8 mm in diameter) as it accelerates out of the die after being dynamically extruded. Microstructural analysis reveals that unlike previous reports on conventional un-stabilized nano or near nano-grained Cu, NC Cu-Ta alloys behave differently. They do not undergo grain coarsening via a nucleation and growth process, but rather behave identically to that of coarse-grained Cu. The NC grains elongate along the extrusion direction and at the same time shrink in diameter and develop a <111> type texture. Ultimately, the occurrence of premature dynamic failure was attributed to the inherent constraints posed by processing defects during synthesis.

A novel fractal-statistical scaling model of rocks considering strain rate

The scaling-dependent behaviors of rocks are significant to the stability and safe operation of the structures built in or on rock masses for practical engineering. Currently, many size effect models are employed to connect laboratory measurements at small scales and engineering applications at large scales. However, limited works consider the strain rate effect. In this study, an fractal-statistical scaling model incorporating strain rate is proposed based on a weakest-link approach, fractal theory and dynamic fracture mechanics. The proposed scaling model consists of 8 model parameters with physical meaning, i.e. rate-dependent parameter, intrinsic material parameter, dynamic strain rate, quasi-static strain rate, quasi-static fracture toughness, micro-crack size, micro-crack intensity and fractal dimension, enabling the proposed scaling model to model the scaling behaviors under different external conditions. Theoretical predictions are consistent with experimental data on red sandstone, proving the reliability and effectiveness of the proposed scaling model. Thus, the scaling behaviors of rocks under dynamic loading conditions can be captured by the proposed fractal-statistical scaling model. The sensitivity analysis indicates that the size effect becomes more obvious with a higher strain rate, larger fractal dimension, smaller micro-crack size or lower micro-crack intensity. Therefore, the proposed scaling model has the potential to capture the scaling behaviors considering the thermal effect, weathering effect, anisotropic characteristic etc., as the proposed scaling model incorporated model parameters with physical meaning. The findings of this study are of fundamental importance to understand the scaling behaviors of rock under dynamic loading condition, and thus would facilitate the appropriate design of rock engineering.

Effect of temperature on the plastic flow and strain hardening of direct-quenched ultra-high strength steel S960MC

This study investigates the plastic deformation and hardening behavior of the direct-quenched ultra-high strength steel S960MC at various temperatures ranging from room temperature to 900 ℃. In this regard, the Hollomon and Voce equations are used to model the hardening behavior of the material at different temperatures. The suitability of each equation to predict the plastic flow of S960MC is evaluated based on the best resulted fit for the material. In addition, microstructural investigations are carried out to indicate the correlations between the microstructural changes, occurring in the range of room temperature to 900 ℃, and hardening behavior and governing parameters. The Hollomon approach showed deviations from the experimental results for room to intermediate temperatures; however, the Voce equation modeled the material's strain hardening and flow behavior more successfully for the entire temperature range of room temperature–900 ℃. Additionally, there was a significant consistency between the Kocks-Mecking and Voce parameters. Dislocation interactions, dynamic strain aging, dynamic recrystallization, dynamic recovery, tempering (martensite decomposition), and austenite formation were the most influential microstructural features on the hardening behavior at various temperatures. The correlations between these microstructural features and hardening parameters were established satisfactorily for both the Hollomon and Voce approaches.