Terms Of Strain Rate Research Articles

Study on the static and dynamic mechanical properties and constitutive models of 3D printed PLA and PLA-Cu materials

The failure of mechanical properties in 3D printed polylactic acid (PLA) for many functional applications has made exploring ways for improving these properties essential; the use of copper powder for producing a composite material known as PLA-Cu is one of these ways. The mechanical responses of both PLA and PLA-Cu under both static and dynamic loading were studied using a universal testing machine and a split Hopkinson pressure bar apparatus, respectively. This experimental study helped to develop a constitutive model for each material according to their mechanical behavior. However, PLA-Cu, affected by ‘impact embrittlement,’ indicates a purely linear elastic behavior during dynamic conditions. Addition of copper powder increases the yield strength of the composite material significantly as compared to pure PLA, with both materials being strain rate sensitive as they change from static to dynamic states. The calibration of the Johnson-Cook constitutive model with the inclusion of the Cowper-Symonds strain rate term for these materials promises useful information for numerical models, improving the predictive models on their behavior under different loading scenarios.

Modelling of the Flame Surface Density Transport During Flame-Wall Interaction of Premixed Flames within Turbulent Boundary Layers

ABSTRACT A priori Direct Numerical Simulation (DNS) analysis of the modelling of the generalised flame surface density (FSD) transport equation in the framework of Reynolds Averaged Navier-Stokes (RANS) simulations has been conducted with a focus on flame-wall interaction (FWI) within turbulent boundary layers. The analysis was performed using two different scenarios: one involving the unsteady head-on interaction of a statistically planar premixed flame as it propagates through a turbulent boundary layer, and the other addressing statistically stationary oblique-wall interaction of a V-shaped premixed flame within a turbulent channel flow. Flame-wall interaction has been observed to exert a significant influence on the statistical behavior of the terms in the FSD transport equation. Throughout all phases of flame-wall interaction in both configurations, the primary source and sink terms in the FSD transport equation are consistently associated with the tangential strain rate and curvature terms. The relative importance of the contributions of the propagation and turbulent transport terms in the FSD transport equation have been found to be influenced by the flame-wall interaction configuration. Existing models for the tangential strain rate term in the FSD transport equation have been identified as inadequate based on a priori DNS assessment. Hence, adjustments to these models have been proposed to address the impact of flame orientation and near-wall effects specifically in the context of flame-wall interaction within turbulent boundary layers. The alignment between the flame normal vector and the wall normal vector has been identified as a crucial factor in modelling the contributions of unresolved dilatation rate and unresolved normal strain rate to the FSD transport equation. New models for these terms have been demonstrated to exhibit satisfactory agreement with the corresponding terms extracted from DNS data.

Constitutive modeling and simulation of polyethylene foam under quasi-static and impact loading

In this paper, quasi-static and dynamic compression experiments were carried out on polyethylene foam by a universal material testing machine and a drop tower impact device. The mechanical response characteristics and energy absorption capacity of polyethylene foam under quasi-static and moderate strain rate (4 × 10−3–102s−1) loading conditions were obtained. An improved constitutive model of strain-rate term coupling strain and strain rate was established based on the Sherwood–Frost phenomenological constitutive model and Johnson–Cook constitutive model. Low Density Foam model combined in the finite element software ABAQUS with the improved constitutive model was used as the parameter definition of polyethylene foam material in the simulation. The drop-tower impact tests at different heights were simulated, and the simulation results were compared with the actual drop tower impact test results. The results showed that the peak acceleration errors between simulation and experiment were less than 7.1%, verifying the accuracy of the constitutive model. This study provides a method of constitutive models and finite element simulation to the performance of polymer foams.

Forced ignition of premixed cool and hot DME/air flames in a laminar counterflow

Recently, low-temperature chemistry (LTC) and LTC-induced cool flames have attracted extensive interest since they can substantially influence the ignition process and accelerate the subsequent hot flame propagation. However, it is unclear how the flow affects the forced ignition of a cool flame and its subsequent transition to a hot flame. In this study, we conduct transient 2D simulations for the forced ignition processes of premixed cool and hot flames in a laminar, axisymmetric, counterflow configuration with well-defined flow field. Different ignition energies and strain rates are used to ignite and stabilize cool and/or hot flames in a counterflow. The critical conditions for the ignition of cool and hot flames are identified, and the cool flame kernel quenching and its transition to hot flame are discussed. It is found that the ignition energy determines the highest temperature and thereby controls the thermal runaway process. The strain rate influences the flame kernel propagation and the transition from cool flame to hot flame. A large strain rate may quench the cool flame, while a small strain rate may lead to the transition from cool flame to hot flame due to the sufficiently long residence time. Therefore, cool flame ignition and stabilization can only be achieved within a certain range of strain rates. Furthermore, an ignition regime diagram in terms of ignition energy and strain rate is proposed, and four regimes are identified: (I) only cool flame, (II) only hot flame, (III) ignition failure, and (IV) transition from cool flame to hot flame (with appearance of double flame structure). These results provide new insights into how the flow affects the cool flame ignition and transition.

Plastic Deformation Characteristics and Calculation Models of Unbound Granular Materials under Repeated Load and Water Infiltration

Unbound granular materials (UGMs) have advantages in their water storage and drainage capabilities in permeable pavement, which is a benefit for urban sustainable development. The plastic strain of UGM is a crucial mechanical property that affects its design and construction. During its service life, repeated load only, repeated load after infiltration, and simultaneous action with load and infiltration are the three inevitable working conditions that will impact plastic strain, especially dynamic water infiltration. How these working conditions influence plastic strain needs to be focused on and solved. This study conducted laboratory tests to investigate plastic strain considering factors such as loading strength and repetitions, as well as infiltration number and duration. The results showed that the plastic strain and plastic strain rate exhibited similar variations during the repeated load only test and repeated load after infiltration test. The plastic strain changed significantly with different infiltration numbers but had relatively small variations in terms of the plastic strain rate. Longer infiltration duration led to greater plastic strain. With the simultaneous action, the plastic strain presented different variation to the other two conditions. The first and second infiltrations had a more obvious influence on the plastic strain when infiltration was applied. Calculation models were established to predict the effects of loading strength and repetitions as well as infiltration number and duration on plastic strains. For the repeated load only test, an error of 4.6% was observed. In terms of the infiltration number and duration, the errors were found to be 18.5% and 8.5%, respectively. The power function and Sigmoidal Logistic model were used to establish calculation models under the simultaneous action test with a maximum error of 11.5% ranging from 100 to 60,000 repetitions. The proposed calculation models can characterize plastic strain under the three working conditions very well, which can help in the design and construction of fully permeable pavement.

Multiple structures and transition mechanisms of laminar fuel-rich ethanol/air counterflowing spray flames

Structures of laminar non-premixed ethanol/air spray flames in the axisymmetric counterflow configuration are studied under fuel-rich conditions by means of numerical simulations. The monodisperse ethanol spray is carried by air and directed against an air stream. Both streams enter at 300 K, and the system is at atmospheric pressure. Up to three different structures of these flames for identical boundary and initial conditions are identified, and regime diagrams are presented that show their conditions of existence in terms of the gas strain rate on the spray side of the configuration, [Formula: see text], starting from 55/s at an initial spray velocity of 0.44 m/s. The equivalence ratio on the spray side, [Formula: see text], is varied between 1.1 and 1.6, and initial droplet radii, [Formula: see text], from 10 to 50 [Formula: see text]m are considered. The most stable spray flame structure is characterized by two chemical reaction zones. For some conditions, single chemical reaction zones on either side of the counterflow configuration are found. Conditions under which these different flame structures exist are analyzed. Previous studies identified only two different structures for non-identical boundary conditions, and in this study, three different structures are presented for the first time. Moreover, the transition mechanisms of one structure to another are analyzed. The competition between the energy-consuming spray evaporation and the exothermic chemical reaction rates as well as the location of the spray determines the existence of the different flame structures. This transition of the different flame structures may explain spray flame characteristics such as flame pulsation or flame instabilities.

A strain rate-dependent analytical approach for low-velocity impact on the beam composed of silicon-nitride and stainless-steel

Purpose The purpose of this study is to investigate the strain rate effect on the problem of low-velocity impact (LVI) on a beam, including silicon nitride and stainless steel materials. Design/methodology/approach Based on the nonlinear Hertz impact mechanism, the energies related to the impactor and the beam are written, and motion equations are derived using the Lagrangian mechanics and Ritz method. The strain rate term is represented as a damping matrix in the equations of motion. In the issue of LVI on the silicon nitride and stainless steel beam, the effect of internal viscous damping coefficient in simply–simply and clamped–free boundary conditions are studied. Also, the influence of the volume fraction index in the range between zero and one and greater than one on the impact response is investigated. Findings The results make it clear that the strain rate parameter had little effect on the response in LVI. Also, an increase in the volume fraction index has led to a decrease in the contact force and an increase in the rebound velocity of the impactor. Originality/value The effect of strain rate on LVI is theoretically studied in this paper, while in most of the papers, this effect is investigated experimentally and numerically.

Turbulence Effects on the Statistical Behaviour and Modelling of Flame Surface Density and the Terms of Its Transport Equation in Turbulent Premixed Flames

The influence of the ratio of integral length scale to flame thickness on the statistical behaviours of flame surface density (FSD) and its transport has been analysed using a Direct Numerical Simulation database of three-dimensional statistically planar turbulent premixed flames for different turbulence intensities. It has been found that turbulent burning velocity based on volume-integration of reaction rate and flame surface area increase but the peak magnitudes of the FSD and the terms of the FSD transport term decrease with an increase in length scale ratio for a given turbulence intensity. The flame brush thickness and flame wrinkling increase with an increase in length scale ratio for all turbulence intensities. However, the qualitative behaviours of the unclosed terms in the FSD transport equation remain unaltered by the length scale ratio and in all cases the tangential strain rate term and the curvature term act as leading order source and sink, respectively. A decrease in length scale ratio for a given turbulence intensity leads to a decrease in Damköhler number and an increase in Karlovitz number. This has an implication on the alignment of reactive scalar gradient with local strain rate eigenvectors, which in turn increases positive contribution of the tangential strain rate term with a decrease in length scale ratio. Moreover, an increase in Karlovitz number increases the likelihood of negative contribution of the curvature term. Thus, the magnitude of the negative contribution of the FSD curvature term increases with a decrease in length scale ratio for a given turbulence intensity. The model for the tangential strain rate term, which explicitly considers the scalar gradient alignment with local principal strain rate eigenvectors, has been shown to be more successful than the models that do not account for the scalar gradient alignment characteristics. Moreover, the existing model for the curvature and propagation term needed modification to account for greater likelihood of negative values for higher Karlovitz number. However, the models for the unclosed flux of FSD and the mean reaction rate closure are not significantly affected by the length scale ratio.

Hot deformation behavior and processing map development of Mg/Al2O3 composite: A case study of extrusion ratio effects

The hot deformation behavior of 2.5 wt.% submicron alumina reinforced magnesium composite manufactured by a new casting method was examined to assess the impact of extrusion ratio and initial microstructure on the hot workability of Mg/Al2O3 composite. The thermomechanical experiments were performed at strain rates from 0.001 s−1 to 0.05 s−1 and the temperature ranging from 523 K to 673 K. The processing map was developed using power dissipation efficiency in terms of temperature and strain rate. Results revealed that the higher extrusion ratio yields finer grain size and a more homogenous distribution of alumina particles resulting in lower flow stress and activation energy. Stable regions with more power efficiency (57%) and less instability were observed in materials that experienced higher strain. Based on the microstructural observation, dynamic recrystallization as the main restoration mechanism occurred at composite with a higher extrusion ratio and finer grains in all conditions. It was deduced that the enhanced workability of fine-grain material is confirmed by steady flow stress and safe zones of the processing map. It was also revealed that twinning–twinning intersection and flow localization are the main reasons for unstable flow in both samples with unlike grain sizes.

Influence of infill density on the dynamic behavior of 3D-printed CF-PEKK composites using split Hopkinson’s pressure bars

The dynamic mechanical behavior of 3D-printed CF-PEKK composites has been studied using the split Hopkinson pressure bar (SHPB). Three sets of samples with different infill densities (20, 50, and 100%) were impacted at different impact pressures (1.4, 1.7, 2.0, 2.4 bar) to characterize their dynamic behavior in terms of strain rate, stress, and strain performance. Moreover, the samples’ dynamic response and failure behavior are cross-referenced with each infill density sample's microstructural behavior and physical parameters, which can give an excellent dynamic response under different strain rate ranges. The results showed that dynamic stress and strain behavior are proportional to the infill density with a maximum dynamic stress of approximately 90 MPa with 100% infill density. In addition, the behavior of the transmitted wave during the dynamic impact showed that a sample with less infill density could attenuate/absorb dynamic impact. These results obtained under this impact pressure indicate the high precision and repeatability of the SHPB approach for the tested 3D composites under dynamic loading and prove that the striker bar velocity significantly impacts the amplitudes of different recorded waves to understand the behavior in detail. In addition, high-speed camera images also showed that the 3D-printed composite sample showed that using a higher infill density enhanced both the damage performance and the impact resistance of the three-dimensionally printed composites at each impact pressure because of the minimized intensity and the amount of final macro damage. This study is useful and helpful for design engineers to study the influence of the process parameter of infill on the dynamic behavior of printed composite materials and confirms the growing interest in 3D printing of composite materials to be employed in different engineering applications which are not limited to static or quasi-static loading circumstances but mainly include dynamic loading conditions.

Study the effects of temperature and strain rates on transient thermomechanical responses on multilayer skin tissue

The present study is focused on understanding the effects of strain and temperature rates on heat transport mechanisms and the related thermo-mechanical interaction with skin tissue, which are essential for the effective application of thermal therapeutic techniques. The goal of this article is to develop a mathematical framework to investigate the thermo-mechanical phenomena occurring on triple-layered skin tissue using the Modified Green-Lindsay model (MGL) by taking into consideration of two thermal relaxation parameters. This model takes into consideration the effect of strain and temperature rate factors in thermoelastic behaviour which was neglected in several other thermoelastic models. The problem is formulated in a unified way to derive the governing equations and constitutive relations under the present model and also the thermoelasticity with two phase-lag parameters. A comprehensive assessment of solution is discussed for MGL model and compared the results with the corresponding results predicted by dual phase lag generalized thermoelastic model that involves two phase-lags. The effect of strain rate term in heat transport on skin tissue are especially highlighted.

Static and dynamic compressive behaviour of 3D printed auxetic lattice reinforced ultra-high performance concrete

This paper presents a systematic experimental study on static and dynamic compressive behaviour of 3D octet, re-entrant honeycomb and triangular lattice reinforced ultra-high performance concrete, i.e., O-UHPC, H-UHPC and T-UHPC as well as steel fibre reinforced UHPC (S-UHPC). Mechanical tests were conducted to investigate the static and dynamic compressive behaviour of UHPC composites including failure pattern, stress-strain curve, dynamic increase factor (DIF), dynamic compressive strain and energy dissipation under various strain rates (i.e., 0, 34.8, 59.7, 86.7, 108.5 and 134.7 s−1). The plain UHPC and S-UHPC were used as references for comparison. Results indicate that H-UHPC has a 14.6–19.4% higher static compressive strength than O-UHPC and T-UHPC. S-UHPC exhibits higher dynamic compressive strength at lower strain rates, while the dynamic strengths of H-UHPC and T-UHPC at higher strain rates reach the highest, i.e., 262.7 MPa and 222.2 MPa, respectively. The highest total energy and post-crack energy at high strain rates take place on H-UHPC. Overall, H-UHPC has comparable static compressive behaviour but better dynamic compressive behaviour at high strain rates in terms of strength, ductility, energy dissipation and DIF, compared with other UHPC specimens, suggesting that re-entrant honeycomb is a better choice for manufacturing UHPC with optimal auxetic 3D lattices.

Effects of ultrasonic vibration cutting trajectories on chip formation of tungsten alloys

Chip morphology has a close correlation with machined surface quality and tool wear in turning process. In the current research on ultrasonic vibration cutting, little is known about the effect of different directions of ultrasonic action on chip formation. In this paper, the effect of ultrasonic vibration on chip formation of tungsten alloy when acting in the direction of cutting speed and cutting depth, respectively, was analyzed by splitting the elliptical trajectory. Furthermore, the advantages of elliptical trajectory machining were also explained in terms of strain rate. The results show that ultrasonic vibration in the direction of cutting depth can effectively suppress the serrated chips and promote the formation of smooth and continuous chips. However, ultrasonic vibration in the direction of cutting speed has the opposite effect. When the tool is superimposed with two-way vibration, the chip morphology formed by the elliptical trajectory is smoother and more continuous. Moreover, it achieves the highest strain rate and the lowest cutting force. Finally, as seen from the experiments of conventional cutting and cutting with variable phase difference, the machined surface roughness decreases with the transition of chip from broken and folded shape to smooth shape. Overall, results of cutting experiment are consistent with simulation results demonstrating the effectiveness of the current work.

Effect of hybrid industrial and recycled steel fibres on static and dynamic mechanical properties of ultra-high performance concrete

Employing recycled tyre steel (RTS) fibres to replace industrial steel (IS) fibres in ultra-high performance concrete (UHPC) can improve its cost-effectiveness and sustainability. However, the lack of research on dynamic properties of such sustainable UHPC would hinder its application in concrete structures such as protective and defence structures which may experience different dynamic loadings. This paper experimentally investigates the effect of various RTS fibre replacement levels (0.5–2.0% by volume) on the flowability and quasi-static compressive, flexural and tensile strengths of UHPC as well as the dynamic splitting tensile behaviour under various strain rates (4.5–6.5 s−1). The conventional UHPC with 2.0% IS fibre was prepared as the reference. Results indicate that the flowability of UHPC containing RTS fibres is about 5–11% higher than that of reference UHPC. Rising the RTS fibre replacement level up to 1.0% increases the compressive, flexural and tensile strengths while after which, the strengths drop. The dynamic splitting tensile behaviour of all UHPC specimens is sensitive to strain rate in terms of failure pattern, dynamic splitting tensile strength, dynamic increase factor and energy absorption capacity. Using 0.5% RTS fibre to substitute IS fibre can bring the best synergy, leading to the highest dynamic splitting tensile properties of UHPC at a strain rate of approximately 4.5–6.5 s−1. The material cost, embodied carbon and embodied energy of UHPC are reduced by 9–57% in the presence of RTS fibres. The optimal RTS fibre replacement dosage for UHPC is 0.5% considering static mechanical properties, dynamic splitting tensile behaviour, material cost and environmental impact.

Plastic deformation and ductile fracture of L907A ship steel at increasing strain rate and temperature

A combined theoretical, numerical, and experimental approach is adopted to systematically characterize the plastic deformation and ductile fracture behaviors of L907A low-alloy ship steel widely used in ship construction, with the effects of strain rate and thermal softening duly accounted for. A mixed Swift-Voce hardening model coupled with strain rate and temperature-dependent terms is proposed, while the Hosford-Coulomb model of ductile fracture is modified by introducing temperature-dependent term to account for the effect of thermal softening. To calibrate the parameters appearing in the constitutive models, dynamic uniaxial tensile tests at varying strain rates (0.001 ∼ 5200 s−1) and quasi-static uniaxial tensile tests at varying temperatures (20 ∼ 800 °C) are separately performed, with the coupling between strain rate and temperature effects ignored. The calibrated plasticity and ductile fracture models are numerically implemented with the method of finite elements (FE), and their applicability to practical applications is validated against experimental results of ballistic impacts. Normal and oblique impacts on L907A target plates with conical, hemispherical, and blunt projectiles are considered. Good agreement between FE simulation results of plastic deformation and ductile fracture modes and those measured experimentally is achieved, thus demonstrating the viability of the established plasticity and fracture models of L907A steel for applications in complex ballistic impact scenarios.

Global Sea Surface Cyclogeostrophic Currents Derived From Satellite Altimetry Data

AbstractSea surface currents (SSC) derived from the sea surface height anomalies (SSHA) as measured by multi‐satellite altimeters are widely used for various applications including studies on ocean dynamics, marine ecology, and climate change. However, present SSC products estimated on the assumption of an idealized geostrophic balance is biased. To overcome this idealization, this study considers flow curvature in the estimation of sea surface velocities in the global ocean, with the computation scheme validated using numerical model results. It is demonstrated that the inclusion of curvature into SSC estimations significantly changes SSC dynamic features in terms of kinetic energy, enstrophy (the maximum spatial difference is about 15%), and strain rate (the maximum spatial difference is about 10%). Such correction is of importance to the application studies relying on the SSC products from the satellite measured SSHA.

Thermodynamically Consistent Modified Lord–Shulman Generalized Thermoelasticity With Strain-Rate

Abstract The analysis of thermoelastic wave propagation in continuum solids at micro/nano-seconds is especially significant for ultra-fast heating technologies, where strain relaxation effects will increase significantly. In most cases, it is commonly accompanied by a relatively small strain-rate; however, this is questionable in the environment of transient thermal wave propagation under the ultra-fast heating case. The present work is dedicated to constitutive modeling of a novel generalized thermoelasticity model by introducing an additional strain-rate term associated with a relaxation time parameter in the Lord–Shulman (LS) thermoelasticity with the aid of an extended thermodynamics framework. As an application, the newly developed model is applied to a one-dimensional half-space problem which is traction free at one end; a time-dependent thermal shock is imposed at the same end to analyze transient responses of thermodynamic field variables (temperature, displacement, strain, and stress). The inclusion of strain-rate in the LS model eliminates the probable propagating jump discontinuities of the strain and stress fields at the wavefront. The current work is expected to be useful in the mathematical modeling and numerical simulation of thermoelastic processes under an ultra-fast heating environment.

Thermal cracking prediction for a squeeze casting process with an approach of multi-scale and multi-model coupling

The smooth particle hydrodynamics (SPH) method is advantageous in tracking a free surface and a moving interface. This paper uses the SPH method to simulate the filling process of squeeze casting. The simulated temperature field at the end of filling was input into a finite element model (FEM) program to simulate the solidification process after squeeze casting. Due to the existence of a liquid phase, a solid phase, and a two-phase mushy zone in the solidification process after squeeze casting, the deformation behavior in the solidification process was modeled with a thermoelasto–viscoplastic constitutive model representing these different phases. In the RDG thermal cracking criterion based on the principle of dendrite gap complement, there are a strain rate term, a secondary dendritic spacing term, and a pressure term. These terms accurately describe the squeeze casting process. Therefore, the RDG criterion was used to predict thermal cracking. The strain rate term in the RDG criterion was calculated by the FEM. For the calculation of the secondary dendritic spacing, the temperature field during the solidification process is locally refined by the FDM method to complete the transition from the macroscale to the mesoscale; then the refinement results are imported into the phase field method for dendritic growth simulation. The results show that the method based on multi-model coupling has satisfactory prediction accuracy for the thermal cracking in the squeeze casting process. The combination of the phase field method and the RDG criterion provides a new approach to the simulation of thermal cracking defects. The prediction results show that the thermal cracking tendency increases with an increase in strain rate. However, the local position C of the bracket sample had a higher strain rate of 7.15/s, and a lower cooling rate of 2.96 K/s offset the effect of the high strain rate. As a result, a low thermal cracking tendency level of 1.13729 was obtained.

Study on Dynamic Impact Response and Optimal Constitutive Model of Al-Mg-Si Aluminum Alloy.

Al-Mg-Si series aluminum alloy is a heat-treatment-strengthened alloy. Research on the impact resistance of Al-Mg-Si series aluminum alloy is of great significance to expand its application in engineering. Taking 6082-T6 aluminum alloy as the concrete research object, using the split Hopkinson pressure bar (SHPB) device, the dynamic mechanical response of the material under different temperatures and average strain rates was studied, and the service performance of the material under extreme conditions was determined. The absolute temperature rise was introduced to optimize the existing constitutive model. The results show that when the environment temperature is 298.15~473.15 K under high-speed impact, the internal thermal softening effect of the material is dominant in the competition with the work hardening, resulting in a decrease in the flow stress of the material. Through the analysis of the real stress-strain curve, it was found that the elastic modulus of the material was negatively correlated with the strain rate, negatively correlated with the temperature, and showed an obvious temperature-softening effect. Yield strength was negatively correlated with temperature and positively correlated with strain rate, which showed an obvious strain rate hardening effect. Based on SEM microscopic analysis, it was found that under given conditions, adiabatic shear bands appeared in some samples, and their internal structures demonstrated obvious change. It was judged that when high-speed impact occurs, cracks are induced at the shear bands, and the cracks will continue to develop along the adiabatic shear bands, resulting in many oblique cracks which will gradually become larger and eventually lead to material failure. Finally, based on the model, the strain rate and temperature softening terms were improved, and a rise in adiabatic temperature rise was introduced. The improved model can better describe the strain rate effect of the material and accurately describe its flow stress. It provides a theoretical basis for the engineering application of materials.

Dynamic Split Tensile Strength of Basalt, Granite, Marble and Sandstone: Strain Rate Dependency and Fragmentation

The aim of this study is to understand the strength behaviour and fragment size of rocks during indirect, quasi-static and dynamic tensile tests. Four rocks with different lithological characteristics, namely: basalt, granite, sandstone, and marble were selected for this study. Brazilian disc experiments were performed over a range of strain rates from ~ 10–5 /s to 2.7 × 101 /s using a hydraulic loading frame and a split Hopkinson bar. Over the range of strain rates, our measurements of dynamic strength increase are in good agreement with the universal theoretical scaling relationship of (Kimberley et al., Acta Mater 61:3509–3521, 2013). Dynamic fragmentation during split tension mode failure has received little attention, and in the present study, we determine the fragment size distribution based on the experimentally fragmented specimens. The fragments fall into two distinct groups based on the nature of failure: coarser primary fragments, and finer secondary fragments. The degree of fragmentation is assessed in terms of characteristic strain rate and is compared with existing theoretical tensile fragmentation models. The average size of the secondary fragments has a strong strain rate dependency over the entire testing range, while the primary fragment size is less sensitive at lower strain rates. Marble and sandstone are found to generate more pulverised secondary debris when compared to basalt and granite. Furthermore, the mean fragment sizes of primary and secondary fragments are well described by a power-law function of strain rate.