Dynamic Increase Factor Research Articles

Dynamic compressive behavior of hybrid basalt-polypropylene fibers reinforced coral aggregate concrete

In this study, the effects of strain rate, fiber type, and hybrid fiber content on the dynamic mechanical properties of basalt-polypropylene fiber reinforced coral aggregate concrete (HBPRCAC) under impact loading are investigated using a split-Hopkinson pressure bar (SHPB) with a 75 mm diameter. The results demonstrated that the incorporation of basalt fiber (BF) and polypropylene fiber (PF), particularly when mixed, effectively reduced the failure of HBPRCAC. With an increase in strain rate, the failure of HBPRCAC exhibited a more severe pattern; even at low strain rates, cracks directly passed through the coral aggregate, causing damage. The failure modes of BF and PF were related to the strain rate. The probability of BF and PF being pulled out was higher at low strain rates than at high strain rates, where BF and PF predominantly exhibited snap failures. Additionally, the dynamic increase factor (DIF) of the dynamic compressive strength and dynamic modulus of elasticity for HBPRCAC demonstrated a decimal logarithmic linear increase with strain rate, while the dynamic critical strain and impact toughness of HBPRCAC exhibited a linear increase with strain rate. The mixed addition of BF and PF had varying effects on the strain rate sensitivity of HBPRCAC's dynamic mechanical properties, but the fiber mixing content was significantly positively correlated with the strain rate effects on the dynamic compressive mechanical properties of HBPRCAC. The dynamic compressive strengths of BPCAC-0.1 and BPCAC-0.2 at strain rates of 128–135 s−1 were increased by 78.66 % and 88.47 %, respectively, compared to those at strain rates of 33–36 s−1. The dynamic moduli of elasticity for BPCAC-0.1 and BPCAC-0.2 showed increases of 16.47 % and 13.06 %, respectively, compared to that of coral aggregate concrete. Moreover, the critical strain and impact toughness of BPCAC-0.2 were the highest at all tested strain rates.

Influence of aggregate content and strain rate on dynamic behaviour and energy consumption characteristics of concrete

Concrete's dynamic performance and energy dissipation are critical areas of interest that are significantly influenced by strain rate and aggregate content. This study investigated concrete's dynamic deformation, strength development and energy dissipation characteristics from specimens containing 0, 32%, 37% and 42% aggregate. These specimens were subjected to impact compression tests using a split Hopkinson compression apparatus, which allowed the effects of strain rate and aggregate content on the deformation, strength and energy dissipation of the concrete to be analysed. The results show that the concrete exhibits deformation hysteresis under impact loading, with splitting tensile failure as the predominant damage mechanism. Dynamic strength was more sensitive to strain rate than aggregate content. The dynamic increase factor (DIF) varied with aggregate content at different strain rates. The extent of specimen damage significantly influenced the energy distribution ratio, with absorbed energy showing a more pronounced strain rate effect than transmitted and reflected energy. Conversely, the amount of transmitted energy had a more pronounced impact on aggregate content than the amount of absorbed and reflected energy.

Dynamic increase factor of concrete compressive strength in confined split hopkinson pressure bar tests

This study presented a methodology to evaluate the pure strain-rate effect on concrete compressive strength and developed a pure rate dynamic increase factor (DIF) model through numerical and experimental investigations into confined split Hopkinson pressure bar (SHPB) tests. The numerical investigation proposed the methodology to determine the pure rate DIF through confined SHPB tests. Subsequently, the confined SHPB tests were conducted on concrete specimens, and a pure rate DIF model was developed based on this methodology. Additionally, conventional SHPB tests were performed to obtain an apparent DIF, which was then compared to the developed pure rate DIF. The results indicated that the apparent DIF exceeded the pure rate DIF, thus confirming its tendency to overestimate the strain-rate effect on concrete. Therefore, the proposed methodology using confined SHPB tests provides an alternative approach to overcome the limitations of the apparent DIF determined from conventional SHPB tests. Lastly, the developed pure rate DIF model was validated through numerical analyses on conventional SHPB tests and drop-weight impact tests of reinforced concrete beams. This validation demonstrated that the proposed pure rate DIF model effectively considers the strain-rate effect on concrete structures, thereby enabling assessment of the performance of concrete structures under extreme loading conditions.

Experimental study on impact behaviour of normal strength mortar at cryogenic temperatures and after freeze-thaw cycles

Concrete structures employed for the storage of Liquefied Natural Gases (LNG) currently undergo temperature as low as −170 °C. These critical engineering structures may also experience dynamic loads such as impact or explosion during service life. Therefore, it is crucial to explore the mechanical response of concrete at intermediate to high strain rates together with low temperatures or cryogenic freeze-thaw (FT) cycles. This study presents experimental research into the combined effects of low temperatures and strain rate on normal strength mortar, providing a preliminary analysis of the dynamic performance of concrete at low and cryogenic temperatures. A Split Hopkinson Pressure Bar (SHPB) device was used to investigate the characteristics of dynamic compression (at strain rates of 40, 80, 120 and 160 s−1) and dynamic split tension (at strain rates of 20, 40, 60 and 80 s−1) of Normal Strength Mortar (NSM) at different low temperatures. In addition, the dynamic compression (at strain rates of 80, 130 and 180 s−1) after cryogenic FT cycles was also explored. The findings revealed that the failure pattern of NSM samples exposed to coupled low temperature or cryogenic FT cycles and high strain rate loading notably varied from that observed under room temperature condition. Both the dynamic compressive and split tensile strengths of NSM increased with the strain rates at all temperatures. At −160 °C, the dynamic compressive and splitting tensile strengths of NSM specimens were greater than those at room temperature (by 10.94 % and 28.29 %, respectively) and −70 °C (by 3.13 % and 4.12 %, respectively). Cryogenic freeze-thaw cycles evidently impacted the material static and dynamic performance. An empirical model was developed to predict the dynamic increase factors (DIFs) for both dynamic compression and splitting tensile strengths of NSM at low/cryogenic temperatures and after freeze-thaw cycles. Scanning electron microscopy (SEM) technique was performed to study and comprehend the microscopic processes and microstructural changes after FT cycles.

Dynamic mechanical behaviors of foamed concrete using modified viscoelastic SHPB

This study aims to investigate the dynamic mechanical behaviors of foamed concrete (FC) utilizing a modified viscoelastic split Hopkinson Pressure Bar (VE-SHPB). The VE-SHPB proposed in this study enables impedance matching between bars and FC, enhancing measurement precision. Dynamic mechanical behaviors of FC with different densities (400, 700, 1000, 1300 kg/m3) under various incident pressure (0.2, 0.5, 0.8, 1.1 MPa) are examined using the VE-SHPB. The failure modes of FC are categorized into Spalling (Mode I), Disintegration (Mode II), and Comminution (Mode III) based on fracture states of post-impact. The mechanism of strain rate and density on failure mode, dynamic strength, dynamic increase factor (DIF), and energy consumption density are discussed. The results show that FC's dynamic mechanical properties increase with increasing strain rate, but present different strain rate sensitivities at different densities. The dynamic mechanical properties of FC are determined by both the pore structure and matrix properties. Notably, Mode II shows better ability of energy consumption, specifically FC with a density around 700 kg/m³ demonstrates higher energy absorption density.

Dynamic mechanical properties of one-part ultra-high performance geopolymer concrete

Geopolymer has been recognized as a promising construction material offering performance comparable to traditional cementitious materials while significantly reducing carbon dioxide emissions. Notably, the recent development of “one-part geopolymer”, which transforms the alkaline activator solution into a solid activator powder, has greatly enhanced construction convenience. One-part ultra-high performance geopolymer concrete (OP-UHPGC), which has mechanical properties comparable to ultra-high-performance concrete (UHPC), has been developed recently. This study investigates the dynamic compressive and splitting tensile properties of OP-UHPGC using a split Hopkinson pressure bar (SHPB). The damage progression, failure mode, dynamic stress and strain, dynamic increase factor (DIF), and energy absorption of OP-UHPGC specimens were systematically studied. Test results showed that OP-UHPGC exhibited strain rate sensitivity. Both compressive and splitting tensile DIFs increased with the strain rate, and empirical formulas were proposed to predict the DIFs of OP-UHPGC. The DIFs of OP-UHPGC were comparable with those of steel fibre-reinforced geopolymer or cementitious composites, yet smaller than those of plain geopolymers or conventional concrete reported in the existing literature. In addition, the energy absorption of OP-UHPGC under dynamic compression and splitting tension both increased with the strain rate. This study provides a valuable reference for the dynamic mechanical properties of OP-UHPGC.

Compression behaviour of self-compacting concrete under dynamic loading at different ages

Self-compacting concrete (SCC) is widely used in reinforced concrete buildings, owing to its ability to consolidate by weight and its lack of requirement for external vibration. Reinforced concrete buildings can be subjected to high strain rate loading during the early days of construction or in their service life. Thus, it is critical to understand the behaviour of concrete under high strain rate loadings at different ages. Minimal studies have previously focused on the early-age behaviour of concrete under high strain rates. This study tries to fill this gap. It focuses on the behaviour of M40 grade SCC under three levels of strain rate loading at ages of 1, 3, 7, 14 and 28 d. The split-Hopkinson pressure bar (SHPB) was used to test 45 SCC specimens of diameter 100 m and thickness 50 mm at high strain rates, ranging from 30 s−1 to 110 s−1, and the determined compressive strength, peak strain and elastic modulus results are compared with quasistatic test results of SCC specimens. The dynamic increase factor (DIF) determined in the SHPB experiment is compared with the CEB-fib code model. The results indicate that the DIF reduces as the concrete's strength and age increase.

Dynamic response and deformation failure microscopic characteristics of cyclic impact-cemented tailing backfill.

Frequent blasting disruptions can lead to cumulative damage within the cemented tailing backfill (CTB), increasing the risks associated with mining operations and reducing the recovery rate of the pillar. To address this issue, the Split Hopkinson Pressure Bar (SHPB) was utilized to conduct cyclic impact tests on CTB containing various cement tailing ratios (CTR) at different curing ages. The tests analyzed the stress-strain curve law, dynamic compressive strength (DCS), dynamic strength increase factor (DIF), absorption energy, and deformation failure characteristics of CTB under different impact velocities. Additionally, nuclear magnetic resonance (NMR) and scanning electron microscopy (SEM) were employed to investigate the internal pore structural properties of CTB. The research findings indicate that (1) Average strain rate exhibits a linear relationship with the DCS and impact velocity. A lower number of impacts occurred at higher impact velocities and shorter curing age. The number of impacts was drastically reduced when the impact velocity surpassed 3m/s. As the CTR increased, the number of impacts also increased. When the number of impacts increased, the elastic modulus, dynamic impact strength, and peak strain initially increased before ultimately decreasing. (2) Under the cyclic impact load, the shear failure and axial splitting failure were the main failure modes of CTB. Increasing the CTR may be a more effective strategy for reducing the degree of CTB fragmentation compared to prolonging the curing age. When the impact velocity is lower than 3m/s, CTB can withstand multiple impacts and maintain high levels of integrity. When the DIF of the first shock is below 1.5, the CTB demonstrates a capability to withstand more than four shocks. If the DIF exceeds 2, the CTB can only endure a single shock. (3) NMR and SEM observations revealed that CTB itself contains more pores. A dense network structure will grow inside CTB as the curing age and CTR are increased, reducing the porosity. The pore size observed in the samples also support that increasing CTR may be a more effective strategy. Our findings contribute to a better understanding of the kinetic response of CTB in deep mines under frequent blasting disruption and offer a valuable reference point for future research in this area.

Mesoscale modeling of dynamic compressive behavior of microcapsule-based self-healing concrete under impact loading

Microcapsule-based self-healing concrete (MSC) has been widely studied, with a focus on static behavior and self-healing effectiveness. However, the dynamic mechanical properties of MSC have rarely been studied. This study presents a mesoscale numerical investigation of the dynamic compressive behavior of MSC under impact loading. In mesoscale, MSC is regarded as a four-phase composite material mainly composed of coarse aggregates, interface transition zones, cement mortar, and microcapsules. A pseudo 3D numerical model is constructed by combining a slice of a detailed mesoscale model with a homogenous 3D model. The mesoscale MSC slice models with different mass fractions of microcapsules (0%, 2%, 5%, and 8%) are constructed. Different coarse aggregate shapes (i.e., circles, ellipses, and polygons) are considered. The uniaxial dynamic compressive behaviors of MSC materials under loads of different strain rates are numerically simulated and compared with those from split Hopkinson pressure bar tests previously done by the authors. The comparison results show that the present mesoscale model can accurately predict the compressive strength and failure mode of MSC. The effects of the microcapsules ratio and strain rate on the dynamic strength are studied. Results show that the MSC compressive strength decreases with the increase in microcapsules and increases with the increase in strain rate. The dynamic increase factor (DIF) of the specimen is jointly contributed by the material DIF, inertial constraints, and heterogeneity. Different aggregate shapes have little effect on the simulation results of MSC behavior. The obtained dynamic mechanical properties of MSC may assist in designing MSC to resist collisions or explosions.

Rate-dependent constitutive model and dynamic response of composite laminates for laser-induced delamination

Laser Bond Inspection is a new technology to quantitatively evaluate the interfacial strength in composite materials. Constructing an effective constitutive model, especially considering strain rate effects, is a critical factor for this technology. In this work, a reliable rate-dependent constitutive model of composite laminates for laser-induced delamination is established. Based on an orthotropic constitutive relationship, we introduce dynamic increase factors in different directions to adjust constitutive parameters. The dynamic increase factors are obtained through an adaptive matching model based on deep transfer learning. Then we effectively determine material rate-dependent constitutive relationship and ultimately achieve numerical simulation of laser-shocked composite laminates. Combining empirical testing with numerical simulation results, we investigate the dynamic response law of composite laminates under different laser parameters. The findings indicate that the rate-dependent constitutive model, effectively describes the mechanical behavior and dynamic response characteristics of composite laminates under laser shock. The dynamic response characteristics are determined by laser energy, pulse width, and spot size. Both laser energy and spot size affect the range of delamination, and pulse width mainly affects the depth of delamination.

Dynamic splitting behavior of microcapsule-based self-healing cementitious composites under SHPB impact loading

This study presents an experimental study on the dynamic splitting tensile performance of microcapsule-based self-healing cementitious composites and fiber-reinforced microcapsule cementitious composites. The research aims to determine the effect of microcapsule dosages, fiber types, and strain rates on the dynamic splitting tensile behavior of materials. A total of 99 specimens were subjected to the split Hopkinson pressure bar (SHPB) impact loading within the strain rates of 0.85–17.12 s−1. A high-speed camera was employed to capture the crack propagation process, and scanning electron microscopy (SEM) was used to characterize the corresponding microstructure. The results indicated that the splitting tensile performance of materials exhibits significant strain rate sensitivity. The addition of microcapsules increases the dynamic splitting tensile strength of the material, and the highest energy absorption capacity can be achieved with a 5 % microcapsule dosage. The incorporation of polyvinyl alcohol (PVA) and polyethylene (PE) fibers effectively enhances dynamic splitting tensile strength and energy absorption capacity, achieving optimal performance with the incorporation of PVA-PE hybrid fibers. Furthermore, the investigation of the dynamic increase factor (DIF) of the material indicates that fibers heighten the strain rate sensitivity of the material.

Axial Impact Resistance of High-Strength Engineering Geopolymer Composites: Effect of Polyethylene Fiber Content and Strain Rate

High-strength engineered geopolymer composite (EGC) materials exhibit excellent mechanical properties under quasistatic loading, thus showing great potential in military and civilian facilities subjected to impact or explosive loading. However, its dynamic mechanical response under high-speed loading is not fully understood. In this study, dynamic compressive test was performed on EGC with PE fiber contents of 0%, 0.5%, 1.0%, 1.5%, and 2.0% using the Split Hopkinson Pressure Bar (SHPB) test. The results indicated that EGC reinforced with 1.5% fiber exhibited optimal static and dynamic mechanical performance. In the strain rate range of 181 s−1 to 201 s−1, when the fiber content increased from 1.0% to 1.5% and 2.0%, the dynamic compressive strength of the EGC increased by 24.3%, 28.8%, and 44.0%, respectively, compared to the matrix without fiber. Dynamic parameters of the EGC, including dynamic compressive strength, dynamic increase factor, and impact toughness, showed sensitivity to strain rates and increased with strain rate. A modified model, incorporating the fiber bridging effect, was proposed based on the CEB-FIP model, providing important guidance for practical engineering applications.

Strain rate-temperature effects and constitutive models for Q690D QT steel

This paper investigates the mechanical properties of the high-strength structural steel Q690D QT (Quenched and Tempered) over a wide temperature range and a wide strain rate range. Firstly, a series of quasi-static and dynamic tests adopting the universal testing machine and Split Hopkinson Pressure Bar were carried out to investigate the mechanical properties at strain rates from 0.00025 s−1 to 5000 s−1 and temperatures from room temperature (20 °C) to 700 °C. Stress-strain curves and dynamic yield strength increase factors were extracted and investigated. Test results show that Q690D QT exhibits different strain rate effects at different temperatures, more significant at the temperatures of 600 and 700 °C, as well as the high-temperature softening effect. Dynamic strain aging effect is identified at temperatures between 300 − 600 °C for plastic strain rates of 800 s−1 and 2300 s−1, nevertheless, this effect is observed at a higher temperature range of 500–700 °C for higher plastic strain rates of 4000 s−1 and 6400 s−1. From the analysis, the adiabatic thermosoftening effect cannot be ignored when the plastic strain rates reach 4000 s−1. Finally, an improved form of the Johnson-Cook model is proposed for capturing the adiabatic temperature effects at different temperatures and validated by the test data. A parameter dynamic temperature factor is proposed to describe the comprehensive effect of strain rate, test temperature, and adiabatic thermosoftening.

Compressive mechanical properties of styrene-butadiene rubber under medium-low strain rates: Experiments and modeling

Styrene-butadiene rubber (SBR) is widely employed as a cushioning material in engineering applications to resist impact loadings due to its excellent mechanical properties and energy absorption capacity. This paper aims to investigate the compressive mechanical properties and constitutive model of SBR under medium–low strain rates both experimentally and theoretically. Firstly, quasi-static and dynamic compression tests of SBR were carried out under the strain rate up to 220 s−1 using an electronic universal testing machine and a drop-weight machine, respectively. Subsequently, the effect of loading rate on mechanical properties, strain rate sensitivity and energy absorption capacity was examined. The results indicate that SBR exhibits visco-hyperelastic characteristics with reversible compression deformation and strain rate dependency, ie., the yield stress, flow stress and dynamic increase factor (DIF) increase approximately exponentially with increasing logarithmic strain rate. In addition, the SBR exhibits excellent energy absorption capacity during compression, especially under higher strain rates and larger strain levels. Finally, a visco-hyperelastic constitutive model was proposed by replacing the nonlinear spring with a hyperelastic element in Zhu-Wang-Tang (ZWT) viscoelastic constitutive model to describe the nonlinear mechanical behaviors in SBR, and an acceptable agreement between experimental results and model predictions were observed. The findings of this research can provide a valuable guide for designing and optimizing the impact resistance of SBR structures.

Physical and mechanical properties of deflection-hardening hybrid fibre-reinforced recycled aggregate concrete

Recycled aggregate concrete (RAC) has been gaining a large interest in recent years due to the depletion of natural aggregates and environmental protection requirements. To improve the ductility of RAC for structural applications and to avoid corrosion risks involved with utilising steel fibres, this study proposes a deflection-hardening hybrid fibre-reinforced recycled aggregate concrete (FRRAC) by combining newly developed macro-basalt fibre (BF, 0.67 % by volume) and recycled macro-polypropylene fibre (PF, 0.67 % by volume). Its fresh, static and dynamic mechanical properties were investigated and compared with the mix containing macro-BF only (1.34 % by volume). A Ø 100 mm split Hopkinson pressure bar (SHPB) system was used to determine the dynamic mechanical properties in compression and tension. The hybrid FRRAC retained up to 90 % of its average first peak load at 3.5 mm crack width and showed better cracking bridging performance under dynamic splitting tension than the specimens with the same volume of macro-BF. Empirical formulae for dynamic increase factors and energy absorption capacities against varying strain rates have also been proposed for the newly developed hybrid FRRAC.

Dynamic compressive behavior of steel fiber synergistically reinforced cellular concrete under high strain-rate loading

To better understand the reinforcement and toughness effects of steel fibers, a 75-mm split Hopkinson pressure bar (SHPB) device was used to test the uniaxial dynamic compression properties of steel fiber synergistically reinforced cellular concrete (SFSRCC) under high strain rates. The dynamic compression performance characteristics of the SFSRCC, including the stressstrain curve, dynamic strength, impact toughness and failure mode, were analyzed. The results showed that the dynamic strength, peak strain and impact toughness of SFSRCC increase with increasing strain rate. Compared with that of cellular concrete (SAP10S0), a higher steel fiber volume ratio corresponded to a greater enhancement in the dynamic performance characteristic indices of the SFRCC. The maximum increases were 138.4%, 180.0% and 280.0% for the DIF, peak strain, and impact toughness, respectively. The damage degree of the SFSRCC specimen decreased with increasing fiber content, and a larger area of residual "core retention" was observed, which indicated that the impact resistance of the SFSRCC with a high fiber content was improved. An empirical formula that can accurately characterize the dynamic strength increase factor (DIF) of SFSRCC with high strain rates was proposed, and the prediction results obtained by using the DIF of the SFSRCC were highly consistent with the test results, which confirmed its effectiveness. To further quantify the strain rate enhancement effect and fiber content for the reinforcement and toughening ability of SFSRCC, the relationships between the peak strength/peak strain/impact toughness and strain rate and between the DIF increment ratio/strain energy density increment ratio and fiber volume fraction were determined. In conclusion, the dynamic compression performance characteristics of SFSRCC can be enhanced by incorporating an appropriate quantity of steel fibers with a dynamic impact load.

Experimental Study on Dynamic Mechanical Performance of Post-Fire Concrete Confined by CFRP Sheets.

Impact tests on post-fire concrete confined by Carbon Fiber-Reinforced Polymer/Plastic (CFRP) sheets were carried out by using Split Hopkinson Pressure Bar (SHPB) experimental setup in this paper, with emphasis on the effect of exposed temperatures, CFRP layers and impact velocities. Firstly, according to the measured stress-strain curves, the effects of experiment parameters on concrete dynamic mechanical performance such as compressive strength, ultimate strain and energy absorption are discussed in details. Additionally, temperature caused a softening effect on the compressive strength of concrete specimens, while CFRP confinement and strain rate play a hardening effect, which can lead to the increase in dynamic compressive strength by 1.8 to 3.6 times compared to static conditions. However, their hardening mechanisms and action stages are extremely different. Finally, nine widely accepted Dynamic Increase Factor (DIF) models considering strain rate effect were summarized, and a simplified model evaluating dynamic compressive strength of post-fire concrete confined by CFRP sheets was proposed, which can provide evidence for engineering emergency repair after fire accidents.

Progressive Collapse of Typical and Atypical Reinforced Concrete Framed Buildings

This paper investigates the progressive collapse potential of eight-story reinforced concrete framed buildings with several atypical structural configurations and compares results with a typical structural configuration. The alternative load path mechanism, the linear-static analysis procedure amplified by dynamic increase factors, and the demand capacity ratio criterion limits from the U.S. General Services Administration guideline were used to evaluate the vulnerability of the different atypical and typical framed structures. Variations in bay size, plan irregularity, and closely spaced columns were used to represent the atypical structural configurations. The extracted demand-capacity ratio (DCR) of the global structural response showed that the demand-capacity ratio for the longitudinal frame with short-span beams had a larger DCR than the transverse frame with longer beam spans with significant potential for progressive collapse. Furthermore, atypical building configurations with closely spaced columns failed by shear and showed the highest DCR limits. In addition to the global structural response, the local member end actions were also evaluated. The evaluation showed that the critical atypical frame configuration with closely spaced columns had a 91% and 127% maximum shear force and support bending moment value difference, respectively, when compared to a baseline typical frame configuration.

Experimental investigation of dynamic bond behaviors between LRS-FRP and concrete

The dynamic bonding behaviour at the interface between a large-rupture-strain fibre-reinforced polymer (LRS-FRP) and concrete was investigated via drop weight impact tests of notched beam specimens. The main experimental variables included the concrete strength grade, number of LRS-FRP layers, and loading rate. With increasing loading rate, the location of the peeling damage at the interface between the LRS-FRP and concrete shifted from the interior of the concrete layer to the concrete–binder layer interface, binder layer, and even binder layer–FRP interface. The ultimate debonding load of the LRS-FRP strips increased with increasing strain rate, reaching more than 1.7 times the static value at a strain rate of approximately 4/s, while the effective bond length did not show a clear increasing or decreasing tendency with increasing strain rate. For the local bond-slip relationship, both the peak interfacial bond stress and interfacial fracture energy increased with increasing strain rate, and the influences of the concrete strength and number of FRP layers on the strain rate sensitivity were insignificant. Based on the experimental results, improved models to predict the ultimate debonding load and effective bond length at the LRS-FRP–concrete interface under both static and dynamic loading conditions were proposed. Furthermore, dynamic increase factor (DIF) formulas for the peak interfacial bond stress and interfacial fracture energy for bond-slip modelling of the interface between a polyethylene naphthalate (PEN)-FRP and concrete were established.

Strain rate and size effects on dynamic tensile behaviour of standard and high-strength concrete: An experimental study

The strain rate and specimen size are the main dominant factors affecting the splitting tensile behaviour of concrete. The static size effect is well-known for concrete behaviour, but it needs more knowledge about the dynamic size effect. The present study investigated the strain rate sensitivity and size effect dependency of dynamic tensile behaviour of two different grades of concretes (M35 and M60) using the Split Hopkinson Pressure Bar (SHPB) setup. From the outcomes of the experimental analysis, it was noted that the quasi-static tensile strength underwent a reduction of 8.96% and 11.39% in standard and high-strength concrete, respectively. This decrease occurred as the diameter increased from 29.5 mm to 45 mm, aligning notably with the principles outlined in the "Bazant Size Effect Law," as proposed by Bazant et al. [52]. Whereas, the dynamic tensile strength and DIF increased with increased specimen diameter, which is opposite to the quasi-static size effect. The maximum split tensile strength observed was 18.56 and 19.86 MPa, corresponding to 13.30 and 12.13 s−1 strain rates with 3.69 and 3.51 dynamic increase factor (DIF) for standard (M35) and high-strength concrete (M60), respectively. The dynamic results also demonstrated a size-effect dependency, where larger diameter specimens exhibited higher strain rate sensitivity, leading to increased strength and DIF due to lateral inertial and crack propagation effects. The modified DIF model of CEB-FIP proposed by the Malvar et al. [17] considering the strain rate and size effect simultaneously strongly supported the experimentally obtained DIF values with an ± 13% deviations. In addition, the strain rate significantly influenced the concrete failure pattern, but no size effect was observed. At a low strain rate, the initiated crack propagated towards the loading ends and split the specimen into two semi-cylindrical halves with penetration cracks. While at higher strain rates, additional wedge-shaped crushed regions formed at the loading end due to tensile and shear damage generated due to stress concentration and local crushing. The crack width becomes wider, and the triangular-shaped local crushing zone continuously moves toward the centre of the specimen from both loading ends and generates the crushed strap.