Strain Rate Loading Research Articles

Measurement of dynamic deformation during shock loading using a fiber-optic loop-sensor

Abstract Characterizing materials under shock loading has been of interest in fields such as protective material development, biomechanics to study the injury mechanics and high-speed aerodynamic structures. However, shock loading of material is a very short duration phenomenon and it is extremely challenging to develop sensors for dynamic measurements under such loading conditions. Optical fiber sensors that present the possibilities to allow high resolution measurement of force or displacement in such high strain rate loading conditions. This work studies the possibility of developing a single mode optical fiber sensor based on the principle of power losses from the curved section for dynamic measurements under shock loading conditions. The strain measurement results obtained from the optical sensors are validated with the controlled digital image correlation measurements are found to be in close correlation. The sensor was able to provide time sensitivity of better than 1 ms. The results show that the fiber sensor has the characteristics of high sensitivity and high precision, which can be used to measure fine vibration in real-time.

A new nanoindentation approach for determining both indentation size effect and continuous apparent activation volume during loading of nanocrystalline Ni and Ni-20 wt.% Fe alloy

A new nanoindentation approach is developed in this study to determine both indentation size effect (ISE) and continuous apparent activation volume () during loading of nanocrystalline nickel (NC Ni) and nanocrystalline nickel-20 wt.% iron alloy (NC Ni-Fe alloy). This approach involves conducting nanoindentation tests under loading modes controlled by both constant strain rate (CSR) and constant loading rate (CLR). Firstly, a new empirical expression for the parameter in the modified Nix-Gao model is established to study the strain rate dependence of the ISEs created in the CSR and CLR tests. Then, continuous data of each individual sample (indentation) during loading are obtained in the CLR test through the alternative use of continuous stiffness measurement technique. The stress dependence of is analyzed based on Duhamel et al.’s model, which considers the role of vacancies generated during inhomogeneous dislocation nucleation. Finally, based on the above experimental and theoretical work as well as transmission electron microscopy observation, the influences of loading mode, loading rate, and material properties (stacking fault energy) on resulting intrinsic hardness of NC Ni and NC Ni-Fe alloy are analyzed. The nanoindentation approach developed in this study provides profound insights into the mechanical behaviors during loading and underlying mechanisms of materials.

A novel impact approach based on electromagnetic loading technology: A case study on CFRP/Al riveted structures

To investigate the mechanical response and damage behavior of aircraft fuselage composite structures under out-of-plane impact loads more efficiently and flexibility, this paper proposed a novel impact approach and testing platform based on inductive coils to yield electromagnetic impact force. The influence of system key parameters on the electromagnetic loading waveforms were analyzed using an electromagnetic field finite element model. Single/repeated impact tests on CFRP/aluminium alloy (Al) riveted structures were conducted at different voltages (energies) based on this approach. The results indicate that the electromagnetic impact (EMI) approach exhibits significant advantages in both variable strain rate loading and continuous impact loading scenarios. This device can efficiently achieve multi-point and multiple impact loading. The electromagnetic impact forces with various amplitudes and pulse-widths can be accurately obtained by altering voltage and capacitance values, which can demonstrate the good experimental consistency of such test approach. Besides, with this test method, the load threshold for damage formation can be clearly defined: once the impact force exceeds the damage threshold load, the delamination area of the CFRP laminates expand as the impact energy increases. Note that when the provided out-of-plane impact load is slightly higher than the damage threshold load by changing the voltage, significant delamination damage may suddenly manifest in any one impact event of the repeated impacts.

Dynamic compressive impact behavior of CFRP composite under high strain rate loading

Carbon Fiber Reinforced Plastics (CFRP) composite exhibits significant sensitivity to strain rate. In this work, authors investigated the CFRP composite’s dynamic compressive impact behavior under a high strain rate. The vacuum bagging technique was used to fabricate the composite specimens to reduce the presence of voids. Compressive mechanical behavior was examined for the CFRP composite for strain rate ranging from 1384 to 1953 s−1 using a Split Hopkinson Pressure Bar (SHPB) test setup. The experiment aims to investigate the effect of strain rate on stresses, strains, failure strengths, fracture energies, and failure of quasi-isotropic CFRP composites. Furthermore, the specimens’ strength initially increases and achieves its maximum strength, followed by a decrease in strength value. Moreover, an optical microscopic examination reveals that damage in composite laminate grows as the strain rate increases.

Quasi-static and dynamic responses of gradient hexachiral auxetics: Experimental and numerical analysis

In the current paper, the mechanical responses of polymer gradient hexachiral auxetic metamaterials were experimentally and numerically investigated under quasi-static and intermediate strain rate loadings. Five gradient design strategies were explored, including uniform, positive, negative, center positive, and center negative gradients. The deformation/failure mechanism, Poisson's ratio, and energy absorption capability were experimentally analyzed, together with the effects of impact velocity and gradient distribution. Experimental results revealed that the gradient design can mitigate the shear deformation of hexachiral auxetics, which efficiently remain its negative Poisson's ratio effect under dynamic loading. Compare with the quasi-static loading, earlier failure of auxetics was observed under dynamic loads due to the strain rate and inertial effect, which diluted their negative Poisson's ratio effect and energy absorption capability. Among the designs, auxetics with negative gradient configurations showed the best energy absorption under dynamic loading. Numerical analysis further supported the experimental findings and provided insights into the influence of geometric parameters. It shows that thicker configurations and non-uniform node gradient series with coefficients of 1.15 (positive, center positive) and 0.87 (negative, center negative) provided optimal energy absorption under the dynamic loading. This work offers profound insights into enhanced performance mechanisms and provides avenues for optimizing structural design of auxetic metamaterials.

Investigation of static mechanical characteristics and numerical simulation of fractal gangue cemented backfill materials

This study investigated the static mechanical responses of gangue cemented backfill materials (GCBM) with aggregate particle size distribution (APSD) satisfied fractal grading theory. The recycling of gangue in GCBM alleviates gangue accumulation pollution and improves mining production efficiency. Macroscopically, uniaxial compression experiments regarding various loading strain rates (ε̇) on gangue cemented backfill specimens (GCBS) were conducted. Acoustic emission monitoring and digital image correlation technique were employed to reveal crack activities and strain field evolution in real time. Microscopically, scanning electron microscopy and numerical specimens considering APSD were utilized to analyze the microstructure and damage process. The deterioration mechanisms and quantified number of cracks were explored at the micro level. The conclusions are as follows: (1) The axial stress (σ) of GCBM increased with fractal dimension (D) of APSD and ε̇. For the same σ, cumulative AE counts decreased with increasing ε̇ and D. (2) The main failure mode of the GCBS under static loading was tensile failure, exhibiting tensile cracks initiating at the bonding–aggregate interface. (3) The increase in the proportion of fine aggregate contributed to the optimization of the microstructures of the GCBS (4) An increased proportion of fine aggregate in the GCBS improved the synergistic load-bearing capacity between the cementing and aggregate mediums, leading to an enhancement in the σ.

Rate-dependent constitutive behavior and mechanism of CMDB under tension loading

The composite modified double-base propellants (CMDB) were experimentally investigated for mechanical behavior under wide tension strain rate loading from 0.0001 s−1 to 2500 s−1, based on Instron mechanical machine and modified Hopkinson tension bar technique. Stress-strain curves were obtained for its strain rate effect and integrality evaluation. The results indicated that CMDB presents high rate-dependence with flow stress distinctly increase as loading strain rate increasing. A succinct constitutive formulation is established with only five parameters, to characterize well the rate-dependence and strain hardening behavior. The fracture morphologies were investigated by scanning electron microscopy, and it is indicated that they are also rate-dependent: the cavitation and matrix damage induced from matrix deformation work less but more RDX particles fractures with strain rate increasing. Equivalent unit cell model with brittle cracking was established to simulate the mechanical behavior and failure characteristics of CMDB. The results reveal that with increasing loading strain rates, CMDB presents a tough-brittle transition, with less cavitation and matrix damage induced by matrix deformation, while more RDX particles fracture. Series of simulated results confirm qualitatively the experimental observations, and the obtained stress contours facilitate to validate the observed characteristics and propose reasonable mechanisms.

Nanosilica reinforced epoxy under super high strain rate loading

AbstractNanosilica reinforced epoxy‐matrix composites have been extensively investigated for higher mechanical strengths since its emergence, while few literatures are available about enhancement characteristics under super high strain rate loading, which is usually encountered during impact. Hereby, this work investigates the composites containing various kinds of nanosilica subjected to compression of strain rate higher than 20,000 s−1. A series of stress:strain curves are obtained and it is found that peak stresses increase with increasing strain rate along with silica fraction. Excitedly, the silica particle plays another enhancement role in anti‐localization of adiabatic shearing which occurs in pure epoxy, as indicated from abruptly dropped strain‐hardening index at ~22,000 s−1. A mechanism is proposed that uniformly distributed silica delays adiabatic shearing localizations to form through cracks, which is confirmed by fracture surface observance.Highlights Higher strain rate is achieved experimentally up to ~20,000 s−1. Strain rate effect is found on the peak stress of composites. Reinforcement of nanosilica is more distinct on strain‐hardening behavior. Silica particles hinder adjacent shearing localizations from abrupt evolution.

Experimental study on dynamic mechanical properties of multidirectional constrained water-bearing coal samples under dynamic-static coupling loading

The objective of this study is to investigate the dynamic mechanical properties of coal and rock under deep water conditions. The research employs an enhanced Split Hopkinson Pressure Bar (SHPB) testing system. Five sets of dynamic impact experiments were conducted on coal samples under varying loading conditions to analyse the changes in dynamic strength, energy dissipation, fractal dimension and other characteristics of coal samples under different water content states were analyzed. The experimental results demonstrate that: (1) Under specific strain rate conditions, the dynamic strength of saturated coal samples is lower than that of natural coal samples. As the strain rate gradually increases, the bonding force generated by free water and the Stefan effect jointly act, and the peak strength of saturated coal samples under high strain rate loading conditions is higher than that of natural coal samples. (2) Under certain strain rate conditions, the absorption energy of saturated coal samples is approximately 10% to30% lower than that of natural coal samples, and deformation hysteresis phenomenon occurs in natural coal samples, thereby improving the dynamic strength of natural coal samples relative to saturated coal samples; (3) The fractal dimension of saturated coal samples with a specific strain rate under three-dimensional dynamic static combination loading is higher than that of natural coal samples, and the percentage of small particle coal samples with debris is higher than that of natural coal samples; Finally, based on the HJC model, some coal samples were selected to simulate the coal rock failure characteristics during the triaxial loading process using ANSYS/LS-DYNA, and their stress–strain curves and failure morphology diagrams were obtained. The discrepancy between the numerical simulation and the experimental results was less than 10%, thereby further elucidating and corroborating the coal failure process and dynamic mechanical characteristics.

Dynamic mechanical behavior of titanium matrix composites reinforced with graphene nanoplatelets

In this investigation, graphene nanoplatelets reinforced pure titanium matrix (GNPs/TA1) composites were synthesized via short-term ball milling followed by spark plasma sintering. The mechanical properties and microstructure evolution of these composites were examined under both quasi-static and dynamic compression conditions. The results indicate that as the strain rate increases from 10−3 to 3000 s−1, the yield strength rises from 436.9 MPa to 1209.6 MPa, consistent with the positive strain rate effect. The superior yield strength of GNPs/TA1 composites arises from the dynamic Hall-Petch effect, dislocation strengthening and load transfer strengthening, with the contribution from load transfer strengthening being the most significant due to the reinforcement's (TiC-GNPs-TiC) facilitation of load transfer. As the strain rate increases, interfacial debonding gradually extends along the reinforcement and grain boundaries, but no macroscopic fracture occurred in this study. At a strain rate of 3000 s−1 during compression, {112‾2}, {101‾2}, and {11 2‾ 1} twins were generated. However, at a strain rate of 10 s−1, only {112‾2} and {101‾2} twins were produced, while {11 2‾ 1} twin was inhibited. Under high strain rate loading, the plastic flow behavior of GNPs/TA1 composites was predicted using the Johnson-Cook constitutive model, modified to account for adiabatic temperature rise, and the predictions showed good agreement with experimental results.

The influence of initial static shear on the torsional performance of BFRP bars-RC beams with different sizes

To reveal the influence of the initial static shear on the torsional performance of Basalt Fiber Reinforced Polymer Bars-Reinforced Concrete (BFRP bars-RC) beams, in this study, 52 BFRP bars-RC beam models with geometric similarity using a three-dimensional mesoscale numerical simulation method were established. The effects of initial shear static loadings (F0 = 0, 0.25Vu, 0.5Vu, and 0.75Vu) on the failure modes, torsional strength, ductility, and size effect of BFRP bars-RC beams under various equivalent strain rates were quantitatively analyzed. The results show that, regardless of whether the beams have initial damage, their load-bearing capacity and deformation ability increase as loading strain rates increase. For beams with initial damage, the increased degrees in load-bearing capacity relative to their respective initial static shear decreases as the initial static shear level increases but then increases as the subsequent loading strain rate increases. Increasing the beams’ initial damage degree makes the beams’ ductility worse. In addition, the more severe the beams’ initial damage, the more significant the strength size effect. However, increasing the strain rate can weaken the beams’ strength size effect.

Mechanical properties and deformation mechanism of AZ31B joints under cryogenic temperature and high strain rate loading

Mechanical properties and deformation mechanism of AZ31B joints under cryogenic temperature and high strain rate loading

On energy mechanism of rate-dependent failure mode evolution in plain weave composite

The intricate failure modes and the yet unclear rate dependency of carbon fiber reinforced plain weave composite materials pose a challenge to mechanics researchers. This study establishes an energy-based evolution mechanism for the compressive failure modes of plain weave composite materials as the strain rate varies. This mechanism illustrates how the rate dependency of failure modes arises from the competitive relationship between strain potential energy and deformation kinetic energy. At low loading rates, the specimen exhibits a progressive crushing failure mode characterized by low peak stress and significant geometric deformation. As the loading strain rate increases, the energy required for this geometric deformation also increases. When the energy expenditure surpasses that needed to elevate the stress level of the specimen, it transitions to an instantaneous failure mode with high peak stress. In this mode, the specimen fractures into multiple small fragments immediately upon failure, lacking the large geometric deformations observed at lower rates. Through calculating this energy mechanism, a transition strain rate of 180 s−1 was determined for both failure modes. The accuracy of this mechanism was further verified by tests conducted near the critical strain rate. The energy-based evolution mechanism for failure modes provides a simplified and concise framework for simplifying complex models of composite material failures.

Multiple Deformation Mechanisms in Adiabatic Shear Bands of a Titanium Alloy during High Strain Rate Deformation.

The occurrence of adiabatic shear bands, as an instability phenomenon, is viewed as a precursor to failure caused by instability at high strain rates. Metastable β titanium alloys are extensively utilized due to their excellent mechanical properties, which are often subjected to high strain rate loads in service conditions. Understanding and studying their adiabatic shear instability behavior is thus crucial for preventing catastrophic failure and enhancing material performance. In this study via detailed microstructural analyses in the adiabatic shear region of a Ti-10V-2Fe-3Al alloy subjected to high strain rates, it was observed that α″ martensitic transformation and nano-twinning plus β-to-α phase transformation with α″ martensite as an intermediate phase occurred, in addition to substantial fine grains. The grain refinement mechanisms were mainly related to dynamic recovery dominated by dislocation migration alongside severe plastic deformation.

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 constitutive modeling of steel fiber reinforced concrete considering damage evolution under high strain rate

This study conducted quasi-static compression and splitting tensile tests on steel fiber reinforced concrete (SFRC), as well as dynamic compression tests using the split Hopkinson pressure bar (SHPB). The mechanical properties of SFRC with varying fiber contents and under different loading strain rates were examined separately. Experimental results indicate that the addition of steel fibers effectively enhances the properties of concrete. The dynamic mechanical performance of SFRC specimens (compressive strength, peak toughness, ultimate toughness, and energy absorption capacity) demonstrated a clear strain enhancement effect. The dynamic stress-strain curves of SFRC reveal the material's good viscoelastic properties. Then, a viscoelastic constitutive model for SFRC considering damage under high strain was proposed, with parameter fitting based on SHPB test results. The constitutive model was applied to the numerical simulation by the user-defined material (UMAT) in ABAQUS. The dynamic stress-strain curves and damage patterns obtained by numerical simulation are basically consistent with the test results. This further demonstrates that the proposed constitutive model effectively describes the dynamic characteristics of SFRC.

Prediction of concrete cracking behavior under different strain rates based on the boundary effects model

Predicting the cracking behavior of concrete under different strain rates through fracture parameters has been a longstanding topic of interest. In this study, the effect of concrete strength and strain rate on the fracture toughness and initial fracture energy for three-point bending notched beams is investigated by boundary effect model (BEM). With the help of BEM, only a series of basic parameters (such as tensile strength, maximum aggregate size and specimen size) are used in the process of calculating the fracture toughness and initial fracture energy. The cumbersome concrete fracture experiment is avoided in this model. The initial fracture toughness and unstable fracture toughness, predicted by BEM are agreed with the experimental results in the literature. The results demonstrate that BEM is valid for predicting the fracture toughness of different concrete strengths, even at increased strain rates. As the loading strain rate increases, the initial fracture toughness of different concrete strength shows a slight growth with increasing loading strain rate, which indicates that the concrete needs more energy to reach the cracking condition.

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.

Topology optimised novel lattice structures for enhanced energy absorption and impact resistance

ABSTRACT This study evaluates topologically optimized lattice structures for high strain rate loading, crucial for impact resistance. Using the BESO (Bidirectional Evolution Structural Optimisation) topology optimisation algorithm, CompIED and ShRIED topologies are developed for enhanced energy absorption and impact resistance. Micromechanical simulations reveal CompIED surpasses theoretical elasticity limits for isotropic cellular materials, while the hybrid design ShRComp achieves theoretical maximum across all relative densities. Compared to TPMS, truss, and plate lattices, the proposed structures exhibit higher uniaxial modulus. Manufactured via fused deposition modeling with ABS thermoplastic, their energy absorption capabilities are assessed through compression tests and impact simulations. The ShRComp lattice demonstrates superior energy absorption under compression compared to CompIED. Impact analyses of CompIED and ShRComp sandwich structures at varying velocities show exceptional resistance to perforation and higher impact absorption efficiency, outperforming other classes of sandwich structures at similar densities. These findings position these new and novel topologies as promising candidates for impact absorption applications.

Pulse Design of Constant Strain Rate Loading in SHPB Based on Pulse Shaping Technique.

The Split Hopkinson pressure bar (SHPB) is widely used for characterizing the mechanical behavior of materials at high strain rates. One of the most challenging factors is achieving constant strain rate (CSR) loading of the specimen at a certain strain rate. Obtaining the effective incident pulse based on the experimental material for achieving CSR loading remains unresolved. This research focuses on obtaining the proper incident pulse for achieving constant strain rate loading using the pulse-shaping technique. A parameterized objective incident model in terms of the strain rate and quasi-static (or dynamic stress-strain) behavior of the material is established utilizing the three-wave method. Experimental pulses that closely resemble the desired objective pulses can be generated by adjusting parameters such as the geometry of the shaper, the shaper material, striker velocities, and the length of the striker according to the pulse-shaping model. The model is applied to the design of the incident pulse for B4CP/2024Al composite material, and the dynamic stress-strain curves at different strain rates are obtained under CSRs. This model provides effective guidance for selecting an appropriate shaper and achieving CSR loading in SHPB tests.