High Strain Rate Loading Conditions Research Articles

A Review of Dynamic Mechanical Behavior and the Constitutive Models of Aluminum Matrix Composites.

Aluminum matrix composites (AMMCs) have demonstrated substantial potential in the realm of armor protection due to their favorable properties, including low density, high specific stiffness, and high specific strength. These composites are widely employed as structural components and frequently encounter high strain rate loading conditions, including explosions and penetrations during service. And it is crucial to note that under dynamic conditions, these composites exhibit distinct mechanical properties and failure mechanisms compared to static conditions. Therefore, a thorough investigation into the dynamic mechanical behavior of aluminum matrix composites and precise constitutive equations are imperative to advance their application in armor protection. This review aims to explore the mechanical properties, strengthening the mechanism and deformation damage mechanism of AMMCs under high strain rate. To facilitate a comprehensive understanding, various constitutive equations are explored, including phenomenological constitutive equations, those with physical significance, and those based on artificial neural networks. This article provides a critical review of the reported work in this field, aiming to analyze the main challenges and future development directions of aluminum matrix composites in the field of protection.

Dynamic Constitutive Model and Numerical Simulation of S32760 Duplex Stainless Steel Based on Dislocation Theory

Background: To describe the complex mechanical behavior of S32760 duplex stain-less steel under high strain rate and high-temperature loading conditions. Objective: The constitutive model of S32760 duplex stainless steel suitable for high strain rate was constructed from the micro-scale. Methods: Based on the theory of dislocation dynamics, the effects of different strain rates and strains on the plastic deformation of ferrite and austenite were analyzed, and the thermal stress term and non-thermal stress term of ferrite and austenite phases were coupled. Results: The simulation results of the model show that the S32760 dual-phase constitutive model has a high degree of fit with the experimental data at high strain rates. Conclusion: Compared with the classical J-C model, the results show that the constitutive model of this patent has more accurate predictability than the J-C model in describing the mechanical behavior of duplex stainless steel in the high strain range of 5000s-1 to 10000s-1.

Dynamic mechanical properties of concrete with freeze-thaw damage under different low-temperature conditions

The mechanical properties of hydraulic concrete structures in cold regions are affected by low temperature and freeze-thaw cycles, and their mechanical properties differ greatly compared with those of the room temperature state. Especially for concrete structures with being susceptible to dynamic loads such as earthquakes and collisions, the mechanism involved the effect of low temperature on the dynamic mechanical properties of concrete with freeze-thaw damage is still not clear. The design of different low-temperature environment containing different freeze-thaw damage of concrete dynamic load tests are conducted to reveal the change patterns of dynamic mechanical properties of concrete with initial freeze-thaw damage in the low temperature range of 0 °C ∼ −30 °C. The results show that low-temperature conditions can improve the concrete compactness, and weaken the enhancement effect of high strain rate loading conditions on the concrete strength, which will reduce rate sensitivity of the mechanical properties. Meanwhile, the effect of low temperature can improve the brittleness and compressive strength of concrete and make up for part of the strength loss caused by freeze-thaw damage, and containing different freeze-thaw damage in the mechanical properties of the concrete gap with the reduction of the temperature gradually narrows. Quadratic function relationship exists between temperature and compressive strength together with other mechanical parameters, and the minimum value of R2 is 0.9721. The stress-strain relationship curve of concrete under low-temperature condition is narrowed, and the brittleness of concrete increases; the damage process becomes more intense, the integrity of concrete is high after the damage, and the number of cracks on the fracture surface decreases significantly.

Fatigue S-N curve approach for impact loading of hyper- and visco-elastic leading edge protection systems of wind turbine blades

Computational evaluation of leading edge erosion remains challenging due to the high-strain rate loading conditions caused by impact of the wind turbine blade leading edge with rain droplets and other environmental particles. Here, a methodology is proposed for obtaining an S-N curve which can be used for impact fatigue evaluation of hyper- and viscoelastic leading edge protection systems for wind turbine blades, in the relevant strain rate domain. Two material systems (hard and soft polyurethane (PU)) are characterised experimentally by dynamic mechanical analysis (DMA) and static tensile tests. Time-temperature superposition is applied to the raw DMA data in order to obtain the material’s mastercurve, describing its visco-elastic behaviour in an expanded strain rate domain. The Yeoh (hyperelastic) and prony series (vis-coelastic) material model parameters are calibrated and form the input for a 2D-axisymmetric finite element model, in which Single Point Impact Fatigue Test (SPIFT) testing conditions are simulated. The stress field experienced by the coating during SPIFT testing is obtained and combined with the experimental measurements, allowing the determination of the material systems S-N curve, in the relevant strain rate domain. Results for a hard and soft PU coating system are compared with rain erosion test (RET) data. The RET data shows higher lifetime for the hard PU systems, a tendency that can be predicted when comparing the S-N curve for the hard and soft PU system. This methodology can be utilised in computational lifetime evaluation of leading edge coating systems. Furthermore, the methodology has the potential to partly alleviate the need of RET in the development and comparison of next-generation leading edge protection systems.

Dynamic mechanical properties and constitutive model of photosensitive resin specimens at different temperatures

In order to reveal the dynamic mechanical properties of resin-molded parts prepared from photosensitive resin composition at different temperatures, four typical service temperatures (26 °C, 50 °C, 70 °C and 90 °C) were selected, and the mechanical properties of photosensitive resin specimens under quasi-static and high strain rate (1200 s−1, 1500 s−1 and 1800 s−1) loading were tested by universal material testing machine and split Hopkinson pressure bar (SHPB) experimental device. The stress–strain data of the material were obtained. Results show that the stress of photosensitive resin specimens decreases with the increase of temperature under quasi-static and high strain rate loading conditions, reflecting a certain temperature softening effect. Two typical stages of strain softening and strain hardening exist in the quasi-static compression process of the specimens at room temperature, while the specimens only exhibit strain hardening at 50 °C, 70 °C and 90 °C. Under dynamic loading, the elastic modulus, peak stress and peak strain of the photosensitive resin increase with the increase of the strain rate, reflecting an obvious effect of strain rate strengthening. The nonlinear thermo-viscoelastic constitutive model can better describe the mechanical behavior of the material under high strain rates and service temperatures, and the experimental values are in good agreement with the fitted values of the model. The results can provide theoretical model and method support for the design and development of resin-based materials and the optimization of their mechanical properties.

Johnson-Cook model parameters determination for 11% and 14% Mn-Steel

The behaviour of high-manganese steel under large strains and different strain rates needs to be investigated to predict its response to various dynamic loading conditions including impact. An empirical constitutive relation developed by Johnson and Cook (JC) is applied at high strain rate and dynamic loading conditions to determine the flow stress and material strength. The deformation behaviour of two high-manganese steel cylindrical specimens (11% and 14% Mn-content) was studied using uniaxial tensile tests, compression tests at various strain rates and finite element (FE) simulation. These tests were conducted at room temperature to examine the effects of strain rate, material plasticity and strain hardening to ultimately determine the JC model parameters. Fracture appearance of tensile test specimens was also studied using optical microscopy and SEM. Results showed that 11%Mn-steel exhibited more toughness, ductility and strain hardening than 14% Mn-steel. The JC model parameters have been evaluated and represented in tabular form. Tensile tests have been compared with recent published works. Good agreement between the results has been observed.

Material characterization and simulation for soft gels subjected to impulsive loading

For impact and blast experiments of traumatic brain injury (TBI), soft gel materials are used as surrogates to imitate the mechanical responses of brain tissue. To properly model a viscoelastic gel brain in a surrogate head using a finite element (FE) model, material parameters such as the shear moduli and relaxation time at high strain rates are required. However, such information is scarce in the literature and its applicability for a range of dynamic conditions is unclear. We used an integrated experiment and simulation approach to efficiently determine mechanical properties of soft gels at finite strains, as well as over a wide range of strain rates. A novel impact experiment using a gel block was developed to capture the high strain rate behavior by maximizing the inherent shear wave motion at different impact conditions. A corresponding computational model was used to simulate the gel dynamics of the impact. Parametric simulations utilizing optimization and correlation analyses were used to calibrate multiple material parameters in the nonlinear viscoelastic model to the experimental data. The optimal parameters for gels, including Sylgards 184, 3–6636, and 527, were found. We ascertained the initial shear stiffening effect in gels at high strain rate loadings experimentally and incorporated this effect in the simulation. We have verified the integrated approach by comparing the material properties of the gels with analytical results based on shear wave propagation. This study provides a new approach to calibrate the material behavior of soft gels under high strain rate loading conditions.

A continuous dynamic constitutive model for normal- and high-strength structural steels

The use of numerical models in the advanced analysis and design of steel structures, particularly under extreme loading conditions, is becoming increasingly widespread. A crucial component of such models is an accurate description of the material response. A systematic study into the dynamic constitutive modelling of structural steels is presented herein. The key features of the dynamic stress–strain characteristics of structural steels at various strain rates, i.e., test methods, material strength, strain-rate effect index and strain-rate effect models, are examined and discussed. Supplementary SHPB tests on both normal- and high-strength structural steels (Q235, Q355, Q460, and S960) under a wide range of strain rates up to 5000 s−1, filling gaps in existing datasets, are then carried out. A database of dynamic test results, containing 453 stress–strain curves, is systematically established and analyzed. Finally, a continuous dynamic constitutive model, capturing the dependency of both yield strength and strain rate, is proposed to predict the dynamic stress–strain response for structural steels, from normal- to high-strength material (235–960 MPa), and from static to high strain rate loading conditions (up to 5000 s−1).

Impact load effects on screw anchors in concrete

The results of a study initiated to investigate the effects of impulse-type loads on mechanical screw anchors, Titen HD® manufactured by Simpson® Strong Tie Inc is presented in this paper. Three anchor diameters (6.4, 9.5 and 12.7 mm) installed at the manufacturer specified embedment depths were tested under static and impulse-type loading in shear and tension. The static test results showed that anchorage failure was by combined pullout and concrete breakout in tension and steel fracture failure in shear. The failure loads were consistent and predictable by the concrete capacity design (CCD) method under both tension and shear loading. The impact test results on the other hand showed that the anchorage systems achieved higher capacities under the high-strain rate loading conditions, yielding dynamic increase factors (DIF) greater than 1.0. DIF of 1.1 has been recommended for all diameter of anchors tested under the impulse-type tension load. The DIF recommended for the anchors under impulse-type shear loading is 1.2 for the 9.5-mm, and 12.7-mm diameter anchors while the 6.4-mm diameter anchors are not recommended for impulse-type loading because of lower capacities achieved under shear loading.

Evaluation of the dynamic response of triply periodic minimal surfaces subjected to high strain-rate compression

Architected cellular structures based on triply periodic minimal surfaces (TPMS) have attracted significant attention due to their lightweight, superior, and controllable mechanical properties. Such lattice structures can be potential candidates for high specific energy absorption (SEA) applications. In this study, five TPMS sheet-based structures (Gyroid, Primitive, IWP, Diamond and Fisher-Koch) were designed, fabricated, and tested under quasi­-static and dynamic loading conditions. Laser powder bed fusion (L-PBF) is employed to facilitate the fabrication of these complex structures using stainless steel (SS316L) at three different relative densities. Scanning electron microscopy (SEM) and micro­ Computed Tomography (micro­CT) were utilized to assess the quality of the printed structures. The dynamic compressive behavior is investigated by conducting direct impact compression tests utilizing a Direct Impact Hopkinson Bar (DIHB) at a strain-rate of 2057 s −1 . Quasi-­static tests are also performed at a strain-rate of 0.005 s −1 . The quasi-static and dynamic mechanical responses are then compared to explore the changes in plateau stress and specific energy absorption values of the five TPMS lattices in these two loading regimes. Furthermore, the effects of changing both architecture and relative density on the properties of lattice structures are investigated. The results show that all five topologies exhibit an enhanced mechanical performance under dynamic loading. In fact, Diamond structure demonstrates the highest SEA value of 35.57 J/g under the high strain-rate loading condition, in comparison to 30.85 J/g in the quasi-static loading. This study suggests that TPMS structures could be potential candidates not only for quasi­-static, but also for dynamic applications related to a high strain-rate loading. • Five TPMS lattices are designed and manufactured using Laser Powder Bed Fusion (LPBF). • Evaluation of the dynamic mechanical performance of lattices based on triply periodic minimal surfaces. • TPMS lattices exhibit enhanced plateau stress and specific energy absorption in high strain-rate loading conditions.

Effects of automated fiber placement defects on high strain rate compressive response in advanced thermosetting composites

The effects of fiber tow gaps, overlaps, and folds on the compressive strength of a fiber-placed composite laminate under dynamic loading conditions are investigated in this work. These layup defects were placed in the 0° fiber direction within a 24-ply quasi-isotropic laminate with a [45/0/–45/90]3S stacking sequence. Different locations of the defect were considered, namely near the bottom (in the 2nd ply), middle (10th ply) and top (23rd ply) of the laminate. High-strain rate compression experiments were conducted on composite that are pristine and with embedded defects using a split Hopkinson pressure bar (SHPB). The results were used to determine the strength knockdown due to the local changes in ply morphology because of fiber bed compaction in the presence of a layup defect. The experimental results revealed the anisotropy of in-plane strength coinciding with the deposited defect orientation. No significant variations in the residual strength were observed regarding the location of the defect (i.e., bottom, middle, or top) within the laminate. A morphological analysis based on microtomography of the cured defects indicates that the sources of the strength knockdown are due to the 0° ply drop-off, fiber misalignment in the adjacent 90° and 45° degree plies and the resin-rich region formed at the corner of the tapered 0° ply, between +45° and –45° laminas. The present study indicates the increased role of local morphological ply variations on the strength of composites under high-strain rate loading conditions, which should be considered during composite design.

Plastic Behavior of Laser-Deposited Inconel 718 Superalloy at High Strain Rate and Temperature

Nickel-based superalloys have several applications for components exposed to high temperatures and high strain rate loading conditions during services. The objective of this study was to investigate the tensile properties of Inconel 718 produced using the laser metal deposition technique. Specimens with different heat treatments were investigated. Experimental tests were performed at the DYNLab at Politecnico di Torino (Italy). The temperature sensitivity was investigated between 20 °C and 1000 °C on a Hopkinson bar setup at a nominal strain rate of 1500 s−1. The specimens heating was obtained by means of an induction heating system, and the temperature control was performed by thermocouples, an infrared pyrometer, and a high-speed infrared camera. The thermal images were analyzed to check the uniformity of the heating and to investigate the presence of adiabatic self-heating. The results showed that the materials strength exhibited a significant drop starting from 800 °C. The strain rate influence was investigated at room temperature, and limited sensitivity was found covering six orders of magnitude in the strain rate. A preliminary analysis of the fracture mode was performed. Finally, different solutions for the strength material modeling were proposed and discussed with the aim of identifying models to be used in finite element simulations.

Evaluation of Energy Absorption Capabilities of Polyethylene Foam under Impact Deformation.

Foams are widely used in protective applications requiring high energy absorption under impact, and evaluating impact properties of foams is vital. Therefore, a novel test method based on a shock tube was developed to investigate the impact properties of closed-cell polyethylene (PE) foams at strain rates over 6000 s−1, and the test theory is presented. Based on the test method, the failure progress and final failure modes of PE foams are discussed. Moreover, energy absorption capabilities of PE foams were assessed under both quasi-static and high strain rate loading conditions. The results showed that the foam exhibited a nonuniform deformation along the specimen length under high strain rates. The energy absorption rate of PE foam increased with the increasing of strain rates. The specimen energy absorption varied linearly in the early stage and then increased rapidly, corresponding to a uniform compression process. However, in the shock wave deformation process, the energy absorption capacity of the foam maintained a good stability and exhibited the best energy absorption state when the speed was higher than 26 m/s. This stable energy absorption state disappeared until the speed was lower than 1.3 m/s. The loading speed exhibited an obvious influence on energy density.

Crash Response of Laser-Welded Energy Absorbers Made of Docol 1000DP and Docol 1200M Steels.

The crushing response of a laser-welded square tube absorber made of two commercial steel grades, Docol 1000DP and Docol 1200M, is presented in the paper. Crush experiments are performed at two different loading conditions, namely, quasi-static loading at 0.5 mm/s deformation speed and impact loading at 25–28 m/s. A new approach has been proposed to study the square tube absorber under impact loading using a direct impact Hopkinson (DIH) method. To characterize the mechanical properties of the tested steels, tensile quasi-static and high strain rate testing are also performed with the use of specimens with a 7 mm gauge length. The applied strain rates are 10−3, 100, and above 103 s−1. The laser-welded joints are also characterized by microhardness test involving the base material, heat-affected zone, and fusion zone. The crashworthiness of model square tube absorbers is estimated based on the following parameters: absorbed energy, mean force, crushing force efficiency factor, and specific energy absorbed. It has been found that the square tube absorbers made of Docol 1200M steel show a higher potential in mechanical energy absorption capacity than Docol 1000DP absorber. Moreover, crushing tests prove that laser-welded joints in 0.6 mm sheets made of Docol 1000DP and Docol 1200M steels reveal high cracking toughness. In turn, strength testing at different strain rates confirms the higher strain rate sensitivity of Docol 1000DP steel than in the case of Docol 1200M steel as well as an increase in the high ductility properties of both steel grades under the high strain rate loading conditions.

On the Dynamic Tensile Behaviour of Thermoplastic Composite Carbon/Polyamide 6.6 Using Split Hopkinson Pressure Bar.

A dynamic tensile experiment was performed on a rectangular specimen of a non-crimp fabric (NCF) thermoplastic composite T700 carbon/polyamide 6.6 specimens using a split Hopkinson pressure (Kolsky) bar (SHPB). The experiment successfully provided useful information on the strain-rate sensitivity of the NCF carbon/thermoplastic material system. The average tensile strength at three varying strain rates: 700, 1400, and 2100/s was calculated and compared to the tensile strength measured from a standardized (quasi-static) procedure. The increase in tensile strength was found to be 3.5, 24.2, and 45.1% at 700, 1400, and 2100/s strain rate, respectively. The experimental findings were used as input parameters for the numerical model developed using a commercial finite element (FE) explicit solver LS-DYNA®. The dynamic FE model was validated against experimental gathering and used to predict the composite system’s behavior in various engineering applications under high strain-rate loading conditions. The SHPB tension test detailed in this study provided the enhanced understanding of the T700/polyamide 6.6 composite material’s behavior under different strain rates and allowed for the prediction of the material’s behavior under real-world, dynamic loading conditions, such as low-velocity and high-velocity impact.

Thermomechanical tensile properties of deposited Inconel 718 superalloy over a wide range of strain rate and temperature

Nickel-based superalloys show high strength retained also at high temperature and they are widespread used for structural components exposed during services to high temperature combined with high strain rate or impact loading conditions. The objective of this study was the investigation of the plastic flow behaviour of Laser Metal Deposited Nickel-based superalloy Inconel718. The material was manufactured at Northwestern Polytechnical University in China. Specimens with three different heat treatment conditions were investigated: as-deposited, directly aged and aged after homogenization and solution. High strain rate tensile tests were performed on the direct Hopkinson bar setup developed at DYNLab laboratory at Politecnico di Torino. At a nominal strain rate of 1500 s-1the temperature sensitivity was investigated between 20 and 1000°C. An induction heating system was adopted, and the temperature was monitored by thermocouples and infrared pyrometer and high-speed camera. The results showed the materials strength decreases as a function of temperature with a significant drop starting from 800 °C. An asymmetric tension-compression behaviour was found by comparing the results with data in compression. The strain rate influence was investigated at room temperature and very limited or negligible sensitivity was found covering six orders of magnitude in strain rate.

Effect of Precipitates on Plastic Deformation Behavior of High Entropy Alloy Al0.3CoCrFeNi Under High Strain Rate Loading

Abstract High entropy alloys (HEAs) are primarily known for their high strength and high thermal stability. These alloys have recently been studied for high strain rate applications as well. HEAs have been observed to exhibit different properties when subjected to different strain rates. Very few published results on HEAs are available for high strain rate loading conditions. In addition, modeling and simulation work of microstructural details, such as grain boundary and precipitates of HEAs have not yet been investigated. However, at an atomistic length scale, molecular dynamics simulation works of HEAs have already been published. In this study, a detailed microstructural analysis of plastic deformation of the material under high strain rate loading has been performed using dislocation density based crystal plasticity finite element modeling. The primary objective is, therefore, to assess the strengthening effects due to precipitates on a particular high entropy alloy Al0.3CoCrFeNi with ultrafine grains having randomly distributed NiAl precipitates.

Dynamic constitutive relationship of CuCrZr alloy based on Johnson-Cook model

Abstract CuCrZr alloy has been acknowledged as one of the most promising candidate materials for the heat sink of plasma facing components in nuclear fusion devices with its excellent thermal conductivity and specific mechanical strength. For the safety concern, it is vital to provide appropriate safety assessment on these mechanical structures with CuCrZr alloy, such as divertor and blanket, under high strain rate loading conditions like displacement events, disruption, and so on. In this work, the dynamic compressive behavior of the CuCrZr alloy over wide range of strain rates and temperatures was investigated using the split Hopkinson pressure bar technique. Based on the experiment results, a constitutive equation is built by using Johnson-Cook model to describe the dynamical property of CuCrZr alloy. However, the results indicated that the influences of the strain, strain rate and temperature on the dynamic behavior are not independent. Therefore, a modified Johnson-Cook model was further developed to take the coupled effects of strain, strain rate and temperature into account. Compared with the original Johnson-Cook model, the modified Johnson-Cook model calculated results show good agreement with the experimental data.

3D Finite Element Modelling of Fracture of Sand Particles Subjected to High Strain Loading Rate

Fracture is a common failure mode of sand particles when they are subjected to high strain rate (HSR) loading conditions such as blast, impact, or projectile penetration. The constitutive behavior and the failure mode of sand particles are influenced by the loading rate; therefore, a particle-scale constitutive model is necessary to address the effects of HSR loading and particle fracture within a sandy material. To that end, a Kolsky test (i.e., a HSR 1D compression test), 3D X-ray computed tomography (CT), and finite element methods were employed in this study to investigate the failure mode of individual natural sand particles when they are subjected to a HSR loading. Individual particles were first imaged using CT technique followed by testing them using Kolsky bar at an approximate strain rate of $$10^{4} S^{ - 1}$$ . The fragments of fractured particles were collected and imaged using synchrotron micro computed tomography (SMT) for further evaluation of the fracture mechanisms within individual particles. A brittle fracture model was adopted to perform 3D Finite element (FE) modelling to capture the fracture of individual sand particles. 3D CT images of the particles were used to generate 3D meshes with similar morphology as the actual sand particles and the particles were loaded similar to Kolsky experiments. The paper discusses the calibration and the validation of the model and compares the fracture mechanisms within the sand particles based on FE simulations with experimental measurements. The brittle fracture model successfully simulated the fracture mechanisms of the experiments. The effect of loading mechanisms on the mechanisms of the fracture of the particles is discussed in detail.

Dynamic response and validation of a flexible matrix composite

Testing and predicting the dynamic response of flexible matrix composites in impact loading condition face two primary challenges: (i) experimentally, existing techniques using existing instruments do not always provide high fidelity material data under simultaneous high strain and high strain rate loading conditions; and (ii) finite element simulations of a highly flexible material require many material parameters and complex mathematical formulations. To address these limitations, this research investigation presents a technique originally developed in-house for modeling and validating hyper-viscoelastic materials and applies it toward the flexible matrix composite. Results from a simple low-velocity impact (2 m/s) test on a 75 × 75 mm2 flexible matrix composite indicate that the critical material properties for the low strength, highly deformable matrix in conjunction with an updated constitutive model can accurately predict the dynamic behavior within 10% with respect to the force time history response using MATLAB and ABAQUS/Explicit. Finite element interrogation also shows full field stress response within the composite specimen not easily measured via sensors and deformation matching the behavior observed via high-speed camera. Finally, on-going research in this arena indicates that the technique can be applied to higher rate loading mechanisms, such as a gas gun and Hopkinson bar apparatus, in order to obtain material parameters for even more devastating impact loading strain rates.