Dynamic Loading Rates Research Articles

Atomistic scale fracture behavior of the bcc iron with {1 1 0} crack under dynamic rectangular loading rate

Dynamic rectangular loading rate is a typical characteristic of the load on tooth root with gear transmission. Upload ratio and contact ratio are its key engineering factors. This work investigates the atomistic scale fracture behavior of bcc iron with {1 1 0} crack under dynamic rectangular loading rate through molecular dynamics simulation, where four crack fronts are considered to illustrate the orientation effect induced by the anisotropy of bcc iron at atomistic scale. The behavior of engineering stress-strain and atomistic scale behavior of crack propagation under various upload ratios and contact ratios are identified to clarify the effect of dynamic load. The {1 1 0} cracks with fronts of [1¯1¯2], [101¯], and [1¯1¯1¯] can propagate not only at model plastic deformation stage under low upload ratio or high contact ratio but also at model elastic deformation stage under high upload ratio or low contact ratio. However, the {1 1 0} crack with front of [01¯0] can propagate at model elastic deformation stage whatever the upload ratio and contact ratio are. According to the critical stress intensity factor for first partial dislocation nucleation and the variation of initiation stress with upload ratio and contact ratio, [01¯0] is proved to be the most dangerous crack front. Considering orientation and key engineering factor effects, this work can well satisfy engineering practice to analyze the atomistic scale mechanism of gear tooth breakage.

AE analysis of damage processes in cast iron and high-strength steel at different temperatures and loading rates

Acoustic emissions originating from damage processes in nodular cast iron and high-strength steel were analyzed. Three point bending tests of notched and precracked bend bars were performed to investigate the onset of crack growth at quasi-static and dynamic loading rates and temperatures of 20 and −40 °C. Additionally, the materials were subjected to uniaxial tensile loading. It was found that the steel emits most of the transient acoustic signals during globally elastic behavior. In contrast, for the cast iron, most of the transient acoustic emissions were detected at small plastic strain. Since the acoustic emission were correlated with the volume of the plastically deformed material in the steel, the size of the plastic zone during fracture toughness testing was estimated. Furthermore, the onset of stable crack initiation was derived from the acoustic signal.

Effects of variation in loading protocol on the strength and deformation capacity of ductile reinforced concrete beams

SummaryUnderstanding the impact of prior earthquake damage on residual capacity is important for postearthquake damage assessment of buildings; however, interpretation of such impact is challenging when based on tests using traditional reversed‐cyclic loading protocols. A new loading protocol, consisting of a dynamic earthquake displacement history followed by quasi‐static reversed‐cyclic loading to failure, is presented as an alternative to traditional simulated seismic loading protocols. Data are analyzed from a set of 12 nominally identical ductile reinforced concrete beams that were tested by using variations of this protocol and traditional reversed‐cyclic and monotonic protocols. Differences in the cycle content of the earthquake displacement histories applied to the test specimens allowed for the effects of load history variation below 2.2% drift to be isolated. It is found that such variation had no effect on the beam deformation capacities. The effects of dynamic loading rates are also analyzed and compared against control quasi‐static specimens. Relative strength increases due to dynamic loading are found to be more significant at yield than at ultimate. Dynamic loading rates led to modest reductions in the beam deformation capacities, but the presence of causality between these variables remains uncertain.

Effect of Strengthening Mechanism on Strain-Rate Related Tensile Properties of Low-Carbon Sheet Steels for Automotive Application

In order to ensure crash resistance of the steels used in automotive components, the ensile deformation behavior needs to be studied and predicted not only under quasi-static condition, but also under dynamic loading rates. In the present study, tensile tests have been performed on four different automobile grade sheet steels, namely interstitial free steel, dual-phase 600 and 800, and a carbon manganese steel over the strain rate regime of 0.001-800/s. Apart from the variation in strength (which always increased with strain rate), the effect of strengthening mechanism on strain rate sensitivity and strain hardening behavior has been evaluated. Strain rate sensitivity was found to increase at high-strain rate regime for all the steels. Contribution of solid solution hardening on strain rate sensitivity at lower plastic strains was found to be higher compared to dislocation strengthening and second-phase hardening. However, precipitation hardening coupled with solid solution hardening produced the highest strain rate sensitivity, in C-Mn-440 steel at high strain rates. Different strain-rate-sensitive models which take into account the change in yield stress and strain hardening behavior with strain rate for ductile materials were used to predict the flow behavior of these sheet steels at strain rates up to 800/s.

Effects of strain rate on the mechanical and fracturing behaviors of rock-like specimens containing two unparallel fissures under uniaxial compression

Rocks containing unparallel fissures are likely to be subjected to dynamic loading resulting from earthquakes in various civil engineering structures. Since dynamic loading rate significantly affects the mechanical behaviors of fissured rocks, understanding the mechanical properties and fracture mechanism of fissured rocks under different loading rates is thus crucial in rock engineering applications. This study investigates the effects of strain rate on the mechanical and fracturing behaviors of rock-like specimens containing two unparallel fissures with varying inclination angles (α2). Our experimental results demonstrate that α2 and strain rate significantly affect the strength and deformation characteristics and the failure modes of fissured specimens. Both the strength and elastic modulus of the rock-like specimens highly depend on the strain rates, and the strain rate dependence is more sensitive for fissured specimen than that for the intact specimen. Under the same strain rate, the strength of fissured specimens decreases as α2 increases up to 60°, and then increases. The fissured specimens with greater α2 are characterized by higher elastic modulus. Furthermore, the fracture mechanism of the fissured specimen is numerically revealed, and the energy characteristics of fissured models are also analyzed on a micro-level.

The compressive properties of sandwich structures based on an egg-box core design

Abstract Lightweight cores, based on an egg-box core design, have been manufactured using a simple compression-moulding technique. Two types of composite prepreg were used to manufacture the core materials, these being a woven carbon fibre reinforced epoxy and a woven glass fibre reinforced epoxy. The resulting cores were of a high quality, exhibiting little or no wrinkling following the manufacturing procedure. Subsequent compression tests at quasi-static rates of loading showed that the compression strength of the core depended strongly on the level of constraint applied during testing, with sandwich panels based on composite skins bonded to an egg-box core offering a load-bearing capability that was more than double that of its unconstrained counterpart. The quasi-static compression strength of the carbon-based cores has been shown to be slightly higher than the glass fibre systems, particularly at higher core densities. Local splitting damage at cell joining regions and crushing of the cell of the egg-box structure was identified as the primary failure mechanism in the sandwich panels. Impact tests, conducted using a drop-weight impact tower, have shown that the compression strength of the egg-box cores is higher at dynamic rates of loading than at quasi-static rates. Here again, the local splitting and crushing was the primary mode of failure in the sandwich structures. Finally, the finite element technique has been used to model the mechanical response of these core designs under both quasi-static and impact loading testing conditions. Here, agreement between the predicted and observed responses was found to be good for both extremes of loading-rate.

Applicability of damage plasticity constitutive model for ultra-high performance fibre-reinforced concrete under impact loads

This paper presents a numerical investigation on assessing whether the concrete damage plasticity (CDP) constitutive model can be used to simulate new ultra-high performance fibre reinforced concrete (UHP-FRC) material under impact loading rates at different damage stages. The performance of the numerical models is verified by comparing numerical results to the experimental data that were previously tested by the authors. This paper also presents experimental tests that aimed to characterize the strain rate effect on UHP-FRC. The numerical simulations have been performed using ABAQUS/Explicit. CDP parameters are identified based on impact test results of a control specimen. Subsequently, the predictive capability of calibrated model has been investigated by simulating two UHP-FRC plates with varied steel reinforcement ratios tested under repeated drop-weight impact loads.It has been found that compressive and tensile strength enhancement predicted using CEB-FIP Model Code (1990) fits well with test results of the strain rate effect on UHP-FRC material. The numerical results demonstrate the feasibility of the CDP constitutive model for analyzing UHP-FRC under dynamic loading rates. Computed responses are sensitive to CDP parameters related to the tension, fracture energy, and plastic volumetric change. The effect of tensile strain hardening response could be ignored in the nonlinear finite element (FE) analysis of UHP-FRC materials with low strain-hardening behaviour.

Atomic behaviors of crack propagation in bcc iron under dynamic loading rate with rectangular fluctuation

This work carries out molecular dynamics simulations to identify the atomic behaviors of the crack initiation and propagation in bcc iron under dynamic loading rate with rectangular fluctuation, where the effects of the upload ratio and contact ratio are revealed. With an increase in upload ratio or a decrease in contact ratio, the plastic behaviors of the crack initiation can transform from only the nucleation of the dislocations to both the dislocation nucleation and the phase transitions. The corresponding behaviors of the crack propagation can transform from only the dislocation emission to both of the emission of the dislocations and the expansions of the stacking faults and twins. The plastic behaviors of the crack initiation and propagation are determined by the stress field around the crack tip. To describe the stress field, the Virial stress tensor and Voronoi volume are introduced. Besides, the simulations and Virial stress are verified through comparing with the results obtained by the continuum mechanics. Since the rectangular loading rate is the typical characteristic of the load applied on the upper part of the tooth root with gear transmission, this work can be used to analyze the atomic mechanisms of the initiation of the gear tooth breakage.

Femur fracture biomechanics and morphology associated with torsional and bending loading conditions in an in vitro immature porcine model

PurposeThe objectives of this study were to describe fracture morphology resulting from common loading mechanisms such as bending and torsion in immature bone and to identify differences in the energy required to produce various fracture types under these two loading mechanisms using an immature porcine animal model. MethodsTwenty-six in vitro immature porcine femora were mechanically tested in 3-point-bending and torsion. Femur specimens were tested with and without soft tissue and at both quasi-static and dynamic loading rates. Bone geometry and density measures were determined for each femur using dual-energy x-ray absorptiometry and plain film x-rays. Failure load, stiffness, and energy to failure were determined for each specimen from the load-displacement history from mechanical tests. Results3-point bending tests resulted in 10 transverse fractures and 2 oblique fractures. Torsion tests resulted in spiral fractures. Mean energy required to produce transverse fractures (3.32 Nm) was double that associated with spiral fractures (1.66 Nm). In bending, specimens with soft tissue intact required significantly greater energy to fracture (4.40 Nm) than specimens with soft tissue removed (2.92 Nm). Torsional loading rate did not significantly affect energy to fracture. ConclusionsFracture morphology is dependent upon loading conditions. Energy to failure allows for comparison across various loading conditions, and thus offers an effective means of characterizing fracture thresholds for a wide range of scenarios. Consideration should be given to whether or not soft tissue is left intact when conducting experiments using whole bone specimens given its influence on energy to failure.

Mechanical Property Evaluation of Polyurethane Foam under Quasi-static and Dynamic Strain Rates- An Experimental Study

Polyurethane foams are widely used as thermal insulators and also as energy absorbers in radioactive material shipping casks. In view of this, an experimental study to observe the change in impact response of rigid polyurethane foam at different strain rates was conducted. For this purpose, uni-axial compression experiments were performed at quasi-static and dynamic rates of loading. The results reveal a significant change in mechanical properties of foam under compression at different strain rates. The response of foam gets stiffer with increase in strain rate, and densification (lockup) occurs well below the strains at which lockup occurs for foam deformed at quasi-static strain rates. Consequently, the energy absorption characteristics of foam are altered with change in strain rate. It is envisioned that nuclear industries could use this information for application of polyurethane foam as an impact limiter in nuclear shipping casks, without causing un-acceptable stresses in the cask structure.

DEM investigation on fracture mechanism of the CCNSCB specimen under intermediate dynamic loading

The cracked chevron notched semi-circular bending (CCNSCB) method falls into a significant testing category of chevron notched specimens for measuring the mode I fracture toughness, of which the progressive fracture mechanism deserves to be further assessed under intermediate dynamic loading rate (IDLR). In this study, the discrete element method (DEM) is adopted to depict the three-dimensional fracture processes of the CCNSCB specimens subjected to different IDLRs considering different supporting spans. The results demonstrate that the crack front of the CCNSCB specimen with any loading condition is prominently curved, which violates the straight-through crack propagation assumption and may induce some errors in the fracture toughness measurements. For each IDLR, the peak force of the CCNSCB specimen evidently increases with decreased supporting span, and the effect of loading rate on this parameter is more prominent for a smaller supporting span. For a relatively large span, the crack grows restrictively in the notched ligament, which conforms to the ideal assumption of the fracture process and contributes to an accurate measurement of the mode I fracture toughness. Thus, a large supporting span is suggested for the semi-circular bend tests. Additionally, the critical crack length and peak force are found dependent on the loading rate, and they are larger for the higher loading rate. Thus, the critical crack length determined under quasi-static conditions is not strictly suitable for the specimens under different IDLRs, especially for the much higher IDLR. This study calls for more attention on how to accurately determine the fracture toughness via chevron notched samples.

Determination of Dynamic Crack Initiation and Propagation Toughness of a Rock Using a Hybrid Experimental-Numerical Approach

AbstractIn order to determine the mode-I (opening mode) dynamic fracture toughness of a rock, cracked-straight-through Brazilian disc (CSTBD) specimens with strain gauges glued on the specimen’s surface were diametrically impacted by a split Hopkinson pressure bar. A hybrid experimental-numerical approach was used to determine the dynamic initiation toughness, and it was also used in conjunction with a universal function to obtain the dynamic propagation toughness. Precautions were taken for getting the time history of dynamic stress intensity factors. Numerical accuracy, stability, and convergence to the solution were guaranteed by analyzing beforehand a widely-recognized benchmark dynamic crack problem. Using the numerical technique the result of the conducted trial analysis corresponded almost exactly with the classical result. The dynamic initiation toughness and dynamic propagation toughness of the rock increase with increasing dynamic loading rate and crack propagation speed, respectively, demonstra...

Loading-rate-dependent progressive fracturing of cracked chevron-notched Brazilian disc specimens in split Hopkinson pressure bar tests

The dynamic progressive fracturing process of the cracked chevron-notched Brazilian disc (CCNBD) specimen, the latest chevron-notched specimen suggested by the International Society for Rock Mechanics (ISRM) for fracture toughness measurements, is numerically assessed via discrete element method. Simulated acoustic emission distributions reveal that the cracking front is rather curved with jags and the critical crack surpasses the location specified by the measuring assumption. Most importantly, even if the dynamic force balance can be achieved by careful pulse shaping, the positions of the critical fracturing profiles remain highly dependent on the dynamic loading rates. Our investigation indicates that unchecked adoption of the quasi-static assumption on the CCNBD specimen in SHPB testing to measure the dynamic fracture toughness of rocks is suspect. The loading-rate-dependent cracking profiles of chevron-notched specimens cannot be ignored in order to accurately determine the dynamic mode I fracture toughness of rocks.

Strain Rate and Anisotropic Microstructure Dependent Mechanical Behaviors of Silkworm Cocoon Shells.

Silkworm cocoons are multi-layered composite structures comprised of high strength silk fiber and sericin, and their mechanical properties have been naturally selected to protect pupas during metamorphosis from various types of external attacks. The present study attempts to gain a comprehensive understanding of the mechanical properties of cocoon shell materials from wild silkworm species Antheraea pernyi under dynamic loading rates. Five dynamic strain rates from 0.00625 s-1 to 12.5 s-1 are tested to show the strain rate sensitivity of the cocoon shell material. In the meantime, the anisotropy of the cocoon shell is considered and the cocoon shell specimens are cut along 0°, 45° and 90° orientation to the short axis of cocoons. Typical mechanical properties including Young’s modulus, yield strength, ultimate strength and ultimate strain are extracted and analyzed from the stress-strain curves. Furthermore, the fracture morphologies of the cocoon shell specimens are observed under scanning electron microscopy to help understand the relationship between the mechanical properties and the microstructures of the cocoon material. A discussion on the dynamic strain rate effect on the mechanical properties of cocoon shell material is followed by fitting our experimental results to two previous models, and the effect could be well explained. We also compare natural and dried cocoon materials for the dynamic strain rate effect and interestingly the dried cocoon shells show better overall mechanical properties. This study provides a different perspective on the mechanical properties of cocoon material as a composite material, and provides some insight for bio-inspired engineering materials.

Effect of Surface Modification on Rice Husk (RH)/Linear Low Density Polyethylene (LLDPE) Composites under Various Loading Rates

The surface modification of RH filler was carried out using silane coupling agents in order to improve the adhesion between LLDPE and RH. RH was treated using silane coupling agent at four different concentrations (1, 3, 5 and 7 %) at room temperature. In this study, both untreated and treated RH/LLDPE composites were tested under static (0.001 s-1, 0.01 s-1 and 0.1 s-1) and dynamic loading rates (650 s-1, 900 s-1 and 1100 s-1) using universal testing machine and split Hopkinson pressure bar apparatus, respectively. Results show that the 5% treated LLDPE/RH composite shows the higher ultimate compressive strength (UCS) and rigidity as compared to untreated LLDPE/RH composites under various loading rates. Overall, it is proved that the surface treatment of RH gives significant contribution towards the UCS and rigidity of LLDPE/RH composites under both static and dynamic loading rates.

Dependence of Dynamic Tensile Strength of Longyou Sandstone on Heat-Treatment Temperature and Loading Rate

As a material for famous historical underground rock caverns, Longyou sandstone (LS) may fail under the combination of high loading rate and high temperature. The thermal damage induced by various heat-treatment temperatures (150, 250, 350, 450, 600 and 850 °C) is first characterized by X-ray Micro-computed tomography (CT) method. The damage variable derived from the average CT value for heat-treated LS specimen and reference specimen without heat treatment was used to quantify the thermal damage. The dynamic tensile strengths of these LS samples under different dynamic loading rates (ranging from 24 to 540 GPa/s) were then obtained using the split Hopkinson pressure bar (SHPB) system. The dynamic tensile strength of LS increases with the loading rate at a given heat-treatment temperature, and the tensile strength at the same loading rate decreases with the heat-treatment temperature except for 450 °C. Based on the experimental data, an empirical equation was established to relate the dynamic tensile strength of LS to the loading rate and the heat-treatment temperature.

An Extended Mohr–Coulomb Model for Fracture Strength of Intact Brittle Materials Under Ultrahigh Pressures

An extended Mohr–Coulomb model is proposed to represent the pressure‐dependent strength of intact structural ceramics under quasi‐static and dynamic loading rates at high pressures. A plot of normalized shear stress versus hydrostatic pressure for a range of structural ceramics revealed that despite the differences in material properties, test methods, and strain rates, the failure strength data fall in a narrow range, which can be represented by a unified model. The overall deformation behavior of structural ceramics and their strain rate dependence of strength in multiaxial loading at high pressure beyond Hugoniot elastic limit (HEL) can be explained by an exponential pressure dependence in the Mohr–Coulomb model. The analysis also suggests that the influence of strain rate on strength of a ceramic diminishes with increase in confinement pressure.

Quantitative Visualization of Dynamic Material Behavior

The dynamic behavior of materials is an extremely active and increasingly relevant area of research, but with many significant scientific challenges due to the extreme time-scales of events, limited by the ability to visualize. Its applications range from traditional ballistics to the design and optimization of next-generation transportation and communication systems, critical areas of energy and the environment through geological resource recovery, and planetary and celestial formation processes. These application areas require an in-depth understanding of material or structural response as a function of dynamic loading, with distinct emphases on extreme conditions such as high strain rates, impact, blast, penetration, and shock loading. In order to successfully understand a dynamic event and its associated mechanisms, it is not only sufficient to visualize the event, but also necessary to quantify the governing parameters through in situ visualization. The transition from exclusively qualitative imaging to the addition of the quantitative aspect of visualization enhances dynamic experimental mechanics research, often by obtaining full-field information from various types of imaging such as optical, thermal, and X-ray, to name a few. Current work in this area has begun to leverage novel experimental configurations and measurement methodologies due to recent advances in spatial and/or temporal resolution of high-speed and ultra-high-speed cameras, microscopes and sensors, consequently transforming the dynamic behavior research landscape. In order to continue to embrace and articulate these advancements, and increase the number of publications inExperimental Mechanics on this relevant topic, beginning in 2014 the SEM Dynamic Behavior Technical Division has conducted three successful sessions with fourteen papers on the topic of Quantitative Visualization. Based on the interest shown by the experimental mechanics community and the importance of the concept of Quantitative Visualization, the Experimental Mechanics editor suggested the creation of this special issue. As such, the following issue includes nine papers focusing on the Quantitative Visualization of Dynamic Material Behavior. Breakthroughs in understanding dynamic material behavior is mostly limited by the availability of experimental methods to conduct investigations to understand the associated mechanisms of deformation and failure in material under dynamic loading. Novel dynamic loading methods with in situ quantitative visualization of deformation and failure help us to overcome formidable challenges and observe these underlying mechanisms and develop associated governing equations. A novel modification of a classical Kolsky (split-Hopkinson) bar system is used to conduct dynamic compression and fourpoint bend experiments on human femoral cortical bone, and is presented in the paper by Sanborn et al. In this paper, they use full-field digital image correlation (DIC) at dynamic loading rates to quantify the deformation response of small transversely isotropic specimens. Another full-field optical technique using a Kolsky bar maps light intensity from the surface of in situ shear evolution in fiberglass composites with varying resin binders, and is presented in the paper by Lamberson et al. A notably novel contribution to the biomedical field is * L. Lamberson les@drexel.edu

Effects of loading rates on concrete double-K fracture parameters

The effects of loading rates on concrete double-K fracture parameters were investigated using central-notched split tension cubes, both experimentally and analytically. Four loading rates varying from 10−5/s to 10−2/s was adopted. Results showed that, with the increase of loading rates, the initiation fracture toughness linearly increased while the unstable fracture toughness varied by a first increase and a followed constant trend. It was also confirmed that double-K fracture model may be further extended to wider dynamic loading rates, such as seismic dynamic excitation. Finally, the models describing the loading rate influences on double-K fracture toughness parameters were developed.

Performance of Denitrifying Stormwater Biofilters Under Intermittent Conditions

Denitrifying stormwater biofiltration systems that include submerged zones containing organic carbon sources can alleviate eutrophication by reducing nitrogen loadings from stormwater runoff. The objective of this research was to evaluate performance of denitrifying biofilters containing wood chip medium under varying dynamic loading rates and antecedent dry conditions (ADCs). Results showed that during ADCs, dissolved organic carbon (DOC) concentrations increased in pore water due to dissolution of the wood chip medium. During a storm event, nitrate (NO3−) removal was enhanced due to high pore water DOC concentrations and mixing of NO3− from the influent with pore water; however, as DOC was gradually flushed out of the biofilter, higher effluent NO3− concentrations were observed over time. At lower hydraulic loading rates, effluent NO3− concentrations were low due to sufficient hydraulic residence time for denitrification. For all storm events tested, an overall NO3− mass removal efficiency of 85% was achieved. Sulfate reduction was observed at long ADCs (up to 30 days). Phosphate release was observed when NO3− was absent from the effluent, possibly due to dissolution of iron oxyhydroxides under low redox conditions. Findings from this study are being used to develop a mathematical model of nitrogen removal in denitrifying stormwater biofilters.