Increasing Impact Energy Research Articles

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.

Shear creep deformation of rock fracture distrubed by dynamic loading

The long-term stability of jointed rock masses is usually dominated by fault activation, which may be triggered by the dynamic disturbance generated by blasting during mining activities, leading to the occurrence of disasters such as landslides in open-pit and rockbursts in deep mining. The initial stress and dynamic disturbance are key factors that strongly affect the shear creep behavior of rock fractures. In this work, the shear failure instability of rock fractures of sandstone under creep-impact loading was experimentally investigated by using a creep-impact test machine, which allows for applying creep loading and an additional dynamic disturbance on rock fractures. Three stages of shear creep deformation, creep strain rate, and time-to-failure are examined under different creep stress levels and impact energies. Experimental results show that the tangential and normal creep rates increase with the increase of creep stress and impact energy, but the increment of tangential creep rate is higher than that of the normal creep rate. The time-to-failure of the creeping specimen is shortened under high creep stress and large impact energy, while the time-to-failure after the last dynamic disturbance of the specimen is determined by the total impact energy and creep stress level. By using high-speed photography, it is found that the failure types of rock depend on the magnitude of impact energy and creep stress level; that is, rock mainly slides with low stress levels and shears off with high stress levels. In addition, under different impact energy and creep stress levels, the variation of height is between 0.38 and 0.52, while the defined fracture factor, which describes the degree of failure of serrations, is between 0.30 and 0.54. The findings can provide deep insight into the fault sliding mechanism caused by mining activities, which provides theoretical support for the safe mining of ore in fault fracture zones.

Investigation of Residual Strength in CFRP Double-Adhesive Single Lap Bonded Joints after Low-velocity Impact

ABSTRACT Single lap adhesive joints are prone to debonding and delamination during impact, affecting the residual tensile strength and mechanical properties. To improve the stress distribution and withstand larger loads, this paper proposes to use Araldite 2015 ductile adhesive at both ends of the joint and AV 138 brittle adhesive in the middle. Through finite element analysis and experiments, the residual strength and damage of the joint under different impact conditions are investigated, and a three-parameter Gram-Charlier model is established. The results show that the model can fit the data points accurately with a coefficient of determination of error above 0.99. As impact energy increases, the residual strength of the joint decreases, especially the AV 138 joint is more sensitive. The residual strength on one side of the impact joint is approximately 20% higher compared to the middle of the impact joint. For the same energy, the residual strength of the secondary impact was about 13% higher than that of the single impact. The main failure mode is cohesive failure, which gradually changes to fiber tear. The numerical simulation matches the experimental results, which verifies the reliability of the simulation and analysis methods.

Dynamic behaviour and failure mechanism of bamboo scrimber panels under single and repeated impacts: Experimental tests

Bamboo scrimber, as a renewable and sustainable material engineered from bamboo, is inevitably subjected to impact loadings in engineering applications. To study the dynamic behaviour and failure mechanism of bamboo scrimber panels under low-velocity impact, a series of drop hammer impact tests were conducted on 36 panels. The peak force, deformation and energy absorption of bamboo scrimber panels were obtained and analysed. The influence of impact energy, impactor shape and impact angle on the dynamic behaviour of panels was quantitatively characterised. Besides, based on test observations and microscopic views, the failure mechanism of bamboo scrimber panels under different impact types was revealed, including the energy absorption mechanism through fibre fracture, fibre debonding, fibre pull-out and matrix failure. Test results showed that with increasing impact energy, the peak force of panels impacted by the spherical and flat impactors increased, while that of panels impacted by the wedge impactor did not vary significantly. The deformation and energy absorption of panels also increased with increasing impact energy. Notably, the impactor shape obviously influenced the dynamic behaviour of panels, causing a higher peak force of panels impacted by the flat impactor and a larger deformation of panels impacted by the wedge impactor. The failure mechanism of panels depended highly on the impact energy and the impactor shape. Finally, a comparative study of single versus repeated impacts revealed that the deformation of bamboo scrimber panels under repeated impacts was less than that of panels under a single impact when the same amount of energy was imposed to the panel. This study provided a basis for the use of bamboo scrimber to resist impact loadings.

Experimental investigation on mechanical properties of the sandwich structure with orthogonal corrugated core reinforced by polyurethane foam

AbstractThe aim of this paper is to explore the effect of polyurethane foam filler on the out‐of‐plane compressive property and low‐velocity impact resistance of the orthogonal corrugated sandwich panel by experimental method. The results show that foam filling increases the energy absorption and specific energy absorption of the orthogonal corrugated sandwich panel by 64.75% and 38.22% under compressive load, respectively. Furthermore, during compression, the filled foam causes the core strut undergo pure buckling failure and gradually folds rather than brittle fracture. Under low‐velocity impact, the strengthening effect of foam filling on the first peak load of the load–displacement of the orthogonal corrugated sandwich panel decreases with the increase of impact energy, while the inhibition effect on the impactor drop increases with the increase of impact energy. The results can provide a reference for the design and optimization of foam‐filled hybrid sandwich structures.Highlights The compressive property and low‐velocity impact resistance of the foam‐filled orthogonal corrugated sandwich panel are tested. The effect of foam filling on the mechanical properties of the orthogonal corrugated sandwich panel is obtained by comparing the out‐of‐plane compressive response and low‐velocity impact response of the empty and foam‐filled orthogonal corrugated sandwich panel and foam sandwich panel. Foam filling can improve the load‐bearing property and energy‐absorbing capacity of the orthogonal corrugated sandwich panel and make it more stable progressive damage.

Numerical Investigation of the Effects of Impactor Geometry on Impact Behavior of Sandwich Structures

The aim of this study is to examine the impact performance and damage behavior of sandwich composite structures with a core material of aluminum and a facesheet of glass fiber composites using the finite element method. In the study, the effects of impactor shape, impact velocity and number of core layers on peak force, absorbed energy efficiency, maximum displacement and damage deformation were examined. For low velocity impact simulation, progressive damage analysis was performed based on the Hashin damage criterion using the MAT 54 material model in the LS DYNA finite element program. While providing the connection between the core structure and its surfaces, a Cohesive Zone Model (CZM) based on the bilinear traction-separation law was created and examined. At the end of the study, it was determined that the shape of the impactor had a significant effect on impact resistance. Energy absorption efficiency may vary as impact energy changes. However, as the impact energy increases, the energy absorption efficiency increases. It was determined that the largest and dominant damage type for all three impactors was matrix damage.

Experimental investigation and optimization for after-impact residual strength of a novel gradient corrugated structure

A novel structure based on a gradient corrugated architecture is introduced, and its after-impact residual strength is numerically and experimentally investigated. Low-velocity impact (LVI) and compression after impact (CAI) tests are conducted on designed specimens made of acrylonitrile butadiene styrene (ABS). The experiments reveal that the penetration depth increases linearly with increase in impact energy while the residual strength does not follow the same trend and its degradation rate is decreasing which implies that the structure tends to maintain its strength. A numerical model is developed to simulate the impact and after-impact response of structures with the error range of 2∼15 % for penetration depth values of LVI and less than 5 % error for the residual strength of CAI in comparison with experimental results. In order to maximize the after-impact tolerability, the structural architecture is optimized and realized that trapezoidal cells with decreasing gradient offer the highest specific strength. The sensitivity of the proposed structure to the impact location, with a higher average residual specific resistance, is lower than similar optimized configurations presented in literature.

Impact of helium nanobubbles on tungsten fuzz nanostructure conductivity

Explosive electron emission splashes occurring in plasma interactions with nanostructured surfaces can be induced by Joule energy release under reduced conductivity. Distribution of helium nanobubbles inside tungsten at an elevated energy of implanted helium ions has been studied via numerical molecular dynamic modeling, and its impact on the nanostructure conductivity has been estimated. Average concentration and size of nanobubbles were calculated to be about n = 1020 cm−3 and r = 3 Å, respectively, at the helium fluence of about 2 × 1015 cm−2. The distribution of nanobubbles becomes more flat and extends deeper into the bulk material with increasing impact energy. At energies below about 300 eV, most nanobubbles form within a depth of 10 nm, corresponding to the characteristic size of the nanowires. At higher energies, a significant portion of the nanobubbles forms deeper in the material. An approach for estimating the electron scattering frequency in tungsten by helium nanobubbles has been proposed, taking into account the volume porosity of the W-fuzz nanostructure and scaling the helium content to the experimentally measured one. The resulting value for the tungsten fuzz nanostructure was 2.27 × 1016 s−1 and the resistivity was 1.92 mΩ cm that is 364 times larger than the normal tungsten resistivity, the conductivity of 521 S/cm was 0.275% from the normal tungsten one. The corresponding estimation of thermal conductivity via Wiedemann–Franz law gave 3.8 mW cm−1 K−1, which agrees well with recent measurements.

Investigation on the dynamic failure characteristics of concrete slab based on mesoscopic simulation and energy conversion analysis

In this study, Continuous Discontinuous Element Method (CDEM) was employed to analyze the failure of concrete slab under drop-hammer impact at the mesoscopic level. Initially, simulation models of the impact system were established, and concrete slab models, including three-dimensional random aggregates, were generated. Mesoscopic simulations of concrete failure were then conducted by considering different variables, such as impact energy, slab size and the number of hammerheads. Corresponding drop hammer tests were used to validate the simulation results. Furthermore, an energy conversion formula for the dynamic failure of concrete slabs was derived, and the energy conversion process within the impact system was analyzed. The study also revealed the dynamic failure mechanisms of concrete slabs under various impact conditions. The research demonstrates that the simulation results are generally consistent with the impact tests. CDEM effectively investigates the impact characteristic and the energy conversion process of concrete slab failure. Under varying impact energies, slab sizes and hammerhead numbers, distinct differences in the failure characteristics of concrete-slab structure were observed. Increased impact energy accelerates the failure of concrete slabs, whereas larger concrete slab sizes inhibit crack propagation. The number of impact heads determines the initial crack position and its propagation path within the concrete slab. Moreover, the energy conversion process of the impact system significantly influences the failure behavior of the concrete slab. The effect of slab size on the energy utilization rate is greater than those of hammerhead number and impact speed.

Flexural behavior of textile reinforced 3D printed concrete under quasi-static and dynamic impact loads

There has been a growing interest in utilizing 3D printing technology for military and civil defense engineering, especially in enhancing the resilience of infrastructure against impacts. Due to its distinctive additive manufacturing process, 3D printed concrete (3DPC) shows anisotropic behavior when subjected to static loads. However, research on its performance under dynamic conditions remains limited. Therefore, this study explores the characteristics of 3DPC under static and dynamic loads. Quasi-static results showed that incorporating textile significantly enhanced the deformation capacity of specimens, with the ultimate deflection and flexural toughness of basalt textile reinforced specimens in the X direction reaching 1.07 mm and 4206.9 N·mm, which are 118 % and 117 % higher than control specimens without textiles, respectively. The mechanical properties of 3DPC specimens showed increasing trend from static to impact loads. The impact results indicated that the peak load increased with the increase in impact energy. Adding two types of textiles showed different anisotropic mechanical properties which are associated with the patterns of cracking and failure. The addition of basalt textiles primarily enhanced the energy dissipation properties of 3DPC, with increases up to 98.2 %. The AR-glass textile was superior in terms of maintaining peak force under multiple impacts.

On Low-Velocity Impact Response and Compression after Impact of Hybrid Woven Composite Laminates

This paper aims to study the low-velocity impact (LVI) response and compression after impact (CAI) performance of carbon/aramid hybrid woven composite laminates employed in marine structures subjected to different energy impacts. The study includes a detailed analysis of the typical LVI responses of hybrid woven composite laminates subjected to the impact with three different energies, as well as a comparative analysis of cracks and internal delamination damage within impact craters. Additionally, the influence of different impact energies on the residual compressive strength of hybrid woven composite laminate is investigated through CAI tests and a comparative analysis of internal delamination damage is also conducted. The results indicate that as the impact energy increases, the impact load and CAI strength show a decreasing trend, while impact displacement and impact dent show an increasing trend. The low-velocity impact tests revealed a range of failure modes observed in the hybrid woven composite laminates. Depending on the specific combination of fiber materials and their orientations, the laminates exhibited different failure mechanisms. Buckling failures were observed in the uppermost composite layers of laminates with intermediate modulus systems. In contrast, laminates with higher modulus systems showed early damage in the form of delamination within the top surface layers.

Study on Low-Velocity Impact and Residual Compressive Mechanical Properties of Carbon Fiber-Epoxy Resin Composites.

Room temperature drop hammer impact and compression after impact (CAI) experiments were conducted on carbon fiber-epoxy resin (CF/EP) composites to investigate the variation in impact load and absorbed energy, as well as to determine the residual compressive strength of CF/EP composites following impact damage. Industrial CT scanning was employed to observe the damage morphology after both impact and compression, aiding in the study of impact-damage and compression-failure mechanisms. The results indicate that, under the impact load, the surface of a CF/EP composite exhibits evident cratering as the impact energy increases, while cracks form along the length direction on the back surface. The residual compressive strength exhibits an inverse relationship with the impact energy. Impact damage occurring at an energy lower than 45 J results in end crushing during the compression of CF/EP composites, whereas energy exceeding 45 J leads to the formation of long cracks spanning the entire width of the specimen, primarily distributed symmetrically along the center of the specimen.

The Fluvial Battering Ram: Collisional Experiments Reveal the Importance of Particle Impact Energies on Bedrock Erosional Efficiency

AbstractThe battering of bedrock by bedload collisions is the primary mechanism by which bedrock rivers erode and landscapes evolve. The energy imparted via impacts acts to detach bedrock via the growth and intersection of surface fractures. We present impact experiments designed to test the influence of particle impact energy on bedrock erosion rates. We found that erosional efficiency increased with increasing impact energy. Notably, these increases in efficiency are not captured by a widely‐used mechanistic bedrock erosion model. Observed increases in erosional efficiency were linked with enhanced elastic energy dissipation captured by differences in the coefficient of restitution. We suggest that this increase in energy dissipation is indicative of enhanced crack extension for high velocity impacts. Our experiments indicate a clear energy‐dependence for bedrock detachment processes that is not yet captured by bedrock incision models but may be integrated into long‐term erosion rates and landscape evolution.

Electron Impact Single Ionization Cross Sections of Ar+ Ion

Binary encounter approximation has been used for theoretical calculations of electron impact single ionization cross sections of singly ionized Ar atom at ground state in the energy range of 29.1eV to 2495.1 eV/amu. The cross sections for energy transfer given by Vriens’ and quantum mechanical Hartree-Fock velocity distributions for target electron have been used in the calculation. The contributions in total single ionization cross sections from 3p and 3s subshells are observed higher than from 2p, and the contributions from 3p first increases with impact energy and then decreases with increase of impact energy whereas the contribution from 3s decreases with impact energy. About 69% of results have ratio factors ≤ 1.5 and 59% have values 1.25. Major contributions to the total ionization cross sections are from 3p and 3s for direct single ionization.

Experimental and numerical investigations on impact response of reinforced concrete beams with a sandwich panel protective layer

This paper investigates the response of reinforced concrete beams protected by an aluminium foam sandwich panel under impact loadings. A series of impact tests were conducted on one reinforced concrete beam and five beams with a protective layer, focusing on their dynamic responses and failure patterns. Test parameters included the type of protective layers (unprotected, aluminium foam and sandwich panel) and impact energy. Test results showed that the aluminium foam and sandwich panel could effectively protect the reinforced concrete beam from severe damage under impact loadings and converted the failure pattern of beams from shear failure to flexure-shear failure. Compared with the unprotected beam, the beams with a protective layer exhibited a lower peak force and developed a smaller mid-span deformation. Besides, the protective effects of the aluminium foam and sandwich panel were found to be nearly the same. Moreover, the peak force, plateau force and deformation of the beams were increased with the increasing impact energy. A numerical model was developed to investigate the energy distribution of beams with a sandwich panel protective layer. Based on the validated model, the effects of longitudinal reinforcement ratio and shear-span ratio on the impact response of beams were further studied. It was found that the deformation of beams increased significantly with the increasing shear-span ratio, whereas an increase in the longitudinal reinforcement ratio led to a decreased deformation. This study provides an important reference for designing reinforced concrete beams with a sandwich panel protective layer to resist impact loads.

Investigating low velocity impact and compression after impact behaviors of carbon fiber/epoxy composites reinforced with helical multiwalled carbon nanotubes

Pre-damage and undetected micro-defects in fiber-reinforced polymer (FRP) composites are significant challenges compromising the integrity and mechanical performance of composite structures in aerospace applications. To address this challenge, this experimental study investigated the low velocity impact (LVI) and compression after impact (CAI) behaviors of carbon fiber/epoxy (CF/E) reinforced with 0.0 (control sample), 0.2, and 0.4 wt% helical multiwalled carbon nanotubes (HMWCNTs). The LVI test results showed that the control samples, with epoxy as the predominant phase, registered the lowest peak force compared to the 0.2 wt and 0.4 wt% HMWCNT/epoxy composite laminates. The CAI test results showed a decrease in strength with increased impact energy and an increase in the weight percent of HMWCNTs. Consequently, the 0.4 wt% HMWCNT ladened composites could withstand higher load without undergoing significant deformations, exhibiting the highest impact resistances due to the presence of CNTs, which function as load-bearing material. The HMWCNT interleaved CF/E composite laminate samples subjected to 25 J of impact energy achieved a higher maximum force of 9870.25 N compared to 8527.26 N for the damaged samples at the same level of impact energies. This fact indicates that the damaged samples could not withstand sufficiently high impact forces due to local instability arising from existing damages. The results strongly suggest a high potential for HMWCNTs CF/epoxy laminate composites in making structural and substructural components in aircraft and automobiles due to their proven superior properties.

Surface engineering of textile structural composites with ZnO nanorods and graphene nanofillers for aircrew helmet applications

AbstractThis research aimed to augment the properties of interfibre interfaces through surface treatment with ZnO nanorods while simultaneously modifying the matrix with graphene nanoplatelets. The strategic approach of this research focused on synergizing these interventions to enhance the mesomechanical, and macromechanical properties, which are specifically targeted at improving the performance of aircrew helmets. This study investigated the effectiveness of these enhancements in improving the mechanical performance of aircrew helmets. The synergy of integrating ZnO nanorods and doped GNPs into Kevlar fabric resulted in a 29% increase in impact energy absorption compared to that of the standard Kevlar composite. Furthermore, the composite samples underwent thorough analysis through techniques such as thermogravimetric analysis (TGA), Raman spectroscopy, Fourier‐transform infrared spectroscopy (FTIR), dynamic mechanical analysis (DMA), and scanning electron microscopy (SEM) imaging. The findings indicate that incorporating 1% graphene nanofillers into Kevlar during the fourth seed cycle of ZnO treatment yields favorable mechanical performance characteristics. SEM at 50 KX magnification provided detailed visualization of the ZnO nanorods grafted onto the fabric substrates, with subsequent evaluation of the morphological damage and fractography of the impacted composites. The findings of this research hold significance for advancing the understanding of composite material behavior under impact loads and contribute to ongoing efforts to enhance the durability and performance of structural composites in diverse applications.Highlights Synergistic treatment with ZnO nanorods and graphene nanoplatelets boosted Kevlar composite properties for aircrew helmets. Adding 1% graphene during ZnO treatment increased impact energy absorption by 29%. Comprehensive analysis validated treatment efficacy, showing substantial mechanical improvements. The research advances composite understanding, paving the way for durable, high‐performance materials for applications like aircrew helmets.

Impact morphology characteristics and damage evolution mechanisms in CFRP laminates for hydrogen storage cylinders

In instances of impact, the preeminent load-bearing framework for on-board hydrogen storage cylinders manifests in the carbon fiber reinforced polymer (CFRP) composite layer. Investigating the morphology of impact and elucidating the mechanism governing damage evolution in CFRP is crucial for optimizing the impact resistance of the cylinder. In this work, impact tests were performed on CFRP laminates with six types of interlaminar mismatch angles, under varying impact energies. The impact damage of laminates was characterized using an extended depth-of-field 3D microscopy. A numerical model, implemented in ABAQUS/Explicit, was devised to scrutinize the mechanical properties and damage mechanisms in laminates. A subroutine (VUMAT) was crafted to effectively predict intralaminar damage, while the application of a bilinear cohesive model served to capture interlaminar damage. In addition, this study delves into the ramifications of impact energy and interlaminar mismatch angles. The results reveal that the increase of impact energy leads to more irreversible damage and energy dissipation within laminates. Compared to damage depth (D) and cross-sectional area (Ac), the assessment of damage volume (V) and surface area (As) are more reflective of energy dissipation in laminates. The laminates with mismatch angle of 0° and “helicoidal” lay-up sequence exhibit the worst impact resistance. Within the range of 24°–90°, laminates with a smaller interlaminar mismatch angle demonstrate better impact resistance. These findings lay the groundwork for optimizing the composite layer to enhance the impact resistance of hydrogen storage cylinders.

Low energy impact damage characteristics of epoxy coating on the surface of sandwich composites

AbstractWhen composite honeycomb sandwich structures are subjected to low energy impacts, the upper panel or the honeycomb core often suffers large damages, which are invisible, but affects the structural safety. To achieve non‐destructive detection of these damages, an epoxy resin film (ERF) was designed as a functional coating to display the internal failure features on structure surface. The effect of low energy impacts on the damage modes of the ERF was first investigated, and then the correspondence between the ERF damage characteristics and the structural internal failure was established. Simulation and experimental results showed that with the increase of impact energy, cracks on the ERF expanded from the radial radiation with a small extension range to the circumferential pattern with an increased damage area. Meanwhile, localized delamination appeared inside the upper panel, while the degree of flexure and crushing damage to the core continued to increase. Based on the analysis of the crack extension pattern of the ERF and the damage state of the upper panel and honeycomb core, a specific link between the ERF crack characteristics and the internal damages to the sandwich structure was obtained, which might offer a novel non‐destructive testing method for composite impact damages.Highlights Low energy impact damage in honeycomb sandwich structures was a concern. Impact damage response of epoxy resin film on sandwich composites was studied. Crack extension of the film showed a particular change from radial to annular. Specific link between film crack and sandwich structure damage was established. The results would be helpful for damage detection in sandwich composites.

Research on size effects in the low‐velocity impact (LVI) and compression after impact (CAI) characteristics of composite laminates

AbstractThe load‐bearing capacity and failure characteristics of composite structures are closely related to their dimensions. In this study, low‐velocity impact, ultrasonic non‐destructive testing, and compression after impact tests were conducted on composite laminates of varying widths to investigate the influence of size effects. Distinct impact response profiles and compression failure modes were characterized. The results indicate that under impact loading, the delamination threshold load (6700 N ~ 7200 N) and the knee‐point energy (40 J) are not affected by width. However, variations in width lead to differences in indentation depth, impact duration, peak load, delamination characteristics, and energy absorption. Furthermore, increasing impact energy further magnifies these differences. Under compression loading, wider laminates exhibit lower residual strength, with the influence of impact energy on residual strength decreasing as width increases. Importantly, the observed compression failure deformation mode transitions from localized buckling to widespread sub‐layer delamination‐induced compression failure. This suggests that changes in width alter the governing mechanical mechanisms of CAI failure. Consequently, the use of a single‐size laminate to represent both LVI and CAI processes is not recommended. Based on experimental results, the reliability of the equivalent damage method in predicting the residual compression strength of laminates of different widths was confirmed, providing valuable insights for practical engineering applications.Highlights Assess the variations in the low‐velocity impact process of laminates with different widths. Evaluate the delamination damage of laminates after impacts by ultrasonic C‐scan techniques. Investigate the effect of variation in widths on the compression behavior of laminates after impact. Validate the feasibility of equivalent damage modeling for calculating residual strength.