Dynamic Loading Conditions Research Articles

Dual-Sliding-Surface Robust Control for the PEMFC Air-Feeding System Based on Terminal Sliding Mode Algorithm

The proton exchange membrane fuel cell (PEMFC) is the most widely used fuel cell, but it also has some limitations. One of the research pain points is controlling the oxygen content in PEMFCs. A moderate excess of oxygen boosts electrochemical reaction efficiency, while an appropriate oxygen content ensures system stability. In this paper, a fourth-order nonlinear mathematical model of a PEMFC stack air supply system is established to solve the problem of optimal oxygen excess ratio (OER) control under dynamic load conditions. Based on the model, a nonsingular terminal sliding mode controller (NTSMC) based on a sliding mode observer (SMO) is proposed. The NTSM exhibits superior robustness and performance compared to other sliding mode structures. Meanwhile, the SMO accurately predicts system states, facilitating precise control actions. Additionally, the dual sliding mode surfaces enhance system stability against parameter uncertainties and external disturbances. Our results demonstrate that the proposed controller outperforms traditional ones in terms of robustness and performance, which significantly enhances PEMFC system efficiency and stability.

How do Ritz Vectors React to the Imposed Load?

All real structures behave dynamically when loaded or displaced. Additional inertial forces are equal to the force in acceleration using Newton's second law. If the forces or the change of places are applied very slowly, the inertial forces can be ignored and a static analysis can be done. Therefore, it can be said that dynamic analysis is a simple extension of static analysis. In addition, all potential real structures have unlimited degrees of freedom. Therefore, the most critical part of structural analysis is creating a model with a limited number of degrees of freedom that has several almost massless members and several nodes, which can estimate the behavior of the structure appropriately. The mass of the structure can be concentrated in the nodes. Also, for a linear elastic system, the stiffness characteristics of the members can be estimated very accurately - according to the experimental data - although the estimation of dynamic loading, energy loss, and boundary conditions can be very difficult. Therefore, the nonlinear dynamic analysis method is usually used in theoretical studies and is not used in routine designs. So, it is a worthwhile task to propose a simple and computer method for seismic estimation of structures. For this purpose, POA has been introduced. In many cases, we can get more valuable information from POA than nonlinear dynamic analysis, this method is simple and economical and has attracted more attention nowadays.

Coordinated Optimization and Management of Oxygen Content and Cathode Pressure for PEMFC based on Hybrid Nonlinear Robust Control

Cathode inlet and exhaust management remains a significant challenge in proton exchange fuel cell (PEMFC). Achieving optimal oxygen content in real-time through precise control of the inlet gas is crucial for maintaining optimal output. Additionally, coordinating the air inlet and exhaust to ensure consistent cathode and anode pressures is essential for balancing the internal stack pressure and preventing nitrogen penetration, thereby enhancing PEMFC’s stability and lifespan. This paper addresses these challenges by introducing a mixed control strategy based on a fifth-order nonlinear mathematical model of the PEMFC stack cathode. Two non-singular fast terminal sliding mode structure controllers are combined as control system to optimize oxygen content and pressure control under dynamic loading conditions. The non-singular terminal sliding mode structure ensures finite-time convergence while mitigating potential singularity issues associated with traditional terminal sliding modes. The results showcase the robustness and effectiveness of the proposed control method in managing load variations, external disturbances, and PEMFC uncertainties.

Application of the Water-Based Electro-Hydraulic Actuator (EHA) to the Heavy-Duty Collaborative Robot

In this paper, the design of a driving mechanism for a heavy-duty collaborative robot (cobot) capable of lifting payloads up to 20 kg is presented. This study focuses on an articulated robot utilizing a water-based Electro-Hydraulic Actuator (EHA). The Denavit–Hartenberg (D–H) representation was employed to relate the rotational angles and the end-effector’s location, facilitating the design of the actuators. The maximum required torques for joints 2 and 3, responsible for lifting for 12 s, were calculated under quasi-static and dynamic loading conditions. The results showed that the maximum required torques were 126.67 Nm and 58.86 Nm for joint 2 and 3, respectively. The maximum torque for joint 2 occurs when the pitch links are fully extended, whereas the maximum torque for joint 3 occurs when the third link is parallel to the ground. The torques, due to the inertia and Coriolis dynamic terms, were also calculated and found to be lower than those required for the gravitational term. Various maneuvering scenarios, along with Ansys Motion simulation, were analyzed for the verification of the results. Based on the calculated maximum torques, the linear actuators of the EHA were designed. The heavy-duty cobot can be built with the developed actuator proposed in this paper. The total weight of the entire frame was measured to be 14.59 kg, resulting in a high Payload/Weight (P/W) ratio of 1.37. In conclusion, the robot was made lighter and can operate more efficiently, particularly for heavy loads up to 20 kg.

Investigation of dynamic impact behavior of bighorn sheep horn

The horn of the bighorn sheep is composed of keratin-based biological material that has a tubule-lamella structure, which gives it anisotropic hardening properties under impact loading. This paper aims to investigate the energy dissipation mechanisms inherent in bighorn sheep horns by developing a numerical material model that accounts for the horn’s anisotropic features and strain-rate effects. To this end, a transversely isotropic constitutive model, which includes both anisotropic hardening and strain-rate effects, was formulated to accurately predict the mechanical behavior of bighorn sheep horns. Material characterization was conducted through uniaxial compression tests that were conducted under quasi-static and dynamic conditions. The developed constitutive model was implemented into LS-Dyna via a user-defined material subroutine and was validated against empirical data. The validated numerical model was used to investigate the horn’s mechanical responses under dynamic loading conditions. The paper focused on impact energy dissipation mechanisms, including energy absorption and transition, stress distribution, and displacement wave propagation. The insights gained from this paper are expected to significantly contribute to the development of novel artificial materials with enhanced energy absorption and impact mitigation properties.

Modelling and theoretical research on transient lubrication and wear coupling behavior of main bearing during start-up of low-speed diesel engine

This study endeavors to establish a transient mixed lubrication model for time-varying wear of main bearings under dynamic loading conditions during the startup process. This model accounts for variations in oil film thickness attributable to deformation, wear profiles, and journal misalignment throughout the operational cycle. The evolution of main bearing lubrication characteristics during the startup process was analyzed, as well as the evolution of wear profiles and their effects on lubricating properties under different numbers of startups. The results indicate that as the number of startup cycles increases, the wear rate gradually levels off. With increasing startup times, there is a decrease in contact pressure and a slight reduction in oil film pressure, resulting in enhanced lubricating performance. Furthermore, the influence of startup duration on wear is significantly greater than that of radial clearance.

Simultaneous nitrification and denitrification framework for decentralized systems: Long-term study utilizing rope-type biofilm media under field conditions

This research introduces a novel approach to achieve simultaneous nitrification-denitrification (SND) under dynamic load conditions using a cost-effective rope-type biofilm technology. The approach represents a significant advancement in wastewater treatment, particularly beneficial for remote and decentralized communities. The biofilm-based SND process was developed using a pilot-scale flow-through reactor by implementing upstream carbon management with constant-timer-based aeration control versus dynamic-sensor-based aeration control strategies. The findings indicate that adding an upstream anaerobic pretreatment process to handle excess carbon plays a substantial role in achieving a sustainable SND process under a dynamic load environment using simple aeration on-off control. The most optimal nitrification performance of 0.32 g NH3-N/m2/d (89 % removal) was achieved under a 1-hour ON/30-minute OFF aeration. The process sustained an average bulk liquid DO of 5.16 mg/L and 3.80 mg/L during the aeration ON and OFF periods, respectively, facilitating a 0.13 g N/m2/d (41 %) total inorganic nitrogen (TIN) removal, notably, implementing advanced aeration strategies driven by DO, NH3, and NO3 sensors enhanced TIN removal efficiency to 72 %. The nitrification performance remained comparable (89 % removal), resulting in 3 and 10 mg N/L effluent ammonia and TIN concentration, respectively. Additionally, utilizing two multivariate approaches accounting for 82 % and 64 % of the variance, this study discerned patterns in monitored variables and performance. Additionally, the analysis underscored the difference of bulk liquid DO levels in the biofilm versus suspended systems inhibiting the SND process. Distinct bacterial communities were established in biofilms under aerobic, anaerobic, and SND conditions, with the SND reactor showing a hierarchy of functional group and enzymes, enriched sequentially from heterotrophs to denitrifiers, nitrifiers, and anammox bacteria. These innovations underline the potential of tailored control strategies to enhance a passive biofilm-based SND process efficiency under dynamic conditions, providing scalable solutions for diverse target water quality demands in remote communities and decentralized systems.

Чисельно-експериментальне дослідження високотемпературної багатоциклової втомної міцності монокристалічних лопаток газових турбін

The subject of the research is anisotropic single-crystal turbine blades of aircraft gas turbine engines (AGTE), as well as their multi-cycle fatigue strength characteristics at high temperatures. The goal of this study was to determine the endurance limit of single-crystal high-pressure turbine blades of an AGTE at high temperatures of 820°C. The objective of the study is to develop a method for calculating and experimentally investigating the characteristics of high-temperature multi-cycle fatigue strength of gas turbine blades made of single-crystal nickel heat-resistant alloys. The research methods used are: method of computer modelling, which was used to create a 3D model of a cooled high-pressure turbine blade; finite element method, which was used to determine the stress-strain state of the blade according to the selected form of resonant vibrations; strain and resonance methods, which were used to determine the fatigue strength characteristics of single-crystal turbine blades under high-temperature loading. The following results were obtained. Literary sources describing theoretical and experimental methods for determining the strength characteristics of blades under combined dynamic and high-temperature loading were analyzed. The developed special installation for testing turbine blades under conditions of temperature and dynamic (resonant) loading was described. A combined method for assessing the multi-cycle fatigue strength at high temperatures is proposed, which includes studies on full-scale turbine blades and finite element calculations. The dynamic and temperature characterization of single-crystal turbine blades selected for the study was carried out and described. Fatigue tests were performed to determine the endurance limit of the blades at a high temperature equal to T = 820 °C. Conclusions. The scientific novelty of the obtained results is as follows. A specialized experimental setup was developed to study the endurance limit of single-crystal AGTE blades under high-temperature loading. A method for combining numerical (ANSYS) and experimental (field tests) study of high-temperature multi-cycle fatigue strength of turbine blades made of single-crystal heat-resistant alloys was developed. The direction of further research is presented.

Digital rock modeling of deformed multi-scale media in deep hydrocarbon reservoirs based on in-situ stress-loading CT imaging and U-Net deep learning

Deep and ultra-deep hydrocarbon reservoirs are regarded as an attractive target for onshore oil and gas exploration and development in China. The multi-scale fractures are widely distributed in this type of reservoir. The fluid-solid coupling effect is strong, which can greatly affect the fluid flow, resulting in a low hydrocarbon recovery with the average value less than 15%. To explore the underlying flow dynamics during efficient development of deep and ultra-deep hydrocarbon reservoirs, it is of great importance to characterize the multi-scale fracture-pore structure evolution of rock affected by strong geo-stress field variation. To tackle the above issues, an actual rock drilled from a typical ultra-deep reservoir in Tarim Basin are selected to conduct in-situ stress-loading computed tomography (CT) scanning experiments, and the CT gray images of rock microstructure under different dynamic loading conditions are obtained. A fully convolutional neural network (U-Net) deep learning segmentation algorithm is introduced to accurately distinguish the rock skeleton, pore space and fractures in deep rock. The three-dimensional (3-D) digital rock model of deformed multi-scale fracture-porous media under different dynamic loading conditions is ultimately established to investigate the evolution of fracture morphology and deep rock microstructure as the in-situ stress is gradually loaded. It indicates that, the U-Net deep learning semantic segmentation algorithm can accurately segment CT images of deep rocks, and the established 3D digital rock model of fractured porous media can accurately represent the pore-throat distribution, fracture morphology, and pore-scale topological connectivity. At the initial stage of stress loading, there are few micro-fractures inside the rock, and the fracture connectivity is poor. Due to effect of rock compaction, the average pore throat radius increases while pore throat ratio, coordination number and tortuosity greatly decrease. As the effective stress is gradually loaded, the micro-fractures begin to propagate, leading to stronger heterogeneity of micro-fractures’ distribution and better topological connectivity, and both the coordination number and tortuosity gradually increase. After the deep rock is fractured, micro-fractures run through a fracture network and all the above topological parameters increase greatly.

Analysis of the Impact of Dynamic Operation of PEMFCs for Ship Applications

<i>Dynamic responses of polymer electrolyte membrane fuel cells (PEMFC) were analyzed under varying loads to understand the performance of PEMFCs for ship applications. Experiments employing single cells were conducted under a static load with a constant current of 6.64 A and dynamic loads at a ramp rate of 2.5%/s and 5.0%/s, representing a simplified ship operation condition. Under the static load, the voltage drop was 0.054 V at 1.00 A/cm<sup>2</sup> and was dominant below 0.40 A/cm<sup>2</sup>. In contrast, under the dynamic load (5.0%/s ramp rate), the voltage drop was 0.061 V at 1.00 A/cm<sup>2</sup> and was dominant above 0.40 A/cm<sup>2</sup>, with similar behavior observed at the ramp rate of 2.5%/s. To compare performance across load conditions, degradation rates were calculated through linear regression of the voltage drop for each current density. The degradation rate at 1.00 A/cm<sup>2</sup> was 0.143 mV/h under static load conditions and 0.174 mV/h under dynamic load conditions (ramp rate: 5.0%/s), indicating approximately 21% greater degradation rates than those observed under static load conditions. These experimental results provide foundational data for PEMFC performance analysis, particularly regarding performance degradation caused by dynamic loads in marine environments.</i>

Mechanical energy absorption capacity of the porous Ti-6Al-4V alloy under quasi-static and dynamic compression

Porous materials are very efficient in absorbing mechanical energy in different applications. In the present study, porous materials based on the Ti-6(wt.%)Al-4V alloy were manufactured with the use of two different powder metallurgy methods: i) blended elemental powder approach using titanium hydride (TiH2) as well as V-Al master alloy powders and ii) using hydrogenated Ti-6-4 pre-alloyed powder. The powder compacts were sintered with additions of ammonium bicarbonate as a pore-holding removable agent. The emission of hydrogen from hydrogenated powders on vacuum sintering and the resulting shrinkage of powder particles permitted the control of the sintering process and creation of anticipated porous structures. Mechanical characteristics were evaluated under quasi-static and dynamic compressive loading conditions. Dynamic compression tests were performed using the direct impact Hopkinson pressure bar technique. All investigations aimed at characterizing the mechanical energy-absorbing ability of the obtained porous structures. The anticipated strength, plasticity, and energy-absorbing characteristics of porous Ti-6-4 material were evaluated, and the possibilities of their application were also discussed. Based on the obtained results, it was found that porous Ti-6-4 material produced with a blended elemental powder approach showed more promising energy absorption properties in comparison with pre-alloyed powder.

Evaluating the Seismic Resilience of Above-Ground Liquid Storage Tanks

Historical seismic events have repeatedly highlighted the susceptibility of above-ground liquid storage steel tanks, underscoring the critical need for their proper design to minimize potential damage due to seismic forces. A significant failure mechanism in these structures, which play essential roles in the extraction and distribution of various raw or refined materials—many of which are flammable or environmentally hazardous—is the dynamic buckling of the tank walls. This study introduces a numerical framework designed to assess the earthquake-induced hydrodynamic pressures exerted on the walls of cylindrical steel tanks. These pressures result from the inertial forces generated during seismic activity. The computational framework incorporates material and geometric nonlinearities and models the tanks using four-node shell elements with two-point integration, specifically Belytschko shell elements. The Arbitrary Lagrangian–Eulerian (ALE) method is employed to accommodate substantial structural and fluid deformations, enabling a full simulation of fluid–structure interaction through highly nonlinear algorithms. Experimental test data are utilized to validate the proposed modeling approach, particularly in replicating sloshing phenomena and identifying stress concentrations that may lead to wall buckling. The study further presents results from a parametric analysis that varies the height-to-radius and radius-to-thickness ratios of a typical anchored flat-bottomed tank, examining the seismic performance of this common storage system. These results provide insights into the relationship between tank properties and mechanical behavior under dynamic loading conditions.

Cold temperature effects on the impact behaviour of glued-laminated timber beams

Engineered wood products, such as glued-laminated timber (glulam), have been and are continuously being utilized in the construction of tall timber buildings and notable landmark bridges. This infrastructure, particularly the latter, may be exposed to hazardous impact loads throughout their service life. As little research has been conducted on the impact behaviour of glulam beams under cold temperature conditions, there is a need to investigate the potential effects of impact loading on glulam structural elements at cold temperatures. This paper presents an experimental investigation aimed at understanding the effects of cold temperatures on the impact behaviour of glulam timber beams. Fifteen glulam beams were tested under quasi-static and impact loading, under ambient and cold temperatures. Drop weight impact testing was performed to simulate dynamic loading conditions similar to those experienced in real-world scenarios. The results indicate that both the loading regime and cold temperatures have a significant influence on the strength and stiffness of glulam beams, whereby statistically significant increases in the moduli of rupture and elasticity were observed, however, no interaction between the two variables occurred. A single-degree-of-freedom (SDOF) model was developed and validated using the experimental test results and found to provide good accuracy.

Dynamic compressive behavior of functionally graded triply periodic minimal surface meta-structures

Triply periodic minimal surface (TPMS) lattice structures have gained considerable attention because of their light weight, high strength, and excellent energy absorption capabilities. However, the effect of the amplitude that can control the topological morphology of a TPMS on the dynamic properties of the TPMS structure is not yet fully understood, as previous studies have focused on the relative density and size as well as their quasi-static mechanical properties. In this study, three types of uniform sheet-based TPMS structures with different amplitudes and three types of functionally graded sheet-based TPMS structures were proposed. Experiments and numerical simulations were conducted under quasi-static and dynamic loading conditions. Six types of TPMS lattice structures made of 316L stainless steel were manufactured via powder bed fusion. Quasi-static compression tests were performed at a strain rate of 0.001 s⁻¹. The experimental results indicate that increasing the amplitude can increase the elastic modulus, plateau stress, and energy absorption capacity of a structure. Moreover, the functional gradient amplitude structure has a higher energy absorption capacity, and the structures with line and log gradient strategies improved by 17.38% and 35.43%, respectively, compared to the uniform structure with an amplitude of 1. Additionally, an idealized rigid-linear plastic hardening (R-LPH) model was proposed to predict the mechanical response of the structures. The finite element method (FEM) was used to construct dynamic compression numerical models, and their validity was verified through split Hopkinson pressure bar (SHPB) tests at a strain rate of 695 s⁻¹. The mechanical response, deformation modes, and stress enhancement effects of the structures under dynamic compression were systematically studied. The results show that the mechanical performance and energy absorption capacity of the structures under dynamic impact loading increase with increasing strain rate. The critical velocity for the transition from the quasi-static mode to the impact mode increases with amplitude. For strain rates below 6000 s⁻¹, the strain rate effect is the main factor influencing the dynamic stress enhancement. As the strain rate continues to increase, the dynamic stress enhancement results from the combined effects of inertia and strain rate, with inertia effects gradually becoming the dominant factor. This study shows that functional gradient TPMS meta-structures have excellent mechanical and energy absorbing properties under quasi-static compression and dynamic compression, with potential applications in passive safety protection.

Static and Dynamic Stress of the Combined Rotor with Curvic Couplings Considering the Rough Three-Dimensional Interface at Extreme Operating Conditions

The curvic coupling, as one of the common connecting structures for gas turbine combined rotors, is more susceptible to various dynamic and static loads at extreme operating conditions. But, traditional combined rotor models tend to neglect the influence of the connection structure, especially failing to consider the contribution of the curvic coupling interfaces. To address this problem, this paper establishes a solid geometric model of the combined rotor with curvic couplings considering the rough three-dimensional interfaces. The effectiveness of the proposed model method is indirectly verified through the compression tests and modal tests. Subsequently, combined with finite element calculations, the mechanical properties of the rotor with curvic couplings considering the rough interface are analyzed under static and dynamic load conditions. The results indicate that the roughness of the interface significantly affects the deformation of the contact surface under static load, but its impact on the overall deformation of the rotor is relatively insignificant. The dynamic stress at the interface exhibits periodic variations at the resonance speed. At the maximum operating speed, the dynamic stress is influenced by the magnitude of imbalance. The aforementioned methods and conclusions provide a reference for the design research and engineering application of combined rotors.

Mechanical properties and biocompatibility characterization of 3D printed collagen type II/silk fibroin/hyaluronic acid scaffold

Damage to articular cartilage is irreversible and its ability to heal is minimal. The development of articular cartilage in tissue engineering requires suitable biomaterials as scaffolds that provide a 3D natural microenvironment for the development and growth of articular cartilage. This study aims to investigate the applicability of a 3D printed CSH (collagen type II/silk fibroin/hyaluronic acid) scaffold for constructing cartilage tissue engineering. The results showed that the composite scaffold had a three-dimensional porous network structure with uniform pore sizes and good connectivity. The hydrophilicity of the composite scaffold was 1071.7 ± 131.6%, the porosity was 85.12 ± 1.6%, and the compressive elastic modulus was 36.54 ± 2.28 kPa. The creep and stress relaxation constitutive models were also established, which could well describe the visco-elastic mechanical behavior of the scaffold. The biocompatibility experiments showed that the CSH scaffold was very suitable for the adhesion and proliferation of chondrocytes. Under dynamic compressive loading conditions, it was able to promote cell adhesion and proliferation on the scaffold surface. The 3D printed CSH scaffold is expected to be ideal for promoting articular cartilage regeneration.

A modified mixed-mode Timoshenko-based peridynamics model considering shear deformation

The original two-dimensional bond-based peridynamic (BBPD) framework, which only considers the pairwise forces (compression and tension) between two material points, is extended by incorporating the effect of shear deformation in the calculations and its influence on the failure of the bonds. To this end, each bond is considered as a short Timoshenko beam, and by doing so, the traditional BBPD is enhanced into a more comprehensive model known as multi-polar peridynamic (MPPD). The proposed novel approach explicitly considers the shear influence factor used in Timoshenko beams and introduces a strain-based shear deformation failure criterion. The model is then validated against two benchmark experimental tests (i.e., a standard pure mode I edge crack, and a Kalthoff-Winkler configuration) reported in the literature under in-plane dynamic loading and plane stress conditions. In most cases, the developed model is shown to be more accurate in predicting the crack paths obtained from the experimental results when compared to other theoretical methods delineated in the literature. Furthermore, a noticeable change in crack branching and crack path is observed in a study on the effects of Poisson's ratio and the loading rate. This investigation also demonstrated that the proposed MPPD model can accommodate materials with Poisson's ratios up to 1/3, expanding the range beyond the traditional BBPD limitations.

Three-dimensional mesoscale analysis of the dynamic tensile behavior of concrete with heterogeneous mesostructure

This paper investigates the dynamic tensile behavior of concrete under high strain rates. An optimized random concrete mesostructure generation procedure is established using the 3D entrance block (3D E(A, B)) algorithm to account for the intrinsic material heterogeneity. This approach avoids repetitive and complicated polyhedral aggregate overlapping checks in traditional methods, resulting in a highly efficient aggregate packing process. The nucleation, propagation, and coalescence of cracks are captured by a properly developed rate-dependent cohesive constitutive law. The mesoscale model is validated through comparison with experimental results. The crack evolution in the concrete under dynamic direct tensile loading conditions is explicitly presented, and the effects of the aggregate volume fraction and ITZ properties on the dynamic tensile strength enhancements are studied. The results indicate that material heterogeneity significantly influences the fracturing process and damage distribution. The dynamic tensile strength of concrete exhibits a two-strain rate regime dependence on the aggregate volume fraction concerning the strain rate. The influence of the mechanical properties of the ITZ on the dynamic tensile strength of concrete increases with the increasing strain rate.

Impact of elevated loading rates on the shape of the Master Curve (ASTM E1921) for a German RPV steel

The Master Curve Methodology (ASTM E1921) experimentally assesses a materials temperature-dependent fracture toughness, predominantly for quasi-static testing conditions. The treatment of elevated loading rates is described by the annex A1 of ASTM E1921 and A14 of ASTM E1820. This paper presents results of the evaluation of a large and standard-conforming database in order to verify the procedures recommended by the standard for elevated loading rates. Testing involved C(T)- and SEN(B)-specimens of the RPV-steel 22NiMoCr3-7 (A508 Grade 2) for loading rates of 100 MPa√m/s ≤ K̇ ≤ 104 MPa√m/s in the ductile to brittle transition region. While valid T0-values were found, single-temperature T0-values were observed to differ more than expected from multi-temperature T0-values, which cannot be explained by the Master Curve uncertainty. The shape and underlying distribution of the Master Curve show deviations with increased loading rate. The shape factor p is optimized with respect to the individual data, and it increases with K̇, but deviations are not completely overcome. This can be linked to a change in distribution, which was demonstrated by an optimization of minimum fracture toughness Kmin, which increases with temperature. It is argued that the cause for the observations is linked to both heating processes and local crack arrest that severely influence macroscopic fracture behavior. Also, an individual adjustment of p or Kmin is not helpful due to the material-dependency in practice. It is recommended that fracture mechanics testing at elevated loading rates is performed close to or below T0 in order to minimize the influence of dynamic loading conditions on the assessment.

Iterative Method of Determining Stress Intensity Coefficients Under Dynamic Loading of the Crack System

An elastic isotropic body in a state of plane deformation, which contains a system of randomly placed cracks under the action of a dynamic (harmonic) loading, is considered. The authors set the problem of determining the stress field around the cracks under the conditions of their wave interaction. The solution method is based on the introduction of displacements in the body in the form of a superposition of discontinuous solutions of the equations of motion constructed for each crack. With this in mind, the initial problem is reduced to a system of singular integro-differential equations with respect to unknown displacement jumps on the crack surfaces. To solve this system, a new iterative method, which involves solving a set of independent integro-differential equations that differ only in their right-hand parts at each iteration, is proposed. For the zero approximation, solutions that correspond to individual cracks under the action of dynamic loading are chosen. Such a new approach allows to avoid the difficulties associated with the need to solve systems of integro-differential equations of large dimensions that arise when traditional methods are used. Based on the results of the iterations, formulas for calculating the stress intensity coefficients for each crack were obtained. In the partial case of four cracks, a good agreement between the results obtained during the direct solution of the system of eight integro-differential equations by the mechanical quadrature method and the results obtained by the iterative method was established. In general, numerical examples demonstrate the convergence and stability of the proposed method in the case of systems with a fairly large number of densely located cracks. The influence of the interaction between cracks on the stress intensity factor (SIF) value under dynamic loading conditions was studied. An important and new result for fracture mechanics is the detection of the absolute maximum of the normal stresses at certain frequencies of the oscillating normal loading. The number of interacting cracks and the configuration of the crack system itself affect the values of the frequencies at which SIF reaches a maximum and the maximum values. These maximum values significantly (by several times) exceed the SIF values of single cracks under a similar loading. At the same time, under conditions of static or low-frequency loading, it is possible to reduce the SIF values compared to the SIF for individual cracks. When cracks are sheared, the values of the tangential stresses have a tendency to decrease with increasing frequency, and their values do not significantly differ from the values of the tangential stress for an individual crack.