Dynamic Damage Model Research Articles

Research on dynamic mechanical properties and damage model of ceramic materials under multi‐axial stress

AbstractDue to their exceptional impact resistance, ceramics are extensively used in various fields. However, unavoidable pores, microcracks, and inherent defects can degrade the performance of ceramic materials. A damage model of SiC ceramics under passive confining pressure was constructed based on the Lemaitre strain equivalence principle and the Weibull distribution function. This paper presented a dynamic damage model for SiC ceramics subjected to passive confinement pressure based on the principles of damage mechanics. Additionally, the split Hopkinson pressure bar device was employed to investigate the compressive strength and damage evolution of SiC ceramics at various shock pressures and confinement degrees. The experimental results indicate that constraints can reduce the damage to ceramics. The metal sleeve increased stiffness when compressing the ceramic material, allowing the specimen to convert from brittle–plastic–brittle. When sufficient constraints can be provided, the peak strain decreases gradually with the increase of the impact air pressure. Experimental data showing good agreement with the proposed model validated and analyzed the established model. Thinner boundary constraints cannot maintain the stability of ceramic structures, thicker boundaries do not significantly improve performance, and thicker boundaries can cause more weak areas. This paper provides guidance for the design of encapsulated ceramic composite armor by quantitatively studying the constraint thickness.

FURTHER DEVELOPMENT OF GDEM FOR THE MODELING OF MULTI-SCALE DYNAMIC RESPONSE OF ROCK SUBJECTED TO BLASTING AND IMPACT

The dynamical responses of rock subjected to blasting and impact have been of concern in most underground projects. Due to the size effects and strain-rate enhancement induced by inertial effects, the dynamic responses of rock and underground structures show multi-scale characteristics. Thus, in order to achieve better understanding of multi-scale dynamic responses of rocks, both computation accuracy and numerical efficiency have been taken into account. This is achieved by further development of a continuum-discontinuous element method code, called GDEM, with a new type of dynamic bounding-surface damage model being implemented, thus forming a bounding-surface dynamic plasticity damage-GDEM model (DB-GDEM). A dynamic bounding-surface damage model is adopted, with the strength surface of Holmquist-Johnson-Cook model being employed as bounding surface. The concept of critical state, strainrate hardening, and continuum damage evolution has been taken into account for both brittle and ductile responses of rock. The model performance has been demonstrated by a few numerical simulations, including the Landau blast model, explosions under various confinements, and trapezoidal impulse loading, etc. By comparing modeling results among DB-GDEM model, linear-elastic model in GDEM, and D-P model in GDEM, it is noted that the contribution of plasticity-damage can result in the decay of stress waves and deterioration of dynamic strength. Both continuous and discontinuous mechanical behaviors of rocks have been captured well by the newly developed DB-GDEM model. The main multi-scale dynamic characteristics of rock subjected to blasting and impact, including particle movement, fragmentation of rock mass, stress-wave propagation, and failure models, have been captured. The introduction of bounding-surface plasticity damage model in GDEM would reproduce a more realistic dynamic damage response of rock compared with the original GDEM model that embedded with conventional constitutive models.

Dynamic stability of concrete structures with varying sections to underwater contact explosion: A case study of gravity dams

Concrete structures with varying sections are widely used in the fields of ocean engineering, hydraulic engineering and civil engineering. And the damage mechanism of variable-section structures to underwater contact explosion, which involves localized damage by explosion impact and instability by overall structural vibration, is very complex. The gravity dam is taken as an example, the coupled analysis model for gravity dams under underwater contact blast is established, a prototype test on the dynamic response of a gravity dam under underwater explosion is conducted to verify the reliability of the fluid-solid interaction method, and the reliability of the concrete dynamic damage model adopted in this paper is validated by a small-scale field test on the internal blast damage of a gravity dam. The damage mechanism of gravity dams subjected to underwater contact explosion is analyzed. A stability analysis method for gravity dams to underwater contact explosion is proposed, which allows simultaneous consideration of the dam stability in the blast-induced vibration phase and the static phase after damage. The dynamic stability performance of gravity dams to underwater contact explosion is analyzed. And a stability assessment criterion that could be used to assess the safety level of dams at various stages is presented.

The rock breaking mechanism of a combined high-voltage electric impulse-PDC bit drilling technology

Low rock breaking efficiency of drilling bit is one of the key factors restricting the large-scale development of oil gas in deep formations and geothermal energy resources in hot dry rock (HDR). The high-voltage electric impulse (HVEI) drilling technology has unique advantages in deep formation and HDR drilling. However, existing electrode bits form low-quality borehole walls and are not capable of performing directional drilling. To broaden the scope of engineering application of HVEI drilling, a new method combining HVEI drilling with mechanical drilling is proposed in this paper. Based on the structure of the existing electrode bits, a combined HVEI- Polycrystalline Diamond Compact (PDC) bit is designed, and the rock breaking mechanism of the bit is studied. A dynamic damage model (DDM) of rock containing an electrode bit is established on the basis of HVEI drilling's basic process. Furtherly, the HVEI-PDC rock fragmentation model is established by coupling the DDM with the heterogeneous granite model which is based on Voronoi subdivision. Through the analysis of granite fragmentation in HVEI-PDC drilling, relevant conclusions are obtained: Compared with conventional PDC bit, there is no significant difference in the torque variation of the combined bit during drilling. When the electrode spacing Le < 40mm, the energy consumption of the combined bit is higher than that of the conventional PDC bit at low rotating speed, and the efficiency is reduced. When Le≥40mm, the larger the Le, the more obvious the speed-up effect of the combined bit compared with that of the conventional PDC bit, and the lower the drilling cost. The conclusions of this paper are expected to provide a reference for promoting HVEI drilling to achieve wider industrial applications.

Coupled Chemical and Mechanical Damage Model for Acid-Corroded Sandstone

Taking the sandstone subjected to pH = 1 and 3 HCl solutions as the research object, a dynamic chemical damage model was established based on mineral dissolution theory and chemical kinetics principles. A mechanical damage model of sandstone was also established by continuous damage mechanics theory. Moreover, a coupled chemical and mechanical damage model was deduced through microstress analysis, and a damage constitutive model for acid-corroded sandstone was constructed based on the Weibull distribution and the D–P criterion. The results showed that the acid–rock reaction showed evident time dependence, and the reaction rate decreased with the prolongation of corrosion time. The chemical damage variables of corroded sandstone subjected to pH = 1 and 3 HCl solutions reached 0.34 and 0.12 after 180 days, respectively. The damages caused by chemical and mechanical actions are nonlinear with the generalized damage. The chemical action can slow down the deterioration rate of sandstone under load, which was more obvious as the immersion time extended and the pH values of the solution declined. The stress state could change the deterioration process of sandstone, and the damage rate declined as the confining pressure increased. Finally, the uniaxial and triaxial compression test results verified the theoretical model, and the two agreed well, which verified that the coupled damage model is reasonable and applicable.

Predicting the electromechanical properties of small caliber projectile impact igniter using PZT dynamic damage constitutive model considering crack propagation

Block piezoelectric ceramics (PZTs) are often used in impact igniters to provide activation energy for electric initiators. Under the action of strong impact stress, PZTs release electric energy accompanied by crack initiation, propagation and crushing. At present, the electrical output performance of PZTs in projectile is usually calculated by quasi-static piezoelectric equation without considering the dynamic effect caused by strong impact and the influence of crack propagation on material properties. So the ignition parameters are always not accurately predicted. To tackle this, a PZT dynamic damage constitutive model considering crack propagation is established based on the dynamic impact test and the crack propagation theory of brittle materials. The model is then embedded into the ABAQUS subroutine and used to simulate the electromechanical response of the impact igniter during the impact of a small caliber projectile on the target. Meanwhile, the experiments of projectile with impact igniter impact on the target are carried out. The comparison between experimental and numerical simulation results show that the established dynamic damage model can effectively predict the dynamic electromechanical response of PZTs in the missile service environment.

Research on Rock Damage Evolution Based on Fractal Theory-Improved Dynamic Tensile-Compression Damage Model

According to the characteristics that the dynamic tension of rock material is elastic brittle and the dynamic compression is elastic plastic, based on previous studies, the influence of initial damage is considered in the established compression damage model, and the calculation formula of the damage threshold used to evaluate whether the surrounding rock is affected by blasting is given. According to the classic rock impact dynamic damage model and statistical damage mechanics theory, a rock compressive and tensile statistical damage constitutive model and impact damage model under blasting load is proposed. Based on the proposed damage model and the classic dynamic tensile damage model, the numerical simulation of blasting damage was carried out, and the numerical calculation results were compared with the field measurement results. Based on the established damage model, to further clarify the damage evolution characteristics of rock under blasting load, fractal dimension theory was introduced to analyze the rock damage under blasting loads with different blasting hole network parameters. The results show that compared with the axial direction of the blast hole, the direction of blast hole diameter is the main direction of blasting fracture extension. Tensile fracture mainly occurs along the hole diameter direction, and compression fracture mainly occurs below the hole bottom. Compared with the numerical calculation results based on the classical dynamic tensile damage model, the blasting fracture range obtained according to the damage model, especially the fracture depth below the bottom of the hole, was not much different from the measured value and was closest to the measured value. The crack density of 1 us, 90 aperture, and 130 aperture was larger than that of the other working conditions. Among them, the crack density of 130 aperture was the largest, followed by 90 aperture. At 2~3 us after initiation, cracks between two blast holes, radial cracks and circumferential cracks around two blast holes, and obvious cracks were formed around blastholes; at 4~5 us after initiation, the shock wave front decreased rapidly and propagated outward in the form of the compression wave. The crack propagation velocity was much smaller than that at 1~3 us after initiation. In summary, the proposed damage model is reasonable and has certain engineering practicability.

Study on Response and Influencing Factors of Shield Single/Twin Tunnel under Seismic Loading using FLAC 3D

The research on the dynamic response and influencing factors of shield tunnel lining under earthquake demonstrates significant engineering value in guiding the design of antiseismic tunnels. In this paper, a nonlinear finite element model of soil-tunnel interaction is established based on FLAC finite difference software, and then Mohr–Coulomb elastoplastic model and dynamic plastic damage model are used to simulate the dynamic characteristics of soil and lining damage of tunnel, and the seismic waves of South Iceland are selected to analyze the residual internal force, dynamic internal force distribution, and the relative deformation of the top and bottom of the arch of the shield tunnel under the earthquake load. Meanwhile, the effects of depth tunnel, lining thickness, and tunnel diameter on the dynamic response of the tunnel are discussed. In addition, the interaction law of horizontal parallel tunnel and the amplification effect on the surface acceleration are also studied. The results show that under the action of a strong earthquake, the bearing capacity of the tunnel decreases sharply, the lining is destroyed, and a large residual internal force appears. When the buried depth of the tunnel is small, the nonlinear effect is more significant, and the R value increases at first and then decreases with the increase in the seismic acceleration. The maximum dynamic bending moment and maximum dynamic axial force of the tunnel lining aggrandize obviously with the increase in tunnel diameter and lining thickness. In particular, the dynamic bending moment has internal force redistribution and deflection under the condition of large tunnel diameter and small lining thickness. Moreover, the interaction of parallel tunnels affects the distribution of internal force and the magnitude of adjacent surface acceleration.

Numerical Simulation of Rock Dynamic NSCB Test Based on a Self-Developed Dynamic Damage Model

Elucidating and understanding the dynamic fracture characteristics of rocks play an essential role in the application of rock engineering and geophysics. In this study, based on a self-developed dynamic damage model, a rock notched semi-circle bend test with the Split Hopkinson Pressure Bar technique is numerically simulated. The study focuses on three aspects including damage evolution, energy evolution, and failure mode of rock under different loading velocities. From the simulated results, the following conclusions can be conducted: 1) the damage range increases gradually with the increase of loading velocity; 2) the crack propagates to the loading point along the symmetry axis of the samples under different loading velocities; 3) the loading velocity has an important influence on the failure mode of straight notch semi-circular marble, whose mechanism can be explained by that the local high strain rate leads to the obvious randomness and uncertainty of crack activation in rock; and 4) the energy evolution of notched semi-circle bend is vitally affected by loading velocity, and the deformation and the failure process of straight notch semicircular marble under dynamic loading can be divided into five stages according to the ratio of internal energy to total energy. The beneficial findings may provide some references in practice design from engineering problems.

Fatigue damage model and parameter estimation of cemented sand and gravel material under cyclic loading

Based on the stress-strain relationship under cyclic loading by large dynamic triaxial test, the cumulative strain distribution law of CSG materials was studied, and a dynamic damage model of CSG material was established by determining reasonable dynamic damage variables, the physical meaning and the values range for CSG material of this mode parameters were studied, too. The results show that the relationship curve between damage variable and cycle number of CSG material under cyclic loading is inverted S-type, which can be divided into three stages, and similar to the distribution law of cumulative strain. The three stages are corresponding to the closure of original defects, the initiation and propagation of new cracks, and the unstable propagation. According to the value of the damage development factors of the CSG material in the damage model, the fatigue life of CSG material under cyclic loading can be determined.

Understanding the effect of nano/micro-structures on anti-impact of nano-boron nitride filled cementitious composites

This paper aims to investigate the effect of nano/micro-structures on anti-impact property of nano-boron nitride (nano-BN) filled cementitious composites, and to predict the dynamic mechanical behavior of the composites by introducing a damage constitutive model. It is found that nano-BN can fundamentally modify the micro- and even nano-structures of cementitious composites, and therefore greatly improve the anti-impact property of the composites at the macro level. Specifically, nano-BN refines the pore structure (especially at nano-scale) of composite matrix and increases its compactness. Furthermore, by enhancing polymerization state of silicate tetrahedron in C-S-H gel, nano-BN improves the micromechanical properties of hydration products at different micro-zones. Consequently, dynamic mechanical property of cementitious composites at macro-level is enhanced, and the energy absorption capacity is improved. In addition, dynamic damage model indicates that nano-BN inhibits the damage of cementitious composites, but its inhibition form changes with the strain rate.

FloodStroem: A fast dynamic GIS-based urban flood and damage model

Due to climate change and urbanization, urban flood modelling has become an increasingly important tool in assessing flooding and associated damage costs. However, large computational demands of state-of-the art hydrodynamic flood models makes multiple and real-time simulations unfeasible. This study presents a fast-dynamic GIS-based flood model, FloodStroem. FloodStroem generates a surface network of depressions (bluespots) and flow paths, and routes surcharged water from a subsurface drainage model through the network resulting in flood depth maps and associated damage costs. FloodStroem is tested on three sub-catchments in Elster Creek Catchment, Melbourne, Australia and benchmarked against the 2D distributed hydrodynamic model MIKE 21 and two other simplified models, RUFIDAM and CA-ffé. FloodStroem is robust to the number of bluespots included. For the three sub-catchments, FloodStroem can reproduce flooding time, pattern, depth, and damage costs sufficiently, but has a tendency to underestimate flooding upstream and overestimate flooding downstream. Performance is best for the large, steep sub-catchments and largest rainstorms, where FloodStroem performs better than the two other simplified models. The Critical Success Index (CSI) ranges from 23% for a 5-year storm event in a flat catchment to 65% for a 100-year return period for a steeper catchment. With respect to simulation time, FloodStroem is five orders of magnitude faster than the 2D hydrodynamic model, and 33 times faster when including the entire model setup time, which has potential for further reduction by optimization of the workflow.

Dynamic compression mechanical behavior and damage model of singly-jointed samples

The dynamic mechanical behavior of jointed rock mass plays a key role in the blasting excavation from mining and tunneling engineering. To investigate the influence of joint parameters (e.g., joint length, joint position and joint type) on the mechanical behavior of singly-jointed samples, dynamic impact compression tests are performed on prefabricated rock-like samples using the Split Hopkinson Pressure Bar system. The test results show that the dynamic stress-strain curves of the samples can be divided into elastic phase, plastic phase, unstable crack propagation phase and post-failure phase. Although the dynamic failure modes of all samples are tensile failures, as recorded by a high-speed camera, the joint position demonstrates an important effect on the crack propagation. It is found that the absorption energy, transmission energy and absorption energy per unit volume are all in a positive linear relation with the strength coefficient, while the reflection energy shows a negative linear correlation. The dynamic peak strength of jointed sample increases with the decrease of the joint length, and increases as the joint closes, whereas it decreases as the distance of the joint from the center of the sample decreases. Combined with the strength damage of jointed samples, the damage weight theory for joint positions of singly-jointed sample is proposed and verified. The theory indicates that the damage weight reduces linearly by ~50% from the sample center to the edge. In addition, a damage model is proposed and verified for the singly-jointed samples to reflect the correlation of damage factor induced by different joint parameters.

Estimation of Fines Generation in Blasting Using Dynamic Rock Properties and a Near-Field PPV Damage Model

In the hard-rock mining industry, the generation of fines during blasting is an important issue because it has a significant effect on production processes. Although various approaches have been used to estimate fines generation in recent decades, as a practical matter, measuring the amount of fines is nearly impossible given the technical limitations and the scale of mine blasts. In this study, a dynamic PPV damage model was developed and applied to predict fines generation as a result of blasting. This modified version of the crushed zone model (CZM) considers dynamic rock properties and peak particle velocity (PPV), which represents the induced stress in blasting. Dynamic rock-fracturing tests were conducted using a split Hopkinson pressure bar (SHPB) to determine the parameters that represent the relationships between rock strength and strain rate as well as the relationships between fines amount and strain rate in the model. A case study was conducted that entailed determining the radius of the crushed zone for given blast designs and rock properties and then measuring the fines amount within this crushed zone. This case study indicated that the dynamic PPV model can provide a rough estimate of fines generation for given dynamic rock properties and blast design parameters and that this method has the potential to be a useful indicator, or index, of fines generation.

Dynamic Mechanical Damage and Non-Shock initiation of a New Polymer Bonded Explosive during Penetration.

Complexities of heating mechanisms make it difficult to investigate the safety of a polymer bonded explosive (PBX) charge of earth-penetrating-weapons (EPWs) during penetration. In this paper, the dynamic damage and non-shock initiation of PBX1314 (60 wt % hexahydro-1, 3, 5-trinitro-1, 3, 5-s-triazine (RDX), 16 wt % aluminum, 24 wt % hydroxy-terminated polybutadiene (HTPB)) during penetration is investigated through experiments and simulations. In the experiments, steel projectiles filled with PBX1314 are launched to penetrate concrete targets. In the results, non-shock initiations occur on the tail surface of PBX1314 along with mechanical damage of the tail and middle part of PBX1314. A dynamic damage and initiation model is proposed to characterize the effects of microcracks on the mechanical and thermal responses of PBX1314. Investigation based on the model suggests that microcrack interfacial friction plays significant roles in damage, heat generation and localization in PBX1314. A non-shock initiation criterion is developed based on macroscale variables in PBX1314. Numerical simulations of the penetration experiments are performed by using the proposed model and criterion. The mechanical damage and non-shock initiation of PBX1314 in the experiments are successfully predicted. The simulation results indicate that the tail of PBX1314 impacts the projectile repeatedly during penetration. Finally, the initiation criterion is satisfied because of frictional heat localization near microcrack surfaces and initiation is activated in the tail of PBX1314.

Investigation into Energy Dissipation During Grouting Uplift

Concrete covering damage is often caused by inadequate control of the grouting process. As such, in this work, a grouting nonlinear dynamic damage model was established to explore the concrete covering damage mechanism, which is crucial to the safety of dam grouting. Specifically, this study was designed to: (1) investigate the hysteresis energy dissipation and hysteresis damage mechanisms during the concrete covering’s dynamic response process and (2) assess the concrete covering’s nonlinear dynamic response and hysteresis energy dissipation under different grouting pressures, joint apertures, cement liquid viscosities, and grouting flows. The results show that the pulsation amplitude and cumulative hysteresis energy dissipation signifcantly affects the concrete covering damage rate, which quickly increases with damage energy dissipation rate in unstable grouting pressure.

A rate-dependent dynamic damage model in peridynamics for concrete under impact loading

To study the dynamic behavior and impact damage and failure of concrete materials and structures, a dynamic damage model was reformulated under the framework of the non-local peridynamic theory in this paper. The stretch rate of material bonds, equivalent to the strain rate in classical continuum mechanics, was introduced, and a rate-dependent peridynamic model describing the dynamic damage and failure of concrete materials was then proposed, taking both the dynamic failure of bonds and the rate-sensitivity of damage evolution under different stretch rate into account. The connection between the stretch rate and strength and tensile and compressive failure of concrete materials was established in the peridynamic model. To verify the proposed dynamic damage model for concrete failure, several typical examples simulating the mixed-mode fracture of concrete specimen were investigated. The failure mode, crack propagation paths and the crack propagation speed in the specimen in different cases were captured, which agree well with the experimental results and available numerical results. After model validation, the effect of the number and length of pre-existing cracks on the dynamic failure of concrete components was investigated further.

A study on low‐velocity impact performance of notched GFRP composites repaired by different composite patches: Experiment and modeling

AbstractLow‐velocity impact performance of notched glass fiber reinforced plastic composites repaired by bonding external composite patches was investigated by experimental and numerical methods. Various patches of different fiber materials such as carbon and glass fiber and thickness were considered under different impact energy levels. The continuum damage mechanics based on a dynamic progressive damage model was using to build the finite element model and cohesive elements were used between the composite patch and notched composite plate. Five different failure criteria based on three‐dimensional Hashin damage models were implemented by the explicit finite element subroutine ABAQUS‐VUMAT with degradation model and used to compare experimental damage areas. The experimental contact force, kinetic energy histories, and experimental damage areas were calculated and compared the numerical ones. While the experimental data confirm the efficiency of the proposed model, they show consistent results with the numerical model. Finally, using the composite patch is succeeded to avoid impact damage. This research provides fundamental support for the appropriate selection of external composite patch type and use of the degradation model with different failure model to achieve high‐efficiency simulation under impact loading.

Experimental investigation on dynamic response and damage models of circular RC columns subjected to underwater explosions

Reinforced concrete (RC) columns are widely used as supporting structures for high-piled wharfs. The study of damage model of a RC column due to underwater explosion is a critical issue to assess the wharf’s antiknock security. In this study, the dynamic response and damage model of circular RC columns subjected to underwater explosions were investigated by means of scaled-down experiment models. Experiments were carried out in a 10.0 m diameter tank with the water depth of 2.25 m, under different explosive quantities (0.025 kg–1.6 kg), stand-off distances (0.0 m–7.0 m), and detonation depths (0.25 m–2.0 m). The shock wave load and dynamic response of experiment models were measured by configuring sensors of pressure, acceleration, strain, and displacement. Then, the load distribution characteristics, time history of test data, and damage models related to present conditions were obtained and discussed. Three damage models, including bending failure, bending-shear failure and punching failure, were identified. In addition, the experience model of shock wave loads on the surface of a RC column was proposed for engineering application.

Numerical analysis of hysteretic behavior for RAC structure under earthquake loading

ABSTRACTThe hysteretic properties of RAC structure subjected to different strain rates are analyzed, and the displacement ductility is assessed. It is revealed that, under earthquake wave excitation with the increasing strain rate, the lateral stiffness, the bearing capacity, and the energy dissipation increases progressively. However, the ductility of RAC structure decreases gradually with the increasing strain rate. The rate-dependent capacity curve model of RAC structure is suggested. The damage evolution of RAC structure subjected to different strain rates is investigated. Furthermore, the dynamic damage model of RAC structure in which the strain rate effect is taken into account is proposed.