Perforation studies of concrete panel under high velocity projectile impact based on an improved dynamic constitutive model

The finite-depth concrete panels have been widely applied in the protective structures,and its impact resistance and dynamic fracture failures,especially the scabbing/perforation limits,under high velocity projectile impact,are mainly concerned by protective engineers,which are numerically studied based on an improved dynamic concrete model in this study.Firstly,based on the framework of the KCC(Karagozian&Case concrete)model,a dynamic concrete model is proposed which considers an independent tensile damage model and a continued transition between dynamic tensile and compressive properties.Secondly,the strength surface,equation of state and damage parameters of the proposed model are comprehensively calibrated by a triaxial compressive test with high confinement pressure,the rationality of which is further verified based on the single element tests,e.g.,uniaxial and triaxial compression as well as uniaxial,biaxial and triaxial tension.Thirdly,a series of projectile high velocity impact tests on thin and thick concrete panels are simulated,which indicates that the projectile residual velocity and dynamic fracture failures are reproduced satisfactorily,while the KCC model underestimates both the spalling and scabbing dimensions severely.Finally,based on the validated concrete model and finite element analyses approach,the validations of the existing five empirical formulae are evaluated,in terms of the depth of penetration(DOP)and scabbing/perforation limits of concrete panel.Both the Army corps of engineers(ACE)and modified National Defense Research Committee(NDRC)formulae are recommended in the design of the protective structure to avoid scabbing failure.

Experimental and numerical investigation on the dynamic shear failure mechanism of sandstone using short beam compression specimen

In this study,a novel testing method is proposed to characterize the dynamic shear property and failure mechanism of rocks by introducing the short beam compression(SBC)specimen into the split Hopkinson pressure bar(SHPB)system.Firstly,the stress distribution of SBC specimen is comprehensively analyzed by finite element method(FEM),and the results show that the optimal notch separation ratio of SBC specimen is C/H?0.2 to achieve successful dynamic simple-shear tests.Then,dynamic shear tests are conducted on sandstone using the SBC-SHPB method.Via careful pulse shaping technique,the dynamic force balance is guaranteed for SBC specimens,and the testing results show that the dynamic shear strength of sandstone is significantly rate-dependent.Combining the results of dynamic compression and tension tests,the failure envelopes of sandstone under different loading rates are obtained in the principle stress plane.It is found that the failure envelope of sandstone constantly expands outwards with increasing loading rate.Moreover,the energy partition of SBC specimen is quantified by virtue of high-speed digital image correlation(DIC)technique.The results show that the kinetic energy portion is non-negligible,and the shear fracture energy increases with increasing loading rate.In addition,the microscopic shear cracking mechanism of SBC specimen is analyzed by the thin section observation:the intra-granular(TG)fracture of minerals dominates the dynamic shear failure of sandstone,and the portion of TG fracture increases with increasing loading rate.This study provides a convenient and reliable method to investigate the dynamic shear property and failure mechanism of rocks.

Predicting impact strength of perforated targets using artificial neural networks trained on FEM-generated datasets

The paper considers application of artificial neural networks(ANNs)for fast numerical evaluation of a residual impactor velocity for a family of perforated PMMA(Polymethylmethacrylate)targets.The ANN models were trained using sets of numerical results on impact of PMMA plates obtained via dynamic FEM coupled with incubation time fracture criterion.The developed approach makes it possible to evaluate the impact strength of a particular target configuration without complicated FEM calculations which require considerable computational resources.Moreover,it is shown that the ANN models are able to predict results for the configurations which cannot be processed using the developed FEM routine due to numerical instabilities and errors:the trained neural network uses information from successful computations to obtain results for the problematic cases.A simple static problem of a perforated plate deformation is discussed prior to the impact problem and preferable ANN architectures are presented for both problems.Some insight into the perforation pattern optimization using a genetic algorithm coupled with the ANN is also made and optimized perforation patterns which theoretically enhance the target impact strength are constructed.

Dynamic tensile behaviour and crack propagation of coal under coupled static-dynamic loading

The fracture behaviour and crack propagation features of coal under coupled static-dynamic loading conditions are important when evaluating the dynamic failure of coal.In this study,coupled static-dynamic loading tests are conducted on Brazilian disc(BD)coal specimens using a modified split Hopkinson pressure bar(SHPB).The effects of the static axial pre-stress and loading rate on the dynamic tensile strength and crack propagation characteristics of BD coal specimens are studied.The average dynamic indirect tensile strength of coal specimens increases first and then decreases with the static axial pre-stress increasing.When no static axial pre-stress is applied,or the static axial pre-stress is 30%of the static tensile strength,the dynamic indirect tensile strength of coal specimens shows an increase trend as the loading rate increases.When the static axial pre-stress is 60%of the static tensile strength,the dynamic indirect tensile strength shows a fluctuant trend as the loading rate increases.According to the crack propagation process of coal specimens recorded by high-speed camera,the impact velocity influences the mode of crack propagation,while the static axial pre-stress influences the direction of crack propagation.The failure of coal specimens is a coupled tensile-shear failure under high impact velocity.When there is no static axial pre-stress,tensile cracks occur in the vertical loading direction.When the static axial pre-stress is applied,the number of cracks perpendicular to the loading direction decreases,and more cracks occur in the parallel loading direction.

A NOVEL METHOD FOR MEASURING AND CHARACTERIZING DYNAMIC FRACTURE-INITIATION TOUGHNESS OF ELASTIC-PLASTIC MATERIALS

The characterization and testing methods of the dynamic fractureinitiation toughness of elas- tic-plastic materials under tensileimpact are studied. By using the self-designed bar-bar tensile impactappa- ratus, a novel test method for studying dynamicfracture-initiation ahs been proposed based on the one-di- mensionaltest principle. The curve of average load v. s. displacement (P-δ)is smooth until unstable crack propagation, and the kinetic energywhich does not contribute to the crack growth can be removed fromtotal work done by external-force to the specimen.

DETERMINATION OF THE DYNAMIC STRESS INTENSITY FACTORS,K_Ⅰ~d AND K_Ⅱ~d,FOR A MIXED-MODE PROPAGATING CRACK

In this paper,the dynamic propagation problem of a mixed-mode crack was studied by means of the experimental method of caustics.The initial curve and caustic equations were derived un- der the mixed-mode dynamic condition.A multi-point measurement method for determining the dy- namic stress intensity factors,K_Ⅰ~d and K_Ⅱ~d,and the position of the crack tip was developed.Several other methods were adopted to check this method,and showed that it has a good precision.Finally, the dynamic propagating process of a mixed-mode crack in a three-point bending beam specimen was investigated with our method.

A NOVEL METHOD FOR EVALUATING PLANE STRESS DYNAMIC FRACTURE TOUGHNESS OF 0Cr18Ni10Ti STAINLESS STEEL WELDED JOINTS

A novel method was proposed for the evaluation of Mode I dynamic fracture toughness （DFT） under plane stress and small scale yielding conditions for welded joints of stainless steel （SS）, 0Cr18Ni10Ti. In a hybrid experimental-numerical approach, the experiments were carried out on the Hopkinson pressure bar apparatus, and three dimensional （3D） transient numerical simulations were performed by a finite element （FE） computer program. Macroscopical plastic deformation was observed at the loading and supporting points, on the specimens, after the test, which could cause a large error if omitted in the numerical simulation. Therefore, elustic-viscoplustic analysis was performed on the specimen by adopting the Johnson-Cook （J-C） model to describe the rate-dependent plastic flow behavior of the material. The material heterogeneity in the mismatched welded joints, induced by the difference in the base metal （BM） and the weld metal （WM） in yield stress, has also been taken into consideration by using the J-C models separately. Good accordance was obtained between the experimental and the computational results by the present approach. The relationship between plane stress DFT and loading rate was also obtained on the order of 108 MPa.m^1/2.s^-1.

Experimental study of coal fracture dynamics under the influence of cyclic freezing-thawing using shear elastic waves

Cyclic freezing-thawing can lead to fracture development in coal,affecting its mechanical and consumer properties.To study crack formations in coal,an ultrasonic sounding method using shear polarized waves was proposed.Samples of three coal types(anthracite,lignite and hard coal)were tested.The research results show that,in contrast to the shear wave velocity,the shear wave amplitude is extremely sensitive to the formation of new cracks at the early stages of cyclic freezing-thawing.Tests also show an inverse correlation between coal compressive strength and its tendency to form cracks under temperature impacts;shear wave attenuation increases more sharply in high-rank coals after the first freezing cycle.Spectral analysis of the received signals also confirmed significant crack formation in anthracite after the first freeze-thaw cycle.The initial anisotropy was determined,and its decrease with an increase in the number of freeze-thaw cycles was shown.The data obtained forms an experimental basis for the development of new approaches to preserve coal consumer properties during storage and transportation under severe natural and climatic conditions.

Dynamic fracture toughness of high strength metals under impact loading:increase or decrease

An elusive phenomenon is observed in previous investigations on dynamic fracture that the dynamic fracture toughness （DFT） of high strength metals always increases with the loading rate on the order of TPa.m1/2.s-1. For the purpose of verification, variation of DFT with the loading rate for two high strength steels commonly used in the aviation industry, 30CrMnSiA and 40Cr, is studied in this work. Results of the experiments are compared, which were conducted on the modified split Hopkinson pressure bar （SHPB） apparatus, with striker velocities ranging from 9.2 to 24.1 m/s and a constant value of 16.3 m/s for 30CrMnSiA and 40Cr, respectively. It is observed that for 30CrMnSiA, the crack tip loading rate increases with the increase of the striker velocity, while the fracture initiation time and the DFT simultaneously decrease. However, in the tests of 40Cr, there is also an increasing tendency of DFT, similar to other reports. Through an in-depth investigation on the relationship between the dynamic stress intensity factor （DSIF） and the loading rate, it is concluded that the generally increasing tendency in previous studies could be false, which is induced from a limited striker velocity domain and the errors existing in the experimental and numerical processes. To disclose the real dependency of DFT on the loading rate, experimentsneed to be performed in a comparatively large striker velocity range.

A fractional differential constitutive model for dynamic stress intensity factors of an anti-plane crack in viscoelastic materials

Fractional differential constitutive relationships are introduced to depict the history of dynamic stress inten- sity factors （DSIFs） for a semi-infinite crack in infinite viscoelastic material subjected to anti-plane shear impact load. The basic equations which govern the anti-plane deformation behavior are converted to a fractional wave-like equation. By utilizing Laplace and Fourier integral transforms, the fractional wave-like equation is cast into an ordinary differential equation （ODE）. The unknown function in the solution of ODE is obtained by applying Fourier transform directly to the boundary conditions of fractional wave-like equation in Laplace domain instead of solving dual integral equations. Analytical solutions of DSIFs in Laplace domain are derived by Wiener-Hopf technique and the numerical solutions of DSIFs in time domain are obtained by Talbot algorithm. The effects of four parameters α, β, b1, b2 of the fractional dif- ferential constitutive model on DSIFs are discussed. The numerical results show that the present fractional differential constitutive model can well describe the behavior of DSIFs of anti-plane fracture in viscoelastic materials, and the model is also compatible with solutions of DSIFs of anti-plane fracture in elastic materials.

Application of split Hopkinson tension bar technique to the study of dynamic fracture properties of materials

A novel approach is proposed in determining dy- namic fracture toughness （DFT） of high strength steel, using the split Hopkinson tension bar （SHTB） apparatus, com- bined with a hybrid experimental-numerical method. The center-cracked tension specimen is connected between the bars with a specially designed fixture device. The fracture initiation time is measured by the strain gage method, and dynamic stress intensity factors （DSIF） are obtained with the aid of 3D finite element analysis （FEA）. In this approach, the dimensions of the specimen are not restricted by the connec- tion strength or the stress-state equilibrium conditions, and hence plane strain state can be attained conveniently at the crack tip. Through comparison between the obtained results and those in open publication, it is concluded that the ex- perimental data are valid, and the method proposed here is reliable. The validity of the obtained DFT is checked with the ASTM criteria, and fracture surfaces are examined at the end of paper.

Numerical modelling of flow and transport in rough fractures

Simulation of flow and transport through rough walled rock fractures is investigated using the latticeBoltzmann method （LBM） and random walk （RW）, respectively. The numerical implementation isdeveloped and validated on general purpose graphic processing units （GPGPUs）. Both the LBM and RWmethod are well suited to parallel implementation on GPGPUs because they require only next-neighbourcommunication and thus can reduce expenses. The LBM model is an order of magnitude faster onGPGPUs than published results for LBM simulations run on modern CPUs. The fluid model is verified forparallel plate flow, backward facing step and single fracture flow; and the RWmodel is verified for pointsourcediffusion, Taylor-Aris dispersion and breakthrough behaviour in a single fracture. Both algorithmsplace limitations on the discrete displacement of fluid or particle transport per time step to minimise thenumerical error that must be considered during implementation. 2014 Institute of Rock and Soil Mechanics, Chinese Academy of Sciences. Production and hosting byElsevier B.V. All rights reserved.

Study on dynamic fracture behavior of TA15ELI alloy under mode-Ⅱ loading by caustics method

The dynamic fracture behavior of TA 15ELI alloy with lath-like microstructure was studied by caustics method. Specimens with double-side pre-notch were tested under the plane-stress condition at mode-II loading with a drop hammer system. Caustics information recorded in films illustrated the histories of both crack length and stress intensity factor. The dynamic fracture toughness and crack growth velocity of TA15ELI with lath-like microstructure were determined to be 279 MPa.m1/2 and 32.6 m/s, respectively. SEM fractograph analysis showed a mixed feature of mainly plastic mode for TA 15ELI alloy in dynamic mode-II fracture. Shear localization was observed in the vicinity of the crack initiation area.

Dynamic stress intensity factor K_(III) and dynamic crack propagation characteristics of anisotropic materials

Based on the mechanics of anisotropic materials, the dynamic propagation problem of a mode Ⅲ crack in an infinite anisotropic body is investigated. Stress, strain and displacement around the crack tip are expressed as an analytical complex function, which can be represented in power series. Constant coefficients of series are determined by boundary conditions. Expressions of dynamic stress intensity factors for a mode Ⅲ crack are obtained. Components of dynamic stress, dynamic strain and dynamic displacement around the crack tip are derived. Crack propagation characteristics are represented by the mechanical properties of the anisotropic materials, i.e., crack propagation velocity M and the parameter ~. The faster the crack velocity is, the greater the maximums of stress components and dynamic displacement components around the crack tip are. In particular, the parameter α affects stress and dynamic displacement around the crack tip.

Experimental study on dynamic pipe fracture in consideration of hydropower plant model

In the case of sudden valve closure, water hammer creates the most powerful pressure and damage to pipeline systems. The best way to protect the pipeline system is to eliminate water hammer. The main reasons for water hammer occurrence are valve closure, high initial velocity, and static pressure. However, it is difficult to eliminate water hammer. Water hammer tends to occur when the valve is being closed. In this study, the pipe fracture caused by static water pressure, gradually increasing pressure, and suddenly increasing pressure were compared experimentally in a breaking PVC test pipe. The quasi-static zone, the dynamic zone, and the transition zone are defined through the results of those experiments, with consideration of the fracture patterns of test pipes and impulses. The maximum pressure results were used to design the pipeline even though it is in the dynamic zone.

DYNAMIC FRACTURE TOUGHNESS OF ULTRASTRENGTH STEELS FOR AIRCRAFT

The plots of load vs deflection(P-D)for two ultra-strength steels 30CrMnSiNi2A and 300M has been examined on a Charpy impact tester with digital memory and microcomputer. A criterion was found to availably represent the dynamic fracture toughness,K_(Ic)~D ,of the steels under impact loading.The K_(Ic)~D,.can be calculated with suggesting that the turning point of change in compliance on the P-D plot is the point of destabilized crack propagation.The K_(Ic)~D of steel 300M,quenched at 870℃ ,separately tempered at 300℃ and 450℃,was esti- mated to be 55—70 MN/m^(3/2)and 54—67 MN/m^(3/2)respectively.The K_(Ic)calculated with accuracy about 20% seems to be available to the engineering evaluation.

CRACK INITIATION POINT DETERMINATION AND DYNAMIC FRACTURE TOUGHNESS FOR CHARPY PRE-CRACKED SPECIMEN

The method to detect the crack initiation point of Charpy pre-cracked specimen under dy- namie loading was studied using strain gauge.The load-time curve and nominal strain-time curve at the crack tip for impact testing specinens may be shnultaneously measured by twin-channel oscilloscope with high speed sampling and diskette storing.Based on the dynam- ic finite element simulation of impact response of Charpy specimen,the measuring method of dynamic fracture toughness was analysed and some problems in previous dynamic fracture toughness measurement were discussed.

Dynamic Fracture of Ti-5553 Alloy in Taylor Impact Test

The dynamic fracture behavior of a new near-beta Ti-5Al-5Mo-5V-3Cr-1Fe（Ti-5553）alloy under a high strain rate loading was investigated systemically using the Taylor impact test,over the impact velocity ranging from156 ms-1 to 256 ms-1.An optical microscope（OM）and a scanning electron microscope（SEM）were used to characterize the microstructure evolution.The experimental results have demonstrated that the velocity from deformation to fracture is 256 ms-1 for the alloy with anα＋βduplex microstructure including more primaryαphase,while the velocity is 234 ms-1 for the alloy with a duplex microstructure including less primaryα phase.From the impact fracture morphologies,smooth and smeared surfaces and ductile dimple areas can be observed.The failure mode of the titanium alloy with both microstructures is adiabatic shear banding.According to the fracture analysis,the ductile fracture area with the dimple area in the alloy with much more primaryαphase were more than that with less primaryαphase.Compared to the duplex microstructure with less primaryα phase,Ti-5553 alloy with more primaryαphase exhibited a better capability to resist an adiabatic shear damage.

Dynamic Fracture of a Semi-Crystalline Bio-Based Polymer Pipe: Effect of Temperature

The influence of temperature on the resistance to rapid crack propagation of a semi-crystalline bio-based polymer was studied. The experimental results described in this study allow to initiate a first discussion on the role of viscosity and its link with the fracture behaviour and a heterogeneous microstructure such as the semi-crysalline polymer. Dynamic fracture tests on pipes were carried out. It would appear that a temperature decrease of approximately 40℃ relative to ambient has no significant influence on the average crack propagation velocity (≈0.6cR), fracture energy and surface roughness. On the contrary, crack propagation paths seem to vary with temperature. The difference in fracture behaviour between the amorphous and crystalline phase varies significantly as a function of temperature. The difference between the initiation resistance and the rapid propagation also varies. This difference seems to be significantly reduced by lowering the temperature. The mechanisms of cavitation damage and plastic flow are increasingly limited by the decrease in temperature (and therefore in macromolecular mobility). Crack propagation in the pipe is more extensive and therefore more critical. This is emphasised in particular by the probability of the material to be macro-branched as the temperature decreases.

Quasimolecular Dynamic Simulation for Bending Fracture of Laminar Composite Materials

Recently, quasimolecular dynamics has been successfully used to simulate the deformation characteristics of actual size solid materials. In quasimolecular dynamics, which is an attempt to bridge the gap between atomistic and continuum simulations, molecules are aggregated into large units, called quasimolecules, to evaluate large scale material behavior. In this paper, a 2-dimensional numerical simulation using quasimolecular dynamics was performed to investigate laminar composite material fractures and crack propagation behavior in the uniform bending of laminar composite materials. It was verified that under bending deformation laminar composite materials deform quite differently from homogeneous