Mesh size sensitivity of the combined FEM/DEM fracture and fragmentation algorithms

In the context of the combined finite-discrete element method a number of algorithms aimed at modelling progressive failure, fracture and fragmentation of solids under extreme loading conditions have been proposed in the last few years. The fracture patterns obtained by recently proposed algorithms are impressive. However, sensitivity of these algorithms to both mesh size and mesh orientation remains an open question. The aim of this paper is to further investigate sensitivity to mesh size of the recently proposed so called combined single and smeared crack model. Sensitivity to mesh orientation is outside scope of this paper and is discussed only qualitatively.     

Deformation and fragmentation behaviour of exploded metal cylinders and the effects of wall materials,configuration, explosive energy and initiated locations

Tubular metal specimens are explosively expanded to fragmentation, and the effects of wall materials, thicknesses, notches in walls, explosive driver diameters and the initiated locations are investigated on the deformation and fracture behavior of the cylinders experimentally and numerically. In the standard tests, the driver is a column of low density powder of high explosive PETN, inserted coaxially into the bore of a smooth-walled cylinder and initiated by exploding a bundle of fine copper wires at the column axis using a discharge current from a high-voltage capacitor bank. Notched cylinders with single axial slit, various grooves in the walls, and smooth cylinders with varied wall thicknesses were tested. Low-carbon steels and an aluminum alloy A5052 were provided in addition to the standard smooth-walled 304 stainless steel cylinder, and they were fully or partially charged with varying explosive column diameters. The initiated locations in the explosive column are changed for comparison, placing the bundle of fine copper wires eccentrically from the central axis or replacing the fine wire bundle into a bold wire line except the middle portion at the central axis for central point initiation. Additionally an explosive-filled cylindrical vessel with welded endplate at the one end is initiated at the other end explosive surface exploding wire-rows and expanded by axially propagating explosive detonation to fracture for comparison with the uniform expansion. Deformation and crack initiation of expanding cylinders are observed with high speed camera, and most of the fragments have been recovered successfully. Recovered fragments have been measured and investigated using a fragmentation model. The effects of test parameters on the deformation and fracture behavior of metallic cylinders are discussed with use of numerical simulations, indicating applicability of the fragmentation model and suggesting future necessary studies.     

Simulations of fracture and fragmentation of geologic materials using combined FEM/DEM analysis

Results are presented from a study investigating the effect of explosive and impact loading on geological media using the Livermore distinct element code (LDEC). LDEC was initially developed to simulate tunnels and other structures in jointed rock masses with large numbers of intact polyhedral blocks. However, underground structures in jointed rock subjected to explosive loading can fail due to both rock motion along preexisting interfaces and fracture of the intact rock mass itself. Many geophysical applications, such as projectile penetration into rock, concrete targets, and boulder fields, require a combination of continuum and discrete methods in order to predict the formation and interaction of the fragments produced. In an effort to model these types of problems, we have implemented Cosserat point theory and cohesive element formulations into the current version of LDEC, thereby allowing for dynamic fracture and combined finite element/discrete element simulations. Results of a large-scale LLNL simulation of an explosive shock wave impacting an elaborate underground facility are also discussed. It is confirmed that persistent joints lead to an underestimation of the impact energy needed to fill the tunnel systems with rubble. Non-persistent joint patterns, which are typical of real geologies, inhibit shear within the surrounding rock mass and significantly increase the load required to collapse a tunnel.     

内部爆炸加载条件下钢管变形与破碎研究

用高速摄影研究了钢管膨胀历程,并对破碎机制进行了分析,结果表明,材料动态塑性是决定破片最终速度的主要因素,圆管膨胀时外表面形成以剪切为主的裂纹,并向内扩展,接近内表面的绝热剪切带伴随着圆管的膨胀而扩展,并未出现失稳现象,但在正应力的作用下成为优先的断裂通道,决定破片的尺寸和形态,中碳Si-Mn贝氏体钢与50SiMnVB钢的破碎性能相近,但贝氏体钢动态塑料性很更好,破碎的膨胀量较大,更有利于提高破片初速,是弹比较理想的候选材料。     

Total Lagrangian SPH modelling of necking and fracture in electromagnetically driven rings

This paper describes research on the prediction of necking and failure in metals at very high strain rates. The model developed in this paper uses a total Lagrangian SPH formulation with a normalised kernel. The detailed data from electromagnetically driven ring experiments by Zhang and Ravi-Chandar (Int J Fract 142:183–217, 2006) is used to evaluate the accuracy of the model predictions. In order to correctly model fracture in the total Lagrangian SPH formulation a visibility criterion based on a truncated cone has been implemented to remove particles obscured by a failed particle. A Johnson-Cook plasticity model is used in combination with a Lemaitredamage model to describe the plastic deformation and fracture of the rings. The effect of Joule heating due to the current induced in the ring is taken into account in the constitutive model. The acceleration due to the ring currents was implemented in the SPH code as a body force. The results demonstrate that this type of model is capable of predicting the number of fragments as well as the time of fracture. In agreement with experimental data, the model also predicts arrested necks and bending in the fragments.     

Experimental studies on the dynamic tensile behavior of Ti–6Al–2Sn–2Zr–3Mo–1Cr–2Nb–Si alloy with Widmanstatten microstructure at elevated temperatures

The tensile behavior of a newly developed Ti–6Al–2Sn–2Zr–3Mo–1Cr–2Nb–Si alloy, referred as TC21, is investigated at temperatures ranging from 298 to 1023 K and under constant strain rate loadings ranging from 0.001 to 1270 s⁻¹. The results show that temperature and strain rate have significant effects on the tensile behavior of the material. At low strain rates of 0.001 and 0.05 s⁻¹, a discontinuity is found in the yield stress–temperature curve. And the discontinuity temperature increases with increasing strain rate. The analysis of temperature and strain rate dependence of unstable strain indicates a high-velocity-ductility phenomenon at elevated temperatures. Scanning electron microscope (SEM) analysis shows that the material is broken in a mixture manner of ductile fracture and intergranular fracture under low strain rates at room temperature, while the fracture manner changes to totally ductile fracture under other testing conditions. The width and depth of ductile dimples increase with increasing temperature. No adiabatic shear band is found in the tensile deformation of the material.     

Detection of fibre fracture and ply fragmentation in thin-ply UD carbon/glass hybrid laminates using acoustic emission

This paper investigates the link between acoustic emission (AE) events and the corresponding damage modes in thin-ply UD carbon/glass hybrid laminates under tensile loading. A novel configuration was investigated which has not previously been studied by AE, where the laminates were fabricated by embedding thin carbon plies between standard thickness translucent glass plies to produce progressive fragmentation of the carbon layer and delamination of the carbon/glass interface. A criterion based on amplitude and energy of the AE event values was established to identify the fragmentation failure mode. Since the glass layer was translucent, it was possible to quantitatively correlate the observed fragmentation during the tests and the AE events with high amplitude and energy values. This new method can be used as a simple and advanced tool to identify fibre fracture as well as estimate the number and sequence of damage events that are not visible e.g. in hybrid laminates with thick or non-transparent layers as well as when the damage is too small to be visually detected.     

Texture evolution and dynamic mechanical behavior of cast AZ magnesium alloys under high strain rate compressive loading

In this study, texture and compressive mechanical behavior of three cast magnesium alloys, including AZ31, AZ61 and AZ91, were examined over a range of strain rates between 1000 and 1400 s⁻¹ using Split Hopkinson Pressure Bar. Texture measurements showed that after shock loading, initial weak texture of the cast samples transformed to a relatively strong (00.2) basal texture that can be ascribed to deformation by twinning. Furthermore, increasing the aluminum content in the alloys resulted in increase in the volume fraction of β-Mg₁₇Al₁₂ and Al₄Mn phases, strength and strain hardening but ductility decreased at all strain rates. Besides, it was found for each alloy that the tensile strength and total ductility increased with strain rate. By increasing the strain rate, the maximum value of strain hardening rate occurred at higher strains. Also, it is suggested that a combination of twinning and second phase formation would affect the hardening behavior of the cast AZ magnesium alloys studied in this research.     

Experimental study on tensile property of AZ31B magnesium alloy at different high strain rates and temperatures

As the lightest metal material, magnesium alloy is widely used in the automobile and aviation industries. Due to the crashing of the automobile is a process of complicated and highly nonlinear deformation. The material deformation behavior has changed significantly compared with quasi-static, so the deformation characteristic of magnesium alloy material under the high strain rate has great significance in the automobile industry. In this paper, the tensile deformation behavior of AZ31B magnesium alloy is studied over a large range of the strain rates, from 700 s⁻¹ to 3 × 10³ s⁻¹ and at different temperatures from 20 to 250 °C through a Split-Hopkinson Tensile Bar (SHTB) with heating equipment. Compared with the quasi-static tension, the tensile strength and fracture elongation under high strain rates is larger at room temperature, but when at the high strain rates, fracture elongation reduces with the increasing of the strain rate at room temperature, the adiabatic temperature rising can enhance the material plasticity. The morphology of fracture surfaces over wide range of strain rates and temperatures are observed by Scanning Electron Microscopy (SEM). The fracture appearance analysis indicates that the fracture pattern of AZ31B in the quasi-static tensile tests at room temperature is mainly quasi-cleavage pattern. However, the fracture morphology of AZ31B under high strain rates and high temperatures is mainly composed of the dimple pattern, which indicates ductile fracture pattern. The fracture mode is a transition from quasi-cleavage fracture to ductile fracture with the increasing of temperature, the reason for this phenomenon might be the softening effect under the high strain rates.     

Impact breach and fragmentation of glass plate

The present paper describes a first-order analytic model of the breach of monolithic glass plate subject to impact by chunky projectiles. The purpose of the model is to provide a theoretical framework for examining the consequences of the impact breach experiments of Sun et al. [Sun X, Khaleel MA, Davies RW. Modeling of stone-impact resistance of monolithic glass ply using continuum damage mechanics. Int J Damage Mech 2005;14:165-78]. A failure criterion of the Tuler-Butcher form [Tuler FR, Butcher BM. A criterion for the time dependence of fracture. Int J Fracture Mech 1968;4:431-7] is used with the model. The experimental impact breach experiments joined with the analytic model demonstrate time-dependent failure and lack of replica scaling for the present data. Methods are explored for the assessment of fragmentation resulting from the impact breach of brittle materials.     

Fragment size distributions from the dynamic fragmentation of brittle solids

Experimental and theoretical size distributions resulting from dynamic fragmentation are briefly surveyed. The power-law character unique to brittle solids is contrasted to fragment distributions of other materials. The catastrophic fracture of competent brittle solids is shown to have close parallels to hydrodynamic turbulence in fluids. Ideas that emerge from the physical similarities suggest methods for extending an earlier energy-based theory of dynamic fragmentation. Features of this theory are compared with limited fragmentation data for brittle solids.     

Superplasticity and grain boundary sliding in rolled AZ91 magnesium alloy at high strain rates

The superplastic deformation characteristics and microstructure evolution of the rolled AZ91 magnesium alloys at temperatures ranging from 623 to 698 K (0.67–0.76 T_m) and at the high strain rates ranging from 10⁻³ to 1 s⁻¹ were investigated with the methods of OM, SEM and TEM. An excellent superplasticity with the maximum elongation to failure of 455% was obtained at 623 K and the strain rate of 10⁻³ s⁻¹ in the rolled AZ91 magnesium alloys and its strain rate sensitivity m is high, up to 0.64. The dominant deformation mechanism in high strain rate superplasticity is still grain boundary sliding (GBS), which was studied systematically in this study. The dislocation creep controlled by grain boundary diffusion was considered the main accommodation mechanism, which was observed in this study.     

Fracture and fragmentation of ice: a fractal analysis of scale invariance

The fracture and fragmentation processes of ice are reviewed using fractal concepts. Numerous evidences for the scale invariance of fracture and fragmentation patterns in ice are given, including fracture networks at small (laboratory) and large (geophysical) scales, the distribution of fragment sizes in crushed ice or the distribution of sea ice floe sizes, or self-affine fracture surfaces. These observations strongly argue for the scale invariance of fracture and fragmentation processes in ice. This implies that the fracture mechanisms and the physical parameters revealed at the laboratory scale are still relevant at large scale. However, apparent scale effects can be observed for some parameters if the fractal geometry is ignored or neglected. Scale invariance also implies that the homogenization procedures used in the damage mechanics of ice have to be taken with caution.     

High strain rate deformation and cracking of AA 2219 aluminium alloy welded propellant tank

Aluminium alloy AA 2219 (Al–6.6Cu–1Mn) is the candidate material for the fabrication of propellant storage tank of launch vehicle. Cold rolled sheets of 6.5 mm thickness are used to make the cylindrical shell, while sheets of 4.5 mm thickness are used for the construction of dome through petal forming technique. Petals, formed through cone rolling, treated to T87 temper condition are welded together by TIG welding to configure the dome. Such domes are joined to the cylindrical shell through a ring by TIG welding.The upper stage consists of two tanks, one oxidizer tank (liq. O₂) and other fuel tank (liq. H₂). After completing various developmental qualification tests, propellant flow rate test of one of the system was carried out. Almost all the liquid oxygen of the tank was removed and only a little quantity remained at the bottom. During one of the subsequent tests; when dry nitrogen gas was purged to evaporate the remaining liquid oxygen, the oxidizer tank dome catastrophically fractured with an audible sound. Fracture of oxidizer tank dome, placed at lower part of the system caused excessive deformation and subsequently it also caused fracture of fuel tank dome placed just over it.Detailed metallurgical investigations were carried out on the failed components and it was found that the tank failed under very high strain rate deformation. This paper brings out the details of the investigation carried out.     

Anisotropic dynamic damage and fragmentation of rock materials under explosive loading

This paper describes the development of a constitutive model for predicting dynamic anisotropic damage and fragmentation of rock materials under blast loading. In order to take account of the anisotropy of damage, a second rank symmetric damage tensor is introduced in the present model. Based on the mechanics of microcrack nucleation, growth and coalescence, the evolution of damage is formulated. The model provides a quantitative method to estimate the fragment distribution and fragment size generated by crack coalescence in the dynamic fragmentation process. It takes account of the experimental facts that a brittle rock material does not fail if the applied stress is lower than its static strength and certain time duration is needed for fracture to take place when it is subjected to a stress higher than its static strength. Numerical results are compared with those from independent field tests.     

Fabrication and properties of WC–10Co cemented carbide reinforced by multi-walled carbon nanotubes

High-velocity parting-off has been applied to 80 mm bars of pearlitic 100CrMn6, resulting in shear localisation and white-etching bands in a severely deformed region below the fracture surface. Electron microscopy showed that going from the bulk material towards the fracture surface the grains become elongated and refined. The region below the fracture surface can be divided into three subzones: 50–100 μm below the surface grains are elongated, cementite lamellae are distorted, break up and the lamellar spacing decreases. <50 μm below the fracture surface the microstructure becomes a mix of cementite lamellae and carbides in a ferrite matrix. Within the white-etching band the microstructure consists of equiaxed ferrite refined to a grain size of 50–150 nm. Several twinned regions caused by the deformation can be observed. Selected area electron diffraction and low angle convergent beam electron diffraction indicate nanocrystalline cementite dispersed in the ferrite matrix.     

Modelling the damage evolution due to second-phase particle fragmentation and decohesion in an Al alloy

Summary In some Al alloys, the damage observed is often associated with fragmentation and decohesion of hard particles. A non-uniform angular distribution of particles can induce an anisotropic damage evolution with respect to the strain paths. A model is-proposed based on a 3D FE simulation of the growth of cavities associated with fragmentation or decohesion. It is shown that the growth increases approximately linearly with strain, and exponentially with triaxiality. A simple phenomenological model is proposed based on the FE results, and makes use of the initial damage value as well as the initial angular distribution of particles. The predicted results are compared with experimental ones.     

High strain rate superplasticity of TiNP/2014Al composite

Superplasticity of the TiN_p/2014AI composite prepared by powder metallurgy method was investigated by tensile tests conducted at different temperatures (773, 798, 818 and 838 K) with different strain rates range from 1·7×10° to 1·7×10^?3s^?1. Results show that a maximum elongation of 351% is achieved at 818 K and 3·3·10^?1s^?1. At different deformation temperatures, the curves of m value can be divided into two stages with the variation of strain rate and the critical strain rate is 10^?1 s^?1. Superplastic deformation activation energy in the TiN_p/2014AI composite is 417 kJ mol^?1, which is related to liquid phase formation at triple points of grain boundaries and interfaces between the matrix and the reinforcement. Superplastic deformation mechanism of the TiN_p/2014AI composite is grain boundary sliding accommodate mechanism when the strain rate is lower than 10^?1 s^?1, and transfers to grain boundary sliding accommodation mechanism plus liquid phase helper accommodation mechanism when the strain rate is higher than 10^?1 s^?1     

Comparison of hypervelocity fragmentation and spall experiments with Tuler–Butcher spall and fragment size criteria

The present investigation compares predictive theories of dynamic spall and fragmentation with previously reported experimental data. In the experimental tests, aluminum spheres normally impacted thin aluminum plates at over approximately 4.5–7.5 km/s. Scaling features of the impact breakup phenomenon were explored through selected variation in sphere size and plate thickness. The principal diagnostic was high-resolution flash radiography. Fragment-size features of resulting fragment clouds were determined through detailed analysis of the recorded radiographs. Other investigators have measured the spall strengths for aluminum at comparable ultra-high strain rates. Spall strength amplitude and the corresponding strain rate dependence are principal results of the study. Existing dynamic fracture criteria are specialized here to the sphere impact spall and fragmentation event, and compared with empirical data. Velocity and strain rate scaling relations are developed for fragmentation size in the sphere impact event.