Bengt Lundberg

Impact of metallic projectiles on ceramic targets: transition between interface defeat and penetration

The purpose of this thesis is to gain understanding of the load on flat target surfaces produced by projectile impact. Models are proposed from which upper and lower bounds can be derived for the transition be-tween interface defeat and normal penetration.It is shown that the dominating contribution to the normal load is generally provided by the hydrodynamic pressure due to the effect of inertia. In addition it is shown that the contributions from yield strength and compressibility are also significant. For a cylindrical tungsten alloy projectile at an impact velocity representative of to-day’s ordnance velocities, the contributions to the load intensity on the axis of symmetry from yield strength and compressibility are shown to be 15% and 3.4%, respectively, of that of inertia.Impact tests have shown that for conical projectiles transition from interface defeat to penetration occurs at a significantly lower impact velocity than for cylindrical projectiles. In order to better understand the influence of projectile shape, a conical projectile in axi-symmetric impact is studied by use of an analytical model for self-similar flow, and the results obtained are compared to results of numerical simula-tions. It is shown how the maximum load intensity, and the position of the maximum, depends on the apex angle. For an apex angle of 90o, the maximum load intensity is found to be almost three times that pro-duced by a cylindrical projectile with the same impact velocity. This maximum occurs well off the axis of symmetry and is 20% larger than the load intensity at this axis. Both the self-similar model and the nu-merical simulations show that the contribution to the load intensity from compressibility is positive below and negative above an apex angle of around 80o. The contribution of yield strength to the load in-tensity at centre of impact depends only weakly on the apex angle and is therefore similar to that of a cylindrical projectile.

Determination of mechanical material properties from the two-point response of an impacted linearly viscoelastic rod specimen

Abstract The theoretical basis is established for a general way of determining mechanical material properties from the measured response to impact at two different cross-sections of a linearly viscoelastic rod specimen. The measured quantities can be either strains or particle velocities. Explicit results are provided for two special cases, the first corresponding to a pre-existing method and the second to a new method. The basic difference between the two methods is that the first involves restrictions concerning wave superposition, whereas the second does not. Experiments were performed with a high polymer, Nylon 6, using both methods and with an elastomer, Vulcanized Polynor, using the new method. The results obtained under various conditions with the same material are in good agreement. The two methods usefully complement each other as well as other methods in a frequency range of approximately 20 Hz-20 kHz.

A split Hopkinson bar study of energy absorption in dynamic rock fragmentation

Abstract Fragmentation of unconfined cylindrical specimens of rock due to stress wave loading has been investigated using a Split Hopkinson Bar (SHB). Photographs were taken during the fracture process using a high-speed framing camera, and incident, reflected and transmitted stress pulses were recorded using a digital transient recorder. The energy absorbed by the specimen during the fragmentation process was evaluated from the recorded stress pulses. Two different rocks were studied, namely Bohus granite and Solenhofen limestone. The specimen length was 50 mm, and the diameter was 25 mm. The incident pulse durations were 50, 100 and 200 μs, and the amplitude was in the range of 0·5−4 kbar . The high-speed photographs show that fracture occurs as previously observed for other rocks using SHB-devices. Notably, the main crack orientation is axial, and the degree of fragmentation increases with increasing load. The energy absorption of the specimen increases markedly when the load applied approaches a certain value. For the Bohus granite specimens the critical load was found to be 1·8 times the static compressive strength, and for Solenhofen limestone it was 1·3 times the static compressive strength. Two simple specimen models were analyzed theoretically, namely, one linearly-elastic and one rigid-plastic. The first model gives the best agreement with experimental results if the degree of fragmentaion is low, the second model gives the best agreement if the degree of fragmentation is high. The rigid-plastic model explains the experimental observation that the specimen always absorbs less than half the incident pulse energy.

Tungsten long-rod penetration into confined cylinders of boron carbide at and above ordnance velocities

The purpose was to investigate the influence of impact velocity and confinement on the resistance of boron carbide targets to the penetration of tungsten long-rod projectiles. Experimental tests wi ...

Analysis of elastic waves in non-uniform rods from two-point strain measurement

Abstract A method is established which permits evaluation of the histories of normal force and particle velocity at an arbitrary cross-section E of a non-uniform linearly-elastic rod from measured strain histories at two different cross-sections, A and B . Other quantities at E , such as stress, strain, displacement, acceleration and power transmission, can be determined in terms of the evaluated normal force and particle velocity. The method is an extension of that developed by Lundberg and Henchoz for uniform rods. Theoretical results, based on one-dimensional elastic wave theory, are provided for the general case as well as for cases of piecewise constant characteristic impedance. Experimental tests with different configurations of non-uniform rods and strain gauges show that the normal force histories determined at E with the present method (from measured strains at A and B ) agree well with those obtained through direct strain measurement at E .

Experimental study of a percussive process for rock fragmentation

Abstract The efficiency of a percussive process for fragmentation of rock and similar materials has been studied experimentally. The percussive system comprised a cylindrical hammer and a cylindrical bit with the same characteristic impedance. The bit was terminated with a wedge. In front of the wedge there was a heavy block of concrete. The length of the bit and the initial gap between bit and concrete were varied systematically. The force versis penetration relationship and the work of fragmentation were determined in each test using a new technique based on measurement of strains at two cross-sections of the bit. Each test was simulated individually using a previously developed one-dimensional model. The results of simulations and experimental tests were found to agree well.

Microcomputer simulation of percussive drilling

Churn drilling, down-the-hole drilling, hammer drilling, and related drilling and breaking processes are simulated by means of a microcomputer. The simulation programs are written in Apple Pascal f ...

Microcomputer simulation of stress wave energy transfer to rock in percussive drilling

Abstract An Apple II Plus microcomputer with high resolution graphics is used to simulate stress wave energy transfer to rock in percussive drilling. The drilling model is based on one-dimensional stress wave theory for the rod and bit, and on a nonlinear history-dependent force/penetration relationship for the bit/rock interaction. The programming language is Applesoft Basic. Input data are given for rod, bit, incident wave and bit/rock interaction. Also the position of a gauge is prescribed. During simulation the wave propagation in rod and bit is visualized. Also the normal force at the gauge station is plotted vs time on a simulated oscilloscope display. After simulation the drill-bit efficiency, defined as the ratio of work on rock to incident wave energy, and the maximum and minimum forces at the gauge station, are displayed. For the case of an integral drill steel and a rectangular incident wave, the computed efficiency differs from the known ideal efficiency by only a few tenths of a per cent. The use of the simulation program ‘Bit’ is illustrated by studying the influence of bit mass and shape on drill-bit effieiency. For the bits chosen mass is shown to be a far more important parameter than shape. The program has uses in research and development as well as in education.

Influence of pole length and stiffness on the energy conversion in pole-vaulting

An impact process similar to pole-vaulting is studied, viz., the impact in a vertical plane between the bottom end of a slightly curved elastic bar (pole), with a point mass (vaulter) at the top end, and a rigid support (pole box). Before impact, the velocity of the pole and the vaulter forms a certain angle (take-off) with the horizontal ground. Finite element calculation of the trajectories of the vaulter are carried out, and a performance figure, defined as the ratio between the maximum potential energy of the vaulter and the initial kinetic energy of the vaulter and the pole, is determined as a function of dimensionless parameters. As the vaulter remains passive during the vault, in contrast to a real vaulter, this performance figure is also the efficiency of conversion of the initial kinetic energy to the achieved potential energy in the vault. It is shown that, under normal pole-vault conditions, there exists a maximum performance figure with respect to pole length and stiffness. For an initial velocity and a body mass which are representative of an elite pole-vaulter, the maximum performance figure 0.87 is obtained for a pole with length 5.5 m.

A method for determination of in-hole dynamic force-penetration data from two-point strain measurement on a percussive drill rod

The aim of the present investigation is to establish a testing method suited for determination of in-hole dynamic force-penetration data for non-uniform standard percussive drill rod-bit configurat ...