G.N. Nurick

The deformation and tearing of thin square plates subjected to impulsive loads—An experimental study

Abstract Experimental results for clamped mild steel square plates subjected to impulsive loads are reported. The strain rate-sensitive plates exhibit mode I (large ductile deformation), mode II (tensile-tearing and deformation) and mode III (transverse shear) failure modes. Three phases of mode II are identified as mode II∗ (partial tearing), mode IIa (complete tearing with increasing mid-point deformation), and mode IIb (complete tearing with decreasing mid-point deformation). For the cases where complete tearing occurs (modes II and III) the velocity of the square disc torn from the base plate is measured. An attempt to measure the speed of rotation of the disc is discussed. Threshold for the onset of failure modes II and III are given. Comparisons between the response of square and circular plates are discussed.

Deformation of thin plates subjected to impulsive loading—a review Part II: Experimental studies

Abstract This two-part article reviews the theoretical predictions and experimental work on the deformation of thin plates subjected to impulsive loading. Part I [Int. J. Impact Engng8, 159–170 (1989)] dealt with the theoretical predictions and focused on the comparisons of the theoretical studies. Experimental-theoretical correlations were also discussed. Part II discusses the experimental results, and presents an empirical relationship between the deflection-thickness ratio and a function of impulse, plate geometry, plate dimensions and material properties.

The deformation and tearing of thin circular plates subjected to impulsive loads

Abstract This investigation examines the failure of circular plates subjected to impulsive velocities. Experiments are conducted on fully clamped circular mild steel plates subjected to a uniformly distributed impulse. The strain rate-sensitive plates exhibit mode I (large ductile deformation), modes II (tensile-tearing and deformation) and mode III (transverse shear) failure modes. An energy analysis is used on the test results which enables an energy balance equation relating input, deformation, tearing and disc energies to be formulated. The input and disc energies are obtained from experimental measurements; the deformation energy is predicted by making use of the final deformed height, a shape function and a rigid-plastic analysis. Good correlation is found and the experiments show good repeatability. The threshold velocities for the onset of failure modes II and III are given.

Tearing of blast loaded plates with clamped boundary conditions

Abstract Extensive experimental results for the prediction of the onset of thinning (necking) and hence subsequent tearing at the boundary of clamped circular plates subjected to uniformly loaded air blasts are presented. The experiments include: plates of diameter ranging from 60mm to 120mm; different clamped edge conditions; (sharp edge; and radii of 1.5mm and 3.2mm) and an examination of the microstructural behaviour. Observations of thinning at the boundary show similar trends for all plate diameters with sharp edge conditions, and where the boundary edge condition is relaxed the deflections are larger before thinning and tearing occurs. Three phases within Mode I (large inelastic deformation) are identified as; Mode I (no visible necking at the boundary); Mode Ia (necking around part of the boundary); and Mode Ib (necking around the entire boundary). Predictions using the code ABAQUS provide, in particular for Mode I, favourable correlations with the experiments.

Deformation and rupture of blast loaded square plates—predictions and experiments

Abstract Experimental and numerical results for clamped square mild steel plates subjected to uniformly distributed blast pressure loading are presented. The strain rate-sensitive plates exhibit mode I (large ductile deformation), mode II (tensile-tearing), and a trend towards mode III (transverse shear) failure as the load intensity increases. The numerical analysis is carried out using a new finite element formulation which incorporates nonlinear geometry and material effects as well as strain rate sensitivity. Initiation of mode II failure is predicted by a maximum strain criterion. Mode I is predicted well for both maximum deflection and deformation shape. The mode II failure prediction correlates reasonably well with the experimental results and provides a clear lower bound for full rupture of the plate.

Deformation and tearing of blast-loaded stiffened square plates

Abstract Experimental and numerical results for fully built-in stiffened square plates subjected to blast pressure loading are presented. The strain rate-sensitive plates exhibit mode I (large ductile deformation) and mode II (tensile tearing) failure as the load intensity increases. The numerical analysis is carried out using a finite element formulation which incorporates non-linear geometry and material effects as well as strain rate sensitivity. Mode I is predicted well for both maximum deflection and deformation shape. Initiation of mode II failure is predicted by a maximum strain criterion, but the limited mode II data is insufficient for conformation.

Large deformation of thin plates under localised impulsive loading

Abstract The response of thin clamped plates to a localised impulsive load imparted over a central circular region is investigated experimentally and theoretically to determine the location of tearing failure and the critical impulse to failure. Over 40 tests were performed with four different loading radii and increasing values of the applied impulse. Typical dish like deflection profiles were produced and measured. It was observed that smaller loading radii led to a more localised bulging near the plate centre. The resulting plate failure took the form of a disc. A more distributed load produced tearing failure at the clamped boundary. In the theoretical development, the plate was modelled as a rigid-plastic membrane. The resulting initial-boundary value problem for the wave equation in the polar co-ordinate system was solved by the eigenfunction expansion method up to the point of first unloading. An approximate closed-form solution was also obtained by combining the wave form solution for early motion with the mode solution for late motion. A good correlation was obtained between the predicted and measured normalised deflection profile. The analysis of the theoretical solution gave strong indication that the initial velocity profile must have a form of a continuous and smooth function near the edge of the burning zone. Precise determination of the deflected shape is a necessary step for strain calculations and the prediction of the onset of tensile necking and failure of plates.

A study of charge motion in rotary mills. Part 2-Experimental work

Abstract The motion of balls deep within the charge of a rotary grinding mill was investigated, using novel techniques to track the balls. These included X-ray filming of both the front and side views of a transparent mill, and gamma-camera filming of a radioactive ball. Analysis of the trajectories of the balls revealed several phenomena in the milling action that have hitherto not been reported in the literature. These include: the non-rotation of the balls which indicates that the grinding does not take place by rotary nipping of the ore between the balls; charge dilation with increased mill speed; longitudinal migration of the balls; further insights into charge segregation; spiralling action of the balls; smooth paths of balls in the bulk of the charge.

A study of charge motion in rotary mills Part 1—extension of the theory☆

Existing theories of the motion of the media in a rotary mill, and the calculation of mill power are extended to account for the actual motion of balls within a mill. A new definition of angle of repose of the charge, which is based upon fundamental properties of the shape of the charge, and remains defined over all mill speeds, is proposed. Mechanistically correct definitions of the centre of circulation and centre of mass of the charge are presented, and the usefulness of these in predicting the power draw of a mill is demonstrated. It is demonstrated that simple theories of the bulk charge motion in a mill that ignore the interaction between the layers of balls yield incorrect predictions.

A study of charge motion in rotary mills part 3—Analysis of results

Results of experiments investigating the motion of balls deep within the charge of a rotary grinding mill are presented. The true centre of mass of the entire charge was determined. The angle of repose of the charge was found to be uniquely defined by the centre of circulation of the charge. The angle of the cascading region is determined by the angle of repose of the charge. The inner part of the cascading region and the toe region are responsible for the majority of the grinding work. The face angle of the lifter bars was found to influence both the maximum impact energy and the amount of work done by the charge. Radial segregation of the balls takes place throughout the charge according to both the mass and size of the balls, even in a mill with smooth end faces.