B. Wang

An experimental study on tearing energy in splitting square metal tubes

Abstract An experiment was performed to study the tearing energy in splitting square aluminium and mild steel tubes of thicknesses ranging from 0.47 to 1.67 mm. It was carried out by driving four rollers each attached to the side wall of the tube, leading to the bending of the wall to a constant curvature and, at the same time, the tearing along the four corners. By pre-cutting some corners to a different length, the tearing energy involved was determined. It was found that the tearing energy per unit torn area (R) may be related to the ultimate stress of the material (σu) and the fracture strain (ef) as R = 8.8σuef for mild steel and R = 37.2σuef for aluminium tubes; here the two coefficients have length dimensions in mm.

Development of constitutive models for metal forming with cyclic strain softening

Abstract Many cold and hot worked metals undergo strain hardening and softening when subjected to cyclic plastic straining. The degree of strain softening depends on the amount of prior cold work or heat treatment introduced into the material and upon the magnitude and the number of cycles of applied cyclic plastic strain. Cyclic strain softening leads to a lower flow stress, higher ductility, reduced tensile strength upon subsequent straining and lower energy consumption during material processing. In order to optimise metal forming processes, the work hardening and softening should be analysed to include the influence of deformation conditions within the constitutive model. This paper developed a constitutive model based on the Estrin and Mecking phenomenological model for cyclic hardening without prestraining whilst using a combined Estrin and Mecking model and Avrami equation for cyclic softening with prestraining. As cyclic softening is largely dependent on the work hardening previously achieved and on deformation conditions, the constitutive model takes account of these conditions in addition to those used in conventional constitutive models.

On the optimisation of two-component plates against ballistic impact

Abstract Based on an existing model, a design criterion has been developed which gives the optimum performance of two-component ceramic armour under a given total thickness. With the threat defined, the approximate thickness ratio of the two plates can be calculated easily. Test findings show reasonable agreement with the predicted values. The criterion provides a quick and simple tool for armour-design engineers to use to evalute the possibilities of two-component ceramic armour.

An empirical equation for crack formation in the laser cutting of ceramic plates

Abstract Industrial lasers have found many applications in materials processing and manufacturing, one of which is to cut ceramic components that are difficult to cut using conventional means due to their high value of hardness and degree of brittleness. However, often one problem associated with this process is the formation of cracks that can result from the thermal stresses that are induced. This paper is concerned with the problem of cracking of ceramic plates when cut using laser beams. Based on the experimental results reported, it is argued that the most relevant operating parameters are the laser power (P) and the feed-rate of the specimens (v). The material properties of interest in this study are: specific heat (c), conductivity (k) and thermal expansion coefficient (α). The only geometrical dimension is the thickness (t). Dimensional analysis was employed to identify four dimensionless groups. On the hypothesis that crack occurs when the tensile strain reaches the material’s critical (fracture) strain, the following empirical equation was obtained, which specifies the safe region in terms of the operating power and feed-rate: P≥1.78×10 11 t 2.41 v where P is in W, t is in m, and v is in m s−1. Qualitative explanations are discussed in relation to the functional dependence of the various parameters. The identified dimensionless groups and empirical equations are of direct use to practising engineers.

The behaviour of laminated composite plates as armour

Abstract A combined experimental and semi-empirical investigation of the penetration resistance of fibreglass reinforced plastic plates under ballistic impact has been undertaken, the ballistic tests being carried out using 7.62 mm armour-piercing rounds. In parallel, a slow penetration test using a fabricated bullet profile was carried out to enable a comparison of the damage mechanism and the energy absorbing characteristics of the composites under the two different loading conditions. It was observed that even though there are some differences in the failure mechanisms, the amount of energy absorbed by the materials is quite close for the two different loading conditions. Thus, from the energy absorption point of view it is feasible to use the slow penetration test to predict the ballistic limit of the target. A semi-empirical model has been developed to describe the resistant force at each penetration stage, from which the energy absorption can be calculated and the residual velocity of the projectile predicted approximately.

Experimental and numerical analysis of the response of aluminium oxide tiles to impact loading

Abstract Ceramics have long been recognised for their outstanding hardness and yield stress under compressive loading. There has been seen an increasing practice of ceramic components being used for impact resistance to foreign objects. However, their brittleness prevents their being used alone for such purposes and special considerations are required to optimise their advantages whilst avoiding their weakness. This paper presents some results from a recent programme on the dynamic response of aluminium oxide tiles to high speed impact, and reports the results of both the experimental and numerical investigation on alumina tiles backed by aluminium plates. Some observations on ceramic failure mechanisms and erosion on the projectile are discussed. Based on the test results, an empirical equation is developed for the energy-absorption characteristics of this two-component composite structure. A two-dimensional axisymmetric numerical analysis of normal impact is performed also. The finite-element package used was DYNA2D hydrodynamic code, and a brittle-fracture material model was used with an erosion condition when the ruptured material limits its role in the penetration process to purely inelastic effects. A detailed picture of the response of the ceramic under projectile impact has been obtained. The results are compared with experimental observations, reasonable agreement being encountered, thus suggesting that the present is an adequate numerical approach to the physical situation.

Yield mechanisms of a bent cantilever beam subjected to a suddenly applied constant out-of-plane tip force

Abstract Previous studies of the out-of-plane deformation of a bent cantilever under a step load applied at its tip have shown that the validity of the deformation mechanism is governed by certain geometrical restrictions. Single and double hinge mechanisms have been proposed previously and the present paper shows that the family of possible mechanisms can be expanded and completed by introducing new double and triple-hinge mechanisms. With the aid of these mechanisms, it is shown that the initial deformation mode can be derived for any bent cantilever regardless of the magnitude of the applied force and the geometry of the beam.

Triple plastic hinge mechanism for a bent cantilever beam subjected to an out-of-plane tip force pulse of finite duration

Abstract In Ref. [1], the need was demonstrated for a deformation mechanism consisting of three plastic hinges (triple-hinge mechanism) to complete the range of possible deformation modes for a bent, rigid perfectly-plastic cantilever beam subjected to a suddenly applied constant tip force applied perpendicular to the plane of the cantilever. This paper provides the analysis of the transient behaviour of such a mechanism when a rectangular force pulse (constant force applied for a finite duration) is applied to the beam. The kinematics of the various hinges are described and the partitioning, of the input energy between the five phases of the motion is evaluated.

Out-of-plane impulsive loading of a right-angled bent cantilever beam

This paper provides an analysis of the response of a right-angled bent cantilever beam subjected to an out-of-plane impulsive loading (i.e. suddenly imposed velocity) applied to a concentrated mass at its tip. If T o and M o are the fully plastic torque and bending moment, of the cross-section respectively, it is shown that for the case T o / M o < 1, a double-hinge mechanism is required, with a pure bending hinge in the first segment of the beam and a combined bending-torsion hinge in the second segment. A complete solution (with travelling hinges in the earlier phases) is achieved and a numerical example is given.