M.P.F. Sutcliffe

Surface asperity deformation in metal forming processes

The crushing of surface asperities by a frictionless die is examined under conditions of bulk deformation of the underlying material. For one-dimensional (ridge-like) asperities aligned perpendicularly to the direction of bulk strain, a slip-line field has been found which enables the growth of real area of contact with bulk strain to be calculated. For asperities aligned in the direction of the bulk strain, an approximate energy method due to Wilson and Sheu has been developed further [W. R. D. Wilson and S. Sheu, Real area of contact and boundary friction in metal forming. Int. J. Mech. Sci.30, 475–489 (1988)]. Both theories predict a large increase in contact area with bulk strain and a reduction in the load needed for bulk yielding. The theories give reasonable agreement with experiments.

Failure mode maps for honeycomb sandwich panels

Failure modes for sandwich beams of GFRP laminate skins and Nomex honeycomb core are investigated. Theoretical models using honeycomb mechanics and classical beam theory are described. A failure mode map for loading under 3-point bending is constructed, showing the dependence of failure mode and load on the ratio of skin thickness to span length and honeycomb relative density. Beam specimens are tested in 3-point bending. The experimental data agree satisfactorily with the theoretical predictions. The effect of honeycomb direction is also examined. The concept of a failure mode map is extended to give a useful design tool for sandwich panels manufacturers and their customers.

A robust model for rolling of thin strip and foil

A new analysis for cold rolling of thin strip and foil is developed. This model follows the approach of Fleck et al. [8], but relaxes their assumption of a central flat neutral zone. Instead of following their inverse method to obtain the pressure distribution in this neutral zone, an explicit equation for the contact pressure variation is obtained from the sticking condition in this region. This significantly simplifies the solution method, leading to a much more robust algorithm. Moreover the method treats the cases either where the roll retains its circular arc or where there is very significant roll deformation in the same way, greatly simplifying the method of obtaining solutions. This will facilitate the incorporation of other effects such as the friction models currently being developed. Results are in line with the theory of Fleck et al. [8]. The effect of entry and exit tensions on the non-dimensional load and forward slip is investigated. It is found that the effect of equal entry and exit tensions is equivalent to reducing the yield stress of the strip by this tension stress.

Indentation failure analysis of sandwich beams

Abstract Failure of sandwich honeycomb structures under indentation loading is considered. A failure criterion for Nomex honeycombs subjected to combined compressive and shear stresses is determined using biaxial tests. By combining this with a theoretical calculation of the stress distribution in the core due to indentation loading, found from a high-order sandwich beam theory (HOSBT), the indentation failure load of the sandwich beam due to core failure can be predicted. It is assumed that both the skin and core are elastic up to failure, which is a reasonable approximation for the GFRP skins and Nomex cores considered. Short beam 3-point bending tests are used to validate the theoretical predictions, using beams made with GFRP skins and Nomex cores with densities between 29 and 128 kg / m 3 . Theoretical predictions of indentation failure load are in excellent agreement with measured values. Inclusion of shear stresses in the failure criterion significantly improves the predictions, correctly modelling the observed stronger behaviour of cores with a longitudinal ribbon direction.

Lubrication in Cold Strip Rolling in the ‘Mixed’ Regime

Lubrication in metal rolling in the mixed lubrication regime has been considered. An inlet analysis has been used to calculate the film thickness and area of contact ratio in the bite, taking into account the effect of roughness on the pressure build-up and the effect of the bulk deformation on the crushing of asperities. The film thickness with rough contact is most strongly dependent on the variables which determine the film thickness with smooth contacts, that is, roiling speed, oil properties and inlet geometry, but the effect of yield stress, strip thickness, roughness geometry and inlet tension are also examined. In a separate calculation hydrodynamic theory has been used to estimate film thickness under the ‘contact’ areas. These two calculations have been combined with recent measurements of oil properties to estimate friction-slip relations when rolling thin aluminium foil. These calculations provide quantitative information on friction conditions to help model the rolling process and to estimate the strip surface quality.

Flattening of Random Rough Surfaces in Metal-Forming Processes

Flattening of random rough surfaces on a workpiece undergoing bulk deformation has been analyzed using a model of the surface consisting of just two wavelength components. Asperities are flattened at a rate which depends on the ratio of the initial r.m.s. amplitudes of the long and short wavelength components. The flattening behavior of the long wavelength asperities only becomes important when the amplitude of the long wavelength asperities is much greater than that of the shorter wavelength asperities. The surface modification was investigated experimentally by cold rolling of aluminium strips. The power spectral density of the roughness was used to extract appropriate amplitudes for the short and long wavelength components of roughness. The change in roughness amplitudes showed excellent agreement with theory.

A multiple field image analysis procedure for characterisation of fibre alignment in composites

A novel method is presented for the characterisation of fibre misalignment in composite specimens. The method is based on analysis of low magnification images in which the local fibre direction can be inferred from the orientation of elongated features in the image. Specimen preparation procedures and the image analysis algorithm employed are presented and their usage is illustrated by application to two types of carbon fibre composite, one of which showed a high degree of alignment while the other exhibited noticeable fibre waviness. Factors affecting the choice of certain image analysis parameters are briefly explored. Comparisons are presented with results obtained using conventional sectioning, followed by measurement of the aspect ratios exhibited by individual fibres. It is shown that the proposed method is robust, sensitive and experimentally convenient. It is particularly well suited to the characterisation of specimens exhibiting significant variations in fibre alignment direction over large distances, i.e. pronounced fibre waviness, and the potential utility of such measurements for the prediction of compressive strength is highlighted.

Microbuckle propagation in a unidirectional carbon fibre-epoxy matrix composite

Out-of-plane microbuckle growth is observed in a unidirectional carbon fibre-epoxy matrix composite under compressive loading. Experimental measurements of the overall kink-band width confirm that a growing microbuckle propagates in a crack-like manner rather than in a dislocation-like manner. The microbuckle is modelled as a bridged Mode I crack with compressive bridging tractions. A large scale bridging model with a crack tip toughness and a constant bridging stress is successful in correlating the length and width of a growing microbuckle with the remote stress.

Microbuckle propagation in carbon fibre-epoxy composites

Abstract Observations of microbuckle propagation in uni-directional carbon fibre-epoxy material are described. The fibres buckle either in the plane of the specimen or out-of-plane, depending on the constraints on the free surface. Large scale bridging models of in-plane and out-of-plane microbuckles are reported. The in-plane and out-of-plane microbuckles are modelled as mode II and mode I cracks, respectively. Sliding behind the microbuckle tip is resisted by a constant shear stress of 90 MPa for the in-plane microbuckle, and by a constant normal stress of 220 MPa for the out-of-plane microbuckle. For both the in-plane and out-of-plane microbuckles a microbuckle tip toughness in the range 10–17 KJ/m2 is inferred from the experiments. The observed relative displacements across an out-of-plane microbuckle agree with theoretical values using the mode I bridging model. Micrographs of the propagating microbuckle tip show that the details of the failure mechanism are similar for both in-plane and out-of-plane microbuckling. Both develop kink bands with a width of between 25 and 70 μm and with a propagation angle β of between 25° and 30°. A process zone extends about 250 μm ahead of the kink band tip, wherein the fibres buckle and break. Fibres in this region become almost straight again on unloading. When the deduced large scale bridging model of microbuckling failure for unidirectional material is applied to failure at a sharpened slit in multi-directional laminates, reasonable agreement is found between the theoretical and the observed compressive fracture toughnesses.

The monitoring of relative changes in compartmental compliances of brain

The study aimed to develop a computational method for assessing relative changes in compartmental compliances within the brain: the arterial bed and the cerebrospinal space. The method utilizes the relationship between pulsatile components in the arterial blood volume, arterial blood pressure (ABP) and intracranial pressure (ICP). It was verified by using clinical recordings of intracranial pressure plateau waves, when massive vasodilatation accompanying plateau waves produces changes in brain compliances of the arterial bed (C(a)) and compliance of the cerebrospinal space (C(i)). Ten patients admitted after head injury with a median Glasgow Coma Score of 6 were studied retrospectively. ABP was directly monitored from the radial artery. Changes in the cerebral arterial blood volume were assessed using Transcranial Doppler (TCD) ultrasonography by digital integration of inflow blood velocity. During plateau waves, ICP increased (P = 0.001), CPP decreased (P = 0.001), ABP remained constant (P = 0.532), blood flow velocity decreased (P = 0.001). Calculated compliance of the arterial bed C(a) increased significantly (P = 0.001); compliance of the CSF space C(i) decreased (P = 0.001). We concluded that the method allows for continuous monitoring of relative changes in brain compartmental compliances. Plateau waves affect the balance between vascular and CSF compartments, which is reflected by the inverse change of compliance of the cerebral arterial bed and global compliance of the CSF space.