(2007) A mathematical representation of the multiaxial Bauschinger effect Materials at High Temperatures: Vol 24, No 1, pp 1-26

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A mathematical representation of the multiaxial Bauschinger effect

http://cats-fs.rpi.edu/~wenj/ECSE446S06/astrom_friction.pdf

Friction Models and Friction Compensation

In this paper we derive a new dynamic friction force model for the longitudinal road/tire interaction for wheeled ground vehicles. The model is based on a dynamic friction model developed previously for contact-point friction problems, called the LuGre model. By assuming a contact patch between the tire and the ground we develop a partial differential equation for the distribution of the friction force along the patch. An ordinary differential equation (the lumped model) for the friction force is developed, based on the patch boundary conditions and the normal force distribution along the contact patch. This lumped model is derived to approximate closely the distributed friction model. Contrary to common static friction/slip maps, it is shown that this new dynamic friction model is able to capture accurately the transient behaviour of the friction force observed during transitions between braking and acceleration. A velocity-dependent, steady-state expression of the friction force versus the slip coefficient is also developed that allows easy tuning of the model parameters by comparison with steady-state experimental data. Experimental results validate the accuracy of the new tire friction model in predicting the friction force during transient vehicle motion. It is expected that this new model will be very helpful for tire friction modeling as well as for anti-lock braking (ABS) and traction control design.

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Dynamic friction models for road/tire longitudinal interaction

Experiments on stainless steel hollow sections—Part 1: Material and cross-sectional behaviour

Static and dynamic axial crushing of square thin-walled aluminium extrusions

A simple formula is suggested for describing the stress-strain curve in terms of three parameters; namely, Young's modulus and two secant yield strengths. Dimensionless charts are derived from this formula for determining the stress-strain curve, the tangent modulus, and the reduced modulus of a material for which these three parameters are given. Comparison with the tensile and compressive data on aluminum-alloy, stainless-steel, and carbon-steel sheet in NACA Technical Note No. 840 indicates that the formula is adequate for most of these materials. The formula does not describe the behavior of alclad sheet, which shows a marked change in slope at low stress. It seems probable that more than three parameters will be necessary to represent such stress-strain curves adequately.

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Description of Stress-Strain Curves by Three Parameters

A fixture is described for making normal-pressure tests of flat plates 5 inches in diameter in which particular care was taken to obtain rigid clamping at the edges Results are given for 19 plates, ranging in thickness from 0015 to 0072 inch The center deflections and the extreme-fiber stresses at low pressures were found to agree with theoretical values; the center deflections at high pressures were 4 to 12 percent greater than the theoretical values Empirical curves are derived of the pressure for the beginning of permanent set as a function of the dimensions of the plate and the tensile properties of the material

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Normal-pressure tests of circular plates with clamped edges

Various methods of obtaining the compressive stress-strain curve of thin sheet metal are described, and their advantages and limitations are briefly discussed. The presentation of stressstrain data in dimensionless form is outlined, and the advantages of such a presentation in correcting for the effect of variations in yield strength and in Young's modulus are brought out. Attention is called to a classification of stress-strain curves by shape factors following a three-parameter formula proposed by Osgood.

Determination and Presentation of Compressive Stress-Strain Data for Thin Sheet Metal

Report presents the results of normal-pressure tests made of 56 rectangular plates with clamped edges and of 5 plates with freely supported edges. Pressure was applied and the center deflection and the permanent set at the center were measured. For some of the plates, in addition, strains and contours were measured.

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Normal-pressure Tests of Rectangular Plates

Critical compressive stresses were computed and were compared with measured values for 26 different aluminum-alloy and magnesium-alloy extrusions. Critical stresses for local instability were computed, considering the flanges as plates of uniform thickness rigidly clamped along one edge. Critical stresses for primary instability were computed from Kappus ' theory of torsional instability, taking account of the stiffening effect of fillets and the effect on the torsion bending constant of bending stresses varying across the thickness of the wall. An estimate of the effect of plastic yielding was made by reducing the critical stresses in the ratio of reduced modulus, for a column of rectangular section, to Young's modulus. The measured and computed critical stresses for 120 of the 125 specimens differed less than 5,000 lbs. per sq.in. Comparison of strength-weight ratios for buckling and for failure showed that in general the Z-sections were most efficient. A procedure is outlined for calculating buckling stresses of unsupported extrusions of one material from measured buckling stresses of similar extrusions of a different material. The procedure was checked by comparing calculated buckling stresses with measured buckling stresses for extruded T-sections, L-sections, and Z-sections of several aluminum and magnesium alloys. The differences between the measured and calculated buckling stresses did not exceed 10,000 lbs. per sq.in. The average difference was lees than 5,000 lbs. per sq.in.

Walter Ramberg

Papers

Description of Stress-Strain Curves by Three Parameters

Normal-pressure tests of circular plates with clamped edges

Determination and Presentation of Compressive Stress-Strain Data for Thin Sheet Metal

Normal-pressure Tests of Rectangular Plates

Instability of Extrusions Under Compressive Loads