Dynamic Steady State by Unlimited Unidirectional Plastic Deformation of Crystalline Materials Deforming by Dislocation Glide at Low to Moderate Temperatures

This paper presents an outline of the quest for the mechanical steady state that an unlimited unidirectional plastic strain applied at low to moderate temperature is presumed to develop in single-phase crystalline materials deforming by dislocation glide, with particular emphasis on its athermal strength limit. Fifty years ago, the study of crystalline plasticity was focused on the strain range covered by tensile tests, i.e., on true strains less than unity; the canonic stress–strain behavior was the succession of stages I, II, and III, the latter supposedly leading to a steady state defining a temperature and strain rate-dependent flow stress limit. The experimentally available strain range was increased up to Von Mises equivalent strains as high as 10 by the extensive use of torsion tests or by combinations of intermittent deformations by wire drawing or rolling with tensile tests during the 1970s. The assumed exhaustion of the strain-hardening rate was not verified; new deformation stages, IV and V, were proposed, and the predicted strength limit for deformed materials was nearly doubled. Since the advent of severe plastic deformation techniques in the 1980s, such a range was still significantly augmented. Strains of the order of several hundreds were routinely reached, but former conclusions relative to the limit of the flow stress were not substantially changed. However, very recently, the plastic strain range has allegedly been expanded to 105 true strain units by using torsion under high pressure (HPT), surprisingly for some common metals, without experimental confirmation of having reached any steady state. This overview has been motivated by the scientific and technological interest of such an open-ended story. A tentative explanation for the newly proposed ultra-severe hardening deformation stage is given.

Seismic performance of external reinforced concrete beam-column joints

Four external beam-column sub-assemblies were tested to investigate the influence of different details on the performance of the Joint zone. All the details conformed to the current New Zealand structural concrete standard (NZS3101-1995). It is shown that anchoring beam reinforcement in external beam- column joints short of the outer column bars results in a reduction in the flexural strength of the column. In tests premature yielding of the longitudinal bars on the inside of the column occurred when bars were anchored at a distance of 1⁄4 of the column depth from the outside face of the column, as permitted by the structural concrete Standard. This yielding had an adverse effect on the performance of the joint zone. A way of detailing external joint zones to compensate for this loss in strength is described. Elongation of plastic hinges in the beams of ductile frames induces unidirectional plastic hinges in the external columns at the first floor level. While this has a strong influence on the distribution of moments and shears in the columns tests indicated that it does not adversely affect the structural performance of the joint zone. The use of continuous bars bent in the form of a U provides a simple detail that worked very effectively. There was little difference in joint behaviour between beams with main bars uniformly distributed over the beam depth to conventionally reinforced beams with their main bars positioned near the top and bottom edges.

Ductility demand for uni-directional and reversing plastic hinges in ductile moment resisting frames

In a major earthquake the beams in moment resisting frames may develop either reversing or unidirectional plastic hinges. The form of plastic hinge depends upon the ratio of the moments induced by the gravity loading to those induced by the seismic actions. Where this ratio is low the plastic hinges form at the ends of the beams and the sign of the inelastic rotation changes with the direction of sway. These are reversing plastic hinges, and the magnitude of the rotation that they sustained is closely related to the inter-storey displacement. However, when the moment ratio exceeds a certain critical value, unidirectional plastic hinges may form. In this case negative moment plastic hinges develop at the column faces and the positive moment plastic hinges form in the beam spans. As the earthquake progresses the positive and negative inelastic rotations accumulate in their respective zones so that peak values are always sustained at the end of the earthquake. With this type of plastic hinge no simple relationship exists between inter-storey drift and inelastic rotation. Several series of time history analyses have been made to assess the relative magnitudes of inelastic rotation that are imposed on the two forms of plastic hinge. It is found that with design level earthquakes typically the unidirectional plastic hinge is required to sustain 21/ 2 to 4 times the rotation imposed on reversing plastic hinges, with the curvature ductilities ranging up to 140. These values are appreciably in excess of the values measured in tests using standard details. This indicates that in structures where unidirectional plastic hinges may form, the design displacement ductility and or the allowable inter-storey drift should be reduced below the maximum values currently permitted in the New Zealand codes. The problems associated with the formation of unidirectional plastic hinges can be avoided by adding positive moment flexural reinforcement in the mid regions of the beams. By this means the potential positive moment plastic hinges can be restricted to the beam ends.

Anomalous Residual Stresses

Residual stresses were measured in hardened and tempered specimens after unidirectional plastic extension. X-ray and strain gage-layer removal methods were compared. Anomalous residual stresses were found in extended samples at hardnesses of Rc 32–35. The X-ray method indicated compressive residual stresses of nearly constant magnitude through ⅓ the thickness of flat samples, while the strain gagelayer removal method indicated that no macrostress existed. A constant anomalous residual stress was also seen by X-ray through ⅗ the thickness of a cylindrical specimen deformed uniformly in tension. Little or no anomalous stress was found in an extended specimen at Re 55 or in a specimen at Rc 44 after uniform bending.