State variable analysis of flow localization in work hardening materials

• Main Author: Christodoulou, Nicholas C.
• Format: Others
• Language: en
• Published: McGill University 1982
• Subjects: Strain hardening.; Metals > Plastic properties.; Dislocations in metals.
• Online Access: http://digitool.Library.McGill.CA:80/R/?func=dbin-jump-full&object_id=68684

Large strain tensile tests were carried out on OFHC Cu and 99.99% Al with the aim of determining the first and second order work hardening and rate sensitivity coefficients. The tests were performed at room temperature and 473 K and at constant true strain rates in the range 5 x 10('-4) to 10('-1) s('-1). With the aid of a diameter transducer, which was set up to measure and control the rate of reduction of the diameter of the tensile specimen, the strain rate at the minimum cross-section was held constant well beyond the point of maximum load. A second diametral sensor was constructed for use at elevated temperatures. In order to extend the range of conditions covered, constant strain rate compression tests were also performed on Cu at 698 K. In a further series of experiments, tensile tests were carried out on Cu and Al samples at 293 and on Al specimens at 473 K in which the flow localization process was followed by photographic means. === It was observed that the values of the rate sensitivity of the work hardening rate B(,(sigma)) beyond the maximum load are not negligible, but that they are less than 1, in opposition to the theoretical predictions of Kocks et al('(47)). Furthermore, it is shown that, contrary to the suggestion of these workers, the rate sensitivity at constant work hardening rate N is not the material coefficient that controls the growth of strain rate gradients at large strains. === The material coefficients determined using the diametral transducer were employed for the numerical integration of the second order differential equation describing flow localization proposed by Kocks et al('(47)). This equation was integrated at the minimum cross-section of the sample, and the solution is compared with the one calculated by integrating the first order differential equation proposed earlier by Jonas et al('(10)). As expected, the strain measurements obtained from the flow localization experiments are reproduced more closely by the second order solution than by the first order one largely because of the non-negligible values of B(,(sigma)). However, at large deformations, there is a discrepancy between the experimental observations and the predictions of the second order theory. This is attributed to the development of triaxial stresses at these strains. A possible modification of the second order treatment is suggested, based on the gradient in the Bridgman correction term.