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Scaling of size/time/temperature — Part 1: Progressive damage in uniaxial tensile specimen

Theoretical and Applied Fracture Mechanics
Publication Date
DOI: 10.1016/0167-8442(89)90028-1
  • Mathematics


Abstract The non-equilibrium states of uniaxial tensile specimens cannot be completely defined without a knowledge of the transient character of size/time/temperature interaction. Changes in the specimen, however small, occur progressively under the influence of mechanical and/or thermal disturbance. While the scale level of observation is a choice of the observer, consistent assessment of the response can only be made by the simultaneous specification of element size, time and temperature. Temperature averaged over a large region within a given time interval can differ completely from that over a smaller region and different time interval. Scaling of size/time/temperature for nonequilibrium states must be defined such that the same event viewed at the atomic, macroscopic and macroscopic level can be characterized without ambiguity. The objective of this study is to quantitatively assess the size/time/temperature interaction in uniaxial tensile specimen by application of the recently developed isoenergy density theory for non-equilibrium and irreversible changes in solids. Mechanical and thermal interdependence is invoked by considering their mutual interaction as one of the same process. Predicted are the progressive damage states in a 2024-T3 aluminum cylindrical bar stretched at a constant displacement rate of 2.117×10 −5 m/s . The region of observation is varied by altering the element size. What appeared as cooling and dilatation on one scale level may correspond to heating and distortion on another scale level. Cooling/heating and dilatation/distortion tend to flip and flop as the size scale is reduced or increased progressively; the details depend on the loading rate and type. The oscillating behavior of temperature in time tends to increase with decreasing size scale and the corresponding displacements become equally disturbed. Such a feature is observed as the element shrinks in size and is deterministic regardless of the system geometry and loading.

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