STATE EQUATIONS AND THERMODYNAMICS OF HYSTERETIC MATERIALS

THE BEHAVIOR OF MANY MATERIALS AND SYSTEMS IS DOMINATED BY HYSTERESIS. THE STRESS REQUIRED TO ACHIEVE A GIVEN STRAIN IN PLASTICS, SHAPE MEMORY ALLOYS, CLOTH, ETC. DEPENDS ON THESTRESS DIRECTION AND PAST HISTORY. MAGNETS, ELECTRETS, HEAT TREATMENT OF METALS, ETC. SHOW SIMILAR BEHAVIOR. ENGINEERING DESIGN IS SEVERELY LIMITED WITH THESE MATERIALS BY THE LACK OF A SIMPLE, SELF-CONSISTENT SET OF PREDICTIVE EQUATIONS. SUCH A SET OF PREDICTIVE EQUATIONS HAVE BEEN DERIVED AND TESTED FOR THE SHAPE MEMORY ALLOY, NITINOL. THIS THEORY HAS TWO PARTS: 1) A STATE EQUATION, WHICH UNIQUELY AND COMPLETELY RELATES STRESS, STRAIN AND TEMPERATURE USING 6 MATERIAL SPECIFIC COEFFICIENTS; & 2) A THERMODYNAMICS WHICH RELATES THE MECHANICAL BEHAVIOR (STATE EQUATION) TO THE HEAT FLOW PROPERTIES. THE STATE EQUATION DESCRIPTION OF MECHANICAL BEHAVIOR HAS BEEN THOROUGHLY TESTED. PRELIMINARY TESTS INDICATE THE SAME FORM OF EQUATION APPLIES TO ELECTRETS AND OTHER HYSTERETIC MATERIALS. THE THERMODYNAMIC PREDICTIONS HAVE NOT YET BEEN TESTED BY SUBSEQUENT MEASUREMENTS. THE PROPOSED PHASE I RESEARCH IS TO TEST THE THERMODYNAMICS. THE PHASE II RESEARCH WILL USE THE THEORY TO STUDY NITINOL FATIGUE, REFINE THE FORM OF THE STATE EQUATIONS, AND APPLY THE THEORY TO OTHER HYSTERETIC MATERIALS.