ABSTRACT
Transformations..................................................................................... 373 9.6 Modeling of Mechanical Interactions ................................................................................ 374
9.6.1 General .................................................................................................................. 374 9.6.2 Constitutive Models .............................................................................................. 374
9.6.2.1 Elasto Plastic Material Models.............................................................. 375 9.6.2.2 Elasto Viscoplastic Models ................................................................... 376 9.6.2.3 Unified Plasticity Models ...................................................................... 376
9.6.3 Prediction of Overall Mechanical Properties of the Phase Mixture ..................... 377 9.6.4 Plastic Memory Loss due to Phase Transformations............................................ 378 9.6.5 Equations Governing Mechanical Behavior ......................................................... 379
9.6.5.1 Formulation of Purely Elastic Behavior................................................ 380 9.6.5.2 Formulation of Purely Thermal Strains................................................. 380 9.6.5.3 Formulation of Dilatational Phase Transformation Strains................... 380
9.6.5.5 Formulation of Plastic Behavior during Quenching ................................. 381 9.6.5.6 Formulation of Plastic Deformation Memory Loss .................................. 382
9.6.6 Thermoelastoplastic Formulation of Quenching..................................................... 383 9.6.6.1 Derivation of Standard and Consistent Tangent
Modular Matrices ...................................................................................... 384 9.6.6.2 Solution Algorithm.................................................................................... 385 9.6.6.3 Integration.................................................................................................. 386
9.6.7 Finite Element Solution of the Thermoelastoplastic Problem ................................ 388 9.6.7.1 Idealization and Discretization .................................................................. 388 9.6.7.2 Derivation of Elemental Equations ........................................................... 389 9.6.7.3 Assembly ................................................................................................... 389 9.6.7.4 Imposition of Boundary Conditions.......................................................... 390 9.6.7.5 Solution of Equations and Convergence................................................... 392
9.6.8 Modeling TRIP ....................................................................................................... 392 9.6.8.1 Parameter Determination for TRIP Models .............................................. 394 9.6.8.2 Incorporation of TRIP in Constitutive Behavior....................................... 396
9.7 Guidelines for Implementation in FEA Software .............................................................. 397 9.7.1 Implementation in ABAQUS.................................................................................. 397
9.7.1.1 Thermal Analysis Procedure ..................................................................... 397 9.7.1.2 Microstructural Evolution Analysis .......................................................... 398 9.7.1.3 Mechanical Analysis Procedure ................................................................ 398
9.7.2 Implementation in MSC.MARC............................................................................. 402 9.7.2.1 Thermal Analysis Procedure ..................................................................... 403 9.7.2.2 Microstructural Evolution Analysis .......................................................... 406 9.7.2.3 Mechanical Analysis Procedure ................................................................ 407
9.8 Conclusion, Remarks, and Recommendations .................................................................. 408 Nomenclature ................................................................................................................................ 409 References ..................................................................................................................................... 412
Quenching in its most general sense refers to rapid cooling. In polymer chemistry and materials science, quenching is used to prevent low-temperature processes such as phase transformations from occurring by providing only a narrow window of time in which the reaction is both thermodynamically favorable and kinetically accessible.
