Efficient thermo-mechanical model for solidification processes

Abstract

SUMMARYA new, computationally efficient algorithm has been implemented to solve for thermal stresses, strains, and displacements in realistic solidification processes which involve highly nonlinear constitutive relations. A general form of the transient heat equation including latent-heat from phase transformations such as solidification and other temperature-dependent properties is solved numerically for the temperature field history. The resulting thermal stresses are solved by integrating the highly nonlinear thermo-elastic-viscoplastic constitutive equations using a two-level method. First, an estimate of the stress and inelastic strain is obtained at each local integration point by implicit integration followed by a bounded Newton-Raphson (NR) iteration of the constitutive law. Then, the global finite element equations describing the boundary value problem are solved using full NR iteration. The procedure has been implemented into the commercial package Abaqus (Abaqus Standard Users Manuals, v6.4, Abaqus Inc., 2004) using a user-defined subroutine (UMAT) to integrate the constitutive equations at the local level. Two special treatments for treating the liquid/mushy zone with a fixed grid approach are presented and compared. ISS, vol. 76, 1993) specialized in thermo-mechanical modelling of continuous casting. Both finite element codes are then applied to simulate temperature and stress development of a slice through the solidifying steel shell in a continuous casting mold under realistic operating conditions including a stress state of generalized plane strain and with actual temperaturedependent properties. Other local integration methods as well as the explicit initial strain method used in CON2D for solving this problem are also briefly reviewed and compared.

Measuring Mechanical Behavior of Steel During Solidification: Modeling the SSCC Test

“…[11] and [12]) are transformed into two integrated equations by invoking the backward Euler method and are solved by using a specialized Newton-Raphson method [10,13,84] The updated global equilibrium equations then are solved using the nonlinear procedures in the commercial software ABAQUS v. 6.9-1. [17] This approach has been implemented successfully [16,57] and has been validated by matching temperature and stress in the semianalytical solidification problem posed by Weiner and Boley. [63] The modeled domain, shown in Figure 5, uses 35,100 4-node linear axisymmetric finite elements for the upper part, lower part, ZrO 2 layer, and steel melt.…”

“…[64,65] Computational modeling evolved to more complex behavior including coupling the heat conduction and mechanical equilibrium equations with creep [66,67] and elasticviscoplastic behavior. [16,[68][69][70][71][72] Koric and Thomas and coauthors implemented the Kozlowski III model for austenite [13] and the Zhu model for delta-ferrite [68] into both implicit [16] and explicit [73] integration schemes to model the high-temperature behavior of steel. These models have been applied to predict crack formation during continuous casting.…”

“…Separate constitutive models of the thermal-mechanical behavior for austenite [13] and delta-ferrite [12] were developed previously by empirically fitting measured data [14,15] to determine the relationship among stress, strain, strain rate, temperature, and carbon content. These models for the separate phases were incorporated into an efficient numerical methodology of modeling solidification developed by Koric and Thomas [16] and implemented into the commercial software ABAQUS (Providence, RI). [17] This modeling approach has been used for a wide range of applications including stress development in solidifying steel [16] and the formation of longitudinal face cracks.…”

“…These models for the separate phases were incorporated into an efficient numerical methodology of modeling solidification developed by Koric and Thomas [16] and implemented into the commercial software ABAQUS (Providence, RI). [17] This modeling approach has been used for a wide range of applications including stress development in solidifying steel [16] and the formation of longitudinal face cracks. [18] However, the constitutive equations were developed based on tensile test and creep experiments on solid steel that was reheated after solidification and cooling.…”

Finite Element Simulation and X-Ray Microdiffraction Study of Strain Partitioning in a Layered Nanocomposite

“…This made the numerical analysis of the refined model extremely difficult even on the latest high performance computing platforms. Within each quasistatic time step, a system of nonlinear equations was linearized and solved with a NewtonRaphson (NR) iteration scheme [30,31] in Abaqus which required several linear solver solutions or global equilibrium iterations. Due to the complexity of this problem (material and geometric nonlinearities, three-dimensional problem involving multiple layers, and complex boundary conditions), the direct multifrontal solver in Abaqus/Standard with hybrid parallelization was used.…”