Internal Variable Method Research Articles

A constitutive model based on internal variable method and its application to the superplastic forming of four-layer structure

A constitutive model based on internal variable method and its application to the superplastic forming of four-layer structure

Internal Variable and Cellular Automata-Finite Element Models of Heat Treatment

Heat treatment is one of the most important process es in advanced steel products manufacturing. While production processes are still being optimised, numerical modelling of heat treatment is very useful. Finite Elements Method (FEM) is widely used in these cases, due to its proved potential fo r modelling of continuous, macroscopic phenomena. However, its capability to simulate microscale and noncontinuous processes is very limited. Introducing e mpirical model of phase changes into FEM, usually based on Internal Variable Method (IVM) is useful when the information about volume fraction of the phases in the domain a nd stresses due to phase change satisfies the requirements. Notwithstanding, it is difficult to obtain information in-depth about microstructure during heat treatment, because it requires more sophisticated description of phase change process. Those problems can be resolved with multiscale modelling. One of the current approaches in this fi eld employs FEM for computing of temperature, stress and strain fields, while non-co ntinuous, microscale model is based on Cellular Automata (CA) method [1]. Recently, several CA models concerning phase transformation have been proposed, e.g. [2]. In th is paper Cellular Automata ‐ Finite Elements (CAFE) is applied for modelling of both macroscopic and microscopic influence of heat treatment. It also takes into acc ount a stochastic character of processes, which is hard to obtain in typical FEM or IVM solut ion. The advantage of CAFE model ensues from direct representation of microstructure. Although the current microstructural CA model is two-dimensional, it reproduces topological and morphological relations between components of microstructure. The state of CA cells is updated synchronically in cons ecutive time steps. Every cell includes state vector representing fractions of all phases. Thermodynamics of phase transition is a base for a rule-based knowledge rep resentation in the CA model. However, the nondeterministic definition of neighbo urhood and probabilistic energy

Interaction Between Interlaminar and Intralaminar Damage in Fiber-Reinforced Composite Laminates

The interaction between interlaminar and intralaminar damage mechanisms, which may notably affect the structural behavior of fiber reinforced polymeric composites, is investigated. The theoretical model is consistent with an approach based on a thermodynamic framework and the internal variable method, in which specific variables are introduced to predict both in-plane and out-of-plane damage mechanisms. In particular, the damage formulation refers to both Continuum Damage Mechanics and Fracture Mechanics approaches to predict homogenized distributed microcraks and interfacial delamination processes, respectively. The laminate description is based on the use of the first-order shear deformable laminate plate theory and the interface methodology, leading to a satisfactory accuracy in the energy release rate mode mix calculation and low computational costs. The numerical modeling is based on a finite element approach, in which proper integration procedures have been considered to solve nonlinearities involved by the interlaminar and intralaminar damage modes. Numerical examples devoted to multidirectional laminate have been proposed to evaluate the interactions between intralaminar and interlaminar damage mechanisms with respect to both energy release rate prediction and crack growth behavior, by calculating energy release rate distribution along the crack front.

Identification of Parameters in the History Dependent Constitutive Model for Steels

The problem of an influence of history of deformation on material behaviour during hot forming of steels is discussed in the paper. The method of description of the yield stress, which accounts for a strain path, is presented. This approach is based on an internal variable method and it uses dislocation density for a description of the state of the material. Identification of the material parameters in this model is the main difficulty, which prevents its practical application. Therefore, an inverse analysis combined with the experimental data is used in this work for an identification of these unknown parameters. The experiment composed axisymmetric hot compression performed at various temperatures and at various strain rates on the Gleeble 3800 simulator. After identification the flow stress model was implemented into the finite element program and simulations of various hot forming processes were performed.

Modelling of thermal fatigue failure in soft-soldered semiconductor devices using the internal variable method

A physical model of thermal fatigue failure in soft-soldered semiconductor devices has been proposed by introducing the internal variable method of thermodynamics. Based on the analysis of experimental results of device power cycling and solder mechanical behaviour, a fatigue damage lifetime diagram for 95% Pb-Sn solder is given. This diagram can be used for estimating the thermal fatigue lifetime of devices.

New prediction methods for composites hygrothermal behavior

The methodology in this paper allows prediction of the thermal expansion and swelling of a composite material to temperature and moisture variations which typically occur in a launch environment. It is demonstrated that constitutive equations for moisture absorption and moisture-induced dimensional changes can be obtained with an internal variable method which is rooted in the theory of irreversible thermodynamics. Realism is injected into the model through the concept of free volume.