Thermal-Mechanical Coupled Manufacturing Simulation in Heterogeneous Materials

This work is aimed to investigate on thermal and thermo-mechanical behaviour of 6061 Aluminium alloy. The main target of the present investigation is to apply a numerical procedure to assess the thermo-mechanical damage. Finite element analyses of the notched tensile specimens at high temperature have been carried out using ABAQUS Software. The objective was to study the combined effects of thermal and mechanical loads on the strength and ductility of the material. The performance of the proposed model is in general good and it is believed that the presented results and experimental–numerical calibration procedure can be used in practical finite-element simulation.


Introduction
The Finite element modeling (FEM) has been widely introduced into the design of manufacturing products because of its high efficiency in predicting several problems and major defects occurring in sheet metal forming manufacturing process like necking. In order to predict those defects within a virtual manufacturing system [1][2], One of the most widely used models is continuum damage. The tensile strength, the yield strength and Young's modulus depend the temperature because Young's modulus of some tempered steels increases slightly at mid temperatures before decreasing at high temperature on mechanical properties is linked to transformations of the material structure due to various processes that inelastic deformation can occur more easily at elevated temperatures, so more plastic deformation and creep occur in the plastic zone of a fatigue crack [3,4]. The damage parameter is not incorporated into the constitutive equation and it is assumed that presence of voids does not significantly alter the behavior of the material. The von Mises criterion is most frequently used as yield criterion in uncoupled models, Damage parameter is incorporated into constitutive equation and crack growth simulation is automatically performed using a complete deterioration of elements in front of the crack tip [5].
To describe the phenomenon of initiation and growth of cavities and micro cracks induced by large deformation in metals and called "ductile damage", within the framework of continuum damage models, either phenomenological or micromechanically based, have been developed. In recent years, several different formulations for a variety of materials and processes have been presented, such as elastic-brittle [6,7], brittle, creep, fatigue and creep-fatigue [8][9][10][11][12][13], among others. However, initially, the development and application of damage models was focused on ductile fracture.
Ductile fracture process is controlled by nucleation, growth and coalescence of micro voids, so it is natural to link material fracture behavior to the parameters that describe the evolution of micro voids rather than conventional global fracture parameters [14].

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In this work, the 6061 Aluminum alloy was studied in order to find out the effect of tensile strength. Both the malleability and the ductility properties relate to the plasticity of the material. Malleability refers to the ability of plastic deformation under compressive loads, while ductility refers to plastic deformation under tensile loads.

Continuum Damage Mechanics Model for Ductile Materials
Kanchanov defined a continuum damage variable as the relationship between the sectional area of voids A v and the overall sectional area A 0 of a given surface in a volume element Equation 1. This definition is the same one as the micro-void area fraction used is some micromechanical theories, such as McClintock's [15]. The damage variable can assume any value between 0 and 1, covering from a virgin state to a completely damaged reaches a critical value, when the effective area can no longer resist the applied load, loading to the formation of a macroscopic crack.
Where is the effective resisting area. It may observe that.
According to Lemaitre's damage model and strain equivalence principle, any constitutive equation for a damaged material may be derived in the same way as for virgin material, replacing the stress tensor by the effective stress tensor ̌, defined by: The effective elastic modulus of damaged material, giving an indirect way to measure the damage in a solid, by monitoring the evolution of the Young modulus with increasing strain: ̌ is the effective elastic modulus and is the elastic modulus for the undamaged material.
The evolution of an internal thermodynamic state variable can be derived assuming the existence of a potential of dissipation and an associated variable , named damage strain energy release rate and defined as [16]: √ ‖ ‖ is the von Mises equivalent stress, is the deviatoric stress tensor, is the Poisson's ratio and ( ) ( ) is the hydrostatic stress. Further, Lemaitre [16] shows that the damage evolution can be written as: With √ ‖ ‖ defined as the accumulated plastic strain and being the plastic strain tensor. The choice of a proper potential of dissipation that can represent experimental results is the core of any CDM model. In Lemaitre and Chaboche's model, the hypothesis of isotropic damage, existence of a strain threshold for damage initiation and linear evolution of the damage with the accumulation plastic strain leads to the following equation for damage evolution: : The accumulated plastic strain threshold and : The damage resistance parameter, which are material dependent properties.
A critical damage value for the uniaxial stress state which can be calculated with the following equation [16]: Where is the critical damage for the uniaxial stress state and can be measured in a tensile test, is the ultimate stress and is Triaxiality factor, which accounts for the difference between the actual stress state and the perfectly uniaxial stress state.
This model was later implemented in the ABAQUS/Explicit solver using subroutine [17] following the numerical algorithm proposed by lee and Pour-Boughrat [18].

Materials and Simulation Method Description
The material considered in this study is 6061 Aluminium Alloy. The main mechanical and thermal properties of tested specimen are summarized in Table 1. The geometry of the tested studied is shown in Figure 1. To obtain a thermal stress loading under homogeneous uniform temperature distribution, the steel was restrained against axial expansion by creating an interaction boundary condition at its outside edge. In order to determine thermal strain in the analysis we have need to the thermal expansion coefficient. Poisson's coefficient does not depend on temperature and takes the constant value.
A displacement boundary condition was applied at the outside extremity of the tensile specimen. The displacement was smoothly ramped up in the first portion of the test and then held constant.
The explicit finite element calculation software, ABAQUS/Explicit, was employed for the simulation of traction deformation and fracture of the 6061 Aluminium alloy. The size of mesh in the element model was 0.05 mm×0.05 mm and 0.1 mm×0.1 mm for the 20 mm and 110 mm sample, respectively. Thus, there were 18785 and 56360 meshes in the 20 mm and 110 mm model, respectively. The mesh was then transitioned toward the boundaries using triangular elements and quad elements where bilinear mapping could be employed. The finite element analysis results are critical for identifying crack propagation parameters during a TMF cycle. The methodology is sensitive to the finite element modelling procedure. Care must be taken in controlling the element selection, material properties definition and applied boundary condition evaluation. The selected element type was an 8-node linear brick, of reduced-integration elements (C3D8R). In the finite element model, the specimen was simplified as a rigid body. The displacement load was applied on the top specimen along the 3-axis direction with the other degrees of freedom fixed. In the traction test, the Steel cylindrical rod suffered damage. The boundary element method (BEM) simplifies the meshing process and has the ability to correctly characterize the singular stress fields near the crack front. The boundary conditions applied to this model were the result of a global/local approach where displacements and temperatures were taken from the results of the global model and applied to the boundaries of the local sub-model studied here. Therefore, in order to gain a further insight into the evolutionary process of the damage to the 6061 Aluminium alloy, a shear damage model built in the standard model library of ABAQUS software was used. The thermal portion of the analysis should consist at least of two steps. The first step is a steady-state analysis in which the blade is brought from an initial temperature of 100 °F to a steady operating temperature distribution and then the second step simulates the cool down. The transient response of the blade is then monitored for flight time.

Table1. Mechanical and Thermal material properties
Density 2700

Heat capacity [19] 900
Heat conduction [19]  The analysis of the results presented in Figure 2. show that in the first 125 seconds the force Reaches 45.5 KN. The tensile behaviour of the specimens was determined as the load-time relation during tensile loading. Furthermore, a change in the loading curve during time was obtained. Load start, i.e. elastic strain start, then plastic strain start point where the maximum force is reached, i.e. the end of homogenous plastic strain (fracture). The results presented in Figure 2. prove that the maximum elongation before final failure line started. The beginning of elastic deformation, the beginning of plastic deformation, reaching maximum force, the homogeneous plastic deformation to the final fracture of specimen and then the temperature distribution is consistent with the equivalent plastic strain one, which shows that the temperature change causes by the plastic work.

Figure 3. Resulting displacement-Number of cycles curves for three different values Pressure
The Figure 3. depicts the elongation (displacement) measured between the 1 st and N th cycles as a function of the number of cycles. In order to evaluate the influence of the maximum cyclic stress on the dimensional changes of the material, the plastic elongation measured between the 1 st and 500 th has been plotted as a function of the plastic elongation during the 1 st cycle. The plastic elongation between the 1 st and 500 th cycle increases rapidly with the deformation. Thus the elongation between the 1 st and the 500 th test cycle initially increase with the maximum stress, then decrease and becomes very small at high stresses. However, the thermo-mechanically coupled problem is not a bifurcation problem, since inelastic heat generation gives rise to an increased temperature in the specimen and convection results in the non-homogeneous temperature distribution. The response is more brittle for the case of combined softening, which is characteristic for metals when loaded in tension.
To demonstrate the influence of the Pressure loads in the model, simulations have been performed with tree different values: 400, 600 and 650 MPa. During the rapid-growth period exhibited in Figure 5. smaller clusters can continue to grow but they are not necessary to complete the failure. For increasing system sizes the NT onset of rapid growth occurs at earlier times, and so there is less other damage and interactions of the largest cluster with the smaller clusters can be neglected for large system sizes. In the time-dependent problem studied here the heterogeneity is self-generated by the evolution of the damage itself, and there is no heterogeneity in the local failure rates. Furthermore, failure in the present problem is not instantaneous but rather stems from the onset of an accelerating growth process. This latter aspect makes the present problem somewhat more tractable than the time-independent problems, where there is an actual fracture threshold. The damage rate is slightly smaller than the rate of effective plastic strain, as the time, displacement and temperature increases the stress state at the center of the specimen Figure 5. causes the damage to increase exponentially whereas the equivalent plastic strain rate remains approximately constant. The reaction forces on the constrained edge of the specimen it is possible to observe the damage influence on the global behaviour of the structure because the softening caused by damage results on the decrease of the reaction force.

Conclusion
This paper has presented a comprehensive numerical study aimed at developing and validating a predictive model of fracture damage in specimen structure under plastic conditions. The material models successfully describe continuum damage mechanics for ductile materials of specimens that are often presented in literature. The method of scaling fracture locus for different temperatures is successful and for plastic response depends on the type of material. The obtained results confirm that it is very useful to use Continuum damage model based on ABAQUS software for early diagnostics of complex metal structures in the exploitation or service conditions. The obtained results prove that the model offers the possibility of non-destructive and real time testing to observe the physical process of metal degradation and to detect the occurrence of energy dissipation. A large-scale grounding experiment is also simulated showing very good agreement with measurements.