Journal of Multiscale Modelling

Accurately predicting the failure of multilayered surface systems, including coatings on tools or products, is of significance for all of the parties concerned within the chain of design, manufacturing and use of a product. Previous modeling work has, however, been focused largely on the effect of individual parameters rather than on the performance of a multilayered system as a whole. Design and manufacture of multilayered surface systems, currently, still relies largely on experiments and failure tests. A parameterized approach which considers geometrical, material, interfacial and loading variables, processing history, thermal effects, surface-failure modeling, etc. has therefore been developed to address the situation in order to be able to improve the efficiency and accuracy of the analysis and design of multilayered coating-systems. Material property values for the hardened case of the substrate are described with a function of the hardened depth and defined with a field method. Initial residual stresses calculated using a newly developed theoretical model are incorporated into the model as initial stress conditions. Thermo-mechanical coupled modeling is incorporated into the model so as to be able to consider temperature effects. These are associated with a cohesive-element modeling approach, which has been used to predict indentation-induced crack initiation and propagation within the coating layer. The comparison of experimental results with those of numerical modeling affords excellent agreement.

The parameterized modeling method developed allows for the parameters to be changed easily during a series analysis. Combined with the capability of the prediction of cracking of the coatings, the developed method/model provides an efficient way for investigating the effects of these parameters on the behavior of multilayered systems, which is demonstrated by the analysis of three cases of the coated tool steels (H11): (i) a substrate without being pre-heat-treated; and (ii) two substrates with a shallow and a deep hardened-case, respectively, (both are treated by plasma-nitriding). The results showed that the case-hardening of a substrate has a significant influence on the performance of the surface system with coating, especially on its load-bearing capacity and the cracking of the coating.

The formation of the interface of a Cu/Ag bilayer during sputtering was studied with molecular dynamics simulations with EAM potential. The results show that the first deposited Ag layer grows on the Cu substrate by the layer mode, while the first deposited Cu layer grows on the Ag substrate by the island mode for both the (111) and (001) orientated growth. The film is epitaxial up to the coverage, reaching about 10 monolayers except for Cu growth on Ag (001). Ag atoms in the (001) orientated substrate diffuse into the Cu film for a longer distance compared to other cases. The interface is sharp and exhibits a (9 × 9) superstructure with hexagonal moiré pattern for both Ag growth on Cu (111) and Cu growth on Ag (111). The displacement of the superposed Cu atoms contributes to the corrugation of the interface for both cases. A c(10 × 2) superstructure forms when Ag grows on Cu (001). When Cu is deposited on Ag (001), partial dislocations are activated near the interface, and a great number of stacking faults form in the Cu film with the significantly curved interface.

On cutting tools for high performance cutting (HPC) processes or for hard-to-cut materials, there is an increased importance in so-called superlattice coatings with hundreds of layers each of which is only a few nanometers in thickness. Homogeneity or average material properties based on the properties of single layers are not valid in these dimensions any more. Consequently, continuum mechanical material models cannot be used for modeling the behavior of nanolayers. Therefore, the interaction potentials between the single atoms should be considered. A new, so-called atomic finite element method (AFEM) is presented. In the AFEM the interatomic bonds are modeled as nonlinear spring elements. The AFEM is the connection between the molecular dynamics (MD) method and the crystal plasticity FEM (CPFEM). The MD simulates the atomic deposition process. The CPFEM considers the behavior of anisotropic crystals using the continuum mechanical FEM. On one side, the atomic structure data simulated by MD defines the interface to AFEM. On the other side, the boundary conditions (displacements and tractions) of the AFEM model are interpolated from the CPFEM simulations. In AFEM, the lattice deformation, the crack and dislocation behavior can be simulated and calculated at the nanometer scale.

A set of continuum viscoplastic damage constitutive equations is presented in this paper. The equations are calibrated for a TiN coating material, and a number of substrate materials, and are implemented into the commercial finite element (FE) solver, ABAQUS, through the user-defined material subroutine, VUMAT, for FE simulation. An FE model has been created to simulate a load-bearing test. Studies are carried out to investigate failure features of the coating with variations in coating thickness for three different substrate materials: pure copper, a gear steel and a tool steel. It has been demonstrated that the proposed damage equations can be used to predict failure features of coatings, which are affected by the thickness of the coating and the stiffness of the substrate.

Local residual stress fields often influence and even govern some of the mechanical properties of multilayered coatings at nanoscale. An approach is developed for the evaluation of the local residual stress with the representative volume element (RVE) of a multilayered coating and the concept of lattice mismatch between neighboring layers, incorporating high-precision density functional theory calculations. The calculated results are in good agreement with experimental reports, even if each individual host constituent is assumed linearly elastic, demonstrating the validity of the proposed approach in the evaluation of the residual stress. In addition, it is found that lattice mismatch is a reasonable key factor to account for the extremely large residual stress in multilayered transitional metal-nitride coatings.

The so-called Gurson model is a well-established micromechanical model of the ductile fracture of porous materials, where the mechanism is void nucleation, growth and coalescence. Although the Gurson model, and particularly its modified form developed by Tvergaard and Needleman, is widely used, its application to void closure has received relatively little attention. The first objective of the current work is to explore the applicability of the Gurson model to void closure. The fixed parameters characterizing the modified Gurson model are not universal and must be calibrated for a particular material, typically by trial and error fitting of finite element (FE) simulations to experimental data. However, the trial and error approach is expensive and time consuming (one test generally corresponds to only one triaxiality level). A novel approach has been developed in the present work to identify the void closure model parameters using a nongradient based optimization search method (pattern search method). Rather than using experimental data for void closure, a series of finite element analyses, one of a representative volume element (RVE) containing a spherical void, and another with an equivalent cell of Gurson–Tvergaard (GT) material, has been performed. Both models have parametric characterizations, enabling simulations under different triaxialities and initial void volume fractions. The numerical results of the discrete void RVE and the GT cell can then be compared and model parameters identified. The new automated method was applied using material properties obtained from high temperature tensile testing of Telby plus steel at 900°C and 1100°C, temperatures in the range of those experienced during a typical steel rolling process. The effect of strain rate on void closure is also investigated using this approach for Telby plus steel.

The stability of coating-substrate systems influences the chip formation and the surface integrity of the new generated workpiece surface, too. Using finite element (FE) simulation, deformations, strains and stresses in coated tools, caused by external and internal loads, can be computed on a microscopic scale. Since both, the whole macroscopic tool (in mm-scale) and the microscopic coating layers (in μm-scale up to nm-scale) must be included in the same geometrical simulation model, graded high-resolution FE meshes must be used. Nevertheless, the number of nodes in the 3D computational FE grid reaches some millions, leading to large computational time and storage requirements. For this reason, an advanced adaptive finite element (AAFEM) software has been developed and used for the simulation.