R.M. Souza

Finite element modeling of the stresses, fracture and delamination during the indentation of hard elastic films on elastic–plastic soft substrates

In this work, the mechanical behavior of hard films on soft substrates was studied based on the finite element analysis of an indentation with normal forces. As an attempt to reproduce situations found in practice, defects were considered during the preparation of the finite element mesh, both in the film and at the interface. A sequence of steps was considered during the loading sequence applied in the models. Initially, the deposition (intrinsic) and thermal (extrinsic) stresses were introduced to account for all residual stresses present in thin films deposited by processes such as sputtering. Later, a normal load of 50 N was applied on the pre-stressed system. The effects of a crack that propagated along the film/substrate interface was studied directly, by calculating the normal and shear stresses that develop at the film surface and the film/substrate interface, and indirectly, by looking at the behavior of cracks located at the film surface and propagating perpendicular to the interface. The results indicated that the suppression of the constraint imposed by the interface resulted in a decrease in the stresses in the film. However, the crack at the interface apparently did not interact with the stresses responsible for the array of circular cracks usually observed at the contact edge of the indentation of coated systems with soft substrates.

A critical reassessment of elastic unloading in sharp instrumented indentation experiments and the extraction of mechanical properties

This work examines the extraction of mechanical properties from instrumented indentation P–h s curves via extensive three-dimensional finite element analyses for pyramidal tips in a wide range of solids under frictional and frictionless contact conditions. Since the topography of the imprint changes with the level of pile-up or sink-in, a relationship is identified between correction factor β in the elastic equation for the unloading indentation stage and the amount of surface deformation effects. It is shown that the presumption of a constant β significantly affects mechanical property extractions. Consequently, a new best-fit function is found for the correlation between penetration depth ratios h e /h max, h r /h max and n, circumventing the need for the assumption of a constant value for β, made in our prior investigation [Acta Mater. 53 (2005) pp. 3545–3561]. Simulations under frictional contact conditions provide sensible boundaries for the influence of friction on both h e /h max and h r /h max. Friction is essentially found to induce an overestimation in the inferred n. Instrumented indentation experiments are also performed in three archetypal metallic materials exhibiting distinctly different contact responses. Mechanical property extractions are finally demonstrated in each of these materials.

Effects of elastic indenter deformation on spherical instrumented indentation tests: the reduced elastic modulus

Although the Hertz theory is not applicable in the analysis of the indentation of elastic-plastic materials, it is common practice to incorporate the concept of indenter/specimen combined modulus to consider indenter deformation. The appropriateness was assessed of the use of reduced modulus to incorporate the effect of indenter deformation in the analysis of the indentation with spherical indenters. The analysis based on finite element simulations considered four values of the ratio of the indented material elastic modulus to that of the diamond indenter, E/Ei (0, 0.04, 0.19, 0.39), four values of the ratio of the elastic reduced modulus to the initial yield strength, Er/Y (0, 10, 20, 100), and two values of the ratio of the indenter radius to maximum total displacement, R/δmax (3, 10). Indenter deformation effects are better accounted for by the reduced modulus if the indented material behaves entirely elastically. In this case, identical load–displacement (P − δ) curves are obtained with rigid and elastic spherical indenters for the same elastic reduced modulus. Changes in the ratio E/Ei , from 0 to 0.39, resulted in variations lower than 5% for the load dimensionless functions, lower than 3% in the contact area, Ac , and lower than 5% in the ratio H/Er . However, deformations of the elastic indenter made the actual radius of contact change, even in the indentation of elastic materials. Even though the load dimensionless functions showed only a little increase with the ratio E/Ei , the hardening coefficient and the yield strength could be slightly overestimated when algorithms based on rigid indenters are used. For the unloading curves, the ratio δe/δmax , where δe is the point corresponding to zero load of a straight line with slope S from the point (Pmax, δmax ), varied less than 5% with the ratio E/Ei . Similarly, the relationship between reduced modulus and the unloading indentation curve, expressed by Sneddons equation, did not reveal the necessity of correction with the ratio E/Ei . The most affected parameter in the indentation curve, as a consequence of the indentation deformation, was the ratio between the residual indentation depth after complete unloading and the maximum indenter displacement, δr/δmax (up to 26%), but this variation did not significantly decrease the capability to estimate hardness and elastic modulus based on the ratio of the residual indentation depth to maximum indentation depth, hr/hmax . In general, the results confirm the convenience of the use of the reduced modulus in the spherical instrumented indentation tests.

A review on the reverse analysis for the extraction of mechanical properties using instrumented Vickers indentation

This work presents a review on recent methodologies for the analysis of data obtained through instrumented indentation testing. Experimental tests, using a Vickers indenter, were carried out on low-carbon and bearing steels and indents were later analyzed in a laser interferometer. The results were used to verify the accuracy of methods proposed to predict the indentation morphology, pile-up or sink-in, and the accuracy of routines proposed to extract the mechanical properties of the indented materials. The occurrence of pile-up in all tested materials indicated that models may fail in predicting this behavior and, consequently, in determining the yield stress and strain-hardening exponent.

Folded Metal and Other Surface Parameters on Combustion Engine Cylinders

In the last years, sophisticated analyses and control of topography parameters have been introduced to study engine bore cylinders. Such surface characteristics have impact on friction and wear of the engine, with effects on fuel consumption and durability. Among such characteristics, folded metal blocking the honing grooves has received much attention, but its quantification and actual impact on engine performance is still under discussion, both in the academia and in the industry. In this work, a methodology was developed to mathematically quantify the folded metal present in engine bores. The method is compared to others described in the literature and in use by some European automotive manufacturers.

Numerical Simulation of Residual Stresses in Quenched Steel Bodies Using Subroutines to Represent TTT and CCT Diagrams

The objective of this work is to analyze residual strains and stresses and volumetric expansion due to phase transformations that occur during quenching of a steel body. Three different models are proposed, based on the finite element software ABAQUS ® and on the use of FORTRAN subroutines. The time-tempreature-transformation (TTT) or continuous-cooling-transformation (CCT) diagrams of SAE 4140 steel are represented differently in each model, depending on the transformed phases and correspondent volumetric expansion. In the first model, diagrams are intentionally simplified in order to consider only the austenite-martensite transformation. In the second model, the thermomechanical-phase transformation coupling is represented through the incorporation of the austenite-pearlite transformation into the TTT diagram used in the first model and considering that this transformation occurs for cooling rates lower than the limit for martensitic transformation. The third model is based on a subroutine that calculates all the microstructures resulting from quenching (ferrite, pearlite, bainite, and martensite), depending on cooling rate. This subroutine includes information from all the TTT and CCT diagrams of SAE 4140 into a FORTRAN code. Model testing was conducted based on the analysis of the quenching of a cylinder with diameter of 45 mm and based on the comparison with results presented in the literature. Significant differences are observed in the numerical results provided by each model, which, in some cases, also provided data with significant differences from literature.

ANALISIS POR ELEMENTOS FINITOS DE LA PROPAGACIÓN DE GRIETAS CIRCULARES DURANTE LA INDENTACIÓN DE SISTEMAS RECUBIERTOS

High stresses and complex stress fields are usually developed in thin films deposited on the coated systems when they are submitted to indentation test. This work was developed to study the stress fields obtained when the indentation test is conducted on coated materials systems. During the indentation, a spherical indenter was considered and applied normal load of 50 N on a system. The results were obtained using the finite element method (FEM), through the software ABAQUS ® , using a axisymmetric bidimensional mesh. The results allowed an analysis of the propagation of the circular cracks as a function of the stresses developed on the film surface.