Three-dimensional numerical simulation of Vickers indentation tests

Abstract

The development of depth sensing indentation equipment has allowed easy and reliable determination of two of the most popular measured mechanical properties of materials: the hardness and the YoungÕs modulus. However, some difficulties emerge in the experimental procedure to calculate accurate values of these properties. This is related to, for example, the tip geometrical imperfections of the diamond pyramidal indenter and the definition of the contact area at the maximum load. Being so, numerical simulation of ultramicrohardness tests can be a helpful tool for better understanding of the influence of these parameters on procedures for determining the hardness and the YoungÕs modulus. For this purpose, specific finite element simulation software, HAFILM, was developed to simulate the ultramicrohardness tests. Different mesh refinements were tested because of the dependence between the values of the mechanical properties and the size of the finite element mesh. Another parameter studied in this work is the value of the friction coefficient between the indenter and the sample in the numerical simulation. In order to obtain numerical results close to reality, a common geometry and size of the imperfection of the tip of Vickers indenter was taken into account for the numerical description of the indenter.

Estudo numérico da influência do coeficiente de atrito no ensaio de indentação em filmes finos

“…Estas observações também foram feitas por Bressan et al [18] e Huang & Pelegri [19]. Desta forma, em simulações numéricas do ensaio de indentação, pode-se desconsiderar o atrito entre o penetrador e a amostra, do ponto de vista da carga de indentação [5][6][7][8][9][10].…”

“…Em função destas limitações na análise dos ensaios de indentação o uso de uma técnica numérica capaz de avaliar os campos de tensões e de deformações durante o ciclo de indentação pode auxiliar em uma interpretação mais segura deste ensaio. Nas últimas décadas, esta metodologia numérica começou a ser estudada através de modelos discretos de elementos finitos para avaliar o comportamento de diferentes materiais sob o ensaio de indentação [5][6][7][8][9].…”

“…Este método tem sido largamente utilizado para simular e resolver inúmeros problemas não lineares nas áreas de instabilidade estrutural, de sistemas dinâmicos, sistemas fluidos, eletromagnéticos e de conformação mecânica. Porém, a utilização desta técnica numérica para avaliar o ensaio de indentação em recobrimentos superficiais finos ainda tem apresentado problemas, sejam pelas limitações computacionais ou pelas dificuldades na implementação de modelos que representem um ensaio real e, principalmente, com a devida caracterização da interface entre o filme e o substrato [2,[5][6][7][8][9][10].…”

Mechanical Properties of Porosity-Free Beta Tricalcium Phosphate (<i>β</i>-TCP) Ceramic by Sharp and Spherical Indentations

“…For a Vickers indenter, King [18] proposed a value of 1.012 whereas Dao et al [19] proposed a value of 1.07. Using a three dimension simulation of the Vickers indentation, Antunes et al [8] give 1.05 independently on the mechanical properties of the material which is the value here considered for . Secondly, another coefficient, γ, has to be introduced to take into account the overestimation of the elastic modulus.…”

“…For example, some models consider the indentation size effect modeled by Nix and Gao [1] into the hardness calculation [2] or in the expanding cavity models for tensile properties determination [3] while other models consider the hardness independently on the load [4,5]. To improve the accuracy on the determination of the elastic modulus from unloading curves, different correction factors proposed by Hay et al [7], Antunes et al [8] and FischerCripps [9] have been introduced into the model of Oliver and Pharr [6] to take into account the geometry of the indenter and the approximation made when applying the contact theory of Hertz. Still, an important question remains that divides the opinions of the researchers into two groups; one group considering that it is the Young's modulus that is determined by IIT and another group stating that only the bulk modulus can be determined by this method.…”