Aplicação do método de análise dimensional para a determinação de propriedades elasto-pláticas de materiais pelo ensaio de indentação instrumentada

Abstract

Instrumented indentation test is a technique that allows obtaining the hardness of small volumes of materials. However, in addition to the hardness, it is of great interest to obtain other elastoplastic properties using information from the curves of these tests. In this work, an inverse algorithm was developed with the help of two dimensionless functions, adjusted using the finite element method, to simulate the instrumented indentation test and the least squares method for the determination of the coefficients of the functions. Subsequently, this algorithm was used for the determination of the modulus of elasticity E, hardness H, hardening exponent and yield stress Y of SAE 1020, SAE 1045 carbon steels and Cr-Mo SAE 4140 steel. These mechanical properties were determined using a instrumented microduometer with a Berkovich diamond indenter. An analysis of the sensitivity of the algorithm to the problem variables was performed, and the results showed that a greater variation in the solution of the hardening exponent calculated by the algorithm can occur as values of the dimensionless variables hf/hmax and/or WP/WT decrease. Also, certain combinations of values in the dimensionless variables can cause negative solutions that are physically impossible, with the limit of applicability of the algorithm given by WP/WT> 0.66. Adjustments of the coefficients of the dimensionless functions also revealed a lack of correlation between the hardening exponent n and the dimensionless ratio between the yield stress and the reduced modulus of elasticity Y/Er. Results for the hardening exponent of normalized SAE 1020 steels, normalized SAE 1045 steels and quenched and tempered SAE 1045 steel presented a maximum error of approximately -10% for normalized SAE 4140 steel, the error was -42,55% and for the sample of SAE 4140 quenched and tempered, a -15,79% error was obtained. The calculated yield stresses for SAE 1020 normalized and SAE 1045 normalized steels presented, respectively, 12,08% and -10,11% error, for the other materials analyzed, the calculated error was greater than approximately 40%. In relation to hardness, the largest error calculated was for quenched and tempered SAE 4140 steel, -13,00%, and the rest of the samples presented errors lower than 4%. The error in the modulus of elasticity estimated by the algorithm was higher for the SAE 1020 normalized steel and SAE 1045 normalized steel, 41,76% and -12,13% respectively, and the remaining samples had errors calculated between -6,15% and –2,17%.