G. Mauvoisin

New procedure to determine steel mechanical parameters from the spherical indentation technique

Abstract A new numerical and experimental approach for determining mechanical properties of steels is presented. This method uses the instrumented spherical-indentation technique. A relationship between applied load, indenter displacement, flow stress and strain hardening exponent of steels, is given. This method is based on the minimisation of error between the experimental curve (applied load–indenter displacement curve) and the theoretical curve which is a function of the mechanical properties of studied materials. Comparison between the results obtained by the proposed method and experimental tensile tests, confirms the interest of the proposed method.

New method to determine the mechanical properties of heat treated steels

Abstract A new numerical approach to indentation problems is developed for hardened materials. A relationship between load, displacement, flow stress and strain hardening exponent of heat treated materials with a hard film, is given. This method is based on the minimisation of the error between the experimental curve (load–displacement of the indenter) and the theoretical curve, function of the mechanical and geometrical properties of the studied materials. Comparison of the numerical results with those experimentally obtained from known materials confirms the interest of the method proposed.

Evaluation of the tensile properties of a material through spherical indentation: definition of an average representative strain and a confidence domain

In the present article, a new method for the determination of the hardening law using the load displacement curve, F–h, of a spherical indentation test is developed. This method is based on the study of the error between an experimental indentation curve and a number of finite elements simulation curves. For the smaller values of these errors, the error distribution shape is a valley, which is defined with an analytic equation. Except for the fact that the identified hardening law is a Hollomon type, no assumption was made for the proposed identification method. A new representative strain of the spherical indentation, called “average representative strain,” εaR was defined in the proposed article. In the bottom of the valley, all the stress–strain curves that intersect at a point of abscissa εaR lead to very similar indentation curves. Thus, the average representative strain indicates the part of the hardening law that is the better identified from spherical indentation test. The results show that a unique material parameter set (yield stress σy, strain hardening exponent n) is identified when using a single spherical indentation curve. However, for the experimental cases, the experimental imprecision and the material heterogeneity lead to different indentation curves, which makes the uniqueness of solution impossible. Therefore, the identified solution is not a single curve but a domain that is called “solution domain” in the yield stress–work hardening exponent diagram, and “confidence domain” in the stress–strain diagram. The confidence domain gives clear answers to the question of uniqueness of the solution and on the sensitivity of the indentation test to the identified hardening laws parameters.

Influence of material properties on the drilling thrust to hardness ratio

A drilling method developed by the authors for the measurement of the hardness profile for surface heat treated steels is based on the proportionality between drilling thrust and material hardness. However, parameters other than hardness related to the material can modify the cutting thrust level. In order to study the influence of the microstructure, the ductility, the toughness and the work hardening of material on the drilling thrust, a few tests were carried out in this work. Tensile and impact tests were carried out on different materials. Moreover, micrographic observations and Vickers micro-hardness were performed on the chips. The study allowed two groups of materials to be distinguished according to the drilling thrust to hardness ratio (R/HV). The first includes not very ductile materials presenting an about constant and low value of R/HV, short, thin and not very work hardened chips. The second includes ductile materials presenting a non constant and high value of R/HV, long, thick and very work hardened chips. As a consequence, the hardness profile determination by drilling method is reliable only if the R/HV ratio is about the same for the treated layer and for the substrate, i.e. if the difference in ductility between the treated layer and the substrate is not very high.

Hardness profile analysis of elasto-plastic heat-treated steels with a gradient in yield strength

An elasto-plastic indentation study on materials with a yield strength gradient like steels which have undergone thermal hardening such as nitriding, is carried out using experimental and finite element methods. The analysis of the normalized mean contact pressure as a function of a dimensionless strain parameter for graded materials shows that the mean contact pressure presents the same tendency as equivalent homogeneous materials. A simple model for the average plastic zone radius of graded materials is given. A relation is developed to predict the hardness variation as a function of the indentation depth. Lastly, a theory based on the effective evolution of hardness is proposed to determine the yield stress and hardness profile for materials with a decreasing yield stress with depth. Results for carbo-nitriding steels obtained by the standard Vickers micro hardness techniques are compared with those obtained by the proposed method.

Determination of the Hardness Profile on Heat Treated Steels by Hole Drilling and Indentation Methods

A new approach to determine the hardness profile of superficially heat treated steels is proposed. This method uses the experimental hole drilling technique based on the measurement of the penetration load of the drill for the treated steels with a non negligible hard film thickness and the indentation technique for the case of thin hard films. The thrust measured during a drilling test is reliable to the hardness of the material being tested. The approach using the indentation technique gives a relationship between load, displacement, flow stress and strain hardening exponent. This method is based on minimization of the error between the experimental curve (load-displacement of the indenter) and the theoretical curve, as a function of the mechanical and geometrical properties of the materials studied. Results for carbo-nitriding steels obtained by the standard Vickers micro hardness technique are very close to those obtained by both methods.

Experimental and numerical analyses of instrumented and continuous indentation of treated steels

Abstract The present paper uses the indentation of materials with a yield strength gradient, by spherical indenters in order to obtain Vickers hardness profile. Using finite element modelling, a simulation of elasto-plastic spherical indentation of materials with a yield stress was carried out. A theoretical model for effective mean pressure evolution of the spherical indentation on the surface of heat treated steels was obtained. Using the preceding model and steepest descent optimisation algorithms, a method for determining Vickers hardness profile (surface hardness and layer thicknesses) of these steels, is given. Results for carbo-nitriding steels obtained by the standard Vickers micro-hardness techniques (on the section taken through the surface) are compared with those obtained by the proposed method.

Material Mechanical Properties Influence on the Ratio of Drilling Thrust to Hardness

A new approach using an experimental hole drilling technique has been developed to determine the hardness profile of superficially heat-treated steels. This method was based on the proportionality between the hardness of the material tested and the cutting thrust measured during the drilling test. Although it was observed that, overall, the increase in the cutting thrust was linear with hardness, locally the variation of thrust was not necessarily regular and linear in particular for iron-carbon alloys. In fact, other parameters related to the material, other than hardness, can modify the cutting thrust level. We report here on the influence of parameters, such as the type of microstructure and the ductility or the work hardening of material, on drilling thrust. The cutting thrust obtained for various brittle or ductile materials will be discussed using results obtained from hardness tests, micrographic observations and microhardness of the chips obtained by drilling test.

Determination of the Plastic Strain by Spherical Indentation of Uniaxially Deformed Sheet Metals

This work consists of determining the plastic strain value undergone by a material during a forming process using the instrumented indentation technique (IIT). A deep drawing steel DC01 is characterized using tensile, shear and indentation tests. The plastic strain value undergone by this steel during uniaxial tensile tests is determined by indentation. The results show that, the identification from IIT doesn’t lead to an accurate value of the plastic strain if the assumption that the hardening law follows Hollomon law is used. By using a F.E. method, it is shown that using a Voce hardening law improves significantly the identification of the hardening law of a pre-deformed material. Using this type of hardening law coupled to a methodology based on the IIT leads to an accurate determination of the hardening law of a pre-deformed material. Consequently, this will allow determining the plastic strain value and the springback elastic strain value of a material after a mechanical forming operation.

Influence of Dissipated Plastic Energies on Indented Load-Depth Curve for Materials with a Yield Strength Gradient

The present paper investigates the indentation of materials with a linear yield strength gradient by spherical indenters. These materials were discretized to several homogeneous layers. The indentation load-depth curve depends on the plastic energies dissipated in each layer made of plastically graded materials. A new mixture model is presented and allows the exact influence of the plastic energies on the load-depth curve (F-δ) obtained from the instrumented indentation test to be determined. On the other hand, the model results show how the response of plastically graded materials can be obtained from the answer of homogenous materials to indentation; The properties of homogenous materials are the same as those of each thin layer in plastically graded layers, and the dissipated plastic energies dissipated in each thin layer. The use of finite element simulations of spherical indentation for materials with a yield strength gradient provide the plastic energies dissipated in plastically graded layers and in the substrate, as well as the indentation load-depth response. The proposed model was tested by using mechanical properties of nitrided steels. The comparison between the results obtained by the proposed model and those obtained numerically from known materials, confirms that the indentation curve F-δ can be reconstructed from the plastic energies in the indented zones. K e y w o r d s : Indentation method, Finite element modeling, Hardness, Plastic energy, Yield stress gradient, Nitrided steels. * Author to whom correspondence should be addressed