Phenomenological study of parabolic and spherical indentation of elastic-ideally plastic material

International audienceA phenomenological study of parabolic and spherical indentation of elastic ideally plastic materials was carried out by using precise results of finite elements calculations. The study shows that no "pseudo-Hertzian" regime occurs during spherical indentation. As soon as the yield stress of the indented material is exceeded, a deviation from the,purely elastic Hertzian contact behaviour is found. Two elastic-plastic regimes and two plastic regimes are observed for materials of very large Young modulus to Yield stress ratio, E/σy. The first elastic-plastic regime corresponds to a strong evolution of the indented plastic zone. The first plastic regime corresponds to the commonly called "fully plastic regime", in which the average indentation pressure is constant and equal to about three times the yield stress of the indented material. In this regime, the contact depth to penetration depth ratio tends toward a constant value, i.e. hc/h=1.47. hc/h is only constant for very low values of yield strain (σy/E lower than 5.10-6) when aE*/Rσy is higher than 10,000. The second plastic regime corresponds to a decrease in the average indentation pressure and to a steeper increase in the pile-up. For materials with very large E/σy ratio, the second plastic regime appears when the value of the nondimensional contact radius a/R is lower than 0.01. In the case of spherical and parabolic indentation, results show that the first plastic regime exists only for elastic-ideally plastic materials having an E/σy ratio higher than approximately 2.000

An expanding cavity model incorporating pile-up and sink-in effects

International audienceA new expanding cavity model (ECM) for describing conical indentation of elastic ideally-plastic material is developed. For the proposed ECM, it is assumed that the volume of material displaced by the indenter is equal to the volume loss, due to elastic deformation, in the material and depends on the pile-up or sink-in. It was shown that the proposed ECM matches very well numerical data in the final portion of the transition regime for which the contact pressure lies between approximately 2.5Y and 3Y. For material of large E/Y ratio, the new ECM also matches very well numerical data in the plastic-similarity regime. For material of smaller E/Y ratio, the proposed ECM gives better results than the Johnson's ECM because pile-up or sink-in is taken into account

Comparaison entre les déformations représentatives de l'indentation Vickers et de l'indentation sphérique Comparison between representative deformations in Vickers indentation and spherical indentation

National audienceThe application of the concept of the representative strain is often used in the stress-strain curve determination from indentation test. A new methodology for determining the representative strain for spherical and for Vickers indentation is presented in this article. The results obtained from this methodology show that there is no universal value of representative strain independent of the mechanical parameters of materials indented by Vickers indentation and spherical indentation. It is also shown that the representative strain, obtained by Vickers or by spherical indentation, is much lower when it is obtained from the relationship between the applied force and the penetration depth, F-h, rather than from the relationship between the applied force and the contact radius, F-a. By choosing the same representative strain value in spherical indentation and in Vickers indentation, the results show that the same constraint factor is obtained. Hence, it is possible to determine a perfect analogy between the two types of indentation. For Vickers indentation, the values of the calculated representative strains show that simultaneous measurement of relationships F-a and F-h allows to characterize the hardening law with two unknown parameters. In the case of the spherical indentation, the identification of a material hardening law from simultaneous measurements relationships F-a and F-h should lead to a more accurate determination of the stress-strain curve

Identification of macroscopic hardening law through spherical indentation: definition of an average representative strain and a confidence domain.

The instrumented indentation test is widely used for the identification of the stress-strain curve. One of the disadvantages of the indentation test is that the plastic strain field in the deformed sample is not homogenous which makes it difficult to identify the hardening law of the material from an indentation curve. This difficulty can lead to some complications such as the uniqueness of the solution due to the sensitivity of the indentation test. The use of the concept of the representative strain can simplify the analysis of the indentation response and has often been used in the stress-strain curve identification. In the present work, a new method based on the definition of an “average representative strain”, εaR, is developed for the determination of the hardening law using the load displacement curve, F-h, of a spherical indentation test. The advantage of the proposed εaR is that it is directly obtained from the material’s response to the indentation test. This method consists to calculate the error between an experimental indentation curve and a number of FE simulation curves. For the smaller values of these errors, the error distribution shape is a valley, which is defined with an analytical equation. Based on a sensitivity study, the εaR and the corresponding value of stress σaR can be calculated for every penetration depth. Hence, the hardening law is constructed with no assumptions on its mathematical form. Because of the local aspect of the indentation test, materials heterogeneities can lead to differences between several indentation curves obtained under the same conditions. The proposed method allows the determination of a confidence domain that takes into account the experimental imprecision and the material heterogeneity using several indentation curves1, 2. The present method points out the limitation od the indentation test to characterize the mechanical behavior for large deformations. The uniqueness of the solution and the sensitivity of the indentation test are also discussed. The results obtained for a 20MnB5 steel alloy show that the identified hardening law (and confidence domain) is in agreement with the tensile test curve (Figure 1). A similar approach can be used for Vickers indentation for determining the representative strain3. Results obtained for Vickers indentation are discussed and compared to the literature. Please click Additional Files below to see the full abstract

Identification of the hardening law of materials with spherical indentation using the average representative strain for several penetration depths

International audienceThe identification of plastic properties with spherical indentation has been the subject of many studies in last decades. In the present work, a new method for the determination of the hardening law of materials using the load-displacement curve of a spherical indentation test is proposed. This method is based on the use of an average representative strain. The advantage of the proposed average representative strain is that it is strictly obtained from the material response to the indentation test. By using various values of penetration depth, the proposed method gives the range of strain for which the hardening law is precisely identified and allows determining a confidence domain that takes into account experimental imprecision and material heterogeneity. The influence of penetration depth and the error formula on the identified Hollomon hardening law are discussed in the present study. The present study clarifies many problems that were observed in previous studies such as the uniqueness solution and the sensitivity of the indentation test to the plastic parameters of the Hollomon hardening law

Revue bibliographique sur la caractérisation mécanique des matériaux utilisant la déformation représentative en indentation sphérique Literature review on mechanical characterization of materials using a representative strain in spherical indentation

National audienceThe instrumented indentation provides access to several mechanical properties of materials, leading in particular to the knowledge of their hardening law. In front of the lack of a standard procedure, many techniques have been proposed in recent decades. The present work is a literature review on the methods of mechanical characterization based on the instrumented indentation, and using a representative strain. There are two families of methods. The first, based on the Meyer hardness, includes methods of conducting hardness tests with different loads and determine, from the hardness and measuring the radius of the corresponding imprint, a representative deformation and the corresponding stress leading to the construction of the work hardenning curve "point by point" of the tested material. The second includes the methods giving the 2 plastic parameters of the Hollomon law that minimize the difference between the experimental indentation F(h) curve, and a model based on a representative deformation, linking the measured quantities (F, h) and the parameters of the Hollomon law. Each family of methods has advantages and disadvantages that should be known for choosing the most suitable method to the studied case and thus makes best use of instrumented indentation testing

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

International audienceIn 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," ε aR was defined in the proposed article. In the bottom of the valley, all the stress-strain curves that intersect at a point of abscissa ε aR 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 σ y, 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 sample thickness and experimental device configuration on the spherical indentation of AISI 1100 steel

International audienceMost instrumented indentation theoretical studies and models consider bulk sample geometry, which implies no influence on the indentation response. In the particular case of thin samples, our previous studies have shown that the thickness has an influence on the experimental device behaviour as well as on the sample and material response. This work is a numerical and experimental illustration of this particularity. Spherical macroindentation tests are performed on AISI 1100 steel samples of thicknesses varying from 10 to 0.55 mm. Experimental and numerical results are compared. Experimental limitations are investigated and solutions to obtain results which are independent of the sample thickness and curvature are proposed. We show that the proposed solution, which is the object of an international patent, leads to a reliable identification of the material mechanical properties of thin and moderately bent samples

Mechanical characterization of carbonitrided steel with spherical indentation using the average representative strain

International audienceThis paper investigates the identification of mechanical properties of carbonitrided steels using the spherical indentation test. The proposed procedure consists in performing the Vickers microindentation hardness test across the carbonitrided steel in order to obtain the thickness of the hardened layers. Thus, with the assumption of a linear variation of the plastic properties in the intermediate layers between surface and substrate, two spherical macroindentation tests, performed on the substrate and on the surface of the carbonitrided steel, are necessary to identify the work hardening laws' variation through the thickness of the carbonitrided steel. The proposed method does not call for inverse analysis but is based on the use of a database of finite element simulation F–h curves obtained by simulating indentation tests on the surface of various pseudo-carbonitrided materials. The advantage of this method compared to those based on inverse analysis is that it allows a representative strain and a confidence domain of the solution to be determined. The confidence domain of the identified solution takes into account the experimental imprecision of the indentation test and of the case depth variability often encountered in carbonitrided parts

Tests d’indentation instrumentée sur granulats de Mâchefers d’Incinération de Déchets Non Dangereux. Influence de la taille de l’indenteur sur le module élastique

Des tests d’indentation instrumentée ont été effectués sur des particules isolées de Mâchefers d’Incinération de Déchets Non Dangereux (MIDND) provenant des carrières de la Garenne à Vignoc (Bretagne, France). Deux indenteurs sphériques en carbure de tungstène de rayon respectifs 0,5 et 140 mm ont été utilisés pour les séries de tests «A» et «B». Les particules étudiées ont des diamètres variant entre 20 et 25 mm. Avec un indenteur de rayon 0,5 mm, des modules élastiques réduits moyens variant de 15 à 68 GPa ont été trouvés. Un module élastique réduit moyen de 15 GPa a été trouvé avec l’indenteur de rayon 140 mm