Dual Indenters Research Articles

HYPERELASTIC INDENTATION MODELS AND THE DUAL-INDENTATION METHOD BASED ON ENERGY DENSITY EQUIVALENCE

For the hyperelastic problems of materials under indentation conditions, based on the mean-value energy density equivalence principle, semi-theoretical hyperelastic-material indentation models(SHIM) are proposed to describe the relationship among load, depth, indenter dimension and Mooney-Rivlin constitutive parameters under independent indentation with spherical indenter, flat indenter and conical indenter, respectively, and then the indentation method due to dual indenters(IMDI) is presented. The forward verification shows that, based on a series constitutive relation parameters of hyperelastic materials, the force-depth curves of spherical, conical and flat indentation respectively predicted by SHIM are closely consistent with the FEA results; and the reverse verification shows that, based on the force-depth curves under FEA conditional constitutive relation of a series of hyperelastic materials, the Mooney-Rivlin constitutive relations predicted by the dual indentation experimental method are closely consistent with the FEA conditional constitutive relations. For three hyperelastic rubbers, the spherical, flat and conical indentation tests were carried out, three constitutive relationships of the hyperelastic rubbers obtained by IMDI are all in good agreement with the uniaxial tensile results.

Determining suitable parameters for inverse estimation of plastic properties based on indentation marks

Tensile elastoplastic properties are extensively used in engineering applications; however, sample preparation for tensile tests is time-consuming. Therefore, a technique to estimate the tensile properties from an indentation test, with relatively easy sample preparation, is useful to reduce effort and accelerate the evaluation of advanced materials. Previously proposed techniques for the inverse estimation of elastoplastic properties used plural load-displacement curves. In this study, the authors proposed an estimation technique based on a single indentation involved using three-dimensional information of an indentation mark in addition to a load-displacement curve. To determine the parameter suitable for use in the inverse estimation of elastoplastic properties, the sensitivity and experimental variation in parameters extracted from the indentation results were investigated. The maximum pile-up height normalized by the maximum indentation depth, Zmax/hmax, was determined as the suitable parameter for inverse estimation owing to its high sensitivity compared to experimental variations. Moreover, the stress-strain curve obtained using this technique agreed with that obtained using dual indenters.

Characterising and Predicting on the Mechanical Behaviour of Dissimilar Spot Welded Joints Base on Dual Indenters

Characterising and Predicting on the Mechanical Behaviour of Dissimilar Spot Welded Joints Base on Dual Indenters

Characterization of Material Parameters by Reverse Finite Element Modelling Based on Dual Indenters Vickers and Spherical Indentation

Significantly advantage in the use of indentation testing its use for the characterization of materials is simple and requires only a small sample. In material characterization by indentation, the material behaviour is represented by the load (P)- depth (h) in the P-h curve. However, despite the breadth of use of indentation in the evaluation of the behaviour of the material has not been able to explicitly relate the behaviour of materials with constitutive material properties. This encourages further research to be able to predict the P-h curves and hardness and indentation resistance of the constitutive parameters of the material, it is also very important for research and practical use to explore the potential for using indentation data for predicting the constitutive properties of a material. This could potentially provide a faster way for identification of material parameters and applied in situations where a standard specimen is not available. In this research, the relationship between the constitutive parameters of the material (represented by the yield stress (σy) and work hardening coefficient (n)) of elasto-plastic materials, Indentation P-h curve, and Hardness value with dual indenters have been systematically investigated by combining the representative stress (σr) analysis and FE modelling using steel as a system materials. FE model of Vickers and Spherical indentation has been developed and validated. Validation conducted on the feasibility of the FE models to investigate approaches to the material system, and establishing factors affecting the accuracy and robustness of the approach finite element programs used. A new approach for predicting the hardness values are developed based on the 3D relationship between hardness, yield stress (σy) and strain hardening coefficient (n). The prediction proposed method has been successfully used to produce hardness values of various material properties and is used to establish the relationship between the hardness values with representative stress. Prediction process of the material parameters based on the intersection between the indentations curves of the material properties of both the dual indenter Vickers and spherical indentation. It provides a useful tool to evaluate the feasibility of using a hardness value in predicting the constitutive material parameters with respect to the accuracy and uniqueness by mapping through all the range of potential materials.

Method for Determining the Plastic Properties of Metallic Materials by Instrumented Indentation with Dual Pyramidal Indenters

Method for determining the plastic properties of metallic materials was proposed based on the functional relationships between representative stress, representative strain and nominal hardness which were established with the aid of dimensional analysis and finite element simulation. The errors of 0.2% yield strength and strain hardening exponent of five engineering metals were from-17.1% to 15.4% and from -0.125 to 0.11, respectively,which satisfied the need of engineering application and verified the effectiveness of the method.

A combined dimensional analysis and optimization approach for determining elastic–plastic properties from indentation tests

Loading–unloading curves obtained from indentation experiments can be used to extract elastic-plastic mechanical properties using the finite element (FE) method. However, extensive computation times are required in such an approach due to the fact that the optimization procedure is based on iterative FE computations. In this study, a combined dimensional analysis and optimization approach is developed for the determination of the elastic-plastic mechanical properties of power law materials, without the need for iterative FE analysis. A parametric study using FE analysis is first conducted to construct the appropriate dimensional functions. The optimization algorithm with either a single indenter or dual indenters is then used to obtain the material properties from the given loading–unloading curves. Different sets of materials properties are used and the accuracy and validity of the predicted mechanical properties using the single indenter or dual indenters are assessed.

Improved reverse analysis for material characterization with dual sharp indenters

It was illustrated by the author in the previous work that combinations between material properties and indentation parameters can be used as mixed parameters in dimensionless functions to capture the indentation response of materials to single and dual sharp indenters. These issues are further extended in the present study. A parametric finite element analysis was performed to investigate the conical indentation response of elasto-plastic solids. Frictional effects are studied. Conical indenters of half-included angles from 50° to 88° are considered to examine several fundamental features of instrumented sharp indentation within the frame work of limit analysis. Regarding dimensional analysis, it is found that a Taylor series expansion according to the elastic indentation work-total indentation work ratio W e / W t can be used to improve dimensionless functions. Within this context, a new set of dimensionless functions is explicitly constructed for hardness and indentation parameters of single and dual indenters. Based on formulated functions, a reverse analysis with dual sharp indenters, which was previously proposed by the author, is improved to extract mechanical properties of materials.

Effect of indenter shapes on inverse materials characterization based on the dual indenters method

Abstract The indentation method is a useful tool for studying the onset of plastic flow and work hardening in small volumes. Several approaches based on either single and dual indenters have been reported to characterise a wide range of materials. In this work, the single and dual indenters approaches, with different indenter types, have been comparatively studied using an inverse finite element modelling program developed based on the Kalman filter method. The effect of indenter shapes on the accuracy and uniqueness of the predicted results, as well as convergence time of the program are systematically analysed by automatically mapping the results with a wide range of initial values.

Material characterization by dual sharp indenters

In a recent study, Le [Le, M.-Q., 2008. A computational study on the instrumented sharp indentations with dual indenters. International Journal of Solids and Structures, 45 (10), 2818–2835.] demonstrated that the yield strength Y can be replaced by the loading curvature C and hence the reduced elastic modulus-loading curvature ratio E ∗ / C and strain hardening exponent n can be used to govern characteristic parameters of indentation load–depth curves. Extending Le’s approach and regarding dimensional analysis, it is found that C / Y and E ∗ / Y can be used to investigate fundamental issues in instrumented sharp indentation. Based on extensive finite element analysis, a set of dimensionless functions are constructed for cone indenters of half included angles of 60° and 70.3°. Dimensionless relationships with respect to dual indenters are further explored. Several features of hardness are also considered. An inverse analysis procedure is suggested to estimate material properties, giving good inverse results for experimental data from the literature and representative materials. Sensitivity of inverse solution are studied and discussed. The results show that the proposed dual indenter method is quite robust and can be applied to a wide range of materials.

A computational study on the instrumented sharp indentations with dual indenters

Finite element analysis was performed to investigate the indentation response of elasto-plastic solids for conical indenters of half included angles of 60° and 70.3°. The interdependence indentation parameters resulting from a single indentation load–depth curve is considered. Regarding dimensional analysis, several dimensionless relationships are constructed as functions of the reduced elastic modulus-loading curvature ratio E ∗/ C and the strain hardening exponent n. Further, the duality between corresponding parameters with dual indenters is explored. Finally, a new method based on dual indenters is proposed to extract the strain hardening exponent and the reduced elastic modulus of an indented material. The accuracy of this method is verified and discussed with experimental data from the literature and representative materials.

Analytical and experimental resolutions in the duality of mechanical property extractions from instrumented indentation experiments: Comments on “On determination of material parameters from loading and unloading responses in nanoindentation with a single sharp indenter” by L. Wang and S.I. Rokhlin [J. Mater. Res. 21, 995, (2006)

A controversial issue in mechanical property extractions from instrumented indentation applied load (P)–penetration depth (hs) curves concerns the possibility of finding more than one solid that essentially exhibits the same contact response. By recourse to finite element simulations of elastic-power law strain hardening solids, it was shown that for both the elasto-plastic and the fully plastic contact regimes it becomes possible to find an arbitrary number of solids whose P-hs curves are visually similar [L. Wang and S.I. Rokhlin, J. Mater. Res. 21, 995 (2006)]. Although this assertion supports prior findings [e.g., C.M. Cheng and Y.T. Cheng, J. Mater. Res. 14, 3493 (1999); K.K. Tho et al., Mater. Sci. Eng.A 390, 202 (2005); and J. Alkorta et al., J. Mater. Res.20, 432 (2005)], it apparently contradicts the work by Casals and Alcalá in which, through similar computational procedures and constitutive theory, it was shown that there can be “only” two solids with strictly the same P-hs curve [O. Casals and J. Alcalá, Acta Mater.53, 3545 (2005)]. The purpose of this comment is to reconcile the different views on the multiplicity of inferred properties that can be extracted from a single P-hs curve, as well as to address the issue of whether visually similar P-hs curves can be taken to be statistically identical both from analytical and experimental standpoints. Some considerations are also given regarding experiments performed with dual indenters.

Determination of Residual Stress and Yield Stress Simultaneously by Indentation Method with Dual Indenters

AbstractIn general, the method of obtaining residual stress from indentation test requires calculating the contact area of indenter and indented material, and also needs to know yield stress of indented material in advance. In this work, the dimensional analysis of indentation loading curve was first analyzed, and then a reverse numerical procedure was explored to show a possibility of determining residual stress and yield stress of materials simultaneously from indentation test. Besides, the calculation of contact area can be also avoided.

Material characterization based on dual indenters

Extensive large strain-large deformation finite element analyses were carried out to investigate the response of elasto-plastic materials obeying power law-strain hardening during the loading and unloading process of instrumented indentation with conical indenters of different apex angles. The relationships between the characteristics of the indentation load–displacement curves and the elasto-plastic material properties were computationally established. A reverse analysis algorithm based on load–displacement curves obtained from dual indenters was presented. It was demonstrated that the proposed reverse analysis algorithm can uniquely recover the elasto-plastic material properties from the load–displacement curves of two conical indenters with different apex angles. The numerical results obtained are in good agreement with published values.