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Indentation as a means to extract creep properties has the advantage that it can be applied directly to micro/nano-structures. Many studies on indentation creep reported at least partially poor agreement with creep parameters derived from uniaxial test. One important reason for the incompatibility is the neglect of transient creep. Another one is the choice of equivalent stress and strain measures to relate the different material responses. Applying a material model that accounts for transient creep effects we propose an efficient method for deriving creep properties from short-time spherical indentation tests. We first determine a subsurface point where the material response is very close to that observed in uniaxial tests. We then map the load–displacement data to the material response, expressed in terms of two dimensionless variables, at this point. Converting the dimensionless variables data to stress, strain, and strain rate data, we finally determine the material's creep coefficient and exponent.
The forming limit strains (FLSs) of zircaloy-4 sheets are studied. After having obtained the true stress–strain curve of zircaloy-4 using the weighted-average method, limit dome height (LDH) tests are performed to establish experimental FLSs. We summarize related theoretical forming limit curves (FLC) and discuss their limitations. Two finite element (FE) models are established for determining FLSs; an LDH test FE model for the negative minor strain sector, and a biaxial tensile FE model for the positive minor strain sector. The numerical FLSs are found to agree well with experimental data. Since the numerical FLC gives the strain at the onset of local thinning (whereas the experimental FLC provides the strain between local necking and ductile fracture), resulting FE FLS values are slightly lower than the experimental ones so that results can be regarded as conservative. Our FE approach substitutes the expensive and time-demanding experimental LDH tests.
In this study, a method using dual triangular pyramidal indenters is suggested for material property evaluation. First, we demonstrate that the load–depth curves and the projected contact areas from conical and triangular pyramidal indentations are generally different. Nonequal projected contact areas of two indenters and nonplanar contact line of Berkovich indenter are the main sources of different indentation characteristics of two indenters. For this reason, an independent approach to the triangular pyramidal indentation is needed. With finite element (FE) indentation analyses for various materials, we investigate the relationships between material properties, indentation parameters, and load–depth curves. Based on the FE solutions, we suggest mapping functions for evaluating material properties from indentations by two triangular pyramidal WC indenters, which differ in their centerline-to-face angles. Elastic modulus, yield strength, and strain hardening exponent are obtained with an average error of <3%.
In this study, we obtain true stress–strain (SS) curves for a sheet specimen under consideration of local necking and material anisotropy. We first extract the SS curve up to the diffuse necking point from the tensile test load–displacement data. The curve's part after the onset of diffuse necking is extrapolated by the weighted-average method proposed by Ling [Y. Ling, AMP J. Technol. 5, 37–48 (1996)]. Initiation of local necking is predicted by means of the minor-to-major strain ratio in the specimen's center. We propose a criterion to determine the strain ratio at the onset of local necking and the major strain corresponding to the strain ratio at local necking. We complete the true SS curve by cutting off the SS curve at the major strains corresponding to the local necking or apparent fracture point. Finally, the effects of material anisotropy on SS curves are discussed.
The numerical approach of Lee et al. [Trans. Korean Soc. Mech. Eng., A28, 816–825 (2004)] to spherical indentation technique for property evaluation of hyperelastic rubber is enhanced. The Yeoh model is adopted as the constitutive form of rubber material because it can express well large deformation and cover various deformation modes with a simple form. We first determine the friction coefficient between a rubber specimen and a spherical indenter in a practical viewpoint and perform finite element simulations for a deeper indentation depth than that selected by Lee et al. [Trans. Korean Soc. Mech. Eng., A28, 816–825 (2004)]. An optimal data acquisition spot is selected, which features sufficiently large strain energy density and negligible frictional effect. We improve then two normalized functions mapping an indentation load–displacement curve onto a strain energy density–invariant curve, the latter of which gives the Yeoh model constants. The enhanced spherical indentation approach successfully produces the rubber material properties with an average error of less than 5%. The validity of our developed approach is verified by experimental evaluation of material properties with three kinds of rubber materials.
Conical indentation methods to determine residual stress are proposed by examining the finite element solutions based on the incremental plasticity theory. We first note that hardness depends on the magnitude and sign of residual stress and material properties and can change by up to 20% over a specific range of elastic tensile and compressive residual stress, although some prior indentation studies reported that hardness is hardly affected by residual stress. By analyzing the characteristics of conical indentation, we then select some normalized indentation parameters, which are free from the effect of indenter tip rounding. Adopting dimensional analysis, we present practical conical indentation methods for the evaluation of elastic/plastic equi- and nonequi-biaxial residual stresses. The validity of developed approaches is confirmed by applying them to the experimental evaluation of four-point bending stress.
Geometrical self-similarity is a feature of mathematically sharp indenters such as conical and Berkovich indenters. However, self-similarity is considered inappropriate for practical use because of inevitable indenter tip blunting. In this study, we analyze the load–depth curves of conical indenters with various tip radii via finite element analyses. Based on the numerical data, we propose a method of restoring the Kick’s law coefficient C of finite tip-radius indenter to that of zero tip-radius indenter, thereby retaining the self-similarity of the sharp indenter. We then regress the unloading slope for the evaluation of elastic modulus in several ways. Finally, we establish a method to evaluate elastic modulus, which successfully provides the value of the elastic modulus with a maximum error of less than 5%, regardless of tip radius and material properties of both indenter and specimen.
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