Elasto-Plastic Indentation of a Layered Medium

1974 ◽  
Vol 96 (2) ◽  
pp. 97-103 ◽  
Author(s):  
F. E. Kennedy ◽  
F. F. Ling
Keyword(s):  
Plastic Deformation ◽  
Layered Medium ◽  
Considerable Effect ◽  
Plastic Layer ◽  
The Finite Element Method ◽  
Rigid Substrate ◽  
Indentation Size ◽  
Indentation Tests ◽  
Plastic Indentation ◽  
Plastic Case

An analysis is performed, using the finite element method, of the indentation of a thin elasto-plastic layer resting on or attached to a substrate of a different material, which may also deform plastically. The indentation size, contact pressure, applied load, and amount of plastic deformation are found for the elasto-plastic case, and the results are compared with those found by an elastic analysis. It is found that plastic deformation, which occurs in all indentation tests, has a considerable effect on the results, and that the deformation in the indented layer is also affected by such variables as: the material properties of both layer and substrate, the thickness of the layer, and the condition of the interface between layer and substrate. The “piling-up” that has been observed experimentally in indentation tests is found to depend on the same variables and occurs especially when a thin layer is adhered to a more rigid substrate. The analysis is valid throughout the loading-unloading cycle.

Semi-inverse method for predicting stress–strain relationship from cone indentations

2003 ◽  
Vol 18 (9) ◽  
pp. 2068-2078 ◽  
Author(s):  
A. DiCarlo ◽  
H. T. Y. Yang ◽  
S. Chandrasekar
Keyword(s):  
A Priori ◽  
Model Material ◽  
Material Behavior ◽  
The Finite Element Method ◽  
Stress Strain ◽  
Indentation Tests ◽  
Strain Relationship ◽  
Initial Force ◽  
Relationship Of ◽  
Force Displacement

A method for determining the stress–strain relationship of a material from hardness values H obtained from cone indentation tests with various apical angles is presented. The materials studied were assumed to exhibit power-law hardening. As a result, the properties of importance are the Young's modulus E, yield strength Y, and the work-hardening exponent n. Previous work [W.C. Oliver and G.M. Pharr, J. Mater. Res. 7, 1564 (1992)] showed that E can be determined from initial force–displacement data collected while unloading the indenter from the material. Consequently, the properties that need to be determined are Y and n. Dimensional analysis was used to generalize H/E so that it was a function of Y/E and n [Y-T. Cheng and C-M. Cheng, J. Appl. Phys. 84, 1284 (1999); Philos. Mag. Lett. 77, 39 (1998)]. A parametric study of Y/E and n was conducted using the finite element method to model material behavior. Regression analysis was used to correlate the H/E findings from the simulations to Y/E and n. With the a priori knowledge of E, this correlation was used to estimate Y and n.

A study of indentation work in homogeneous materials

2006 ◽  
Vol 21 (6) ◽  
pp. 1363-1374 ◽  
Author(s):  
Mengxi Tan
Keyword(s):  
Plastic Deformation ◽  
Elastic Modulus ◽  
Elastic Energy ◽  
Size Effects ◽  
Unit Volume ◽  
Plastic Work ◽  
Total Work ◽  
Indentation Size ◽  
Scaling Relationships ◽  
Homogeneous Materials

The work of indentation is investigated experimentally in this article. A method of using the elastic energy to extract the elastic modulus is proposed and verified. Two types of hardness related to the work of indentation are defined and examined: Hwtis defined as the total work required creating a unit volume of contact deformationand Hwp is defined as the plastic work required creating a unit volume of plastic deformation; experiments show that both hardness definitions are good choices for characterizing hardness. Several features that may provide significant insights in understanding indentation measurements are studied. These features mainly concern some scaling relationships in indentation measurements and the indentation size effects.

Further analysis of the size effect in indentation hardness tests of some metals

1995 ◽  
Vol 10 (11) ◽  
pp. 2908-2915 ◽  
Author(s):  
M. Atkinson
Keyword(s):  
Size Effect ◽  
Strain Hardening ◽  
Indentation Size Effect ◽  
Plastic Hinge ◽  
Small Scale ◽  
Indentation Hardness ◽  
Vickers Indentation ◽  
Indentation Size ◽  
Hardness Tests ◽  
Indentation Tests

The variation of apparent hardness observed in previously reported Vickers indentation tests of metals is reexamined. Common deseriptions of the effect are shown to be inaccurate: the variation of apparent hardness is monotonic but not simple. The effect is consistent with varying size of a previously postulated “plastic hinge” at the perimeter of the indent. This complexity confers uncertainty on the estimation of characteristic macrohardness from small scale tests. Association of the indentation size effect with friction and with strain hardening is confirmed.

A New Method for Elastic-Plastic Contact Analysis of a Deformable Sphere and a Rigid Flat

2005 ◽  
Vol 128 (2) ◽  
pp. 221-229 ◽  
Author(s):  
Li Po Lin ◽  
Jen Fin Lin
Keyword(s):  
New Method ◽  
Contact Load ◽  
Rigid Sphere ◽  
The Finite Element Method ◽  
Numerical Errors ◽  
Elastic Regime ◽  
Contact Loads ◽  
Indentation Tests ◽  
Metal Materials ◽  
Contact Parameters

A new method is developed in the present study to determine the elastoplastic regime of a spherical asperity in terms of the interference of two contact surfaces. This method provides an efficient way to solve the problem of discontinuities often present in the reported solutions for the contact load and area or the gradients of these parameters obtained at either the inception or the end of the elastoplastic regime. The well-established solutions for the elastic regime and experimental data of metal materials using indentation tests are provided as the references to determine the errors of these contact parameters due to the use of the finite-element method. These numerical errors provide the basis to adjust the contact area and contact load of a rigid sphere in contact with a flat such that the dimensionless mean contact pressure Pave∕Y (Y: the yielding strength) and the dimensionless contact load Fpc∕Fec (Fec, Fpc: the contact loads corresponding to the inceptions of the elastoplastic and fully plastic regimes, respectively) reaches the criteria arising at the inception of the fully plastic regime, which are available from the reports of the indentation tests for metal materials. These two criteria are however not suitable for the present case of a rigid flat in contact with a deformable sphere. In the case of a rigid flat in contact with a deformable sphere, the proportions in the adjustments of these contact parameters are given individually the same as those arising in the indentation case. The elastoplastic regime for each of these two contact mechanisms can thus be determined independently. By assuming that the proportion of adjustment in the elastoplastic regime is a linear function, the discontinuities appearing in these contact parameters are absent from the two ends of the elastoplastic regime in the present study. These results are presented and compared with the published results.

Elasto-Plastic Indentation of Auxetic and Metal Foams

2019 ◽  
Vol 87 (1) ◽  
Author(s):  
N. Kumar ◽  
S. N. Khaderi ◽  
K. Tirumala Rao
Keyword(s):  
Poisson’S Ratio ◽  
Strain Energy ◽  
Metal Foams ◽  
Poisson's Ratio ◽  
Indentation Hardness ◽  
The Finite Element Method ◽  
Yield Strain ◽  
Plastic Dissipation ◽  
Auxetic Materials ◽  
Plastic Indentation

Abstract The elasto-plastic indentation of auxetic and metal foams is investigated using the finite element method. The contributions of yield strain, elastic, and plastic Poisson’s ratio on the indentation hardness are identified. For a given yield strain, when the plastic Poisson’s ratio is reduced from 0.5, the indentation hardness decreases first and then increases. This trend was found to be valid for a wide of yield strains. For yield strains less than 0.08, the hardness of auxetic materials is much larger when compared with materials having positive plastic Poisson’s ratio. As the plastic Poisson’s ratio approaches −1, the elastic deformations dominate over the plastic deformations. The plastic dissipation, when compared with the elastic work, is lower for materials with negative Poisson’s ratio. There is no effect of elastic Poisson’s ratio on the indentation hardness when the plastic Poisson’s ratio is more than −0.8. When the plastic Poisson’s ratio is less than −0.8, the hardness increases with a decrease of elastic Poisson’s ratio. The plastic dissipation per unit strain energy is maximum for materials with vanishing plastic Poisson’s ratio.

Length Scale Dependent Deformation in Polymers

2012 ◽  
Author(s):  
F. Alisafaei ◽  
Seyed Hamid Reza Sanei ◽  
Chung-Souk Han
Keyword(s):  
Liquid Crystal ◽  
Size Effects ◽  
Liquid Crystal Polymers ◽  
Length Scale ◽  
Indentation Testing ◽  
Indentation Size ◽  
Length Scales ◽  
Indentation Tests ◽  
Length Scale Dependent Deformation ◽  
Beam Bending

Length scale dependent deformation of polymers has been observed in different experiments including micro-beam bending and indentation tests. Here the length scale dependent deformation of polydimethylsiloxane is examined in indentation testing at length scales from microns down to hundreds of nanometers. Strong indentation size effects have been observed in these experiments which are rationalized with rotation gradients that can be related to Frank elasticity type molecular energies known from liquid crystal polymers. To support this notion additional experiments have been conducted where Berkovich and spherical indenter tips results have been compared with each other.

Crystallographic Textures Variation in Asymmetrically Rolled Steel

2010 ◽  
Vol 638-642 ◽  
pp. 2811-2816 ◽  
Author(s):  
Sebastian Wroński ◽  
Krzysztof Wierzbanowski ◽  
Brigitte Bacroix ◽  
Mirosław Wróbel ◽  
M. Wroński
Keyword(s):  
Finite Element Method ◽  
Plastic Deformation ◽  
Low Carbon Steel ◽  
Deformation Model ◽  
Texture Formation ◽  
Rolled Steel ◽  
Low Carbon ◽  
The Finite Element Method ◽  
Asymmetric Rolling ◽  
Macro Scale

The crystallographic texture formation in low carbon steel during asymmetric rolling was studied experimentally and analysed numerically. Modelling of plastic deformation was done in two scales: in the macro-scale using the finite element method ( FEM) and in crystallographic scale using the polycrystalline deformation model (LW model). The stress distribution in the rolling gap was calculated using FEM and next these stresses were applied in LW model of polycrystalline plastic deformation. In general, the predicted textures agree very well with experimental ones.

Indentation Size Effect on Hardness of Nanostructured Thin Films

2006 ◽  
Vol 312 ◽  
pp. 363-368 ◽  
Author(s):  
Chun Sheng Lu ◽  
Yiu Wing Mai ◽  
Yao Gen Shen
Keyword(s):  
Thin Films ◽  
Plastic Deformation ◽  
Grain Boundary ◽  
Size Effect ◽  
Indentation Depth ◽  
Indentation Size Effect ◽  
Indentation Size ◽  
Nanostructured Thin Films ◽  
Measured Hardness

Based on nanoindentation techniques, the evaluation of hardness of two nanostructured thin films, AlN and Ti-Al-N, is discussed. In the case of AlN films, the indentation size effect of hardness can be modeled using the concept of geometrically necessary dislocations, whereas in the case of Ti-Al-N films, the measured hardness increases exponentially as the indentation depth decreases. The results show that, as thin films approach superhard, dislocation-based plastic deformation is gradually replaced by grain-boundary mediated deformation.

scholarly journals Atomic force microscopy study of nanoindentation deformation and indentation size effect in MgO crystals

1999 ◽  
Vol 14 (10) ◽  
pp. 3973-3982 ◽  
Author(s):  
K. Sangwal ◽  
P. Gorostiza ◽  
J. Servat ◽  
F. Sanz
Keyword(s):  
Experimental Data ◽  
Plastic Deformation ◽  
Atomic Force Microscopy ◽  
Size Effect ◽  
Deformation Zone ◽  
Indentation Size Effect ◽  
Indentation Size ◽  
Depth Of Penetration ◽  
Force Microscopy ◽  
Atomic Force

The dependences of various nanoindentation parameters, such as depth of penetration d, indentation diameter a, deformation zone radius R, and height h of hills piled up around indents, on applied load were investigated for the initial (unrecovered) stage of indentation of the (100) cleavage faces of MgO crystals by square pyramidal Si tips for loads up to 10 μN using atomic force microscopy. The experimental data are analyzed using theories of elastic and plastic deformation. The results revealed that (i) a, R, and h linearly increase with d; (ii) the development of indentation size and deformation zone and the formation of hills are two different processes; (iii) the load dependence of nanohardness shows the normal indentation size effect (i.e., the hardness increases with a decrease in load); and (iv) there is an absence of plastic deformation involving the formation of slip lines around the indentations. It is found that Johnson's cavity model of elastic–plastic boundary satisfactorily explains the experimental data. The formation of hills around indentations is also consistent with a new model (i.e., indentation crater model) based on the concept of piling up of material of indentation cavity as hills.

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