A gradient elasticity approach to the indentation size effect at very small depths

2011 ◽  
Vol 20 (1-3) ◽  
pp. 35-40 ◽  
Author(s):  
George P. Mokios ◽  
Elias C. Aifantis
Keyword(s):  
Plastic Deformation ◽  
Size Effect ◽  
Indentation Size Effect ◽  
Gradient Elasticity ◽  
Gradient Plasticity ◽  
Indentation Size ◽  
The Past ◽  
Small Depth ◽  
Alternative Approach ◽  
Macroscopic Plasticity

AbstractOver the past two decades, the indentation size effect (ISE) has been studied extensively by several authors. A common point among all these studies has been the premise that during the indentation process sufficient plastic deformation is developed so that a gradient plasticity framework can be employed in order to capture this effect. However, recent studies have shown that a more detailed analysis of the deformation mechanism during nanoindentation reveals often situations that vary significantly from commonly held beliefs, i.e., configurations where plastic deformation is almost absent, yet an ISE is still observed. This paper deals with such situations and proposes an alternative approach based on a gradient elasticity framework that is capable of capturing the ISE in nanoindentations of small depth, where traditional macroscopic plasticity approaches may not be adopted.

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.

The use of nanoindentation for determining internal lengths and the constitutive response of monument materials: models and experiments

2016 ◽  
Vol 25 (1-2) ◽  
pp. 57-60 ◽  
Author(s):  
Avraam A. Konstantinidis ◽  
George Frantziskonis ◽  
Harm Askes ◽  
Elias C. Aifantis
Keyword(s):  
Experimental Data ◽  
Size Effect ◽  
Indentation Size Effect ◽  
Gradient Elasticity ◽  
Alternative Interpretation ◽  
Indentation Size ◽  
Elasticity Equation ◽  
Constitutive Response

AbstractAn alternative interpretation of nanoindentation experimental data and the associated phenomenon of indentation size effect (ISE) is proposed on the basis of a simple gradient elasticity equation, used to account for the development of elastic gradients generated by the geometry characterizing the indenter-specimen system. An application is considered for marble, i.e. a construction/restoration material.

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.

A Generalized Load-Penetration Relation for Sharp Indenters and the Indentation Size Effect

2002 ◽  
Vol 69 (3) ◽  
pp. 394-396 ◽  
Author(s):  
Z. Y. Li ◽  
S. Chandrasekar ◽  
H. T. Yang
Keyword(s):  
Size Effect ◽  
Indentation Size Effect ◽  
Material Model ◽  
Plastic Behavior ◽  
Gradient Plasticity ◽  
Indentation Size ◽  
Pressure Sensitive ◽  
Self Similar ◽  
Isotropic Solids

A dimensional analysis has been made of elastic-plastic indentation of an anisotropic solid, and of a solid showing pressure-sensitive yield behavior. It is found that, P∝δ2, for indentation with sharp, self-similar indenters, where P is the load applied by the indenter and δ is the corresponding distance of penetration of the indenter into the solid. This extends and generalizes a similar result obtained for isotropic solids showing conventional plastic behavior. When a strain-gradient plasticity is incorporated into the material model, then it is found that P is no longer proportional to δ2. Implications of the results for the indentation size-effect and for the determination of stress-strain curves from indentation are discussed.

scholarly journals Characterization of strain amplitude-dependent behavior of hardness and indentation size effect of SS400 structural steel

2020 ◽  
Vol 14 (3) ◽  
pp. 15-25
Author(s):  
Nguyen Ngoc Vinh ◽  
Vu Quoc Anh ◽  
Hong Tien Thang
Keyword(s):  
Mechanical Properties ◽  
Cyclic Loading ◽  
Size Effect ◽  
Strain Rate ◽  
Structural Steel ◽  
Indentation Size Effect ◽  
Low Cycle Fatigue ◽  
Indentation Hardness ◽  
Gradient Plasticity ◽  
Indentation Size

In this paper, the continuous stiffness measurement (CSM) indentation is employed to investigate fatigue mechanical properties of structural steel under cyclic loading. For this purpose, several representative analytical approaches were introduced to estimate the basic mechanical properties including Young’s modulus and indentation hardness from the characteristics of the loading/unloading curves. Several experiments including CSM nanoindentation, low-cycle fatigue experiment for four strain amplitude levels, optical microscope (OM), and transmission electron microscopy (TEM) examinations were conducted to observe the variation characteristics of mechanical properties at the microscale and their micro-mechanisms. The microstructural evolution of the specimens deformed by the low-cycle fatigue was observed using the OM and TEM examinations. The standard nanoindentation experiments were then performed at different strain rate levels to characterize the influences of strain rate indentation on hardness of the material. The micro-mechanisms established based on the microstructural evolution and strain gradient plasticity theory were introduced to be responsible for the variation of indentation hardness under cyclic loading. Finally, the indentation size effect (ISE) phenomenon in SS400 structural steel was investigated and explained through the strain gradient plasticity theory regarding geometrically necessary dislocations underneath the indenter tip. The experimental results can be used for practical designs as well as for understanding the fatigue behavior of SS400 structural steel. Keywords: cyclic loading; fatigue; nanoindentation; indentation size effect; strain rate sensitivity; structural steel.

An Examination of the Indentation Size Effect and Bi-Linear Behavior of FCC Metals

2012 ◽  
Vol 1424 ◽  
Author(s):  
D.E. Stegall ◽  
B. Crawford ◽  
A.A. Elmustafa
Keyword(s):  
Size Effect ◽  
Indentation Size Effect ◽  
Shear Stresses ◽  
Test Machine ◽  
Gradient Plasticity ◽  
Indentation Size ◽  
Fcc Metals ◽  
Linear Behavior ◽  
Copper Zinc ◽  
Self Similar

AbstractWe investigated pure FCC metals including Aluminum, Nickel, Silver, and 70/30 Copper Zinc (alpha-brass) alloy for the indentation size effect (ISE) and the bilinear behavior using a single Berkovich indenter tip in a single test machine. The results were consistent with those reported by Elmustafa and Stone, 2003 of the ISE and the bilinear behavior using two separate indenter tips (Berkovich and Vickers) from two separate machines. This behavior is mechanistic in nature and is observed regardless of the type of the self similar indenter tip employed. Furthermore, the research presented in this paper would seem to also validate the conclusions that Elmustafa et al (2004) articulate that the Strain Gradient Plasticity collapses at small scales and that the bilinear behavior of these FCC metals is attributed to the presence of long range shear stresses induced by geometrically necessary dislocations. Also, we observed what has been defined as a “tapping” issue for materials with high E/H ratios when using the CSM. The CSM protocol results in erroneous hardness results at very shallow depths for high E/H ratio soft metals due to the so called “tapping” of the stylus as articulated by Pharr et al. (2009). This method should only be used as a secondary technique to the load control protocol when examining the ISE effect.

Experimental Verification of the Strain-Gradient Plasticity Model for Indentation

2005 ◽  
Vol 20 (11) ◽  
pp. 3150-3156
Author(s):  
Linmao Qian ◽  
Hui Yang ◽  
Minhao Zhu ◽  
Zhongrong Zhou
Keyword(s):  
Size Effect ◽  
Yield Stress ◽  
Strain Gradient ◽  
Indentation Size Effect ◽  
Linear Increase ◽  
Strain Gradient Plasticity ◽  
Plasticity Model ◽  
Gradient Plasticity ◽  
Indentation Size ◽  
Tensile Yield Stress

The indentation size effect of pure iron samples with various pre-plastic tensile strains has been experimentally investigated and analyzed. With the increase in the strain, the indentation size effect of iron samples becomes weak, accompanied by the multiplication of the statistically stored dislocations. All of the hardness (H) versus indentation depth (h) curves fit the strain-gradient plasticity model for indentation of Nix and Gao well. Two fitting parameters, the hardness in the limit of infinite depth (H0) and the characteristic length (h*), were obtained for each curve. The hardness (H0) of iron samples can also be estimated as the microhardness (H) at a very large depth, h ≅ 10h*. Both the fitted H0 and the measured H0′ increase linearly with the tensile yield stress σy of iron samples, indicating a dependence of H0 on the statistically stored dislocation density through σy. Furthermore, 1/√h* shows a linear increase with the tensile yield stress σy, which also agrees qualitatively with the general prediction of the Nix and Gao theory. Therefore, our experiments and analysis demonstrate that the strain-gradient plasticity model for indentation of Nix and Gao can interpret the indentation size effect with satisfied precision.

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