Indentation load–displacement curve, plastic deformation, and energy

2002 ◽  
Vol 17 (2) ◽  
pp. 502-511 ◽  
Author(s):  
J. Malzbender ◽  
G. de With
Keyword(s):  
Experimental Data ◽  
Plastic Deformation ◽  
Finite Element ◽  
Indentation Load ◽  
Analytical Models ◽  
Dissipated Energy ◽  
Displacement Curve ◽  
Pile Up ◽  
Analytic Expressions ◽  
Hardening Coefficient

Various methods to access indentation data are considered on the basis of the load P–displacement h curve, its derivative, or its integral. This paper discusses and extends the various analytical models to estimate the indentation P–h curve, the slope, and the dissipated energy to aid the development of a concise methodology to analyze indentation data. Special consideration is given to the effect of pile-up and sink-in. Relationships for sharp and spherical indenters are presented and in addition for sharp indenters with a rounded tip. An overview over analytic expressions for the P–h curve is given and compared to finite element simulations and experimental data. An expression derived for the representative strain at the onset of yield under sharp and spherical indenters compares well with literature results. The effect of a rounded tip on the yielding under a sharp indenter is discussed. The ratio of loading to unloading slope and the ratio of the plastically dissipated energy to the total energy is related to hardness and elastic modulus. In combination these ratios can be used to determine the strain-hardening coefficient.

Indentation Curve Analysis for Pile-up, Sink-in and Tip-Blunting Effects in Sharp Indentations

2003 ◽  
Vol 795 ◽  
Author(s):  
Yeol Choi ◽  
Baik-Woo Lee ◽  
Ho-Seung Lee ◽  
Dongil Kwon
Keyword(s):  
Finite Element ◽  
Material Constant ◽  
Indentation Load ◽  
Curve Analysis ◽  
Analysis Method ◽  
Indentation Curve ◽  
Element Simulation ◽  
Maximum Indentation Depth ◽  
Pile Up ◽  
Loading And Unloading

ABSTRACTHardness and elastic modulus can be derived from instrumented sharp indentation curves by considering the effects of materials pile-up and sink-in and tip blunting. In particular, this study quantifies pile-up or sink-in effects in determining contact area based on indentation-curve analysis. Two approaches, finite-element simulation and theoretical modeling, were used to describe the detailed contact morphologies. The ratio of contact depth to maximum indentation depth was proposed as a key indentation parameter and was found to be a material constant independent of indentation load. In addition, this parameter can be determined strictly in terms of indentation-curve parameters, such as loading and unloading slopes at maximum depth and indentation energy ratio. This curve-analysis method was verified by finite-element simulations and nanoindentation experiments.

Analysis of sharp-tip-indentation load–depth curve for contact area determination taking into account pile-up and sink-in effects

2004 ◽  
Vol 19 (11) ◽  
pp. 3307-3315 ◽  
Author(s):  
Yeol Choi ◽  
Ho-Seung Lee ◽  
Dongil Kwon
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Contact Area ◽  
Indentation Depth ◽  
Indentation Load ◽  
Real Contact Area ◽  
Elastic Deflection ◽  
Contact Depth ◽  
Real Contact ◽  
Pile Up

Hardness and elastic modulus of micromaterials can be evaluated by analyzing instrumented sharp-tip-indentation load–depth curves. The present study quantified the effects of tip-blunting and pile-up or sink-in on the contact area by analyzing indentation curves. Finite-element simulation and theoretical modeling were used to describe the detailed contact morphologies. The ratio f of contact depth, i.e., the depth including elastic deflection and pile-up and sink-in, to maximum indentation depth, i.e., the depth measured only by depth sensing, ignoring elastic deflection and pile-up and sink-in, was proposed as a key indentation parameter in evaluating real contact depth during indentation. This ratio can be determined strictly in terms of indentation-curve parameters, such as loading and unloading slopes at maximum depth and the ratio of elastic indentation energy to total indentation energy. In addition, the value of f was found to be independent of indentation depth, and furthermore the real contact area can be determined and hardness and elastic modulus can be evaluated from f. This curve-analysis method was verified in finite-element simulations and nanoindentation experiments.

THE PLASTICITY OF MONOCRYSTALLINE SILICON UNDER NANOINDENTATION

2008 ◽  
Vol 22 (31n32) ◽  
pp. 6022-6028 ◽  
Author(s):  
LI CHANG ◽  
L. C. ZHANG
Keyword(s):  
Plastic Deformation ◽  
Shape Change ◽  
Indentation Load ◽  
Monocrystalline Silicon ◽  
Displacement Curve ◽  
Wide Range ◽  
Rapid Loading ◽  
Load Displacement ◽  
The Difference ◽  
Critical Contact

This paper focuses on a fundamental understanding of the plastic deformation mechanism in monocrystalline silicon subjected to nanoindentation. It was found that over a wide range of indentation loads from 100 μN to 30 mN and loading/unloading rates from 3.3 μN/s to 10 mN/s, the plasticity of silicon is mainly caused by stress-induced phase transitions. The results indicate that the critical contact pressure for phase transition at unloading is almost constant, independent of the maximum indentation load ( P max ) and loading/unloading rates. However, the shape of the load-displacement curves greatly relies on the loading/unloading conditions. In general, higher P max and lower unloading/loading rates favor an abrupt volume change and thus a discontinuity in the load-displacement curve, commonly referred to as pop-in and/or pop-out events; whereas smaller P max and rapid loading/loading processes tend to generate gradual slope changes of the curves. This study concludes that the difference in the curve shape change does not indicate the mechanism change of plastic deformation in silicon.

Plastic and Elastic Behavior of Sputtered Bilayered Films by Nanoindedtation

1999 ◽  
Vol 594 ◽  
Author(s):  
N. Kikuchi ◽  
E. Kusano ◽  
Y. Sawahira ◽  
A. Kinbara
Keyword(s):  
Plastic Deformation ◽  
Elastic Modulus ◽  
Yield Stress ◽  
Sapphire Substrate ◽  
Elastic Energy ◽  
Deformation Behavior ◽  
Elastic Behavior ◽  
Dissipated Energy ◽  
Displacement Curve ◽  
Plastic Energy

AbstractDeformation behavior of sputtered Al/TiN and Cu/TiN bilayered films was examined by using dissipated and elastic energies estimated from the area enclosed by the load-displacement curve of nanoindentation. These films studied consisted of TiN top-layer of 500 nm and Al or Cu underlayer of 0 - 500 nm on glass or sapphire substrate. The dissipated energy for plastic deformation increased with increasing thickness of metal underlayer, while the elastic energy remained constant. A decrease in plastic energy was observed by changing the underlayer material from Al to Cu. Further, a reduction in elastic energy was observed when a sapphire was used as a substrate. Experimental results show that the plastic deformation mainly occurred in metal underlayer and the elastic deformation did in TiN layer and in the substrate. It was concluded that the yield stress and elastic modulus of layers and substrate strongly affect the deformation behavior of the films.

DOE Analysis of the Effects of Geometrical Parameters on the Self-Piercing Riveting of Aluminium Alloy AA6060T4

2011 ◽  
Vol 473 ◽  
pp. 733-738 ◽  
Author(s):  
Giuseppe Casalino
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Statistical Analysis ◽  
Element Model ◽  
The Self ◽  
Geometrical Parameters ◽  
Displacement Curve ◽  
Design Problems ◽  
Riveting Process ◽  
Force Displacement

The design of experiments (DOE) is a very useful tool to design and analyze complicated industrial design problems. They help to understand the variability a manufacturing process by investigating which parameters and their interaction mainly affect the output repeatability. As a consequence, it enables to individuate the combination of parameters that optimize the output avoiding misinterpretation that can be due to the singularity of the experimental data. In this study the factorial analysis was used to investigate the effects of the major geometrical parameters on the shape of the force-displacement curve of the self piercing riveting (SPR) process. A full two level three-factorial design (23) was completed, three-way interaction was not considered. The statistical analysis was carried out at four different points of the force-rivet displacement curve. These points can be considered critical since they limit the four steps in which the process is commonly divided for studying purpose. The experimental data did not fulfil the required design points, the missing points were obtained by a finite element model of the riveting process, which furnished the force versus the rivet run.

scholarly journals Nanoscale Deformation and Nanomechanical Properties of Soft Matter Study Cases: Polydimethylsiloxane, Cells and Tissues

2011 ◽  
Vol 2011 ◽  
pp. 1-13 ◽  
Author(s):  
Costas Charitidis
Keyword(s):  
Experimental Data ◽  
Finite Element Method ◽  
Plastic Deformation ◽  
Finite Element ◽  
Soft Matter ◽  
Loading Rate ◽  
Soft Materials ◽  
Hertzian Contact ◽  
Nanomechanical Properties ◽  
Experimental Protocols

Nanoindentation technique was used to investigate the nanomechanical behaviour of different soft materials. Polydimethylsiloxane (PDMS), cells and tissues were examined. The nanomechanical properties (with loading rate and creep study), namely, the hardness () and the elastic modulus () of PDMS, were determined. A classical Hertzian contact analysis was also performed in order to obtain values of . Moreover, the plastic deformation where no load had yet been applied to PDMS was investigated (zero load plastic deformation). Finally, the difficulties of measuring the nanomechanical properties (&) of cells and tissues were evaluated, showing the need for a modification of the current experimental protocols for preparing and mechanically testing in a mode that maintains their structure and their biological functioning in order to make indentation results more reproducible. Additionally, finite element method is used in order to simulate the nanoindentation of PDMS in correlation with experimental data.

Improved Analytical and Semi-Analytical Durability Models (Constrained Models) for Various Surface-Mount Configurations

2002 ◽  
Author(s):  
Pradeep Sharma ◽  
James Loman
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Solder Joint ◽  
Thermal Cycling ◽  
Deformation Process ◽  
Analytical Models ◽  
Surface Mount ◽  
Constrained Models ◽  
Constraint Approach ◽  
Finite Element Calibration

Several analytical and semi-analytical models to predict solder joint durability under thermal cycling loadings have been proposed. In general, these models are overtly conservative often requiring extensive experimental and/or finite element calibration. We present, based on the physics of the deformation process, a direct approach to improve these classes of model by resolving one of the major causes of conservatism. Our contribution is applicable to virtually all known surface mount configurations. The improved models (henceforth termed as constraint models) retain the simplicity of use of the existing ones. The efficacy of constraint approach is demonstrated on leadless resistors and comparisons are made with existing models and experimental data.

Analytical Modelling of I-V Characteristics for 4H-SiC Enhancement Mode VJFET

2006 ◽  
Vol 527-529 ◽  
pp. 1195-1198
Author(s):  
Praneet Bhatnagar ◽  
Alton B. Horsfall ◽  
Nicolas G. Wright ◽  
C. Mark Johnson ◽  
Konstantin Vassilevski ◽  
...  
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Analytical Model ◽  
Computational Efficiency ◽  
Analytical Models ◽  
Analysis Tool ◽  
Power Devices ◽  
Enhancement Mode ◽  
High Computational Efficiency ◽  
Single Set

Physics-based analytical models are seen as an efficient way of predicting the characteristics of power devices since they can achieve high computational efficiency and may be easily calibrated using parameters obtained from experimental data. This paper presents an analytical model for a 4H-SiC Enhancement Mode Vertical JFET (VJFET), based on the physics of this device. The on-state and blocking behaviour of VJFETs with finger widths ranging from 1.6+m to 2.2+m are studied and compared with the results of finite element simulations. It is shown that the analytical model is capable of accurately predicting both the on-state and blocking characteristics from a single set of parameters, underlining its utility as a device design and circuit analysis tool.

Finite element analysis of CFRP-externally strengthened reinforced concrete beams subjected to three-point bending

2019 ◽  
Vol 17 (2) ◽  
pp. 183-202
Author(s):  
Sabiha Barour ◽  
Abdesselam Zergua ◽  
Farid Bouziadi ◽  
Waleed Abed Jasim
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Comparative Study ◽  
Finite Element Model ◽  
Element Model ◽  
Analytical Models ◽  
Element Analysis ◽  
Content Type ◽  
Linear Finite Element ◽  
Non Linear

Purpose This paper aims to develop a non-linear finite element model predicting the response of externally strengthened beams under a three-point flexure test. Design/methodology/approach The ANSYS software is used for modeling. SOILD65, LINK180, SHELL181 and SOLID185 elements are used, respectively, to model concrete, steel reinforcement, polymer and steel plate support. A parametric study was carried out. The effects of compressive strength, Young’s modulus, layers number and carbon fiber-reinforced polymer thickness on beam behavior are analyzed. A comparative study between the non-linear finite element and analytical models, including the ACI 440.2 R-08 model, and experimental data is also carried out. Findings A comparative study of the non-linear finite element results with analytical models, including the ACI 440.2 R-08 model and experimental data for different parameters, shows that the strengthened beams possessed better resistance to cracks. In general, the finite element model’s results are in good agreement with the experimental test data. Practical implications This model will predict the strengthened beams behavior and can describe the beams physical conditions, yielding the results that can be interpreted in the structural study context without using a laboratory testing. Originality/value On the basis of the results, a good match is found between the model results and experimental data at all stages of loading the tested samples. Crack models obtained in the non-linear finite element model in the beams are also presented. The submitted finite element model can be used to predict the behavior of the reinforced concrete beam. Also, the comparative study between an analytical model proposed by of current code of ACI 440.2 R-08 and finite element analysis is investigated.

scholarly journals Modeling Thermomechanical Stress with H13 Tool Steel Material Response for Rolling Die under Hot Milling

Metals ◽  
2019 ◽  
Vol 9 (5) ◽  
pp. 495 ◽  
Author(s):  
Mesay Alemu Tolcha ◽  
Hirpa Gelgele Lemu
Keyword(s):  
Experimental Data ◽  
Finite Element ◽  
Temperature Distribution ◽  
Finite Element Simulation ◽  
Thermal Stresses ◽  
Stress Generation ◽  
Analytical Models ◽  
Material Response ◽  
Thermomechanical Stress ◽  
Element Simulation

For the extreme pressure and temperature arising in the hot rolling process, thermomechanical (TM) models are used to predict the residual stresses on the surface of the die because a quantification of the TM stresses allows a prediction of the life span of the rolling die. As the accuracy and consistency of models developed in this area show a large variation due to the considered parameters, conditions, and assumptions, the capability of the developed models needs to be verified for a particular set of circumstances. In this study, new constitutive equations are proposed and a model consisting of five sub-models that computes temperature distribution, thermal stresses, mechanical stresses, and thermomechanical stress for the rolling die under continuous casting application has been developed and presented in this paper. The first sub-model describes the temperature distribution on the rolling die surface by accounting for the effects of different process parameters such as the initial temperature of the slab, reduction ratio, and the rolling speed, while the second and the third sub-models describe the thermal cyclic stress and the elasticity deformation of mechanical stress, respectively. Furthermore, the fourth sub-model describes the TM stress generation through inheriting numerical approaches, and the last sub-model is developed for the H13 tool material response at a high temperature. To verify the developed analytical models, a finite element simulation and the experimental data are considered. The analytical models are computed using Python, and the ABAQUS software has been used for the finite element simulations. The results show a good agreement with the finite element simulation and experimental data.

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