Evaluation of the Effectiveness of Representative Methods for Determining Young's Modulus and Hardness from Instrumented Indentation Data

The effectiveness of Oliver & Pharr's (O&P's) method, Cheng & Cheng's (C&C's) method, and a new method developed by our group for estimating Young's modulus and hardness based on instrumented indentation was evaluated for the case of yield stress to reduced Young's modulus ratio (sigma(y)/E-r) >= 4.55 x 10(-4) and hardening coefficient (n) <= 0.45. Dimensional theorem and finite element simulations were applied to produce reference results for this purpose. Both O&P's and C&C's methods overestimated the Young's modulus under some conditions, whereas the error can be controlled within +/- 16% if the formulation was modified with appropriate correction functions. Similar modification was not introduced to our method for determining Young's modulus, while the maximum error of results was around +/- 13%. The errors of hardness values obtained from all the three methods could be even larger and were irreducible with any correction scheme. It is therefore suggested that when hardness values of different materials are concerned, relative comparison of the data obtained from a single standard measurement technique would be more practically useful. It is noted that the ranges of error derived from the analysis could be different if different ranges of material parameters sigma(y)/E-r and n are considered.

An Energy-Based Method for Analyzing Instrumented Spherical Indentation Experiments

Using dimensional analysis and finite element calculation, we studied spherical indentation in elastic-plastic solids with work hardening. We report two previously unknown relationships between hardness, reduced modulus, indentation depth, indenter radius, and work of indentation. These relationships, together with the relationship between initial unloading stiffness and reduced modulus, provide an energy-based method for determining contact area, reduced modulus, and hardness of materials from instrumented spherical indentation measurements. This method also provides a means for calibrating the effective radius of imperfectly shaped spherical indenters. Finally, the method is applied to the analysis of instrumented spherical indentation experiments on copper, aluminum, tungsten, and fused silica.

Methods of Obtaining Instantaneous Modulus of Viscoelastic Solids Using Displacement-Controlled Instrumented Indentation with Axisymmetric Indenters of Arbitrary Smooth Profiles

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic–plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a “hold” period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and “hold-at-the-maximum-indenter-displacement” for determining the instantaneous modulus using spherical indenters.

An Improved Energy Method For Determining Young'S Modulus By Instrumented Indentation Using A Berkovich Tip

We previously proposed a method for estimating Young's modulus from instrumented nanoindentation data based on a model assuming that the indenter had a spherical-capped Berkovich geometry to take account of the bluntness effect. The method is now further improved by releasing the constraint on the tip shape, allowing it to have a much broader arbitrariness to range from a conical-tipped shape to a flat-ended shape, whereas the spherical-capped shape is just a special case in between. This method requires two parameters to specify a tip geometry, namely, a volume bluntness ratio V-r and a height bluntness ratio h(r). A set of functional relationships correlating nominal hardness/reduced elastic modulus ratio (H-n/E-r) and elastic work/total work ratio (W-e/W) were established based on dimensional analysis and finite element simulations, with each relationship specified by a set of V-r and h(r). Young's modulus of an indented material can be estimated from these relationships. The method was shown to be valid when applied to S45C carbon steel and 6061 aluminum alloy.

Numerical verification for instrumented spherical indentation techniques in determining the plastic properties of materials

 Instrumented indentation tests have been widely adopted for elastic modulus determination. Recently, a number of indentation-based methods for plastic properties characterization have been proposed, and rigorous verification is absolutely necessary for their wide application. In view of the advantages of spherical indentation compared with conical indentation in determining plastic proper-ties, this study mainly concerns verification of spherical indentation methods. Five convenient and simple models were selected for this purpose, and numerical experiments for a wide range of materials are carried out to identify their accuracy and sensitivity characteristics. The verification results show that four of these five methods can give relatively accurate and stable results within a certain material domain, which is defined as their validity range and has been summarized for each method.

Methods of Obtaining Instantaneous Modulus of Viscoelastic Solids Using Displacement-Controlled Instrumented Indentation with Axisymmetric Indenters of Arbitrary Smooth Profiles

We derive a relationship between the initial unloading slope, contact depth, and the instantaneous relaxation modulus for displacement-controlled indentation in linear viscoelastic solids by a rigid indenter with an arbitrary axisymmetric smooth profile. While the same expression is well known for indentation in elastic and in elastic-plastic solids, we show that it is also true for indentation in linear viscoelastic solids, provided that the unloading rate is sufficiently fast. When the unloading rate is slow, a "hold" period between loading and unloading can be used to provide a correction term for the initial unloading slope equation. Finite element calculations are used to illustrate the methods of fast unloading and "hold-at-the-maximum-indenter-displacement" for determining the instantaneous modulus using spherical indenters.

Determination of plastic properties by instrumented spherical indentation: Expanding cavity model and similarity solution approach

The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of-piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity Solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed oil three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.

Determination Of Plastic Properties By Instrumented Spherical Indentation: Expanding Cavity Model And Similarity Solution Approach

The present paper aims to develop a robust spherical indentation-based method to extract material plastic properties. For this purpose, a new consideration of-piling-up effect is incorporated into the expanding cavity model; an extensive numerical study on the similarity Solution has also been performed. As a consequence, two semi-theoretical relations between the indentation response and material plastic properties are derived, with which plastic properties of materials can be identified from a single instrumented spherical indentation curve, the advantage being that this approach no longer needs estimations of contact radius with given elastic modulus. Moreover, the inconvenience in using multiple indenters with different tip angles can be avoided. Comprehensive sensitivity analyses show that the present algorithm is reliable. Also, by experimental verification performed oil three typical materials, good agreement of the material properties between those obtained from the reverse algorithm and experimental data is obtained.

An Instrumented Indentation Method for Young's Modulus Measurement with Accuracy Estimation

The relationships between indentation responses and Young's modulus of an indented material were investigated by employing dimensional analysis and finite element method. Three representative tip bluntness geometries were introduced to describe the shape of a real Berkovich indenter. It was demonstrated that for each of these bluntness geometries, a set of approximate indentation relationships correlating the ratio of nominal hardness/reduced Young's modulus H (n) /E (r) and the ratio of elastic work/total work W (e)/W can be derived. Consequently, a method for Young's modulus measurement combined with its accuracy estimation was established on basis of these relationships. The effectiveness of this approach was verified by performing nanoindentation tests on S45C carbon steel and 6061 aluminum alloy and microindentation tests on aluminum single crystal, GCr15 bearing steel and fused silica.

Design of Low Power Multi-Standard Active-RC Filter for WLAN and DVB-H

In this paper, a low-power, highly linear, integrated, active-RC filter exhibiting a multi-standard (IEEE 802.11a/b/g and DVB-H) application and bandwidth (3MHz, 4MHz, 9.5MHz) is present. The filter exploits digitally-controlled polysilicon resister banks and an accurate automatic tuning scheme to account for process and temperature variations. The automatic frequency calibration scheme provides better than 3% corner frequency accuracy. The Butterworth filter is design for receiver (WLAN and DVB-H mode) and transmitter (WLAN mode). The filter dissipation is 3.4 mA in RX mode and 2.3 mA (only for one path) in TX mode from 2.85-V supply. The dissipation of calibration consumes 2mA. The circuit has been fabricated in a 0.35um 47-GHz SiGe BiCMOS technology, the receiver and transmitter occupy 0.28-mm(2) and 0.16-mm(2) (calibration circuit excluded), respectively.

Experiment on Qinghai-Tibet railroad subgrade temperature monitoring based on FBG sensors

Qinghai-Tibet Railway is the longest and highest plateau railway in the world. A long term monitoring system of the stability of the subgrade in the permafrost regions should be put forward immediately to prevent damage to the railway. As it's very difficult to set up the long-distance automatic monitoring system which contains a lot of measure points along the 550 kilometers railway in the permafrost area, we present a subgrade temperature monitor system based on fiber Bragg grating (FBG). In this paper the principles of the FBG was presented, and the feasibility of the FBG sensors in the permafrost area of Qinghai-Tibet plateau was analysized. We embedded fifteen FBG temperature sensors and thermal resistance temperature sensors. A contrast experiment is made while the two kinds of sensors are arranged in the same position. The result of the experiment shows that the accuracy of the FBG temperature sensors is less than 0.1 degrees C. and the FBG sensors can do well in the measurement of pattern which the temperature varies with the depth of the permafrost soil. The result also shows the stability of the FBG sensors in the bad environmental condition of Qinghai-Tibet plateau, which proves the feasibility of the application of FBG sensors and our monitoring system on the Qinghai-Tibet railway.

A multi-standard active-RC filter with accurate tuning system

A low-power, highly linear, multi-standard, active-RC filter with an accurate and novel tuning architec-ture is presented. It exhibits 1EEE 802. 11a/b/g (9.5 MHz) and DVB-H (3 MHz, 4 MHz) application. The filter exploits digitally-controlled polysilicon resistor banks and a phase lock loop type automatic tuning system. The novel and complex automatic frequency calibration scheme provides better than 4 comer frequency accuracy, and it can be powered down after calibration to save power and avoid digital signal interference. The filter achieves OIP3 of 26 dBm and the measured group delay variation of the receiver filter is 50 ns (WLAN mode). Its dissipation is 3.4 mA in RX mode and 2.3 mA (only for one path) in TX mode from a 2.85 V supply. The dissipation of calibration consumes 2 mA. The circuit has been fabricated in a 0.35μm 47 GHz SiGe BiCMOS technology; the receiver and transmitter filter occupy 0.21 mm~2 and 0.11 mm~2 (calibration circuit excluded), respectively.

一种带有精准调谐结构的有源RC低通滤波器的设计

提出了一种带有精准调谐结构的有源RC低通滤波器的设计方案,其截止频率为5MHz,并在0.18μm标准CMOS工艺线上流片得到验证.调谐精度达到(-1.24%,+2.16%),测试中得到验证.调谐系统所占芯片面积仅为主滤波器面积的1/4.调谐系统完成调谐功能后会自动关闭,降低了功耗以及对主滤波器的串扰.以50Ω作为源阻抗,滤波器带内3阶交调量(IIP3)好于16.1dBm.滤波器输入参考噪声为36μVrms.滤波器群延迟时间波动测试结果为24ns.滤波器功耗为3.6mW.带有这种调谐结构的滤波器容易被实现,可以用于很多无线低中频应用中,例如全球定位系统、全球通和码分多址等芯片系统中.