Size Effect and Geometrical Effect of Polycrystals and Thin Film/Substrate System in Micro-indentation Test

Micro-indentation test at scales on the order of sub-micron has shown that the measured hardness increases strongly with decreasing indent depth or indent size, which is frequently referred to as the size effect. Simultaneously, at micron or sub-micron scale, the material microstructure size also has an important influence on the measured hardness. This kind of effect, such as the crystal grain size effect, thin film thickness effect, etc., is called the geometrical effect by here. In the present research, in order to investigate the size effect and the geometrical effect, the micro-indentation experiments are carried out respectively for single crystal copper and aluminum, for polycrystal aluminum, as well as for a thin film/substrate system, Ti/Si3N4. The size effect and geometrical effect are displayed experimentally. Moreover, using strain gradient plasticity theory, the size effect and the geometrical effect are simulated. Through comparing experimental results with simulation results, length-scale parameter appearing in the strain gradient theory for different cases is predicted. Furthermore, the size effect and the geometrical effect are interpreted using the geometrically necessary dislocation concept and the discrete dislocation theory. Member Price: $0; Non-Member Price: $25.00

Nonuniformity Effect of Surface-Nanocrystalline Materials in Nanoindentation Test

In the present research, microstructures of the surface-nanocrystalline Al alloy material are observed and measured based on the transmission electron microscopy (TEM) technique, and the corresponding mechanical behaviors are investigated experimentally and theoretically. In the experimental research, the nanoindentation test method is used, and the load and microhardness curves are measured, which strongly depend on the grain size and grain size nonuniformity. Two kinds of the nanoindentation test methods are adopted: the randomly selected loading point method and the continuous stiffness method. In the theoretical modeling, based on the microstructure characteristics of the surface-nanocrystalline Al alloy material, a dislocation pile-up model considering the grain size effect and based on the Mott theory is presented and used. The hardness-indent depth curves are predicted and modeled.

Revelation of a Functional Dependence of the Sum of Two Uniaxial Strengths/Hardness on Elastic Work/Total Work of Indentation

Dimensional and finite element analyses were used to analyze the relationship between the mechanical properties and instrumented indentation response of materials. Results revealed the existence of a functional dependence of (engineering yield strength sigma(E,y) + engineering tensile strength sigma(E,b))/Oliver & Pharr hardness on the ratio of reversible elastic work to total work obtained from an indentation test. The relationship links up the Oliver & Pharr hardness with the material strengths, although the Oliver & Pharr hardness may deviate from the true hardness when sinking in or piling up occurs. The functional relationship can further be used to estimate the SUM sigma(E,y) + sigma(E,b) according to the data of an instrumented indentation test. The sigma(E,y) + sigma(E,b) value better reflects the strength of a material compared to the hardness value alone. The method was shown to be effective when applied to aluminum alloys. The relationship can further be used to estimate the fatigue limits, which are usually obtained from macroscopic fatigue tests in different modes.

Size Effect and Geometrical Effect of Solids in Micro-Indentation Test

Micro-indentation tests at scales of the order of sub-micron show that the measured hardness increases strongly with decreasing indent depth or indent size, which is frequently referred to as the size effect. At the same time, at micron or sub-micron scale, another effect, which is referred to as the geometrical size effects such as crystal grain size effect, thin film thickness effect, etc., also influences the measured material hardness. However, the trends are at odds with the size-independence implied by the conventional elastic-plastic theory. In the present research, the strain gradient plasticity theory (Fleck and Hutchinson) is used to model the composition effects (size effect and geometrical effect) for polycrystal material and metal thin film/ceramic substrate systems when materials undergo micro-indenting. The phenomena of the "pile-up" and "sink-in" appeared in the indentation test for the polycrystal materials are also discussed. Meanwhile, the micro-indentation experiments for the polycrystal Al and for the Ti/Si_3N_4 thin film/substrate system are carried out. By comparing the theoretical predictions with experimental measurements, the values and the variation trends of the micro-scale parameter included in the strain gradient plasticity theory are predicted.

Factors Resulting In Micron Indentation Hardness Descending In Indentation Tests

Some factors that affect the experimental results in nanoindentation tests such as the contact depth, contact area, load and loading duration are analyzed in this article. Combining with the results of finite element numerical simulation, we find that the creep property of the tested material is one of the important factors causing the micron indentation hardness descending with the increase of indentation depth. The analysis of experimental results with different indentation depths demonstrates that the hardness decrease can be bated if the continuous stiffness measurement technique is not adopted; this indicates that the test method itself may also be one of the factors causing the hardness being descended.

Nano-hardness Techniques and Its Applications in Mechanical Property Measurements for Surface Engineering

结合纳米硬度技术测量各类薄膜和块体材料表层的纳米压痕硬度、弹性模量、断裂韧性、膜厚、微结构的弯曲变形,采用纳米划痕硬度技术测量各类薄膜和块体材料的粗糙度、临界附着力、摩擦系数、划痕横剖面.纳米硬度计是检测材料表层微米乃至几十纳米力学性能的先进仪器,可广泛应用于表面工程中的质量检测.

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.

Direct numerical test of the B-G-K model equation by the DSMC method

In the present paper the rarefied gas how caused by the sudden change of the wall temperature and the Rayleigh problem are simulated by the DSMC method which has been validated by experiments both in global flour field and velocity distribution function level. The comparison of the simulated results with the accurate numerical solutions of the B-G-K model equation shows that near equilibrium the BG-K equation with corrected collision frequency can give accurate result but as farther away from equilibrium the B-G-K equation is not accurate. This is for the first time that the error caused by the B-G-K model equation has been revealed.

Nano-Hardness Tester and its Application in MEMS

微机电系统(MEMS)技术的迅速崛起,推动了对其所用材料和结构的力学性能研究。简要介绍纳米硬度技术的发展展、理论模型和MTS公司的Nano Indenter XP系统的配置、测量原理及功能。并根据我们的一些研究结果,说明它在微机电系统中的应用。

Relationships between hardness, elastic modulus, and the work of indentation

The work done during indentation is examined using dimensional analysis and finite element calculations for conical indentation in elastic-plastic solids with work hardening. An approximate relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work in indentation is found. Consequently, the ratio of hardness to elastic modulus may be obtained directly from measuring the work of indentation. Together with a well-known relationship between elastic modulus, initial unloading slope, and contact area, a new method is then suggested for estimating the hardness and modulus of solids using instrumented indentation with conical or pyramidal indenters.

Theory and Application of the Transient Injection Well Test

Based on the theory of the pumping well test, the transient injection well test was suggested in this paper. The design method and the scope of application are discussed in detail. The mathematical models are developed for the short-time and long-time transient injection test respectively. A double logarithm type curve matching method was introduced for analyzing the field transient injection test data. A set of methods for the transient injection test design, experiment performance and data analysis were established. Some field tests were analyzed, and the results show that the test model and method are suitable for the transient injection test and can be used to deal with the real engineering problems.

Assessment of Microscale Test Methods of Peeling and Splitting along Surface of Thin-Film/Substrates

Peel test methods are assessed through being applied to a peeling analysis of the ductile film/ceramic substrate system. Through computing the fracture work of the system using the either beam bend model (BB model) or the general plane analysis model (GPA model), surprisingly, a big difference between both model results is found. Although the BB model can capture the plastic dissipation phenomenon for the ductile film case as the GPA model can, it is much sensitive to the choice of the peeling criterion parameters, and it overestimates the plastic bending effect unable to capture crack tip constraint plasticity. In view of the difficulty of measuring interfacial toughness using peel test method when film is the ductile material, a new test method, split test, is recommended and analyzed using the GPA model. The prediction is applied to a wedge-loaded experiment for Al-alloy double-cantilever beam in literature.

What is indentation hardness?

Using dimensional analysis and finite element calculations, we derive simple scaling relationships for loading and unloading curve, contact depth, and hardness. The relationship between hardness and the basic mechanical properties of solids, such as Young's modulus, initial yield strength, and work-hardening exponent, is then obtained. The conditions for 'piling-up' and 'sinking-in' of surface profiles during indentation are determined. A method for estimating contact depth from initial unloading slope is examined. The work done during indentation is also studied. A relationship between the ratio of hardness to elastic modulus and the ratio of irreversible work to total work is discovered. This relationship offers a new method for obtaining hardness and elastic modulus. Finally, a scaling theory for indentation in power-law creep solids using self-similar indenters is developed. A connection between creep and 'indentation size effect' is established.