Welding Metallurgy of

We provide an overview of the basic concepts of scaling and dimensional analysis, followed by a review of some of the recent work on applying these concepts to modeling instrumented indentation measurements. Specifically, we examine conical and pyramidal indentation in elastic-plastic solids with power-law work-hardening, in power-law creep solids, and in linear viscoelastic materials. We show that the scaling approach to indentation modeling provides new insights into several basic questions in instrumented indentation, including, what information is contained in the indentation load-displacement curves? How does hardness depend on the mechanical properties and indenter geometry? What are the factors determining piling-up and sinking-in of surface profiles around indents? Can stress-strain relationships be obtained from indentation load-displacement curves? How to measure time dependent mechanical properties from indentation? How to detect or confirm indentation size effects? The scaling approach also helps organize knowledge and provides a framework for bridging micro- and macroscales. We hope that this review will accomplish two purposes: (1) introducing the basic concepts of scaling and dimensional analysis to materials scientists and engineers, and (2) providing a better understanding of instrumented indentation measurements.

Scaling, dimensional analysis, and indentation measurements

Optimization Techniques with FORTRAN

Modern computer microprocessor chips are marvels of engineering complexity. For the current 45 nm technology node, there may be nearly a billion transistors on a chip barely 1 cm2 and more than 10 000 m of wiring connecting and powering these devices distributed over 9-10 wiring levels. This represents quite an advance from the first INTEL 4004B microprocessor chip introduced in 1971 with 10 μm minimum dimensions and 2 300 transistors on the chip! It has been disclosed that advanced microprocessor chips at the 32 nm node will have more than 2 billion transistors.1 For instance, Figure 1 shows a sectional 3D image of a 90 nm IBM microprocessor, containing several hundred million integrated devices and 10 levels of interconnect wiring, designated as the back-end-of-the-line (BEOL). Since the invention of microprocessors, the number of active devices on a chip has been exponentially increasing, approximately doubling every two years. This trend was first described in 1965 by Gordon Moore,2 although the original discussion suggested doubling the number of devices every year, and the phenomenon became popularly known as Moore’s Law. This progress has proven remarkably resilient and has persisted for more than 50 years. The enabler that has permitted these advances is known as scaling, that is, the reduction of minimum device dimensions by lithographic advances (photoresists, tooling, and process integration optimization) by ∼30% for each device generation.3 It allowed more active devices to be incorporated in a given area and improved the operating characteristics of the individual transistors. It should be emphasized that the earlier improvements in chip performance were achieved with very few changes in the materials used in the construction of the chips themselves. The increase of performance with scaling * Corresponding author. E-mail: gdubois@us.ibm.com. † IBM Almaden Research Center. ‡ Stanford University. Willi Volksen received his B.S. in Chemistry (magna cum laude) from New Mexico Institute of Mining and Technology in 1972 and his Ph.D. in Chemistry/Polymer Science from the University of Massachusetts, Lowell, in 1975. He then joined the research group of Prof. Harry Gray/Dr. Alan Rembaum at the California Institute of Technology as a postdoctoral fellow and upon completion of the one-year appointment joined Dr. Rembaum at the Jet Propulsion Laboratory as a Senior Chemist in 1976. In 1977 Dr. Volksen joined the IBM Research Division at the IBM Almaden Research Center in San Jose, CA, where he is an active research staff member in the Advanced Materials Group of the Science and Technology function.

Low dielectric constant materials.

http://doras.dcu.ie/17607/1/Review_of_residual_stresses-Final.pdf

Methods of measuring residual stresses in components

The ball indentation technique has the potential to be an excellent substitute for a standard tensile test, especially in the case of small specimens or property-gradient materials such as welds. In our study, the true stress–true strain relationships of steels with different work-hardening exponents (0.1–0.3) were derived from ball indentations. Four kinds of strain definitions in indentation were attempted: 0.2sinγ, 0.4hc/a, ln[2/(1 + cosγ)], and 0.1tanγ. Here, γ is the contact angle between the indenter and the specimen, hc is the contact depth, and a is the contact radius. Through comparison with the standard data measured by uniaxial tensile testing, the best strain definition was determined to be 0.1tanγ. This new definition of strain, in which tanγ means the shear strain at contact edge, reflected effectively the work-hardening characteristics. In addition, the effects of pileup or sink-in were considered in determining the real contact between the indenter and the specimen from the indentation load–depth curve. The work-hardening exponent was found to be a main factor affecting the pileup/sink-in phenomena of various steels. These phenomena influenced markedly the absolute values of strain and stress in indentation by making the simple traditional relationship Pm/σR ≈ ≈ 3 valid for the fully plastic regime.

https://www.cambridge.org/core/services/aop-cambridge-core/content/view/S0884291400065183

Derivation of plastic stress–strain relationship from ball indentations: Examination of strain definition and pileup effect

Estimation of biaxial surface stress by instrumented indentation with sharp indenters

Measurement of residual-stress effect by nanoindentation on elastically strained (100) W

Influence of surface-roughness on indentation size effect

An instrumented indentation technique for estimating fracture toughness of ductile materials: A critical indentation energy model based on continuum damage mechanics

Dongil Kwon

Papers

Derivation of plastic stress–strain relationship from ball indentations: Examination of strain definition and pileup effect

Estimation of biaxial surface stress by instrumented indentation with sharp indenters

Measurement of residual-stress effect by nanoindentation on elastically strained (100) W

Influence of surface-roughness on indentation size effect

An instrumented indentation technique for estimating fracture toughness of ductile materials: A critical indentation energy model based on continuum damage mechanics