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.

Scaling approach to conical indentation in elastic-plastic solids with work hardening

We derive, using dimensional analysis and finite element calculations, several scaling relationships for conical indentation in elastic-plastic solids with work hardening. Using these scaling relationships, we examine the relationships between hardness, contact area, initial unloading slope, and mechanical properties of solids. The scaling relationships also provide new insights into the shape of indentation curves and form the basis for understanding indentation measurements, including nano- and micro-indentation techniques. They may also be helpful as a guide to numerical and finite element calculations of indentation problems.

Essential and Non-Essential Work of Fracture of PI/SiO2 Hybrid Thin Films

Essential work of fracture (EWF) analysis is used to study the effect of the silica doping level on fracture toughness of polyimide/silica (PI/SiO2) hybrid films. By using double-edge-notched-tension (DENT) specimens with different ligament lengths, it seems that the introduction of silica additive can improve the specific essential work of fracture (w (e) ) of PI thin films, but the specific non-essential work of fracture (beta w (p) ) will decease significantly as the silica doping level increasing from 1 to 5 wt.%, and even lower than that of neat PI. The failure process of the fracture is investigated with online scanning electron microscope (SEM) observation and the parameters of non-essential work of fracture, beta and w (p) , are calculated based on finite element (FE) method.

Effect of Work of Adhesion on Nanoindentation

Three adhesion contact models, JKR (Johnson-Kendall-Roberts), DMT (Derjaguin-Muller-Toporov) and MD (Maugis-Dugdale) are compared with the Hertz model in dealing with the nano-contact problems. It has been shown that the dimensionless load parameter, $\bar{P}=P/(\pi\Delta\gamma R)$, and the transition parameter, $\Lambda$, have significant influences on the contact stiffness (contact area) at micro/nano-scale and should not be ignored in shallow nanoindentation.

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.

Style and the “Idea” of the sophist after Plato : the impact of form typology on sophistic teaching and writing on interdisciplinary scholarly work

Resumen: Después de la primera sofística, los sofistas actuaron entre el resto de los pensadores del Mediterráneo como un grupo definido. Dado que hay muchos ejemplos que muestran que los sofistas ejercían sus prácticas y que también eran personas comprometidas en otras actividades, vamos a examinar aquí diversos casos de semejanzas y diferencias entre ellos y otros grupos de pensadores. Nuestras tres preguntas fundamentales son: qué, cómo y por qué los sofistas escribían y enseñaban. Intentaremos responder haciendo un análisis diacrónico de las principales formas y géneros de escritura que produjeron (qué). El cómo lo responderemos en su desenvolvimiento como una actividad comunicativa más allá de las fronteras de las disciplinas de la época. El por qué tendrá su respuesta al enfatizar la necesidad de la actividad de los sofistas en la socialización de la época y en la educación de la antigüedad. Al aseverar que el estilo era la idea de los sofistas, ponemos la noción de idea en Platón en el contexto de idea derivado de los sofistas contemporáneos a él y de los sofistas posteriores (segunda sofística) y centramos el foco en la función de visualidad expresada en su concepto de idea desde las obras sofísticas más tempranas en la época de Platón hasta las contribuciones posteriores.

Characterization of the Fracture Work for Ductile Film Undergoing the Micro-Scratch

The interface adhesion strength (or interface toughness) of a thin film/substrate system is often assessed by the micro-scratch test. For a brittle film material, the interface adhesion strength is easily obtained through measuring the scratch driving forces. However, to measure the interface adhesion strength (or interface toughness) for a metal thin film material (the ductile material) by the microscratch test is very difficult, because intense plastic deformation is involved and the problem is a three-dimensional elastic-plastic one. In the present research, using a double-cohesive zone model, the failure characteristics of the thin film/substrate system can be described and further simulated. For a steady-state scratching process, a three-dimensional elastic-plastic finite element method based on the double cohesive zone model is developed and adopted, and the steady-state fracture work of the total system is calculated. The parameter relations between the horizontal driving forces (or energy release rate of the scratching process) and the separation strength of thin film/substrate interface, and the material shear strength, as well as the material parameters are developed. Furthermore, a scratch experiment for the Al/Si film/substrate system is carried out and the failure mechanisms are explored. Finally, the prediction results are applied to a scratch experiment for the Pt/NiO material system given in the literature.

Steady-state crack growth and fracture work based on the theory of mechanism-based strain gradient plasticity

Mode I steady-state crack growth is analyzed under plane strain conditions in small scale yielding. The elastic-plastic solid is characterized by the mechanism-based strain gradient (MSG) plasticity theory [J. Mech. Phys. Solids 47 (1999) 1239, J. Mech. Phys. Solids 48 (2000) 99]. The distributions of the normal separation stress and the effective stress along the plane ahead of the crack tip are computed using a special finite element method based on the steady-state fundamental relations and the MSG flow theory. The results show that during the steady-state crack growth, the normal separation stress on the plane ahead of the crack tip can achieve considerably high value within the MSG strain gradient sensitive zone. The results also show that the crack tip fields are insensitive to the cell size parameter in the MSG theory. Moreover, in the present research, the steady-state fracture toughness is computed by adopting the embedded process zone (EPZ) model. The results display that the steady-state fracture toughness strongly depends on the separation strength parameter of the EPZ model and the length scale parameter in the MSG theory. Furthermore, in order for the results of steady crack growth to be comparable, an approximate relation between the length scale parameters in the MSG theory and in the Fleck-Hutchinson strain gradient plasticity theory is obtained.

Work Softening And Annealing Hardening Of Deformed Nanocrystalline Nickel

We reported that work softening takes place during room-temperature rolling of nanocrystalline Ni at an equivalent strain of around 0.30. The work softening corresponds to a strain-induced phase transformation from a face-centered cubic (fcc) to a body-centered cubic (bcc) lattice. The hardness decreases with increasing volume fraction of the bcc phase. When the deformed samples are annealed at 423 K, a hardening of the samples takes place. This hardening by annealing can be attributed to a variety of factors including the recovery transformation from the bcc to the fcc phase, grain boundary relaxation, and retardation of dislocation gliding by microtwins.

Experimental Verification And Theoretical Analysis Of The Relationships Between Hardness, Elastic Modulus, And The Work Of Indentation

The relationship between hardness (H), reduced modulus (E-r), unloading work (W-u), and total work (W-t) of indentation is examined in detail experimentally and theoretically. Experimental study verifies the approximate linear relationship. Theoretical analysis confirms it. Furthermore, the solutions to the conical indentation in elastic-perfectly plastic solid, including elastic work (W-e), H, W-t, and W-u are obtained using Johnson's expanding cavity model and Lame solution. Consequently, it is found that the W-e should be distinguished from W-u, rather than their equivalence as suggested in ISO14577, and (H/E-r)/(W-u/W-t) depends mainly on the conical angle, which are also verified with numerical simulations. (C) 2008 American Institute of Physics.

Barium-Functionalized Multiwalled Carbon Nanotube Yarns As Low-Work-Function Thermionic Cathodes

Barium-functionalized multiwalled carbon nanotube yarns were fabricated by drawing and twisting multiwalled carbon nanotube forests through a solution containing barium nitrate. After heat activation under vacuum, the functionalized yarns were enriched in barium oxide due to the high surface-to-volume ratio of the nanotubes. The cathodes exhibited good thermionic properties, with a work function as low as 1.73-2.06 eV and thermionic current density that exceeded 185 mA/cm(2) in a field of 850 V/5 mm at 1317 K. The barium-functionalized yarns had high tensile strength of up to 420 MPa and retained strength of similar to 250 MPa after a 2 h activation process. (C) 2008 American Institute of Physics.

Migración y misión : una mirada desde Aparecida

Resumen: Considerando la preocupación de los obispos latinoamericanos y del Caribe en la V Conferencia General de Aparecida sobre los migrantes como nuevos actores sociales destinatarios de la evangelización y futuros misioneros, se hace una reflexión interdisciplinaria, entre la teología y las ciencias sociales, sobre el trabajador migrante como lugar teológico. Poniendo en equivalencia las categorías de éxodo y migración, se intenta hacer manifiesto el camino del esfuerzo del trabajador migrante que, en tiempos de globalización, ve en el trabajo una vía de movilidad social ascendente desde la pobreza del ser a la dignidad del trabajador asalariado como creatura de Dios. Como ejemplo de solidaridad, de trabajadores misionando en función de trabajadores, se presenta el caso de la integración regional sindical en red, y sus modos de irrupción en el mundo de la determinación