Analysis of Dislocation Mobility under Concentrated Loads at Indentations of Single Crystals

Abstract

An approximate solution is given for the dependence of the dislocation track length, t , around a microhardness indentation in single crystals on the load applied t o the indenter (P), the temperature (T), and the duration under load ( t ) :The assumption is made that dislocations move from the indenter in plane arrays alid that the dislocation velocity is vt m exp (-U / k T ) , where t is an effective stress, U is the activation energy.I n a definite range of parameters the equation agrees satisfactorily with the literature data and those obtained in the present work, and may be used t o estimate the dislocation mobility from the dislocation track length. The value of the ratio l/d ( d is the indentation diagonal) is constant for ionic crystals but depends on the temperature and the load in the case of covalent crystals. l is connected with the yield strengt,h ts a s Zrs = const for covalent crystals (m. = l), but 12ts = const for ionic crystals ( m > 2). Es wird eineNaherungslosung fur die Abhangigkeit der Verset,zungslLnge I urn einen Nikrohiirteeindruck in Einkristallen von der angewandten Last auf den Stempel (P), der Temperatur (T) und der Dauer der Last (t)angegeben: Z-Pm/(Zm+1)tli@m+l) exp[-UlkT(2m + l)]. Es wird dieAnnahme gemacht, dalJ Versetzungen sich vom Stempel in ebenen Anordnungen bewegen und daB die Versetzungsgeschwindigkeit wt l ) l exp (-U / k T ) ist. u-obei s eine effektive Spannung und U die Aktivierungsenergie ist. I n einem definierten Bereich von Parametern stimmt die Gleichung befriedigend mit Literaturwerten uberein und solchen, die in der vorliegenden Arbeit erhalten werden, und kann zur Berechnung der Versetzungsbeweglichkeit a u s der Lange des Versetzungspfades benutzt werden. Der Wert des Verhaltnisses Z/d (d ist die Eindruckdiagonale) ist fur Ionenkristalle konstant, hangt jedoch von der Temperatur und Last im Fall der kovalenten Kristalle ab. l ist mit der FlulJstarke ts wie Is, = const fur kovalente Kristalle ( m z l), jedoch wie Pt, z const fur Ionenkristalle ( m > 2) verknupft.

Deformation of MgO by Vickers microindentation tests

“…These observations are consistent with the model of Gridneva et al [13] (Fig. 4) ; 2 1 and Hv are minimum for the indenter diagonal parallel to 110 > (Fig.…”

Estimations of Low Temperature Dislocation Mobility in GaN

“…The stress dependence of the dislocation velocity is usually described by the empirical formula where the constants V 0 and τ 0 are usually determined experimentally for different materials and Δ E is the activation energy for dislocation mobility . As shown in, if the dislocation velocity can be described by the Equation and τ is equal to AP / r 2 , where , ν is the Poisson ratio and P is the applied load, the Equation can be rewritten as and where L is the traveling distance of leading dislocations measured from the imprint center and t d is the deformation dwell time. From Equation it can be obtained that …”

“…In this case the distance from the imprint center to the leading dislocation varies from a to ( a 2 + L 1 2 ) 0.5 , where a is the distance between the acting slip plane and the imprint center and L 1 is the traveling distance of cross‐slip dislocation. These parameters are illustrated by (Figure ) on the CL image of imprint made by indentation at 573 K. The integration procedure similar to that used in and in Equation , assuming that m is the integer, gives for L 1 …”

Application of the Improved Inclusion Core Model of the Indentation Process for the Determination of Mechanical Properties of Materials

“…In the framework of the dislocation theory, the zone of elastoplastic deformation with the radius bS is the zone with a sharp increase in the dislocation density around the indentation imprint with a symmetry center at the very point 0 in Figure 1. Dislocations are nucleated near the indenter and move in the radial directions to the boundaries of the elastoplastic zone under the action of shear stress, caused by the load on indenter [19]. The comparison of calculated values of bS with the experimental data is given in the Section 3.6.…”