Size effects on material yield strength/deformation/fracturing properties
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INTRINSIC AND EXTRINSIC SIZE EFFECTS IN MATERIALS
Size effects on material yield strength/deformation/ fracturing properties Ronald W. Armstrong1,a) 1
Department of Mechanical Engineering, University of Maryland, College Park, Maryland 20742, USA Address all correspondence to this author. e-mail: [email protected]
a)
Received: 3 August 2018; accepted: 3 October 2018
The effects of specimen size, Hall–Petch (H-P) grain or subgrain size, particle size plus spacing, and crack size on the yield strength, plastic deformation, and fracturing properties of crystalline materials are described on a dislocation mechanics basis. The size effects are assessed at relevant macro- and/or micro-and/or nano-scale dimensions; in the latter case, at the upper-limiting strength levels. The description is applied mostly to facecentered cubic (FCC), body-centered cubic (BCC), and hexagonal close-packed (HCP) metals but also involves grain size/particle size–dependent (composite) steel material behaviors. Competition is described for the role of dislocation pile-ups versus hole-joining mechanisms for ductile failure. Grain size–dependent microhardness and strain rate sensitivity measurements are presented for nano-grain size strengthening and grain size weakening, respectively. An intrinsic size effect is demonstrated for silicon crystal nano-indentation hardness testing, which, on microscale loading, leads to evaluation of crack size dependence and, for polycrystalline alumina, to associated H-P behavior for the fracture mechanics stress intensity.
Introduction There are size effects involved in determining the strength of materials at every level from the atomic scale to the macroscale. A number of size effects are reviewed in the present report. We start with the Hall–Petch (H-P) relation for an inverse square root of grain size, ℓ1/2, dependence of the unidirectional plastic flow stress, re, at strain value, e:
h i re ¼ r0e þ ke ‘1=2 ¼ mT s0e þ kSe ‘1=2
:
ð1Þ
In Eq. (1), r0e is a Taylor-type “friction” stress for strain hardening within the grain volumes and ke is a Griffith-type microstructural stress intensity factor that applies for local stress enhancement at an average grain boundary needed for transmission of plastic flow by slip or twinning [1]. Also in Eq. (1), r0e is shown to connect with a resolved shear stress, s0e, multiplied by the Taylor orientation factor, mT, for resolution of re onto the slip system geometry and relates ke to the shear stress intensity, kSe, multiplied by the same mT factor. The mention of Griffith connection for grain size
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dependence follows from the model of a dislocation pile-up in a slip band, when blocked at a grain boundary, behaving similarly to a shear crack. Consideration is given in route to assessing Eq. (1) applications at several dimensional levels, first, in section “Specimen size/grain size relationship”, to strength/d
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