An Intrinsic Size-Effect in Machining Due to the Strain Gradient

Abstract

It has been suggested recently [1–4] that an increase in the hardness value often observed when the indentation size is reduced (indentation size effect) in metals is a consequence of the dependence of the flow stress of the metal on the strain gradient. Here, we show based on an analysis of the strain gradient in machining, that a similar size effect should be observable when machining at small values of the undeformed chip thickness. Such a size effect will manifest itself as a continuous increase in the specific cutting force as the chip thickness is reduced. Furthermore, the size effect in machining is likely to be much more pronounced than in indentation, because of the more intensive strain gradient prevailing in the deformation field in machining. The dependence of the flow stress on strain gradient is not an artificial construct but has a well-established basis in the dislocation theory of hardening [5]. Our analysis suggests that an effective test of plasticity constitutive laws that incorporate the strain gradient as a parameter can be achieved using a simple 2-D cutting experiment with a sharp tool carried out at very low speeds. Such a test may be carried out with ductile pure metals as workpieces wherein this size effect is expected to be most significant.

Numerical modelling of size effects in micro-cutting of f.c.c. single crystal: Influence of strain gradients

“…8d-f also demonstrate that the density of PDs is larger in the primary deformation zone for the (111) orientation compared to others as the length of the shear plane is smaller. This is consistent with the analytical model in [16] explaining the size-effect in machining.…”

“…These observations suggest that a larger shear angle (with a smaller shear-plane length) results in higher specific cutting energy in the cutting of copper single-crystals. This is consistent with the analytical model of the machining process developed by Joshi and Melkote [16], where shear strength of the material in the PDZ is inversely proportional to the length of the shear plane. It is noteworthy that the ratio of the specific cutting energy for the (111) and (110) orientations is 1.27, which is in good proximity to the experimental one with a value of 1.29 [31].…”

“…Dinesh et al [15] related the size effect in indentation to that in machining and suggested that the strain gradient in the latter may be much larger than that of the former. Based on this study, Joshi and Melkote [16] developed a strain-gradient plasticity-based analytical model of the orthogonal cutting process to explain the material deformation in the primary deformation zone (PDZ) and ultimately the size effect. Later Liu and Melkote [17] developed a two-dimensional finite-element (FE) model of machining incorporating the strain gradient effect to investigate the influence of radius of tool edge on the size effect.…”

510 An Explanation for the Size-effect in Machining using Strain Gradient Plasticity

“…phenomenon in g;adient ,approach the strength is considered a machining has been attributed to'inhomogeneous fi}nctipnofthestFaingradientalso, strains and number of imperfectiens per unit .An.understanding of dislocation processes volume [6'7],subsurfaoe plastic work [8], and.the ptovides'a,･framework for incorporating'the strain plowing force [9]. Recently, Dinesh.,eV al [10] gr, adients mto constitutive equations. Presence of postulated thqt.ihe strain gradieut in machining ai'strain.…”

“…Ftatistiba4y stoived dislocations, leading to an [EFhis,pap.er builds on the work ofDinesh, et aL, rpcreetse E,i stFength･ It is'ehfrrefore Possible to [10]. i eometry of the strain field, ii) evaluation of th6 strain gradient, iiD evaluation of density of dislecations, and iv) Evaluation of material strength as a function of material length scale.…”