Modeling of the Size Effects on the Behavior of Metals in Microscale Deformation Processes

Abstract

For the accurate analysis and design of microforming process, proper modeling of ma-terial behavior at the micro/mesoscale is necessary by considering the size effects. Two size effects are known to exist in metallic materials. One is the “grain size ” effect, and the other is the “feature/specimen size ” effect. This study investigated the feature/ specimen size effect and introduced a scaling model which combined both feature/ specimen and grain size effects. Predicted size effects were compared with three separate experiments obtained from previous research: a simple compression with a round speci-men, a simple tension with a round specimen, and a simple tension in sheet metal. The predicted results had a very good agreement with the experiments. Quantification of the miniaturization effect has been achieved by introducing two parameters, and , which can be determined by the scaling parameter n, to the Hall–Petch equation. The scaling model offers a simple way to model the size effect down to length scales of a couple of grains and to extend the use of continuum plasticity theories to micro/mesolength scales. DOI: 10.1115/1.271458

Accuracy of Model Force Prediction in Closed Die Coining Process

“…By incorporating the expanded Hall-Petch expression from [20] and [30] into Eq. (4), the next formulation for forging force is obtained, in which the forging force depends on true strain and the crystalline grain size:…”

“…K hp is interpreted as the resistance of the grain boundary to deformation (parameter from a HallPetch model), and d is the size of the crystalline grain. Parameters α SE and β SE are determined on the basis of the findings of [20] and [30]. The size factor (λ) is obtained from the diagram on Fig.…”

Fundamentals of Micro‐Manufacturing

“…In this chapter, an attempt has been made to quantify the size effect on the flow stress by considering the fundamental properties of single and polycrystal plasticity. According to Armstrong [30] and Kim et al [31], the size effects can be investigated under two categories-the "grain size effect" and the "feature/specimen size effect." The "grain size effect" has been known to follow the Hall-Petch equation [32,33].…”

“…The "specimen size effect" (t 0 or D 0 ) on the material flow curve as a measure of material response was observed in various tensile test conditions for a variety of materials such as CuAl alloy [35], CuNi18Zn20, CuZn15 [36], CuZn36 [37], and aluminum [38,39]. While the grain size shows a strong effect on the material response at all length scales (i.e., from macro-to micro-scale), it is not until the N value is around 10-15 that the "specimen size effect" starts to influence the material response [31,38,40]. In general, the tensile test results showed a decreasing trend of the flow stress with the decreasing specimen size (i.e., decreasing N value) as illustrated in Fig.…”

On the size effect for micro-scale structures under the plane bulge test using the modified strain gradient theory

“…[9][10][11][12] However, this theory cannot explain the opposite size effect, in which smaller grains are softer. 13,14 The "surface model" and several modifications 15,16 can explain this size effect using the assumption that the surface grains are less restricted than the bulk grains. However, this model cannot explain the other size effect, that smaller grains are harder.…”