Grain size dependence of the strength of metals: The Hall-Petch effect does not scale as the inverse square root of grain size
Grain size dependence of the strength of metals: The Hall-Petch effect does not scale as the inverse square root of grain size
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DOI：
10.1016/j.ijplas.2013.07.004
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发表时间：
2014-02-01
影响因子：
9.8
通讯作者：
Bushby, A. J.
中科院分区：
文献类型：
--
作者：
Dunstan, D. J.;Bushby, A. J.
回顾了许多金属强度与晶粒尺寸关系的文献中的经典数据。与强度和晶粒尺寸d（-x）相关的指数x通常不是epsilon倒数平方根关系（称为Hall-Petch效应），而是从低至x = 0.2的值到高至x = 1的值广泛分散。单个数据集的这些指数在很大程度上是没有意义的。对于n个选定数据集的集合，发现具有n + 1个自由拟合参数的函数形式ln[d]/d + const的拟合几乎与具有2n个拟合参数的1/Sqrt[d] + const的拟合（Hall-Petch拟合）一样好。前者是更好的匹配的可能性很高。有些数据集与In[d]/d拟合不一致，但它们的偏差很容易用简单的物理基础来解释。此外，即使将它们包括在拟合中，统计检验仍然表明In[d]/d形式更可取。结论是霍尔-佩奇效应不是另一种独特的尺寸效应，而是与外延薄膜生长和小试样微机械测试中观察到的尺寸效应相同的尺寸效应。因此，我们建议，晶粒尺寸强化的金属驱动的应力和位错曲率的限制，根据可用的空间。(C)2013爱思唯尔有限公司保留所有权利。
The classic data in the literature for the grain size dependence of the strength in many metals are reviewed. The exponent x relating strength to grain size d(-x) is not often the eponymous inverse square-root relationship (known as the Hall-Petch effect), but is widely scattered from values as low as x = 0.2 to values as high as x = I. These exponents for individual datasets are shown to be largely meaningless. For an ensemble of n selected datasets, the fit to the functional form ln[d]/d + const with n + 1 free fitting parameters is found to be almost as good as the fit to 1/Sqrt[d] + const with 2n fitting parameters (the Hall-Petch fit). The probability that the former is the preferable fit is high. Some data sets do not agree with the In[d]/d fit, but their deviation is readily explained on simple physical grounds. Moreover, even when they are included in the fit, statistical tests still show that the In[d]/d form is preferable by a wide margin. The conclusion is that the Hall-Petch effect is not another size effect sui generis but is the same size effect as that observed in epitaxial thin film growth and in micromechanical testing of small specimens. Consequently we propose that grain size strengthening of metals is driven by constraints on stress and dislocation curvature according to the space available. (C) 2013 Elsevier Ltd. All rights reserved.