On the pile-up model of the grain size-yield stress relation for nanocrystals
On the pile-up model of the grain size-yield stress relation for nanocrystals
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DOI：
10.1016/1359-6462(95)00572-2
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发表时间：
1996-03-01
影响因子：
6
通讯作者：
Nazarov, AA
中科院分区：
文献类型：
--
作者：
Nazarov, AA
常规多晶体的屈服应力σ Y或硬度FZ对晶粒尺寸的依赖性遵循公知的Hall-Petch（HP）关系式σ Y = μ 0 + μ 1”或HZ = μ 0 + k 1 "[1 -3]。同时，最近的纳米晶体的硬度测试表明，这些关系是违反晶粒尺寸小于约100 nm。在实验中得到了斜率kH减小的正关系[4，5]以及从正关系到负关系的过渡[6，7]。已经提出了一系列模型来解释这种现象。已尽最大努力描述从正常HP行为到异常HP行为的转变[S-12]。然而，对实验数据的分析表明，随着晶粒尺寸的减小而软化不是纳米晶材料的固有行为，而是由于残余孔隙率或内应力[13]。然而，毫无疑问，纳米晶区域中HP关系的斜率小于粗晶多晶体[4，5，13]。最近，Armstrong及其同事[141]已经清楚地证明，小晶粒尺寸下ky的降低可以在传统位错堆积模型的框架内解释。问题的关键是，对于少量位错（n< 20）的堆积问题的解与通常引用的对于大n有效的解[151]有很大不同。因此，在小晶粒尺寸下，相关性cr，（d”）变成阶梯函数，其在n= 1时达到等于aTy”"= 1%的平台，其中M是泰勒因子，t是位错穿过晶界所需的临界剪切应力（更多细节，参见下一节）。
The dependences of the yield stress oY or hardness FZ, of conventional polycrystals on the grain size obey the well known Hall-Petch (HP) relations oY= u0+ VI” or H,= Hyo+ k& ‘”[l-3]. Meanwhile, recent hardness tests ofnanocrystals have shown that these relations are violated at grain sizes less than approximately 100 nm. A positive relation with decreased slope kH [4, 5] as well as a transition from positive to negative relation [6, 7] have been obtained in experiments. A series of models have been proposed to account for this phenomenon. The most effort has been made to descrilbe the transition from a normal HP behaviour to an abnormal one [S-12]. However, an analysis of experimental data has shown that the softening with decreasing grain size is not an intrinsic behaviour of nanocrystalline materials but may be due to residual porosity or internal stresses [13]. Though, there is no doubt that the slope of HP relation in nanocrystalline region is less than for coarse grained polycrystals [4, 5, 13].Quite recently, Armstrong and co-workers [141 have clearly demonstrated that the decrease of ky at small grain sizes can be explained in the framework of traditional dislocation pile-up model. The point is that the soluti’on of the pile-up problem for small numbers of dislocations (n< 20) considerably differs from the usually cited solution [151 valid for large n. Due to this, at small grain sizes the dependence cr,,(d”) becomeis a staircase fimction which reaches a plateau equal to aTy””= I%, at n= 1, where M is the Taylor factor and t, the critical shear stress required for the dislocation passing through grain boundaries (for more details, see the next section).