Strengthening of materials caused by dispersion of doughnut-like second phase

为了了解第二相弥散对材料力学性能的影响，我们对Cu-Si合金进行了如下研究：Cu-Si合金在不同Si原子处与氧发生内氧化，在晶界上形成薄膜状SiO_2沉淀。Si原子与氧反应后，首先形成带孔的薄膜状SiO_2沉淀，露出Cu的晶界。在内氧化温度下，孔洞迅速长大，膜状SiO_2形态通过形成二维SiO_2网络向颗粒平衡形态演变。平均Eshelby张量，涉及均匀本征应变和平均总应变甜甜圈状夹杂物。这些比较与Eshelby张量的扁球形和棒状夹杂物。我们发现，平面上的甜甜圈状夹杂物的平均Eshelby张量几乎是相同的随机取向的杆状夹杂物在同一平面上的Eshelby张量的平均值。这对于两种“薄的”甜甜圈状夹杂物都是满意的。本文还讨论了均匀本征应变和纯本征应变引起的环形夹杂的应变场。在环状包涵体附近，有两个点，菌株的所有组分均为零。利用所得结果，讨论了环状夹杂物对材料力学性能的影响。

We have made the following studies to understand the change of mechanical properties of materials caused by dispersion of doughnut-like second phase.Cu-Si alloys are internally oxidized at various of Si atoms with oxygen, film-like SiO_2 precipitates formed on grain boundaries (GBs) is observed. After the reaction of Si atoms with oxygen, film-like SiO_2 precipitates with holes which expose GB of Cu are initially formed. At temperatures used for the internal oxidation, the holes rapidly grow and the morphology of the film-like SiO_2 evolves to a particulate equilibrium shape through formation of two-dimensional SiO_2 network.Theoretical calculations to understand effects of doughnut-like inclusions on the mechanical properties of materials are made. The averaged Eshelby tensors that relate uniform eigenstrains and average total strains in doughnut-like inclusions are obtained. These are compared with the Eshelby tensors of oblate spheroidal and rod-like inclusions. We show that the averaged Eshelby tensors of the doughnut-like inclusions on a plane are almost the same as the average of the Eshelby tensors of randomly oriented rod-like inclusions on the same plane. This is satisfied for both "thin" doughnut-like inclusions. The strain field caused by uniform and purely dilatational eigenstrains is also discussed for a doughnut-like inclusion. Near the doughnut-like inclusion, there are two points where all components of the strains are null. Using the results results obtained, we have discussed the effects of the doughnut-like inclusions on the mechanical properties of materials.