Consistent determination of geometrically necessary dislocation density from simulations and experiments
Consistent determination of geometrically necessary dislocation density from simulations and experiments
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DOI：
10.1016/j.ijplas.2018.05.001
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发表时间：
2018-10-01
影响因子：
9.8
通讯作者：
Tarleton, Edmund
中科院分区：
文献类型：
--
作者：
Das, Suchandrima;Hofmann, Felix;Tarleton, Edmund
利用奈位错张量计算几何必要位错（GND）密度在塑性变形材料的研究中被广泛采用。寻找Nye张量所涉及的“旋度”操作，虽然概念上很简单，但由于不一致和使用了几种不同的定义而受到损害。对于三个最常见的定义，我们展示了它们的一致应用会导致相同的结果。为了消除经常遇到的混淆，总结了Nye张量在弹性和塑性变形梯度以及小变形和大变形方面的表达式。估计GND密度时的另一个问题涉及用于解决连接Nye张量和GND密度的欠定方程组的优化技术。对两种广泛使用的技术（L-1和L-2最小化）获得的密度进行系统比较，表明这两种方法产生的总GND密度非常相似。因此，数学上较简单的L-2可能优于L-1，除非需要关于特定滑移系统的密度分布的信息。为了说明这一点，我们比较了实验测量的纯钨纳米压痕下的晶格畸变，使用3D分辨同步加速器x射线微衍射探测，与3D应变梯度晶体塑性有限元计算预测的晶格畸变。结果一致，表明弹性应变场的体积分量对确定的奈张量的影响小得惊人。这对于实验技术很重要，例如微束劳厄测量和HR-EBSD，其中只测量偏差应变分量。
The use of Nye's dislocation tensor for calculating the density of geometrically necessary dislocations (GND) is widely adopted in the study of plastically deformed materials. The "curl" operation involved in finding the Nye tensor, while conceptually straightforward has been marred with inconsistencies and several different definitions are in use. For the three most common definitions, we show that their consistent application leads to the same result. To eliminate frequently encountered confusion, a summary of expressions for Nye's tensor in terms of elastic and plastic deformation gradient, and for both small and large deformations, is presented. A further question when estimating GND density concerns the optimization technique used to solve the under-determined set of equations linking Nye's tensor and GND density. A systematic comparison of the densities obtained by two widely used techniques, L-1 and L-2 minimisation, shows that both methods yield remarkably similar total GND densities. Thus the mathematically simpler, L-2, may be preferred over L-1 except when information about the distribution of densities on specific slip systems is required. To illustrate this, we compare experimentally measured lattice distortions beneath nano-indents in pure tungsten, probed using 3D-resolved synchrotron X-ray micro-diffraction, with those predicted by 3D strain-gradient crystal plasticity finite element calculations. The results are in good agreement and show that the volumetric component of the elastic strain field has a surprisingly small effect on the determined Nye tensor. This is important for experimental techniques, such as micro-beam Laue measurements and HR-EBSD, where only the deviatoric strain component is measured.