Quantifying the Scatter: Statistical Analysis and Stochastic Modelling of Microplasticity

当固体材料的载荷超过临界水平时，它们可能会永久性地改变其形状：它们会经历塑性变形。以一个圆柱体为例，我们通过自上而下的推动来压缩它。如果载荷较小，则圆柱体首先弹性变形(在移除载荷后恢复为其原始形状)。超过一定的载荷，会留下一些永久性的变形。现在，如果我们使用一个宏观圆柱体，比方说，几厘米大小，那么获得给定的相对变形所需的应力(单位面积的力)将不取决于圆柱体的大小。它会随着变形量的增加而逐渐增加，这种‘硬化行为’对于相同材料制成的圆柱体和在相同条件下变形的圆柱体将是相同的。如果圆柱体中所有地方的应力都相同，变形也将是均匀的-圆柱体将变得更短、更厚，但仍将保持其圆柱形。但当变形体变得非常小--直径约为几微米--时，我们观察到完全不同的行为：(1)材料样品变形所需的应力随着样品变小而增加。(2)即使应力缓慢而稳定地增大，变形也不是逐渐增大，而是大幅度跳跃。这些跳跃随机发生，并导致样本的一小部分发生大变形。因此，在我们的圆柱体示例中，样本呈现不规则的手风琴形状。如果我们弯曲非常细的电线，它们可能不会变形为平滑弯曲的形状，而是随机形状，类似于畸形的回形针。(3)即使材料性能相同(例如，如果我们所有的气缸都是从同一块加工出来的)，变形样品所需的应力可能会非常分散。在两个明显相同的微米大小的样品中，启动或维持塑性变形所需的应力很容易相差两倍。显然，如果我们想要避免或控制非常小的部件的不可逆变形，这会带来严重的问题。对其中的第一个方面进行了较为详细的研究，对第二个方面也做了一些工作。然而，没有系统的研究来量化不同小样本之间的变形行为的分散，并提供工具来评估不想要的变形行为的风险。我们与德国研究人员合作，进行微变形实验，并与其他人合作，通过跟踪产生不可逆变形的材料缺陷的运动来模拟这种变形过程。我们将一起进行和分析大量的实验和模拟，以表征变形行为中的散射，并了解它如何依赖于样本大小、材料准备和变形方法。然后，我们将使用该数据库开发模拟工具，使工程师能够评估不良结果的风险。这个问题为什么重要呢？想象一下，你想要弯曲厘米到米大小的金属片，比如把它们制成生产罐头或制造车门的圆柱体。要得到想要的形状相对容易。然而，如果您尝试在非常小的范围内执行相同的操作，结果可能会完全不同！变形性能的微观分散可能会影响我们将材料成形为非常小的形状和为微技术生产非常小的部件的能力。一个引人注目的例子是为微芯片提供电气连接的非常细的电线。如果这些电线的形状分散得太多，其中两根可能会接触到，并产生短路，使设备无法使用。随着零部件和设备小型化的发展，我们需要获得在微尺度上处理成形过程所需的知识和专业知识。我们的研究希望能为这一目的做出贡献。

When solid materials are loaded above a critical level, they may change their shape permanently: they undergo plastic deformation. Consider, for example, a cylinder which we compress by pushing from top to bottom. If the load is small, the cylinder first deforms elastically (it reverts to its original shape after the load is removed). Above a certain load, some permanent deformation remains. Now if we use a macroscopic cylinder, say, several centimetres in size, then the stress (the force per unit area) needed to obtain a given relative deformation will not depend on the size of the cylinder. It will increase gradually with increasing deformation, and this 'hardening behavior' will be identical for cylinders made of the same material and deformed under the same conditions. If the stress is everywhere the same in the cylinder, also the deformation will be homogeneous - the cylinder will get shorter and thicker but will retain its cylindrical shape. But when the deforming body becomes very small - of the order of a few micrometers in diameter - then we observe quite different behavior: (1) The stress required to deform samples of material increases as the samples become smaller. (2) Even if the stress is increased slowly and steadily, the deformation does not increase gradually but in large jumps. These jumps occur randomly, and lead to large deformations in small parts of the sample. As a consequence, in our cylinder example the samples assume irregular accordeon-like shapes. If we bend very thin wires, they may not deform into smoothly curved but into random shapes resembling mis-shapen paperclips. (3) Even if the material properties are the same (for instance, if all our cylinders have been machined out of the same block) the stresses required to deform samples may scatter hugely. In two apparently identical micrometer sized samples, the stresses required to initiate or sustain plastic deformation may easily differ by a factor of two. Obviously this poses serious problems if we want to avoid or control irreversible deformation in very small components. The first of these aspects have been studied in some detail, and some work has also been done on the second one. However, there is no systematic study which quantifies the scatter in deformation behaviour between different small samples and provides tools for assessing the risk of unwanted deformation behaviour. We have teamed up with German researchers who conduct micro-deformation experiments and with others who simulate such deformation processes by tracing the motion of material defects which produces the irreversible deformation. Together we will conduct and analyze large series of experiments and simulations to characterize the scatter in deformation behaviour and to understand how it depends on sample size, material preparation, and method of deformation. We will then use this database to develop simulation tools that allow engineers to assess the risk of undesirable outcomes. Why is it important? Imagine you want to bend sheets of metal with a size of centimetres to meters, say for making them into cylinders for producing cans, or for making car doors. It is comparatively easy to get the desired shapes. However, if you try to do the same on a very small scale, the result might look quite different! Micro-scale scatter of deformation properties may affect our ability to form materials into very small shapes and to produce very small parts for microtechnologies. A striking example are the very thin wires that provide electrical connections for microchips. If the shape of these wires scatters too much, two of them may get into contact and produce a short-circuit that makes the device useless. As miniaturization of components and devices proceeds, we need to gain the knowledge and expertise needed to handle forming processes on the microscale. Our research wants to make a contribution to this purpose.