Quantifying the Scatter: Statistical Analysis and Stochastic Modelling of Microplasticity

量化分散：微塑性的统计分析和随机建模

• 批准号: EP/J003387/1
• 负责人: Michael Zaiser
• 金额: $ 27.32万
• 依托单位: University of Edinburgh
• 依托单位国家: 英国
• 项目类别: Research Grant
• 财政年份: 2012
• 资助国家: 英国
• 起止时间: 2012 至 无数据
• 项目状态: 已结题
• 来源: https://gtr.ukri.org/projects?ref=EP%2FJ003387%2F1
• 关键词: Quantifying; Scatter; Statistical; Analysis; Stochastic

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.

当固体材料的载荷超过临界水平时，它们可能会永久地改变形状：它们会发生塑性变形。例如，考虑一个圆柱体，我们通过从上往下推来压缩它。如果载荷很小，圆柱体首先发生弹性变形（在载荷解除后恢复到原来的形状）。超过一定的载荷，一些永久的变形仍然存在。现在，如果我们使用一个宏观的圆柱体，比如说，几厘米的大小，那么获得给定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。它将随着变形的增加而逐渐增加，并且这种“硬化行为”对于由相同材料制成并在相同条件下变形的圆柱体将是相同的。如果圆柱体各处的应力都相同，那么变形也将是均匀的——圆柱体将变得更短、更厚，但仍将保持其圆柱体形状。但是，当变形体变得非常小时——直径只有几微米——我们就会观察到完全不同的行为：(1)使材料试样变形所需的应力随着试样变小而增大。(2)即使应力缓慢而稳定地增加，变形也不是逐渐增加，而是有较大的跳跃。这些跳跃是随机发生的，并导致样本的一小部分发生大的变形。因此，在我们的圆柱体示例中，样本采用不规则的手风琴状形状。如果我们弯曲非常细的电线，它们可能不会变形成平滑的弯曲，而是变成不规则的形状，就像畸形的回形针一样。(3)即使材料的性质是相同的（例如，如果我们所有的圆柱体都是用同一个块加工而成的），使样品变形所需的应力可能会大大分散。在两个明显相同的微米尺寸的样品中，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，这将带来严重的问题。本文对第一个方面进行了较详细的研究，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变形行为的分散，并提供评估不必要变形行为风险的工具。我们与德国研究人员合作，他们进行微变形实验，并与其他研究人员合作，通过追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，以表征变形行为的散射，并了解它如何取决于样品大小，材料制备和变形方法。然后，我们将使用该数据库开发仿真工具，使工程师能够评估不良结果的风险。为什么它很重要？想象一下，你想把几厘米到几米大小的金属片弯曲，比如把它们做成圆柱体，用来制造罐头，或者用来制造车门。得到想要的形状比较容易。然而，如果你尝试在一个非常小的范围内做同样的事情，结果可能看起来完全不同！变形特性的微尺度分散可能会影响我们将材料形成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过于分散，其中两根电线可能会接触并产生短路，使设备失效。随着组件和设备的小型化，我们需要获得在微观尺度上处理成形过程所需的知识和专业知识。我们的研究希望为这一目的做出贡献。

项目成果

Stress and strain fluctuations in plastic deformation of crystals with disordered microstructure

• DOI: 10.1088/1742-5468/2015/08/p08009
• 发表时间: 2015-08
• 期刊: Journal of Statistical Mechanics: Theory and Experiment
• 作者: O. Kapetanou;D. Weygand;M. Zaiser

Universal features of amorphous plasticity.

非晶塑性的普遍特征。

• DOI: 10.1038/ncomms15928
• 发表时间: 2017-07-03
• 期刊: Nature communications
• 影响因子: 16.6
• 作者: Budrikis Z;Castellanos DF;Sandfeld S;Zaiser M;Zapperi S
• 通讯作者: Zapperi S

Universality of Avalanche Exponents in Plastic Deformation of Disordered Solids

无序固体塑性变形中雪崩指数的普遍性

• DOI: 10.48550/arxiv.1511.06229
• 发表时间: 2015
• 作者: Budrikis Z

Internal length scale and grain boundary yield strength in gradient models of polycrystal plasticity: How do they relate to the dislocation microstructure?

多晶塑性梯度模型中的内部长度尺度和晶界屈服强度：它们与位错微观结构有何关系？

• DOI: 10.1557/jmr.2014.234
• 发表时间: 2014-09
• 期刊: Journal of Materials Research
• 影响因子: 2.7
• 作者: K. E. Aifantis;J. Senger;D. Weyg;M. Zaiser
• 通讯作者: M. Zaiser

Strain localization and strain propagation in collapsible solid foams

• DOI: 10.1016/j.msea.2012.12.038
• 发表时间: 2013-04
• 期刊: Materials Science and Engineering A-structural Materials Properties Microstructure and Processing
• 影响因子: 6.4
• 作者: M. Zaiser;F. Mill;A. Konstantinidis;K. Aifantis