Indentation size effects in crystalline materials: A law for strain gradient plasticity
Indentation size effects in crystalline materials: A law for strain gradient plasticity
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DOI：
10.1016/s0022-5096(97)00086-0
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发表时间：
1998-03-01
影响因子：
5.3
通讯作者：
Gao, HJ
中科院分区：
文献类型：
--
作者：
Nix, WD;Gao, HJ
我们表明，晶体材料的压痕尺寸效应可以使用几何必要位错的概念精确地建模。根据该模型，硬度的深度依赖关系的特征形式为：H/H-0 =根1 + H */ H，其中H为给定压痕深度下的硬度。h， h -0是无限深度极限下的硬度，h*是由压头形状、剪切模量和h -0决定的特征长度。对退火（111）铜单晶和冷加工多晶铜的压痕实验表明，这种关系是完全符合的。我们还证明了这种关系描述了在银单晶中观察到的压痕尺寸效应。我们使用这个模型推导应变梯度塑性:以下法律(σ/σ(0))(2)= 1 +(左)/气帽,其中σ是有效的流压力梯度的存在,σ(0)是如何在没有压力梯度,气是有效的应变梯度和(左)在帽材料长度尺度是一个特点,那就是,反过来,相关材料的流动应力在缺乏应变梯度,(左)/帽近似b(μ/σ(0))(2)。对于以幂律sigma(0) = sigma(ref)epsilon（l/n）为特征的材料，可以将上述定律改写为与应变无关的材料长度尺度l，(sigma/sigma(ref)) = epsilon(2/n+)l chi l = b (mu/sigma(ref))(2) = (l) / cap (sigma(0)/sigma(ref))(2)。这个定律类似于Fleck和Hutchinson提出的现象学定律，他们的现象学长度尺度用可测量的物质参数来解释。1998爱思唯尔科学有限公司版权所有。
We show that the indentation size effect for crystalline materials can be accurately modeled using the concept of geometrically necessary dislocations. The model leads to the following characteristic form for the depth dependence of the hardness:H/H-0 = root 1 + h*/h,where H is the hardness for a given depth of indentation. h, H-0 is the hardness in the limit of infinite depth and h* is a characteristic length that depends on the shape of the indenter, the shear modulus and H-0. Indentation experiments on annealed (111) copper single crystals and cold worked polycrystalline copper show that this relation is well-obeyed. We also show that this relation describes the indentation size effect observed for single crystals of silver.We use this model to derive the following law for strain gradient plasticity:(sigma/sigma(0))(2) = 1 + (l) over cap chi,where sigma is the effective flow stress in the presence of a gradient, sigma(0) is the how stress in the absence of a gradient, chi is the effective strain gradient and (l) over cap is a characteristic material length scale, which is, in turn, related to the flow stress of the material in the absence of a strain gradient,(l) over cap approximate to b (mu/sigma(0))(2).For materials characterized by the power lawsigma(0) = sigma(ref)epsilon(l/n),the above law can be recast in a form with a strain-independent material length scale l,(sigma/sigma(ref)) = epsilon(2/n+)l chi l = b (mu/sigma(ref))(2) = (l) over cap (sigma(0)/sigma(ref))(2).This law resembles the phenomenological law developed by Fleck and Hutchinson, with their phenomenological length scale interpreted in terms of measurable material parameters. (C) 1998 Elsevier Science Ltd. All rights reserved.