Spherical indentation of elastic–plastic solids
Spherical indentation of elastic–plastic solids
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DOI：
10.1098/rspa.1999.0423
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发表时间：
1999-07
期刊：
影响因子：
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通讯作者：
S. Mesarovic;N. Fleck
中科院分区：
文献类型：
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作者：
S. Mesarovic;N. Fleck
有限元方法用于对刚性球体对弹塑性半空间的法向压痕进行精确的数值研究。探讨了半空间的弹性和应变硬化率的影响，并通过分析无摩擦接触和粘着摩擦的极限情况来评估摩擦的作用。压痕图是用接触半径a的轴构建的（通过压头半径R和半空间的屈服应变标准化）。确定变形模式的竞争状态并绘制在压痕图上：（i）弹性赫兹接触；（ii）弹塑性变形；（iii）塑性相似状态；（iv）有限变形弹性接触；和（v）有限变形塑性接触。变形状态之间的边界位置仅随着变形程度的变化而轻微变化。研究发现，刚性-应变-硬化相似解的有效性范围相当有限：它仅与屈服应变小于 2 x 10−4 且 a/R < 0.16 的固体相关。压头和基体之间的摩擦力对压头下方的应变场有很大影响，并且对接触尺寸具有显着影响，其为压痕深度的函数。还进行了探索；发现除了弹塑性压痕状态之外，压痕响应几乎不受影响。
The finite–element method is used to perform an accurate numerical study of the normal indentation of an elastic–plastic half–space by a rigid sphere. The effects of elasticity and strain–hardening rate of the half–space are explored, and the role of friction is assessed by analysing the limiting cases of frictionless contact and sticking friction. Indentation maps are constructed with axes of contact radiusa (normalized by the indenter radiusR and the yield strain of the half–space. Competing regimes of deformation mode are determined and are plotted on the indentation map: (i) elastic Hertzian contact; (ii) elastic–plastic deformation; (iii) plastic similarity regime; (iv) finite–deformation elastic contact; and (v) finite–deformation plastic contact. The locations of the boundaries between deformation regimes change only slightly with the degree of strain–hardening rate and of interfacial friction. It is found that the domain of validity of the rigid–strain–hardening similarity solution is rather restricted: it is relevant only for solids with a yield strain of less than 2 x 10−4 anda/R < 0.16. Friction between the indenter and the substrate strongly affects the strain field beneath the indenter, and has a significant effect on the contact size as a function of indent depth. The effect of pre–stress within the half–space is also explored; it is found that the indentation response is hardly affected, except for the case of the elastic–plastic indentation regime.