| 其他摘要 | The spherical indentation method has been developed to evaluate material mechanical properties in the base of nanoindentation theory. The method is nondestructive and easy to use. The determining results are accurate under a ball indenter. The more wide the application of material of small size is, The importance of the method of evaluating local properties of material with the application of material of small size is more clear. The nondestructive spherical indentation methods combined with finite element simulation and dimensional analysis were employed to determine local properties of material such as yield strength, strain hardening exponent, and the rules of piling-up and sinking-in of material as well as the relationship of indentation hardness and yield strength. The beneficial results obtained in the paper are as follows:
1）Spherical indentation method was used to obtain yield strength and strain hardening exponent. It was discovered that the range of yield strain of materials selected in the paper of Cao et al is narrow from 0.001429 to 0.01538. The number of materials is only 24. Therefore, the error of the material with yield strain beyond the range is large. In order to save the problem, the 56 kinds of materials of yield strain ranging from 0.007692 to 0.04 were analyzed in the paper. Dimensional analysis was constructed to derive the dimensionless functions of spherical indenter（ ）, and used to extract yield strength and strain hardening exponent of material combined with finite element analysis. In the paper, the fitting functions have been obtained and used to analyze yield strength and strain hardening exponent of materials with yield strain ranging from 0.007692 to 0.04. Lastly，the results were validated. The accuracy of prediction is high and more material properties are available using the new method in the paper. The average error of yield strength and strain hardening exponent are 0.01578 and 0.12571, respectively.
2) Spherical indentation method was used to obtain the relationship between hardness and yield strength ( ) of material. The ratio of hardness to initial yield strength is given by the following dimensionless function.
The relationship has been observed between , and . For a certain penetration depth of , the relationship between and was obtained as following. From the indentation data, It shows that is not constant. It varies with and . For and , is about 2.03-2.39. For and , increases slightly with decreasing and increases fast for to reach the maximal value of 15.77.
The value of hardness also varies with penetration depth. For , Hardness increases slightly with penetration depth. For , hardness increases greater with penetration depth. It can be also observed that hardness increases with penetration depth, the increasing values decreases and it becomes a constant at last.
3) It was observed in the present paper that using spherical indentation, for materials with large values of strain hardening exponent ( ) , sinking-in was observed for all values of during indenting. On the other hand, for materials with small value of ( ), both pile-up and sinking-in can be observed depending on the increasing of . For materials with large values of ( ), sinking-in is observed for all values of during the indenting. On the other hand, for materials with small value of ( ), both pile-up and sink-in can be observed depending on the increasing of n. The results are consistent with the conclusion from sharp indentation. The general conclusion is that pile-up/sinking-in behavior depends on strain hardening exponent and the ratio of .
In the present paper, the relationships between pile-up/sinking-in and (residual indentation depth/ maximum indentation depth) has been obtained for several values of . It is observed that for <0.76( >0.02), the material shows sinking-in behavior, and the larger hardening exponent is, the more sinking-in is; for >0.76 and >0.023, the material shows pile-up and sinking-in behaviors. And the more pile-up is, the smaller is.
Further more, the relationships between and contact area were obtained, where indicates the feature of pile-up or sinking-in. According to the relationships, the effects of on error of hardness were also obtained. |
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