弹塑性比例叠加的锥压入半解析模型与试验方法

张思宇; 蔡力勋; 司淑倩; 陈辉; 刘晓坤

doi:10.6052/j.issn.1000-4750.2021.09.0684

弹塑性比例叠加的锥压入半解析模型与试验方法

doi: 10.6052/j.issn.1000-4750.2021.09.0684

张思宇^1,,
蔡力勋^1, ,,
司淑倩^1,,
陈辉^2,,
刘晓坤^1,

1.
西南交通大学力学与工程学院应用力学与结构安全四川省重点实验室，成都 610031
2.
长沙理工大学土木工程学院，长沙 410114

基金项目: 国家自然科学基金项目(11872320，12072294)

详细信息

作者简介:
张思宇(1997−)，女，四川南充人，硕士生，主要从事材料测试理论与技术研究(E-mail: zhang_syyy@163.com)

司淑倩(1995−)，女，河南新乡人，硕士，主要从事材料测试理论与技术研究(E-mail: 2920792196@qq.com)

陈　辉(1990−)，男，湖南衡阳人，副教授，博士，主要从事材料力学性能表征与测试方法研究(E-mail: chen_hui5352@163.com)

刘晓坤(1991−)，男，河南商丘人，博士生，主要从事材料测试理论与技术研究(E-mail: 1010727036@qq.com)

通讯作者:
蔡力勋(1959−)，男，山东曹县人，教授，硕士，主要从事断裂力学研究，材料测试理论与技术研究(E-mail: lix_cai@263.net)

中图分类号: O34
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- HTML全文浏览量: 99
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- 被引次数: 0
出版历程
- 收稿日期: 2021-09-02
- 修回日期: 2021-11-30
- 录用日期: 2021-12-10
- 网络出版日期: 2021-12-10
- 刊出日期: 2023-02-01

SEMI-ANALYTICAL MODEL AND TEST METHOD OF CONE INDENTATION BASED ON ELASTOPLASTIC PROPORTIONAL SUPERPOSITION

ZHANG Si-yu^1
,,
CAI Li-xun^{1
, ,},
SI Shu-qian^1
,,
CHEN Hui^2
,,
LIU Xiao-kun^1
,

1.
Applied Mechanics and Structure Safety Key Laboratory of Sichuan Province, School of Mechanics and Engineering, Southwest Jiaotong University, Chengdu 610031, China
2.
School of Architecture and Construction, Changsha University of Science and Technology, Changsha 410114, China

摘要

摘要: 基于能量密度等效，考虑圆锥压入(锥压入)过程中线性律纯弹性和幂律纯塑性的应变能比例叠加，提出了弹塑性应变能比例叠加的锥压入载荷-位移模型(Load vs. Displacement Model based on Proportional Superposition of elastoplastic-energy under conical indenting，LDM-PS)，进而提出了获取材料Ramberg-Osgood律(R-O律)应力-应变关系的锥压入试验方法。针对80种设定材料，通过LDM-PS预测的载荷-位移曲线(正向预测)与有限元分析结果密切吻合，并且以有限元分析(Finite Element Analysis，FEA)所得载荷-位移曲线作为试验模拟曲线，采用两种锥角圆锥压头分别对平滑材料表面进行两次单锥压入加载(双锥压入)，可通过对双锥压入的两个载荷-位移曲线的加载阶段按抛物律(Kick律)回归可实现R-O律参数的求解。由LDM-PS预测的R-O律应力-应变关系曲线(反向预测)与FEA的条件关系曲线密切吻合；针对8种金属材料完成了双锥压入试验，通过锥压入试验新方法预测的应力-应变关系、弹性模量和强度与传统单轴拉伸试验结果吻合良好。
- 能量密度等效 /
- 应力-应变关系 /
- 半解析模型 /
- 锥压入 /
- 试验方法
Abstract: A load vs. displacement model LDM-PS is proposed, and a conical indentation test method for obtaining the stress-strain relationship of the material under the Ramberg-Osgood law (R-O law) is proposed by the grounds of energy density equivalence, considering the proportional superposition of strain energy between linear law pure elasticity and power law pure plasticity in conical indentation. For 80 set materials, the load-displacement curve (forward prediction) predicted by LDM-PS is in a close agreement with the results of Finite Element Analysis (FEA), and the load-displacement curve obtained by FEA is taken as the experimental simulation curve. Two kinds of cone angle conical indenters are used to carry out single conical indentation (double conical indentation) twice on the surface of smooth material, and the R-O law parameters can be solved by parabolic law regression of the two loading vs. displacement curves of double conical indentation at the loading stage. The stress vs. strain curve of R-O law predicted by LDM-PS (inverse prediction) is in a close agreement with the condition curve of FEA. The stress vs. strain relationship, Young's modulus and strength predicted by the new method are in a good agreement with the results of the traditional uniaxial tensile test.
- energy density equivalence /
- stress-strain relations /
- semi-analytical model /
- conical indenting /
- test method

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图 1 不同材料常数的h−h/(h_e+h_p)曲线

Figure 1. h−h/(h_e+h_p) curves of different material constants

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图 2 锥压入有限元对称模型

Figure 2. The axisymmetric FEA model under conical indenter loading

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图 3 锥压入计算云图

Figure 3. nephogram for conical indenting

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图 4 A_p~1+1/N曲线

Figure 4. The curve of A_p~1+1/N

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图 5 压入载荷-位移曲线与FEA比较(纯塑性)

Figure 5. Comparisons of load-displacement curves and those from FEA(Pure plastic)

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图 6 压入载荷-位移曲线与FEA比较

Figure 6. Comparisons of load-displacement curves and those from FEA

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图 7 预测应力-应变关系与FEA对比{60°，70.3° }组合

Figure 7. Comparisons of predicted stress-strain curves and those from FEA({60°，70.3° })

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图 8 预测应力-应变关系与FEA对比{53°，65° }组合

Figure 8. Comparisons of predicted stress-strain curves and those from FEA ({53°，65° })

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图 9 试验设备

Figure 9. Test equipment

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图 10 压入曲线示意图

Figure 10. Schematic diagram of indentation curves

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图 11 多级卸载试验P-h曲线(θ=60°)

Figure 11. Multi-stage unloading P-h curves for Aluminum and Steel (θ=60°)

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图 12 多级卸载试验P-h曲线(θ=70.3°)

Figure 12. Multi-stage unloading P-h curves for Aluminum and Steel (θ=70.3°)

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图 13 压头系数β与h/h^*的关系曲线(θ=60°)

Figure 13. Relation curve between indenter coefficient and h/h^* curves for Aluminum and Steel (θ=60°)

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图 14 压头系数β与h/h^*的关系曲线(θ=70.3°)

Figure 14. Relation curve between indenter coefficient and h/h^* curves for Aluminum and Steel (θ=70.3°)

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图 15 压入P-h曲线(θ=60°)

Figure 15. Indentation P-h curve for Aluminum and Steel (θ=60°)

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图 16 压入P-h曲线(θ=70.3°)

Figure 16. Indentation P-h curve for Aluminum and Steel (θ=70.3°)

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图 17 R-O律预测曲线与单轴拉伸对比

Figure 17. Comparisons between predicted curves and those from uniaxial tension for Aluminum and Steel

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表 1 纯塑性锥压入模型参数值

Table 1. Parameters of pure plastic conical indenting model

压头半锥角θ/(°)	有效体积系数k₁	有效应变系数k₂
53	26.42	0.1715
60	24.95	0.1789
65	23.40	0.1866
70.3	21.01	0.1997

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表 2 弹塑性比例因子c参数值

Table 2. Elastoplastic scaling factor c parameter value

压头半锥角θ/(°)	比例系数c₁	比例指数c₂	比例指数c₃
53	0.6225	−0.06703	−0.05327
60	0.6406	−0.06287	−0.06503
65	0.6245	−0.06544	−0.06877
70.3	0.6304	−0.06404	−0.08170

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表 3 材料力学性能与单轴拉伸R-O律塑性参数

Table 3. Mechanical properties of materials and plastic parameters of uniaxial tensile R-O law

材料	材料常规力学性能			材料R-O律塑性参数
材料	弹性模量 E/GPa	屈服强度 R_p0.2/MPa	抗拉强度 R_m/MPa	硬化系数 Κ/MPa	硬化指数 N
6061-T6511	71.00	376.1	390.6	498.2	14.310
7075-T6511	71.40	517.6	631.9	845.2	11.970
5083-H116	70.30	159.3	276.2	519.4	3.623
6082-T6	71.50	326.4	348.1	448.2	14.710
P92	210.0	548.3	715.1	1076	7.337
16Mn	212.0	309.9	521.1	876.8	4.978
1Cr12Mo	219.9	616.6	767.1	1119	8.446
2Cr12MoV	216.9	772.2	976.1	1314	9.661

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表 4 压头系数β模型参数

Table 4. Parameters of indenter coefficient β model

压头半锥角θ/(°)	弹性模量E/GPa	模型系数e₁	模型指数e₂
60	60~80	0.8055	−0.1958
60	180~220	0.6258	−0.2075
70.3	60~80	0.6929	−0.2004
70.3	180~220	0.4944	−0.2509

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表 5 R-O律参数及σ-ε曲线优度

Table 5. Parameters of R-O law and σ-ε curve goodness

材料	R-O律参数			弹性模量E/GPa		σ-ε曲线优度/(%)
材料	弹性模量 E/GPa	硬化系数 Κ/MPa	硬化指数 N	单轴拉伸	误差/(%)	σ-ε曲线优度/(%)
6061-T6511	68.32	563.9	9.195	71.00	3.770	98.0
7075-T6511	75.20	927.1	9.202	71.40	5.320	98.0
5083-H116	68.74	475.3	5.291	70.30	2.220	97.0
6082-T6	71.90	472.6	13.230	71.50	0.557	96.0
P92	209.10	1041.0	7.074	210.00	0.409	97.0
16Mn	209.70	883.5	4.633	212.00	1.090	97.0
1Cr12Mo	213.00	1117.0	10.060	219.90	3.120	96.0
2Cr12MoV	219.70	1277.0	10.890	216.90	1.290	99.0

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表 6 抗拉强度与单轴拉伸结果的对比

Table 6. Comparison of tensile strength with uniaxial tensile results

材料	抗拉强度R_m/MPa
材料	锥压入	单轴拉伸	误差/(%)
6061-T6511	397.3	390.6	1.73
7075-T6511	653.4	631.9	3.40
5083-H116	287.2	276.2	3.98
6082-T6	360.5	348.1	3.57
P92	685.4	715.1	4.16
16Mn	511.4	521.1	1.86
1Cr12Mo	804.3	767.1	4.85
2Cr12MoV	935.8	976.1	4.12

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表 7 屈服强度与单轴拉伸结果的对比

Table 7. Comparison of yield strength with uniaxial tensile results

材料	屈服强度R_p0.05/MPa			屈服强度R_p0.1/MPa			屈服强度R_p0.2/MPa
材料	锥压入	单轴拉伸	误差/(%)	锥压入	单轴拉伸	误差/(%)	锥压入	单轴拉伸	误差/(%)
6061-T6511	345.9	363.5	4.84	347.7	364.8	4.67	351.1	376.1	6.65
7075-T6511	582.9	590.2	1.24	585.4	592.1	1.13	590.1	517.6	14.00
5083-H116	156.2	157.8	1.01	161.9	159.1	1.76	188.5	159.3	18.30
6082-T6	333.1	324.6	2.62	334.5	325.9	2.64	337.0	326.4	3.25
P92	497.5	529.9	6.11	504.6	537.0	6.03	517.1	548.3	5.69
16Mn	246.2	275.7	10.7	257.1	285.4	9.92	274.4	309.9	11.50
1Cr12Mo	659.0	611.8	7.71	665.9	618.2	7.72	678.0	616.6	9.95
2Cr12MoV	819.4	766.4	6.91	824.5	774.1	6.51	833.6	772.2	7.95

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