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摘要: 为了提高随机疲劳长裂纹扩展率预测精度, 基于Forman方程, 发展了随机疲劳长裂纹扩展概率模型及其参数测定方法, 考虑数据分散性规律和试样数量对概率评价的影响, 得到了包含存活概率曲线、置信度曲线和两者融合曲线在内的长裂纹扩展率关系曲线, 在给定应力强度因子范围内, 裂纹扩展率服从对数正态分布条件下, 采用线性回归和极大似然法测定模型参数。对铁道车辆LZ50车轴钢裂纹扩展数据分析表明, 该模型反映了材料断裂韧度对长裂纹扩展率的影响, 克服了基于Paris-Er-dogan方程的概率模型在高应力强度因子范围预测偏于危险的缺陷, 验证了该模型的合理性。Abstract: In order to improve the prediction precision of random fatigue crack propagation, its probabilistic models based on Forman equation and the estimation method of its parameters were developed, the effect of test data scattering regularity and sampling size on probabilistic assessment was taken into account, the models consisted of survival probability-based curves, confidence-based curves and survival-probability-and-confidence-based curves, their parameters of were measured by linear regression technique and maximum likelihood method.The prediction data of LZ50 axle steel indicate that the models show the effect of material rupture temper on long crack propagation, over come the non-conservative prediction of conventional models based on Paris-Erdogan equation in high intensity factor range, which shows that the models are reasonable and feasible.
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Key words:
- vehicle engineering /
- long fatigue crack /
- probabilistic model /
- Forman equation
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表 1 典型P-d a/d N-ΔK曲线方程参量
Table 1. Tab.1 Parameters of P-da/dN-ΔK Curves
存活概率P 材料常数DP 断裂韧度KICP/ (MPa·mm1/2) 材料指数mP 0.500 0 0. 663 972×10-10 1 341.06 3.563 79 0.900 0 0. 521 662×10-9 1 309.24 3.320 01 0.990 0 0. 280 245×10-8 1 283.29 3.121 02 0.999 0 0. 958 435×10-8 1 264.32 2.975 36 0.999 9 0. 263 775×10-7 1 248.71 2.855 38 
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表 2 典型C-d a/d N-ΔK曲线方程参量
Table 2. Parameters of C-d a/d N-ΔK Curves
置信度C/% 材料常数DC 断裂韧度KICC/ (MPa·mm1/2) 材料指数mC 50 0. 663 972×10-10 1 341.06 3.563 79 90 0. 169 706×10-9 1 341.06 3.563 79 95 0. 226 508×10-9 1 341.06 3.563 79 99 0. 410 499×10-9 1 341.06 3.563 79
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表 3 典型P-C-d a/d N-ΔK曲线方程参量
Table 3. Parameters of P-C-d a/d N-ΔK Curves
存活概率P 置信度C/% t分布函数t1-C (ns-2) 材料常数DP-C 断裂韧度KICP-C/ (MPa·mm1/2) 材料指数mP-C 0.900 0 50 0 0. 521 662×10-9 1 309.24 3.320 01 90 1.414 9 0. 133 333×10-8 1 309.24 3.320 01 95 1.894 6 0. 177 960×10-8 1 309.24 3.320 01 99 2.998 0 0. 322 516×10-8 1 309.24 3.320 01 0.990 0 50 0 0. 280 245×10-8 1 283.29 3.121 02 90 1.414 9 0. 716 286×10-8 1 283.29 3.121 02 95 1.894 6 0. 956 029×10-8 1 283.29 3.121 02 99 2.998 0 0. 173 261×10-7 1 283.29 3.121 02 0.999 0 50 0 0. 958 435×10-8 1 264.32 2.975 36 90 1.414 9 0. 244 969×10-7 1 264.32 2.975 36 95 1.894 6 0. 326 961×10-7 1 264.32 2.975 36 99 2.998 0 0. 592 550×10-7 1 264.32 2.975 36 0.999 9 50 0 0. 263 775×10-7 1 248.71 2.855 38 90 1.414 9 0. 674 190×10-7 1 248.71 2.855 38 95 1.894 6 0. 899 843×10-7 1 248.71 2.855 38 99 2.998 0 0. 163 078×10-6 1 248.71 2.855 38
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