Dual-parameter elastic-plastic fracture criterion of metals and alloys in the plane strain case

In recent years, some investigators discussed the applicability of the HRR theory for engineering materials based on the results of numerical analyses and experimental studies. In the present paper, the finite element method is employed to analyze the crack tip fields of the engineering elastic-plastic material with a variety of geometry configurations of cracked specimens from elastic state to intensely general yielded state in the plane strain case. The results indicate that the HRR theory loses its validity of application for engineering elastic-plastic materials in the plane strain case. The reasons for this are analyzed. A dual-parameter fracture criterion is suggested for this case.     

再论Mobius变换中的n阶循环群判据

用二阶方阵的幂运算取代Mobius变换的迭代运算,导出了Mobius变换为n阶循环群的判据,并对判据进行了简化,最后给出了它们的应用.     

空化现象的模拟准则

本文在现有理论基础上导出空化现象的模拟准则.为模拟空化现象提供依据.     

H-矩阵的实用判定

H-矩阵在许多领域中都发挥着重要作用，但在实用中要判别H-矩阵却是很困难的．本文中，我们获得了H-矩阵判别的新的实用充分条件，所得结果包含了[1]的一个主要结果，并用例子说明了文中结果的有效性.     

On the efficiency of selection criteria in spline regression

This paper concerns the cubic smoothing spline approach to nonparametric regression. After first deriving sharp asymptotic formulas for the eigenvalues of the smoothing matrix, the paper uses these formulas to investigate the efficiency of different selection criteria for choosing the smoothing parameter. Special attention is paid to the generalized maximum likelihood (GML), C _p and extended exponential (EE) criteria and their marginal Bayesian interpretation. It is shown that (a) when the Bayesian model that motivates GML is true, using C _p to estimate the smoothing parameter would result in a loss of efficiency with a factor of 10/3, proving and strengthening a conjecture proposed in Stein (1990); (b) when the data indeed come from the C _p density, using GML would result in a loss of efficiency of ; (c) the loss of efficiency of the EE criterion is at most 1.543 when the data are sampled from its consistent density family. The paper not only studies equally spaced observations (the setting of Stein, 1990), but also investigates general sampling scheme of the design points, and shows that the efficiency results remain the same in both cases.This work is supported in part by NSF grant DMS-0204674 and Harvard University Clark-Cooke Fund. Mathematics Subject Classification (2000):Primary: 62G08; Secondary: 62G20     

韧脆转变的一种细观随机模糊统计分析

对不同温度和应力状态下40Cr材料进行大子样宏观试验和细观观测,提出了一种新的材料断裂韧脆转变统计随机模糊模型。该模型认为,在统计意义上,材料的韧性断裂为空穴机制,临界空穴扩张比参数可以作为韧性断裂的判据;材料的脆性断裂可以用内嵌币状裂纹的脆性断裂模型来模拟,为此测量断裂特征长度,提出并具体计算了控制币状裂纹失稳扩张的细观临界应力强度因子;在韧脆转变区域内,这两种机理并存并相互竞争,为此提出了模糊准则。对模型参数进行了测量和统计分析,给出分布规律,给出了计算断裂特征的概率模型。计算了韧脆转变区域内的细观机制变化和宏观响应。结果表明,该模型及分析方法可以很好地模拟应力状态及温度对韧脆转变的影响。     

短脉冲载荷下金属材料的层裂破坏

 本文用点炮加载聚酯薄膜飞片撞击金属靶材料，飞片速度0.714~2.24 km/s，脉冲宽度40~80 ns，击靶压力为2.280~11.952 GPa。在回收的铝、铜和钢靶样品上观察到层裂现象。通过金相分析发现它们的破坏方式与在一般较长脉冲加载下的破坏方式相似，铝和铜以延性方式破坏；钢则以脆性方式破坏。一维和二维数值模拟结果表明通常的几种层裂判据在这个应力、应变和应变率范围内也基本上适用。     

用峰面积判据改善Delsuc法预测的谱

基于Prony算法的Delsuc谱预测是目前NMR LPSVD(Linear Prediction SingularValue Decomposition)法中比较实用的方法。但在高噪声的条件下,时有失峰和假峰出现且要事先知道谱的峰数。本文通过跟踪迭代过程发现Delsuc法的判别因子r_(mis) 很难选定。如果它太小会失峰,而过大又会出现假峰。同时,由于噪声的影响,弱信号的采样点之间的相关性比强信号小,从而在迭代过程中会增加数值不稳定性。文中引入峰面积判据来改善Delsuc法,经模拟与实验均证明结果有效。     

整系数多项式在整数环上不可约性的探讨

本文在艾森斯坦因判别法的基础上，对整系数多项式的次高项系数进行了讨论，得到了整系数多项式在整数环上不可约的一个新的判别法。     

对薄层柱壳爆炸膨胀断裂过程的研究

 本文提出了一个用于描述动态破坏发展过程的损伤度函数。从这个损伤度函数出发,把材料特征性方程取为强化粘塑性本构方程形式,导出了薄层柱壳爆炸膨胀运动在两种近似下（恒定膨胀速度近似合恒定应变速率近似）断裂判据的解析表达式。结果分析表明,在上述条件下,存在着一个动态断裂“塑性峰”,在这个峰值条件的应变率下,柱壳出现贯穿断裂时刻的应变最大。以软钢为算例,本断裂判据可以比较好地解释Иванов和陈大年等给出的实验结果。这时,动态断裂“塑性峰”对应的应变率为4×10⁴ s^-1,相应的应变约为60%~80%。