结构陶瓷弯曲强度的Weibull统计实验研究

本文在强度统计方法的Weibull模数估计及试样数量优化研究基础上,对氧化铝陶瓷进行了弯曲强度统计的大子样模拟母体试验,同时也对碳化硅、氮化硅、氧化铅增韧氧化铝等典型结构陶瓷进行了实验研究。实验结果表明,利用无偏极大似然估计的理论结果及置信度和相对误差双参数可以明确材料强度及其强度统计数据的精度。     

陶瓷断裂强度Weibull统计分析的可靠性

脆性陶瓷材料的断裂强度通常表现出显著的离散性,其统计性质需要借助于一个Weibull分布函数加以描述;而作为Weibull分布函数中的一个重要参数,Weibull模数则通常用于描述断裂强度实测值的离散程度。从统计学上说,对于同一种材料,采用点估计方法由不同的强度样本得到的Weibull模数估计值之间总是会存在一些偏差,这就导致了两个基本问题的出现,即：(1)如何评估Weibull模数估计值与其真实值之间的差异？(2)采用多大容量的强度样本才可能获得较为可靠的Weibull模数值？此外,断裂强度服从Weibull分布这一说法仅仅是一个假设,在断裂强度并不服从Weibull分布的情况下,采用Weibull分布描述强度数据是否可以对材料的可靠性给出准确评价？在过去几十年间,学者们借助于Monte Carlo模拟技术对上述问题进行了较为深入的研究。本文简要回顾了这些研究所取得的成果,以期对Weibull分布在陶瓷材料断裂强度统计性质研究中应用的可靠性做出一个较为完整的描述。     

碳纤维强度的Weibull分析

碳纤维属于脆性材料。抗拉强度随着测试样品长度的增加而降低,这是缺陷控制强度的主要实验依据,对于同样长度的测试样品,强度值的分散性非常大,这表明缺陷在碳纤维表面和内部是随机分布。碳纤维经气相氧化后,抗拉强度可得到提高,这归因于表面裂纹的消除,或因氧化刻蚀而使裂纹尖端钝化。碳纤维强度的统计性质可用Weibull统计理论来分析。Weibull模数m可作为裂纹频率分布因子。     

预氧化处理对反应烧结碳化硅微观结构和弯曲强度的影响

本文提出了一种简单有效的预氧化处理方法,用来强化反应烧结碳化硅(RBSC),研究了800~1 300 ℃预氧化处理对其微观结构和力学性能的影响,探究了含不同尺寸压痕裂纹的材料在氧化前后残余弯曲强度的变化规律。结果表明,随着氧化温度的升高,RBSC的室温强度和Weibull模数均存在先下降后上升,然后再下降的趋势,主要原因是不同温度氧化后的RBSC表面形貌不同。在1 200 ℃下预氧化2 h,RBSC的弯曲强度和Weibull模数都明显变大,强度提升了19.9%,Weibull模数由7.3提升到11.8。然而,800 ℃低温氧化不完全和1 300 ℃高温氧化反应过于强烈均会导致弯曲强度和Weibull模数下降。在最优氧化条件(1 200 ℃氧化2 h)下,含压痕裂纹(载荷20 N)的RBSC试样的残余弯曲强度在氧化后由201.1 MPa提高到324.2 MPa,强化机理是高温氧化生成的SiO₂能够消除材料表面缺陷和微裂纹。     

多晶石墨材料强度统计评价的两种Weibull方法

本文给出了从断裂强度数据及断裂位置数据出发推出多晶石墨材料Weibull系数的两种方法以及对日本四种各向同性石墨材料的强度统计评价结果,概述了线弹性体假设条件对用两种方法推算Weibull系数的影响。     

脆性材料强度的Weibull统计

断裂前发生塑性变形的材料,强度变化不会超过其平均强度的4～8%。因此,在工程材料设计中,其强度可以用平均强度来量度。而脆性材料则不一样,同样尺寸试样的强度变化可以是其平均强度的100%甚至更大。因此,在工程材料设计中,不能仅用平均强度作脆性材料的强度指标,还需从统计角度来考虑其强度的可靠性与分散程度。脆性材料强度的这种分散性,主要与制造及加工过程中引入的种种缺陷有关。均质     

MgO-C耐火材料抗折强度分布规律的研究

以两种不同碳含量的MgO-C耐火材料为研究对象,对试验测得的抗折强度数据采用Weibull函数进行统计分析,并结合试样的断口形貌研究了MgO-C耐火材料的抗折强度分布规律。结果表明:MgO-C耐火材料的抗折强度服从Weibull分布;增大材料的致密度和石墨含量能够降低MgO-C耐火材料抗折强度的离散性,提高强度的可靠性。     

用Weibull统计方法来评价上浆对炭纤维强度的影响

炭纤维属于脆性材料,其拉伸强度具有分散性,基本服从Weibull统计分布。本文采用这种方法对未上浆与上浆炭纤维的拉伸强度数据进行分析,说明上浆可使炭纤维的拉伸强度提高,分散性减小。     

碳纤维的强度理论

石墨和碳纤维的理论强度约为104～108GPa。目前,工业生产碳纤维的最高强度为4.6GPa,约是理论强度的2.5～4.4%。理论强度与实测强度相差如此悬殊,其原因在于各种实际碳素材料存在多种类型的缺陷。换言之,缺陷牢牢地控制着强度。本文主要论述碳纤维的强度理论、缺陷对强度控制的实验依据以及用Weibull统计方法表征脆性材料强度的分散性。     

FSMF填充树脂浇铸体的轴向拉伸性能实验研究

对FSMF矿物复合填料填充树脂浇铸体的轴向拉伸性能进行了实验研究,并采用Weibull模数m和特征强度σ0评价了该树脂浇铸体在加入FSMF前后的强度变化.结果表明,加入该矿物复合填料后树脂浇铸体的轴向拉伸强度略有提高,但拉伸弹性模量E和Weibull模数m增加显著,显示出该矿物复合填料良好的功能性.     

不同拉伸条件下基于Weibull模型的粘胶基碳纤维强度分布研究

从粘胶基碳纤维的拉伸实验得到其 S-S曲线和强度、模量、断裂伸长等力学性能数据 ,表明该材料是典型的脆性断裂 ,且断裂分散性较大。采用 VB编程软件设计了 Weibull程序 ,该模型能计算出碳纤维的平均强度、Weibull模数、尺度参数 ,并能模拟碳纤维强度的累积概率分布和概率密度曲线。不同氧化拉伸条件下强度的实验数据基本上落在程序模拟出的累积概率分布直线上 ,证明了该数学模型适用于分析碳纤维强度分布。在氧化完全松弛的条件下 ,粘胶基碳纤维的平均强度较高 ,但 Weibull模型分析的结果表明氧化拉伸比为 -5 %时 ,Weibull模数最大 ,不匀率最小 ,而氧化拉伸对粘胶基碳纤维模量没有显著影响。     

Evaluation of Strut Strength in Open-Cell Ceramics

The strength of cellular materials is dependent on the strength of the solid making up the cellular structure, but this parameter is often difficult to quantify. In order to better evaluate these materials, a technique has been developed to measure the strength ofthe cell struts in open-cell ceramics. The strut strength was measured in two commercially available, open-cell ceramics and evaluated in terms of a two parameter Weibull distribution. The strut strength distribution was found to be very wide with the Weibull modulusin the range 1 to 3. In addition, it was found that the strut strength was invariant withdensity (at constant cell size) but could be dependent on cell size. This behavior was inqualitative agreement with the failure statistics of brittle materials, once the variations in the microstructural geometry are understood. Based on these data and the observations of flaws within the struts, it is clear that careful processing of these materials could significantly improve the strut strength distribution, in terms of reducing its width and increasing its magnitude. Such microscopic improvements would lead to similar benefits in the strength and toughness of the bulk cellular ceramics.     

Confidence interval estimation of Weibull lower percentiles in small samples via Bayesian inference

Weibull distribution has been vastly used for modeling fracture strength of ceramic and composite materials. Confidence interval estimation of Weibull parameters and percentiles in small samples has been an important concern due to high experimental costs. It was shown previously that in classical inference the Maximum Likelihood Estimation Method is the best method among several alternatives for estimating 95% one-sided confidence lower bounds on the 1st and 10th Weibull percentiles, namely A-basis and B-basis material properties. This study proposes the Bayesian Weibull Method as an alternative using the information that ceramic and composite materials have increasing failure rates, which requires the Weibull shape parameter to be at least 1. Through Monte Carlo simulations, it is shown that the performance of the Bayesian Weibull Method is superior in that it achieves the precision levels of the Maximum Likelihood Estimation Method with significantly smaller sample sizes.     

Some notes on the correlation between fracture and defect statistics: Are Weibull statistics valid for very small specimens?

Strength data of brittle materials show a significant scatter. Therefore probabilistic methods have to be used for designing with these materials. So far this has been done on the basis of the Weibull statistics. The Weibull statistics (implicitly) implies a particular type of defect distribution, which can be observed in many (but not in all) ceramic materials. The correlation between the strength and the flaw size distribution is discussed in some simple examples. Then the situation for very small specimens is discussed. This case will be of high relevance for the testing of miniaturised electroceramic components and materials of the microsystem technique. It is shown that the Weibull theory gets inconsistent and should overestimate the strength of the specimens (components), due to the fact that the effective volume becomes smaller than the fracture origin.     

Modeling of Probabilistic Failure of Polycrystalline Silicon MEMS Structures

Microelectromechanical Systems (MEMS) devices typically need to be designed against a very low failure probability, which is on the order of or lower. Experimental determination of the target strength for such a low failure probability requires testing of tens of thousands of specimens, which can be cost prohibitive for the design process. Therefore, understanding the probabilistic failure of MEMS devices is of paramount importance for design. Currently available probabilistic models for predicting the strength statistics of MEMS structures are based on classical Weibull statistics. Significant advances in experimental techniques for measuring the strength of MEMS devices have produced data that have unambiguously demonstrated that the strength distributions consistently deviate from the Weibull distribution. Such deviations can be explained by the fact that the Weibull distributions are derived based on extreme value statistics, which is inapplicable to MEMS devices where the dimensions of the material microstructure are not negligible compared to the characteristic structural dimensions. This paper presents a robust probabilistic model for strength distribution of polycrystalline silicon (poly‐Si) MEMS structures that could be extended to other brittle materials at the microscale. The overall failure probability of the structure is related to the failure probability of each material element along its sidewalls through a weakest‐link statistical model. The failure statistics of the material element is determined by both the intrinsic random material strength as well as the random stress field induced by the sidewall geometry. Different from the classical Weibull statistics, the present model is designed to account for structures consisting of a finite number of material elements, and it predicts a scale effect on their failure statistics. It is shown that the model agrees well with the measured strength distributions of poly‐Si MEMS specimens of different sizes, and the calibrated mean strength of the material element is consistent with the theoretical strength of silicon. Meanwhile, it is shown that the two‐parameter and three‐parameter Weibull distributions cannot provide optimum and consistent fits of the observed size‐dependent strength distributions, and thus have very limited prediction capability. The present model explicitly relates the strength statistics to the size effect on the mean structural strength, and therefore provides an efficient means of determining the failure statistics of MEMS structures.     

玻纤增强尼龙材料强度的Weibull统计分析

对不同短玻纤含量的尼龙复合材料的拉伸强度和弯曲强度的Weibull分布的特征进行初步分析,指出不同玻纤含量的尼龙复合材料的拉伸强度具有相近的Weibull模量,而不同玻纤含量的尼龙复合材料弯曲强度的Weibull模量相差较大。     

Random glass mat reinforced thermoplastic composities. Part VII: A statistical approach to strength

Large macroscopic-scale variations in the tensile moduli and tensile strengths are charcteristic of random glass mat composites (GMT). The large-scale, point-to-point variations in the local stiffness is characterized by a probability density function that can be used to predict the stiffness of parts only in a statistical sense. Weibull statistics widely used for modeling the scatter in the strength of brittle materials cannot be applied to the large variations in the strength of GMTs: The macroscopic stress field in brittle materials is assumed to be deterministic, while the stress field in GMTs varies randomly on a macroscopic scale. A statistical approach for characterizing the strength of GMTs is developed by combining an empirically established strength-modulus correlation with the statistical characterization of the tensile modulus.