1.1 本标准规程提供了将断裂强度参数（主要是平均强度和威布尔特征强度）转换为代表其他测试几何形状的强度参数的方法，这些参数是从一种测试几何形状获得的数据中估计的。这种做法涉及单轴强度数据以及一些双轴强度数据。它也可用于更复杂的几何形状，证明可以估算有效面积和有效体积。它用于评估以脆性方式失效的先进陶瓷的威布尔概率分布参数。 图1 显示了强度随尺寸的典型变化。试样或组件越大，其强度可能越弱。 几何形状和应力分布 附件A3 1.5 以国际单位制表示的值应被视为标准值。 本标准不包括其他计量单位。 1.5.1 以SI单位表示的值符合IEEE/ASTM SI 10。 1.6 本标准并不旨在解决与其使用相关的所有安全问题（如果有的话）。本标准的使用者有责任在使用前建立适当的安全、健康和环境实践，并确定监管限制的适用性。 1.7 本国际标准是根据世界贸易组织技术性贸易壁垒委员会发布的《关于制定国际标准、指南和建议的原则的决定》中确立的国际公认的标准化原则制定的。 =====意义和用途====== 5.1 高级陶瓷通常显示线性应力- 将行为推向失败。缺乏延展性，加上各种尺寸和方向的缺陷，通常会导致破坏强度的大幅分散。强度不是一种确定性属性，而是反映了材料中固有的断裂韧性和缺陷的分布（尺寸和方向）。本标准适用于因缺陷灾难性传播而失效的脆性单片陶瓷。也没有考虑可能的R曲线上升效应，但这些效应本身就被纳入强度测量中。 5.2 威布尔分布存在二参数和三参数公式。本标准仅限于双参数公式。 5.3 拉伸和弯曲试样是先进陶瓷最常用的测试配置。 还包括具有多轴向应力状态的环对环和环对环压力试样。这些配置包括有效体积和有效表面的闭式解以及威布尔材料比例因子。这种做法还结合了C形环试样的尺寸缩放方法，对于这些方法，需要数值方法。本文介绍了一种利用有限元分析的任意形状试样或部件的通用方法 附件A3 . 5.4 通过断口分析可以确定失效试样的断裂起源。这些强度控制缺陷的空间分布可以在体积或面积上（如表面缺陷的情况）。该标准允许转换与任何一种空间分布相关的强度参数。 本规程不包括沿试样边缘定位的强度控制缺陷的长度缩放。 5.5 根据威布尔模型，强度随尺寸的缩放基于几个关键假设 ( 5. ) 假设相同的特定缺陷类型控制着各种试样配置中的强度。假设材料是均匀、均质和各向同性的。如果材料是复合材料，则假设复合相足够小，使得该结构在工程尺度上表现为均匀各向同性体。复合材料必须包含足够数量的均匀分布、随机取向的增强元件，使材料有效均匀。晶须增韧陶瓷复合材料可能是这类材料的代表。 这种做法也适用于没有表现出任何明显的双线性或非线性变形行为的复合陶瓷。该标准和传统的威布尔强度随尺寸缩放可能不适用于连续纤维增强复合陶瓷。假设材料以脆性方式断裂，这是应力导致缺陷灾难性传播的结果。假设材料是一致的（批次间、日常等）。假设强度分布遵循威布尔双参数分布。假设每个试件都有统计上显著的缺陷数量，并且这些缺陷是随机分布的。假设缺陷相对于试样横截面尺寸较小。如果存在多种缺陷类型并控制强度，那么每种缺陷类型的强度可能会有所不同。 咨询实践 C1239 例如 9.1 了解如何在此类情况下应用审查统计数据的进一步指导。还假设准确地确定了试样应力状态和最大应力。假设一组断裂试样的实际数据准确无误。（见术语 E456 关于后两个术语的定义。）因此，本标准经常引用其他已知在这方面可靠的ASTM标准测试方法和实践。 5.6 即使测试数据得到了准确和精确的测量，也应该认识到，从测试数据中确定的威布尔参数实际上是估计值。估计值可能与实际（总体）材料强度参数不同。咨询实践 C1239 以进一步指导基于有限样本大小的测试裂缝的测试数据的威布尔参数估计的置信区间。 5.7 当将一个试样几何形状的测试数据中的强度参数与第二个试样几何形状相关联时，相关性的准确性取决于中列出的假设是否 5.5 满足。此外，统计抽样效应如 5.6 也可能导致计算和观察到的强度尺寸缩放趋势之间的变化。 5.8 应该考虑威布尔强度标度的实际限制。例如，Weibull模型隐含地假设缺陷相对于试样尺寸较小。直径为50μm（0.050mm）的孔是横截面尺寸为5mm或更大的抗拉或抗弯强度试样中的体积分布缺陷。如果横截面尺寸仅为100μm，则情况可能并非如此。

1.1 This standard practice provides methodology to convert fracture strength parameters (primarily the mean strength and the Weibull characteristic strength) estimated from data obtained with one test geometry to strength parameters representing other test geometries. This practice addresses uniaxial strength data as well as some biaxial strength data. It may also be used for more complex geometries proved that the effective areas and effective volumes can be estimated. It is for the evaluation of Weibull probability distribution parameters for advanced ceramics that fail in a brittle fashion. Fig. 1 shows the typical variation of strength with size. The larger the specimen or component, the weaker it is likely to be. Geometries and Stress Distributions Annex A3 1.5 The values stated in SI units are to be regarded as standard. No other units of measurement are included in this standard. 1.5.1 The values stated in SI units are in accordance with IEEE/ASTM SI 10. 1.6 This standard does not purport to address all of the safety concerns, if any, associated with its use. It is the responsibility of the user of this standard to establish appropriate safety, health, and environmental practices and determine the applicability of regulatory limitations prior to use. 1.7 This international standard was developed in accordance with internationally recognized principles on standardization established in the Decision on Principles for the Development of International Standards, Guides and Recommendations issued by the World Trade Organization Technical Barriers to Trade (TBT) Committee. ====== Significance And Use ====== 5.1 Advanced ceramics usually display a linear stress-strain behavior to failure. Lack of ductility combined with flaws that have various sizes and orientations typically leads to large scatter in failure strength. Strength is not a deterministic property, but instead reflects the intrinsic fracture toughness and a distribution (size and orientation) of flaws present in the material. This standard is applicable to brittle monolithic ceramics which fail as a result of catastrophic propagation of flaws. Possible rising R-curve effects are also not considered, but are inherently incorporated into the strength measurements. 5.2 Two- and three-parameter formulations exist for the Weibull distribution. This standard is restricted to the two-parameter formulation. 5.3 Tensile and flexural test specimens are the most commonly used test configurations for advanced ceramics. Ring-on-ring and pressure-on-ring test specimens which have multi-axial states of stress are also included. Closed-form solutions for the effective volume and effective surfaces and the Weibull material scale factor are included for these configurations. This practice also incorporates size-scaling methods for C-ring test specimens for which numerical approaches are necessary. A generic approach for arbitrary shaped test specimens or components that utilizes finite element analyses is presented in Annex A3 . 5.4 The fracture origins of failed test specimens can be determined using fractographic analysis. The spatial distribution of these strength-controlling flaws can be over a volume or an area (as in the case of surface flaws). This standard allows for the conversion of strength parameters associated with either type of spatial distribution. Length scaling for strength-controlling flaws located along edges of a test specimen is not covered in this practice. 5.5 The scaling of strength with size in accordance with the Weibull model is based on several key assumptions ( 5 ) . It is assumed that the same specific flaw type controls strength in the various specimen configurations. It is assumed that the material is uniform, homogeneous, and isotropic. If the material is a composite, it is assumed that the composite phases are sufficiently small that the structure behaves on an engineering scale as a homogeneous and isotropic body. The composite must contain a sufficient quantity of uniformly distributed, randomly oriented reinforcing elements such that the material is effectively homogeneous. Whisker-toughened ceramic composites may be representative of this type of material. This practice is also applicable to composite ceramics that do not exhibit any appreciable bilinear or nonlinear deformation behavior. This standard and the conventional Weibull strength scaling with size may not be suitable for continuous fiber-reinforced composite ceramics. The material is assumed to fracture in a brittle fashion, a consequence of stress causing catastrophic propagation of flaws. The material is assumed to be consistent (batch to batch, day to day, etc.). It is assumed that the strength distribution follows a Weibull two-parameter distribution. It is assumed that each test piece has a statistically significant number of flaws and that they are randomly distributed. It is assumed that the flaws are small relative to the specimen cross section size. If multiple flaw types are present and control strength, then strengths may scale differently for each flaw type. Consult Practice C1239 and the example in 9.1 for further guidance on how to apply censored statistics in such cases. It is also assumed that the specimen stress state and the maximum stress are accurately determined. It is assumed that the actual data from a set of fractured specimens are accurate and precise. (See Terminology E456 for definitions of the latter two terms.) For this reason, this standard frequently references other ASTM standard test methods and practices which are known to be reliable in this respect. 5.6 Even if test data has been accurately and precisely measured, it should be recognized that the Weibull parameters determined from test data are in fact estimates. The estimates can vary from the actual (population) material strength parameters. Consult Practice C1239 for further guidance on the confidence bounds of Weibull parameter estimates based on test data for a finite sample size of test fractures. 5.7 When correlating strength parameters from test data from one specimen geometry to a second, the accuracy of the correlation depends upon whether the assumptions listed in 5.5 are met. In addition, statistical sampling effects as discussed in 5.6 may also contribute to variations between computed and observed strength-size scaling trends. 5.8 There are practical limits to Weibull strength scaling that should be considered. For example, it is implicitly assumed in the Weibull model that flaws are small relative to the specimen size. Pores that are 50 μm (0.050 mm) in diameter are volume-distributed flaws in tension or flexural strength specimens with 5 mm or greater cross section sizes. The same may not be true if the cross section size is only 100 μm.