A mathematically transparent and robust experimental method has been developed to estimate the yield stress of brittle materials through the analysis of depth-sensing spherical indentation. Employing Hertzian contact mechanics, an elastically invariant ratio based on the simple equation , (where S and P are contact stiffness and indentation load, respectively) has been derived that enables more accurate and confident determination of the transition from elastic to inelastic deformation; a transition that the yield stress dictates and represents. Using two diamond spheres with radii of 3.2 and 8.6 μm, the indentation test method and analyses are applied to two vitreous silicates: Corning's HPFS 7980® fused silica and Vitro's Starphire® soda-lime silicate. The estimated yield strengths are 8.15 GPa 2.5 % for the fused silica and 6.1 GPa 3.3 % for the soda-lime silicate, and both were independent of indenter radius. Verification of this new experimental method is demonstrated with an as-drawn titanium by showing equivalence of measured yield stress by its spherical indentation and that from uniaxial compression testing. This method will enable easier and more confident estimation of yield stress in brittle materials - a property that historically has been elusive to measure for these materials using common laboratory mechanical test methods.

中文翻译：

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球形压痕和 S3/P 的实施用于脆性材料屈服应力的测定

我们开发了一种数学上透明且稳健的实验方法，通过分析深度传感球形压痕来估计脆性材料的屈服应力。采用赫兹接触力学，导出了基于简单方程 的弹性不变比（其中 S 和 P 分别是接触刚度和压痕载荷），可以更准确、更可靠地确定从弹性变形到非弹性变形的转变；屈服应力决定和代表的转变。使用半径分别为 3.2 和 8.6 μm 的两个金刚石球，将压痕测试方法和分析应用于两种玻璃硅酸盐：康宁的 HPFS 7980® 熔融石英和 Vitro 的 Starphire® 钠钙硅酸盐。熔融石英的估计屈服强度为 8.15 GPa·2.5%，钠钙硅酸盐的估计屈服强度为 6.1 GPa·3.3%，并且两者均与压头半径无关。通过显示球形压痕测得的屈服应力与单轴压缩试验测得的屈服应力的等效性，用拉制钛证明了这种新实验方法的验证。这种方法将能够更容易、更自信地估计脆性材料的屈服应力——历史上使用常见的实验室机械测试方法难以测量这些材料的屈服应力。