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Use of normalized porosity in models for the porosity dependence of mechanical properties

机译：归一化孔隙率在模型中用于机械性能的孔隙率依赖性

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The use of normalized porosity in models for the porosity dependence of mechanical properties is addressed first for the frequently used power law expression for such dependence, i.e., E/E 0 = (1−P)n where E is the property of interest at any volume fraction porosity (P) and E 0 is the value of E at P = 0. Normalizing P by P C, the value of P at which the property of interest inherently goes to zero, giving E/E 0 = (1−P/P C)n, clearly calls attention to the importance of P C values < 1 (e.g., potentially as low as ∼ 0.2), a fact long known but inadequately recognized. Serious problems from the arbitrary use of both n and P C as fitting parameters with little or no guidance as to the dependence that n and P C (which is microstructurally sensitive) have on the type of porosity are shown. Further, porosity normalization of the power law model indicates at best limited compression of different porosity dependences into a single universal porosity dependence function and little distinguishing of property dependences as a function of the type of porosity. However, normalized porosity of minimum solid area (MSA) models gives a single universal porosity dependence. The difference in responses to P normalization of the two modeling approaches is attributed to their being based respectfully on little or no pore character and on detailed pore character. Thus, P normalization may be a valuable tool for evaluating porosity models, but must be applied in a more rigorous fashion, i.e., P C determined primarily by measurement and correlation with the type of porosity (as with MSA models) and not as an arbitrary fitting parameter as used in the evaluations of the power law model.
机译：首先针对模型的归一化孔隙度对机械性质的孔隙度依赖性的使用，首先针对这种依赖性的常用幂定律表达式，即E / E 0 =（1-P）n E是任何体积分数孔隙率（P）时的目标属性，E 0 是P = 0时E的值。通过PC标准化P ，即目标属性下P的值固有地为零，给定E / E 0 =（1-P / PC ）n ，显然需要引起人们对PC 值<1的重要性的关注（例如，可能低至0.2），这一事实早已为人所知，但却未被充分认识。由于随意使用n和P C 作为拟合参数，而对n和P C （对微观结构敏感）对孔隙类型的依赖关系很少或没有指导，这显示出严重的问题。此外，幂律模型的孔隙度归一化最多表明将不同孔隙度依赖性有限地压缩为单个通用孔隙度依赖性函数，并且几乎没有区分作为孔隙度函数的性质依赖性。但是，最小实体面积（MSA）模型的归一化孔隙度具有单个通用孔隙度依赖性。两种建模方法对P归一化的响应差异归因于它们分别基于很少或没有孔特征以及详细的孔特征。因此，P归一化可能是评估孔隙度模型的有价值的工具，但必须以更严格的方式应用，即PC 主要由孔隙度的测量和相关性确定（如MSA模型），而不是作为幂律模型评估中使用的任意拟合参数。

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    《Journal of Materials Science》 |2005年第4期|983-989|共7页
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