Effect of branched cracks on the elastic compliance of a material

The paper focuses on the elastic properties of a material containing multiple branched cracks with pores in their centers. First, we estimate compliance contribution tensor of such a crack and identify the proper microstructural parameters to describe its effect on the elastic properties. The compliance contribution tensor is used then to predict overall elastic properties of the considered material using various averaging schemes. It is shown that three microstructural parameters have to be combined – relative volume of pores, pore shapes, and relative length of the crack branches. Neglecting any of these parameters may lead to a substantial error in estimation of the effective elastic moduli. As an illustration, we consider example of sintering of metal fibers when all these parameters vary with temperature. It is shown how this variation can be incorporated in the model to monitor changes in the elastic properties with sintering temperature.

► We estimate compliance contribution tensor of a branched crack crossing deltoidal pore and identify the proper microstructural parameters to describe its effect on the elastic properties.
► The compliance contribution tensor is used then to predict overall elastic properties of the considered material using various averaging schemes.
► We show that three microstructural parameters have to be combined – relative volume of pores, pore shapes, and relative length of the crack branches. Neglecting any of these parameters may lead to a substantial error in estimation of the effective elastic moduli.
► Example of sintering of metal fibers when all these parameters vary with temperature is considered.