Experimental testing of V notched radially graded materials under static loading

Abstract

The growing interest in additive manufacturing and printed materials has opened new possibilities for the development and application of Graded Materials (GMs). However, capturing the strength and fracture behavior of GMs presents challenges, as the extent to which classical theories for homogeneous materials apply remains uncertain. For example, it has been recently suggested that in the classical problem of a sharp wedge or crack loaded in-plane (mode I and/or mode II), the stress singularity can be mitigated by grading the elastic properties of the material near the notch tip according to a power-law distribution, $E\sim r^{\beta }$. This suggests that sharp geometrical discontinuities can exist without causing sharp stress concentrations. Under these conditions, it is conceivable that structural optimization should aim to achieve uniform stress distribution or, more specifically, consistent strength throughout the material. Since material resistance typically follows a power-law function of the elastic modulus, a state of uniform stress is not optimal. However, a state of uniform strength may also be considered less than ideal with respect to the homogeneous material since the softer material used to reduce stress concentration reduces also the strength of the specimen. Here, we report experiments conducted on V-notched specimens, varying the grading exponent $\beta$, and compare the results for homogeneous material specimens with those of GMs. We find that the cancellation of singularity effect competes with the reduction of strength due to the use of softer materials, but when the latter effect is accounted for or reduced, we observe an improvement compared to the homogeneous V-notched case. Further, when the strength-modulus exponent $m=0$, structural optimization is equivalent to minimizing stress concentration. For most materials with $m<1$, the optimal behavior occurs near this criterion. In our case, we found $m\approx 0.5$, which is significant because strain energy density, a function of both stress and strain, acts as a dual-purpose criterion. This criterion is similar to the $\sigma /{\sigma }_{\text{a}}$ ratio used in homogeneous materials like Rankine or Von Mises. Notably, in fatigue tests, we anticipate that the benefits of material grading will be more pronounced.