J-integral testing on micro-scale cantilever beam specimens

Abstract

The current paper presents a modified procedure for the J-integral testing on micro-scale cantilever beam specimens. For such tests, a non-dimensional factor is required that relates the plastic part of the area below the load vs. load-point displacement curve to J. This parameter is called the “plastic eta-factor”, ηpl. Up to now, a constant value of ηpl≈2 has been used, which is also valid for deeply notched single-edge bend specimens. A comprehensive numerical case study is performed to determine ηpl for cantilever beam specimens as a function of the relative crack length a/W, the relative cantilever length L/W, the relative base distance d/W, and the load, i.e. the degree of plasticity in the specimen. It is shown that ηpl≈2 is applicable only, if the crack length is large, a/W⩾0.5. For smaller a/W-ratios, which are commonly used in the fracture mechanics testing of nano- and micrometer sized materials, ηpl can become much smaller and also dependent on the d/W-ratio. A fitting procedure is presented that enables the determination of the correct value of ηpl, and modifications of the J-integral testing procedure for cantilever beam specimens are proposed. Finally, a numerical validation of the procedure is presented.