On the fracture mechanics validity of small scale tests

There is growing interest in conducting small-scale tests to gain additional insight into the fracture behaviour of components across a wide range of materials. For example, micro-scale mechanical tests inside of a microscope (in situ) enable direct, high-resolution observation of the interplay between crack growth and microstructural phenomena (e.g., dislocation behaviour or the fracture resistance of a particular interface), and sub-size samples are increasingly used when only a limited amount of material is available. However, to obtain quantitative insight and extract relevant fracture parameters, the sample must be sufficiently large for a $J$- (HRR) or a $K$-field to exist. We conduct numerical and semi-analytical studies to map the conditions (sample geometry, material) that result in a valid, quantitative fracture experiment. Specifically, for a wide range of material properties, crack lengths and sample dimensions, we establish the maximum value of the $J$-integral where an HRR field ceases to exist (i.e., the maximum $J$ value at which fracture must occur for the test to be valid, $J_{\max }$). Maps are generated to establish the maximum valid $J$ value ($J_{\max }$) as a function of yield strength, strain hardening and minimum sample size. These maps are then used to discuss the existing experimental literature and provide guidance on how to conduct quantitative experiments. Finally, our study is particularised to the analysis of metals that have been embrittled due to hydrogen exposure. The response of relevant materials under hydrogen-containing environments are superimposed on the aforementioned maps, determining the conditions that will enable quantitative insight.