Robust nanostructures for future devices will depend increasingly on their reliability. While great strides have been achieved for precisely evaluating electronic, magnetic, photonic, elasticity and strength properties, the same levels for fracture resistance have been lacking. Additionally, one of the self-limiting features of materials by computational design is the knowledge that the atomistic potential is an appropriate one. A key property in establishing both of these goals is an experimentally-determined effective surface energy or the work per unit fracture area. The difficulty with this property, which depends on extended defects such as dislocations, is measuring it accurately at the sub-micrometer scale. In this Full Paper the discovery of an interesting size effect in compression tests on silicon pillars with sub-micrometer diameters is presented: in uniaxial compression tests, pillars having a diameter exceeding a critical value develop cracks, whereas smaller pillars show ductility comparable to that of metals. The critical diameter is between 310 and 400 nm. To explain this transition a model based on dislocation shielding is proposed. For the first time, a quantitative method for evaluating the fracture toughness of such nanostructures is developed. This leads to the ability to propose plausible mechanisms for dislocation-mediated fracture behavior in such small volumes.