Natural opening-mode fractures existing in the subsurface can be partially or completely sealed by diagenetic cements (e.g., joints and veins), and these cemented fractures may reopen during core recovery to the ground surface. Depending on the cement/host-rock material properties, debonding or re-fracturing may happen within the cement or at the cement/rock interface. We demonstrate the role of induced stresses in opening cemented fractures (veins) during cores recovery to the surface and to determine whether cracks form along the vein interface or through the core and why. We consider vein as a thin layer sandwiched inside the rock mass, and use the theory of eigenstrain to calculate stress disturbances at the core surface due to the release of in-situ stresses and the difference between surface and downhole temperatures. Then, we employ the theory of elasticity to calculate the maximum tensile stress at the edge of the vein. This tensile stress can be used to estimate the tensile strength of the diagenetic cements inside natural fractures. Using the developed technique, we solve practical examples to determine whether debonding is more likely within the natural cement or at cement/host-rock bonding. For the case of core recovery in Marcellus Shale with a calcite vein, we find that the maximum tensile stress normal to the vein plane happens at the center of the vein. We observe this phenomenon for both alignment of c-axis orientation with the layering, perpendicular to the fracture wall (⊥c-axis) and parallel to the fracture wall (∥c-axis). Therefore, theoretically, cracks likely form at the center of the calcite vein rather than the Marcellus Shale/calcite interface. Laboratory tests to date have shown that re-fracturing of calcite veins in Marcellus Shales can occur either within the calcite or at the calcite/Shale interface. For the case of core recovery in sandstone with fractures cemented with continuous crystallized quartz grains, the proposed solution predicts re-breaking at the center of the vein. For this case, we investigate two crystallographic orientations of quartz, c-axis orientation perpendicular to the fracture wall and a-axis orientation perpendicular to the fracture wall. Based on the current calculations for both crystallography of quartz, the tensile stress normal to the quartz plane is maximum at the center of the vein. Petrographic evidence, using secondary electron (SE) and cathodoluminescence (CL) images, supports our model predicting breakage within quartz veins as opposed to at the cement/sandstone host-rock interface. However, in a hypothetical case in which the calcite c-axis forms parallel to fracture walls in sandstone host-rock, debonding is predicted at the interface rather than within the vein cement.