Smart stress-memory patch is a promising method for monitoring long-term fatigue damage in structure. The patch can estimate the number of cycles and the stress amplitude using fatigue crack growth properties of thin metal sheets. In this study, fatigue crack growth behavior of thin pure copper sheet was investigated by changing the specimen shape under strain-controlled testing in order to improve measuring range of smart stress-memory patch. To characterize the initiation as well as the stable growth of fatigue cracks, the relationship between stress intensity factor range and crack growth rate was successfully fitted to one equation regardless of strain amplitude, strain ratio and specimen shape. Based on the experimental results, an equation for estimating fatigue cycles from fatigue crack length was derived. In addition, the detectable range of stress amplitude was evaluated and its dependence on sensor shape and stress ratio was shown. Since this patch needs neither power supply nor wiring, it provides a great potential for long-term structural health monitoring with easy maintenance.