Two experiments employed attunement and calibration training to investigate whether observers are able to identify material break points in compliant materials through haptic force application. The task required participants to attune to a recently identified haptic invariant, distance-to-break (DTB), rather than haptic stimulation not related to the invariant, including friction. In the first experiment participants probed simulated force-displacement relationships (materials) under 3 levels of friction with the aim of pushing as far as possible into the materials without breaking them. In a second experiment a different set of participants pulled on the materials. Results revealed that participants are sensitive to DTB for both pushing and pulling, even in the presence of varying levels of friction, and this sensitivity can be improved through training. The results suggest that the simultaneous presence of friction may assist participants in perceiving DTB. Potential applications include the development of haptic training programs for minimally invasive (laparoscopic) surgery to reduce accidental tissue damage.