The term for the development of a crack that grows larger over time is:

Propagation refers to the process where a crack initiates at a certain point and enlarges over time due to various factors such as stress, fatigue, or environmental conditions. This term is widely used in materials science and engineering to describe how cracks can grow or spread within materials, which can ultimately lead to material failure if not addressed.

The other options fail to capture the specific nature of the crack's growth over time. Widening generally describes an increase in size but doesn’t convey the ongoing development or growth aspect inherent in the term propagation. Creeping typically refers to slow deformation or movement under stress, but it does not specifically relate to the growth of cracks. Expansion suggests a general increase in size but lacks the precise context applied to the crack growth phenomenon. Thus, propagation is the most accurate term to describe the continuous growth of a crack.