Final answer:
Ductility is the primary factor in determining if sheet metal can be bent and formed without experiencing stress fractures and other undesirable effects. It reflects the material's ability to sustain plastic deformation under tensile stress. Other properties, such as modulus of elasticity and surface hardness, inform about stiffness and strength but do not directly determine formability to the same extent as ductility.
Step-by-step explanation:
The primary factor that determines if sheet metal can be bent and formed without experiencing stress fractures and other undesirable effects is ductility. Ductility is a measure of a material's ability to undergo significant plastic deformation before rupture or fracture. It indicates how a material can be deformed under tensile stress. Materials with high ductility, such as some metals, can be stretched into a wire or bent into shapes without breaking.
When considering the bending and forming of metals, the characteristic of interest is the material's ability to withstand deformation within the region of plasticity as opposed to elasticity. Within the stress-strain diagram, the elastic modulus, also known as Young's modulus, defines the behavior in the elastic region, but it is the transition to and the extent of the plastic region (before reaching the fracture point) is integrated with ductility.
Factors such as martensitic structure and surface hardness provide information on the strength and hardness of a material, but they do not directly indicate how well a material can sustain being formed or bent. The modulus of elasticity provides insight into the material's stiffness; however, it does not solely dictate the material's formability without fracture. Ultimately, ductility is the defining property when it comes to bending and forming sheet metal.