Stress and Strain
I. Stress:
A. When an object experiences stress, it experiences a force per unit area. This force can either be a pulling force (in which case the stress is called tension stress) or a pushing force (in which case the stress is called compression stress). Additionally, the object may experience 2 forces acting parallel to each other but in opposite directions (in which case the stress is called shear stress).
B. As mentioned above, there are 3 types of stress: tension stress, compression stress, and shear stress. An object experiences tension stress when its sides are pulled, an object experiences compression stress when its sides are pushed inward, and an object experiences shear stress when 2 forces acting parallel to each other but in opposite directions act on the object (such that one part of the object goes one way and another part goes the other). An example of shear stress includes tearing a piece of cloth with your hands.
C. The Breaking Stress/The Ultimate Tensile Stress/The Ultimate Tension Strength: these 3 names all refer to the same thing. An object’s ultimate tension strength is the maximum tension force per unit area (the maximum tension stress) it can withstand without breaking. Recall that tension is a pulling force. Therefore, when an object reaches this point, it experiences the maximum tension (pulling) that can be exerted onto it without breaking. Once an object exceeds this point, it breaks.
D. Stress can be calculated using the following equation below:
II. Strain:
A. When an object experiences strain, it experiences a change in shape or size (deformation) due to stress. In other words, strain is a measure of how much an object is stretched/elongated (deformed).
B. Strain can be calculated using the following equation below:
III. Stress vs. Strain Graph:
A. When an object’s stress v. strain graph is generated, a linear region is produced. In this linear region, stress and strain are proportional to each other (if one increases/decreases the other does as well). This linear region and proportional relationship only exists when the strain is small. Therefore, once the strain gets large, the graph is no longer linear and a proportional relationship no longer exists. This linear region is called Hooke’s Law Region because Hooke’s Law can be applied to it. Robert Hooke was a 17th century British physicist who pointed out this proportional relationship between stress and strain and thus force and elongation (recall that force is the numerator in the stress equation, and elongation is the numerator in the strain equation).
B. A stress v. strain graph can be generated for every object. Therefore, every object can be associated with a linear region of a certain slope/stress-strain ratio. The slope produced for an object’s linear region is called Young’s Modulus and is expressed in the equation below. Because a stress v. strain graph can be generated for every object, every object has a Young’s Modulus.
C.