Summary and Terms

Terms

Mechanical Properties: Materials properties that have to do with how a material responds to applied forces. Section 11.2.1

Stress: The applied force divided by the cross sectional area of a specimen. Because cross-sectional area changes during tensile tests, we often use Engineering Stress, which normalizes to only the initial cross section of the sample. We use $\sigma$ to represent stress Section 11.3.2

Strain: A measure of a sample's deformation, defined as the change in length of the specimen divided by the initial length of the specimen. We use $\epsilon$ Section 11.3.2

Elastic Deformation: Deformation that disappears once the force acting on the specimen has been removed. Question 11.3.1.3

Plastic/Inelastic Deformation: deformation that remains permanently after the force acting on the specimen has been removed. Question 11.3.1.3

Modulus of Elasticity: The relationship between stress and strain (the slope) in the linear region of a stress-strain curve. We use $E$ to denote a material's elastic modulus, and it gives us information about a material's stiffness. Section 11.4.2

Poisson's Ratio: The ratio between how much a material lengthens in tension and how much it contracts in the perpendicular directions. Given by:

$\nu=-\frac{\epsilon_x}{\epsilon_z}=-\frac{\epsilon_y}{\epsilon_z}$

Where the subscript on each $\epsilon$ represents the direction of the strain. Section 11.4.6

Auxetic Materials: An unusual class of materials which expands under tension, and thus has a negative Poisson's ratio. Section 11.4.9

Yield Stress: The stress required to initiate plastic deformation in a material. On a stress-strain curve, yield stress occurs at the point where the linear-elastic region ends. Section 11.5.3

(Ultimate) Tensile Strength: The amount of stress required to break a material, given by the maximum on a stress-strain curve. If stress is increased beyond the tensile strength, the material will break. Section 11.5.4

Ductility: A measure of the amount of plastic deformation a material can undergo before breaking. Materials with low ductility are often called brittle. Ductility can be quantified in terms of Percent Elongation, the amount the material lengthened normalized by its original length, or Percent Area Reduction, the percent difference between the final and initial cross sectional areas of the sample. Section 11.5.5

Resilience: Refers to the amount of elastic energy a material can store and release during loading and unloading, given by the area under the curve of the linear-elastic region of a stress-strain curve. This is known as $U_r$, the modulus of resilience. Section 11.5.7

Tensile Toughness: A measure of the amount of energy it takes to deform a material. In a tensile test, this is given by the area under the entire stress-strain curve until fracture. Section 11.5.10

Common States of Stress: Typical stress states include: Section 11.6.3

Uniaxial Simple Tension: The sample is placed in tension along only one axis. Section 11.6.4

Uniaxial Simple Compression: The sample is compressed along only one axis. Section 11.6.5

Pure Shear Stress: A stress state where two parts of a material are pushed in different directions. Section 11.6.5