Practice Quiz

Explanation

Brinell, Vickers and Rockwell tests are all hardness tests, which are used to measure the resistance of a material to localised plastic deformation by indentation.

Explanation

The stiffness matrix represents the inherent resistance of an element to deformation due to applied loads. It is formulated based on the elastic properties of the material (like Young's modulus and Poisson's ratio) and the element's geometry. The actual loads applied on the element do not directly influence the formulation of the stiffness matrix.

Explanation

Resilience is the ability of a material to deform elastically without permanent plastic deformation. Highly resilient materials are able to absorb large amounts of energy without deforming plastically.

The modulus of resilience is the strain energy per unit volume that can be absorbed without plastic deformation, from zero strain up to the elastic limit. It is equal to the area under the stress-strain curve, up to the yield point.

Explanation

The normal stress in the bar is calculated as the applied force divided by the cross-sectional area of the bar.

$$\sigma = \frac{F}{A}$$

The strain in the longitudinal direction can then be calculated using Hooke's law:

$$\varepsilon_{long} = \frac{\sigma}{E} = \frac{F/A}{E}$$

Due to the Poisson effect, the strain in the longitudinal direction will cause the bar to get thinner in the lateral direction. Poissons ratio is defined as:

$$\nu = \frac{- \varepsilon_{lat}}{\varepsilon_{long}}$$

We can then calculate the lateral strain:

$$\varepsilon_{lat} = - \nu \varepsilon_{long} = - \nu \frac{F/A}{E} = - 0.27 \% $$

Explanation

Unlike ductile materials, brittle materials fracture when very small deformations are applied to them.

Material A fractured in the tensile test at a lower strain than Material B or Material C, and as such is the most brittle of the three materials.