## Chapter 18

A rod subjected to a load undergoes elongation. A load-deformation diagram can represent the elongation but cannot predict deformation in different rods. …

## Stress-Strain Diagram

Consider a cylindrical specimen placed in a system to measure its tensile strength. Two gauge marks are inscribed on the central portion of the specimen. …

## Stress-Strain Diagram – Ductile Materials

When a specimen is subjected to loading the length first increases linearly at a slow rate, resulting in an initial straight line with a steep slope on …

## Stress-Strain Diagram – Brittle Materials

Brittle materials, under tensile stress, do not elongate much before rupturing, meaning their ultimate and breaking strengths are identical. Compared with …

## True Stress and True Strain

Engineering stress is the ratio of the load and the undeformed original cross-sectional area. Engineering stress approximates strain which represents the …

## Hooke’s Law

Hooke's law states that stress applied to a material is directly proportional to the strain it experiences within the elastic limit. For ductile …

## Plastic Behavior

Materials under stress due to tensile loading exhibit elastic and linear behavior until the yield point. Removing the load at the yield point, stress and …

## Fatigue

Fatigue occurs when the materials, under repeated loads for thousands or millions of cycles, rupture at a stress level much lower than the material's …

The deformation of a rod with different materials and cross-sections is computed by dividing it into parts, each characterized by individual parameters. …

## Statically Indeterminate Problem Solving

Consider two cylindrical rods, one of steel and another of brass, joined at point B and restrained by rigid supports at points A and C. Determine the …

## Thermal Strain

A homogeneous rod with a uniform cross-section, resting freely on a horizontal surface, expands when heated. The expansion is proportional to the …

## Temperature Dependent Deformation

Consider a non-homogenous rod made of steel and brass, restrained at both ends and subjected to a temperature change. The stress and load on the rod are …

## Poisson’s Ratio

When a slender bar is subjected to an axial load, the bar material undergoes axial strain, causing it to deform in the axial direction. Simultaneously, …

## Generalized Hooke’s Law

The generalized Hooke's Law extends Hooke's Law to all stress types and directions, aiding in understanding materials under multiaxial stress …

## Bulk Modulus

The bulk modulus measures a material's resistance to uniform compression. It is defined as the proportionality constant between a change in pressure …

## Shearing Strain

In a cubic element with a general state of stress, the shearing stresses can deform a cube into an oblique parallelepiped without affecting normal …

## Relation between Poisson’s ratio, Modulus of Elasticity and Modulus of Rigidity

A slender bar subjected to an axial load undergoes deformation in the axial and transverse directions. The deformation affects the cubic elements within …

## Saint-Venant’s Principle

Consider a member with plates on both ends. When loads are applied centrally on the plates, they move towards each other without rotating, causing the …

## Stress Concentrations

Stress concentration refers to the amplification of stress in a structural member near points of discontinuity, such as holes or abrupt changes in …

## Residual Stresses

When a rod is stretched beyond its yield point, it permanently deforms and doesn't regain its original length. The stresses created during loading are …

## Strain Sensing Based on Multiscale Composite Materials Reinforced with Graphene Nanoplatelets

The electrical response of NH2-functionalized graphene nanoplatelets composite materials under strain was studied. Two different manufacturing methods are …

## Full-field Strain Measurements for Microstructurally Small Fatigue Crack Propagation Using Digital Image Correlation Method

A novel measurement approach is used to reveal the cumulative deformation field at a sub-grain level and to study the influence of microstructure on the …

## Intermediate Strain Rate Material Characterization with Digital Image Correlation

The mechanical response of a material under dynamic load is typically different than its behavior under static conditions; therefore, the common …