# THEORIES OF FAILURE 1: BASIC TERMINOLOGIES

Theories of failure (TOF) and its concept has a great importance in design section.

In TOF , it is important to be perquisite with the knowledge of various notations and terms used in this theory.

This blog puts emphasis on all these terms and notations.

#### 1.STRESS

The internal resistance offered by a body against an acting load.

STRESS = RESISTING FORCE /AREA

TYPES OF STRESSES:

a.NORMAL STRESSES : Stresses acting along the axis of load . Denoted by σ . Causes change in volume of an object.

σ = F/A F= Resisting force

b.SHEAR STRESSES: Stresses acting due to a tangential load along the face of body. Denoted by  τ (Greek: tau). Causes change in overall shape of the body.

τ = F/A

#### 2.STRENGTH :

A material’s capacity to sustain load without getting failed.

a.YIELD STRENGTH ( σyt ) : The strength of a material at its yield point. Usually defined for ductile materials.

b.ULTIMATE STRENGTH ( σut ) : The strength of a material at its ultimate point. Usually defined for brittle materials.

#### 3.STRAIN :

Change in dimensions to the original dimensions.

a. Longitudinal strain : Strain that occurs because of Normal stress. Denoted by ε. Here, length is the varying dimension.

ε = ΔL / L

b. Shear strain : Strain that occurs because of Shear stress. Denoted by γ . Here, angle is the varying dimension.

γ = 90 – α

#### 4. POISSON RATIO :

Ratio of lateral strain to longitudanal strain . Denoted by µ.

µ = (Δd/d) / (ΔL/L)

#### 5. FACTOR OF SAFETY :

Factor of safety (FOS) is the ratio of maximum allowable stress (yield or ultimate) to the maximum working stress.

FOS = (Max. allowable or permissible stress)/ (max .working stress) = σmax or σyt or σut /  σworking

FOS is one of the important aspects of THEORIES OF FAILURE.

#### 6.PRINCIPAL STRESS AND STRAINS :

Stresses and strains acting along the principal plane of a body.

σ1 = Max.principal normal stress

σ2 = Min. principal normal stress

τ1 = Max. principal shear stress= τmax

τ2 = Min. principal shear stress

#### CONDITION OF FAILURE IN A MACHINE ELEMENT

A machine element is said to be undergo failure in two conditions :

1. On undergoing permanent deformation: Usually this condition is analysed in ductile materials .It is due to the fact that Permanent deformation (plastic deformation) occurs after yield point.
2. On material breakdown or fracture : Usually this condition is analysed in brittle materials . It is due to the fact that with no yield point , this material breaks on fracture point.