MECH 4650 Definitions

Linear Damage Model

(# of periods)((n1 /nf1) + (n2/nf2) + (n3/nf3)) < 1 is safe, = 1 is a fail

Traction Free Surface

A surface with no normal shear stress component applied

Modified Goodman Type Analysis

Can be used to account for the effect of mean stress on fatigue performance

Stress Intensity Factor

Characterize how quickly the stress goes to infinity by scaling the stress. The opening mode, shearing mode, tearing mode in which have these constants/factors for each mode, KI. This value should always be less than 1.

Antielastic curgature

Curvature in transverse direction in a beam in bending due to poissons effect

Plastic Moment

Entire cross section has reached yield stress

Dummy Force, Moment

Fake load applied in the direction where deflection is to be determined using Castiglione's theorem.

Fatigue

Fatigue - a mode of failure experienced due to repeated loading or stress. The fatigue performance of materials is often characterized using an S-N curve. It is a time dependent material response.

Castiglinaos Theorem

If the strain energy of a linearly elastic structure can be expressed as a function of generalized force Q, then the partial derivative of the strain energy with respect to generalised force gives the generalised displacement q in the direction of Q.

Relaxation

Material response where the stress rate decreases for a constant strain.

Tresca

Maximum shear stress yield criteria (the difference between principal stresses must be less than the yield stress)

Modes of Fracture

Mode 1: Opening Mode 2: Shearing of Sliding Mode 3: Tearing

Goodman Type Analysis

Most often used analysis for machine components subjected to cyclic loads

Yield Criteria

Predict the onset of plastic deformation for a multi axial state of stress

Fracture Strength

Property of a material, stress as which material fractures

Elastoplastic

Reacts as an elastic material until the yield point at which the material plastically deforms under the constant loadin

Deviartoric (Distortional) Stress

Related to shape change, the stress left after subtracting the hydrostatic stress.

Volumetric (Hydrostatic) Stress

Related to volumetric change, simply the average between the 3 normal stress components.

Polar Moment of Inertia

The capacity of a circular cross section to resist torsion. How spread out the material is from its rotational axis stiffness of geometry to resist torsion

Fracture Toughness

The critical value of stress intensity

Modifying Factors

The external factors that actually influence the actual endurance limit, such as corrosion, temperature, load type, material, size, surface finish, and more.

Stress Signularity

The point in the material where the stress does not converge on one specific value, it goes till infinity.

Elastic Core

Zones where stress varies linearly with the strain

Mohr's Circle

a 2-D representation of the transformation law for the stress tensor in plane stress can be used when all non-zero stresses are in 1 plane and is on traction free surface

Coefficient of thermal expansion

a constant characteristic of a material that causes it to expand or contract due to a change in temperature.

SN Curve

a curve used to identify endurance limit and prevent failure due to fatigue. The stress by the number of cycles to failure.

Dislocations

a displacement of part of the crystal lattice structure of a material.

Plastic Torque

a fully plastic deformation, when the distribution of strain remains linear after the onset of yield in shear vs strain plot

Homogeneous

a material in which properties are not a function of position within the material they are constant throughout

Torque

a moment produced by some force acting at a perpendicular distance away from a point causing rotation of an object. A measure of force that is applied about an axis of rotation

Viscoelastic

a property of a material that exhibits both viscous and elastic characteristics when undergoing deformation. It resists shear flow and strain linearly with time when a stress is applied. When stretched it will quickly return to its original state once the stress is removed. It exhibits time-dependent strain.

Stress concentration factor

a ratio of the maximum stress to the applied tensile stress. refers to the stress concentration in loaded materials caused by holes, fillets, and flaws.

Shear Flow

a reorientation of the shear stress due to the presence of a traction free surface

Von Mises Yield Criterion

a structure is safe as long as the max value of the distortion energy per unit volume in the material is smaller than the distortion energy per unit volume to cause yield in a tensile test specimen

Critical Buckling Load

aka euler buckling load. The maximum compressive load a member can support before failure due to buckling.

Plastic Deformation

any kind of deformation beyond yield stress of material results in permanent deformation

perfectly plastic

behavior of a material in which stress remains constant throughout the plastic region as strain increases

Variable Amplitude Loading

cyclic loading situation where the amplitude of the loading is variable and not constant.

Plastic deofmation

deformation that is permanent or non-recoverable after the load is released

Elastic/perfectly plastic

describes the behavious of a material when a load is applied, behaves linearly in the elastic region and stress is constant in the plastic region when strain increases

Shear stress

engineering measure of how forces are transmitted through a body from a force applied parallel to the surface

Normal stress

engineering measure of how forces are transmitted through a body from a force applied perpendicular to the surface

Shear strain

engineering measure of the relative deformation in the change in angle

Normal strain

engineering measure of the relative deformation per unit length of a specimen

Reciprocal work theorem

for linear elastic structure subjected to two forces P and Q the work done by P through the displacement produced by Q is equal to the work done by Q through the displacement produced by P

Axial Load

forces are directed along the axis of the member, normal to the cross sectional area

Anticlastic

having a curvature at a given point and in a particular direction, that is the opposite sign to the curvature at that point in a perpendicular direction

Residual Stress

if a load is applied causing plastic deformation, there will be stress in the material after the load is removed

Stress Redesbtribution

in the plastic deformation, stress is linear until it reaches plastic deformation. The linear section increases to make up the flat portion where stress cannot go further.

Small Scale Yielding

is the argument for using the stress intensity factor and explains why it does (or sometimes doesn't) work.

Slenderness Ratio

l/r the length of the column over the radius of gyration is used in the calculation of the critical stress due to buckling

Ultimate strength

maximum stress that can be sustained without fracture

Centroid

mean position of all the points in all the coordinate directions.

Degrees of Freedom

minimum number of independent coordinates that can specify the position of the system completely

Youngs modulus

modulus of elasticity of a material, the slope of the linear elastic region on a stress strain graph

Creep

occurs when materials are subjected to high loads continuously, they may experience progressive elongation over time. it is a time dependent material response. since creep often takes a long time, so accelerated testing is often done to characterize a material's creep characteristics.

Strain energy density

of a material will be defined as the strain energy per unit volume; it will be seen that it is equal to the area under the stress-strain diagram of the material

Stress redistribution

once material has yielded fully, any additional stress changes the stress distribution and is shifted to an area where it remains in equilibrium and forces are conserved

Classical Beam Theory

planes perpendicular to the neutral axis after deofmration

Principal Planes

planes that have no shear stress (only normal stresses or principal stresses) and are on oblique angles

Stress Factor

ratio of the ultimate load. should be used in the design of a given structure upon a number of considerations

Poisson's Ratio

relates lateral and axial stress for elastic deformation, the negative ratio of a lateral and axial strains that results from an applied axial stress

Modulus of Rigidity

relates shear stress to strain

Small Angle Approximation

simplification of basic trig functions which is approximately true when the limit where the angle approaches 0

Hydrostatic Stress

state of stress where only normal stresses exist and they are all equal

Superposition

states that the resultant stress or displacement at a point can be determined by first finding the stress or displacement caused by each component load separately on the member. The effect of combined loading on a structure can be obtained by determining the effects of the various loads separately and combining the results

Eccentric loading

stress directed anywhere on a component other than where the component is designed to accept the force.

Neutral Axis

the axis of a cross section where there are no longitudinal stresses or strains.

Linear elastic

the behavior of a material to act linearly when a load is applied and resumes it original shape when the load is released as long as the stress is kept below the yield point

Moment of Interitia

the capacity of a cross section to resist bending. Considered with respect to a reference axis and the center of mass or centroid of the cross section. how spread out a material is from the central axis

St Vernant's Principle

the difference between the effects of two different but statically equivalent loads become very small at sufficiently large distances from the load. Other than in the immediate vicinity of the points of application of loads, the distribution may be assumed independent of the actual mode of application of the load> We can replace a boundary condition with one that is energetically equivalent without affecting the state of stress away from the boundary condition

Small Deformation Theory

the displacements of the material particles are assumed to be much smaller than any relevant dimension of the body and material properties can assumed to be unchanged by deformation.

Strain energy

the increase in energy associated with the deformation of the member

Crack Length

the length of a crack. Failure occurs at the point when the crack length is at its critical point and the material fails.

Effective Length

the length used to make the formula applicable to various end conditions

Mean Stress Effect

the mean stress between the maximum stress and minimum stress for a cyclic loading condition.

Isotropic

the mechanical properties of a material are independent of the direction considered, has same mechanical behaviors in all directions.

Se'

the pristine endurance limit. It is the stress below which failure due to fatigue is unlikely under ideal conditions.

Plane Stress

the state of stress in which the normal stress and the shear stresses directed perpendicular to the x-y plane are assumed to be 0

Yield strength

the strength at which a material enters the plastic region of deformation. Commonly uses a strain offset of 0.002

moment

the tendency of a force to rotate an object when it acts at a perpendicular distance from the point considered, force applied at a distance.

Rheological Elements

there are 3 basic building elements: spring (elastic), stick-slip (plastic), damper (viscous)

Endurance Limit

this is the point at below which failure to fatigue is unlikely. Note some materials such as aluminum don't exhibit a true endurance limit. The actual endurance limit is going to be influenced by many external factors called modifying factors.

Radius of Gyration

used to calculate the slenderness ratio

Parallel Axis Theorem

used to determine the mass moment of inertia or a rigid body about any axis, given the body's moment of inertia about a parallel axis through the object's center of mass and the perpendicular distance between the axes.

Statically Indeterminate

when statics equations are insufficient for determining the internal forces and reactions on the structure.

Buckling

when structure fails under a compressive stress that is below the ultimate compressive stresses that the material is capable of handling