Glossary

A

ASTM

American Society for Testing and Materials.

B

Block loading

A time series generated by repeating a shorter time series.

C

Compressive strength

The ultimate stress of the material in compression.

Constant amplitude loading

A load history where all peak (maximums) are equal and all valleys (minimums) are equal.

Crack initiation

The process of producing a small crack in a component of some definable size, such as 0.1 mm in length.

Cycle

A completed hysteresis loop in the stress-strain space.

Cyclic hardening coefficient (K’)

The coefficient for the plastic strain term in the Ramberg-Osgood equation that describes the cyclic stress-strain curve. It is the intercept on the stress axis that corresponds to a plastic strain amplitude of 1 on the log-log plot of plastic strain amplitude vs. stress amplitude determined from a stabilized cyclic stress-strain test.

Cyclic hardening exponent (n’)

The exponent for plastic strain term in the Ramberg-Osgood equation that describes the cyclic stress-strain curve. It is the slope of the log-log plot of plastic strain amplitude vs. stress amplitude determined from a stabilized cyclic stress-strain test.

D

Damage fraction

The amount of damage calculated per cycle.

Damage parameter

A formula that relates stress ranges, strain ranges, and other relevant quantities to fatigue life.

E

Elastic material

A material that recovers all deformation upon releasing the load.

Elastic-plastic material

A material in which there is a combination of recoverable deformation (that is, elastic strain) and non-recoverable deformation (that is, plastic strain). Most metals behave in this manner after the yield stress is reached.

Element

In finite element analysis, a discrete portion of the structure, such as a small cube of material in the component.

Endurance limit

The stress level below which fatigue failures are not likely to occur, typically exhibited for most steels. For other alloys (such as aluminum), a pseudo endurance limit may be defined which is the stress level that corresponds to a large number of cycles.

Engineering stress

Stresses calculated based on the reference area in the unstrained configuration (that is, the original area before loading).

Equivalent stress

A scalar stress value determined from the components of the stress tensor; often calculated by the von Mises formula.Note: In the context of this Specialist Durability help, we often use the term equivalent stress in a broader sense to mean any scalar stress value that is used in a fatigue analysis, including, for example, stress projections in critical plane approaches.

Eurocode

A European welding code for seam welds.

F

Fatigue

The process that occurs in a material subjected to fluctuated stresses and strains leading to permanent structural changes. Due to these changes at some point or points cracks may build up or complete fracture may happen to occur after a sufficient number of fluctuations.

Fatigue ductility coefficient (εʹf)

The coefficient for the reversals to failure in the Manson-Coffin-Morrow relation for the plastic strain amplitude term. It is the plastic strain level that corresponds to one reversal for the curve fit line of plastic strain amplitude vs. reversals to failure.

Fatigue ductility exponent (c)

The exponent for the reversals to failure in the Manson-Coffin-Morrow relation for the plastic strain amplitude term. It is the slope of the line in the log-log fit of plastic strain amplitude vs. reversals to failure.

Fatigue life

The number of loading cycles of a given type that a given component may sustain before failure of a specified nature (for example, crack initiation, rupture) occurs.

Fatigue life for p% survival

An estimate of the fatigue life that p% of a given sample would attain under a given loading.

Fatigue notch factor(Kf)

The ratio of the endurance limit of an unnotched material to the endurance limit of the notched material.

Fatigue strength coefficient (σʹf)

The coefficient for the reversals to failure in the Manson-Coffin-Morrow relation for the elastic strain amplitude term that is divided by the modulus of elasticity. It is stress level that corresponds to one reversal for the curve fit line of stress amplitude vs. reversals to failure.

Fatigue strength exponent (b)

The exponent for the reversals to failure in the Manson-Coffin-Morrow relation for the elastic strain amplitude term. It is the slope of the line in the log- log fit of elastic strain amplitude vs. reversals to failure.

Filter width

The value of the hysteresis filter used in deleting small cycles from time histories. Cycles smaller than the filter width are omitted.

Finite element analysis (FEA)

A numerical technique commonly used to calculate the structural response of components and structures. In this process, the continuous structure is sub-divided into a discrete (finite) number of small pieces (elements).

Flow rule

In plasticity, the formula that relates the plastic strain increment tensor to the current stress state.

Fully reversed loading

A load history in which the maximum and minimum load have the same magnitude but opposite sign.

H

Hardening rule

In plasticity, the formula that relates the evolution of the yield surface (that is, motion) in stress space to material properties and the stress history.

High-cycle fatigue

The region of fatigue life that corresponds to a large number of cycles, typically greater than 105 cycles to failure.

Hysteresis filter

In filtering time histories, it is the value that determines the size of the cycles to omit from the time history.

I

IIW

International Institute of Welding.

Intermediate principal stress

Of the three principal stresses, the intermediate principal stress is the stress whose magnitude is less than (or equal to) the maximum principal stress but greater than (or equal to) the minimum principal stress.

L

Limit damage sum

The damage value associated with crack initiation of the component; often 1.0 when using Miner’s rule to accumulate damage.

Limit load ratio (Kp)

The ratio of the load when the component is fully plastic to the load when the component first yields.

Linear cumulative damage rule

A method of accumulating damage in which the damage calculated from each cycle is added directly.

Linearized SWT parameter

A method to convert the strain-life SWT damage parameter curve to a linear segment on a log-log SN-curve for use in stress-life analysis.

Load influence factor (c)

The quantity (c) that is multiplied by the load so that the local elastic stress results: for a uniaxial stress or for the multiaxial case.

Load histogram

A plot that indicates the number of cycles at different load amplitudes for a time history.

Load ratio (R)

The ratio between the minimum and the maximum value of a load cycle.

Load-notch strain relation

A formula or graphical plot that directly relates applied load (or nominal stress) to the local strain behavior at a notch.

Local stress-strain behavior

The stress-strain behavior at a stress concentrator or notch.

Low-cycle fatigue

The region of fatigue life that corresponds to a small number of cycles, typically less than 103 cycles to failure.

M

Manson-Coffin-Morrow relation

A damage parameter based on decomposing the elastic and plastic portions of the total strain amplitude and fitting them to experimental data.

Maximum principal stress

The principal stress with the largest magnitude.

Mean stress influence

The affect on the fatigue life resulting from the presence of mean stresses.

Memory model

A method to track material hysteresis response, or memory of past loading events.

Miner's rule

A damage accumulation method in which the damage fraction from each cycle is assumed to be additive in a linear manner.

Modal contribution factors

The coefficients of the mode shapes as determined in a modal analysis of the structure.

Modal superposition

The process of linearly adding mode shapes together (using modal contribution factors).

Morphology

Internal structure, used in this document in relation to grains or constituents in metals.

Multiaxial

A stress state with more than one non-zero stress components. If used in reference to loads, a time series with multiple channels.

Multiaxial fatigue

A fatigue process that is sensitive to the affects of multiaxial stress states.

N

Node

A point in a finite element model at which two or more elements are connected (sometimes referred to as a grid).

Nominal stress

A calculated stress value that is typically calculated based on elastic material behavior and for a reference area. Nominal stresses are usually used for convenience to normalize loads.

Non-local effects

Factors that affect the fatigue behavior of a component such as surface factors and stress gradients.

Non-proportional stresses

Stress component time histories at a point that different from each other by phase or other than by just a multiplicative factor are considered non-proportional (that is, anything other than proportional stresses).

Notch

See Stress concentration.

P

Peak

For a given load history, any point where the slope changes from positive to non-positive. For constant amplitude loading, the maximum load.

Proportional stresses

Stress component time histories at a point that differ only by a multiplicative factor are considered proportional.

Pseudo stress

A type of nominal stress determined by elastic calculations, even if the yield stress of the material is exceeded. The reference area used in the calculations is the same as if the material were elastic; therefore the pseudo stresses are the same as the actual stresses in a structure until the material yields.

Q

Quasi-static superposition

A linear combination of elastic stress states.

R

Rainflow counting

A numerical technique that identifies closed hysteresis loops in the stress-strain response of a material.

Rainflow matrix

A matrix representation of the number of occurrences of a cycle of a certain range with a particular mean load.

Rainflow projector

A method of resolving stress components to particular planes and rainflow counting on the planes.

Ramberg-Osgood relation

An equation used to relate total strain to stress by the use of Hooke’s law for the elastic portion of the strain and by a two-parameter log-log fit of plastic strain and stress for the plastic strain portion. For fatigue loading, the coefficients for the plastic strain portion are determined by cyclic load experiments.

Ratcheting

The directional accumulation of plastic strain due to cyclic loading in one direction with static or cyclic loading in another direction.

Ratcheting parameter

In plasticity, a parameter that controls the rate of plastic strain accumulation in the coupled stress- plastic strain relations.

Rate independent

A process that does not depend on the time scale used.

Residual stress

Stress in a component due to a manufacturing process such as welding or bolting.

Residue

The unmatched peaks or valleys left over after rainflow counting a time history.

Reversal

The occurrence in a time history where the sign of the slope (first derivative) changes sign (see: peak, valley).

S

SAE

Society of Automotive Engineers.

Seam weld

A joint made between two plates by a process of arc welding such as, for example, metal-inert-gas (MIG) or tungsten-inert-gas (TIG) welding.

Signed von Mises stress

A scalar stress calculated from the components of the stress tensor by using the von Mises equivalent stress formula (which is always positive valued) and giving it the same sign as the principal stress with the largest magnitude.

SN-curve

A plot, usually on log-log scales, that relates nominal stress or other quantity linearly related to load, to fatigue life, typically in cycles to crack initiation.

Spot weld

A joint made in two sheets of metal by the means of contact between two (typically cylindrical) electrodes. When current flows though the electrodes the contact area between the two sheets melts and then solidifies to bond the sheets.

Static failure

The failure of a material or structure by exceeding the ultimate or maximum stress of the material.

Strain

The change in length per reference length for a material.

Strain-controlled

A region of a material that has deformation or strain controlled to certain levels.

Strain-life approach

A fatigue analysis approach in which local strain is taken as the primary parameter to relate to fatigue life. This approach is able to account for the effects of local plasticity.

Stress

The intensity of force; for engineering stress it is the load divided by the original reference area.

Stress concentration

An area on a structure or component at which elevated stresses and strains occur, typically due to a change in local geometry from the surrounding area of the component.

Stress concentration factor (Kt)

A dimensionless value that is multiplied to the nominal stress (Kt) so that the local elastic stress results:

Stress gradient

The rate of change of stress with distance.

Stress-controlled

A region of material that is controlled by stresses or loads to certain levels.

Stress-life approach

A fatigue analysis approach in which stress is taken as the primary parameter to relate to fatigue life.

T

Tensile strength

Ultimate stress of a material in tension.

Time series

A or more time histories of load, strain, or other measured value.

True stress

Stresses calculated based on the instantaneous area in the strain configuration (that is, the area that changes as the material is loaded).

U

Ultimate stress

The highest stress level a material can sustain based on the engineering stress-strain curve.

Uniaxial stress

A state of stress in which a coordinate direction can be found in which there is only one non-zero stress component.

V

Valley

For a given load history, any point where the slope changes from negative to non-negative. For constant amplitude loading, the minimum load.

Variable amplitude loading

A load history in which the amplitude does not remain constant throughout the entire load history.

W

Weld nugget

The melted and solidified volume of material produced during the spot welding process.

Y

Yield criterion

In plasticity, a formula used to determine if the material’s yield stress has been exceeded.

Yield function

See yield criterion.

Yield stress

The stress level at which the material transitions from elastic deformation to elastic-plastic deformation.

Yield surface

In plasticity, a plot of the yield function in stress space.

Yielding

The behavior of a material after the yield stress has been reached or exceeded.

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