Historical Perspective

For Extreme Environments

Fatigue Analysis

Historical PerspectivePresented by

Calvin M. Stewart, PhD

MECH 5390-6390

Fall 2020

Outline

• Societal Aspects

• Historical Perspective

• Recent Advances

Societal AspectsConnotation, Etymology, Terminology

Connotation

• Society's perspective of fatigue is of extreme tiredness resulting from mental or physical exertion or illness.

• Tiredness

• Exhaustion

• weariness

• Drowsiness

• Often arbitrated to overwork.

Etymology

• The word fatigue originated from the Latin expression fatigare which means “to tire”.

• Although commonly associated with physical and mental weariness in people, the word fatigue has also become a widely accepted terminology in engineering vocabulary for the damage and failure of materials under cyclic loads.

Terminology

• A descriptive definition of fatigue is found in the report entitled General Principles for Fatigue Testing of Metals which was publishedin 1964 by the International Organization for Standardization (ISO) in Geneva.

• In this report, fatigue is defined as a term which “applies to changes in properties which can occur in metallics material due to the repeated application of stresses or strain, although usually this term applies specifically to those changes which lead to cracking or failure.”

• ISO/R 373:1964 – Published in August 1, 1964

Historical PerspectiveThe nineteenth century onward..

Introduction

• Fatigue of materials is still only partly understood.

• What we do know has been developed step by step and has become quite complex.

• To gain a general understanding, it is best to start with a brief historical perspective of fatigue developments.

• While there is considerable evidence of ancient knowledge concerning fatigue failure, most our current knowledge originates from Western knowledge gain during and after the nineteenth century.

Nineteenth Century (1800-1900)

Albert (1829)

Poncelet (1839)

Rankine (1843)

Wohler (1860s)

Bauschinger (1886)

Wilhelm Albert

• In 1829, studied the failure of iron mine hoist chains arising from repeated small loadings, the first recorded account of metal fatigue.

• He built a machine which repeatedly loaded a chain.

• His finding that fatigue was not associated with an accidental overload, but was dependent on load and the number of repeated load cycles.

https://en.wikipedia.org/wiki/Wilhelm_Albert_(engineer)

Wilhelm Albert

1787-1846

Jean-Victor Poncelet

• In 1839, coined the term fatigue

• Used the term to refer to “tired” metals that had been worn down via cyclic loading

• Studied waterwheels and turbines

J.-V. Poncelet

1788-1867

Versailles train crash

The first major impact of failures due to repeated stresses involved the railway industry in the 1840s,where railroad axles failed regularly at shoulders.

On May 8th, 1842 a train returning to Paris derailed at Meudon after the leading locomotive broke an axle, and the carriages behind piled into it and caught fire. It was the first French railway accident and the deadliest in the world at the time, causing between 52 and 200 deaths.

Versailles train crash

• Caused by fatigue failure of a locomotive axle at a sharp cornered shoulder

• Notes:

• Occurred on May 8th, 1842

• Carriages behind piled into the wrecked engines and caught fire

• Problem solved with better axles designs

William John Macquorn Rankine

• Worked with railroad axles and other stress concentrations

• Participated studies following the Versailles accident

• In 1843, recognized the distinctions between fatigue cracks from other cracks

• Recognized the importance of stress concentrations in his investigation of railroad axle failures

W. J. M. Rankine (1820-1872)MAX

NOM

SCF

=

August Wohler

• In Germany during the 1850s and 1860s August Wöhler performed many fatigue tests on railway axles. These are the first systematic investigation of fatigue.

• He showed from stress versus life (S-N) diagrams how fatigue life decreased with higher stress amplitudes and that below a certain stress amplitude, the test specimens did not fracture.

• Introduced the concept of the S-N diagram & the fatigue limit.

• Concluded that cyclic stress range is more important than peak stress.

A. Wohler

1819-1914

August Wohler

Publication of Wöhler's fatigue experience, 1871

Johann Bauschinger

• Bauschinger in 1886 showed the yield strength in tension or compression was reduced after applying a load of the opposite sign that caused inelastic deformation.

• This was the first indication that one single reversal of inelastic strain could change the stress-strain behavior of metals.

• Discovered fatigue was associated with plastic strains in metals

• Developed a mirror extensometer capable of measuring one microstrain

• Essentially discovered cyclic strain hardening and softening

J. Bauschinger

1834 - 1893

Bauschinger Effect

• After a certain amount of plastic deformation in tension or compression, the material yields at a lower stress when the direction of loading is reversed than for continued forward deformation

Compression and Reversal

Twentieth Century A (1900-1940)

Ewing & Humfrey (1903)

Goodman (1904)

Basquin (1910)

Griffith (1920)

Palmgren (1924)

Almen (1930s)

Nueber (1937)

Ewings and Humphries

• In the early 1900s Ewing and Humfrey used the optical microscope to pursue the study of fatigue mechanisms. Localized slip lines and slip bands leading to the formation of microcracks were observed.

• Using micrographs, they determined fatigue crack initiation is related to the evolution of the crystal structure

• Discovered the progression of slip bands and slip steps formed surface cracks

Microstructure after

1K, 4K, 10K, and 40K

Reversals

John Goodman

• Gerber along with Goodman investigated the influence of mean stress and proposed simplified theories concerning mean stresses.

• Goodman published the widely used textbook Mechanics Applied to Engineering (1st ed., 1904; 8th ed., 1914), in which he said, “it is assumed that the varying loads applied to test bars by Wohler and others produce the same effects as suddenly applied loads.”

• This statement has been modified for application to actual behavior and gives what is called the “modified Goodman diagram” for mean stress.

John Goodman

1862-1935

1a m

f US S

+ =

Basquin and Gough

• Basquin in 1910 showed that alternating stress amplitude versus number of cycles to failure (S-N) in the finite life region could be represented as a log-log linear relationship.

• Resulted in Basquin’s Equation

• In the 1920s Gough and associates contributed heavily to the understanding of fatigue mechanisms. They also showed the combined effects of bending and torsion (multiaxial fatigue).

( )B

a fS A N= ( ) ( ) ( )log log loga fS A B N= + or

O. H. Basquin, “The Exponential Law of Endurance Tests,” American Society for Testing and Materials Proceedings, Vol. 10, 1910, pp. 625-630.

Alan A. Griffith

• In 1920 Griffith published the results of his theoretical calculations and experiments on brittle fracture using glass.

• He found the strength of glass depended on the size of microscopic cracks.

• Found that

• By this classical pioneering work Griffith become the “early father” of linear elastic fracture mechanics (LEFM).

Alan A. Griffith (1893-1963)

constanta =

Palmgren, McAdam, and Haigh

• In 1924 Palmgren suggested a linear cumulative damage model for variable amplitude loading.

• McAdam in the 1920s completed extensive corrosion fatigue studies where he showed significant degradation of fatigue resistance in various water solutions.

• In 1929/30 Haigh presented his rational explanation of fatigue when notches are present. He used concepts of notch strain analysis and residual stresses that were later more fully developed by others.

Almen

• During the 1930s an important practical advance was achieved by the introduction of shot peening in the automobile industry.

• Where fatigue failures of springs and axles had been common, they then became rare.

• Almen correctly explained the spectacular improvements by compressive residual stresses produced in the surface layers of peened parts and promoted the use of peening and other processes that produce beneficial residual stresses.

Heinz Neuber

• In 1937 Neuber introduced stress gradient effects at notches and the elementary block concept, which states that the average stress over a small volume at the root of the notch is more important than the peak stress at the notch.

• Generally, in fatigue some metals are less sensitivity to the presences of a notch.

• Resulted in Nueber’s constant, q for Fatigue Notch Sensitivity

Heinz Neuber (1906-1989)

1

1q

p r=

+( )1 1f tK q K= + −1 f tK K

Twentieth Century B (1940-2000)

Miner (1945)

Irwin (1950s)

Coffin and

Manson (1960s)

Paris (1961)

Rice (1968)

Landes, Bagley (1970s)

Saxena (1986)

WWII Liberty Ships

During World War II many brittle fractures in welded tankers and Liberty ships motivated substantial efforts concerning preexisting defects and cracks and the influence of stress concentrations.

The S.S. Schenechtady as she appeared on the morning of Jan. 17, 1943, after suddenly and unexpectedly cracking in half for no apparent reason while moored at the fitting dock at Swan Island. (Image: U.S. GPO)

WWII Liberty Ships

• Early ships suffered hull and deck cracks

• Number of ships that broke in half: 19

• Failure mechanism due to brittle crack growth at stress concentration

• Temperature of the Steel submerged in water fell below the Brittle to Ductile Transition Temperature

Liberty Ship Schenectady in the port of Portland fractured

from deck to keel.

Miner and ASTM E-09

• In 1945 Miner formulated a linear cumulative fatigue damage criterion suggested by Palmgren in 1924. This linear fatigue damage criterion is now recognized as the Palmgren-Miner rule.

• The formation of ASTM committee E-09 on fatigue in 1946 provided a forum for fatigue testing standards and research.

George Rankin Irwin

• Born in El Paso, Texas

• The fracture mechanics research group at the Naval Research Laboratory was led by Dr. Irwin

• In 1948, Irwin extended the work of Griffith by extending theories to ductile materials by including the energy dissipated by local plastic flow

• In 1956, developed the energy release rate concept and leveraged Westergaardssolution to identify the Stress Intensity Factors

Irwin (1907-1998)cK K

Ushering the Era of Modern Fracture Mechanics

George R. Irwin (1907-1998)

• In 1945, independently proposed the same

modification to Griffith’s theory as Orowan

• Generalized the Griffith’s theory for cracked bodies

of arbitrary shape and loading for Mode I cracks

• In 1956, used Westergaard’s analysis to introduce

the concept of stress intensity parameter, K, as the

amplitude of the crack tip stress field

• In 1957, derived the relationship between the

Griffith’s Crack Extension Force and K establishing

K based Fracture Mechanics on a very firm footing

• Estimated the size of the plastic zone and

proposed a method to account for small-scale-

yielding (SSY)

• Derived the relationship between crack tip opening

displacement and K

• ASTM and ICF have medals named after Dr. Irwin

• De Havilland Comet• The Comet, the first jet propelled passenger airplane, started service in May

1952 after more than 300 hours of flight tests. • Three plane crashes caused by repeated pressurization of the metallic fuselage

skin at sharp corners near windows

De Havilland Comet

• After exhaustive investigations it was concluded that the accidents were caused by fatigue failure of the pressurized cabin.

• All Comet aircraft of this type were taken out of service and additional attention was focused on airframe fatigue design.

• Shortly after this, the first emphasis on fail-safe design in aircraft rather than safe-life gathered momentum in the USA. This would place much more attention on maintenance and inspection.

Paul C. Paris

• In 1955 with working as a faculty associate for Boeing he investigated the “De Havilland Comet” Failures

• In 1961, Discovered that the Fatigue Crack Growth Rate is related to the stress intensity factor range

• Resulted in Paris Law

( )mda

C KdN

= Paul C Paris (1930-2017)

• Extended the use of K, ∆K, for characterizing Fatigue Crack Growth, known as the Paris-Law

• Proposed the concept of threshold value of ∆K and the effects of load ratio, R.

• Envisioned the relationship between K and the environment assisted rate of crack growth

• Led the adoption of damage tolerant approach to design in aerospace and power generation industries

• Collaborated with George Irwin and Hiroshi Tada to produce the first compendium of K solutions

• Made seminal contributions to the development of elastic-plastic fracture mechanics

• ICF established the Paul Paris Gold Medal to memorialize his contributions and impact on the field

Paul C. Paris

1950s

• Major contributions to the subject of fatigue in the 1950s included the introduction of closed-loop servohydraulic test systems. This allowed better simulation of load histories on specimens, components, and total mechanical systems.

• Electron microscopy opened new horizons to better understanding of basic fatigue mechanisms.

• The Weibull distribution provided statistical distributions for probabilistic fatigue life testing and analysis.

Coffin and Manson

• In the early 1960s Coffin and Manson independently and simultaneously reports linkages between low cycle fatigue and cyclic plastic strain range

• Coffin considered constrained thermal fatigue of power plant components

• Manson considered isothermal fatigue of ground vehicles

ASTM E-24 to ASTM E-08

• ASTM committee E-24 on fracture testing was formed in 1964. This committee has contributed significantly to the field of fracture mechanics and fatigue crack growth.

• ASTM Committee E08 on Fatigue and Fracture was formed in 1993 as a result of a merger between Committees E09 and E24. E08 meets twice a year, in May and November, with about 75 members attending two days of technical meetings and one or two days of workshops and symposia. The Committee has approximately 500 members and has jurisdiction of 32 standards, published in the Annual Book of ASTM Standards, Volume 3.01.

1960s

• Schijve in the early 1960s emphasized variable amplitude fatigue crack growth testing in aircraft along with the importance of tensile overloads in the presence of cracks that can cause significant fatigue crack growth retardation.

• In 1967, the Silver Bridge Disaster occur which uncovered the need for fatigue resistance design in civil infrastructure

Silver Bridge Disaster

• Opened in 1928

• Collapsed on December 15, 1967

• Resulted in the deaths of 46 people.

• Failure due to Stress Corrosion Cracking and Fretting Wear (Contact Fatigue)

Silver Bridge Disaster

• An extensive investigation of the collapse showed that a cleavage fracture in an eyebarcaused by the growth of a flaw to critical size was responsible for the collapse.

• The initial flaw was due to fatigue, stress corrosion cracking, and/or corrosion fatigue.

• This failure has had a profound influence on subsequent design requirements established by AASHTO(American Association of State and Highway and Transportation Officials).

Late 1960s

• In the late 1960s the catastrophic crashes of F-111 aircraft were attributed to brittle fracture of members containing pre-existing flaws.

• These failures, along with fatigue problems in other U.S. Air Force planes, laid the groundwork for the use of fracture mechanics concepts in the B-1 Bomber development program of the 1970s.

• This program included fatigue crack growth life considerations based on a pre-established detectable initial crack size.

B-1 Bomber

First flight 23 December 1974; 45 years ago

Introduction 1 October 1986

Status In Service

MIL SPEC

• In 1974 the U.S. Air Force issued Mil A-83444, which defines damage tolerance requirements for the design of new military aircraft. This brought out an increased need for improved quantitative non-destructive inspection capability as an integral part of the damage tolerance requirements.

1970s

• Elber brought out the importance of crack closure on fatigue crack growth. The crack closure model is commonly used in current fatigue crack growth calculations.

• Paris demonstrated that a threshold stress intensity factor could be obtained for which fatigue crack growth would not occur.

• Rice introduced the J-Integral for Elastic-Plastic Fracture Mechanics which encompasses both the elastic and plastic energy of fatigue and fracture.

James R. Rice

• In 1968, Rice considered the potential energy changes involved in crack growth in non-linear elastic material.

• Rice derived a fracture parameter called the J-integral, a contour integral that can be evaluated along any arbitrary path enclosing the crack tip.

• He showed J to be equal to the energy release rate for a crack in non-linear elastic material, analogous to G for linear elastic material.

J. R. Rice (1940 - )

Elastic-Plastic Fracture Mechanics

John D. Landes (1942- )

James A. Begley (1940 - )

Landes and Begley

• J-Integral as a Fracture Criterion, 1972

Landes and Begley

• Landes and Begley proposed the use of a J-integral like parameter, C*-integral, for characterizing creep crack growth rates at elevated temperatures under steady-state creep conditions.

• Three groups independently developed C*• Landes JD, Begley JA. A fracture mechanics approach to creep

crack growth. In: Mechanics of Crack Growth. ASTM STP 590. Philadelphia, 1976. p. 128–148

• Ohji, K., Ogura, K., and Kubo, S., Creep crack propagation rate in SUS 304 stainless steel and interpretation in terms of modified J-integral. Transactions, Japanese Society of MechanicalEngineers, 42, 1976, 350–358

• Nikbin KM, Webster GA, Turner CE. Relevance of nonlinear fracture mechanics to creep cracking. In: Crack and Fracture. ASTM STP 601. Philadelphia, 1976. p. 47–62

John D. Landes (1942- )

James A. Begley (1940 - )

Ashok Saxena

• In the 1980’s, Saxena applied the C*-integral to experimentally characterize creep crack growth of alloys subject to elevated temperatures.

• In 1986, developed the C(t)-parameter for characterizing the non-linear creep crack growth behavior over a wide range of creep and creep-fatigue conditions (small scale to steady-state creep).

• Under steady-state creep conditions, C(t) is shown to reduce to the familiar C*-integral.

Ashok Saxena

1980s

• During the 1980s and 1990smany researchers were investigating the complex problem of multiaxial fatigue.

• The small crack problem was noted during this time period and many workers attempted to understand the behavior. The small crack problem is important, since these crack conditions grew faster than longer cracks based upon the same driving force.

• Interest in fatigue of electronic materials increased along with significant research in thermo-mechanical fatigue.

1980s

• Composite materials based on polymer, metal, and ceramic matrices were being developed for many different industries.

• The largest accomplishments and usage involved polymer and metal matrix composites.

• These were heavily motivated by the aerospace industry, but also involved other industries.

• During this time period many complex expensive aircraft components designed using safe-life design concepts were routinely being retired with potential additional safe usage (Fatigue of Aging Structures).

• This created a need to determine a retirement for cause policy.• From a fatigue standpoint this meant significant investigation and application of non-

destructive inspection and fracture mechanics.

1990s

• Also during the 1980s and 1990s significant changes in many aspects of fatigue design were attributed to advances in computer technology.

• This included software for different fatigue life (durability) models and in the ability to simulate real loadings under variable amplitude conditions with specimens, components, or full-scale structures.

• This significantly brought more field testing into the laboratory.• Integrated computer aided engineering, CAE, involving dynamic simulation,

finite element analysis and life prediction models motivated the idea of restricting testing to component durability rather than for development.

• Increased digital prototyping with less testing has become a goal for the 21stcentury fatigue design.

Recent Advances

Recent Advances

Generally recent advances and challenges in fracture mechanics have been concerned with problems of Multi-Physics where one or more physical field enhances or degrades the fracture resistance of a volume of matter.

Recent Work inMultiscale ModelingAtomistic FracturePeridynamicsThermoMechanical CrackingAdditive Manufactured MaterialsChemically-Assisted Cracking

Multiscale Modeling Concept

Atomistic Aspects of Fracture

https://link.springer.com/article/10.1007/s10704-015-9988-2

Chemical aspects of fracture and sub-critical crack growth

Chemically induced dynamical crack deflection

Peridynamics

• Peridynamics is a nonlocal formulation of solid mechanics capable of unguided modelling of crack initiation, propagation and fracture.

• Peridynamics is based upon integral equations, in contrast with Continuum Mechanics which is based on partial differential equations, thereby avoiding spatial derivatives, which are not defined at discontinuities, such as crack surfaces.

• A nonlocal J-integral has been derived for peridynamic modelling.

https://link.springer.com/article/10.1007/s10704-019-00351-3

ThermoMechanical Fatigue and Fracture

• Thermomechanical Fatigue (TMF) and Fracture is the combination of thermal and mechanical loads that contribute to fracture.

• TMF can induce oxidation and corrosion within a material which can enhance or degrade fracture resistance.

• In-Phase | Out-of-Phase• LCF | HCF

ThermoMechanical

https://link.springer.com/article/10.1007/s10704-015-9994-4

Additive Manufactured Materials

Tensile test results for 316L stainless steel

show reasonable consistency in yield strength,

ultimate strength, and modulus (unloading

lines on left), but there is significant variability

in strain-to-failure. Sandia is working to

understand and control this variability.

https://www.sandia.gov/am/materials_reliability/process/index.html

Additive Manufactured Materials

Crystal Elasticity simulations of LENS-built cylinders.

X-Ray Tomography of AM Specimen

Fatigue Journals

• International Journal of Fatigue

• Fatigue and Fracture of Engineering Materials & Structures

• Engineering Failure Analysis

• Engineering Fracture Mechanics

• Materials Science and Engineering

• Journal of Mechanical Sciences

Summary➢ The history of fatigue and fracture are intimately linked because fatigue

ultimately leads to the fracture in structure and materials.

➢ The mathematically framework of fatigue and fracture are the same with one distincition.➢ Fatigue is the accumulation of defects during cycling.

➢ Fracture is the point at which those defects exceed the capacity of the material and structure to resist them.

➢ The advances in designing against fatigue failure are a culmination of…➢ Research in the areas of materials, mechanical design, and advances in experimental and

computational techniques

➢ Accidents that promote deeper analysis of a specific phenomenon

➢ Development of new technology

Homework 2

• Problem 1 – Read a “most downloaded” article from one of the fatigue journals listed in this lecture.

• Develop 3-5 slides that summarize the recent advances described in the journal article.

• Record a short presentation (<5 minutes) where you go over the slides and explain the findings in the paper.

• Submit both the .pptx file and a link to you video on Microsoft Teams.

Technical Support• How to Record a Presentation• How to Save a Video• How to Upload a Video to YouTube

References

• Stephens, R.I., Fatemi, A., Stephens, R.R., Fuchs, H.O., 2000, Metal Fatigue in Engineering 2nd Edition, Wiley.

• Suresh, S., 1998, Fatigue of Materials 2nd Edition, Cambridge University Press.

• Bannantine, J., 1989, Fundamentals of Metal Fatigue Analysis, Pearson.

• Schijve, J., 2008, Fatigue of Structure and Materials 2nd Edition, Springer.

CONTACT INFORMATION

Calvin M. Stewart

Associate Professor

Department of Mechanical Engineering

The University of Texas at El Paso

500 W. University Ave, Suite A126, El Paso, TX 79968-0521

Ph: 915-747-6179

cmstewart@utep.edu

me.utep.edu/cmstewart/