MECH 5390 – Fatigue Analysis for Extreme Environments

Dr. Calvin M. Stewart

Department of Mechanical Engineering

The University of Texas at El Paso

Objective

• To provide a historical context of the advancements in understand of fatigue in materials.

Fatigue - A Historical Context

• Introduction

• Versailles train crash

• 1840-1940

• Liberty Ship Disasters

• De Havilland Comet

• 1950-1990

• Summary

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 context of fatigue development.

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

Versailles train crash

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

Jean-Victor Poncelet

• 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

William John Macquorn Rankine

• Worked with railroad axles and other stress concentrations

• Participated in studies following the Versailles accident

• 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

August Wohler

• In Germany during the 1850s and 1860s August Wöhler performed many fatigue tests on railway axles. These are considered to be 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.

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

• Concluded that cyclic stress range ismore important than peak stress.

A. Wohler

1819-1914

August Wohler

Publication of Wöhler's fatigue experience, 1871

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

1962-1935

1a m

f US S

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

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

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

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

Liberty Ships of WWII

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)

Liberty Ships of WWII

• 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.

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.

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.

• Irwin introduced the stress intensity factor, which has been accepted as the basis of linear elastic fracture mechanics (LEFM) and of fatigue crack growth life predictions.

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

IK a

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.

Paul C. Paris

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

• 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)

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.

• 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.

B-1 Bomber

First flight 23 December 1974; 45 years ago

Introduction 1 October 1986

Status In Service

James Robert Rice

• In 1968, J. R. Rice developed the Path Independent Integral for the approximate analysis of strain concentration by notches and cracks.

• Encompasses both elastic and plastic energy of material.

• Large Plastic Zones (Ductile Fracture)J. R. Rice (1940 - )

i

i

duJ Wdy T ds

dx

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).

1970s

• In 1970 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.

• In 1970, Paris demonstrated that a threshold stress intensity factor could be obtained for which fatigue crack growth would not occur.

• 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.

Landes & Bagley and Nikbin et al., (1976)

• Two groups of researchers independently developed the time-dependent analogy of the J-integral, called the C*-integral for TDFM

• 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

• 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

Kamran Nikbin

1980s

• During the 1980sand 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.

Ashok Saxena

• In the 2000s, Saxena developed the Ct-parameter to characterize creep crack growth under conditions from small-scale creep to extensive creep.

• This methodology has been extended for issues of thermomechanical fatigue crack growth.

Ashok Saxena

On-going Fatigue Challenges

• Development of reliable methods to predict very low cycle fatigue (VLCF)

• Determination and development of models for the effect of alternating high temperature and mechanical fatigue (e.g., creep fatigue, thermomechanical fatigue)

• Development of models appropriate for variable amplitude fatigue crack growth

• Multistage Modeling of Fatigue and Fracture

Summary

• 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

Assignments

• Extra Credit

• Watch a documentary concerning one of the major engineering disasters discussed in this lecture or other recent disasters related to fatigue and fracture.

• Write a 300 word summary of what you learned.

Contact Information

Calvin M. StewartAssociate ProfessorDepartment of Mechanical EngineeringThe University of Texas at El Paso500 W. University Blvd.Suite A126El Paso, Texas 79968-0717

Email: cmstewart@utep.eduURL: http://me.utep.edu/cmstewart/Phone: 915-747-6179Fax: 915-747-5019

References

• https://en.wikipedia.org/wiki/Versailles_rail_accident

• https://asmedigitalcollection.asme.org/tribology/article/101/3/245/410136/Men-of-Tribology-John-Goodman-1862-1935-and-Albert

• https://www.mdpi.com/2078-1547/7/2/20/htm

• https://engineering.wustl.edu/news/Pages/Former-professor-Paris-law-of-engineering-lives-on-beyond-his-death.aspx