Fracture Mechanics

Historical Prospective Historical Prospective Presented by Calvin M. Stewart, PhD MECH 5390-6390 Fall 2020 Outline

• Societal Aspects • Historical Prospective • Recent Advances

YouTube Videos https://www.youtube.com/playlist?list=PLvC7PjgHRlu6L1tgLEpOXabSpr5uhhsWY Societal Aspects Prospective and Connotation Perspectives of Fracture Connotation of Fracture

• Society’s perspective of fracture is that the cracked object(s) is • preventable • harmful • irreparable Historical Prospective Arrowheads, Stone Cutting, Materials, the Industrial Revolution onwards Arrowhead Making

• Fracture Mechanics has been exploited by humans from time immemorable.

• The earliest humans exploited fracture mechanics to craft Arrowheads from brittle rock materials.

• The earliest evidence is 64,000 years ago from Sibudu Cave in South Africa Stone Cutting

• Egyptians became masters of fracture mechanics exploiting the brittle fracture of rocks to construct massive structures. (3000 BC>) Giza pyramid complex One of the Seven Wonders of the Ancient World • Knowledge from the Ancient Africa spread into Europe through war, conflict and conquest, resulting in many of the structures admired by West Society such as the roman Colosseum Materials

• The primary construction materials prior to the nineteenth century were timber, stone, brick and mortar; only the latter three materials were usually practical for large structures such as cathedrals, because trees of sufficient size for support beams were rare.

• Consequently, pre-Industrial Revolution structures were usually designed to be loaded in compression. Industrial Revolution

• With the Industrial Revolution came mass production of iron and steel. • These ductile materials removed the earlier restrictions on tensile designs. • Occasionally, steel structures in tensile failed well below the anticipate tensile strength. • Failures in railway equipment, boilers, and tanks due to a lack of understanding the Fracture Mechanics Contributors to Fracture

In the nineteenth century, the quantitative connection between fracture stress and flaw size started to be explored.

Rankine Griffith Paris Rice Saxena (1842) (1920s) (1961) (1960s) (1990)

Inglis Irwin Wells Nikbin (1913) (1950s) (1961) (1976) 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 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) SCF = MAX  NOM ASTM formed

• In 1898, Charles Benjamin Dudley investigated problems with the chemistry of materials used by the Pennsylvania Railroad • He later went on to found the ASTM, a committee-based organization focused on industrial progress • Much later, the committee on fracture was formed in the 1950’s Sir Charles Edward (C.E.) Inglis

• In 1913, Inglis considered the fracture behavior of thin glass plates with elliptical holes. • Derived the distribution of elastic stress field in the front of the elliptical notch • Determined that the ratio of dimensions a to b plays a great role in determining the stress at point A.

C.E. Inglis (1875-1952) H.M. Westergaard

• Using a complex variables approach derived the stress distribution in front of an atomically sharp crack, the worst case, recognizing the stress singularity at the crack tip

퐾 휎푖푗 = 푓푖푗 휃 2휋푟 Westergaard (1888-1950) Alan Arnold Griffith

• In 1920s, he extended the work of Inglis to the unstable propagation of a crack in linear-elastic brittle solids. • Invoking the first law of thermodynamics, he found that A flaw becomes unstable, and thus fracture occurs, when the strain energy change that results from an increment of crack growth is sufficient to overcome the surface energy of the material.

• Origins of the Energy Approach!!! GG c • Only applicable to Brittle Solids, Not Ductile Metals

A. A. Griffith (1893-1963) WWII Liberty Ships

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)

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. 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. 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 Westergaards solution to identify the Stress Intensity Factors KK c Irwin (1907-1998) Ushering the Era of Modern Fracture Mechanics • 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 George R. Irwin (1907-1998) 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. Alan Arthur Wells

• In 1956, Wells used fracture mechanics to show that the fuselage failures in several Comet jet aircraft resulted from fatigue cracks reaching a critical size. • In 1961, in parrallel with Irwin, Dugdale, and Barenblatt, developed a correction for crack tip plasticity • First proposed using Crack Tip Open Displacement (CTOD) as an alternative fracture criterion when significant plasticity proceeds failure. Wells (1924-2005) 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

da m =CK( ) dN Paul C Paris (1930-2017) Paul C. Paris

• 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 ASTM Committees

• 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. ASTM Test Methods for LEFM Test Method and Year of First Leaders Publication of Select Standards ASTM E-399 (1964): Measurement Edward T. Wessel, William Brown, of Plane Strain Fracture Toughness John Srawley, George Irwin, Paul Paris, J.G. Kaufman ASTM E-561 (1968): Measurement Donald McCabe, George Irwin of Crack Growth Resistance Curve, R- Curve ASTM E-647 (1978): Measurement William G. Clark, Stephen Hudak, of Fatigue Crack Growth Rate Robert Bucci, Ashok Saxena, ASTM E-1681 (1989): Robert P. Wei, Steve Novak, Al Van Measurement of Environment DerSluys, Stephen J. Hudak Assisted Cracking Fracture Conferences

• International Conference on Fracture (ICF) started in 1965 • European Conference on Fracture (ECF) started in 1976 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 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 W. Hutchinson

• Author of the paper on the HRR singularity (1968) • Co-authored a paper with his PhD student C. Fong Shih on the relationship between J-integral and the crack tip opening displacement, (CTOD) (1975) • Co-authored a seminal paper with Paul Paris on J-controlled stable crack growth during ductile fracture • Contributed several papers to the understanding of interface fracture JW. Hutchinson (1939- ) 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 and Begley

• J-Integral as a Fracture Criterion, 1972

John D. Landes (1942- )

James A. Begley (1940 - ) 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. John D. Landes (1942- ) • 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 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 ASTM Test Method for EPFM/TDFM

First Publication Dates of Select ASTM Leaders Standards ASTM Standard E1820 on Fracture John Landes, Jim Toughness Testing (1998) Joyce, Richard Link, • ASTM Standard E813 on the John Gudas Measurement of 퐽퐼푐 (1981) • ASTM Standard E1152 on the Measurement of 퐽푅 −Curve (1986) ASTM Standard E1457 on Creep Crack A. Saxena, Kamran Growth Measurement (1992) Nikbin ASTM Standard E2760 on Creep-Fatigue A. Saxena, Santosh Crack Growth (2010) Narasimhachary 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 in Fracture Recent Advances Multiscale Modeling Concept

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 in Multiscale Modeling Atomistic Fracture Peridynamics ThermoMechanical Cracking Additive Manufactured Materials Chemically-Assisted Cracking Atomistic Aspects of Fracture

Chemical aspects of fracture and sub-critical crack growth

Chemically induced dynamical crack deflection

https://link.springer.com/article/10.1007/s10704-015-9988-2 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 X-Ray Tomography of AM Specimen cylinders. Fracture Journals

• International Journal of Fracture • Engineering Fracture Mechanics • Fatigue and Fracture of Engineering Materials & Structures • Engineering Failure Analysis • Materials Science and Engineering Fracture Texts • FIU Bridge Failure March 15, 2018 • Ignore the Historical Prospective of Fracture • We are Doomed to Repeat Failures !!! Summary

➢ The development of Fracture Mechanics started from the earliest days of humanity and continue into modern times. ➢ Neglecting Fracture Mechanics in Design is a common source of failure. ➢ New developments in Fracture Mechanics tend to be spurred on by new technology and major engineering disasters. ➢ Recent advances in Fracture Mechanics generally focus on Multi-Physics Problems. Homework 2

• 12-point Font, New Times Roman, double spaced. • Obtain an original paper from one of the Founders of Fracture Mechanics listed in this lecture. Copy the abstract and a key equation, figure, and/or table from the paper. Write a critical review and analysis of the paper. Describe the impact the paper had on the field of Fracture Mechanics. (250 words) • Perform literature review and investigate the Sandia Fracture challenge. Describe the purpose and objectives of the three challenges. Why is the challenge important? How can the research impact society? What innovate technologies and tools were employed to generated the experimental data and simulate the AM material processing and performance? What are the current outcomes of the challenge? (500 words) • Word limited does not include the references, equations, or figures.

• Optional - Register as a ASTM Student member References

• Janssen, M., Zuidema, J., and Wanhill, R., 2005, Fracture Mechanics, 2nd Edition, Spon Press • Anderson, T. L., 2005, Fracture Mechanics: Fundamentals and Applications, CRC Press. • Sanford, R.J., Principles of Fracture Mechanics, Prentice Hall • Hertzberg, R. W., Vinci, R. P., and Hertzberg, J. L., Deformation and Fracture Mechanics of Engineering Materials, 5th Edition, Wiley. • https://www.fracturemechanics.org/ Calvin M. Stewart Associate Professor Department of Mechanical Engineering The University of Texas at El Paso CONTACT 500 W. University Ave, Suite A126, El INFORMATION Paso, TX 79968-0521 Ph: 915-747-6179 [email protected] me.utep.edu/cmstewart/