Crack Interaction With Microstructure-Ch 10

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Crack interaction with

microstructure

MSE 527



• Definition of J Integral Consider a nonlinear elastic body containing a crack,

• the J integral is defined as

• where is the strain energy density, is the traction vector, is an arbitrary contour around the tip of the crack, n is the unit vector normal to ; , , and u are the stress,strain, and displacement field, respectively.



Rice, J. R., 1968, showed that the J integral is a path-independent line integral and it represents the strain energy release rate of

nonlinear elastic materials:

where

is the potential energy, the strain energy U stored in the body

minus the work W done by external forces and A is the crack area.

The dimension of J is



For linear elastic materials, the J integral J is in fact the strain

energy release rate,























Schematic illustrations of advancing crack

interaction with microstructure.











Outline

• Experimental observations

• Crack interaction with grain boundaries

• Crack interaction with second phase andother interfaces

• Crack-tip stress-induced microstructure

modification • Outlook

• References



• Designing microstructure for damage tolerance requires a detailedunderstanding of how an advancing crack interacts with the microstructure(and sometimes modifies it locally) at multiple length scales.

• Advances in experimental techniques, such as the availability of well-controlled straining stages for optical and electron microscopes, the focusedion beam, electron backscattered diffraction, and nanoindentation, enableprobing at these length scales in real time and through interrupted tests.

• Simultaneously, increasing computational power coupled with newcomputational methods, such as finite element analysis (FEA) incorporatingcohesive elements at the continuum level, discrete dislocation methodologyat the mesoscopic level, and coupled atomistic/continuum methods thattransitions atomic level information to the mesoscopic level, have made itpossible to begin addressing these complex problems.

• By reviewing crack growth in a variety of multiphase alloys including steels,titanium aluminides, Mo alloys, and nanocrystalline metals, we demonstratevarious aspects of crack interaction with microstructure, and how theseproblems are being addressed through experiments and computations.



• Developing materials to withstand stress, often combined with an extremeenvironment, is central to many current technologies such as aircraftstructures, gas turbines, and lightweight engines for automotive and marineapplications.

• These materials derive their properties from a complex microstructure inwhich a matrix phase is combined with a distribution of a second phase(particles, rods, plates) to achieve a desirable mechanical response. Their properties can, in principle, be adjusted by tuning the microstructureappropriately.

• Properties such as modulus, flow stress, ductility, fracture toughness, andfatigue resistance can be optimized by engineering the grain size andtexture; the size, shape, and distribution of the second phase; and/or thechemistry, structure, and strength of the grain boundaries and interfacesbetween the matrix and second phase.

• A quantitative understanding of the relationship between thesemicrostructural variables and the performance of a material is critical toenhancing its performance.

• Progress has been slow, however, particularly in the area of understandingmicrostructural effects on failure resistance, which is determined by acomplex interaction of physical processes involving material features

ranging in size from 1 nm to 100 μm or more.



• Classical research has involved careful examination of the surfacemicrostructure of polished specimens by periodically interruptingmechanical tests and post-mortem examination of fractured surfaces.

• Significant knowledge of crack interaction with microstructure has beengained over the years; toughening and embrittlement mechanisms havebeen identified and understood[1] - [16], the former based on ideas such ascrack bridging by ductile ligaments, crack deflection by second-phaseparticles, microcrack formation, and stress-induced phase transformations(next slides), and the latter based on crack tip chemistry modification.

• With the enhancements in the capabilities of in situ scanning andtransmission electron microscopy (SEM and TEM, respectively) strainingstages[17] - [20], as well as the development of new experimentaltechniques over the past two decades, including focused ion beam (FIB) for

micromachining and characterization21,in situ

Auger spectroscopy22,electron backscattered diffraction (EBSD) coupled with selected areachanneling patterns (SACP)[23]- [25], Moire interferometry26, synchrotronX-ray tomography27, and neutron diffraction28, substantial progress isbeing made in furthering our understanding in this arena.





Schematic describing the crack plane misorientation across a grain

boundary in terms of the kink angle α (top), and the twist angle β

(bottom).



• Over the past two decades, there has been a significantamount of research on the mechanical behavior of intermetallic compounds with particular emphasis on thetitanium aluminides.

• Various research efforts have been devoted to

understanding the mechanisms controlling cracknucleation and growth in these materials[23] - [43].

• The microstructure of this alloy includes two phases, themajor phase TiAl and the minor phase Ti3Al, in alamellar morphology within each grain called a ‘colony’.

The microstructure is hierarchical in length scale;colonies are in the range 100 –500 μm, and individuallamellae are 100 –300 nm wide.

• An example of this microstructure is shown in the nextslide.





• The in situ testing of these specially configuredspecimens has enabled observation of the sequence inwhich damage evolves in the vicinity of these colonyboundaries and the mechanisms that contribute to thetoughness enhancement.

• These include multiple cracking in the participatinggrains (a), plastic deformation of the ligaments betweenthe cracks, crack bridging by ligaments (b), and thesubsequent translamellar rupture of these ligaments (c).

• In contrast, a kink misorientation across the grain

boundary – as opposed to a twist misorientation – isineffective in arresting a crack at the boundary, becausein this case the crack path in the two participating grainsis coplanar.



Effect of lamellar

misorientation across acolony boundary on damage

generated in the vicinity of

the boundary: (a) multiple

microcracking; (b) bridging

ligament at the boundary

caused by a large twistmisorientation during the test

as the crack crosses the

boundary; and (c) ligament

fracture later in the test,

accompanied by substantial

plastic deformation of the

ligament. Arrows indicate

direction of crack growth.



• If two grains are stacked on top of each other

and are in the way of an advancing crack, then a

large kink misorientation between the top and

bottom grains is effective at splitting the crack asopposed to a twist misorientation that produces

a coplanar crack path (as illustrated in a and b).

• Both kink and twist misorientations combine to

enhance participation of high-energy crack pathsin polycrystalline materials exhibiting

crystallographically preferred fracture paths.



When the two grains are stacked on top of each other (grains 2 and 3),

a twist misorientation (a) produces a coplanar crack in the two grains

whereas a kink misorientation (b) results in crack splitting.



(a) Microstructure ahead of agrowing crack tip in a Mo –Si –B alloy, obtained byinterrupting a 1400°C three-

point bend test at a loadingrate of 10−5 mm/s. Isolatedpatches of recrystallizedregions are observed; ahigher magnification imagefrom within one such patchconfirms creep cavities at

triple junctions.(b) An SEM image showing thecrack path and finerecrystallized grains (3 –5 μm)on either sides of the crack;the white arrow illustratesgrain boundary relief fromsliding.

(c) Even finer grains (1 –2 μm)are observed ahead of themain crack and evidence isseen for linking of creepcavities to generate severalmicron-long microcracks.



Reference

• Sharvan Kumar and William A. Curtin, Crack interaction with

microstructure, Materials Today, Sept 2007, Vol. 10, Number 9.

www.materialstoday.com

http://www.materialstoday.com/

http://www.materialstoday.com/

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Crack Interaction With Microstructure-Ch 10