Crack Behavior

1. Crack Behavior MSE 527

2. 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.

8. Crack interaction with microstructure MSE 527

16. Schematic illustrations of advancing crack interaction with microstructure.

21. Outline Experimental observations Crack interaction with grain boundaries Crack interaction with second phase and other interfaces Crack-tip stress-induced microstructure modification Outlook References

22. Designing microstructure for damage tolerance requires a detailed understanding 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 focused ion beam, electron backscattered diffraction, and nanoindentation, enable probing at these length scales in real time and through interrupted tests. Simultaneously, increasing computational power coupled with new computational methods, such as finite element analysis (FEA) incorporating cohesive elements at the continuum level, discrete dislocation methodology at the mesoscopic level, and coupled atomistic/continuum methods that transitions atomic level information to the mesoscopic level, have made it possible 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 demonstrate various aspects of crack interaction with microstructure, and how these problems are being addressed through experiments and computations.

23. Developing materials to withstand stress, often combined with an extreme environment, is central to many current technologies such as aircraft structures, gas turbines, and lightweight engines for automotive and marine applications. These materials derive their properties from a complex microstructure in which 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 microstructure appropriately. Properties such as modulus, flow stress, ductility, fracture toughness, and fatigue resistance can be optimized by engineering the grain size and texture; the size, shape, and distribution of the second phase; and/or the chemistry, structure, and strength of the grain boundaries and interfaces between the matrix and second phase. A quantitative understanding of the relationship between these microstructural variables and the performance of a material is critical to enhancing its performance. Progress has been slow, however, particularly in the area of understanding microstructural effects on failure resistance, which is determined by a complex interaction of physical processes involving material features ranging in size from 1 nm to 100 µm or more.

24. Classical research has involved careful examination of the surface microstructure of polished specimens by periodically interrupting mechanical tests and post-mortem examination of fractured surfaces. Significant knowledge of crack interaction with microstructure has been gained over the years; toughening and embrittlement mechanisms have been identified and understood[1] - [16], the former based on ideas such as crack bridging by ductile ligaments, crack deflection by second-phase particles, 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 and transmission electron microscopy (SEM and TEM, respectively) straining stages[17] - [20], as well as the development of new experimental techniques 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 area channeling patterns (SACP)[23]- [25], Moire interferometry26, synchrotron X-ray tomography27, and neutron diffraction28, substantial progress is being made in furthering our understanding in this arena.

25. Crack interaction with grain boundaries Several polycrystalline materials exhibit preferred crack paths within a grain that could be a crystallographic cleavage plane or an interphase interface. When such a crack arrives at a grain boundary, the change in orientation of this preferred path in the adjacent grain serves to arrest the crack and enhance cleavage-cracking resistance. This orientation change can be quantified through a tilt and a twist misorientation (next slide). As an example, Argon and Qiao[32], [33] and [34] have examined how cleavage cracks break through specific grain boundaries with known tilt and twist misorientations in Fe-3 wt.% Si bicrystals. They conclude that twist misorientation has a more profound influence on fracture resistance than the tilt misorientation. A similar conclusion has been reached by Zhai et al.35 in a study on fatigue crack propagation in the Al–Li alloy 8090. They argue that the area between the traces on the grain boundary plane of the crack planes across the boundary has to be fractured for the crack to propagate through the boundary, which presents resistance to crack growth. These studies were, however, conducted ex situ and the mechanisms and evolution of events were inferred from examination of the deformed/fractured specimens subsequently.

26. Schematic describing the crack plane misorientation across a grain boundary in terms of the kink angle a (top), and the twist angle ß (bottom).

27. Over the past two decades, there has been a significant amount of research on the mechanical behavior of intermetallic compounds with particular emphasis on the titanium aluminides. Various research efforts have been devoted to understanding the mechanisms controlling crack nucleation and growth in these materials[23] - [43]. The microstructure of this alloy includes two phases, the major phase TiAl and the minor phase Ti3Al, in a lamellar morphology within each grain called a ‘colony’. The microstructure is hierarchical in length scale; colonies are in the range 100–500 µm, and individual lamellae are 100–300 nm wide. An example of this microstructure is shown in the next slide.

28. Microstructure of a binary lamellar Ti-46% Al alloy showing (a) 500 µm size colonies and (b) 100–300 nm scale lamellae of the TiAl (?) and Ti3Al (a2) phases. In this material, fracture occurs parallel to the lamellar interface.

29. The in situ testing of these specially configured specimens has enabled observation of the sequence in which damage evolves in the vicinity of these colony boundaries and the mechanisms that contribute to the toughness enhancement. These include multiple cracking in the participating grains (a), plastic deformation of the ligaments between the cracks, crack bridging by ligaments (b), and the subsequent translamellar rupture of these ligaments (c). In contrast, a kink misorientation across the grain boundary – as opposed to a twist misorientation – is ineffective in arresting a crack at the boundary, because in this case the crack path in the two participating grains is coplanar.

30. Effect of lamellar misorientation across a colony boundary on damage generated in the vicinity of the boundary: (a) multiple microcracking; (b) bridging ligament at the boundary caused by a large twist misorientation 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.

31. 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 as opposed 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 paths in polycrystalline materials exhibiting crystallographically preferred fracture paths.

32. 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.

33. (a) Microstructure ahead of a growing crack tip in a Mo–Si–B alloy, obtained by interrupting a 1400°C three-point bend test at a loading rate of 10-5 mm/s. Isolated patches of recrystallized regions are observed; a higher magnification image from within one such patch confirms creep cavities at triple junctions. (b) An SEM image showing the crack path and fine recrystallized grains (3–5 µm) on either sides of the crack; the white arrow illustrates grain boundary relief from sliding. (c) Even finer grains (1–2 µm) are observed ahead of the main crack and evidence is seen for linking of creep cavities to generate several micron-long microcracks.

34. Reference Sharvan Kumar and William A. Curtin, Crack interaction with microstructure, Materials Today, Sept 2007, Vol. 10, Number 9. www.materialstoday.com