a review of the relationship between crystallographic texture and material fracture properties is presented.

1. Crystallographic texture correlation with
fracture toughness and fatigue crack growth
behaviour
Term Paper for the course of
Texture in Engineering Materials
Department of Metallurgical and Materials Engineering
IIT KHARAGPUR

2. Introduction
In this report, a short review of influence of material texture on crack propagation is
presented. Material texture results in anisotropy of material properties which impact its
fracture toughness and crack initiation and propagation rate. A number of papers are
reviewed ranging from initial macrotexture experiments to recently developed
microtexture methods. Dynamic crack propagation and crack arrest is an important
factor in determining structural integrity. Focus is usually placed on the initiation step
(KIc) to avoid catastrophic failures of structures. Structural materials manufactured in
industrial processes do not produce defect free materials. Due to residual stresses and
strain inhomogeneities, nanoscale cracks or defects may be present. Thus for safety
analysis, it is better to consider cracks inherently present in the material and focus on
retarding crack growth. It is important to know whether or not the material will be able to
arrest that crack before it goes through the entire structure. To answer this question it is
essential to understand cleavage micromechanisms during crack propagation.1 It is
known that crack propagation is arrested by grain boundaries: boundaries act like a pile
up of dislocations blocking further movement of dislocations into other grains. But this
does not consider micro-texture effects like grain boundary misorientation on crack
growth. Fatigue cracks are assumed to form in the most favourably oriented grains on
the surface of the specimen and propagate through less well oriented grains. In this
report, the effect of texture on crack propagation has been analysed with a multiscale
approach. It starts with macrotexture and bulk orientation and goes deeper into local
texture and grain boundary.
Crystallography and Local Failure
Consider (fig. 1).2 The crack on reaching the triple point in a
grain boundary has 2 choices for further propagation. It will
either continue along one of the grain boundaries or continue
on directly through the grain. The path selection will depend
on the character of the grain boundaries as well as the
orientation of the grain with respect to the imposed stress
state. The latter factor depends upon the Schmid factor or the
Taylor factor of the preferential slip planes. Depending on the
crack propagation trajectory two types of fracture are
possible:
Figure Error! No sequence
specified.: schematic of
crack propagation

3. Transgranular fracture
gA with respect to the stress state is critical, i.e. the resolved shear stress on
crystallographic planes in grain A. For a polycrystalline material, grains having slip
planes with lower Taylor factor will undergo transgranular fracture.
Intergranular fracture
The orientation of boundary plane (nAB and nAC) with respect to the stress state and the
misorientation between the grains(ΔgAB and ΔgAC) separated by the boundary are
critical. Also some grain boundaries may be weaker than the others due to lattice
incompatibility and impaired strain transfer across the boundary.
Effect of Macro-Texture on Crack Growth Behaviour
AZ61 Mg alloy is considered. Mg and other hcp metals have preferable slip in the basal
plane. During rolling of Mg, the rolling plane aligns parallel to the basal plane.[3] Due to
this uniformity in texture; it is experimentally easier in hcp metals to explore the effect of
fatigue crack orientation and loading direction on crack propagation rate. The following
observations are observed in AZ61 and also have been verified in other hcp systems
like Ti alloys. The specimen orientations are shown in fig. 2.
The longitudinal specimen, where the basal plane is parallel to the loading axis,
indicated high fatigue limit compared to the 45° and transverse specimens [4]. This is
due to the absence of slip systems at 45° in the longitudinal specimen.
In the near-threshold region the longitudinal specimen indicated high fatigue crack
growth resistance and high threshold value (fig. 3). For long cracks spanning more than
one grain, the crack growth rate becomes roughly independent of the orientation [5]. In
fig. 4, crack growth rate is plotted against (ΔKeff) effective stress intensity factor. The
plots approximately coincide for short or long cracks. Thus, the effect of texture is
mainly due to the difference of crack closure in different crack growth orientation.
Figure 2: Orientations of specimens taken

4. Figure 3: Crack growth rate vs. stress intensity
factor range
Figure 4: Crack growth range vs. effective
stress intensity factor range
A bimodal TiAl6V4 alloy is considered with 50% αp (hcp) and 50% of αs in β grains of
average grain size of 15 microns [6]. Fig. 6 is an optical microscope image of an etched
sample. It shows 2 distinct dark and clear patches of roughly 1mm size throughout the
surface which have been labelled as macrozone 1 and 2. X-ray diffraction shows that
macrozones have different αp phase texture. It is observed that short cracks produced
coincide either with basal or prismatic planes of αp grains depending upon the resolved
shear stress. As shown in (fig. 7), the sudden increase of crack length corresponds to
crack coalescence. Thus, in macrozones exhibiting a high crack density, a major
contribution of crack coalescence to crack growth was observed. The orientation of
macrozones governs the crack initiation on slip bands in αp grains, but has no significant
effect on crack growth in the Paris regime.
Figure 5: Scanning electron micrograph of
the electrolytically polished TiAl6V4
Figure 6: optical micrograph of the TiAl6V4
etched by an ethanol solution of 0.5% HF.

5. Figure 7: Crack length vs. number of cycles
Crack Tip
Fatigue crack propagation is presented for high strength steel. Dislocations generated in
slip bands, because of the plastic deformation, can pile up against the high-angle grain
boundaries and form micro-voids. Crack growth occurs by incorporation of these voids
in the main crack [7]. Two maps are constructed: Grain reference orientation deviation
(GROD) and Grain orientation spread (GOS) [8]. GROD measures angular deviation of
each point relative to a reference orientation. GOS shows the distribution of orientation
spread within a grain. Fig. 8 shows the predominant presence of HAGB surrounding the
crack tip [9]. Fig.9 shows that cracking occurs through the grains with the least lattice
rotation and it deflects when the grains have misorientation higher than 7°. From fig.10 it
can be inferred that the least strained grains are affecting the crack path direction. It is
presumed to be due to the hardening of highly deformed grains. It can be seen from fig.
11 that in the immediate vicinity of the crack there are grains with very low Taylor factor, thus
these grains can be deformed easily. But the crack trajectory also coincides with grains that
have high Taylor factor values. By comparing identical regions in Fig. 9, 10, 11, it is observed
that be seen that most of the grains with high Taylor factor which the crack propagated through
are either strained or rotated. In the Schmid factor map, the red area is indicative of large scale
yield and plasticity that may have activated a number of slip systems around the crack
trajectory.

6. Fig. 8: Low medium and high
angle grain boundaries in the
crack tip region
Fig. 9: Grain reference
orientation deviation (GROD)
map with respect to the lowest
average kernel misorientation
Fig.10: Grain orientation
spread (GOS) with respect to
all data points
inside a grain.
Fig.11: Taylor factor map of crack region Fig.12: Schmid factor map of crack region
Conclusion
Crack propagation mechanism has been studied. It is observed that orientation has impact on
short fatigue cracks but not on large cracks. Texture causes difference in fatigue crack closure
for different orientations. Further analysis of crack trajectory and tip mechanism is to be carried
out which should include impact of grain boundary types like tilt and twist and also various types
of CSL boundaries.

7. References
[1] Bouyne, E et al. "Use of EBSD technique to examine microstructure and cracking in
a bainitic steel." Scripta Materialia 39.3 (1998): 295-300.
[2] Wright, Stuart I, and David P Field. "Recent studies of local texture and its influence
on failure." Materials Science and Engineering: A 257.1 (1998): 165-170.
[3] T. Mukai, M. Yamanoi, H. Watanabe, K. Higashi “Ductility enhancement in Z31
magnesium alloy by controlling its grain structure” Scripta Materilia, 45 (2001), 89–94
[4] Sajuri, Zainuddin Bin et al. "Effects of Mn content and texture on fatigue properties of
as-cast and extruded AZ61 magnesium alloys." International journal of mechanical
sciences 48.2 (2006): 198-209.
[5] Navarro, A, and ER De Los Rios. "Short and long fatigue crack growth: a unified
model." Philosophical Magazine A 57.1 (1988): 15-36.
[6] Le Biavant, K, S Pommier, and C Prioul. "Local texture and fatigue crack initiation in
a Ti‐6Al‐4V titanium alloy." Fatigue & Fracture of Engineering Materials & Structures
25.6 (2002): 527-545.
[7] Tanaka, K, and T Mura. "A dislocation model for fatigue crack initiation." Journal of
Applied Mechanics 48.1 (1981): 97-103.
[8] Kobayashi, S. "Orientation dependence of local lattice rotations at precipitates."
2010. <http://www.sciencedirect.com/science/article/pii/S1359645410005446>
[9] Azar, Amin S, Lars-Erik Svensson, and Bård Nyhus. "Effect of crystal orientation
and texture on fatigue crack evolution in high strength steel welds." International Journal
of Fatigue 77 (2015): 95-104.