THERMOELASTIC INVESTIGATION OF CRACK PATH
1
M. Zanganeh, 2R.A. Tomlinson and 3J.R. Yates
Department of Mechanical Engineering,The University of Sheffield
1
m.zanganeh@sheffield.ac.uk, 2r.a.tomlinson@sheffield.ac.uk, 3j.yates@sheffield.ac.uk
ABSTRACT
The interaction of cracks and corresponding paths are investigated experimentally and numerically in five sets of double edge
cracked specimens with different vertical offsets. Due to the great potential of the thermoelastic stress analysis (TSA)
technique in fatigue and fracture applications, i.e. the non contacting feature, ability to yield full field data and working under
cyclic load, this method is used as the experimental technique. The influence of the range of the mixed mode stress intensity
factor and T-stress on crack path has been examined experimentally and using the finite element method.
Introduction
Traditionally fracture mechanics is mostly concerned with the opening mode of crack growth. Stability and crack path problems
are relatively well understood in this case and it is expected that a crack grows in its own plane. However, cracks may exist in
different orientations and moreover more than one crack may be found in a structure. The growth of these cracks even under
uniaxial tensile loading may not be so easily predicted. The direction of crack initiation under different loading conditions, the
path that a crack extends after initiation, directional stability even under pure mode I loading and interation of cracks with each
other, are problems that are not still fully understood, despite the extensive amount of research undertaken in these areas.
Having greater knowledge of these problems will be helpful in crack arrest problems, safety issues and many other problems
that exist in industrial applications.
In 1963, Erdogan et al. [1] showed that the crack grows in a direction normal to the maximum tension at the tip of the crack
and this growth releases the maximum of energy. Later, Cotterell [2], made the conclusion that the line of local symmetry is a
highly probable path for macroscopic growth. Sih [3], developed the Minimum Strain Energy Density criterion and predicted
that the crack grows in a direction along which the strain energy density factor is minimum. The instability occurs when the
minimum strain energy factor reaches a critical value. Cotterell and Rice [4], stated that in a non uniform stress field the cracks
generally follow a curved path which in a brittle homogeneous isotropic material is the same as the path in which the local
stress field ahead of crack tip is a mode I type. In other words, the crack prefers to grow in a direction where there is no mode
II stress intensity factor. It can be said that these criteria are the base of all other criteria that have been developed later. The
first one is based on the concept of stress, the Sih criterion is based on the energy concept and the Cotterell et al. criterion is
based on the observations. However, it was first by Pook [5] that the concept of chaos theory was used to explain the
behaviour of crack propagation. He drew it to our attention that since the conditions for the mode I branch crack are not
completely understood, any metallurgical discontinuities or pre-crack front curvature may influence the crack tip surface
deformation or in chaos theory terms the mode I branch crack formation has a chaotic behaviour which strongly depends on
the initial conditions.
It may be assumed that theoretically the crack path is predictable, but even if the loading is such that straight mode I crack
growth could be expected for symmetry reasons, the path might be directionally unstable [6]. Generally speaking, it is not easy
to predict the crack path and as already stated there are discussions about criteria that can control the direction in which a
crack goes. A double cantilever beam specimen under tension is a good example of directional instability. Under mode I
loading one expects that the crack will grow in a self similar manner but the crack in this type of specimen usually changes its
path toward the boundaries of the specimen and it deviates from the original direction of the crack. To interpret and predict this
phenomenon many theories have been developed since 1960s.
In 1966, Cotterell [7] stated that in a perfect isotropic elastic solid a crack will grow in the direction of principle stress which
passes through the crack tip. However, in real material there may be deviation from the perfect path caused by irregularities.
To consider these irregularities and based on the local symmetry criterion, he used the expanded form of the stress distribution
at the crack tip as a power series, in which the first term is proportional to the stress intensity factor and he concluded that the
second term (also called T-stress or stress parallel to the crack tip [4]) controls the stability of the crack direction. He assumed
the ideal direction for crack growth is along the symmetric line and concluded that if the sign of the second term is negative the
crack path has a tendency to return to its original path (or it is directionally stable) but if the second term is positive the path
does not return to the original path. In 1975, Katagawa et al. [8] stated that it seems difficult to explain the zig-zagging crack by
the model of Cotterell [7]. They proposed that it is more natural to consider the zig-zagging crack as a stochastic process.
Pook [5], in 1995, after reviewing the works done by other authors made the point that because of using the linear elastic
approach the effects of crack tip plasticity are not taken into account, thus it makes the use of the refined theories [9] of
doubtful utility. Later in [10], he introduced an alternative crack path stability parameter. Referring to the fact that, in contrast to
Cotterell et al., sometimes even under positive T-stress the cracks are stable; he proposed the T-stress ratio TR which is
defined as the ratio of T-stress to σx at some characteristic value of r, i.e. rch. According to his criterion for a given material
there is a critical value of TR, TRC, in which the crack path becomes unstable. However, the validity of this criterion is limited to
the experiments carried out by himself and more experiments are needed for verification.
In 2002, Melin [11], questioned the reliability of using T-stress as criterion for directional stability prediction. She showed that
the T-stress criterion has been derived for a single crack case, growing in a large plate and it cannot be applied for the other
situations. She has used three different counterexamples to show the limitations of the application of the T-stress criterion. For
example, in the case of an array of collinear cracks under remote mode I loading [11], directional stability always prevails and
does not depend on the T-stress. As another example, wedging of a strip [11], she showed that neither the sign nor the
magnitude of T-stress, does not considerably affect the directional stability.
What attract one’s attention is that there is no definite answer to the problem of directional stability of cracks. Regarding the
T-stress as a controlling parameter in crack directional stability it should be mentioned that it might be used as a necessary
condition for crack stability/instability but it definitely can not be used as the only parameter to predict instability. The authors
agree with [11, 12] that the directional stability is not a local phenomenon, because in each step of crack growing even if the
crack deviates from the original plane it does not guarantee that it does not return to its original path and vice versa. So, the
directional stability is controlled by the resultant changes in each step of the crack growth. Thus, the definition of directional
stability is pointless and it can not be predicted by the local criteria. However, the crack path might be predictable using the
local criteria if the criteria are used incrementally and if the criteria are modified in such a way that they include the effect of
influential parameters such as T-stress, plasticity ahead of crack tip, fracture orthotropy and microstructure. This paper shows
the influence of some of these parameters which affect the crack path in the case of two interacting cracks using thermoelastic
stress analysis due to its great potential which has been shown in fatigue and fracture applications [13, 14].
Experiments
Offset double edge slit fatigue specimens were manufactured to explore the trajectory and crack tip stress states of a pair of
interacting fatigue cracks. A specimen is shown in Figure 1. The specimens 6mm thick, 40mm wide and 250mm long were
machined from a plate of 7010 T7651 aluminium alloy. The specimens were cut along the rolling direction of the plates. Two
slits, each 8mm long, were electric discharged machined using 0.3mm diameter wire on opposite sides of the specimens.
Before machining the slits different models were created using ANSYS [15] and it was found out that for 2b values more than
48 the two slits have no interaction with each other (Figure 2). Therefore, the vertical offset between the two cracks (named 2b
in Figure 1) was set at 0, 8, 16, 32 and 48mm for the series of tests conducted. In total 17 specimens with different offsets
were used for the tests. Table 1 shows the different offsets used for different specimens.
One face of each specimen was painted with a thin coat of matt black paint (RS type 496-782) to provide a surface of uniform
and known emissivity. An orthogonal strain gauge rosette (Tokyo Sokki Kenkyujo Co., 1 mm, 120 ± 0.5Ω) was bonded to a
similar specimen in a region of uniform and known elastic stress to provide a calibration for the thermoelastic data.
Figure 1. Specimen dimensions
Specimens were loaded through the pins located 210 mm apart (Figure 1). Fatigue tests were conducted under load control at
a frequency of 20 Hz, a range of 3.6 kN and a mean load of 14.4 kN for No. 4 and No. 5 specimens and a range of 3.5 kN and
a mean load of 8.5 kN for specimen No’s. 6, 7 and 8 (Table 1). The load range was reduced since considerable plasticity was
Table 1. Values of vertical offset (2b) and loading conditions for different specimens
Specimen No.
3
4
5
6
7
8
9
10
11
12
15
16
17
18
19
20
21
2b [mm]
0
0
8
16
32
48
16
16
16
0
0
0
8
8
8
32
48
Mean load [kN]
4
14.4
14.4
8.5
8.5
8.5
4
4
4
4
4
4
4
4
4
4
4
Load Range [kN]
3
3.6
3.6
3.5
3.5
3.5
3
3
3
3
3
3
3
3
3
3
3
observed in the first two tests (specimen No. 4 and 5). To decrease the crack growth rate, the rest of specimens were tested at
a range of 3 kN and a mean load of 4 kN. The frequency was chosen to be sufficiently high for adiabatic conditions to be
attained in the material ahead of the crack tip. By doing so, we ensure that the thermoelastic signal contains information about
the sum of the elastic principal stresses from which the mode I and mode II stress intensity factor ranges can be evaluated.
Figure 2. Stress field around crack tip in different vertical offset between two slits
A Deltatherm 1550 instrument manufactured by Stress Photonics Inc. was used to gather thermoelastic data from the matt
black surface. The images particularly ahead of the crack tips are quite good at the beginning but as the cracks grow
saturation of the signal is observed at the crack tip. So, to have a better image quality, different iris values which give different
calibration factors have been used throughout the tests.
The crack tip position and the mode I and mode II stress intensity factor ranges occurring in the specimen were evaluated
using the FATCAT software [16]. The methodology used in FATCAT is based on the combination of two numerical techniques,
namely, a genetic algorithm (GA) and downhill simplex method, which avoid the need to define any initial value for the problem
or an initial location for the crack tip. This method also makes it possible for the software to search for a crack tip position.
After choosing a position in the thermoelastic image the software collects experimental data points in the thermoelastic image
from the region dominated by the crack tip stress field. Then it uses the collected data points to fit a mathematical model
(Muskhelishvili’s model) to the experimental data in order to describe the stress field ahead of the crack tip and finally uses the
resultant fitting equation to determine the stress intensity factor range.
The finite element method, FRANC2DL package [17], was also used to find the stress intensity factors and the crack paths.
The maximum tangential stress criterion, minimum strain energy density criterion and maximum energy release rate criterion
were used as the crack path prediction criteria. Additionally, different methods for calculating stress intensity factors are used
for one of the specimens. Because of the relatively good agreement between the FE results for that specimen, the maximum
tangential stress criterion and J integral were used for determining the crack path and stress intensity factors respectively for
the remaining specimens in numerical simulations.
Results
A qualitative comparison between the thermoelastic and the finite element data is made in Figure 3. It seems that in early
stages of crack growth FRANC2DL has a good prediction of crack paths especially in cases where the interaction between the
two cracks is not strong. But as the interaction between cracks becomes stronger, for example in the 0 and 8mm offset cases,
where in most of these cases one of the cracks starts growing before the other one, FRANC2DL cannot predict the crack
paths accurately.
Quantitative comparisons are made in Figures 4 to 7. The crack tip positions throughout the tests were located from the
thermoelastic data using the FATCAT software and compared with the positions predicted by the FRANC2DL finite element
package.
In the 16mm offset case (Figure 6), FRANC2DL path prediction for both left and right cracks are quite good up to 9 mm crack
growth. In this case both left and right cracks grow almost with the same rate. After 9mm the crack paths deviate from
theoretical prediction but some sort of agreement can still be observed. The interesting thing is that regardless of different
paths the stress intensity factor ranges are in good agreement in specimens themselves and theoretical values. However there
are some deviations in the region where the interaction of left and right crack is stronger.
In the 8mm offset case (Figure 5), the left and right cracks in all the specimens do not grow at the same rate (except no 5
which was under higher level of load). The left crack in all the specimens except No. 19 started to grow before the right one.
The cracks which started to grow later didn’t grow as long as the other cracks. Crack path predictions by FRANC2DL almost
agree with the experimental results but only for the cracks that are dominant in growing. It is mostly due to the fact that
FRANC2DL presumes that both cracks start growing at the same time and at the same rate but in reality it is not the case.
Even in these cases there are some regions (9mm to 17mm in No 17 and 18 for example) where a good consistency is not
observed between the FRANC2DL predictions and experiments. This is because of the fact that when a crack starts growing
before the other one and in different rate the region of interaction between the stress fields ahead of the crack tips would be
different. This is why particularly in the middle of the crack growing path there is a difference in the predicted and observed
crack growths. As it is observed in No. 19 for instance, the closer the crack growth rate for left and right cracks the better
prediction is yielded in crack path by FRANC2DL.
KI range prediction by FRANC2DL and experimental results are in a very good agreement for the dominant crack in the whole
of the path of growing but it is very poor for the other crack. Again the interesting point is that despite disagreement in crack
paths predictions and experimental data, there is a good agreement for SIF ranges.
In the 0mm offset case (Figure 4), as stated before, one of the cracks starts growing before the other one and it was observed
that the other crack stops growing after only a short amount of growth. As the cracks move toward each other they try to avoid
each other which is in agreement with the observations of [18]. Again in this case theoretical predictions are acceptable for the
dominant crack and like the previously stated cases values of predicted KI ranges are less than the values gained from
experiments.
In the 32mm offset case (Figure 7), both cracks grow with almost equal growth rate (particularly No. 7 in which the load level is
higher). So it is expected that the crack paths should be predictable and of course this is true for No. 7. However, in specimen
No. 20 the predicted paths are completely in the opposite direction but still the predicted mode I stress intensity factor ranges
are in harmony with experimental values except that unlike the other cases the predicted values are higher than the
experimental values.
In the 48mm offset case, like the 32mm offset case both cracks grew with almost the same growth rate except that in this case
the left and right cracks growth rates in the specimen which had been under lower level of load match better than the other
specimen. Theoretical and experimental values of stress intensity factor ranges in this case especially in early stages of crack
growth are in good agreement with each other.
Analysis of the Results
∆KI range predictions by FRANC2DL almost agree with the experimental results but only in the cases in which both cracks
grow at almost the same rate or for the crack which dominates in growth. However, even in these cases, the crack path
predictions do not completely agree with experiments. At the early stages of crack growth the crack follows the path where the
mode I stress intensity factor is practically zero. However, there are some regions (Figure 8) where the effect of mode II stress
intensity factors is noticeable and this is exactly in these regions where the deviation of the predicted crack paths from the
experimental crack path is observed.
As it can be observed in the TSA image in Figure 9 there are some other regions where it seems a contact exists between the
crack faces in that region. The possibility of crack face contact and the extent of plasticity at the crack tip were explored using
finite element analysis. An elastic plastic code was developed in ANSYS to simulate the crack path observed experimentally. A
fine mesh using 8 node elements was used to model the region ahead of the crack tip and a bihardening model was used for
material behaviour modelling. Figure 10 shows the results obtained from FE analysis. It shows the sum of the principal strains
in the specimen. As is well known, the sum of principal strains is proportional to the thermoelastic signal. By comparing the two
figures (9 and 10) it can be seen that the FE image shows a similar pattern in areas of contact of the crack faces were
suspected. Since the FE model had no contact between the crack faces, it could be suggested that no contact is present in the
experimental test specimen.
To consider the effect of T-stress on the crack path a modification to the FATCAT code was carried out in order for FATCAT to
be able to determine the T-stress as well. Originally, the FATCAT used the Muskhelishvili model as the mathematical model to
find the stress intensity factors. The Westergard model is an alternative for the Muskhelishvili model. These two models yield
the same results for stress intensity factors except in situations where mode I and mode II SIFs are in the same order. So, in
order to find the T-Stress the Westergard equations were implemented in the modified version of FATCAT. Using the modified
version of FATCAT the T-stress was calculated experimentally using the TSA images. The results for both left and right cracks
in specimen No. 19 are shown in Figure 11.
It can be observed that the T-stress is negative for whole the crack path and especially at the end of the route where the
deviation is stronger a higher value of T-stress is experienced and therefore, according to the Cotterell and Rice [4] criterion no
directional instability should be pronounced, which is obviously not the case. So, since neither the sign nor the magnitude of
the T-stress is not the base of instability, this example also might be considered as another counter example of the applicability
of T-stress criterion for predicting the so called directional instability.
0 mm
8 mm
16 mm
32 mm
48 mm
No 15
No 19
No 11
No 12
No 18
No10
No 4
No 17
No 9
No 20
No 21
No 3
No 5
No 6
No 7
No 8
No 16
Figure 3. Comparison between TSA images and FEM simulation
2b=0
2b=0
1.5
1.5
(a)
No4 Left Crack Path 10.8-18 kN
No12 Left Crack Path 1-7 kN
1
No 15 Left Crack Path 1-7 kN
No 16 Left Crack Path 1-7 kN
FRANC2DL Left Crack Path 1-7 kN
0.5
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
-0.5
Vertical offset from crack starting point (mm)
Vertical offset from crack starting point (mm)
1
(b)
No3 Right Crack Path 1-7 kN
No4 Right Crack Path 10.8-18 kN
No12 Right Crack Path 1-7 kN
No 15 Right Crack Path 1-7 kN
No 16 Right Crack Path 1-7 kN
FRANC2DL Right Crack Path 1-7 kN
No3 Left Crack Path 1-7 kN
0.5
0
0
2
4
6
8
10
12
16
18
20
22
24
26
-0.5
-1
-1
-1.5
-1.5
Fatigue Crack Length (mm)
Fatigue Crack Length (mm)
2b=0
2b=0
50
50
(c)
(d)
40
40
30
30
20
20
10
10
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
-10
∆KI, MPa√m
∆KI, MPa√m
14
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
-10
-20
No 3 Left Crack KI 1-7 kN
-20
No 3 Right Crack KI 1-7 kN
No 4 Left Crack KI 10.8-18 kN
-30
No 12 Left Crack KI 1-7 kN
No 4 Right Crack KI 10.8-18 kN
-30
No 15 Left Crack KI 1-7 kN
No 12 Right Crack KI 1-7 kN
No 15 Right Crack KI 1-7 kN
No 16 Left Crack KI 1-7 kN
-40
No 16 Right Crack KI 1-7 kN
-40
FRANC2DL Left Crack 1-7 kN
FRANC2DL Right Crack 1-7 kN
-50
-50
Fatigue Crack Length (mm)
Fatigue Crack Length (mm)
Figure 4. Comparison (a) Left crack paths (b) Right crack paths (c) Left crack ∆KI (d) Right crack ∆KI for 0mm offset
specimens
2b=8 mm
2b=8 mm
3
3
(b)
(a)
No 5 Left Crack Path 10.8-18 kN
No 17 Left Crack Path 1-7 kN
2
No 18 Left Crack Path 1-7 kN
No 19 Left Crack Path 1-7 kN
FRANC2DL Left Crack Path 1-7 kN
1
0
0
2
4
6
8
10
12
14
16
-1
18
20
22
24
26
Vertical offset from crack starting point (mm)
Vertical offset from crack starting point (mm)
2
1
0
0
4
6
8
10
12
14
16
-1
No 5 Right Crack Path 10.8-18 kN
-2
-2
2
No 17 Right Crack Path 1-7 kN
No 18 Right Crack Path 1-7 kN
No 19 Right Crack Path 1-7 kN
FRANC2DL Right Crack Path 1-7 kN
-3
-3
Fatigue Crack Length (mm)
Fatigue Crack Length (mm)
18
20
22
24
26
2b=8 mm
2b=8 mm
70
(c)
(d)
50
50
30
30
∆KI, MPa√m
∆KI, MPa√m
70
10
0
2
4
6
8
10
12
14
16
18
20
22
24
10
26
0
-10
2
4
6
8
10
12
14
16
18
20
22
24
26
-10
No 5 Left Crack KI 10.8-18 kN
No 5 Right Crack KI 10.8-18 kN
No 17 Left Crack KI 1-7 kN
-30
No 17 Right Crack KI 1-7 kN
No 18 Left Crack KI 1-7 kN
-30
No 18 Right Crack KI 1-7 kN
No 19 Left Crack KI 1-7 kN
No 19 Right Crack KI 1-7 kN
FRANC2DL Left Crack KI 1-7 kN
FRANC2DL Right Crack KI 1-7 kN
-50
-50
Fatigue Crack Length (mm)
Fatigue Crack Length (mm)
Figure 5. Comparison (a) Left crack paths (b) Right crack paths (c) Left crack ∆KI (d) Right crack ∆KI for 8mm offset
specimens
2b=16 mm
2b=16 mm
3
3
(a)
(b)
No 6 Left Crack Path 5-12 kN
No 9 Left Crack Path 1-7 kN
2
No 10 Left Crack Path 1-7 kN
No 11 Left Crack Path 1-7 kN
FRANC2DL Left Crack Path 1-7 kN
1
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
-1
Vertical offset from crack starting point (mm)
Vertical offset from crack starting point (mm)
2
-2
1
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
-1
No 6 Right Crack Path 5-12 kN
No 9 Right Crack Path 1-7 kN
-2
No 10 Right Crack Path 1-7 kN
No 11 Right Crack Path 1-7 kN
FRANC2DL Right Crack Path 1-7 kN
-3
-3
Fatigue Crack Length (mm)
Fatigue Crack Length (mm)
2b=16 mm
2b=16 mm
50
50
(d)
40
30
30
20
20
10
10
0
0
2
4
6
8
10
12
14
16
-10
18
20
22
24
26
∆KI, MPa√m
∆KI, MPa√m
(c)
40
0
0
-20
6
8
10
12
14
16
18
20
22
No 6 Right Crack KI 5-12 kN
No 9 Left Crack KI 1-7 kN
-30
No 9 Right Crack KI 1-7 kN
No 10 Right Crack KI 1-7 kN
No 10 Left Crack KI 1-7 kN
-40
4
-20
No 6 Left Crack KI 5-12 kN
-30
2
-10
No 11 Left Crack KI 1-7 kN
-40
FRANC2DL Left Crack KI 1-7 kN
-50
No 11 Right Crack KI 1-7 kN
FRANC2DL Right Crack KI 1-7 kN
-50
Fatigue Crack Length (mm)
Fatigue Crack Length (mm)
Figure 6. Comparison (a) Left crack paths (b) Right crack paths (c) Left crack ∆KI (d) Right crack ∆KI for 16mm offset
specimens
24
26
2b=32 mm
2b=32 mm
3
3
(a)
(b)
No 7 Left Crack Path 5-12 kN
2
No 20 Left Crack Path 1-7 kN
FRANC2DL Left Crack Path 1-7 kN
1
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
-1
Vertical offset from crack starting point (mm)
Vertical offset from crack starting point (mm)
2
1
0
0
2
4
8
10
12
14
16
18
20
22
24
26
-1
No 7 Right Crack Path 5-12 kN
-2
-2
6
No 20 Right Crack Path 1-7 kN
FRANC2DL Right Crack Path 1-7 kN
-3
-3
Fatigue Crack Length (mm)
Fatigue Crack Length (mm)
2b=32 mm
2b=32 mm
50
(c)
40
40
30
30
20
20
10
10
0
0
2
4
6
8
10
12
14
16
18
20
22
24
26
-10
∆KI, MPa√m
∆KI, MPa√m
50
(d)
0
0
2
4
6
8
10
12
14
16
18
20
22
-10
-20
-20
No 7 Left Crack KI 5-12 kN
-30
No 7 Right Crack KI 5-12 kN
-30
No 20 Left Crack KI 1-7 kN
-40
No 20 Right Crack KI 1-7 kN
-40
FRANC2DL Left Crack KI 1-7 kN
-50
FRANC2DL Right Crack KI 1-7 kN
-50
Fatigue Crack Length (mm)
Fatigue Crack Length (mm)
Figure 7. Comparison (a) Left crack paths (b) Right crack paths (c) Left crack ∆KI (d) Right crack ∆KI for 32mm offset
specimens
3
10
FRANC2DL
TSA crack path
TSA KII
8
6
4
1
2
0
0.00
5.00
10.00
15.00
20.00
0
25.00
-2
∆KII, MPa√m
Vertical offset from crack starting point [mm]
2
-1
-4
-6
-2
-8
-3
-10
Fatigue crack length [mm]
Figure 8. Crack path determined by FRANC2DL and TSA as
well as mode II SIF determined by FATCAT for specimen
No.19
Figure 9. (a) TSA image for specimen No.19
24
26
0
0
2
4
6
8
10
12
14
16
18
20
-50
-100
T-stress [MPa]
-150
-200
-250
-300
-350
-400
-450
Poly. (Right Crack)
Poly. (Left Crack)
-500
X [mm]
Figure 10. FE results for specimen No. 19
Figure 11. Left and right cracks T-stress in specimen No. 19
Conclusions
The effect of elastic parameters such as mode I and II stress intensity factors as well as the T-stress was explored using the
TSA technique and finite element modeling. It seems the cracks do not always grow in the pure mode I path especially when
the tunneling effect or large plastic flows are observed. The negative T-stress criterion does not necessarily guarantee the
directional stability. It seems that paths predicted by criteria based on the stress or energy concepts are more likely to occur
experimentally. So, it is believed that in contrary with Broberg [6] the crack growth should be predicted by a criteria which is
combination of mode I and II stress intensity factors. Thus, if the criteria like the one proposed as the generalized version of
maximum tangential stress [19] are modified to consider the effect of fracture orthotropy and plasticity ahead of crack tip it is
hoped that the crack path can be characterized.
References
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