Abstract
The present study evaluates the J-integral resulting from cold rolling
and aging treatments applied to TiNbSn alloys comprising different
contents of Nb (35% and 42%) and Sn (0% and 2.5%). The alloys were
arc melted, homogenized, solution heat treated, cold-rolled and aged at
400 °C during different aging times. A set of characterization tests,
including microstructural, scanning electron microscopy, work hardening
coefficients and fracture analysis were performed. The cold worked
alloys with the highest Nb content showed the highest toughness. The
addition of Nb in these alloys is beneficial for toughness since Nb
stabilizes the β phase. In alloys with lower Nb content, cold forming
causes a greater amount of α” and this disfavors toughness. Aging caused
a reduction in the alloys’ toughness, since the formation of
precipitates in aging causes shallower and smaller dimples in the
fracture, corroborating to a lower toughness.
Keywords: TiNbSn alloys, aging, J-integral, work hardening coefficient,
fracture mechanics.
* Corresponding author: thiago.azevedo@ifal.edu.br (T.F.
Azevedo).
Introduction
TiNbSn alloys have aroused interest due to their good relation of
mechanical properties for application in biomaterials, shape memory,
superelasticity, resilient elements, among others [1-5]. The
development of new Ti alloys aims to obtain materials with good relation
of mechanical properties applied in structural and biomedical areas
[6]. Ti alloys with the addition of niobium and tin have been
gaining prominence due to their relation of properties and performance
[1-9]. The researchers seek to develop alloys whose high
strength-to-weight ratio, low modulus of elasticity, high resistance to
corrosion and fatigue and good ductility can be easily manipulated
through thermomechanical processes.
The production and control of mechanical properties of these alloys
involve thermomechanical treatments of hot [6-9] and cold [10]
plastic deformation, solution heat treatment and aging [10]. By
combining these methods, it is possible to highlight some properties
over others. For example, cold worked alloys have a high relation
between tensile strength and modulus of elasticity, in addition to high
ductility [10]. On the other hand, the aging of these same alloys
can further increase tensile strength, but with a significantly adverse
impact on ductility reduction and elasticity modulus increase [10].
The fracture toughness of the new alloys is also an important parameter
to be investigated. Some studies have allowed obtaining
Klc of some of these alloys that fit in the elastic
linear fracture mechanics regime [11]. However, the application of
J-integral can have an advantage because it is possible to obtain the
fracture mechanics parameter comparable to both considerably ductile
alloys and alloys that follow the elastic linear regime.
J-integral is an energy conservation theorem formulated by Eshelby,
which represents the variation rate of potential energy in relation to
the length of the crack [12]. The J-integral is obtained by the sum
of the elastic component and the plastic component of J, according to
Eq. 1. Both parts are based on the area below the load curve versus
displacement, recorded during the crack opening test to obtain the
fracture toughness.
\(J=\ J_{\text{el}}+J_{\text{pl}}\) (Eq. 1)
Where:
\(J_{\text{el}}\) = Elastic component of J;
\(J_{\text{pl}}\) = Plastic component of J.
The calculation of the J-integral by the basic method (ASTM
E1820 ) is given by Eq. 2:
\(J=\ \frac{K{(1-\nu}^{2})}{E}+\frac{\eta_{\text{pl}}A_{\text{pl}}}{Bb_{0}}\)(Eq. 2)
Where:\(A_{\text{pl}}\) = area under force versus displacement record;\(K=\) stress-intensity factor;\(\nu=\) Poisson’s ratio;\(E=\) Young’s modulus;\(\eta_{\text{pl}}\) = Constant, (1.9);\(B\) = Specimen thickness;\(b_{0}\) = uncracked ligament, (W - \(a_{0}\));\(W\ \)= Specimen width;\(a_{0}\ \)= Initial crack length.
When obtaining the plastic area of J by controlling the Crack Mouth
Opening Displacement (CMOD), \(\eta_{\text{pl}}\) assumes a resulting
value of Eq. 3 for Single Edge Notched Bend (SENB) specimen.
\(\eta_{\text{pl}}=3,667-2,199\ \left(\frac{a_{0}}{W}\right)+0,437\ \left(\frac{a_{0}}{W}\right)^{2}\ \)(Eq. 3)
However, studies on the properties of elastoplastic fracture mechanics
for the TiNbSn alloy system are not widely disseminated in the
literature. Therefore, studies of these characteristics are necessary to
broaden the understanding of the performance of these new alloys.
This study aims to observe the
elastoplastic behavior of cold worked and aged TiNbSn alloys, by
calculating the values of the J-integral, according to different Nb
contents (35% and 42% wt.) and Sn (0% and 2.5% wt.).
2. Materials and methods
The high-purity raw materials (99.99% Ti, 99.50% Nb and 99.98% Sn)
were arc melted under controlled argon atmosphere to produce the
Ti35Nb2.5Sn, Ti42Nb2.5Sn and Ti42Nb alloys.
The alloys were homogenized at 1000 ºC for 4h and experienced slow
cooling inside the furnace (model FL-1300 Maitec). The solution heat
treatment was performed at 900 ºC for 15 minutes, followed by ice
cooling (0 ºC) to ensure β phase maintenance and higher ductibility of
the alloys. The ingots were hot-rolled at 850°C to uniform the plate
thickness, and experienced solution heat treatment followed by ice
cooling at 0°C. Then, cold rolling was performed on the plates applying
conventional deformation of 0.55 (55%), to refine the microstructure.
After performing the mechanical processing described above, the Ti422
and Ti420 alloys were aged at 400 °C for 48h and the Ti352 alloy was
aged at 400 °C for 72 h, seeking to achieve greater hardness in the peak
aging of each alloy, according to Azevedo, et. al. [9]. Figure 1
shows the procedures of thermomechanical treatments used to produce each
sample. The following alloys were studied:
Ti352C – Ti35Nb2.5Sn, cold rolled alloy;
Ti352A – Ti35Nb2.5Sn, alloy aged at peak-aged stage;
Ti422C – Ti42Nb2.5Sn, cold rolled alloy;
Ti422A – Ti42Nb2.5Sn, alloy aged at peak-aged stage;
Ti420C – Ti42Nb, cold rolled alloy;
Ti420A – Ti42Nb, alloy aged at peak-aged stage.
Figure 1 – Steps in the alloys processing. Cold rolling process (above)
and cold rolling followed by aging at 400ºC (below).
2.1. Microstructures
The microstructures of the samples in the rolling direction of the
plates were analyzed. The metallographic samples were polished in
alumina solution (particle size: 0.5 micrometers). The chemical etching
to reveal the microstructures was achieved through Kroll’s solution (12
ml HNO3, 6 ml HF and 82 ml H2O). The
microstructural aspects were observed through Optical Microscopy (Zeiss
Axioscope A1) and Scanning Electron Microscopy (SEM Jeol-JCM-5700 Carry
Scope).
2.2. Work hardening coefficient
The method described in the literature [9] was used in this study to
obtain the work hardening coefficients of the cold worked and aged
TiNbSn alloys. The method consists on the transformation of the
conventional tensile curves of the alloys under study, previously
presented [9] into a true curve. The true stress (σ ) and true
strain (ε ) were obtained through Eq. 4 and 5, respectively.
\(\sigma=S(1+\mathcal{e)}\) (Eq. 4)
\(\varepsilon=\ln\ (1+\mathcal{e)}\) (Eq. 5)
Where:
S = Conventional stress or engineering stress;
\(\mathcal{e}\) = Conventional strain or engineering strain.
The true curve is then transformed into a logarithmic scale (logσ x log ε ) whose slope in the plastic deformation region,
prior to maximum engineering strain (or similarly, before the maximum
engineering stress), is the work hardening coefficient.
2.3. J-integral test
Six single edge notch bend (SENB) specimens type three points, which
were machined from each alloy, have provided the crack opening
displacement (COD) tests. The dimensions of the specimens, as well as
the other test procedures, were been set according to the plate’s
thickness, following the appropriate standards
(ASTM E399-19,
ASTM E1290-08 and
BS
7448-1). Thus, the dimensions of the specimens were as follows:
Height, W = 9 mm;
Thickness, B = 4.5 mm;
Length, L = 60 mm;
Span between bending rollers, S = 40 mm;
Notch = 3.2 mm;
Pre-crack, a = 4.2 mm.
The notch was machined with 1 mm thickness. The length of the fatigue
pre-crack was controlled by clip gauge (632.02F-20, MTS), which was
assembled to the specimen by wedge-shaped brackets (Figure 2). The
pre-cracks were opened in servohydraulic machine (MTS Landmark 100 kN),
applying bending cyclic loading at 10 Hz, load ratio R = 0.1 and maximum
stress intensity factor at the crack tip ΔK of 11 MPa.m1/2 (Figure 3).
The pre-cracked specimens were subjected to monotonic bending load at 1
mm/min. The load and crack-mouth opening displacement (CMOD) were
acquired until reaching the unstable fracture of the specimens. The
J-value is calculated by its expression for static cracks.
Figure 2 – Dimensions exhibited on the frontal view of the specimen
whose thickness was 4.9 mm.
All results were compared using variance analysis One way ANOVA with
significance index p ≤ 0.05.
The fracture micromechanisms were performed by Scanning Electron
Microscopy (SEM JEOL Carry Scope JCM-5700).
3. Results and discussions
3.1. Microstructures
In previous studies, through the combination of microstructural analyses
and XRD analyses, it was observed that these alloys present the
predominant formation of α” (deformation-induced martensite) and β
phases after solidification and slow cooling; preponderant retention of
β phase due to rapid cooling after solution heat treatment and the
formation of metastable phases α” during cold forming. Furthermore,
aging after cold forming promotes the formation of precipitates
predominantly of α phase [9 -10].
Figure 3 shows the micrographs representing all the alloys studied. The
microstructural analyses of Ti352C and Ti352A alloys (Figures 3(a) and
3(b), respectively) show that cold rolled alloys as well as aged alloys
presented the same microstructural aspects. The microstructures consist
on elongated primary β grains in the rolling direction, α” needles and
slip bands originating from cold forming [9].
Through the microstructural analyses of Ti352C and Ti420C alloys
(Figures 3(a) and 3(c), respectively) it is possible to verify that the
Ti352C alloy has more α” needles in relation to the samples with higher
Nb content. The effect of Nb on the Ti alloy is to stabilize the β phase
[13]. Several studies show that Nb at 35% already allows
stabilizing the β phase depending on the thermomechanical process [7,
9]. However, the increase of Nb to 42% stabilizes more β.
Figure 4 shows SEM images of the Ti352C alloy microstructure with more
details of the slip bands morphology and the deformation-induced
martensite phase (α”).
Figure 3 – Metallographic images of alloys (a) Ti352C, (b) Ti352A, (c)
Ti420C. Elongated primary β grains in the rolling direction, α” phase
disperses amongst the slip bands. The amount of α” phase is clearly
higher in the alloy with lower Nb content. The aged alloy has the same
microstructural characteristics as the cold rolled alloy.
Figure 4 – SEM image of the Ti352C alloy showing slip bands network
within the β grains and α” needles.
3.2. Work hardening coefficient
The work hardening coefficient is a measure of an alloy’s ability to
promote slip bands [14-15]. The main purpose of this approach in the
present study was to prove the microstructural results. Figure 5 shows a
logarithmic true curve representative of all alloys, which was used to
obtain the coefficient. Figure 6 shows the results of the work hardening
coefficient for TiNbSn alloys influenced by the Nb and Sn content, and
aged. Well, as the work hardening coefficients were similar in cold
rolled alloys, regardless of the alloy content, this proves that the
difference in the microstructures seen in the metallographic analysis of
Fig. 3 is the greater amount of α” of the 35 Nb alloy, since the amount
of the slip bands must be very similar.
Figure 5 – Logarithmic true curve representation of the Ti352A alloy to
obtain the work hardening coefficient.
It can be observed that both cold rolled alloys and aged alloys present
statistically similar values of work hardening coefficients. In the aged
alloys there was an increase in the work hardening coefficient in
relation to the rolled alloys, with significant differences for the
alloys of Nb-42%. This is due to the appearance of precipitates in
aging, as explained by Azevedo et. al. [9], which promote
greater restriction to the movement of dislocations, causing a higher
rate of stress increase due to plastic deformation.
The literature indicates that the addition of Sn in larger amounts (5
and 7.5%) causes reduction of ductility and work hardening coefficient.
Comparing the work hardening coefficient of the hot rolled Ti352 alloy
studied by Griza et al. [8] with the results of this same
cold and aged rolled alloy produced in this study, it is possible to
note that there was no significant change in the work hardening
coefficient. Therefore, it can be concluded that the addition of Sn up
to 2.5% does not influence the work hardening coefficient, regardless
of the used manufacture thermomechanical routes.
Figure 6 – Work hardening coefficient for the rolled and aged TiNbSn
alloys.
3.3. J-integral test
The Figure 7 shows a CMOD curve of the Ti422C alloy, representative of
all the alloys analyzed, where we can observe the two different areas
that were used for the J calculation.
Figure 7 – CMOD curve representation of the Ti422C alloy. The two
different areas (elastic and plastic) are highlighted.
Figure 8 shows the values of J-integral for the alloys. It was observed
that the Nb increase promoted the significant increase of J. This should
be related to β stabilization, which the literature indicates that it
has greater toughness than α and α”, as well as other phases that occur
in β-Ti alloys. This is in accordance with our microstructural
evaluation, from which we find more α” in the Nb-35% alloy.
The Ti422C and Ti420C alloys presented the highest toughness values,
with no significant difference between them. This indicates that the
Sn-2.5% increase did not influence the toughness of the cold rolled
alloys. The Ti352C alloy presented lower J-integral compared to the
previous two alloys. This indicates that the Nb content increasing from
35 to 42% impacts positively the toughness of these Ti alloys. Well, as
the increase in Nb stabilizes β, this should have a positive impact on
the toughness increase of the alloys.
The aged alloys had a decrease in J-integral compared to cold rolled
alloys. The aging causes ductility and toughness decrease, and it
increases the mechanical strength and Young’s modulus [9 - 11]. In
addition, for aged alloys, the difference in toughness among them is
more evident. The Nb-35% alloy has low J-integral. Increasing to
Nb-42% (Ti420A alloy), we noticed significant increase of J-integral.
By observing the Ti422A and Ti420A alloys, Sn influences significantly J
values, since the Ti422A alloy was the one with the highest J value
among the aged alloys. So, we can conclude that the Sn in solution
favored the toughness for the aged alloy, because it should stabilize
more β and reduce the formation of precipitates, obtaining fewer
barriers to dislocation.
Figure 8 –J-integral values.
The analyses performed in the flat zone of propagation of the fractured
specimens after tests of J-integral allowed to observe the predominant
fracture micromechanisms and their morphologies. Figure 9 shows the
fractographic details by SEM of the alloys’ flat fracture regions. The
coalescence of shallow microcavities is observed on the alloys tested in
both manufacturing processes, characteristic of the fracture behavior of
low toughness alloys.
These fractographs indicate that the aged alloys had a decrease in the
size of dimples, which are shallower when compared to the only cold
rolled alloys. The dimples are formed from the difference of ductility
between the matrix and the precipitates, which allows the interfacial
separation (nucleation), the growth and coalescence of the
microcavities. The formation of these small and shallower voids is
related to the presence of precipitates.
The interfacial separation between matrix and precipitates due to
differences in their deformation behavior allows microcavities to grow
and coalesce. The thin precipitates of the aged alloys provide the
formation of the smaller and shallower dimples, which coalesce after
little deformation due to the precipitates dispersion and, consequently,
cause the fracture of lower ductility.
Through the SEM fracture surface of aged alloys, it is possible to
observe that the increase in Nb causes an increase in the size of the
coalescence micromechanisms of microcavities [16]. This is related
to toughness, since, for example, the Ti352A alloy has lower toughness
and, thinner and shallower microcavities than the other alloys (Figure
9).
Figure 9 – SEM images of the alloys: (a) Ti352C, (b) Ti352A, (c)
Ti422C, (d) Ti422A, (e) Ti420C and (f) Ti420A. The elongated primary β
grains are in the rolling direction. Aged alloys presented coalescence
of small and less deep microcavities compared to alloys subjected to
cold rolling.
4. Conclusions
The present study aimed to observe the fracture toughness as a function
of the J-integral of the TiNbSn alloys as a function of the alloying
element content and thermomechanical treatment. The following
conclusions were obtained:
- The cold rolled alloys with the
highest Nb content were the ones with the highest toughness. The
addition of Nb in these alloys is beneficial for toughness because Nb
stabilizes the β phase.
- In alloys with lower Nb content, cold rolling causes a greater amount
of α”, and this disfavors toughness.
- The aging caused a reduction in the alloys toughness, since the
formation of precipitates in aging causes shallower and smaller
dimples in the fracture, which causes less toughness.
- The addition of 2.5% Sn did not influence the toughness of the Ti-Nb
cold rolled alloys.
Acknowledgements
The authors would like to thank the financial support of CAPES and CNPq.
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