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Dynamic mechanical properties in relation to adiabatic shear band formation in titanium alloy-Ti17
Materials Science and Engineering A358 (2003) 128 /133 www.elsevier.com/locate/msea
Dynamic mechanical properties in relation to adiabatic shear band formation in titanium alloy-Ti17 Li Qiang a,1, Xu Yongbo b, M.N. Bassim a,* a
Faculty of Engineering, Department of Mechanical and Industrial Engineering, The University of Manitoba, Manitoba R3T 5V6, Canada b Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110015, China Received 28 October 2002; received in revised form 21 March 2003
Abstract A Split-Hopkinson Pressure Bar system was used to determine the dynamic mechanical properties in relation to the formation of adiabatic shear bands in titanium alloy-Ti17. Cylindrical and conical frustum specimens were impacted between the incident and transmitted bars. The experimental results showed that the dynamic yield stress (syd) and impact strength (sbd) were both higher than the corresponding static values, and the failure was sensitive to the strain rate, but insensitive to the applied stress level. The critical strain rate for failure was o˙c/ /2000 s 1. Microscopic examinations revealed that the break of specimen frequently occurred along the shear band. A hemicyclic shear band appeared on the transverse section of the conical frustum, while a straight shear band developed at the location of maximum shear stress and propagated along the trace of the maximum shear stress, which was determined by the analysis of the stress distribution. # 2003 Elsevier Science B.V. All rights reserved. Keywords: Dynamic mechanical properties; Failure; Adiabatic shear band
1. Introduction Dynamic mechanical properties and adiabatic shear bands have been widely investigated in the last 40 years. Harding [1] gave a critical review on the effect of high strain rate on material properties. Chichili et al. [2] reported that true stress of a -Ti increased with true strain rates ranging from 1.16 /10 5 to 6.0 /103 s 1, which is in agreement with experimental evidence that most metals and alloys exhibit some increase in strength with increasing strain rate. Adiabatic shear bands usually dominate the deformation process and are the usual damage of metals at high strain rates [3]. Many studies focused both on various mechanical models and microstructure evolution of the adiabatic shear bands [4 /8]. It was recognized that the
* Corresponding author. Tel.: /1-204-474-8524; fax: /1-204-2757507. E-mail address: [email protected] (M.N. Bassim). 1 Present address: Faculty of Engineering, Department of Mechanical and Industrial Engineering, The University of Manitoba R3T 5V6, Canada and Tianjin University, Tianjin 300072, China
behavior of shear bands was a simple balance between hardening and softening of the material. Several kinds of configuration of adiabatic shear bands were observed. Most of them were concerned with an isolated shear band in two dimensions. Recently, however, Meyers et al. [9,10] found the formation of multi-shear bands in space through self-organization. In this current study, we report experimental results of dynamic mechanical properties of titanium alloy (Ti / 17) at high strain rates and show that the strain rate plays a key role in the failure of Ti /17 during deformation. From experimental observations of adiabatic shear bands in the conical frustum specimens, it is confirmed that the deformation localization is always formed on the maximum shear stress plane and the highly deformed region in the conical frustum specimen is confined in a thin conical shell in three dimensions.
2. Experimental procedure A modified compression Split-Hopkinson bar was used to study the dynamic behavior of titanium alloy
0921-5093/03/$ - see front matter # 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0921-5093(03)00292-2
L. Qiang et al. / Materials Science and Engineering A358 (2003) 128 /133
129
Table 1 Chemical compositions of Ti /17 (wt.%) Al
Mo
Sn
Cr
Zr
Fe
Si
C
N
H
O
Ti
4.0
4.0
2.69
4.03
1.99
0.12
0.04
0.10
0.018
0.01
0.096
remainder
(Ti /17) with initially equiaxed grains having an average size of 100 mm. The composition (wt.%) of the alloy is given in Table 1. The alloy was forged to the form of rod at 930 8C. It was heated at 800 8C for 5 h, followed by a water quenching and then tempered at 630 8C for 8 h. This treatment produced two-phase (a/b ) structure. The grain size was about 50 mm. The conventional mechanical properties at room temperature were as follows:
3. Results and discussion
1220 M Nm 2 1235 M Nm 2 15.5% 35%
Yield strength Tensile strength Elongation Reduction
3.1. Impact characteristics of cylindrical specimen
Two types of specimens were used in the SplitHopkinson pressure bar (SHPB). The first were cylindrical bars with diameters ranging from 3.0 to 5.50 mm, and with lengths from 4.0 to 5.50 mm. The second type was of conical frustums shown in Fig. 1. Two types of frustum were tested with the following dimensions respectively, (1) the diameter of the upper base f1 / 3.00 mm and the lower base f2 /5.50 mm, the height (h) being 5.20 mm and the angle of the side (uI), 76.78; and (2) the diameter of the upper base f1 /3.00 mm, the lower f2 /10.0 mm, the height (h ) being 5.00 mm and the angle of the side (uII), 65.08. The stress (s ), strain (o ) and strain rate (o) ˙ of the specimen are expressed as follows respectively: s E o o˙
A As
2C0 Ls 2C0 Ls
o T (t)
(1)
t
g (o (t) o (t))dt
(2)
(o I (t) o T (t))
(3)
I
T
0
Fig. 1. Schematic diagram of conical frustum specimen.
where E , C0 and A are the elastic modulus, the elastic wave speed and the sectional area of the Hopkinson pressure bar respectively. As and Ls are the section area and length of the specimen. oI(t) and oT(t) are experimentally measured strain of incident and transmitted stress pulse on the Hopkinson bars. Following the testing, the impacted specimens were examined using an optical microscope.
From equations Eqs. (1) /(3), the curves of strain rate /strain and stress /strain were obtained after oI(t) and oT(t) had been recorded by the data acquisition computer. The results presented in Fig. 2 were obtained over a wide range of impact speeds, using cylindrical specimens. From these curves, it is possible to determine the critical strain rate for fracture and the dynamic impact strength of Ti/17 at strain rates ranging from 1600 to 2200 s 1. Based on the principle of the SHPB, the stress pulse (oI(t)) measured on the incident bar was only dependent on the impact speed of the striker, while the other pulse (oT(t)) measured on the transmitted bar was determined by specimens’ characteristics and the incidental stress pulse. Therefore, if the specimen was fractured at a moment during the action of the incidental pulse, the specimen could not bear any force after the specimen had been fractured and thus the transmitted pulse (or stress) would be equal to zero after that moment. As a result, from equation Eq. (3), the value of (oI(t)/oT(t)) should increase with time after the moment of specimen failure. Inversely, it means that for the specimen to be fractured, (o˙ o) or (o˙ t) would increase sharply at a certain point in the duration of the stress pulse. From Fig. 2(a and c), it can be determined that the critical strain rate for the failure of Ti/17 was about 2000 s 1. Consequently, the flow stress and the impact strength of Ti /17 at high strain rates, of the order 103 s 1 increased with the strain rate and were in the range from 1250 to 1500 MPa, and from 1700 to 1800 MPa respectively as shown in Fig. 2(b and d). These figures show that the flow stress and impact strength of Ti /17 at high strain rates are obviously greater than those at quasi-static state. These experimental results of Ti /17 are similar to those of Ti /6Al / 4V reported earlier by Meyers et al. [11] and Harding [1].
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L. Qiang et al. / Materials Science and Engineering A358 (2003) 128 /133
Fig. 2. Impacting effects on Ti /17 at wide range of speeds (a) strain rate /strain for the fractured cylindrical specimens, (b) stress /strain for the fractured cylindrical specimens. (c) Strain rate /strain for the non fractured cylindrical specimens and (d) stress /strain for the non fractured cylindrical specimens.
3.2. Impact characteristics of frustum specimen The frustum specimen was loaded by SHPB to study the sensitivity of Ti/17 to stress at high-strain-rate deformation. After the specimen was impacted at different velocities, it was either broken or not broken. The breakage occurred at the smaller diametrical end, shown in Fig. 3. In Fig. 4 s1 and s2 represent the stress on the upper and the lower base of the frustum, respectively, and o˙ is strain rate just before the specimen being fractured. Obviously, there was a great stress gradient along the central axis within the frustum. Although the maximum stress on the upper base reached as high as 2750 MPa shown in Fig. 4(a), which
was even greater than the impact strength measured using cylindrical specimen (seeing Section 3.1 and Fig. 2(b)), the specimen did not show any fracture at all. The reason was that the strain rate was of 1750 s 1 (see Fig. 4(a)), which was less than the critical value (/o˙c/ /2000 s 1) for failure. Once the strain rate was over the critical value on a frustum specimen, as shown in Fig. 4(b), the specimen broke, and the (o˙ o) or (o˙ t) presented a sharp increase at a certain point. These results clearly show that the failure of Ti /17 is more sensitive to the strain rate than to the stress. In other words, Ti /17 alloy is able to bear overload impact if the strain rate is less than a critical strain rate for failure. Thus, the failure of Ti /17 is controlled by the impact speed, not by impact load. 3.3. Adiabatic shear band and failure
Fig. 3. Broken and unbroken frustum specimens.
3.3.1. Cylinder As shown in Fig. 5, the adiabatic shear band appeared as a hemicycle on the cross section of the cylindrical specimen, and the micro cracks were along with it. Xue et al. [12] have reported that the adiabatic shear bands
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131
adiabatic shear bands near the broken end of the frustum, shown in Fig. 6. However, a fully developed adiabatic shear band having a special form was observed on the transverse cross section and longitudinal section at the smaller end of unbroken specimen. This is shown in Fig. 7. Generally, the appearance of the adiabatic shear band was circular on the transverse cross section (see Fig. 7(a)). On the longitudinal section, it started on both sides, stretched to the center, then connected to each other (see Fig. 7(b)). From the combination of adiabatic shear bands on the two planes, it can be deduced that the shear localization zone is a conical shell in three dimensions. The adiabatic shear bands were only the traces between the conical shell and the observation plane. For type (1) impacted frustum, the measured angle between the shear band and the upper base in the longitudinal section through the central axis is 408, for type (2), the angle is 37.58. As shown in Fig. 8, inhomogeneous stresses are distributed within the frustum. There is experimental evidence that the whole material on one side of an adiabatic shear band is moved very large amounts of displacement relatively to the other side. The average shear stress on the shear plane corresponds to this movement. A simple analysis presented in Fig. 9 shows that the average shear stress (t¯a ) on a shear plane is: Fig. 4. Nominal stress /strain and strain rate /strain curves for a frustum specimen of Ti /17. s1 is the stress on the smaller diametrical plane, s2 is the stress on the larger diametrical plane. (a) For unbroken specimen (b) for broken specimen.
always precede the failure mechanism of titanium alloy (Ti /6Al /4V), and it has already been recognized that, for many metals and alloys, the cracking usually starts along the adiabatic shear band. The appearance of adiabatic shear band in the form of a hemicycle will be discussed in a later section.
3.3.2. Conical frustum Impacted frustums were observed under the optical microscope to examine the longitudinal section and transversal cross section. There still remained some
Fig. 5. Cracks along the adiabatic shear band on the transverse section of a cylindrical specimen.
t¯a p sin(2a)f21 s1 16s s 2
g
f1 =2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aby cy2 dy
(4a) (4b)
0
where a (f1 =2)(1ctg(u)tg(a))2 ; b f1 ctg(u)tg(a) (1ctg(u)tg(a)); c 1 ctg2 (u)tg2 (a): t¯a is a function of u and a . Fig. 9 shows that when s1 is constant, the average shear stress varies with the shear plane angle (a ) for four different types of frustum. For the two types of impacted specimens in our experiment, the angles of the side (u ) are equal to 76.78 and 658. As a result of calculation from equation Eqs. (4a) and (4b), the maximum average shear stress is located at a /41.38 and 37.28 respectively (see Fig. 9). For the two types of impacted specimens, measurements of the angle between the adiabatic shear band and the upper base are
Fig. 6. Adiabatic shear band at the smaller diametrical end of a broken conical frustum specimen.
132
L. Qiang et al. / Materials Science and Engineering A358 (2003) 128 /133
Fig. 7. Adiabatic shear band configuration in the unbroken conical frustum specimen. (a) On the transverse section and (b) on the longitudinal section through the central axis.
consistent with the calculated angles cited above. This means that the deformation localization (or adiabatic shear band) starts at the position where the shear stress reaches its maximum and propagates along the trace of the maximum shear stress. Shockey [13] have reported that the trajectory of shear bands near the dent in the target impacted by a projectile corresponds to the trace of maximum shear stress which is determined by a finite difference calculation of stress field. According to the geometry, the trace of maximum shear stress directions on the specimen with axial symmetry lies on a cone in three dimensions. When the specimen is loaded at a high impacting speed, the deformation localization happens
Fig. 8. Schematic diagram of the stress distribution near the smaller diametrical end. ta and sa represent shear stress and compressive stress on a shear plane respectively.
on the cone firstly. The deformation process could be described to be similar to a cone projectile penetrating into a plate. The deformation localization region is limited within the thin conical shell so that different appearances of adiabatic shear bands were observed on the longitudinal and the transverse sections respectively. The slight deflection and branching of shear band is obviously due to the microstructural features of the titanium alloy (Ti /17) studied. Kalthoff [14] reported on the modes of dynamic shear failure in solids. His experimental results showed that for high strength steel with mode-II crack, when the strain rate was sufficiently high enough (the impact velocity was above a certain value), the failure occurred by adiabatic shear bands. In the present study, the specimens were compressed by Hopkinson bar so that the compressive stress and shear stress are distributed within them. The micro cracks formed and propagated along the adiabatic shear band as shown in Figs. 5 and 6. The adiabatic shear band controlled the failure process. However, the formation of the band in most metals and alloys requires a sufficiently high strain rate. The existing critical strain rate for the failure of Ti/17 indicated that the failure resulted from the adiabatic shearing during impacting at high strain rate, which is consistent with Kalthoff’s results.
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Fig. 9. The variation of shear stress with shear plane angle (a is the angle between shear plane and the smaller diametrical plane) for four different types of frustum specimen (angle of half-cone u : 85, 76.7, 65 and 558).
4. Conclusions The following conclusions can be made about the dynamic behavior and the formation of adiabatic shear bands in a titanium alloy-Ti17: (1) The flow stress and the impact strength of Ti/17 both increased with strain rate of about 103 s 1. (2) The critical strain rate for failure of Ti/17 was about 2000 s 1, and the failure is more sensitive to the strain rate than to the applied stress. The experimental results show that Ti /17 can withstand a much higher stress pulse instantaneously if the strain rate is less than the critical value. (3) Before failure, the adiabatic shear band was formed initially at the location of the maximum shear stress, and actual deformation localization zone was confined in a conical shell in the specimen with axial symmetry.
Acknowledgements The specimens were impacted at the Laboratory for Non-linear Mechanics of Continuous Media; Institute of Mechanics, Chinese Academy of Sciences. The help of Professor Yilong Bai and Letain Shen is greatly appreciated. Also, the support of the Natural Science
and Engineering Research Council of Canada to one of the authors (M.N. Bassim) is acknowledged.
References [1] J. Harding, in: T.Z. Blazynshi (Ed.), Materials at High Strain Rates, Elsevier Applied Science, London and New York, 1987, p. P133. [2] D.R. Chichili, K.T. Ramesh, K.J. Hemker, Acta Mater. 46 (1998) 1025. [3] Y. Bai, B. Dodd, Adiabatic Shear Localization, Pergamon, Oxford, 1992, p. 24. [4] D. Kuhlmann-Wilsdorf, Met. Trans. 11A (1985) 2091. [5] L.P. Kubin, Phys. Stat. Sol. 135 (1993) 433. [6] T.G. Shawki, J. Appl. Mech. (Trans. ASME) 61 (1994) 538. [7] M.N. Bassim, J. Mater. Process. Tech. 119 (2001) 234. [8] S.P. Timothy, Acta Metall. 35 (1987) 301. [9] M.A. Meyers, V.F. Nesterenko, J.C. LaSalvia, Q. Xue, Mater. Sci. Eng. A317 (2001) 204. [10] V.F. Nesterenko, M.A. Meyers, T.W. Wright, Acta Mater. 46 (1998) 327. [11] M.A. Meyers, G. Subhash, B.K. Kad, L. Prasad, Mech. Mater. 17 (1994) 175. [12] Q. Xue, M.A. Meyers, V.F. Nesterenko, Acta Mater. 50 (2002) 575. [13] D.A. Shockey, in: L.E. Murr, K.P. Staudhammer, M.A. Meyers (Eds.), Metallurgical Applications of Shock-Wave and HighStrain-Rate Phenomena, Dekker, New York, 1986, p. 633. [14] J.F. Kalthoff, Inter. J. Fracture 101 (2000) 1.
Dynamic mechanical properties in relation to adiabatic shear band formation in titanium alloy-Ti17 Li Qiang a,1, Xu Yongbo b, M.N. Bassim a,* a
Faculty of Engineering, Department of Mechanical and Industrial Engineering, The University of Manitoba, Manitoba R3T 5V6, Canada b Institute of Metal Research, Chinese Academy of Sciences, Shenyang 110015, China Received 28 October 2002; received in revised form 21 March 2003
Abstract A Split-Hopkinson Pressure Bar system was used to determine the dynamic mechanical properties in relation to the formation of adiabatic shear bands in titanium alloy-Ti17. Cylindrical and conical frustum specimens were impacted between the incident and transmitted bars. The experimental results showed that the dynamic yield stress (syd) and impact strength (sbd) were both higher than the corresponding static values, and the failure was sensitive to the strain rate, but insensitive to the applied stress level. The critical strain rate for failure was o˙c/ /2000 s 1. Microscopic examinations revealed that the break of specimen frequently occurred along the shear band. A hemicyclic shear band appeared on the transverse section of the conical frustum, while a straight shear band developed at the location of maximum shear stress and propagated along the trace of the maximum shear stress, which was determined by the analysis of the stress distribution. # 2003 Elsevier Science B.V. All rights reserved. Keywords: Dynamic mechanical properties; Failure; Adiabatic shear band
1. Introduction Dynamic mechanical properties and adiabatic shear bands have been widely investigated in the last 40 years. Harding [1] gave a critical review on the effect of high strain rate on material properties. Chichili et al. [2] reported that true stress of a -Ti increased with true strain rates ranging from 1.16 /10 5 to 6.0 /103 s 1, which is in agreement with experimental evidence that most metals and alloys exhibit some increase in strength with increasing strain rate. Adiabatic shear bands usually dominate the deformation process and are the usual damage of metals at high strain rates [3]. Many studies focused both on various mechanical models and microstructure evolution of the adiabatic shear bands [4 /8]. It was recognized that the
* Corresponding author. Tel.: /1-204-474-8524; fax: /1-204-2757507. E-mail address: [email protected] (M.N. Bassim). 1 Present address: Faculty of Engineering, Department of Mechanical and Industrial Engineering, The University of Manitoba R3T 5V6, Canada and Tianjin University, Tianjin 300072, China
behavior of shear bands was a simple balance between hardening and softening of the material. Several kinds of configuration of adiabatic shear bands were observed. Most of them were concerned with an isolated shear band in two dimensions. Recently, however, Meyers et al. [9,10] found the formation of multi-shear bands in space through self-organization. In this current study, we report experimental results of dynamic mechanical properties of titanium alloy (Ti / 17) at high strain rates and show that the strain rate plays a key role in the failure of Ti /17 during deformation. From experimental observations of adiabatic shear bands in the conical frustum specimens, it is confirmed that the deformation localization is always formed on the maximum shear stress plane and the highly deformed region in the conical frustum specimen is confined in a thin conical shell in three dimensions.
2. Experimental procedure A modified compression Split-Hopkinson bar was used to study the dynamic behavior of titanium alloy
0921-5093/03/$ - see front matter # 2003 Elsevier Science B.V. All rights reserved. doi:10.1016/S0921-5093(03)00292-2
L. Qiang et al. / Materials Science and Engineering A358 (2003) 128 /133
129
Table 1 Chemical compositions of Ti /17 (wt.%) Al
Mo
Sn
Cr
Zr
Fe
Si
C
N
H
O
Ti
4.0
4.0
2.69
4.03
1.99
0.12
0.04
0.10
0.018
0.01
0.096
remainder
(Ti /17) with initially equiaxed grains having an average size of 100 mm. The composition (wt.%) of the alloy is given in Table 1. The alloy was forged to the form of rod at 930 8C. It was heated at 800 8C for 5 h, followed by a water quenching and then tempered at 630 8C for 8 h. This treatment produced two-phase (a/b ) structure. The grain size was about 50 mm. The conventional mechanical properties at room temperature were as follows:
3. Results and discussion
1220 M Nm 2 1235 M Nm 2 15.5% 35%
Yield strength Tensile strength Elongation Reduction
3.1. Impact characteristics of cylindrical specimen
Two types of specimens were used in the SplitHopkinson pressure bar (SHPB). The first were cylindrical bars with diameters ranging from 3.0 to 5.50 mm, and with lengths from 4.0 to 5.50 mm. The second type was of conical frustums shown in Fig. 1. Two types of frustum were tested with the following dimensions respectively, (1) the diameter of the upper base f1 / 3.00 mm and the lower base f2 /5.50 mm, the height (h) being 5.20 mm and the angle of the side (uI), 76.78; and (2) the diameter of the upper base f1 /3.00 mm, the lower f2 /10.0 mm, the height (h ) being 5.00 mm and the angle of the side (uII), 65.08. The stress (s ), strain (o ) and strain rate (o) ˙ of the specimen are expressed as follows respectively: s E o o˙
A As
2C0 Ls 2C0 Ls
o T (t)
(1)
t
g (o (t) o (t))dt
(2)
(o I (t) o T (t))
(3)
I
T
0
Fig. 1. Schematic diagram of conical frustum specimen.
where E , C0 and A are the elastic modulus, the elastic wave speed and the sectional area of the Hopkinson pressure bar respectively. As and Ls are the section area and length of the specimen. oI(t) and oT(t) are experimentally measured strain of incident and transmitted stress pulse on the Hopkinson bars. Following the testing, the impacted specimens were examined using an optical microscope.
From equations Eqs. (1) /(3), the curves of strain rate /strain and stress /strain were obtained after oI(t) and oT(t) had been recorded by the data acquisition computer. The results presented in Fig. 2 were obtained over a wide range of impact speeds, using cylindrical specimens. From these curves, it is possible to determine the critical strain rate for fracture and the dynamic impact strength of Ti/17 at strain rates ranging from 1600 to 2200 s 1. Based on the principle of the SHPB, the stress pulse (oI(t)) measured on the incident bar was only dependent on the impact speed of the striker, while the other pulse (oT(t)) measured on the transmitted bar was determined by specimens’ characteristics and the incidental stress pulse. Therefore, if the specimen was fractured at a moment during the action of the incidental pulse, the specimen could not bear any force after the specimen had been fractured and thus the transmitted pulse (or stress) would be equal to zero after that moment. As a result, from equation Eq. (3), the value of (oI(t)/oT(t)) should increase with time after the moment of specimen failure. Inversely, it means that for the specimen to be fractured, (o˙ o) or (o˙ t) would increase sharply at a certain point in the duration of the stress pulse. From Fig. 2(a and c), it can be determined that the critical strain rate for the failure of Ti/17 was about 2000 s 1. Consequently, the flow stress and the impact strength of Ti /17 at high strain rates, of the order 103 s 1 increased with the strain rate and were in the range from 1250 to 1500 MPa, and from 1700 to 1800 MPa respectively as shown in Fig. 2(b and d). These figures show that the flow stress and impact strength of Ti /17 at high strain rates are obviously greater than those at quasi-static state. These experimental results of Ti /17 are similar to those of Ti /6Al / 4V reported earlier by Meyers et al. [11] and Harding [1].
130
L. Qiang et al. / Materials Science and Engineering A358 (2003) 128 /133
Fig. 2. Impacting effects on Ti /17 at wide range of speeds (a) strain rate /strain for the fractured cylindrical specimens, (b) stress /strain for the fractured cylindrical specimens. (c) Strain rate /strain for the non fractured cylindrical specimens and (d) stress /strain for the non fractured cylindrical specimens.
3.2. Impact characteristics of frustum specimen The frustum specimen was loaded by SHPB to study the sensitivity of Ti/17 to stress at high-strain-rate deformation. After the specimen was impacted at different velocities, it was either broken or not broken. The breakage occurred at the smaller diametrical end, shown in Fig. 3. In Fig. 4 s1 and s2 represent the stress on the upper and the lower base of the frustum, respectively, and o˙ is strain rate just before the specimen being fractured. Obviously, there was a great stress gradient along the central axis within the frustum. Although the maximum stress on the upper base reached as high as 2750 MPa shown in Fig. 4(a), which
was even greater than the impact strength measured using cylindrical specimen (seeing Section 3.1 and Fig. 2(b)), the specimen did not show any fracture at all. The reason was that the strain rate was of 1750 s 1 (see Fig. 4(a)), which was less than the critical value (/o˙c/ /2000 s 1) for failure. Once the strain rate was over the critical value on a frustum specimen, as shown in Fig. 4(b), the specimen broke, and the (o˙ o) or (o˙ t) presented a sharp increase at a certain point. These results clearly show that the failure of Ti /17 is more sensitive to the strain rate than to the stress. In other words, Ti /17 alloy is able to bear overload impact if the strain rate is less than a critical strain rate for failure. Thus, the failure of Ti /17 is controlled by the impact speed, not by impact load. 3.3. Adiabatic shear band and failure
Fig. 3. Broken and unbroken frustum specimens.
3.3.1. Cylinder As shown in Fig. 5, the adiabatic shear band appeared as a hemicycle on the cross section of the cylindrical specimen, and the micro cracks were along with it. Xue et al. [12] have reported that the adiabatic shear bands
L. Qiang et al. / Materials Science and Engineering A358 (2003) 128 /133
131
adiabatic shear bands near the broken end of the frustum, shown in Fig. 6. However, a fully developed adiabatic shear band having a special form was observed on the transverse cross section and longitudinal section at the smaller end of unbroken specimen. This is shown in Fig. 7. Generally, the appearance of the adiabatic shear band was circular on the transverse cross section (see Fig. 7(a)). On the longitudinal section, it started on both sides, stretched to the center, then connected to each other (see Fig. 7(b)). From the combination of adiabatic shear bands on the two planes, it can be deduced that the shear localization zone is a conical shell in three dimensions. The adiabatic shear bands were only the traces between the conical shell and the observation plane. For type (1) impacted frustum, the measured angle between the shear band and the upper base in the longitudinal section through the central axis is 408, for type (2), the angle is 37.58. As shown in Fig. 8, inhomogeneous stresses are distributed within the frustum. There is experimental evidence that the whole material on one side of an adiabatic shear band is moved very large amounts of displacement relatively to the other side. The average shear stress on the shear plane corresponds to this movement. A simple analysis presented in Fig. 9 shows that the average shear stress (t¯a ) on a shear plane is: Fig. 4. Nominal stress /strain and strain rate /strain curves for a frustum specimen of Ti /17. s1 is the stress on the smaller diametrical plane, s2 is the stress on the larger diametrical plane. (a) For unbroken specimen (b) for broken specimen.
always precede the failure mechanism of titanium alloy (Ti /6Al /4V), and it has already been recognized that, for many metals and alloys, the cracking usually starts along the adiabatic shear band. The appearance of adiabatic shear band in the form of a hemicycle will be discussed in a later section.
3.3.2. Conical frustum Impacted frustums were observed under the optical microscope to examine the longitudinal section and transversal cross section. There still remained some
Fig. 5. Cracks along the adiabatic shear band on the transverse section of a cylindrical specimen.
t¯a p sin(2a)f21 s1 16s s 2
g
f1 =2 pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi aby cy2 dy
(4a) (4b)
0
where a (f1 =2)(1ctg(u)tg(a))2 ; b f1 ctg(u)tg(a) (1ctg(u)tg(a)); c 1 ctg2 (u)tg2 (a): t¯a is a function of u and a . Fig. 9 shows that when s1 is constant, the average shear stress varies with the shear plane angle (a ) for four different types of frustum. For the two types of impacted specimens in our experiment, the angles of the side (u ) are equal to 76.78 and 658. As a result of calculation from equation Eqs. (4a) and (4b), the maximum average shear stress is located at a /41.38 and 37.28 respectively (see Fig. 9). For the two types of impacted specimens, measurements of the angle between the adiabatic shear band and the upper base are
Fig. 6. Adiabatic shear band at the smaller diametrical end of a broken conical frustum specimen.
132
L. Qiang et al. / Materials Science and Engineering A358 (2003) 128 /133
Fig. 7. Adiabatic shear band configuration in the unbroken conical frustum specimen. (a) On the transverse section and (b) on the longitudinal section through the central axis.
consistent with the calculated angles cited above. This means that the deformation localization (or adiabatic shear band) starts at the position where the shear stress reaches its maximum and propagates along the trace of the maximum shear stress. Shockey [13] have reported that the trajectory of shear bands near the dent in the target impacted by a projectile corresponds to the trace of maximum shear stress which is determined by a finite difference calculation of stress field. According to the geometry, the trace of maximum shear stress directions on the specimen with axial symmetry lies on a cone in three dimensions. When the specimen is loaded at a high impacting speed, the deformation localization happens
Fig. 8. Schematic diagram of the stress distribution near the smaller diametrical end. ta and sa represent shear stress and compressive stress on a shear plane respectively.
on the cone firstly. The deformation process could be described to be similar to a cone projectile penetrating into a plate. The deformation localization region is limited within the thin conical shell so that different appearances of adiabatic shear bands were observed on the longitudinal and the transverse sections respectively. The slight deflection and branching of shear band is obviously due to the microstructural features of the titanium alloy (Ti /17) studied. Kalthoff [14] reported on the modes of dynamic shear failure in solids. His experimental results showed that for high strength steel with mode-II crack, when the strain rate was sufficiently high enough (the impact velocity was above a certain value), the failure occurred by adiabatic shear bands. In the present study, the specimens were compressed by Hopkinson bar so that the compressive stress and shear stress are distributed within them. The micro cracks formed and propagated along the adiabatic shear band as shown in Figs. 5 and 6. The adiabatic shear band controlled the failure process. However, the formation of the band in most metals and alloys requires a sufficiently high strain rate. The existing critical strain rate for the failure of Ti/17 indicated that the failure resulted from the adiabatic shearing during impacting at high strain rate, which is consistent with Kalthoff’s results.
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Fig. 9. The variation of shear stress with shear plane angle (a is the angle between shear plane and the smaller diametrical plane) for four different types of frustum specimen (angle of half-cone u : 85, 76.7, 65 and 558).
4. Conclusions The following conclusions can be made about the dynamic behavior and the formation of adiabatic shear bands in a titanium alloy-Ti17: (1) The flow stress and the impact strength of Ti/17 both increased with strain rate of about 103 s 1. (2) The critical strain rate for failure of Ti/17 was about 2000 s 1, and the failure is more sensitive to the strain rate than to the applied stress. The experimental results show that Ti /17 can withstand a much higher stress pulse instantaneously if the strain rate is less than the critical value. (3) Before failure, the adiabatic shear band was formed initially at the location of the maximum shear stress, and actual deformation localization zone was confined in a conical shell in the specimen with axial symmetry.
Acknowledgements The specimens were impacted at the Laboratory for Non-linear Mechanics of Continuous Media; Institute of Mechanics, Chinese Academy of Sciences. The help of Professor Yilong Bai and Letain Shen is greatly appreciated. Also, the support of the Natural Science
and Engineering Research Council of Canada to one of the authors (M.N. Bassim) is acknowledged.
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