- Email: [email protected]
Tensile properties of a type 316 stainless steel strained in air and vacuum
Materials Science and Engineering A256 (1998) 34 – 38
Tensile properties of a type 316 stainless steel strained in air and vacuum A.A. Abduluyahed, K.J. Kurzydłowski * Department of Materials Science and Engineering, Warsaw Uni6ersity of Technology, Narbutta 85, 02 -524 Warsaw, Poland Received 1 April 1998; received in revised form 17 July 1998
Abstract Results on the tensile properties of a type 316 austenitic stainless steel deformed in two test environments (air and vacuum) are presented. Specimens strained in vacuum at temperatures ranging from 673 to 873 K exhibit systematically higher resistance to plastic deformation. The same applies to specimens pre-aged either in vacuum or air and strained at room temperature. The lower values of flow stress for specimens annealed/strained in air are explained in terms of free-surface softening due to stress concentrations at the oxide–substrate interface and oxidized grain boundaries in the near-surface zone. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Austenitic stainless steel; Tensile properties; Environmental effect
1. Introduction The dependence of the flow stress, s, on test temperature, T, for type 316 austenitic stainless steels exhibit three characteristics regions. The flow stress decreases with increasing temperature in the ranges T 5500 or T ] 1000 K. On the other hand for 5005 T 51000 K the flow stress at a given plastic elongation is approximately constant and in some cases a local maximum of s is observed (e.g. [1,2]). In recent years a large number of papers reported that the flow stress of metals and intermetallics depends on the test environment (e.g. [3 – 14]). In the present paper the combined effect of test temperature and environment on the tensile properties of type 316 stainless steel has been studied. The two test environments used in the present case were atmospheric air and vacuum.
2. Materials and heat treatments The experiments were performed on two types of commercial austenitic stainless steels: AISI 316 and * Corresponding author. Tel.: + 48 22 499929; fax: + 48 22 484875.
AISI 316L. The chemical compositions of the materials are given in Table 1. The materials were delivered in the form of rods after cold drawing. Cylindrical (4 mm diameter) and flat (1.8 mm× 3.0 mm) tensile specimens were recrystallized in air at two temperatures: 1173 and 1323 K. All specimens were water quenched after recrystallization. Some of the specimens were additionally annealed at 873 K for 30 min–2 h in air or in vacuum. Tensile tests were performed at a constant cross-head speed of 0.5 mm min − 1, which corresponds to an engineering strain rate of 2× 10 − 4 s − 1. All the tensile tests were carried out on the same universal testing machine manufactured by INSTRON and equipped with a standard furnace and vacuum system. The machine was calibrated before each test and at least two specimens were strained for each combination of specimen geometry, recrystallization temperature, test environment, and test temperature. The time required to stabilize the temperature of specimens at elevated temperatures before straining was 30 min. Tests at room temperature were carried out only in air. Load and displacement were logged and processed numerically. The load–displacement data were analyzed using a computer routine to compute the stress– strain curves. The load–extension curves and stress–strain curves were characterized in terms of:
0921-5093/98/$ - see front matter © 1998 Elsevier Science S.A. All rights reserved. PII S0921-5093(98)00841-7
A.A. Abduluyahed, K.J. Kurzydłowski / Materials Science and Engineering A256 (1998) 34–38
35
the number of serrations per interval of strain, the flow stress s at a given strain o (o = 2, 4, and 6%), ultimate tensile strength, UTS. The grain size of the recrystallized specimens was measured using the random sections method. Specimens for grain size measurements were prepared according to standard metallographic procedures. Transverse and longitudinal sections were polished and etched using a 60% solution of HNO3 (this method of etching ensured that twin boundaries were not revealed).
3. Results
3.1. Stress –strain cur6es Some stress–strain curves for specimens strained at elevated temperatures are shown in Fig. 1. Both specimens, whether strained in vacuum or in air, display serrations typical of the Portevin – LeChatelier effect. As reported elsewhere [14] the frequency of the serrations is higher for straining in air. On the other hand straining in vacuum results in: higher values of the flow stress s for a given value of plastic strain, higher values of ultimate tensile strength, UTS, lower values of strain to fracture, of. The values of flow stress, s(o), for o =2, 4 and 6% are plotted against the test temperature in Fig. 2. An environmental effect on the flow stress for 316 steel is seen at temperatures higher than 673 K, as shown in Fig. 2(a). For both 316 steel shown in Fig. 2(b) and 316L shown in Fig. 2(c) the flow stress measured in vacuum is consistently higher. Since the tensile tests in the present study were restricted to one strain rate, an explanation of the critical test temperature (683 K in the present case) above which the environmental effect is observed is not possible. However, it has been noted that this temperature coincides with the minimum temperatures at which oxidation of 316 steel in atmospheric air proceeds at a noticeable rate. The difference between the flow stress measured in Table 1 Chemical composition of the austenitic stainless steels used in the present study Steel
C
Cr
Ni
Mo
Mn
Si
P
S
316L 316
0.02 0.04
16.5 17.0
10.9 15.9
2.0 2.7
1.4 2.0
0.77 0.19
0.031 0.023
0.044 0.005
Values are in in wt.%.
Fig. 1. Stress – strain curves typical of the specimens of steels 316 and 316L recrystallized at 1173 K in air and strained at 773 K in vacuum [vac.] and in air [air].
vacuum and air for test temperatures higher than 673 K ranges from 30 to 50 MPa. This is approximately 15% of the value measured in air. The flow stress of 316 steel, in the given range of temperatures, increases with increasing temperature (clear evidence of dynamic strain aging (DSA)) while the flow stress of 316L is basically constant.
3.2. The effect of specimen geometry The effect of specimen geometry on the flow stress in air at 873 K has been studied by comparing data between flat and cylindrical specimens. The result is shown in Fig. 3. These two sets of 316 steel specimens differ in terms of the surface-to-volume ratio, SV, of their gauge sections. Simple calculations give (SV)c =1 mm − 1 for cylindrical and (SV)f = 1.8 mm − 1 for flat specimens. Fig. 3 shows that the flow stress of flat specimens at early stages of plastic deformation is significantly lower than the one recorded for cylindrical specimens. This suggests a softening of the specimens’ surface.
3.3. The influence of grain size In order to estimate the relative contributions of grain size and environment (vacuum/air) to the flow stress of the material at 873 K, tensile tests were carried out on specimens recrystallized at 1173 and 1325 K. These two recrystallization temperatures led to grain size (l) of 11 and 18 mm, respectively. This
36
A.A. Abduluyahed, K.J. Kurzydłowski / Materials Science and Engineering A256 (1998) 34–38
Fig. 2. Plot of the dependence of the mean values (three specimens) of the flow stress at a given plastic strain, s(o), on the test temperature, T, for specimens strained in vacuum (open symbols) and air (solid symbols) for steels 316 (a and b) and 316L (c).
implies that the difference in the values of l − 1/2 exceeds 20%. The corresponding stress – strain curves are shown in Fig. 4. Comparison of the curves for these two recrystallization temperatures leads to the conclusion that the flow stress at 873 K depends more on the test environment than on the grain size of the specimens.
3.4. Room temperature properties Room temperature tensile properties were examined in addition to those determined at elevated tempera-
tures. Room temperature tensile tests were performed on: as-recrystallized specimens (recrystallization temperature 1173 K) additionally annealed at 873 K in air additionally annealed at 873 K in vacuum The stress–strain curves are shown in Fig. 5. It should be noted that the additional annealing of recrystallized specimens in vacuum brings about an increase of the flow stress in the range of small plastic strains. (Further results on room temperature properties can be found in [15].)
A.A. Abduluyahed, K.J. Kurzydłowski / Materials Science and Engineering A256 (1998) 34–38
Fig. 3. Stress – strain curves for flat and cylindrical specimens of steel 316 strained in air at 873 K.
4. Discussion The results obtained in the present study reveal a significant effect of test environment on tensile properties of type 316 austenitic stainless steel. Similar results have recently been published for a number of metals and intermetallics. An environmental effect has been also reported for an austenitic stainless steel (e.g. [16]). However, the present results seem to be the first evidence of this effect in austenitic stainless steel in a standard tensile test.
Fig. 4. Stress – strain curves obtained at 873 K, as a result of straining in air and in vacuum, (see curve labels) for specimens of steel 316 recrystallized at 1173 and 1325 K.
37
Fig. 5. Stress – strain curves obtained at room temperature for specimens of steel 316 recrystallized at 1173 K and additionally annealed at 873 K (static annealing) in vacuum and air (see curve labels).
The test environment effect observed in the present study can be attributed the state of the specimens’ surface and can be explained using the concept of a softening effect of the surface on the properties of the materials (e.g. [17]). Similar results for the test environment on Cr have recently been reported by Morinaga et al. [17] (a surface softening effect has also been observed in Nb, Ta, Mo, W). Using specially designed equipment for cleaning and straining in a vacuum chamber they found that the intrinsic yield stress of Cr is higher than the one measured under standard conditions in which specimens are covered with oxide scales. It has been suggested that the flow stress of most metals is probably higher than the reported values which have been obtained in conventional mechanical tests in air. Observation of surface effect on the plasticity of an austenitic stainless steel calls for revision of the standard equations used in modeling the flow stress of polycrystals. It is suggested here that these relationships (e.g. Hall–Petch equation) should contain an additional term describing the softening/hardening contribution of the surface. In general this term should be weighted by an SV ratio for a given geometry of the specimens. The discussion presented here concentrates attention on the mechanical properties of the materials studied. Microstructural observations of the surface, near-surface zone and core of the specimens are reported in [18] (details can be found in [19]). These observations revealed the presence of environment-controlled surface stress concentrators in the form of cracks in the oxide scales and oxidized grain boundaries. Such concentra-
38
A.A. Abduluyahed, K.J. Kurzydłowski / Materials Science and Engineering A256 (1998) 34–38
tors lower the flow stress of the material in the nearsurface zone. Under the conditions of stress localization this reduction of the flow stress may significantly lower the macroscopic flow stress of strained specimens leading to the effect of environmental surface softening. The effect of surface on the properties of materials has been discussed previously in proceedings edited by Latanision and Fourie [20]. In the introductory the lecture Latanision [21] stated that ‘‘the surface effect has been by and large ignored in modern theories of work hardening’’ and that ‘‘qualitatively and quantitatively the influence of surface structure on mechanical properties is virtually un-explored’’. The results reported here seem to substantiate this remark and call for further theoretical and experimental studies of the environmental effect on tensile properties of austenitic stainless steels and perhaps other metals.
References [1] K.J. Kurzydłowski, K.J. McTaggart, K. Tangri, Phil. Mag. A61 (1990) 61. [2] V.S. Srinivasan, R. Sandhya, M. Valsan, K. Bhanu Sankara Rao, S.L. Mannan, D.H. Sastry, Scr. Mater. 37 (1997) 1593.
.
[3] M. Garland, J. Mendez, P. Violan, A. Ait Saadi, Mater. Sci. Eng. A118 (1988) 83. [4] R.D.K. Misra, Scr. Mater. 35 (1996) 1347. [5] D. Bika, C.J. McMahon Jr., Acta Metall. Mater. 43 (1995) 1909. [6] G. Itoh, K. Kayoma, M. Kanno, Scr. Mater. 35 (1996) 695. [7] C.G. McKamey, E.H. Lee, J.W. Cohron, E.P. George, Scr. Mater. 35 (1996) 181. [8] K. Seith, R. Gibala, Acta Metall. 25 (1977) 321. [9] T. Tottori, J.E. Talia, R. Gibala, Scr. Metall. 14 (1980) 1153. [10] J.E. Talia, L. Fernandez, R. Gibala, Scr. Metall. 12 (1978) 737. [11] V.K. Sethi, R. Gibala, Scr. Metall 11 (1977) 635. [12] V.K. Sethi, R. Gibala, Scr. Metall 9 (1975) 527. [13] L. Hong, G. Kewei, C. Wuyang, Scr. Mater. 37 (1997) 1387. [14] A.A. Abduluyahed, K. Roz; niatowski, K.J. Kurzydłowski, Scr. Mater. 33 (1995) 1489. [15] K.J. Kurzydłowski, Mater. Sci. Eng. A234-236 (1997) 1083. [16] T. Magnin, Mater. Sci. Forum 202 (1996) 3. [17] M. Morinaga, Y. Murata, M. Furui, T. Wada, Scr. Mater. 37 (1997) 699. [18] W. Zielin´ski, A.A. Abduluyahed, K.J. Kurzydłowski, Mater. Sci. Eng. (in press). [19] A.A. Abduluyahed, PhD Thesis, Warsaw University of Technology, 1998. [20] R.M. Latanision, J.T. Fourie (Eds.), Surface Effects in Crystal Plasticity, NATO Advanced Study Institutes Series, Series E: Applied Science No. 17, Noordhoff-Leyden, 1977. [21] R.M. Latanision, Surface Effects in crystal plasticity: general overview, in: R.M. Latanision, J.T. Fourie (Eds.), Surface Effects in Crystal Plasticity, NATO Advanced Study Institutes Series, Series E: Applied Science No. 17, Noordhoff-Leyden, 1977, p. 3
Tensile properties of a type 316 stainless steel strained in air and vacuum A.A. Abduluyahed, K.J. Kurzydłowski * Department of Materials Science and Engineering, Warsaw Uni6ersity of Technology, Narbutta 85, 02 -524 Warsaw, Poland Received 1 April 1998; received in revised form 17 July 1998
Abstract Results on the tensile properties of a type 316 austenitic stainless steel deformed in two test environments (air and vacuum) are presented. Specimens strained in vacuum at temperatures ranging from 673 to 873 K exhibit systematically higher resistance to plastic deformation. The same applies to specimens pre-aged either in vacuum or air and strained at room temperature. The lower values of flow stress for specimens annealed/strained in air are explained in terms of free-surface softening due to stress concentrations at the oxide–substrate interface and oxidized grain boundaries in the near-surface zone. © 1998 Elsevier Science S.A. All rights reserved. Keywords: Austenitic stainless steel; Tensile properties; Environmental effect
1. Introduction The dependence of the flow stress, s, on test temperature, T, for type 316 austenitic stainless steels exhibit three characteristics regions. The flow stress decreases with increasing temperature in the ranges T 5500 or T ] 1000 K. On the other hand for 5005 T 51000 K the flow stress at a given plastic elongation is approximately constant and in some cases a local maximum of s is observed (e.g. [1,2]). In recent years a large number of papers reported that the flow stress of metals and intermetallics depends on the test environment (e.g. [3 – 14]). In the present paper the combined effect of test temperature and environment on the tensile properties of type 316 stainless steel has been studied. The two test environments used in the present case were atmospheric air and vacuum.
2. Materials and heat treatments The experiments were performed on two types of commercial austenitic stainless steels: AISI 316 and * Corresponding author. Tel.: + 48 22 499929; fax: + 48 22 484875.
AISI 316L. The chemical compositions of the materials are given in Table 1. The materials were delivered in the form of rods after cold drawing. Cylindrical (4 mm diameter) and flat (1.8 mm× 3.0 mm) tensile specimens were recrystallized in air at two temperatures: 1173 and 1323 K. All specimens were water quenched after recrystallization. Some of the specimens were additionally annealed at 873 K for 30 min–2 h in air or in vacuum. Tensile tests were performed at a constant cross-head speed of 0.5 mm min − 1, which corresponds to an engineering strain rate of 2× 10 − 4 s − 1. All the tensile tests were carried out on the same universal testing machine manufactured by INSTRON and equipped with a standard furnace and vacuum system. The machine was calibrated before each test and at least two specimens were strained for each combination of specimen geometry, recrystallization temperature, test environment, and test temperature. The time required to stabilize the temperature of specimens at elevated temperatures before straining was 30 min. Tests at room temperature were carried out only in air. Load and displacement were logged and processed numerically. The load–displacement data were analyzed using a computer routine to compute the stress– strain curves. The load–extension curves and stress–strain curves were characterized in terms of:
0921-5093/98/$ - see front matter © 1998 Elsevier Science S.A. All rights reserved. PII S0921-5093(98)00841-7
A.A. Abduluyahed, K.J. Kurzydłowski / Materials Science and Engineering A256 (1998) 34–38
35
the number of serrations per interval of strain, the flow stress s at a given strain o (o = 2, 4, and 6%), ultimate tensile strength, UTS. The grain size of the recrystallized specimens was measured using the random sections method. Specimens for grain size measurements were prepared according to standard metallographic procedures. Transverse and longitudinal sections were polished and etched using a 60% solution of HNO3 (this method of etching ensured that twin boundaries were not revealed).
3. Results
3.1. Stress –strain cur6es Some stress–strain curves for specimens strained at elevated temperatures are shown in Fig. 1. Both specimens, whether strained in vacuum or in air, display serrations typical of the Portevin – LeChatelier effect. As reported elsewhere [14] the frequency of the serrations is higher for straining in air. On the other hand straining in vacuum results in: higher values of the flow stress s for a given value of plastic strain, higher values of ultimate tensile strength, UTS, lower values of strain to fracture, of. The values of flow stress, s(o), for o =2, 4 and 6% are plotted against the test temperature in Fig. 2. An environmental effect on the flow stress for 316 steel is seen at temperatures higher than 673 K, as shown in Fig. 2(a). For both 316 steel shown in Fig. 2(b) and 316L shown in Fig. 2(c) the flow stress measured in vacuum is consistently higher. Since the tensile tests in the present study were restricted to one strain rate, an explanation of the critical test temperature (683 K in the present case) above which the environmental effect is observed is not possible. However, it has been noted that this temperature coincides with the minimum temperatures at which oxidation of 316 steel in atmospheric air proceeds at a noticeable rate. The difference between the flow stress measured in Table 1 Chemical composition of the austenitic stainless steels used in the present study Steel
C
Cr
Ni
Mo
Mn
Si
P
S
316L 316
0.02 0.04
16.5 17.0
10.9 15.9
2.0 2.7
1.4 2.0
0.77 0.19
0.031 0.023
0.044 0.005
Values are in in wt.%.
Fig. 1. Stress – strain curves typical of the specimens of steels 316 and 316L recrystallized at 1173 K in air and strained at 773 K in vacuum [vac.] and in air [air].
vacuum and air for test temperatures higher than 673 K ranges from 30 to 50 MPa. This is approximately 15% of the value measured in air. The flow stress of 316 steel, in the given range of temperatures, increases with increasing temperature (clear evidence of dynamic strain aging (DSA)) while the flow stress of 316L is basically constant.
3.2. The effect of specimen geometry The effect of specimen geometry on the flow stress in air at 873 K has been studied by comparing data between flat and cylindrical specimens. The result is shown in Fig. 3. These two sets of 316 steel specimens differ in terms of the surface-to-volume ratio, SV, of their gauge sections. Simple calculations give (SV)c =1 mm − 1 for cylindrical and (SV)f = 1.8 mm − 1 for flat specimens. Fig. 3 shows that the flow stress of flat specimens at early stages of plastic deformation is significantly lower than the one recorded for cylindrical specimens. This suggests a softening of the specimens’ surface.
3.3. The influence of grain size In order to estimate the relative contributions of grain size and environment (vacuum/air) to the flow stress of the material at 873 K, tensile tests were carried out on specimens recrystallized at 1173 and 1325 K. These two recrystallization temperatures led to grain size (l) of 11 and 18 mm, respectively. This
36
A.A. Abduluyahed, K.J. Kurzydłowski / Materials Science and Engineering A256 (1998) 34–38
Fig. 2. Plot of the dependence of the mean values (three specimens) of the flow stress at a given plastic strain, s(o), on the test temperature, T, for specimens strained in vacuum (open symbols) and air (solid symbols) for steels 316 (a and b) and 316L (c).
implies that the difference in the values of l − 1/2 exceeds 20%. The corresponding stress – strain curves are shown in Fig. 4. Comparison of the curves for these two recrystallization temperatures leads to the conclusion that the flow stress at 873 K depends more on the test environment than on the grain size of the specimens.
3.4. Room temperature properties Room temperature tensile properties were examined in addition to those determined at elevated tempera-
tures. Room temperature tensile tests were performed on: as-recrystallized specimens (recrystallization temperature 1173 K) additionally annealed at 873 K in air additionally annealed at 873 K in vacuum The stress–strain curves are shown in Fig. 5. It should be noted that the additional annealing of recrystallized specimens in vacuum brings about an increase of the flow stress in the range of small plastic strains. (Further results on room temperature properties can be found in [15].)
A.A. Abduluyahed, K.J. Kurzydłowski / Materials Science and Engineering A256 (1998) 34–38
Fig. 3. Stress – strain curves for flat and cylindrical specimens of steel 316 strained in air at 873 K.
4. Discussion The results obtained in the present study reveal a significant effect of test environment on tensile properties of type 316 austenitic stainless steel. Similar results have recently been published for a number of metals and intermetallics. An environmental effect has been also reported for an austenitic stainless steel (e.g. [16]). However, the present results seem to be the first evidence of this effect in austenitic stainless steel in a standard tensile test.
Fig. 4. Stress – strain curves obtained at 873 K, as a result of straining in air and in vacuum, (see curve labels) for specimens of steel 316 recrystallized at 1173 and 1325 K.
37
Fig. 5. Stress – strain curves obtained at room temperature for specimens of steel 316 recrystallized at 1173 K and additionally annealed at 873 K (static annealing) in vacuum and air (see curve labels).
The test environment effect observed in the present study can be attributed the state of the specimens’ surface and can be explained using the concept of a softening effect of the surface on the properties of the materials (e.g. [17]). Similar results for the test environment on Cr have recently been reported by Morinaga et al. [17] (a surface softening effect has also been observed in Nb, Ta, Mo, W). Using specially designed equipment for cleaning and straining in a vacuum chamber they found that the intrinsic yield stress of Cr is higher than the one measured under standard conditions in which specimens are covered with oxide scales. It has been suggested that the flow stress of most metals is probably higher than the reported values which have been obtained in conventional mechanical tests in air. Observation of surface effect on the plasticity of an austenitic stainless steel calls for revision of the standard equations used in modeling the flow stress of polycrystals. It is suggested here that these relationships (e.g. Hall–Petch equation) should contain an additional term describing the softening/hardening contribution of the surface. In general this term should be weighted by an SV ratio for a given geometry of the specimens. The discussion presented here concentrates attention on the mechanical properties of the materials studied. Microstructural observations of the surface, near-surface zone and core of the specimens are reported in [18] (details can be found in [19]). These observations revealed the presence of environment-controlled surface stress concentrators in the form of cracks in the oxide scales and oxidized grain boundaries. Such concentra-
38
A.A. Abduluyahed, K.J. Kurzydłowski / Materials Science and Engineering A256 (1998) 34–38
tors lower the flow stress of the material in the nearsurface zone. Under the conditions of stress localization this reduction of the flow stress may significantly lower the macroscopic flow stress of strained specimens leading to the effect of environmental surface softening. The effect of surface on the properties of materials has been discussed previously in proceedings edited by Latanision and Fourie [20]. In the introductory the lecture Latanision [21] stated that ‘‘the surface effect has been by and large ignored in modern theories of work hardening’’ and that ‘‘qualitatively and quantitatively the influence of surface structure on mechanical properties is virtually un-explored’’. The results reported here seem to substantiate this remark and call for further theoretical and experimental studies of the environmental effect on tensile properties of austenitic stainless steels and perhaps other metals.
References [1] K.J. Kurzydłowski, K.J. McTaggart, K. Tangri, Phil. Mag. A61 (1990) 61. [2] V.S. Srinivasan, R. Sandhya, M. Valsan, K. Bhanu Sankara Rao, S.L. Mannan, D.H. Sastry, Scr. Mater. 37 (1997) 1593.
.
[3] M. Garland, J. Mendez, P. Violan, A. Ait Saadi, Mater. Sci. Eng. A118 (1988) 83. [4] R.D.K. Misra, Scr. Mater. 35 (1996) 1347. [5] D. Bika, C.J. McMahon Jr., Acta Metall. Mater. 43 (1995) 1909. [6] G. Itoh, K. Kayoma, M. Kanno, Scr. Mater. 35 (1996) 695. [7] C.G. McKamey, E.H. Lee, J.W. Cohron, E.P. George, Scr. Mater. 35 (1996) 181. [8] K. Seith, R. Gibala, Acta Metall. 25 (1977) 321. [9] T. Tottori, J.E. Talia, R. Gibala, Scr. Metall. 14 (1980) 1153. [10] J.E. Talia, L. Fernandez, R. Gibala, Scr. Metall. 12 (1978) 737. [11] V.K. Sethi, R. Gibala, Scr. Metall 11 (1977) 635. [12] V.K. Sethi, R. Gibala, Scr. Metall 9 (1975) 527. [13] L. Hong, G. Kewei, C. Wuyang, Scr. Mater. 37 (1997) 1387. [14] A.A. Abduluyahed, K. Roz; niatowski, K.J. Kurzydłowski, Scr. Mater. 33 (1995) 1489. [15] K.J. Kurzydłowski, Mater. Sci. Eng. A234-236 (1997) 1083. [16] T. Magnin, Mater. Sci. Forum 202 (1996) 3. [17] M. Morinaga, Y. Murata, M. Furui, T. Wada, Scr. Mater. 37 (1997) 699. [18] W. Zielin´ski, A.A. Abduluyahed, K.J. Kurzydłowski, Mater. Sci. Eng. (in press). [19] A.A. Abduluyahed, PhD Thesis, Warsaw University of Technology, 1998. [20] R.M. Latanision, J.T. Fourie (Eds.), Surface Effects in Crystal Plasticity, NATO Advanced Study Institutes Series, Series E: Applied Science No. 17, Noordhoff-Leyden, 1977. [21] R.M. Latanision, Surface Effects in crystal plasticity: general overview, in: R.M. Latanision, J.T. Fourie (Eds.), Surface Effects in Crystal Plasticity, NATO Advanced Study Institutes Series, Series E: Applied Science No. 17, Noordhoff-Leyden, 1977, p. 3