DISLOCATION STRUCTURE AND NON-PROPORTIONAL HARDENING OF TYPE 304 STAINLESS STEEL

-This paper describes the microstructure of Type 304 stainless steel after cyclic loading at room temperature under tension-torsion non-proportional strain paths. The degree of cyclic non-proportional hardening is correlated with changes in the dislocation substructure. Dislocation cells, dislocation bundles, twins and stacking faults are all observed. The type of microstructure formed and resultant stress response is dependent on the degree of non-proportional loading and strain range. Cyclic stress range was uniquely correlated with mean cell size


INTRODUCTION
Many practical applications such as the nuclear vessel of a fast breeder reactor have nonproportional stresses and strains under the combination of thermal and mechanical loading. Type 304 stainless steel is known as a material which shows a significant additional cyclic hardening under non-proportional loading in comparison with proportional loading. Recent studies have shown that the degree of the additional cyclic hardening is material dependent. Doong et al. [ 11 reported the relationship between the microstructure and additional cyclic hardening behavior of 1100 aluminum alloy, oxygen free pure copper and Type 304 and 3 10 stainless steels. They reported that no additional hardening occurred in aluminum alloy but significant additional hardening in stainless steel. Non-proportional cyclic hardening was reported for pure copper. They discussed the microstructure change with proceeding cycles in detail for a limited number of strain paths.
Cailletaud et al. [ a ] compiled much of the published data and concluded that the main parameter governing the degree of non-proportional hardening in solid solution material is the ease of cross slip. Itoh [ 3,4] studied non-proportional cyclic hardening of Type 304 stainless steel, pure copper, pure nickel, pure aluminum and 6061-T6 aluminum and reported that the degree of additional cyclic hardening is related to the stacking fault energy of the material. For a material with a low stacking fault energy, such as Type 304 stainless steel, planar slip occurs and results in a large amount of additional cyclic hardening. This is caused by the interaction of many slip systems. Materials with a high stacking fault energy such as pure aluminum and 6061-T6 aluminum alloy deform by wavy slip. These materials do not show additional cyclic hardening during nonproportional loading. The difference in the additional hardening behavior between high and low stacking fault energy materials is to be related to the microstructure of the material but extensive and systematic studies have not yet been reported.
Several investigators have examined the dislocation structure for room temperature tests. Doquet [ 51 reported twin deformation as a primary deformation mechanism under non-proportional loading for binary Co33Ni. She reported that the increase in the amount of twin deformation is a cause of additional cyclic hardening during non-proportional loading. Jiao et al.
[ 61 examined alloy 800 H and observed deformation twins and suggested that the formation of twins depends not only on the shear stress but also on the normal stress acting on the slip plane. McDowell et al. [7] found that the heterogeneity of emartensite and other planar slip deformation products (e.g. d-martensite) are a function of a non-proportionality in 304 stainless steel. They found that the homogeneity and morphology of the deformation products is of key importance. Cailletaud et al. [2]  Microstructural studies of additional non-proportional cyclic hardening have been limited to a small number of strain paths so that the results of these studies are rather qualitative. Little quantitative discussion has been reported. This paper studies the microstructure and cyclic stressstrain relationships obtained at room temperature under 14 non-proportional strain paths for Type 304 stainless steel, and will discuss the relationship between stress response and cell structure quantitatively.

EXPERIMENTAL PROCEDURE
The material tested is Type 304 stainless steel that received a solution treatment at 1373 K for 1 h. Hollow cylindrical specimens with 9 mm I.D., 12 mm O.D., and 4.6 mm gage length were employed in this study. Strain controlled cyclic loading tests at a Mises' effective strain rate of O.l%/s were carried out at ambient temperature. Testing details are reported by Itoh et at. [9]. Figure 1 shows the 14 proportional and non-proportional loading histories employed, where E and y are the axial and shear strains, respectively. Case 0 is a push-pull proportional test which is the basic data for examining the microstructure. Case 0 testing was carried out at strain ranges between 0.5 and 1.5%. Case 5 is also a proportional test as in Case 0, but is a combined push-pull and reversed torsion test. The other cases are non-proportional tests in which the severity of nonproportional loading is determined by the strain history. In all the tests except for Case 0, axial and shear strain ranges were 0.5 and 0.8% Mises' equivalent strain.
One cycle is defined here as a full straining for both axial and shear strain. All the tests except Cases 3, 4 and 13 were counted as one cycle and these tests were counted as two cycles for a full straining along the strain path chosen in Fig. 1. The number of cycles to failure (Nf) was defined as the cycle at which the axial stress amplitude decreased to 5% of the saturation stress in tension.
After the cyclic loading tests, thin foils of 3 mm diameter were cut from specimens away from cracks by a wire cutter to observe the microstructure. They were polished down to about 0.2 mm in thickness with emery papers and were jet-electropolished in acetic and perchloric acid. A JEOL JEM-100C (100 kV) was used to observe the microstructure and diffraction pattern.

DEFINITION OF PRINCIPAL STRAIN AND STRESS RANGES AND NON-PROPORTIONAL PARAMETER
During non-proportional loading, stress and strain amplitudes vary with time, so that the principal strain and stress ranges must be defined. In a previous paper [9], the authors have proposed a definition of the maximum principal strain and stress ranges for non-proportional loadings and this paper follows that definition.
The maximum principal strain range, Acl, is defined as, In this equation, EI(t) is the maximum absolute value of principal strain at time t and where cl(t) and c 3 ( t ) are the maximum and minimum principal strains at time t, respectively.  The maximum principal stress range, Aol( t) has a similar definition to Aq, A o l = 4 4 + cos(S(B))@) ai(t)= Ioi(t)I for ICi(t)I 2 Io3(t)I, oi(t)= Ios(t)I for I C i ( t ) I G /a&)/ where ol(t) and 0 3 ( t ) are the maximum and minimum principal stresses, respectively. The two times A and B correspond with those defined for the maximum principal strain range.
A non-proportional factor, fNp, was proposed by the authors to express the severity of nonproportional loading [9].
where T is the time for a cycle shown in Fig. 1. The value off,, is zero under proportional loading and is the range of 0 *fNp + 1 under non-proportional loading. As shown in Eq. (4), fNp is a function of only the applied strain history to avoid the need to compute stresses and plastic strains.
The authors [ 91 have proposed the following strain parameter to correlate non-proportional LCF lives, where 01 is a material parameter related to the additional hardening of the material under nonproportional loading, and 01 is defined as the ratio of stress range under non-proportional circular loading in y / q 3 -~ plot to that under proportional loading at the same Mises equivalent strain.
The value of CI becomes larger for lower stacking fault energy materials [l-41. Murakami et al.
[lo] showed that this parameter will decrease with increasing temperatures. For Type 304 stainless steel at room temperature, c( takes the value of 0.9. Benallal and Marquis [ 111 show a small strain range dependence of a but here we take it as a constant. The term (1 + txfNp) accounts for the additional cyclic hardening observed during non-proportional cyclic loading and is similar to damage parameters that are based on the product of stress and strain range. The advantage of this parameter is that it does not require a sophisticated transient cyclic plasticity model to obtain the stress ranges.

EXPERIMENTAL RESULTS AND DISCUSSION
A complete tabular listing of all test data is available in [9]. Table 1 is a condensed version that gives the stress and strain ranges, fatigue lives and computed non-proportional loading factor for the 14 strain paths in Fig. 1. Mean cell size is also included. Fatigue lives for cases 0-13 significantly depend on the strain history. Rotating principal strain directions in tests such as Cases 8-10, 12 and 13 yields the largest reduction in fatigue lives by as much as a factor of 10. In Cases 6-9, steps in the path can have a large influence on fatigue lives when the number of steps is small and the path length is large. Thus, Case 6 shows a small reduction in fatigue life as the strain history is nearly proportional loading because of the small step length. Figure 3 correlates LCF lives with principal stress range. The figure shows that a significant additional hardening occurs under non-proportional loadings. Greater additional cyclic hardening results in smaller fatigue lives. Thus, an estimate of additional hardening is necessary for predicting fatigue lives under non-proportional loading in the LCF regime. Figure 4 correlates the non-proportional LCF lives with equivalent strain given in Eq. (5). Most of the data are correlated within a factor of two scatter bands. Figure 5 shows the relationship between the stabilized axial and shear stresses for twelve of the fourteen loading histories. The stress response for Case 8 is the mirror image of Case 9 and was omitted from the figure. In the figures, solid lines are the results at As = 0.5%, and dashed lines are the results at As = 0.8%. The shear stress scale has been plotted as one half of the axial stress scale so that stresses can easily be compared on the basis of maximum shear stress. Comparing the equivalent stresses in Table 1 for Cases 1 and 2 with Case 0 at A s = 0.5 and 0.8% shows significant non-proportional hardening due to the change of principal strain direction at zero strain. The normal stress-shear stress relationship of Case 1 is different from that of Case 2 which shows that a fully reversed straining has a different influence on stress response from a zero-tomaximum straining, and the former strain history causes greater additional hardening than the latter one. This additional hardening also results in a lower fatigue life for Case 2. The shape of the T-C plot of Cases 3 and 4 is similar to that of Cases 1 and 2, respectively, after giving a rotation of 45" to the former two cases. However, the stress amplitude of Cases 3 and 4 is larger than that of Cases 1 and 2 because the shear and axial strains are applied simultaneously resulting in a cyclic strain range in the former two cases that is larger by about 1.4 times.
A simple method of visualizing the degree of non-proportionality is useful when interpreting the stresses in Fig. 5. If an ellipse is drawn so as to circumscribe the entire stress path, nonproportionality can be thought of as the ratio of the minor axis to the major axis. In Case 5, the minor axis of an ellipse circumscribing the loading history is small which corresponds to a low degree of non-proportionality. The degree of non-proportionality increases in going from Case 5 to Case 10. This is easily visualized as an increasingly circular ellipse circumscribing the stress history. The size of the ellipse also increases as the degree of non-proportionality increases. Case 5 is proportional loading where the normal stress amplitude c is the same as the shear stress amplitude V3.r since the normal strain equals the shear strain on Mises basis. Comparing the    stress response in Table 1 and Fig. 5 of Case 5 with that of Cases 6, 7 and 8 shows that the normal and shear stress amplitudes are larger as the degree of non-proportionality increases. Fatigue lives tend to decrease as these stresses increase.

Fail-Nr
Comparison of the stress response between Cases 5, 11 and 12 illustrates the effect of loading phase between the normal and shear strains. A linear stress-strain relationship is obtained on T-0 plot for Case 5, but a box 7-0 relationship is found for Cases 11 and 12. The normal and shear stress ranges in Cases 11 and 12 are significantly larger than those of Case 5 and the stresses in Case 12 are somewhat larger than in comparison with Case 11. The principal strain amplitude of Case 12 is smaller than that of Case 11. This indicates that the 90" phase difference has a greater hardening effect than a 45" phase difference. Case 13 exhibits a much more significant additional hardening than Case 12, which indicates that the turn around of straining increases the additional hardening effect. Cases 8, 9 and 10 give the largest additional hardening among the 13 strain paths. A 40-60% normal stress increase is found in these three strain paths in comparison with the Case 0 test. Socie [ 123 has reported the circular strain path has a more pronounced additional hardening than the box strain path for this material where a 90% stress increase was found in the circular strain path.

OBSERVATIONS OF DISLOCATION STRUCTURE
Additional hardening has been reported to have a close connection with dislocation structure [9], but there have been few systematic and quantitative studies of the relationship between the microstructure and additional hardening. Figure 6(a)-( j) show the microstructure observed by TEM. Figure 6(a) shows the dislocation structure before testing where the dislocation density is very low and no specific substructure is identified.
A cell structure is observed in Case 0, Fig. 6(b) where the mean cell diameter is around 1 pm. Cell formation was also observed in the specimens cyclically loaded at large strain ranges (> 1%) in Case 0. Dislocation bundles which indicates the cluster of dislocations were observed at low strain ranges (< 0.8%) in Case 0.
Cell structures, twins and stacking faults were observed in Case 1, Fig. 6(c), but only twins and stacking faults were observed in Case 3, Fig. 6(d). No clear cell formation was found in Case 3, and dislocation bundles were observed. Many stacking faults occurred before cell formation and they appear to hinder the cell formation in Case 3. The number of stacking faults in Case 3 is larger than that in Case 1. The phasing of the applied strains produces larger stress and strain ranges for Case 3. Nishino et al.
[ 81 reported that a ladder of maze structure was a common structure for Type 304 stainless steel in proportional straining and a cell structure was primarily found in the nonproportional straining like Case 1 at high temperature. At room temperature, however, cell structures formed and no ladder or maze structures were observed in Case 0 loading. This difference in dislocation structure between room and elevated temperatures results from the difference in the thermal activation. At elevated temperatures, dislocations glide more easily to form a structure of low elastic energy by the assistance of thermal activation so that a ladder or maze structure, which is a lower elastic energy microstructure than the cell, was found. In Case 5, which is a proportional straining, Fig. 6(e), cell structures were observed. A deformation twin boundary was also observed at the center of the photograph. Diffraction patterns were taken for all of the dislocation structures but it was difficult to distinguish between stacking faults and martensite that was observed by McDowell et al. [7]. Case 7, Fig. 6(f), shows a coherent boundary of an annealing twin at the center of the photograph. It's role is similar to a grain boundary for the deformation microstructure. Dislocation walls are observed in the right of the photograph, and a cell structure is found in the left of the photograph. In Case 7, columnar cells were formed and Fig. 6(f) shows the two different sections of the columnar grains; the left is the normal section to columnar axes and the right is the parallel section of them. In Case 7, the maximum shear strain direction changed its direction, so that dislocations would easily rearrange to columnar structure by the cross steps.
Cases 5-10 all have the same maximum shear strain ranges. Cases 8-10 have a rectangular or box strain history. In these strain paths, the maximum shear strain direction rotates continuously, so that many slip systems operate. The additional hardening was most significant in these strain paths. Cases 11-13 are also rectangular strain paths but the phasing of the strains is such that the maximum shear strain range is smaller than Cases 5-10. In Case 9, Fig. 6(g), cell boundaries are not clear, but many dislocations exist even in the cells. The maximum shear stress direction rotates continuously in Case 9, so many slip planes operate and interact, which results in the significant additional hardening.
In Cases 10 and 11, Figs 6(h) and (i), many stacking faults or martensite was observed. There is little difference between a stacking fault and martensite formation. A stacking fault forms when one atomic plane is dropped off and when more than two atomic planes have a disordering it is a different structure which may be martensite. Since Type 304 stainless steel is a material of low stacking fault energy, slip is planar and there are many partial dislocations which make a stacking fault between them. Long stacking faults exceeding several subgrains in length were formed in Case 10 with short stacking faults formed within cells in Case 11. The long stacking faults were formed by the severe box non-proportional straining and which hindered the cell formation, while, in Case 11, the cells were formed earlier than the stacking faults and stacking faults were stopped by the cell boundaries. For Case 13, fine cells are found and they are rather close to subgrain since thc cell boundaries are rigid and misorientation angle between cells is rather large. This strain path made resulted in clear cells and rigid cell boundaries. Figure 7 is a microstructure map showing the cell, dislocation bundle and stacking fault boundaries as functions of maximum principal strain range and non-proportional factor for all the strain paths. In the figure, solid symbols indicate tests in which only cells were observed, while open symbols represent tests in which cells and other dislocation structures were found. Asterisks indicate tests where stacking faults were observed and the number at the data indicates the strain path number shown in Fig. 1. This figure shows that stacking faults were observed in almost all the tests and did not depend on the principal strain range and non-proportional factor. Type 304 is a low stacking fault energy material and a dislocation easily splits into partial dislocations, making a stacking fault between them. A partial dislocation glides on the slip plane, and a stacking fault arises between the partial dislocations. Many stacking faults seem to be generated by this mechanism. There is a critical combination of strain range and non-proportional factor for forming cells indicated by the solid line. In the region above the line, the microstructure is dominated by cells with other microstructures in addition to cells observed for the test conditions below the solid line. Figure 8 shows the relationship between the mean cell size and the maximum principal stress range for all the tests where the cell structure was observed. The mean cell size was determined by the Heyn method (JIS G0552), observing 3 or 4 locations of each specimen. Maximum principal stress range and mean cell size can be approximated by a straight line for all of the strain histories. The relationship is, The values of m and n are 975 MPa and -0.57, respectively when d is measured in pm. The value of exponent is close to -1/2, so that the Hall-Petch relationship holds in proportional and nonproportional loadings. As shown in Fig. 7, various microstructures are formed under nonproportional loading. However, the results in Fig. 8 indicate that the additional hardening in non-proportional loading is mainly caused by reduction of cell size. The severe interaction of slip systems under non-proportional loading reduces the cell size and results in the additional hardening.
The results also imply that microstructures other than cell structure have almost no influence on the additional hardening.

CONCLUSIONS
( 1) Dislocation substructures observed under non-proportional loading were associated with cells, stacking faults, twins and bundles.
(2) A microstructure map was proposed that show conditions for forming cells and stacking faults as functions of the maximum principal strain range and a non-proportional factor. There exists a critical boundary for forming cells. Stacking faults were observed in almost all the proportional and non-proportional tests.
( 3 ) The principal stress range was uniquely correlated with the mean cell size and is independent of the strain loading path which indicates that the additional hardening was mainly associated with a reduction of cell size.