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Dislocation Structure and Non-proportional Hardening of Type SUS304 Stainless Steel at Elevated Temperature
Sun Liang
Abstract: This paper describes the microstructure especially the dislocation structure of SUS304 stainless steel after tension-torsion non-proportional cyclic loading at elevated temperature. We use the principal strain range and non-proportional factor to describe the non-proportional loading. Regarding the dislocation structure we will use TEM to observe the typical structures of the specimen. Then we compare the dislocation microstructure of different non-proportional loadings and try to throw light on the relationship between them.
Keywords: Non-proportional loading, Cyclic plastic, Multiaxial fatigue, Dislocation structures
1. Introduction
Components of machine operating at high temperature receive multi-axial damage (non-proportional loading) rather than uni-axial damage. In non-proportional loading tests, some materials’ fatigue lives are decreased by as much as a factor of 10 compare with those in proportional loading tests with the same strain range. Recent studies have shown that the decrease happened in non-proportional fatigue life is mainly because of the additional cyclic hardening happened in materials when non- proportional loading is employed. But systematic studies in this field have not yet been reported. SUS304 stainless steel is one of the materials with significant additional cyclic hardening under non-proportional loading. In this research we take SUS304 as an example. We hope to throw light on the relationship between non-proportional loading and microstructure mechanism of additional cyclic hardening.
2. Experimental Procedure
2.1 Non-proportional fatigue test
The material tested is SUS304 stainless steel that received a solution treatment at high enough temperature for one hour. Dimensions of the specimen are shown in Fig.1. To explorer the relationship between microstructure we carried out non-proportional fatigue experiments with the following loading paths (Fig.2). Loading parameters of different cases are described in Table.1.
Fig.1 Dimensions of the specimen tested (mm)
Table.1. Loading Parameters and Experiment Results of Every Case with Different Loading Path
|
Specimen No
|
Starin path number (Case) |
Failure cycle Nf Cycles |
Axial strain range Δε,％ |
Shear strain range Δγ,％ |
ASME strain range ΔεASME,％ |
Path strain range Δεpath,％ |
Principal strain range ΔεⅠ,％ |
COD strain range Δε*,％ |
Axial stress range Δσ,MPa |
Shear stress range Δτ,MPa |
Principal stress range ΔσⅠ,MPa |
|
1143 |
0 |
7200 |
0.40 |
0.00 |
0.40 |
0.40 |
0.40 |
0.40 |
401 |
0 |
401 |
|
1127 |
0 |
3000 |
0.50 |
0.00 |
0.50 |
0.50 |
0.50 |
0.50 |
456 |
0 |
456 |
|
1168 |
0 |
400 |
1.00 |
0.00 |
1.00 |
1.00 |
1.00 |
1.00 |
531 |
0 |
531 |
|
1135 |
5 |
3000 |
0.40 |
0.69 |
0.57 |
0.57 |
0.56 |
0.54 |
383 |
148 |
431 |
|
1185 |
6 |
3200 |
0.40 |
0.69 |
0.57 |
0.80 |
0.56 |
0.54 |
388 |
184 |
444 |
|
1163 |
10 |
1200 |
0.40 |
0.69 |
0.57 |
0.80 |
0.56 |
0.54 |
447 |
284 |
493 |
|
1134 |
11 |
3000 |
0.40 |
0.69 |
0.45 |
0.57 |
0.45 |
0.44 |
428 |
248 |
446 |
|
1136 |
12 |
3200 |
0.40 |
0.69 |
0.40 |
0.57 |
0.40 |
0.40 |
473 |
300 |
476 |
|
1138 |
13 |
2600 |
0.40 |
0.69 |
0.40 |
0.57 |
0.40 |
0.40 |
475 |
257 |
476 |
|
1158 |
14 |
1200 |
0.40 |
0.69 |
0.40 |
0.63 |
0.40 |
0.40 |
497 |
319 |
499 |
|
1113 |
1 |
1100 |
0.50 |
0.87 |
0.50 |
1.00 |
0.50 |
0.50 |
612 |
377 |
616 |
|
1116 |
2 |
1300 |
0.50 |
0.87 |
0.50 |
1.00 |
0.50 |
0.50 |
497 |
320 |
509 |
|
1114 |
3 |
1400 |
0.50 |
0.87 |
0.71 |
0.71 |
0.70 |
0.67 |
501 |
278 |
610 |
|
1120 |
4 |
1100 |
0.50 |
0.87 |
0.71 |
0.71 |
0.70 |
0.67 |
374 |
257 |
566 |
|
1184 |
7 |
750 |
0.50 |
0.87 |
0.71 |
1.00 |
0.70 |
0.67 |
461 |
267 |
512 |
|
1153 |
10 |
500 |
0.50 |
0.87 |
0.71 |
1.00 |
0.70 |
0.67 |
582 |
342 |
617 |
|
1119 |
11 |
900 |
0.50 |
0.87 |
0.56 |
0.71 |
0.56 |
0.55 |
492 |
311 |
526 |
|
1118 |
12 |
830 |
0.50 |
0.87 |
0.50 |
0.71 |
0.50 |
0.50 |
524 |
345 |
532 |
|
1141 |
13 |
1300 |
0.50 |
0.87 |
0.50 |
0.71 |
0.50 |
0.50 |
547 |
354 |
557 |
|
1157 |
14 |
920 |
0.50 |
0.87 |
0.50 |
0.79 |
0.50 |
0.50 |
531 |
350 |
535 |
|
1126 |
1 |
575 |
0.70 |
1.21 |
0.70 |
1.40 |
0.70 |
0.70 |
658 |
395 |
664 |
|
1180 |
2 |
280 |
0.70 |
1.21 |
0.70 |
1.40 |
0.70 |
0.70 |
615 |
353 |
624 |
|
1182 |
4 |
581 |
0.70 |
1.21 |
0.99 |
0.99 |
0.97 |
0.94 |
456 |
276 |
607 |
|
1131 |
5 |
990 |
0.70 |
1.21 |
0.99 |
0.99 |
0.97 |
0.94 |
441 |
196 |
511 |
|
1170 |
6 |
450 |
0.70 |
1.21 |
0.99 |
1.40 |
0.97 |
0.94 |
457 |
242 |
494 |
|
1171 |
10 |
250 |
0.70 |
1.21 |
0.99 |
1.40 |
0.97 |
0.94 |
480 |
315 |
630 |
|
1132 |
11 |
650 |
0.70 |
1.21 |
0.78 |
0.99 |
0.78 |
0.78 |
495 |
343 |
541 |
|
1123 |
12 |
310 |
0.70 |
1.21 |
0.70 |
0.99 |
0.70 |
0.70 |
583 |
374 |
598 |
|
1130 |
13 |
440 |
0.70 |
1.21 |
0.70 |
0.99 |
0.70 |
0.70 |
575 |
378 |
606 |
|
1159 |
14 |
335 |
0.70 |
1.21 |
0.70 |
1.10 |
0.70 |
0.70 |
593 |
391 |
600 |
Fig.2 Proportional and non-proportional loading paths.
2.2. Non-proportional loading parameters
We choose principal strain rangeΔεⅠ, principal stress range and non- proportional factor to describe the non- proportional loading. These three parameters are defined as follow:
In the first Eq., ε1(t) and ε3(t) are the maximum and minimum principal strains at time t. ε1max in above Eq. is the maximum value of ε1(t) in a cycle and ξ(t) is the angle between ε1max and ε1(t) directions. Thus Δε1(t) is determined by the two strains, ε1(A) and ε1(B), and by the angle between the two strain directions where A is the time giving ε1max and B the time maximizing the strain range in above Eq.
In the second Eq., σ and σ3 are the maximum and minimum principal stresses, respectively. The two time A and B correspond with those defined for the maximum principal strain range.
In the third Eq., T is the time for a cycle shown in Fig.1. The value of is zero under proportional loading and is the range of 0< <1 under non-proportional loading. is a function of only the applied strain history to avoid the need to compute stresses and plastic strains.
Table.2. Non-proportional Factor of Different Case
|
Strain Path Number |
Non-proportional Factor |
|
0 |
0.00 |
|
1 |
0.34 |
|
2 |
0.34 |
|
3 |
0.39 |
|
4 |
0.39 |
|
5 |
0.00 |
|
6 |
0.10 |
|
7 |
0.20 |
|
8 |
0.77 |
|
9 |
0.77 |
|
10 |
0.77 |
|
11 |
0.46 |
|
12 |
0.77 |
|
13 |
0.77 |
|
14 |
0.88 |
The first two parameters of every loading path was calculated and established in Table.1. As for non-proportional factor, I put the results of calculation in Table.2.
2.3. Microstructure Observation
TEM photos were taken with the typical structure of different loading paths. We want to throw some light on the relationships between microstructure and the different non-proportional loading paths.
The positions of TEM specimen on the multi-axial fatigue tested experiment pieces are illustrated on Fig.2. as follow:
Fig.2 Field of TEM observation (mm)
3. Experiment Results and Discussion
|
|
|
|
|
|
|
|
|
|
|
|
Fig. 3 Microstructure observed by JEOL 200V TEM (in all Photos: 200nm ___ )
Microstructures can be observed in Fig.3 (Page 6). The photos in Fig.3 are order in the following sequence:
|
Normal State |
Diffraction of left field |
|
Case 0, Δε=1.0% |
Diffraction of left field |
|
Case 3, Δε=0.5% |
Case 7, Δε=0.5% |
|
Case 11, Δε=0.7% |
Case 13, Δε=0.7% |
In Fig.3, Dislocation cells, dislocation bundles, twins and stacking faults are all observed. The typical microstructure found in different cases is dependent on the degree of non-proportional loading and strain range (Fig.4).
Fig.4 Relationship between microstructure, maximum principal strain range and non-proportional factor
The filled black point in Fig.4 represents that the microstructure of this case is mainly sub-cells no obvious dislocation bundles. Correspondingly, the unfilled point represents the microstructure of sub-cells and dislocation bundles. There is a solid line between two kinds of microstructure in Fig.4. In the region above the line, the microstructure is dominated by cells with different microstructure from the cells in the region below this line.
3. 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 an non-proportional tests.
4. Bibliography
1) D. F. Socie (1987) Multi-axial fatigue damage models. J. Engng Mater. Technol. 109(3), 293-298.
2) S. H. Doong, D. F. Socie and I. M. Robertson (1990) Dislocation substructure and non-proportional hardening. J. Engng Mater. Technol. 112(4), 456-465
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