Deformation Behavior and Load Sequence Effects
4.3 Effect of Loading Sequence or History on Cyclic Deformation
To demonstrate the difference in material response with respect to loading sequence, incremental step tests were conducted on the three materials. A single
63 specimen of each material was subjected to increasing and then decreasing strain amplitudes. Each strain level was maintained for a number of cycles large enough to obtain a fairly constant response (i.e. saturated response).
The applied strain history for SS304L is presented in Figure 4.11. Only three strain levels were used for this material, as a relatively high number of cycles was required to obtain fairly steady (i.e. saturated) stress response (see Figure 4.12). For aluminum, four strain levels were used, with several increasing and decreasing sequences.
As expected, the stress response for SS304L, as shown in Figure 4.12, is strongly affected by the prior higher strain amplitude cycles in the sequence. In contrast, for aluminum, the stress response was similar for identical total strain amplitude and the prior loading did not affect subsequent stress response of the material. This can be explained in terms of the difference in SFE for the two materials, discussed earlier.
During cyclic loading, cross slip is difficult in stainless steel with low SFE making its deformation behavior dependent on the prior loading, while cross slip is easier in aluminum with high SFE making its deformation behavior independent of prior loading.
Stable results from the incremental step tests of stainless steel and aluminum are presented in Figure 4.13. For aluminum (see Figure 4.13(c)), the stress response does not depend on previous loading, as it is stable and independent of the prior higher loads in the loading sequence. For SS304L (Figures 4.13(a) and 4.13(b)), however, the stress response is greatly affected by the prior higher loading. Aluminum is thus considered a material with little or no deformation history effect, whereas SS304L possesses a strong deformation history effect.
64 An incremental step test up to 1% strain amplitude was also carried out on a prestrained SS304L CLI specimen. Prestraining at 2% strain amplitude for 10 cycles induced strong hardening and the material had a different behavior as compared to the virgin material. The stress amplitude for the prestrained specimen was about 25% higher than for the virgin specimen, resulting in lower plastic strain amplitude at a given strain amplitude. Continuous softening was observed throughout the prestrained incremental step test, regardless of the loading sequence. In addition, while the unloading curve in the incremental step test for the virgin (V) specimen was above the loading curve (see Figure 4.13(a) where the results for the prestrained (PS) tests are superimposed), the loading and unloading curves were nearly identical for the prestrained specimen. This indicates that if the stress is saturated at a prior higher loading (i.e. 2% strain amplitude here), deformation behavior at subsequent loading-unloading to a lower level (i.e. 1% strain amplitude here) is independent of the load sequence (i.e. load history independent).
4.4 Conclusions
1) Stainless steel 304L and aluminum 7075-T6 represent extreme cases with respect to strain history dependence, and the deformation behavior with respect to loading history is related to their stacking fault energy.
2) Stainless steel 304L investigated in this study continuously hardens with increasing cycles in LCF as well as HCF, whereas for aluminum 7075-T6 steady state behavior was observed for the entire life regime. While the deformation curves under monotonic and cyclic loading are similar for the aluminum alloy, strong cyclic hardening was observed for stainless steel, which became more significant at higher strain amplitude.
65 3) While monotonic stress-strain curves are nearly identical for the two grades of SS304L, the cyclic deformation behaviors differ, due in part to the bilinearity in the behavior of the SS304L CLI grade.
4) Austenitic stainless steel presents a transient behavior in the stress response under strain control and in the strain response under load control, under fully-reversed constant amplitude cyclic loading. Also due to its low stacking fault energy, deformation behavior of this type of material is greatly dependent on prior loading history (strong deformation history effect), as shown by the incremental step tests for which the stress-strain loading and unloading paths do not coincide.
5) Aluminum possesses a higher SFE and thus has less sensitivity to overloading (i.e. little or no deformation history effect). Therefore, no effect of prestraining was observed for this material, while prestraining induced strong hardening in SS304L.
66 Table 4.1 Summary of the mechanical tensile properties for SS304L CLI, SS304L
THY and Al 7075-T6.
Monotonic Properties SS304L CLI SS304L THY Al 7075-T6
Modulus of elasticity, E (GPa) 196 193 70.6
Yield strength (0.2% offset), Sy (MPa) 208 202 533
Ultimate tensile strength, Su (MPa) 585 608 578
Percent reduction in area, %RA 84 83 34
Strength coefficient, K (MPa) 680 804 704
Strain hardening exponent, n 0.214 0.255 0.05
True fracture strength, σf (MPa)* 2051 1763 737
True fracture ductility, εf (%) 186 178 41
Cyclic Properties SS304L CLI SS304L THY Al 7075-T6
Cyclic modulus of elasticity, E ' (GPa) 196 193 70.6
Fatigue strength coefficient,
bilinear fit, σf1' / σf2' (MPa) 330 / 1,890 2,558 / 819 689 / 1,587 Fatigue strength exponent,
bilinear fit, b1 / b2 -0.037 / -0.204 -0.239/ -0.104 -0.032/ -0.145 Fatigue ductility coefficient, εf',
bilinear fit, εf1' / εf2' 0.133 0.5218 / 0.0242 0.110 Fatigue ductility exponent, c,
bilinear fit, c1 / c2 -0.374 -0.5566 / -0.2033 -0.509
Cyclic strength coefficient, K',
bilinear fit, K1' / K2' (MPa) 434 / 4742 2224 790
Cyclic strain hardening exponent n',
bilinear fit, n1' / n2' 0.111/ 0.512 0.341 0.062
Cyclic yield strength, Sy' (MPa) 220 238 540
*using Bridgman correction factor for necking
67
(a)
(b)
(c)
Figure 4.1 True stress versus true plastic strain for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.
68
(a)
(b)
(c)
Figure 4.2 Monotonic tension experimental stress-strain curves and superimposed Ramberg-Osgood fits for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.
69
Figure 4.3 Comparison of the monotonic tension experimental stress-strain curves between SS304L CLI and THY grades.
0 50 100 150 200 250 300 350
0.0% 0.5% 1.0% 1.5% 2.0% 2.5%
Strain
Stress (MPa)
Monotonic curve (experimental) THY Monotonic curve (experimental) CLI
70
100 1000
0.01% 0.10% 1.00% 10.00%
Plastic Strain Amplitude
Stress Amplitude (MPa)
UT data MMC data
(a)
100 1000
0.10% 1.00% 10.00%
Plastic Strain Amplitude
Stress Amplitude (MPa)
(b)
100 1000
0.10% 1.00% 10.00%
Plastic Strain Amplitude
Stress Amplitude (MPa)
(c)
Figure 4.4 Stress amplitude versus calculated plastic strain amplitude data and fits for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.
71
(a)
(b)
(c)
Figure 4.5 Stress amplitude versus strain amplitude for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.
72
(a)
(b)
(c)
Figure 4.6 Stress response in fully-reversed constant amplitude strain-controlled tests for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.
1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7 1E+8 Number of Cycles, N
1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7
Number of Cycles, N
1E+1 1E+2 1E+3 1E+4 1E+5 1E+6 1E+7
Number of Cycles, N
73
(a)
(b)
(c)
Figure 4.7 Strain response in fully-reversed constant amplitude load-controlled tests for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.
74
(a)
(b)
(c)
Figure 4.8 Hysteresis loops for fully-reversed constant amplitude strain-controlled tests for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.
-700
εa (starting on the outside)
-700
εa (starting on the outside)
-700
εa (starting on the outside)
75
(a)
(b)
(c)
Figure 4.9 Superimposed monotonic tension and cyclic curves for (a) SS304L CLI, (b) SS304L THY, and (c) Al 7075-T6.
76
0 100 200 300 400 500 600 700
0.0% 0.5% 1.0% 1.5% 2.0% 2.5%
Strain Amplitude
Stress Amplitude (MPa)
Cyclic curve THY Cyclic curve CLI
Figure 4.10 Comparisons between cyclic stress-strain curves for SS304L CLI and THY grades.
Figure 4.11 Strain history for the incremental step test on SS304L (CLI and THY).
77
(a)
(b)
Figure 4.12 Stress response from incremental step tests for SS304L (a) CLI, and (b) THY.
78
Figure 4.13 Superimposed stress response for incremental step tests in strain control for (a) SS304L CLI, SS304L THY, and (c) Al 7075-T6.
79