Andrew J. Ring

Ohio Aerospace Institute, Brook Park, Ohio

Eric H. Baker

Connecticut Reserve Technologies, Inc., Cleveland, Ohio

Jonathan A. Salem and John C. Thesken

Glenn Research Center, Cleveland, Ohio

Yield Behavior of Solution Treated

and Aged Ti-6Al-4V

NASA/TM—2014-218322

June 2014
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Andrew J. Ring

Ohio Aerospace Institute, Brook Park, Ohio

Eric H. Baker

Connecticut Reserve Technologies, Inc., Cleveland, Ohio

Jonathan A. Salem and John C. Thesken

Glenn Research Center, Cleveland, Ohio

Yield Behavior of Solution Treated

and Aged Ti-6Al-4V

NASA/TM—2014-218322

June 2014

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Acknowledgments

The authors thank Joe Lewis, NASA Jet Propulsion Laboratory (JPL) for valuable input and comments on the testing and results.

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Level of Review: This material has been technically reviewed by technical management. 
NASA/TM—2014-218322 1 

Yield Behavior of Solution Treated and Aged Ti-6Al-4V 

Andrew J. Ring 

Ohio Aerospace Institute 

Brook Park, Ohio 44142 

Eric H. Baker 

Connecticut Reserve Technologies, Inc. 

Cleveland, Ohio 44040 

Jonathan A. Salem and John C. Thesken 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

Summary 

Post yield uniaxial tension-compression tests were run on a solution treated and aged (STA), titanium 

6-percent aluminum 4-percent vanadium (Ti-6Al-4V) alloy to determine the yield behavior on load 

reversal. The material exhibits plastic behavior almost immediately on load reversal implying a strong 

Bauschinger effect. The resultant stress-strain data was compared to a 1D mechanics model and a finite 

element model used to design a composite overwrapped pressure vessel (COPV). Although the models 

and experimental data compare well for the initial loading and unloading in the tensile regime, agreement 

is lost in the compressive regime due to the Bauschinger effect and the assumption of perfect plasticity. 

The test data presented here are being used to develop more accurate cyclic hardening constitutive models 

for future finite element design analysis of COPVs. 

Introduction 

Monolithic metallic propellant tanks have been used in a variety of space-related missions such as the 

Space Shuttle, the International Space Station, and the Apollo missions. The stresses in these tanks were 

always elastic. Such tanks can be made lighter and more reliable than the metallic counterparts by 

overwrapping a metallic liner with epoxy impregnated fibers such as Kevlar or carbon, and shedding 

much of the load to the relatively strong fibers. In such composite overwrapped pressure vessels, the 

metallic liner is usually yielded due to an initial autofrettage process, but still shares some of the load with 

the dominant composite overwrap. In order to further reduce the mass of spacecraft propellant tanks, 

ultra-thin liners that bear little load but act as a compatibility and gas barrier are being developed for 

missions such as the Europa Clipper, the Mars Skycrane, and the Mars 2020 mission. 

Design of COPVs using ultra-thin metallic liners requires an understanding of the fully reversed, 

plastic behavior of the liner material, and mechanics models that match the material behavior. In this 

work, the uniaxial tensile behavior of a solution treated and aged Ti-6Al-4V alloy was determined in 

strain control and compared to the expected, analytically derived COPV response. 

Theoretical Considerations and Analysis of the Mars 2020 COPV 

1D Mechanics Model 

The stress-strain histories applied to the test specimens were derived from the expected response of 

the Mars 2020 COPV. Thus a brief overview of the fundamental behavior of metal liner COPVs is given. 

The COPV mechanical response follows from a 1D closed-form representation of the major hooporiented principal strain. For cylindrical vessels, hoop strain is often the dominant fiber and liner strain 
NASA/TM—2014-218322 2 

unless there are specific geometric details causing stress and strain concentrations. Early forms of this 

theoretical development are given in References 1 and 2, and a recent NESC report Reference 3 

demonstrates the value of these methods for interpreting COPV test data and providing accurate bounds 

of the maximum hoop strains. 

The COPV hoop strain is usually graphed on the vertical axis as a function of vessel pressure on the 

horizontal axis as done schematically in Figure 1(a). Strain continuity is assumed between a linear-elastic 

overwrap and a linear-elastic, perfectly-plastic (PP) liner. The resultant, individual strain-stress curves are 

shown in Figures 1(b) and (c) for correlation of common strain points. The bi-linear vessel strain-pressure 

response for the initial autofrettage cycle to proof pressure is shown as two intersecting green lines in 

Figure 1(a). The post-autofrettage unloading and all future operational loads trace the blue line. The 

residual tensile strain in the overwrap is represented by the offset of the blue line at the origin when 

pressure returns to zero. 

The adjacent, composite overwrap strain-stress response is assumed to be linear-elastic, as shown by 

the yellow strain-stress curve in Figure 1(b). The corresponding liner strain-stress response is assumed to 

be linear-elastic, perfectly-plastic (PP) with green and blue lines corresponding to the vessel autofrettage 

and operating response, respectively. Note that above the liner yield point, the perfectly-plastic liner 

carries no further load so its plastic strain is controlled by the deformation of the composite. The 

accumulated plastic strain becomes an interference strain between the overwrap and liner. Post 

autofrettage, the blue unloading line for the liner material reveals that a portion of the interference strain 

is shared by the liner as a residual compressive stress that balances the residual tensile stress in the 

composite. Subsequent loads to burst retrace the operating blue line to reinitiate yield at the former 

autofrettage pressure; the path to burst above autofrettage is shown as red line segments in the vessel and 

liner response curves. 

If the liner had been simulated using a cyclic hardening constitutive model, it would be possible to 

initiate reverse yielding at a lower flow stress and allow relaxation of the residual stresses, thereby 

mimicking the Bauschinger effect. 

Figure 1.—Composite pressure vessel strain-pressure response correlated with composite and liner 

strain–stress responses assuming continuity between vessel constituents, a linear-elastic composite 

overwrap, and a linear-elastic, perfectly-plastic liner: (a) Vessel strain-pressure, (b) Composite strainstress, and (c) Liner strain-stress. The vessel reflects a piece-wise linear response due to the combined 

effects of the liner and the composite overwrap. The green lines represent the vessel response post 

cure due to autofrettage to proof pressure. Subsequent unload and reload to operating pressures less 

than or equal to proof follow the blue lines and produce strains within the shaded region of the curve.

(a) (b) (c) 
NASA/TM—2014-218322 3 

Finite Element Analysis 

Besides a 1D mechanics approach, the Mars 2020 COPV has been modeled (by the COPV vendor) 

using ABAQUS based Finite Element Analysis (FEA). Figure 2 shows a swept segment of the FEA 

model developed by the COPV vendor. Colors in Figure 2(a) represent the various material properties 

where the range of colors in the dome region represents the changing material properties as a function of 

changing fiber wind angle in the vessel dome. The solid colors in the cylinder (red) and skirt (blue) 

represent a uniform fiber angle in those regions. Figure 2(b) shows the hoop strain distribution in the 

vessel at burst pressure. 

The liner hoop stress-strain response and equivalent stress-strain response from the Mars COPV finite 

element analysis are shown in Figure 3(a) and (b), respectively. The hoop stress-strain response from the 

finite element analysis results are quite similar to but discernable from the 1D elastic perfectly-plastic 

representation of the liner constitutive response shown in Figure 1(c). The intial load to autofrettage 

pressure (0-AF) cycle traces the initial yield of the liner to about 1.2 percent hoop strain. The unload 

pressure cycle (AF-0) shows that the liner behaves linear elastically down to –50,000 psi as there is no 

reverse yielding of the liner in compression with the removal of pressure. Subsequent loading cycles do 

not appear to reinitiate liner yield until the prior AF pressure is exceeded at 1.2 percent strain during the 

MDP-Burst cycle enroute to vessel burst at a hoop strain above 1.4 percent. 

The equivalent stress-strain curve provides a complete representation of the multi-axial stress-strain 

response in scalar form. The equivalent stress-strain response includes not only the axial and radial 

normal stresses and strains, but the shear stresses and strains in the radial-axial plane induced by the 

geometric asymmetry of this vessel. These additional contributions result in a uniaxial equivalent strain of 

1.6 percent at AF, making a discernable difference between the 1D and FEA approaches. Note that 

equivalent stress is always positive even though the liner is in compression during unloading. Without 

cyclic hardening effects in this consitutive model, there is no Bauschinger effect occurring during the 

unload; additional load cycles will retrace this unloading curve as long as the peak load remains less than 

the peak load at AF. 

In order to understand the significance of the model’s limitations, tensile tests were designed to 

explore the reversed load response of the liner. The tests and results are discussed in the following 

sections. 

Figure 2.—(a) ABAQUS Finite Element Model of the Mars 2020 COPV with color coded material properties, and 

(b) Hoop strain distribution at burst pressure. 
NASA/TM—2014-218322 4 

Figure 3.—Pressure cycle induced (a) hoop stress-strain response and (b) uniaxial 

equivalent stress-strain response via COPV FEA. 

Experimental Procedure 

Eight ASTM E8 subsize sheet-type specimens (Ref. 1) were extracted from a Ti-6Al-4V (STA) 

forging that was processed per AMS 81200 and proprietary specifications. Uniaxial tension-compression 

tests were performed by loading in strain control. A 1-in. gage length extensometer was used to control 

the test at a strain rate of 830 microstrain per second. Four of the specimens were subjected to a specific 

load history in order to simulate potential autofrettage, proof, and maximum design pressure (MDP) 

cycles: 

TL-1—The specimen was loaded in tension to 1.6 percent strain followed by compression of 

–2 percent from the zero-load strain value. The specimen was then loaded in tension to a proof stress of 

167 ksi and unloaded. 

TL-2—Loaded in tension to 1.6 percent strain and unloaded. The specimen was then subjected to five 

compression–tension cycles of –55.4 to 150 ksi. 

 

(a) 

(b) 

Linear response in compression after reversal 

A 

B

C 

F

D

E
NASA/TM—2014-218322 5 

TL-3—Loaded in tension to 1.6 percent strain and unloaded. The specimen was then subjected to two 

compression–tension cycles between –55.3 and 166.7 ksi, and unloaded. Next, two cycles of compression 

to –55.3 ksi with tension to 127.8 ksi followed by unloading were performed. Finally, the specimen was 

compressed to –55.3 ksi and then loaded monotonically in tension to failure. To ensure the strain-tofailure would not exceed the 10 percent strain range of the extensometer, the control mode was switched 

to stroke upon the final load reversal. A stroke rate of 0.00296 in./sec was set in an attempt to 

approximate the 830 microstrain per second strain rate used during the rest of the test. 

TL-4—Identical to the loading of TL-3 except for the strain rate during loading to failure: After 

6 percent strain the control mode was switched to stroke at a rate of 0.00095 in./sec to better approximate 

a strain rate of 830 microstrain per second. 

In order to determine the effect of the various load cycles on tensile strength properties, an additional 

test (specimen TL-7) was run per ASTM E8. 

Experimental Results 

Figures 4 to 7 show the measured stress-strain curves corresponding to the load histories described 

previously. As with annealed Ti-6Al-4V (Ref. 3), solution treated and aged material clearly exhibits a 

Bauschinger effect with nonlinear behavior occurring almost immediately upon load reversal. The loops 

are fairly stable and the strain curve continues to failure almost contiguously: only a 15 ksi increase in 

stress is required to continue extension, as shown in Figures 6 and 7. Table 1 summarizes tensile 

properties derived from the test specimen measurements. It should be noted that Young’s modulus and the 

yield strength were determined from the initial loading in the usual way (Ref. 4), however, the reported 

ultimate and break strengths for cases TL-3 and TL-4 were determined after multiple load cycles. Despite 

the load cycles, the results are similar to Ti-6Al-4V STA tested monotonically per ASTM E8, shown in 

Figure 8 and Table 1. 

Figure 4.—Stress-strain history for specimen TL-1. 

200

100

0

100

200

1.5 1 0.5 0 0.5 1 1.5

Stress[ksi]

Strain[%]

TL1
NASA/TM—2014-218322 6 

Figure 5.—Stress-strain history for specimen TL-2. 

 

75

0

75

150

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Stress[ksi]

Strain[%]

TL2
NASA/TM—2014-218322 7 

Figure 6.—(a) Stress-strain history for specimen TL-3; (b) Enlarged view of the cyclic portion. 

75

0

75

150

0 1 2 3 4 5 6 7 8 9 10

Stress[ksi]

Strain[%]

TL3 (a)

75

0

75

150

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Stress[ksi]

Strain[%]

TL3,enlarged (b)
NASA/TM—2014-218322 8 

Figure 7.—(a) Stress-strain history for specimen TL-4; (b) Enlarged view of cyclic portion. 

75

0

75

150

0 1 2 3 4 5 6 7 8 9 10

Stress[ksi]

Strain[%]

TL4

75

0

75

150

0 0.2 0.4 0.6 0.8 1 1.2 1.4 1.6

Stress[ksi]

Strain[%]

TL4,enlarged

(a)

(b)
NASA/TM—2014-218322 9 

Figure 8.—Stress-strain history for specimen TL-7. 

TABLE 1.—TENSILE PROPERTIES 

Specimen 

number 

Young’s 

modulus, 

Msi 

Yield 

strength, 

ksi 

Maximum 

stress, 

ksi 

Break 

stress, 

ksi 

Elongation, 

percent 

TL-1 17.4 167 ---- ---- ---- 

TL-2 17.4 165 ---- ---- ---- 

TL-3 17.5 165 176 157 9.7 

TL-4 17.2 165 173 154 12.4 

TL-7 

(Monotonic per E8) 

17.3 160 174 150 10.8 

Discussion of Results and Correlation With FEA Analysis 

Further insight into measured stress-strain responses can be gained by recasting the results in terms of 

stress as a function of either elastic strain or plastic strains. These forms of the experimental results clarify 

when plastic strain is changing, and can be used to separate elastic strain energy from the dissipated 

plastic work. Having the experimental data in this format is often preferred when deriving constitutive 

models for computational analysis. Typically, the separation is achieved by deriving the effective elastic 

modulus from the stress-strain data, computing the elastic strain for each stress data point, and subtracting 

that elastic strain from the total strain to determine the plastic strain corresponding to that data point. An 

example is given in Figure 9 where the results from test TL-1 (blue) are shown along with the stresselastic strains (magenta) and stress-plastic strains (green). The vertical green lines represent the segments 

of the load cycle where plastic strains are not changing, generally at the beginning of each new load 

segment. The Bauschinger effect is clearly seen during the first unload cycle as stress changes from 

tensile to compression and plastic strain reverses immediately. Recall no such nonlinear response was 

present in the FEA representation of the vessel response (see arrow in Fig. 3(a)). 

0

50

100

150

200

0 1 2 3 4 5 6 7 8 9 10

Stress[ksi]

Strain[%]

TL7
NASA/TM—2014-218322 10 

 

Figure 9.—The stress-strain response shown from case TL-1 separated into stresselastic strain and stress-plastic strain curves to clearly show changes in plastic strain 

due to reverse yielding during unloading and reloading. 

Figure 10.—Comparison of the measured and predicted uniaxial equivalent stress-strain 

results for the Mars 2020 COPV. 

Direct correlation of the uniaxial results with the FEA results can be made by computing the 

equivalent stress-strain response from the experimental data and co-plotting with the equivalent stressstrain response of the vessel. This is shown for TL-2 in Figure 10 where the red curve represents the 

experimental data and the underlying segment curve with data points is the same equivalent stress-strain 

curve shown in Figure 3(b). 

Yield 

A

B

Compression 

C
NASA/TM—2014-218322 11 

The uniaxial test specimen equivalent stress-strain response (red) in Figure 10 indicates a slightly 

greater elastic modulus during the initial loading than was used in the FEA model. The uniaxial yield 

stress is also slightly greater. Despite these modeling input differences, strain control during the uniaxial 

test matched the unload portion of the FEA response curve closely until zero stress is reached. 

The uniaxial test specimen response clearly changes to a nonlinear trajectory while passing through 

zero stress as the specimen goes into compression (Figs. 4 and 9). Thus negative strains occur. The 

pressure vessel liner, however, is predicted to experience only linear behavior. Note that the inflection 

points in the equivalent stress-strain plot of the experimental data that occur are associated with strain 

sign changes and also when unloading begins from maximum compression stress. The nonlinear portion 

of the uniaxial unload-reload trace would have collapsed to the FEA unload-reload line if the plastic strain 

had remained constant and there were no Bauschinger effect present in the measured data. 

Conclusion 

Tensile tests run in order to simulate the behavior of ultra-thin liners in light-weight composite 

overwrap pressure vessels imply a Bauschinger effect and immediate nonlinearity upon load reversal. The 

tensile properties after several load reversals were similar to those determined monotonically. 

Mass-efficient COPVs using ultra-thin Ti-6Al-4V STA liners cannot be designed to have elastically 

responding liners but must be designed with plastically responding liners. 

Comparison of experiments and models implies reasonable agreement until compressive stresses are 

induced into the liner. As demonstrated by the experimental results, an elastic perfectly-plastic analysis is 

inadequate to estimate liner stress and strain states. Strain hardening, as experimentally measured herein, 

needs to be incorporated in future COPV models. 

References 

1. Thesken, J. NASA/TM—2009-215683, Composite Overwrap Pressure Vessels: Mechanics and Stress 

Rupture Lifing Philosophy. 

2. Thesken, J. NASA/TM—2009-215684, A Theoretical Investigation of Composite Overwrap Pressure 

Vessels (COPV) Mechanics Applied to NASA Full Scale Tests. 

3. NESC CPVWG Task 4: A Theoretical and Experimental Investigation of COPV Autofrettage, 

NASA Engineering and Safety Center Technical Assessment Report, NESC-RP-09-00537, Dec 2013. 

4. ASTM E8, in Annual Book of Standards, volume 03.01, American Society for Testing and Materials, 

W. Conshohocken, Pennsylvania (2003). 

5. SAE AMS-H-81200-2001, Heat treatment of titanium and titanium alloys, SAE International, 

Warrendale, PA. 

6. J.A. Salem, B. Lerch, J.C. Thesken, J. Sutter and R. Russell, “Strength, Fatigue and Fracture 

Toughness of Ti-6Al-4V Liner from a Composite Over-Wrapped Pressure Vessel,” NASA/TM—

2008-215147, March 2008.