The strain path dependence of plastic deformation response of AA5754: Experiment

and modeling

Minh-Son Pham, Lin Hu, Mark Iadicola, Adam Creuziger, and Anthony D. Rollett

Citation: AIP Conference Proceedings 1567, 500 (2013); doi: 10.1063/1.4850021

View online: http://dx.doi.org/10.1063/1.4850021

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The Strain Path Dependence of Plastic Deformation 

Response of AA5754: Experiment and Modeling 

Minh-Son Phama,b*, Lin Hua,c, Mark Iadicolab, Adam Creuzigerb, and Anthony D. Rolletta

a

 Materials Science and Engineering, Carnegie Mellon University, 5000 Forbes Avenue, Pittsburgh, PA 15213, USA 

b NIST Center for Automotive Lightweighting, National Institute of Standards and Technology, 100 Bureau Drive, 

Gaithersburg, MD 20899-8553, USA 

c Now at IBM, USA 

Abstract. This work presents modeling of experiments on a balanced biaxial (BB) pre-strained AA5754 alloy, 

subsequently reloaded uniaxially along the rolling direction and transverse direction. The material exhibits a complex 

plastic deformation response during the change in strain path due to 1) crystallographic texture, 2) aging (interactions 

between dislocations and Mg atoms) and 3) recovery (annihilation and re-arrangement of dislocations). With a BB prestrain of about 5 %, the aging process is dominant, and the yield strength for uniaxially deformed samples is observed to 

be higher than the flow stress during BB straining. The strain hardening rate after changing path is, however, lower than 

that for pre-straining. Higher degrees of pre-straining make the dynamic recovery more active. The dynamic recovery at 

higher strain levels compensates for the aging effect, and results in: 1) a reduction of the yield strength, and 2) an increase

in the hardening rate of re-strained specimens along other directions. The yield strength of deformed samples is further 

reduced if these samples are left at room temperature to let static recovery occur. The synergistic influences of texture 

condition, aging and recovery processes on the material response make the modeling of strain path dependence of 

mechanical behavior of AA5754 challenging. In this study, the influence of crystallographic texture is taken into account 

by incorporating the latent hardening into a visco-plastic self-consistent model. Different strengths of dislocation glide 

interaction models in 24 slip systems are used to represent the latent hardening. Moreover, the aging and recovery effects 

are also included into the latent hardening model by considering strong interactions between dislocations and dissolved

atom Mg and the microstructural evolution. These microstructural considerations provide a powerful capability to 

successfully describe the strain path dependence of plastic deformation behavior of AA5754. 

Keywords: Latent hardening, Strain path dependence, Aging, Recovery, AA5754

PACS: 00. GENERAL

INTRODUCTION 

It is necessary to accurately simulate material response during metal forming processes in order to increase the 

productivity of automotive part manufacture. However, during metal forming processes, the materials often exhibit 

complex anisotropic plastic behavior. In particular, multiaxial stress states promote strong multiple slip activities, 

leading to frequent dislocation interactions, and in turn resulting in different hardening rates for different slip 

systems. Consequently, it is challenging to simulate material deformation responses as a continuum model. To 

overcome these challenges, accurate models require an in-depth understanding of plastic deformation mechanisms. 

Over past decades, there have been great efforts to understand the mechanism of plastic deformation, in particular 

the relationships between dislocations, texture and plastic anisotropy of polycrystalline materials. These efforts have 

developed effective models for simulating anisotropic plastic response of materials [1-3]. Here, the visco-plastic 

self-consistent (VPSC) model is used with the incorporation of (i) latent hardening, (ii) interactions between 

dislocations and dissolved atoms, and (iii) static recovery to enhance the linkage between constitutive models and 

underlying physical mechanisms, and ultimately to model the plastic deformation response of AA5754 during multipath straining. 

PLASTIC STRESS-STRAIN BEHAVIOR OF AA5754: EXPERIMENT 

The material used in this investigation is a commercially available AA5754-O sheet. The as-received (AR) 

material exhibits a higher strain hardening rate for balanced bi-axial (BB) than for uniaxial tension loading 

conditions, in particular after a high degree of plastic deformation (Fig. 1a). The material also undergoes dynamic 

strain aging (DSA) due to strong interactions between dislocations and solute atoms (e.g., Mg). The dynamic strain 

NUMISHEET 2014

AIP Conf. Proc. 1567, 500-503 (2013); doi: 10.1063/1.4850021

© 2013 AIP Publishing LLC 978-0-7354-1195-1/$30.00

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aging results in an increase in yield strength accompanied by serrated flow stress (Fig. 1b) and negative strain rate 

sensitivity (i.e., the material tends to be stronger during plastic deformation with a lower strain rate) [4, 5]. 

0 5 10 15 20 25

0

50

100

150

200

250

300

350

400

True strain (g

11 or g22) (%)

True stress (u11 or u22) (MPa)

0 2 4 6 8 10

100

150

200

250

g

11 (%)

u11 (MPa)

Exp-URD-AR

Exp-URD-AR

Exp-UTD-AR

Exp-BB-RD-AR

Exp-BB-TD-AR

0 5 10 15 20

50

100

150

200

250

300

350

g

11 (%)

u11 (MPa)

(c)

0 5 10 15 20

50

100

150

200

250

300

350

g

11 (%)

u11 (MPa)

(d)

5 10 15

160

210

260

Serrated flow stress

Exp-BB-RD-AR

Exp-BB-RD-AR

Pre-strained BB 5.3%

Recovery time: 0

Pre-strained BB 5.3%

Recovery time: 3 months

Recovery time: 0

Recovery time: 3 days

Recovery time: 3 months

(b) (a)

FIGURE 1: (a) Stress-strain response of AA5754 as-received (AR) material during BB, URD and UTD (The 11 (or 22) direction 

corresponds to the rolling (or transverse) direction). (b) Serrated flow stress. (c) Flow stresses in the RD during BB straining and 

URD reloading intermediately after BB straining and after 3 months of recovery. (d) Yield strength of AA5754 during URD 

reloading (shown as single points) with respect to degrees of pre-straining and to time of static recovery. Note: The yield strength 

is measured as the proof stress at 0.1 % offset strain. 

Changing the strain path from BB to uniaxial tension significantly affects the plastic stress-strain response of the 

material. Here we focus on the material deformation response when changing path from BB to uniaxial tension in 

the rolling direction (URD) since the same response reported below is also observed when changing path from BB 

to uniaxial tension in the transverse direction (UTD), but to a smaller extent. This may be due to the fact that the 

material hardens slightly less for UTD than for URD (inset in Fig. 1a). The error bars associated with each 

experimental data point are measurement uncertainties described in Iadicola et al. [6]. Depending on the degree of 

pre-straining, the yield strength of the material during reloading along the second path can be either higher or lower 

than the flow stress during previous plastic deformation. The yield strength during URD is observed to be higher 

than the flow stress during BB pre-straining of about 5.3 % true strain (Fig. 1c). The strain hardening rate of the 

material after changing path at small strains is, however, lower than that for BB pre-straining. Larger BB pre-strains 

reduce the yield strength (and increase the hardening rate – not shown here) of BB deformed specimens. For 

example, the yield stress of a sample reloaded uniaxially along RD after BB straining of 7.8 % true strain is almost 

the same as it was during BB straining (Fig. 1d). The yield strength of the material during URD reloading is usually 

lower than that during BB straining higher than 10 % true strain (Fig. 1d). This is because of dynamic recovery 

which, through mechanisms such as cross slip, reduces the dislocation density and rearranges dislocations to form 

more stable energetic configurations such as dislocation cells and walls [7]. Static recovery (in air) at room 

temperature helps pre-strained samples regain strain hardening and therefore ductility (Fig. 1c, d). 

MODELING 

There are 24 } ʼ 111 110 > @ slip systems for face-centered-cubic (FCC) materials. Twelve of these are depicted in 

the Thompson tetrahedron in Fig. 2a. Beside the self-interaction of dislocations in the same slip plane, there are four 

typical types of latent interactions between dislocations moving in primary slip plane and those in secondary slip 

planes (Fig. 2b): The Lomer-Cottrell (LC), Hirth (H), co-planar (Cop) and co-linear (Col) interactions [4, 8, 9]. The 

stress-strain deformation behavior of AA5754 during BB loading along RD direction is modeled by VPSC program 

with basic self-hardening values (shown in Table1) and with different latent hardening strengths relative to selfhardening. The values of latent hardening strengths used and shown in Fig. 3a (which were calibrated based on the 

BB data) can pretty well model both stress-strain behavior (Fig. 3a) and texture development after 20 % BB 

straining (Fig. 3b) (Note: VPSC with the same self-hardening values and no latent hardening gives a much 

underestimate of stress response during BB loading, Fig. 3a). These same values of self- and latent hardening also 

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predict the material response well during URD straining of the as-received material (Fig. 3a) and the corresponding 

texture evolution after 15 % strain (Fig. 3c). 

FIGURE 2: (a) Expansion of the Thompson tetrahedron and (b) sources of latent hardening interactions in FCC materials. 

TABLE 1: Main input parameters for VPSC with the Voce constitutive model (Equation 6-1 in [10]) 

Inclusion-Matrix interaction 0

v 1

v s 0

s1

n

eff=10 81 30 100 0 

FIGURE 3: (a) Modeling of flow stress during BB and URD of AR samples. Texture conditions after (b) BB straining of 20 % 

and (c) URD of 15 % of AR samples. 

Since the material is strengthened by solid solution which delays cross slip activity, it is likely that dynamic 

strain aging (DSA) is dominant in uniaxial deformation response of the BB deformed material (which was prestrained less than 10 %). In contrast, the influence of aging in the response of the material (which was pre-strained 

more than 10 %) is compensated by dynamic recovery. The strong interaction between dislocation lines and solute 

atoms requires higher stress to keep dislocations moving, resulting in higher yield stress. The DSA process also 

results in a low hardening rate and a higher damage because: 1) the resistance to dislocation movement is mainly 

governed by short-range interactions between dislocations and dissolved atoms, and 2) jerky movement of 

dislocations under the presence of dissolved atom atmospheres and negative strain rate sensitivity promotes 

deformation localization [4]. This explains why: (i) there is overshoot in the yield strength during reloading of prestrained material of 5.3 %, and (ii) the ductility and hardening rate of the pre-strained sample are low (Fig. 1c, Fig. 

4a). In other words, the latent hardening can be negligible compared with hardening induced by self-interaction and 

interaction between dislocation and dissolved atoms. Consequently, for modeling the material response after prestraining of less than 10 %, it is necessary to use (1) only self-hardening term, and (2) a higher yield stress than that 

during pre-straining. Indeed, VPSC with only self-hardening term and a higher stress value (which was obtained 

from experimental data) can successfully model the flow stress response during URD after BB pre-straining of about 

5.3 % (Fig. 4a). 

Static recovery (under zero-load) returns strained material towards the annealed state. During static recovery, (1) 

dislocations migrate, annihilate and form more stable energetic configurations, and (2) the interactions between 

dislocations and solute atoms are relaxed. The reduction in dislocation density and the relaxation of interactions 

between dislocations and solute atoms cause a decrease in yield stress. However, the formation of more stable 

configurations of dislocations provides effective means to restrict the movement of dislocations during reloading, 

resulting in an increase in hardening rates during reloading of recovered samples. Nes showed that the reduction in 

E 2 ( ) E if th Th t t h d d (b) f l t t h d i i t ti i FCC

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yield stress during static recovery of deformed Al-Mg alloys due to the annealing out of dislocations can be modeled 

by the following equation [11]: 

1 ln(1 ) kT t R

A v

?/ - with R is the fraction of residual yield strength, 0 0

0 0 0

deformed as received

t

deformed as received

t

R

u u

u u

/

/

?

/

?

/

 (1) 

 k is Boltzmann's constant, T: Temperature (K), A: Coefficient relating to annealing process of dislocations 

during static recovery, t: recovery time, 0 u :measured yield strength, v : Coefficient relating to initial dislocation 

density and solute atom concentration during static recovery. 

103104105106107

0.6

0.8

1

1.1

Time (s)

Residual yield strength,R

Exp.

Model by Eqn. 1

0 5 10 15

0

100

200

300

g

11 (%)

u11 (MPa)

0 5 10 15

0

100

200

300

g

11 (%)

u11 (MPa)

Exp-BB-RD-AR

Pre-deformed BB(7.77,8.19) rec=0

Pre-deformed BB(9.9,10.4) rec=3m

Model:Self+aging

Model:Recovery

Exp-BB-RD-AR

Pre-deformed BB(5.3,4.7)

Self-hardening + Aging

(a) (b) (c) Recovery time: 3 months

Recovery time: 0

Recovery time: 0

FIGURE 4: (a) Modeling of flow stress during URD of BB deformed sample. (b) Residual yield strength of deformed materials 

after static recovery. (c) The simulation of flow stress of recovered sample. 

In this study, (1) the reduction of the yield stress during recovery is first modeled by using Equation 1 (Fig. 4b) 

and (2) the latent hardening is considered to be the same as it was during BB pre-straining. Indeed, the visco-plastic 

self-consistent model including these two factors successfully modeled the flow stress during URD reloading after 

static recovery of BB pre-strained material (Fig. 4c). 

CONCLUSIONS 

The response of pre-strained AA5754 materials during a strain path change is strongly governed by the degree of 

pre-straining amplitude, and is a consequence of the competition between dynamic strain aging and dynamic 

recovery. In addition, static recovery also significantly influences the stress-strain behavior of deformed AA5754 

material, e.g., lowering the yield strength, increasing both ductility and strain hardening rate. As shown in this study, 

the incorporation of latent hardening into the VPSC model is an effective technique to model the plastic deformation 

response and texture development during BB and uniaxial straining. Including aging and recovery are necessary to 

successfully simulate the plastic stress-strain response of the material after changing path as well as after static 

recovery. 

ACKNOWLEDGEMENTS 

We would like to thank Dr. Carlos Tomé and Dr. Ricardo Lebensohn for providing the VPSC program. Dr. 

Andrew Reid (Center for Theoretical and Computational Materials, NIST) is thanked for his kind support in 

providing computational capabilities. This work was supported by the NIST Center for Automotive Lightweighting. 

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