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Research Papers

Uniaxial Tension of a Class of Compressible Solids With Plastic Non-Normality

[+] Author and Article Information
Nisha Mohan

Division of Engineering and Applied Sciences,
California Institute of Technology,
Pasadena, CA 91125
e-mail: nmohan@caltech.edu

Justine Cheng

Polytechnic School,
Pasadena, CA 91106
e-mail: jcheng13@students.polytechnic.org

Julia R. Greer

Division of Engineering and Applied Sciences,
California Institute of Technology,
Pasadena, CA 91125
e-mail: jrgreer@caltech.edu

Alan Needleman

Department of Material Science and Engineering,
University of North Texas,
Denton, TX 76207
e-mail: needle@unt.edu

Manuscript received February 7, 2013; final manuscript received March 6, 2013; accepted manuscript posted April 10, 2013; published online May 31, 2013. Editor: Yonggang Huang.

J. Appl. Mech 80(4), 040912 (May 31, 2013) (8 pages) Paper No: JAM-13-1064; doi: 10.1115/1.4024179 History: Received February 07, 2013; Revised March 06, 2013; Accepted April 10, 2013

Motivated by a model that qualitatively captured the response of vertically aligned carbon nanotube (VACNT) pillars in uniaxial compression, we consider the uniaxial tensile response of a class of compressible elastic-viscoplastic solids. In Hutchens et al. [“Analysis of Uniaxial Compression of Vertically Aligned Carbon Nanotubes,” J. Mech. Phys. Solids, 59, pp. 2227–2237 (2011), Erratum 60, 1753–1756 (2012)] an elastic viscoplastic constitutive relation with plastic compressibility, plastic non-normality, and a hardening-softening-hardening hardness function was used to model experimentally obtained uniaxial compression data of cylindrical VACNT micropillars. Complex deformation modes were found in uniaxial compression, which include a sequential buckling-like collapse of the type seen in experiments. These complex deformation modes led to the overall stress-strain signature of the pillar not being of the same form as the input material hardness function. A fundamental question that motivates exploring the deformation of this class of materials—both experimentally and theoretically—is how to extract the intrinsic material response from simple tests. In this study we explore the relation between the input material response and the overall stress strain behavior in uniaxial tension using the constitutive framework of Hutchens et al. A simple one-dimensional analysis reveals the types of instability modes to be expected. Dynamic, finite deformation finite element calculations are carried out to explore the dependence of diffuse necking, localized necking, and propagating band deformation modes on characteristics of the hardness function. Attention is devoted to uncovering implications for obtaining intrinsic material properties of complex hierarchical structures; for example, vertically aligned carbon nanotubes (VACNTs), from uniaxial tension experiments.

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Figures

Grahic Jump Location
Fig. 1

The hardness function g(ɛp) as a function of plastic strain ɛp for material A (h2=5.0, h3=15.0, and ɛ2=0.6) and for material B (h2=h3=5.0)

Grahic Jump Location
Fig. 2

Overall nominal stress sn and true stress σt versus ɛt=ln(H/H0) for material A (h2=5.0, h3=15.0, and ɛ2=0.6) and for material B (h2=h3=5.0)

Grahic Jump Location
Fig. 3

Distributions of normalized plastic strain rate e·=ɛp/(W/H0) for material A: (a) ɛt=0.50 and (b) ɛt=0.76

Grahic Jump Location
Fig. 4

Distributions of normalized plastic strain rate e·=ɛp/(W/H0) for material B: (a) ɛt=0.50 and (b) ɛt=0.76

Grahic Jump Location
Fig. 5

The hardness function g(ɛp) as a function of plastic strain ɛp for material B (h2=h3=5.0), material C (h2=h3=1.0), and material D (h2=h3=0.5)

Grahic Jump Location
Fig. 6

Overall nominal stress sn and true stress σt versus ɛt=ln(H/H0) for material B (h2=h3=5.0), material C (h2=h3=1.0), and material D (h2=h3=0.5)

Grahic Jump Location
Fig. 7

Distributions of normalized plastic strain rate e·=ɛ·p/(W/H0): (a) material C at ɛt=0.30 and (b) material D at ɛt=0.14

Grahic Jump Location
Fig. 8

The hardness function g(ɛp) as a function of plastic strain ɛp for material E, h2=-3.90, h3=15.0, ɛ2=0.6, material F, h2=0.5, h3=15.0, ɛ2=0.6, and material G, h2=-3.90, h3=15.0, ɛ2=5.0

Grahic Jump Location
Fig. 9

Overall nominal stress sn and true stress σt versus ɛt=ln(H/H0) for material E, h2=-3.90,h3=15.0, ɛ2=0.6

Grahic Jump Location
Fig. 10

Distributions of normalized plastic strain rate e·=ɛ·p/(W/H0) for material E, h2=-3.90,h3=15.0, ɛ2=0.6: (a) ɛt=0.20, (b) ɛt=0.40, and (c) ɛt=0.50

Grahic Jump Location
Fig. 11

Overall nominal stress sn and true stress σt versus ɛt=ln(H/H0): material F, h2=0.5, h3=15.0, ɛ2=0.6 and material G, h2=-3.90, h3=15.0, ɛ2=5.0

Grahic Jump Location
Fig. 12

Distributions of normalized plastic strain rate e·=ɛ·p/(W/H0) for material F, h2=0.5, h3=15.0, ɛ2=0.6: (a) ɛt=0.20 and (b) ɛt=0.50

Grahic Jump Location
Fig. 13

Distributions of normalized plastic strain rate e·=ɛp/(W/H0) for material G, h2=-3.90, h3=15.0, ɛ2=5.0: (a) ɛt=0.20 and (b) ɛt=0.50

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