Abstract

A lot of research has shown that the strength of nanoparticle composites increases first and then decreases with the decrease of particle size when particle size is at nanoscale, which is the so-called positive-inverse Hall–Petch effects, or called the strengthening-softening characteristic. In this paper, the strengthening-softening behavior of cylindrical nanoparticle composites with periodic distribution of particles is studied. By selecting the representative single cylindrical cell model, the mechanic’s solution is obtained strictly by using the strain gradient viscoelastic theory established previously by the present authors. The results clearly show the strengthening-softening behavior of the nanoparticle composite. In the process of solution, first, the strain gradient elasticity theory is used to strictly solve the problem of the cylindrical cell under uniform external pressure. Then, using the correspondence principle of the strain gradient viscoelastic theory, the solution for the strain gradient viscoelastic theory is obtained through Laplace inversion transformation, and its dependence on the time-space two-scale parameters is analyzed. The results showed a significant positive-inverse Hall–Petch effects.

References

1.
Schiøtz
,
J.
, and
Jacobsen K
,
W.
,
2003
, “
A Maximum in the Strength of Nanocrystalline Copper
,”
Science
,
301
(
5638
), pp.
1357
1359
.
2.
Li
,
X.
,
Wei
,
Y.
,
Lu
,
L.
,
Lu
,
K.
, and
Gao
,
H.
,
2010
, “
Dislocation Nucleation Governed Softening and Maximum Strength in Nano-Twinned Metals
,”
Nature
,
464
(
7290
), pp.
877
880
.
3.
Jun
,
S.
,
Tashi
,
T.
, and
Park H
,
S.
,
2011
, “
Size Dependence of the Nonlinear Elastic Softening of Nanoscale Graphene Monolayers Under Plane-Strain Bulge Tests: A Molecular Dynamics Study
,”
J. Nanomater.
,
2011
, pp.
1
6
.
4.
Fan
,
G. J.
,
Choo
,
H.
,
Liaw
,
P. K.
, and
Lavernia
,
E. J.
,
2005
, “
A Model for the Inverse Hall–Petch Relation of Nanocrystalline Materials
,”
Mater. Sci. Eng. A
,
409
(
1
), pp.
243
248
.
5.
Lu
,
L.
,
Chen
,
X.
,
Huang
,
X.
and
Lu
,
K.
,
2009
, “
Revealing the Maximum Strength in Nanotwinned Copper
,”
Science
,
323
(
5914
), pp.
607
610
.
6.
Song
,
J.
,
Fan
,
C.
,
Ma
,
H.
, and
Wei
,
Y.
,
2015
, “
Hierarchical Structure Observation and Nanoindentation Size Effect Characterization for a Limnetic Shell
,”
Acta Mech. Sin.
,
32
(
2
), p.
349
.
7.
Gan
,
Z.
,
He
,
Y.
,
Liu
,
D.
,
Zhang
,
B.
, and
Shen
,
L.
,
2014
, “
Hall–Petch Effect and Strain Gradient Effect in the Torsion of Thin Gold Wires
,”
Scr. Mater.
,
87
, pp.
41
44
.
8.
Long
,
X.
,
Tang
,
W.
,
Feng
,
Y.
,
Chang
,
C.
,
Keer
,
L. M.
, and
Yao
,
Y.
,
2018
, “
Strain Rate Sensitivity of Sintered Silver Nanoparticles Using Rate-Jump Indentation
,”
Int. J. Mech. Sci.
,
140
, pp.
60
67
.
9.
Li
,
X.
,
Wang
,
X.
,
Xiong
,
Q.
, and
Eklund
,
P. C.
,
2005
, “
Mechanical Properties of ZnS Nanobelts
,”
Nano Lett.
,
5
(
10
), pp.
1982
1986
.
10.
Gurtin
,
M. E.
,
2002
, “
A Gradient Theory of Single-Crystal Viscoplasticity That Accounts for Geometrically Necessary Dislocations
,”
J. Mech. Phys. Solids
,
50
(
1
), pp.
5
32
.
11.
Kuroda
,
M.
, and
Tvergaard
,
V.
,
2006
, “
Studies of Scale Dependent Crystal Viscoplasticity Models
,”
J. Mech. Phys. Solids
,
54
(
9
), pp.
1789
1810
.
12.
Borg
,
U.
,
Niordson
,
C. F.
,
Fleck
,
N. A.
, and
Tvergaard
,
V.
,
2006
, “
A Viscoplastic Strain Gradient Analysis of Materials With Voids or Inclusions
,”
Int. J. Solids Struct.
,
43
(
16
), pp.
4906
4916
.
13.
Cottura
,
M.
,
Le Bouar
,
Y.
,
Finel
,
A.
,
Appolaire
,
B.
,
Ammar
,
K.
, and
Forest
,
S.
,
2012
, “
A Phase Field Model Incorporating Strain Gradient Viscoplasticity: Application to Rafting in Ni-Base Superalloys
,”
J. Mech. Phys. Solids
,
60
(
7
), pp.
1243
1256
.
14.
Bargmann
,
S.
,
Reddy B
,
D.
, and
Klusemann
,
B.
,
2014
, “
A Computational Study of a Model of Single-Crystal Strain-Gradient Viscoplasticity With an Interactive Hardening Relation
,”
Int. J. Solids Struct.
,
51
(
15–16
), pp.
2754
2764
.
15.
Huang
,
Y.
,
Qu
,
S.
,
Hwang
,
K. C.
,
Li
,
M.
, and
Gao
,
H.
,
2004
, “
A Conventional Theory of Mechanism-Based Strain Gradient Plasticity
,”
Int. J. Plast.
,
20
(
4–5
), pp.
753
782
.
16.
Lin
,
Z.
, and
Wei
,
Y.
,
2020
, “
A Strain Gradient Linear Viscoelasticity Theory
,”
Int. J. Solids Struct.
,
203
, pp.
197
20169
.
17.
Lin
,
Z.
,
Yu
,
Z.
,
Wei
,
Y.
, and
Wang
,
Y.
,
2021
, “
Strain Gradient Viscoelastic Solution and Cross-Scale Hardening-Softening Behavior for a Pressurized Thick Spherical Shell Cell
,”
Mech. Mater.
,
159
, p.
103902
.
18.
Gao
,
X. L.
, and
Park
,
S. K.
,
2007
, “
Variational Formulation of a Simplified Strain Gradient Elasticity Theory and Its Application to a Pressurized Thick-Walled Cylinder Problem
,”
Int. J. Solids Struct.
,
44
(
22–23
), pp.
7486
7499
.
19.
Toupin
,
R. A.
,
1964
, “
Theories of Elasticity With Couple-Stress
,”
Arch. Rational Mech. Anal.
,
17
(
2
), pp.
85
112
.
You do not currently have access to this content.