Nanoindentation study of plasticity length scale effects in LIGA Ni microelectromechanical systems structures

2003 ◽  
Vol 18 (3) ◽  
pp. 719-728 ◽  
Author(s):  
J. Lou ◽  
P. Shrotriya ◽  
T. Buchheit ◽  
D. Yang ◽  
W. O. Soboyejo
Keyword(s):  
Plastic Deformation ◽  
Strain Gradient ◽  
Indentation Depth ◽  
Microelectromechanical Systems ◽  
Scale Parameter ◽  
Scale Effects ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Cube Corner

This paper presents the results of a nanoindentation study of the effects of strain gradient plasticity on the elastic–plastic deformation of lithographie, galvanoformung, abformung (LIGA) Ni microelectromechanical systems (MEMS) structures plated from sulfamate baths. Both Berkovich and North Star/cube corner indenter tips were used in the study to investigate possible effects of residual indentation depth on the hardness of LIGA Ni MEMS structures between the micro- and nanoscales. A microstructural length scale parameter, , was determined for LIGA nickel films. This is shown to be consistent with a stretch gradient length-scale parameter, ls, of approximately 0.9 μm.

A Study on Length Scale Effects on Indentation Delamination of Thin Films

2004 ◽  
Author(s):  
W. Li ◽  
S. Qu ◽  
T. Siegmund ◽  
Y. Huang
Keyword(s):  
Plastic Deformation ◽  
Strain Gradient ◽  
Cohesive Zone ◽  
Cohesive Zone Model ◽  
Scale Effects ◽  
Scale Dependence ◽  
Zone Model ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Elastic Substrates

Simulations of indentation delamination of ductile films on elastic substrates are performed. A cohesive zone model accounts for initiation and growth of interface delaminations and a strain gradient plasticity framework for the length scale dependence of plastic deformation. With the cohesive zone model and the strain gradient formulation two length scales are introduced in to the analysis.

A Modified Gradient Plasticity Theory for Micro-Bending and Micro-Torsion Size Effects

2004 ◽  
Author(s):  
George Z. Voyiadjis ◽  
Rashid K. Abu Al-Rub
Keyword(s):  
Size Effects ◽  
Scale Parameter ◽  
Plasticity Theory ◽  
Material Behavior ◽  
Length Scale Parameter ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Non Local ◽  
Material Length Scale ◽  
Material Length

The definition and magnitude of the intrinsic length scale are keys to the development of the theory of plasticity that incorporates size effects. Gradient plasticity theory with a material length scale parameter is successfully in capturing the size dependence of material behavior at the micron scale. However, a fixed value of the material length-scale is not always realistic and that different problems could require different values. Moreover, a linear coupling between the local and non-local terms in the gradient plasticity theory is not always realistic and that different problems could require different couplings. A generalized gradient plasticity model with a non-fixed length scale parameter is proposed. This model assesses the sensitivity of predictions in the way in which the local and non-local parts are coupled. The proposed model gives good predictions of the size effect in micro-bending tests of thin films and micro-torsion tests of thin wires.

A Cyclic Microbend Study on LIGA Ni Microelectromechanical Systems Thin Films

2005 ◽  
Vol 127 (1) ◽  
pp. 16-22 ◽  
Author(s):  
J. Lou ◽  
P. Shrotriya ◽  
W. O. Soboyejo
Keyword(s):  
Thin Films ◽  
Strain Gradient ◽  
Cyclic Deformation ◽  
Microelectromechanical Systems ◽  
Fatigue Behavior ◽  
Cyclic Stress ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Scale Parameters ◽  
Reversed Cyclic

This paper presents the results of recent studies of cyclic microbend experiments and their consequences for plasticity length-scale phenomena in LIGA Ni microelectromechanical systems (MEMS) thin films. The strain–life fatigue behavior of LIGA Ni thin films is studied by performing fully reversed cyclic microbend experiments that provide insights into cyclic stress/strain evolution and cyclic failure phenomena. The effects of cyclic deformation on the plasticity length-scale parameters are also considered within the context of strain gradient plasticity theories. The implications of the results are then discussed for the analysis of plasticity and cyclic deformation in MEMS structures and other microscale systems.

scholarly journals Thermo-electro-mechanical behaviour of Nano-sized structures

2020 ◽  
Vol 310 ◽  
pp. 00060
Author(s):  
Miroslav Repka ◽  
Ladislav Sator
Keyword(s):  
Size Effect ◽  
Mechanical Behaviour ◽  
Strain Gradient ◽  
Mechanical Response ◽  
Scale Parameter ◽  
Theory Of Elasticity ◽  
Strain Gradient Theory ◽  
Length Scale Parameter ◽  
Gradient Theory ◽  
Length Scale

Thermo-electro-mechanical behaviour of the nano-sized structures is analysed by the finite element method (FEM). The mechanical response of the nano-sized structures cannot be modelled with classical continuum theories due to the size effect phenomenon. The strain gradient theory with one length scale parameter has been applied to study size effect phenomenon. The coupled theory of thermo-electricity has been used together with strain gradient theory of elasticity. The governing equations have been derived and incorporated into the commercial software Comsol via weak form module. The influence of the length scale parameter on mechanical response of the structures is investigated by some numerical examples.

Strain gradient solution for Eshelby’s ellipsoidal inclusion problem

2010 ◽  
Vol 466 (2120) ◽  
pp. 2425-2446 ◽  
Author(s):  
X.-L. Gao ◽  
H. M. Ma
Keyword(s):  
Strain Gradient ◽  
Scale Parameter ◽  
Gradient Elasticity ◽  
Inclusion Size ◽  
Ellipsoidal Inclusion ◽  
Eshelby Tensor ◽  
Length Scale Parameter ◽  
Inclusion Problem ◽  
Length Scale ◽  
Classical Counterpart

Eshelby’s problem of an ellipsoidal inclusion embedded in an infinite homogeneous isotropic elastic material and prescribed with a uniform eigenstrain and a uniform eigenstrain gradient is analytically solved. The solution is based on a simplified strain gradient elasticity theory (SSGET) that contains one material length scale parameter in addition to two classical elastic constants. The fourth-order Eshelby tensor is obtained in analytical expressions for both the regions inside and outside the inclusion in terms of two line integrals and two surface integrals. This non-classical Eshelby tensor consists of a classical part and a gradient part. The former involves Poisson’s ratio only, while the latter includes the length scale parameter additionally, which enables the newly obtained Eshelby tensor to capture the inclusion size effect, unlike its counterpart based on classical elasticity. The accompanying fifth-order Eshelby-like tensor relates the prescribed eigenstrain gradient to the disturbed strain and has only a gradient part. When the strain gradient effect is not considered, the new Eshelby tensor reduces to the classical Eshelby tensor, and the Eshelby-like tensor vanishes. In addition, the current Eshelby tensor for the ellipsoidal inclusion problem includes those for the spherical and cylindrical inclusion problems based on the SSGET as two limiting cases. The non-classical Eshelby tensor depends on the position and is non-uniform even inside the inclusion, which differ from its classical counterpart. For homogenization applications, the volume average of the new Eshelby tensor over the ellipsoidal inclusion is analytically obtained. The numerical results quantitatively show that the components of the newly derived Eshelby tensor vary with both the position and the inclusion size, unlike their classical counterparts. When the inclusion size is small, it is found that the contribution of the gradient part is significantly large. It is also seen that the components of the averaged Eshelby tensor change with the inclusion size: the smaller the inclusion, the smaller the components. Moreover, these components are observed to approach the values of their classical counterparts from below when the inclusion size becomes sufficiently large.

Free Vibration Analysis of a Spinning Smart Piezoelectrically Actuated Heterogeneous Nanoscale Shell with Nonlocal Strain Gradient Theory

2020 ◽  
Vol 64 ◽  
pp. 1-19
Author(s):  
Sadegh Sadeghzadeh ◽  
Mohammad Mahinzare
Keyword(s):  
Natural Frequency ◽  
Strain Gradient ◽  
Scale Parameter ◽  
Nonlocal Parameter ◽  
Angular Speed ◽  
Strain Gradient Theory ◽  
Length Scale Parameter ◽  
Gradient Theory ◽  
Length Scale ◽  
Nonlocal Strain Gradient

In this paper, a numerical procedure is proposed for analyzing the effects of length scale parameter, external electric field, angular speed and nonlocal parameter on the free vibration of a functionally graded piezoelectric cylindrical nanoshell. Nonlocal strain gradient theory (NSGT) is employed to study Eringen’s size-dependent effect and the length scale parameter. This new proposed method can be considered as a combination of Eringen’s nonlocal model and classical strain gradient theory. The obtained results show that this model can be used reliably for small-scale systems. The effects of boundary conditions, applied voltage, nonlocal parameter, rotational speed and length scale parameter on natural frequencies are presented. Compared to other elasticity theories, NSGT achieves the highest natural frequency and critical rotational speed and also a wider stability region. Doubling and tripling the length scale increases the natural frequency by approximately 1.8 and 2.6 times, respectively; while doubling and tripling the nonlocal parameter value reduces the natural frequency by approximately 1.2 and 1.4 times, respectively. Therefore, the natural frequency is more sensitive to the length scale parameter than the nonlocal parameter. Finally, it was shown that the critical angular speed goes up by increasing the length scale parameter, applied voltage, or nonlocal parameter.

Sign in / Sign up

Export Citation Format

Share Document