Temperature dependence of material length scale for strain gradient plasticity and its effect on near-tip opening displacement

2013 ◽  
Vol 37 (2) ◽  
pp. 157-170 ◽  
Author(s):  
X. Qian ◽  
S. Zhang ◽  
S. Swaddiwudhipong ◽  
L. Shen
Keyword(s):  
Temperature Dependence ◽  
Strain Gradient ◽  
Strain Gradient Plasticity ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Opening Displacement ◽  
Material Length Scale ◽  
Material Length

The correlation between the internal material length scale and the microstructure in nanoindentation experiments and simulations using the conventional mechanism-based strain gradient plasticity theory

2009 ◽  
Vol 24 (3) ◽  
pp. 1197-1207 ◽  
Author(s):  
B. Backes ◽  
Y.Y. Huang ◽  
M. Göken ◽  
K. Durst
Keyword(s):  
Yield Stress ◽  
Strain Gradient ◽  
Plasticity Theory ◽  
Strain Gradient Plasticity ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Hardening Behavior ◽  
Material Length Scale ◽  
Material Length ◽  
Strain Gradient Plasticity Theory

In the present work a new equation to determine the internal material length scale for strain gradient plasticity theories from two independent experiments (uniaxial and nanoindentation tests) is introduced. The applicability of the presented equation is verified for conventional grained as well as for ultrafine-grained copper and brass with different amounts of prestraining. A significant decrease of the experimentally determined internal material length scale is found for increasing dislocation densities due to prestraining. Conventional mechanism strain gradient plasticity theory is used for simulating the indentation response, using experimentally determined material input data as the yield stress, the work-hardening behavior and the internal material length scale. The work-hardening behavior and the yield stress were taken from the uniaxial experiments, whereas the internal material length scale was calculated using the yield stress from the uniaxial experiment, the macroscopic hardness H0 and the length scale parameter h* following from the nanoindentation experiment. A good agreement between the measured and calculated load–displacement curve and the hardness is found independent of the material and the microstructure.

Length Scale in Solder Joints Materials

2006 ◽  
Author(s):  
Juan Gomez ◽  
Cemal Basaran
Keyword(s):  
Strain Gradient ◽  
Constitutive Models ◽  
Strain Gradient Plasticity ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Additional Material ◽  
Size Dependent ◽  
Dependent Behavior ◽  
Material Length Scale ◽  
Material Length

Strain gradient plasticity theories that have emerged during recent years to provide an explanation for size dependent behavior exhibited by some materials have also created a need for additional material parameters. In this study on Pb/Sn solder alloys the material length scale, which is needed for use in strain gradient plasticity type constitutive models, is determined. The value of length scale is in agreement with values available in the literature for different materials like copper, nickel and aluminum.

Determination of Strain Gradient Plasticity Length Scale for Microelectronics Solder Alloys

2006 ◽  
Vol 129 (2) ◽  
pp. 120-128 ◽  
Author(s):  
Juan Gomez ◽  
Cemal Basaran
Keyword(s):  
Strain Gradient ◽  
Constitutive Models ◽  
Strain Gradient Plasticity ◽  
Length Scale ◽  
Gradient Plasticity ◽  
Solder Alloys ◽  
Additional Material ◽  
Dependent Behavior ◽  
Material Length Scale ◽  
Material Length

Strain gradient plasticity theories that have emerged during recent years to provide an explanation for size dependent behavior exhibited by some materials have also created a need for additional material parameters. In this study on Pb∕Sn solder alloys’ material length scale, which is needed for use in strain gradient plasticity type constitutive models, is determined. The value of length scale is in agreement with values available in literature for different materials like copper, nickel, and aluminum.

Localization-Induced Band and Cohesive Model1

2000 ◽  
Vol 67 (4) ◽  
pp. 803-812 ◽  
Author(s):  
S. Hao ◽  
W. K. Liu ◽  
D. Qian
Keyword(s):  
Strain Gradient ◽  
Multiple Scale ◽  
Strain Gradient Theory ◽  
Gradient Theory ◽  
Length Scale ◽  
Finite Width ◽  
Opening Displacement ◽  
One Dimensional ◽  
Material Length Scale ◽  
Material Length

A localization-induced cohesive model has been proposed for shear band evolution, crack growth, and fracture. Strain gradient theory has been applied to establish the criterion of the onset of localization and the governing equation in the post-bifurcation stage. Analytical solutions in one-dimensional case are used to establish the “traction-separation” law, in which strain gradient and material intrinsic length scale present strong effects. In addition, the solution predicts a finite width for the localization-induced band. It is observed that a larger length scale contributes to the growth of a larger width of localization region and separation for softening materials. The proposed model provides a procedure to establish the fracture toughness analytically since the material length scale is taken into account. From the traction-separation analysis, it is found that damage decreases separation, whereas an increase in material length scale increases the opening displacement; however, the traction-normalized opening displacement curves (with respect to the material length scale) are identical. Based on the methodology of multiple scale analysis in meshfree method, a computational approach has been proposed to enrich the one-dimensional traction-separation law to define fracture. [S0021-8936(00)01104-1]

An Explanation for the Size-Effect in Machining Using Strain Gradient Plasticity

2004 ◽  
Vol 126 (4) ◽  
pp. 679-684 ◽  
Author(s):  
Suhas S. Joshi ◽  
Shreyes N. Melkote
Keyword(s):  
Size Effect ◽  
Strain Gradient ◽  
Shear Plane ◽  
Strain Gradient Plasticity ◽  
Gradient Plasticity ◽  
Gradient Density ◽  
Experimental Values ◽  
Material Length Scale ◽  
Material Length ◽  
Shear Energy

This paper aims to explain the size-effect in the Primary Deformation Zone (PDZ) in machining using strain gradient plasticity theory. Considering a parallel-sided shear zone configuration, models are formulated for the evaluation of strain gradient, density of geometrically necessary dislocations, shear strength and the specific shear energy. The analysis of deformation in the PDZ shows that the length of the shear plane represents the fundamental material length scale governing the size-effect. It also provides an estimate of the lower bound on the size-effect observed in the specific shear energy. The general trends predicted by the model are shown to agree well with the experimental values obtained from the literature.

Strain gradient plasticity to study hardness behavior of magnetite (Fe3O4) under multicyclic indentation

2009 ◽  
Vol 24 (3) ◽  
pp. 749-759 ◽  
Author(s):  
D. Chicot ◽  
F. Roudet ◽  
V. Lepingle ◽  
G. Louis
Keyword(s):  
Strain Gradient ◽  
Peak Load ◽  
Scale Factor ◽  
Strain Gradient Plasticity ◽  
Dislocation Network ◽  
Length Scale ◽  
Relevant Parameter ◽  
Characteristic Scale ◽  
Gradient Plasticity ◽  
Scale Length

The hardness of a material is generally affected by the indentation size effect. The strain gradient plasticity (SGP) theory is largely used to study this load dependence because it links the hardness to the intrinsic properties of the material. However, the characteristic scale-length is linked to the macrohardness, impeding any sound discussion. To find a relevant parameter, we suggest introducing a hardness length-scale factor that only depends on the shear modulus and the Burgers vector of the material and is easily calculable from the relation of the SGP theory. The variation of the hardness length-scale factor is thereafter used to discuss the hardness behavior of a magnetite crystal, the objective being to study the effect of the cumulative plasticity resulting from cyclic indentation. As a main result, the hardness length-scale factor is found to be constant by applying repeated cycles at a constant peak load whereas the macrohardness and the characteristic scale-length are both cycle dependent. When using incremental loads, the hardness length-scale factor monotonically decreases between two limits corresponding to those obtained at high and low loading rates, while the dwell-load duration increases. The physical meaning of such behavior is based on the modification of the dislocation network during the indentation process depending on the deformation rate.

scholarly journals A nonlocal strain gradient shell model incorporating surface effects for vibration analysis of functionally graded cylindrical nanoshells

2019 ◽  
Vol 40 (12) ◽  
pp. 1695-1722 ◽  
Author(s):  
Lu Lu ◽  
Li Zhu ◽  
Xingming Guo ◽  
Jianzhong Zhao ◽  
Guanzhong Liu
Keyword(s):  
Strain Gradient ◽  
Scale Parameter ◽  
Nonlocal Parameter ◽  
Functionally Graded ◽  
Length Scale ◽  
Proposed Model ◽  
Material Length Scale Parameter ◽  
Material Length Scale ◽  
Material Length ◽  
Nonlocal Strain Gradient

AbstractIn this paper, a novel size-dependent functionally graded (FG) cylindrical shell model is developed based on the nonlocal strain gradient theory in conjunction with the Gurtin-Murdoch surface elasticity theory. The new model containing a nonlocal parameter, a material length scale parameter, and several surface elastic constants can capture three typical types of size effects simultaneously, which are the nonlocal stress effect, the strain gradient effect, and the surface energy effects. With the help of Hamilton’s principle and first-order shear deformation theory, the non-classical governing equations and related boundary conditions are derived. By using the proposed model, the free vibration problem of FG cylindrical nanoshells with material properties varying continuously through the thickness according to a power-law distribution is analytically solved, and the closed-form solutions for natural frequencies under various boundary conditions are obtained. After verifying the reliability of the proposed model and analytical method by comparing the degenerated results with those available in the literature, the influences of nonlocal parameter, material length scale parameter, power-law index, radius-to-thickness ratio, length-to-radius ratio, and surface effects on the vibration characteristic of functionally graded cylindrical nanoshells are examined in detail.

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