The M-Integral Analysis for a Nano-Inclusion in Plane Elastic Materials Under Uni-Axial or Bi-Axial Loadings

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Tong Hui ◽  
Yi-Heng Chen
Keyword(s):  
Surface Effect ◽  
Continuum Theory ◽  
Elastic Materials ◽  
Hard Inclusion ◽  
Surface Parameters ◽  
Integral Analysis ◽  
Axial Tension ◽  
Soft Inclusion ◽  
Tension Loading ◽  
M Integral

This paper deals with the M-integral analysis for a nano-inclusion in plane elastic materials under uni-axial or bi-axial loadings. Based on previous works (Gurtin and Murdoch, 1975, “A Continuum Theory of Elastic Material Surfaces,” Arch. Ration. Mech. Anal., 57, pp. 291–323; Mogilevskaya, et al., 2008, “Multiple Interacting Circular Nano-Inhomogeneities With Surface/Interface Effects,” J. Mech. Phys. Solids, 56, pp. 2298–2327), the surface effect induced from the surface tension and the surface Lamé constants is taken into account, and an analytical solution is obtained. Four kinds of inclusions including soft inclusion, hard inclusion, void, and rigid inclusions are considered. The variable tendencies of the M-integral for each of four nano-inclusions against the loading or against the inclusion radius are plotted and discussed in detail. It is found that in nanoscale the surface parameters for the hard inclusion or rigid inclusion have a little or little influence on the M-integral, and the values of the M-integral are always negative as they would be in macroscale, whereas the surface parameters for the soft inclusion or void yield significant influence on the M-integral and the values of the M-integral could be either positive or negative depending on the loading levels and the surface parameters. Of great interest is that there is a neutral loading point for the soft inclusion or void, at which the M-integral transforms from a negative value to a positive value, and that the bi-axial loading yields similar variable tendencies of the M-integral as those under the uni-axial tension loading. Moreover, the bi-axial tension loading increases the neutral loading point, whereas the bi-axial tension-compression loading decreases it. Particularly, the magnitude of the negative M-integral representing the energy absorbing of the soft inclusion or void increases very sharply as the radius of the soft inclusion or void decreases from 5 nm to 1 nm.

Surface Effect and Size Dependence on the Energy Release Due to a Nanosized Hole Expansion in Plane Elastic Materials

2008 ◽  
Vol 75 (6) ◽  
Author(s):  
Q. Li ◽  
Y. H. Chen
Keyword(s):  
Energy Release ◽  
Surface Stress ◽  
Size Dependence ◽  
Surface Effect ◽  
High Surface ◽  
Plane Elasticity ◽  
Elastic Materials ◽  
Residual Surface Stress ◽  
Surface Lamé Constants ◽  
M Integral

This paper deals with the surface effect and size dependence on the M-integral representing the energy release due to a nanodefect expansion in plane elasticity. Due to the high surface-to-volume ratio for reinforcing particles in the nanometer scale, the surface effect along the nanosized hole may be induced from the residual surface stress and the surface Lamé constants. The invariant integrals such as the Jk-integral vector and the M-integral customarily used in macrofracture mechanics are extended to treat plane elastic materials containing a nanosized hole. It is concluded that both components of the Jk-integral vanish when the contour selected to calculate the integral encloses the whole nanosized hole. This leads to the independence of the M-integral from the global coordinate shift. It is concluded that the surface effect and the size dependence on the energy release due to the nanohole expansion are significant especially when the hole size is less than 40 nm. This present study reveals that the discrepancies of the M-integral value with the surface effect from the referenced value M0 without the surface effect are mainly induced from the residual surface stress τ0 rather than from the surface Lamé constants μs and λs.

Two State M-Integral Analysis for a Nano-Inclusion in Plane Elastic Materials Under Uni-Axial or Bi-Axial Loadings

2009 ◽  
Vol 77 (2) ◽  
Author(s):  
Tong Hui ◽  
Yi-Heng Chen
Keyword(s):  
Surface Tension ◽  
Dominant Role ◽  
Elastic Materials ◽  
Integral Analysis ◽  
Surface Lamé Constants ◽  
M Integral

In this paper, the two state M-integral is extended from macrofacture to nanodefect mechanics. The question as to why the M-integral for a nanovoid or a soft nano-inclusion might be negative is clarified. It is concluded that the surface tension plays a dominant role in evaluating the M-integral, whereas the surface Lamè constants yield much less influence than the surface tension. Their influence on the M-integral for a nanovoid or a soft nano-inclusion could be neglected.

scholarly journals Formation Mechanism of Voids around Hard Inclusion during Hot Rolling Processes

2018 ◽  
Vol 37 (8) ◽  
pp. 717-723
Author(s):  
Rong Cheng ◽  
Jiongming Zhang ◽  
Bo Wang
Keyword(s):  
Formation Mechanism ◽  
Hot Rolling ◽  
Rolling Process ◽  
Relative Displacement ◽  
Hard Inclusion ◽  
Hot Rolling Process ◽  
The Matrix ◽  
Soft Inclusion ◽  
Contact Surfaces ◽  
Plastic Slab

AbstractTo investigate the mechanism by which voids form around hard inclusions, the deformations of a plastic slab with hard and soft inclusions that form inside it during the hot rolling process have been simulated with a finite element method. By comparing plastic strain distributions, the relative displacements of contact surfaces, and the deformations between hard and soft inclusions have preceded analysis of the formation mechanism of these voids. The variations of strain measurements between the matrix and hard inclusions cause relative displacement of their contact surfaces. Therefore, voids occur at the front and rear of the hard inclusions. Trials on the slab deformations using a titanium ball instead of the soft inclusion inside the slab during the hot rolling process are conducted. The simulated shapes of the soft inclusions with different reductions mostly agree with the experimental results.

scholarly journals Measurement of Stress Concentration Factor for Shoulder Fillet on Flat Plate under Axial Tension using Photoelasticity Method and FEA

2019 ◽  
Vol 8 (3) ◽  
pp. 8546-8556
Keyword(s):  
Stress Concentration ◽  
Flat Plate ◽  
Stress Concentration Factor ◽  
Concentration Factor ◽  
Loading Condition ◽  
Tensile Loading ◽  
Element Analysis ◽  
Axial Tension ◽  
The Finite Element Analysis ◽  
Tension Loading

Many researchers have made attempt to investigate stress concentration factor (SCF) for different discontinuities under different loading conditions and applications, but still failures of components take place which having discontinuities. Number of applications under which the components or parts working under tensile loading. Here, efforts are made to investigate the SCF of flat plate with shoulder fillet under axial tension loading using the approach of Photoelasticity for different D/d ratios. The Finite Element Analysis (FEA) approach used to validate the results of experimentation and found that the results are reasonably at acceptable level. One can utilize the outcome of this research for similar application having same discontinuity and loading condition.

Optimal Design of a Composite Scarf Repair Under Uni-Axial Tension Loading

2008 ◽  
Author(s):  
T. D. Breitzman ◽  
B. M. Cook ◽  
G. A. Schoeppner ◽  
E. V. Iarve
Keyword(s):  
Tensile Load ◽  
Optimal Designs ◽  
Analytical Models ◽  
Linear Elastic ◽  
Repair Patch ◽  
Axial Tension ◽  
Axial Tensile ◽  
Notched Strength ◽  
Tension Loading ◽  
Good Agreement

Benchmark un-notched strength testing was used to characterize material properties for IM6/3501-6 composite material and to establish parameters for critical failure volume (CFV) (see [8]) analysis tools. Critical failure volume was used to predict the strength of scarfed composites, as well as composites having a scarf repair patch. Baseline repairs were created both without and with over-plies. Simplex optimization was performed on the analytical models to determine the repair stacking sequence that would result in the largest tensile strength for the repairs. The repair was optimized in the linear elastic regime, but strength predictions took into account both geometric nonlinearities of the respective materials and the material nonlinearities of the adhesive. Predicted strengths were in good agreement with experimental results, and the resultant optimal designs increased the strength of the repair under uni-axial tensile load by 10–20%.

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