A Theoretical Study on the Indentation of Viscoelastic Materials

2003 ◽  
Vol 795 ◽  
Author(s):  
Guanghui Fu
Keyword(s):  
Mechanical Properties ◽  
Half Space ◽  
Theoretical Study ◽  
Contact Region ◽  
Indentation Load ◽  
Fundamental Relation ◽  
Polymeric Thin Films ◽  
Complete Contact ◽  
Simply Connected ◽  
Rigid Smooth

ABSTRACTNanoindentation experiments have been used to investigate mechanical properties of polymeric thin films. In this paper, the problem is modeled as normal indentation of a viscoelastic half-space by a rigid smooth frictionless axisymmetric polynomial indenter. An analytical solution, which relates the indentation load to the penetration depth, is presented. The solution is valid as long as the contact region is simply connected and the indenter is in complete contact with the half-space. It shows that a similar fundamental relation exists in Laplace space.

Normal Indentation of Elastic Half-Space With a Rigid Frictionless Axisymmetric Punch

2001 ◽  
Vol 69 (2) ◽  
pp. 142-147 ◽  
Author(s):  
G. Fu
Keyword(s):  
Half Space ◽  
Complex Variable ◽  
Contact Region ◽  
Pressure Profile ◽  
Elastic Half Space ◽  
Final Solution ◽  
Special Cases ◽  
Complete Contact ◽  
Simply Connected ◽  
Variable Analysis

The contact of a simply connected axisymmetric punch with an elastic half-space is examined. The problem is mathematically formulated by using potential theory and complex variable analysis. The final solution of these equations is obtained by assuming a polynomial punch profile. The conditions for complete contact and incomplete contact are also derived. The solutions give the pressure profile at the punch–elastic half-space interface for any polynomial punch profile, even for noninteger power polynomials, as long as the contact region is simply connected. The results show that some classic solutions in linear elasticity are special cases of the derived solution and determine the range of validity for those solutions.

Multiple Region Contact Solutions for a Flat Indenter on a Layered Elastic Half Space: Plane-Strain Case

1989 ◽  
Vol 56 (2) ◽  
pp. 251-262 ◽  
Author(s):  
T. W. Shield ◽  
D. B. Bogy
Keyword(s):  
Plane Strain ◽  
Half Space ◽  
Contact Region ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Geometrical Parameters ◽  
Restricted Range ◽  
Complete Contact ◽  
The One ◽  
Layered Half Space

The plane-strain problem of a smooth, flat rigid indenter contacting a layered elastic half space is examined. It is mathematically formulated using integral transforms to derive a singular integral equation for the contact pressure, which is solved by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with two or three contact regions. The parameter space divisions between the one, two, or three contact region solutions depend on the material and geometrical parameters and they are found for both the one and two layer cases. As the modulus of the substrate decreases to zero, the two contact region solution predicts the expected result that contact occurs only at the corners of the indenter. The three contact region solution provides an explanation for the nonuniform approach to the half space solution as the layer thickness vanishes.

Some Axisymmetric Problems for Layered Elastic Media: Part I—Multiple Region Contact Solutions for Simply-Connected Indenters

1989 ◽  
Vol 56 (4) ◽  
pp. 798-806 ◽  
Author(s):  
T. W. Shield ◽  
D. B. Bogy
Keyword(s):  
Half Space ◽  
Singular Integral Equations ◽  
Integral Transforms ◽  
Elastic Half Space ◽  
Geometrical Parameters ◽  
Restricted Range ◽  
Axisymmetric Problems ◽  
Complete Contact ◽  
Simply Connected ◽  
Layered Half Space

The contact of a flat, simply-connected axisymmetric indenter with a layered elastic half space is examined. The problem is mathematically formulated using integral transforms to derive singular integral equations for the contact pressure. The solution of these equations is obtained by expansion in orthogonal polynomials. The solution predicts complete contact between the indenter and the surface of the layered half space only for a restricted range of the material and geometrical parameters. Outside of this range, solutions exist with multiple contact regions. A parameter space is divided into zones for single and multiple contact solutions and comparisons are made with the solutions for the analogous plane-strain problem.

Development of Low Carbon High Strength H-Beam Steel

2010 ◽  
Vol 168-170 ◽  
pp. 969-972
Author(s):  
Jian Qing Qian ◽  
Ji Ping Chen ◽  
Bao Qiao Wu ◽  
Jie Ca Wu
Keyword(s):  
Mechanical Properties ◽  
Laboratory Experiments ◽  
Theoretical Study ◽  
High Strength ◽  
Rolling Process ◽  
Low Carbon ◽  
Study Product ◽  
H Beam ◽  
Nitrogen Alloy

The application of vanadium-nitrogen alloy to develop a certain low carbon high strength H-beam steel was determined through the combination of theoretical study, product requirements and existing practical conditions. The specific rolling process was further defined through laboratory experiments. The developed low carbon high strength H-beam steel was trial produced and its properties were also analyzed. The results showed that the newly developed low carbon high strength H-beam steel had excellent mechanical properties and good weldability.

scholarly journals Application of the plasticity characteristic determined by the indentation technique for evaluation of mechanical properties of coatings: I. specific features of the test method procedure

2004 ◽  
Vol 36 (1) ◽  
pp. 27-41 ◽  
Author(s):  
A.V. Byakova ◽  
Yu.V. Milman ◽  
A.A. Vlasov
Keyword(s):  
Mechanical Properties ◽  
Indentation Load ◽  
Test Method ◽  
Simplified Model ◽  
Micro Hardness ◽  
Properties Of Coatings ◽  
Modified Model ◽  
Plasticity Characteristic ◽  
Measurement Results ◽  
Hardness Values

Specific features of the test method procedure capable for determining the plasticity characteristic dH by indentation of inhomogeneous coatings affected by residual stress was clarified. When the value of the plasticity characteristic for coating was found to be as great as dH > 0.5 a simplified model was found to be reasonably adequate, while a modified model assumed compressibility of the deformation core beneath indentation. The advantage of the modified approach compared to the simplified one was grounded experimentally only if the elastic deformation for coating becomes greater than ?e ? 3.5%, resulting in the decrease of plasticity characteristic dH < 0.5. To overcome non accuracy caused by the effect of the scale factor on measurement results a comparison of different coatings was suggested using stabilized values of the plasticity characteristic dH determined under loads higher than critical, P ? Pc, ensuring week dependence of micro hardness values on the indentation load.

Contact Stress Analysis of a Layered Transversely Isotropic Half-Space

1992 ◽  
Vol 114 (2) ◽  
pp. 253-261 ◽  
Author(s):  
C. H. Kuo ◽  
L. M. Keer
Keyword(s):  
Half Space ◽  
Mixed Boundary ◽  
Contact Region ◽  
Three Dimensional ◽  
Transversely Isotropic ◽  
Hankel Transform ◽  
Elastic Half Space ◽  
Contact Stresses ◽  
Stress Components ◽  
Contact Failure

The three-dimensional problem of contact between a spherical indenter and a multi-layered structure bonded to an elastic half-space is investigated. The layers and half-space are assumed to be composed of transversely isotropic materials. By the use of Hankel transforms, the mixed boundary value problem is reduced to an integral equation, which is solved numerically to determine the contact stresses and contact region. The interior displacement and stress fields in both the layer and half-space can be calculated from the inverse Hankel transform used with the solved contact stresses prescribed over the contact region. The stress components, which may be related to the contact failure of coatings, are discussed for various coating thicknesses.

Theoretical study on the electrical and mechanical properties of MXene multilayer structures through strain regulation

2020 ◽  
Vol 760 ◽  
pp. 137997
Author(s):  
Yaqing Zhang ◽  
Xian-Hu Zha ◽  
Kan Luo ◽  
Yanqing Qin ◽  
Xiaojing Bai ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Theoretical Study ◽  
Multilayer Structures

Rayleigh wave motions in an orthotropic half-space under time-harmonic loadings: A theoretical study

2020 ◽  
Vol 87 ◽  
pp. 171-179
Author(s):  
Duy Kien Dao ◽  
VanTrung Ngo ◽  
Haidang Phan ◽  
Chi Vinh Pham ◽  
Jaesun Lee ◽  
...  
Keyword(s):  
Rayleigh Wave ◽  
Half Space ◽  
Theoretical Study ◽  
Time Harmonic

scholarly journals Theoretical study of the mechanical properties of CrFeCoNiMox (0.1 ≤ x ≤ 0.3) alloys

RSC Advances ◽  
2020 ◽  
Vol 10 (24) ◽  
pp. 14080-14088 ◽  
Author(s):  
Yu Liu ◽  
Kai Wang ◽  
Hui Xiao ◽  
Gang Chen ◽  
Zhipeng Wang ◽  
...  
Keyword(s):  
Mechanical Properties ◽  
Elastic Constants ◽  
Theoretical Study ◽  
Deformation Resistance ◽  
Mo Content

There is a dramatic change of the elastic constants when Mo content increases from 0.26 to 0.28, indicating that the deformation resistance of CrFeCoNiMox (0.26 ≤ x ≤ 0.28) HEAs has changed greatly.

Vickers Microhardness Dependence Load and Determining of Tensile Strength of HQ 705 Steel from Microhardness Curves

2016 ◽  
Vol 842 ◽  
pp. 43-52 ◽  
Author(s):  
Viktor Malau ◽  
Latif Arifudin
Keyword(s):  
Mechanical Properties ◽  
Tensile Strength ◽  
Alloy Steel ◽  
Vickers Hardness ◽  
Vickers Microhardness ◽  
Hardness Test ◽  
Indentation Load ◽  
Holding Time ◽  
Raw Material ◽  
Vickers Hardness Number

Vickers microindentation hardness test has been applied for a long time to determine the mechanical properties of a small volume of samples. The procedure of this hardness test consists of using a constant load on a rigid indenter and measuring the dimensions of the indenter residual impression (indentation imprint) on the surface of the sample tested after loading and unloading. The objective of this research is to characterize the mechanical properties and material constants of HQ (High Quality) 705 alloy steel mainly its VHN (Vickers Hardness Number) and tensile strength before and after quenching and tempering heat treatments. The characterization is based on Vickers microhardness dependence load curves.Quenching treatment was performed in a furnace by heating the samples at austenite temperature of 850 o C with holding time of two hours and then the samples were rapidly cooled in oil bath. Tempering processes were conducted by heating again the quenching samples to temperatures of 150, 200, 250, 300, 350, 400, 450, 500, 550 and 600 o C with holding time of two hours for each sample. Finally, all samples were slowly cooled in atmospheric temperature. The mechanical properties of samples were characterized by using Vickers microhardness dependence load curves.The results show that VHN (Vickers Hardness Number) depends on indentation load and VHN increases with increment of load for indentation load lower than 5 N. VHN is almost constant for indentation load greater than 5 N. The raw material (without heat treatment) has the VHN and tensile strength of 3413 MPa and 1050.61 MPa respectively and the quenched samples have the VHN and tensile strength of 5407 and 1861 MPa respectively. The Vickers hardness and tensile strength decrease with the increment of tempering temperatures. The higher tempering temperature produces lower hardness and tensile strength. The raw material tensile strength of 1058.8 MPa obtained by tensile test is comparable to its tensile strength of 1050.61 MPa obtained by Vickers indentation. This result indicates that Vickers microindentation is valid to use for evaluating the tensile strength of HQ 705 alloy steel.

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