Analysis of the effects of conical indentation variables on the indentation response of elastic–plastic materials through factorial design of experiment

2009 ◽  
Vol 24 (3) ◽  
pp. 1222-1234 ◽  
Author(s):  
Sara Aida Rodríguez Pulecio ◽  
María Cristina Moré Farias ◽  
Roberto Martins Souza
Keyword(s):  
Factorial Design ◽  
Strong Dependence ◽  
Plastic Materials ◽  
Dimensionless Function ◽  
Dimensionless Variables ◽  
Input Variables ◽  
Elastic Plastic Materials ◽  
Geometry Analysis ◽  
Indenter Geometry ◽  
Conical Indentation

In this work, the effects of conical indentation variables on the load–depth indentation curves were analyzed using finite element modeling and dimensional analysis. A factorial design 26 was used with the aim of quantifying the effects of the mechanical properties of the indented material and of the indenter geometry. Analysis was based on the input variables Y/E, R/hmax, n, θ, E, and hmax. The dimensional variables E and hmax were used such that each value of dimensionless Y/E was obtained with two different values of E and each value of dimensionless R/hmax was obtained with two different hmax values. A set of dimensionless functions was defined to analyze the effect of the input variables: Π1 = Pl/Eh2, Π2 = hc/h, Π3 = H/Y, Π4= S/Ehmax, Π6 = hmax/hf, and Π7 = Wp/WT. These six functions were found to depend only on the dimensionless variables studied (Y/E, R/hmax, n, θ). Another dimensionless function, Π5 = β, was not well defined for most of the dimensionless variables and the only variable that provided a significant effect on β was θ. However, β showed a strong dependence on the fraction of the data selected to fit the unloading curve, which means that β is especially susceptible to the error in the calculation of the initial unloading slope.

On Determining Elastic Modulus from Instrumented Indentation

2013 ◽  
Vol 668 ◽  
pp. 616-620
Author(s):  
Shuai Huang ◽  
Huang Yuan
Keyword(s):  
Finite Element ◽  
Elastic Modulus ◽  
Plastic Material ◽  
Instrumented Indentation ◽  
Computational Simulations ◽  
Elastic Plastic ◽  
Modified Method ◽  
Plastic Materials ◽  
Elastic Plastic Material ◽  
Elastic Plastic Materials

Computational simulations of indentations in elastic-plastic materials showed overestimate in determining elastic modulus using the Oliver & Pharr’s method. Deviations significantly increase with decreasing material hardening. Based on extensive finite element computations the correlation between elastic-plastic material property and indentation has been carried out. A modified method was introduced for estimating elastic modulus from dimensional analysis associated with indentation data. Experimental verifications confirm that the new method produces more accurate prediction of elastic modulus than the Oliver & Pharr’s method.

The Propagation of Plasticity in Uniaxial Compression

1948 ◽  
Vol 15 (3) ◽  
pp. 256-260 ◽  
Author(s):  
M. P. White ◽  
LeVan Griffis
Keyword(s):  
Uniaxial Compression ◽  
Thin Sheet ◽  
High Stress ◽  
Stress And Strain ◽  
Velocity Range ◽  
Plastic Materials ◽  
The Face ◽  
Elastic Plastic Materials ◽  
The Impact ◽  
Type Of Behavior

Abstract A theoretical investigation of the mechanism of uniaxial compression impact on elastic-plastic materials is described in this paper. The method of analysis is similar in some respects to that previously given for tension impact on such materials. It is concluded that four different kinds of behavior can occur, depending upon the impact velocity. In the lowest velocity range the behavior in compression is similar to that found in tension. In this case stress and strain are propagated from the point of impact as a zone or wave front of ever-increasing length. This type of behavior ends at a velocity corresponding to the “critical” velocity found in tension impact. Within the next higher velocity range, stress and strain are propagated as a shock-type wave, or wave of very small length in which the transition from low to high stress and strain is very abrupt. At still higher impact velocities, there occurs “flowing deformation” in which the material is too weak to maintain coherency. Here there is a steady flow of the material toward and against the hammer, after which it flows in a thin sheet radially outward over the face of the hammer. The final possible state occurs at impact velocities greater than the speed of an elastic wave, so that no disturbance can escape from the hammer into the medium. Here the behavior is essentially that of a fluid, impact force being independent of strength of material.

Modeling the Stress-Strain Curve of Elastic-Plastic Materials

2021 ◽  
Vol 316 ◽  
pp. 936-941
Author(s):  
Natalya Ya. Golovina
Keyword(s):  
Mathematical Models ◽  
Strain Curve ◽  
Variational Model ◽  
Linear Deformation ◽  
Plastic Materials ◽  
Non Linear ◽  
Linear Sections ◽  
Elastic Plastic Materials ◽  
Deformation Section ◽  
St3sp Steel

The work is devoted to the formulation of mathematical models of plastic materials without hardening. A functional is proposed, the requirement of stationarity of which made it possible to formulate the differential equation of stress as a function of deformation. On the linear deformation section, a second-order functional is proposed; on the non-linear deformation section, a fourth-order functional is proposed. A range of boundary value problems is formulated, that ensure the continuity of the function at the boundary of the linear and non-linear sections of the deformation curve. The theoretical strain curve was compared with the samples of experimental points for materials: St3sp steel, steel 35, steel 20HGR, steel 08Kh18N10, titanium alloy VT6, aluminum alloy D16, steel 30KhGSN2A, steel 40Kh2N2MA, and showed a good agreement with the experiment. Thus, a variational model is constructed, that allows one to construct curve deformations of various physically non-linear materials, which will allow one to construct further mathematical models of the resource of such materials.

scholarly journals The influence of pavement degradation caused by cyclic loading on its failure mechanisms

2016 ◽  
Vol 11 (3) ◽  
pp. 179-187 ◽  
Author(s):  
Marcin Gajewski ◽  
Stanisław Jemioło
Keyword(s):  
Yield Condition ◽  
Limit Load ◽  
Flow Rule ◽  
Smooth Approximation ◽  
Simple Method ◽  
Plastic Properties ◽  
The Road ◽  
Plastic Materials ◽  
Number Of Cycles ◽  
Elastic Plastic Materials

In this paper, a simple method is proposed to estimate capacity of multilayered road structure including the degradation of the elastic and plastic properties of the constituent materials. In the study boundary value problem modeling interaction of wheels with road surface layer in the frame of large deformation theory for elastic-plastic materials was formulated. Plastic properties of the material were described by the flow rule un-associated with yield condition. The Coulomb-Mohr yield condition was assumed and the potential for plasticity is its smooth approximation. In addition, in constitutive modeling the dependence of the Young’s modulus and cohesion of the material from the number of cycles is taken into account. This paper presents qualitative findings in relation to mechanical behavior of the road structure, i.e., for example, the development of plastic zones with increasing load for un-degraded and degraded materials. In addition, a parametric study of the influence of the degradation ratio of the elasticity and plasticity properties for road structure failure mechanism (limit load value) was made.

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