Identification of Plastic Properties From Conical Indentation Using a Bayesian-Type Statistical Approach

2018 ◽  
Vol 86 (1) ◽  
Author(s):  
Yupeng Zhang ◽  
Jeffrey D. Hart ◽  
Alan Needleman
Keyword(s):  
Indentation Depth ◽  
Statistical Approach ◽  
Surface Profile ◽  
Uniaxial Stress ◽  
Strain Response ◽  
Profile Data ◽  
Stress Strain ◽  
Plastic Properties ◽  
Indentation Force ◽  
Depth Response

The plastic properties that characterize the uniaxial stress–strain response of a plastically isotropic material are not uniquely related to the indentation force versus indentation depth response. We consider results for three sets of plastic material properties that give rise to essentially identical curves of indentation force versus indentation depth in conical indentation. The corresponding surface profiles after unloading are also calculated. These computed results are regarded as the “experimental” data. A simplified Bayesian-type statistical approach is used to identify the values of flow strength and strain hardening exponent for each of the three sets of material parameters. The effect of fluctuations (“noise”) superposed on the “experimental” data is also considered. We build the database for the Bayesian-type analysis using finite element calculations for a relatively coarse set of parameter values and use interpolation to refine the database. A good estimate of the uniaxial stress–strain response is obtained for each material both in the absence of fluctuations and in the presence of sufficiently small fluctuations. Since the indentation force versus indentation depth response for the three materials is nearly identical, the predicted uniaxial stress–strain response obtained using only surface profile data differs little from what is obtained using both indentation force versus indentation depth and surface profile data. The sensitivity of the representation of the predicted uniaxial stress–strain response to fluctuations increases with increasing strain hardening. We also explore the sensitivity of the predictions to the degree of database refinement.

Influence of Assumed Strain Hardening Relation on Plastic Stress-Strain Response Identification From Conical Indentation

2020 ◽  
Vol 142 (3) ◽  
Author(s):  
Yupeng Zhang ◽  
Alan Needleman
Keyword(s):  
Strain Hardening ◽  
Power Law ◽  
Indentation Depth ◽  
Uniaxial Stress ◽  
Strain Response ◽  
Stress Strain ◽  
Indentation Force ◽  
Engineering Materials ◽  
Plastic Stress ◽  
Conical Indentation

Abstract Instrumented indentation tests provide an attractive means for obtaining data to characterize the plastic response of engineering materials. One difficulty in doing this is that the relation between the measured indentation force versus indentation depth response and the plastic stress-strain response is not unique. Materials with very different uniaxial stress-strain curves can give essentially identical curves of indentation force versus indentation depth. Zhang et al. (2019, “Identification of Plastic Properties From Conical Indentation Using a Bayesian-Type Statistical Approach,” ASME J. Appl. Mech., 86, p. 011002) numerically generated “experimental” conical indentation data and showed that using surface profile data and indentation force versus indentation depth data together with a Bayesian-type statistical analysis permitted the uniaxial plastic stress-strain response to be identified even for materials with indistinguishable indentation force versus indentation depth curves. The same form of hardening relation was used in the identification process as was used to generate the “experimental” data. Generally, a variety of power law expressions have been used to characterize the uniaxial plastic stress-strain response of engineering materials, and, of course, the form that gives the best fit for a material is not known a priori. Here, we use the same Bayesian statistics-based analysis but consider four characterizations of the plastic uniaxial stress-strain response and show that the identification of the hardening relation parameters and the associated uniaxial stress-strain response is not very sensitive to the form of the power law strain hardening relation chosen even with data that have significant noise.

scholarly journals Instrumented indentation for determination of full range stress-strain curves

2014 ◽  
Vol 5 (1) ◽  
pp. 6
Author(s):  
Andreas De Smedt ◽  
Stijn Hertelé ◽  
Matthias Verstraete ◽  
Koen Van Minnebruggen ◽  
Wim De Waele
Keyword(s):  
Full Range ◽  
Accurate Determination ◽  
Strain Curve ◽  
Uniaxial Stress ◽  
Instrumented Indentation ◽  
Stress Strain ◽  
Indentation Force ◽  
Strain Behaviour ◽  
Depth Curve

One common method for the determination of full range stress-strain curves by instrumented indentation is presented and validated for an aluminium alloy. This method relates properties describing the indentation force-depth curve with those describing the uniaxial stress-strain curve as traditionally obtained from a tensile test. The first aim of this paper is to explain the basic concepts of instrumented indentation. Next, the analysis method is presented and validated. This study ends with discussing the uniqueness of the obtained solution. It is concluded that accurate determination of stress-strain behaviour can be realized, but for certain materials two indentations are needed.

Delamination in the scoring and folding of paperboard

TAPPI Journal ◽  
2012 ◽  
Vol 11 (1) ◽  
pp. 61-66 ◽  
Author(s):  
DOEUNG D. CHOI ◽  
SERGIY A. LAVRYKOV ◽  
BANDARU V. RAMARAO
Keyword(s):  
Finite Element ◽  
Plane Deformation ◽  
Strain Analysis ◽  
Local Strain ◽  
Uniaxial Stress ◽  
Material Model ◽  
Element Model ◽  
Plastic Behavior ◽  
Stress Strain ◽  
Strain Fields

Delamination between layers occurs during the creasing and subsequent folding of paperboard. Delamination is necessary to provide some stiffness properties, but excessive or uncontrolled delamination can weaken the fold, and therefore needs to be controlled. An understanding of the mechanics of delamination is predicated upon the availability of reliable and properly calibrated simulation tools to predict experimental observations. This paper describes a finite element simulation of paper mechanics applied to the scoring and folding of multi-ply carton board. Our goal was to provide an understanding of the mechanics of these operations and the proper models of elastic and plastic behavior of the material that enable us to simulate the deformation and delamination behavior. Our material model accounted for plasticity and sheet anisotropy in the in-plane and z-direction (ZD) dimensions. We used different ZD stress-strain curves during loading and unloading. Material parameters for in-plane deformation were obtained by fitting uniaxial stress-strain data to Ramberg-Osgood plasticity models and the ZD deformation was modeled using a modified power law. Two-dimensional strain fields resulting from loading board typical of a scoring operation were calculated. The strain field was symmetric in the initial stages, but increasing deformation led to asymmetry and heterogeneity. These regions were precursors to delamination and failure. Delamination of the layers occurred in regions of significant shear strain and resulted primarily from the development of large plastic strains. The model predictions were confirmed by experimental observation of the local strain fields using visual microscopy and linear image strain analysis. The finite element model predicted sheet delamination matching the patterns and effects that were observed in experiments.

Experimental Characterization of Mechanical Behavior of Cord-Rubber Composites

1982 ◽  
Vol 10 (1) ◽  
pp. 37-54 ◽  
Author(s):  
M. Kumar ◽  
C. W. Bert
Keyword(s):  
Response Characteristic ◽  
Cord Compression ◽  
Complete Characterization ◽  
Strain Response ◽  
Strain Gages ◽  
Experimental Characterization ◽  
Rubber Composites ◽  
Stress Strain ◽  
Strain Data

Abstract Unidirectional cord-rubber specimens in the form of tensile coupons and sandwich beams were used. Using specimens with the cords oriented at 0°, 45°, and 90° to the loading direction and appropriate data reduction, we were able to obtain complete characterization for the in-plane stress-strain response of single-ply, unidirectional cord-rubber composites. All strains were measured by means of liquid mercury strain gages, for which the nonlinear strain response characteristic was obtained by calibration. Stress-strain data were obtained for the cases of both cord tension and cord compression. Materials investigated were aramid-rubber, polyester-rubber, and steel-rubber.

Cyclic stress-strain response of porous aluminum

1990 ◽  
Vol 6 (2) ◽  
pp. 207-230 ◽  
Author(s):  
Han C. Wu ◽  
Paul T. Wang ◽  
W.F. Pan ◽  
Z.Y. Xu
Keyword(s):  
Cyclic Stress ◽  
Strain Response ◽  
Stress Strain ◽  
Porous Aluminum

Impact of random soil properties on stress–strain response

2004 ◽  
Vol 41 (2) ◽  
pp. 351-355 ◽  
Author(s):  
Dieter Stolle ◽  
Peijun Guo ◽  
Gabriel Sedran
Keyword(s):  
Soil Properties ◽  
Constitutive Modelling ◽  
Soil Parameters ◽  
Strain Response ◽  
Constitutive Behaviour ◽  
Stress Strain ◽  
Deterministic Analysis ◽  
Model Predictions ◽  
Random Variability ◽  
The Impact

This paper analyzes the impact of natural random variation of soil properties on the constitutive modelling of geomaterial behaviour. A theoretical framework for accommodating variation in soil properties is presented. The framework is then used to examine the consequence of parameter variability on stress–strain relations. An important observation is that average soil parameters from a series of tests on small specimens, in which density of the specimens varies randomly, do not necessarily reflect the average constitutive behaviour of soil. Model predictions are shown to be consistent with the experimental data.Key words: random variability, deterministic analysis, soil parameters, constitutive model.

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