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.

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.

Evaluation of Anisotropic Pipe Steel Stress-Strain Relationships Influence on Strain Demand

2012 ◽  
Author(s):  
James D. Hart ◽  
Nasir Zulfiqar ◽  
Joe Zhou
Keyword(s):  
Strain Hardening ◽  
Pipe Steel ◽  
High Strain ◽  
Strain Curve ◽  
High Strength ◽  
Strain Response ◽  
Stress Strain Curve ◽  
Stress Strain ◽  
Hardening Modulus ◽  
Strain Relationship

Buried pipelines can be exposed to displacement-controlled environmental loadings (such as landslides, earthquake fault movements, etc.) which impose deformation demands on the pipeline. When analyzing pipelines for these load scenarios, the deformation demands are typically characterized based on the curvature and/or the longitudinal tension and compression strain response of the pipe. The term “strain demand” is used herein to characterize the calculated longitudinal strain response of a pipeline subject to environmentally-induced deformation demands. The shape of the pipe steel stress-strain relationship can have a significant effect on the pipe strain demands computed using pipeline deformation analyses for displacement-controlled loading conditions. In general, with sufficient levels of imposed deformation demand, a pipe steel stress-strain curve with a relatively abrupt or “sharp” elastic-to-plastic transition will tend to lead to larger strain demands than a stress-strain curve with a relatively rounded elastic-to-plastic transition. Similarly, a stress-strain curve with relatively low strain hardening modulus characteristics will tend to lead to larger strain demands than a stress-strain curve with relatively high strain hardening modulus characteristics. High strength UOE pipe can exhibit significant levels of anisotropy (i.e., the shapes of the stress-strain relationships in the longitudinal tension/compression and hoop tension/compression directions can be significantly different). To the extent that the stress-strain curves in the different directions can have unfavorable shape characteristics, it follows that anisotropy can also play an important role in pipeline strain demand evaluations. This paper summarizes a pipeline industry research project aimed at evaluation of the effects of anisotropy and the shape of pipe steel stress-strain relationships on pipeline strain demand for X80 and X100 UOE pipe. The research included: a review of pipeline industry literature on the subject matter; a discussion of pipe steel plasticity concepts for UOE pipe; characterization of the anisotropy and stress-strain curve shapes for both conventional and high strain pipe steels; development of representative analytical X80 and X100 stress-strain relationships; and evaluation of a large matrix of ground-movement induced pipeline deformation scenarios to evaluate key pipe stress-strain relationship shape and anisotropy parameters. The main conclusion from this work is that pipe steel specifications for high strength UOE pipe for strain-based design applications should be supplemented to consider shape-characterizing parameters such as the plastic complementary energy.

Effect of Interfaces in the Work Hardening of Nanoscale Multilayer Metallic Composites During Nanoindentation: A Molecular Dynamics Investigation

2013 ◽  
Vol 135 (2) ◽  
Author(s):  
S. Shao ◽  
H. M. Zbib ◽  
I. Mastorakos ◽  
D. F. Bahr
Keyword(s):  
Molecular Dynamics ◽  
Plastic Deformation ◽  
Strain Hardening ◽  
Power Law ◽  
Indentation Depth ◽  
Constitutive Law ◽  
Atomistic Simulations ◽  
Depth Data ◽  
Strain Data ◽  
Metallic Composites

To study the strain hardening in nanoscale multilayer metallic (NMM) composites, atomistic simulations of nanoindentation are performed on CuNi, CuNb, and CuNiNb multilayers. The load-depth data were converted to hardness-strain data that were then modeled using power law. The plastic deformation of the multilayers is closely examined. It is found that the strain hardening in the incoherent CuNb and NiNb interfaces is stronger than the coherent CuNi interface. The hardening parameters are discovered to be closely related to the density of the dislocations in the incoherent interfaces, which in turn is found to have power law dependence on two length scales: indentation depth and layer thickness. Based on these results, a constitutive law for extracting strain hardening in NMM from nanoindentation data is developed.

Effect of Lüders Plateau on Fracture Response and Toughness of Pipelines Subject to Extreme Plastic Bending

2011 ◽  
Vol 133 (5) ◽  
Author(s):  
Nikzad Nourpanah ◽  
Farid Taheri
Keyword(s):  
Strain Hardening ◽  
Limit State ◽  
Stress Triaxiality ◽  
Crack Tip ◽  
Thick Wall ◽  
Integral Model ◽  
Tensile Fracture ◽  
Strain Response ◽  
Stress Strain ◽  
Plastic Bending

The reeling technique presents an economical pipeline installation method for offshore oil and gas applications, especially for thick-wall (low D/t) pipelines. During reeling, the pipe is subjected to large plastic bending strains up to 3%. In thick-wall pipes, the tensile fracture response of the pipeline/girth weld would normally be the governing limit state. Seamless line pipes are preferred for the reeling applications in which the Lüders plateau is often exhibited in materials stress-strain response. In this paper, the fracture response of such pipelines is investigated from a continuum perspective using a nonlinear 3D finite element analysis. A typical pipeline with a hypothetical defect is considered, with the material having a range of Lüders strains and strain hardening indices. Results show that the Lüders plateau modifies the shape of the moment-strain response curves of the pipe, as well as the J-integral fracture response. It is observed that the response is always bounded between two limiting material models, which are (i) the elastic-perfectly plastic stress-strain response and (ii) the conventional elastic-strain hardening plasticity response, without a Lüders plateau. Also, the Lüders plateau was observed to decrease the crack opening stress ahead of the crack tip and thus the crack tip constraint. On the other hand, the presence of a Lüders plateau elevates the near tip plastic strain and stress triaxiality fields, thus promoting ductile fracture. A micromechanical damage integral model coupled with a modified boundary layer analysis was incorporated to study this aspect. Based on the findings of this study, it is believed that the presence of Lüders plateau could significantly alter the fracture response and toughness of pipes subject to relatively high strains.

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.

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